CTU SEMINAR 94 - IAEA · P. Zamarovsky NONLINEAR MODELS IN QUANTUM PHYSICS 81 G. Chadzitaskos, A. Kostdi SOUND PROPAGATION IN KLADNO SANDSTONES 83 A". Malinsky DYNAMIC MODEL OF THE

->•• >' jr...

CZECH TECHNICAL UNIVERSITY IN PRAGUE

ZIKOVA 4,166 35 PRAGUE 6, CZECH REPUBLIC

INIS-mf—13870

CTU SEMINAR 94PRAGUE, JANUARY 17 - 20, 1994

PART A

Mathematics - Nuclear Engineering - Physics - Development of CTU Study - Fluid Mechanics- Theory of Constructions

CZECH TECHNICAL UNIVERSITY IN PRAGUE

ZIKOVA 4, 166 35 PRAGUE 6, CZECH REPUBLIC

CTU SEMINAR 94PRAGUE, JANUARY 17 - 20, 1994

PART AMathematics - Nuclear Engineering - Physics - Development of CTU Study - Fluid Mechanics- Theory of Constructions

These arc the Proceedings of the Third Annual univerity-wide seminar CTU SEMINAR 94

which will take place at the Czech Technical University in Prague from 17-20 January, 1994.

The aim of the seminar is to present and discuss the latest results obtained by researchers

at the University and at collaborating institutions.

The organizing committee has selected a total of more than 310 contributions divided into

17 different areas of interest.

The program for CTU SEMINAR 94 consists of an introductory plenary session followed

by three concurrent sessions: A. B. and C.

The Proceedings has been organized to correspond to the sessions. Each part contains

contributions from several areas of interest.

Part A has contributions in the areas of :

• mathematics

• nuclear engineering

• physics

• development of CTU study

• fluid mechanics

• theory of construction

Organizing committee CTU SEMINAR 94:

Chairman: J. VrbaMembers: M. Vrbova, M. Kalal, L. Pfibyl, V. Weiss, A. Pokorny, I. Rousar, F. Cermak,

A. Strejc, M. Naprstek

Prague, December 1993

This documentation was prepared with lATgX from the input files supplied by the authors.General style and final composition of this book is by A. Strejc (CTU Computing Centre).

Published by the Czech Technical University in Prague. Printed out by CTU PublishingHouse in 200 copies. Unsalable publication.

CTU SEMINAR 94 CONTENTS

CONTENTS

1. MATHEMATICSNUMERICAL SIMULATION OF SEVERAL PROBLEMS OF INVISCID ANDVISCOUS FLOWS 13,). Fort, K. hozcl, M. Vavrincovd, L. Benes, M. Fialovd, J. Prokopec

MATHEMATICAL MODELLING IN FLUID MECHANICS 15./. Nnistupa, J. Bcnda, S. Kracmar, M. Machalicky, S. MatuSu.

STABILITY OF VIBRATING PLATE SUBJECTED TO A CONFINED FLUIDFLOW 17('. Simcrskd. J. Hordce.k

NUMERICAL ANALYSIS OF THE FLOW IN CORRUGATED TUBES 19Z. Skaldk, P. Kucc.ra

NUMERICAL SIMULATION OF PULSATILE FLOW IN THE AORTA 21I'. Burda, J. Korendr

GENERALISATION OF ELLIPTIC MOTION 23M. Knryerovd

MODEL OF SURFACE CREATED BY DOUBLE ROTATIONAL MOTION 25E. Kopincovn

SOME RESULTS FROM THEORY OF HOMOGENEOUS OPERATORS 27-9. Burysek, V. Burjjskovd

STABILITY ANALYSIS BY QUANTIFIER ELIMINATION 29H. Liska, S. Steinberg

ON VARIANCES IN SPATIAL STATISTICS AND STEREOLOGY 31V. BencS, B. Vtseld

STATISTICAL METHODS USED IN BERNESE GPS SOFTWARE 33L. Mervart, M. Cimbdlntk

\ THE BAYESIAN INFERENCE WITH MODIFIED NORMAL DISTRIBUTION 35|-* L. Soukup

| - SKETCHES AND PRESENTATION OF STRUCTURES 37£?:, J. Adnmck

% NONCOMMUTATJVE PROBABILITY THEORY AND ITS APPLICATIONS 39I : .7. Tkadlec

i


STATES ON VON NEUMANN ALGEBRAS AND NON-COMMUTATIVEMEASURE THEORY 41J. Hamhalter

MATHEMATICAL METHODS OF QUANTUM THEORIES 43P. Ptdk

DISCRETE N-DIMENSIONAL DYNAMICAL SYSTEMS 45J. Grtgor, E. Krajntk

THE PERIODICAL SOLUTIONS OF THE NAVIER-STOKES EQUATIONS 47P. Kucera, Z. Skaldk

PROBLEMS OF IMPLEMENTATION OF SPECTRAL ELEMENT METHODS 49M. Pultar

ON A THEORETICAL ENGINEERING PROBLEM WITH AN INTEGRALCONDITION 51A'. Rektorys, I. Zahrddka

2. NUCLEAR ENGINEERING

A COMPUTER PROGRAM FOR STEAM GENERATOR PGV-1000THERMAL-HYDRAULIC ANALYSIS 550. libra, M. Doubek, Z. Zuna

TEXTBOOKS FOR TRAINING AND EXAMINING THE STAFF OFRESEARCH NUCLEAR REACTORS 57J. Zeman, K. Matejka, J. Fleischhans

PROGRAM DYNAMIKA FOR THE REACTOR KINETIC CALCULATIONS 595. Krops

AN EXAMPLE OF THE LABORATORY EXERCISE ON THE FNSPE VR-1REACTOR 61«/. Fleischhans

SOFTWARE FOR NUCLEAR SAFETY CRITICAL APPLICATIONS 63K. Matejka, J. Fhiorhhan.t. M. Kropik. T. Sejba

PIXE ANALYSIS - EQUIPMENT AND TECHNIQUES 65

s' J. Krai, J. Voltr, V. Potocck, R, Salomonovic

J DEVELOPMENT AND TESTING OF COMPOSITE ION-EXCHANGERS 67p; F. Sebesta, J. John, A. Motl, J. Steinervvd

I RADIATION INFLUENCING OF CATALYTIC ACTIVITY ANDI REACTIVITY OF TWO-COMPONENT MIXED OXIDES 69I V. Mucka, M. Pospisil, R. Silber

GAMMA MONITORING ARROUND THE TRAINING NUCLEAR REACTORVR-1 71A. Kolros

A

VTV SEMINAR!)! CONTENTS

3. PHYSICS

NATURAL FREQUENCY OF AN AIRCRAFT TIRE 75E. Vcsctd

COMPUTER AIDED SEMINARS OF PHYSICS AND SW FAMULUS 77E. Veseld, J. Kvarda

COMMENTS ON TIME, TENSE AND PHYSICS 79P. Zamarovsky

NONLINEAR MODELS IN QUANTUM PHYSICS 81G. Chadzitaskos, A. Kostdi

SOUND PROPAGATION IN KLADNO SANDSTONES 83A". Malinsky

DYNAMIC MODEL OF THE RAIL PLASMA ACCELERATOR 85J. Maloch, P. Koniftk

DIAGNOSTICS AND DYNAMICS OF THE Z-PINCH 87J. Hakr, J. Kravdrik, P. Kubes, P. Kulhdnek, J. Pichal

OPTIC DIAGNOSTIC DEVICES FOR PULSE DISCHARGE PLASMA 89j . Kravdrik, J. Hakr, P. Kubes, P. Kulhdnek, J. Pichal

ABSORPTION OF FEMTOSECOND LASER PULSES IN SOLID TARGETS 91! J. Limpouch, L. Drska, A. Andreev

PARTICLE TRANSPORT COEFFICIENTS FOR EXTREME SYSTEMS 93L. Drska, M. Sinor, J. Vondrasek

RADIATIVE CHARACTERISTICS OF EXTREME SYSTEMS 95L. Drska, M. Sinor

INFORMATION PHYSICS OF EXTREME SYSTEMS 97L. Drska

LASER PATTERNING OF THIN FILMS 99K. Hamal, M. Jeltnek, M. Cech, J. Lancok, V. Olsan

SYNTHESIS OF Ni SILICIDES INDUCED BY EXCIMER LASER PULSES 101R. Cerny, P. Pfikryl, A.M. A. El-Kadtr, V. Chdb*

NEUTRON DIFFRACTION ANALYSIS OF BaCuO2 AT 7 K 103if M. Dlouhd, S. Vratislav, Z. Jirdk

\ OPTICAL PROPERTIES OF NOMINALLY PURE AND CR-DOPED PLZTf CERAMICS 105!& Z. Bryknar, L. Jastrabik, A. Kondkovd

I ^ LUMINESCENCE OF DEFECTS IN MERCUROUS CHLORIDE CRYSTALS 107f\ Z. Bryknar, A. Kondkovd, P. Jimusek, J. Krdl, V. Potocekif *

•- " 5i

CTi: SEMINAR 91 CONTENTS

GaAs PARTICLE AND GAMMA-RAY DETECTORS 109Z. Toniiak, B. Sopko, 1. Mdrlia. II. Frank

APPLICATION OF RADIATION DAMAGE IN SEMICONDUCTORS I l lB. Sopko, I. Mdcha. 1. Prochdzku. h. Hainal. H. Frank, M. Virius, B. Lonck, P. tiazdra

ANALYTICAL SENSITIVITIES FOR NEUTRON CAPTURE GAMMA-RAYANALYSIS 113S. Pospisil, J. Kubasta, I. Stekl, M. Vobtcbj

SEMICONDUCTOR DETECTORS FOR NUCLEAR INSTRUMENTATION 1155. Pospi'sil. A. Gasman, K. Hamal. Z. Jnnoul, ('. .Itch, J. Kont'cek, J. h'vbasta. I. Mdcha,I. Prochdzkn, .]. (h'dky, B. Sopko, Z. Tovtiak, I. Wilhehn

DETECTION OF RADON AND THORON DAUGHTERS USINGELECTROSTATIC COLLECTION 117('. Jf.ch. Z. Janout, J. Konicfk. S. Pospisil

SOME CONNECTIONS OF DETERMINISTIC CHAOS 119./. Men

A THEORETICAL METHOD FOR DETERMINING THE VISCOSITY OFGASES 121R. C'crny, F. Voddk

NONLINEAR MODELS IN QUANTUM PHYSICS 1237. Tolar. M. Hnvllrd: /,. Hlanuly, P. Sfovicd; ('. Burdik

N-N ELASTIC SCATTERING AND TRANSMISSION EXPERIMENTS 125International tram

NARROW STRUCTURE IN pp SCATTERING AROUND 2.11 GVV 127International team

4. DEVELOPMENT OF CTU STUDY

INTERACTIVE EDUCATIONAL PROGRAMS FOR MULTIMEDIA SYSTEMS . . . . 131/{. Sykora, Z. Zoclwrd, G. Dolinal, L. Kolck, S. Viinra. C. Zlatvi'k

MULTIMEDIA PROGRAMMES FOR LANGUAGE TEACHING INAUDIO-VISUAL STUDY AT THE CTU IN PRAGUE 133

:•; M. Tlalkovd, L. Mikysn

ft A COMPUTERIZED COURSE OF COMPUTER ALGEBRA 135% L. Drska, .1. Limpourh, H. Liska, M. Sivor, J. Vondrnstkff COORDINATED SYSTEM OF PROGRAMS FOR PHYSICS INSTRUCTION 137|; /,. Drska, J. Lintpouch. M. Sinor, S. Vagntr, ./. Vontlrasrk

I FIRST CONTA("IS WITH INTERNET 139

I A C'<Pfk

err SEMINAR '.U CONTENTS

THE INTRODUCTION OF A MODERN DATA ACQUISITION SYSTEM INTOTHE STUDENTS EXPERIMENTAL TRAINING 141J. Nozifka

LABORATORY FOR MICROPROCESSOR APPLICATIONS ININSTRUMENTATION 143J. Fischer. T. Juki, P. Kocounk, J. Novak, M. Stdldcfk

COMPUTER ASSISTED LEARNING OF STATIC AND DYNAMIC ANALYSISOF STRUCTURAL SYSTEMS 145./. Mdcn, P. Konvalinka. Z. Bit'nar

ADVANCED FORMS OF EXPERIMENTAL MECHANICS EDUCATION 147S. Holy, J. Bencs

UNIVERSITY STUDIES OF VISUALLY HANDICAPPED STUDENTS 149/. Nemecrk

INFORMATION SUPPORT FOR THE ENVIRONMENTAL ENGINEERINGSTUDY BRANCH 151./. Vtcrk, F. IMal, P. Moo*

MODERNIZATION OF PhD. STUDIES IN RADIOELECTRONICS 153A'. Novotny, M. Mazdnek, Z. Skvor, F. Vcjrnzkn, Z. Hrdina, J. Sykora

DEVELOPING A NEW PhD COURSE IN A SUGGESTED DISCIPLINEPHOTONICS 155E. Kosfdl, K. Novotny, J. Schrofel, M. Klima

DEVELOPMENT OF NEW SPECIALIZATIONS OF PGS IN MATHEMATICS,SOLID AND FLUID MECHANICS 157V. Stejskal, A'. Kozel, J. Jezek

EDUCATION OF EMC EXPERTS 159J. Svoboda, B. Simdk, M. Vondrak, T. Ztman

ELECTRIC TRACTION AS A NEW TOPIC IN POSTGRADUATE STUDIESAT FEE-CTU 161J. Kadlec, J. Zdenek, J. Geriich

THE CONSULTING CENTRE FOR STUDENTS AND PUBLIC RELATIONS 163P. Novotny, M. Molhanec, M. Fenclovd

5. FLUID MECHANICS

AERODYNAMIC INVESTIGATIONS OF THE WEAVING REED 167f| V. Tesaf

TEST EQUIPMENT FOR MEASURING ENERGY LOSSES IN WET STEAMFLOW 169V. Petr, M. Kolovratnik, J. Mek


ON OPTIMAL PARAMETERS OF SHOCK WAVE SYSTEMS 171.4. Poiak, P. Safnnlc

SIMILARITY SOLUTION OF THE PLANE JET USING ADVANCEDTURBULENCE MODELS 173I . Tesar, ./. Lain

COHERENT STRUCTURES IN TRANSITIONAL WALL JET 175./. Lain

LAMINAR FLOW IN SPIRAL DUCT OF RECTANGULAR CROSS SECTION 177J. Se.stdk, M. Postal, R. Zitny, F. Ambros

MACRO-INSTABILITY MEASUREMENT IN AGITATED SYSTEMS 179P. Smolka, O. Britha, I. Foil, T. Makovsky

OPTIMIZATION OF MIXING EQUIPMENT: PROCESS AND DESIGNPARAMETERS 181F. Rir.ger

FLOW OF LIQUID IN AGITATED FERMENTOR WITHCOUNTERCURRENT IMPELLERS 183/. Fort, V. Stnjc

TRANSIT TIME METHOD IN LAMINAR FLOWS 185R. Zitny, J. Sesidk, F. Ambros

MICROMIXING AND ITS EFFECT ON POLYMERIZATION 1S7J. Volaim, P. Dill

EVALUATION OF ENGINE WORKING CYCLE 189M. Taknts

ZONE MODELS OF INTERNAL COMBUSTION ENGINE CYCLE APPLIEDFOR TURBULENCE MODELLING 191./. MaakPIPE DIAMETER EFFECT AND DRAG REDUCTION BY SURFACTANTA DDITIVES 193./. Pollert. P. Komrzy. A. Vo~i nilrk

POWER ECONOMY IN HEATING AND COOLING SYSTEMS (MEASURINGOF THE COEFFICIENT OF HEAT TRANSFER) 195J. Ota, V. Sykora, J. Mclirlmr

¥= THE SHIELDED THERMOCOUPLE AS A SIMPLE TEMPERATURE PROBE . . . . 197f J. Nozirka

I SIMULATION OF FLOW PATTERNS IN COMBINED SEWER OVERFLOWS . . . . 199'•>[, P. Komrzy, K. Svcjkovsky, Z. Konink

| GROUND WATER FLOW IN A MULTILAYERED CONTINUUM 201%• I. Kazda, P. Vahnia

I!II

CTU SEMINAR 9-1 CONTENTS

6. THEORY OF CONSTRUCTIONS

CIVIL ENGINEERING PROSPECTING 205P. Droz, M. Hmbdntk

THE STEEL FRAME, FOUNDATION AND SOIL INTERACTION 207/•'. Wold, M. Jvchelka, J. Zdksky, M. Drddcky, M. Pultar

SIZE EFFECT IN PUNCHING SHEAR FAILURE OF CONCRETE SLABS 209P. Bouskn, J. Margoldova, 0. Svtvrr

THE COLUMN-BASE COMPONENT TESTS 211/•'. Wnld, .]. Scifert. 1. Simek. Z. Sokol, J. Pert old

STEEL-CONCRETE COMPOSITE ELEMENTS AND/OR STRUCTURES 213./. Pfrhar, .1. Pvochnzka, V. Weiss

CO-OPERATION OF CORRUGATED SHEETING k NON-BEARING BOARDS ...215'/'. Vratty, .1. Studnicka

THE BEAM-TO-BEAM BOLTED CONNECTION EXPERIMENTS 217/. Simck, F. Wald

NON-DESTRUCTIVE DEFLECTION TESTING OF PAVEMENTS 219B. Novotny

PEDESTRIAN DYNAMIC LOADING AND RESPONSE OF FOOTBIDGES 221M. Studnickot'd

MATHEMATICAL MODEL OF RAIL VEHICLE GUIDING QUALITIES 223J. Siba, T. Hrptntr, ./. h'oldr, R. Mitsil

ASSESSMENT OF DIFFERENT METHODS FOR MEASURING THEEFFECT ON A TRACK STRUCTURE UNDER LOADING 225//. Krejcirikom, B. h'ubdt

FATIGUE CRACK GROWTH PREDICTION UNDER RANDOM LOADING 227M. Ruzickn

VISCOELASTIC INSTABILITY IN THEORY OF STRUCTURES 229V. Kovafik

OBSERVATION METHOD OF TUNNELING 231J. Bart.dk

A METHOD FOR ASSESSING OPTIMAL HEAT POWER 233/;. Vytlncil

Section 1

MATHEMATICS

i

CTU SEMINAR 9-1 MATHEMATICS

NUMERICAL SIMULATIONOF SEVERAL PROBLEMS

OF INVISCID AND VISCOUS FLOWSJ. Fort, K. Kozel, M. Vavfincova,L. Benes, M. Fialova, J. Prokopec

CTU. Fac. of Mechanical Eng., Dept. of Technical MathematicsKarlovo 11am. 13, 121 35 Praha 2

Key words: numerical simulation, inviscid flow, viscous flow

The WOIA deals with numerical solution of

a) steady transonic flows through a new turbine cascade of Skoda Pilsen,

b) unsteady transonic flows through a turbine and compressor cascade caused by a timechange of downstream pressure or upstream velocity (upstream Mach number),

c) direct, problem of the steady subsonic and transonic flows through a radial compressorcascade,

d) steady subsonic and transonic flows through a 2D curved channel,

e) extension of 2D method for numerical solution of flow in a channel to 3D case,

f) 2D steady viscous incompressible flows through a curved channel or a branched channelor through a cascade for increasing fk (Reynolds number) computed by artificialcompressibility methoa.

Our group used H - type grid with quadrilateral cells and the following finite volume methods

a) Mac Cormack cell centered explicit predictor - corrector method in older form or inmodern TVD form (method Mi),

b) Ron-Ho-Ni cell vertex form (method A/2),

c) cell centered multistep Runge-Kutta method in several modifications,

d) generalized Lax-Friedrichs cell centered scheme extended to viscous case.

We can present several numerical results. Fig.l presents numerical results of transonic flowsthrough a turbine cascade of Skoda Pilsen achieved by two methods. The results are mappedby isolines of Mach numbers. Fig. 2 shows numerical results of transonic flows through aradial cascade of VZLU Letnany. The results are also considered in the form of isolines ofMach numbers.

13

CTU SEMINAR 91 MATHEMATICS

References:

[1] JAMESON..A. SCHMIDT.W. TURKEL.E.: Numerical Solution of the Euler e-quations by finite Volume Methods Using Runyi-hulta Time-Stepping schemes AIAAPaper 81-1250. 1981

[2] NI, R. H. .4 Multiple. Grid scheme for Solving the Euler Equations AIAA Journal, Vol.20,pp. 1565-1581. 1982

[3]

[41

SWANSON,R.C. Tl'RKEL K. A multistage Timc-Slepping Sche:mi for tin Navirr-Stokes Equations K'ASE Report No 8)-C2J9S5

FORT J. KOZEL.K. VAVRINCOVA Numerical Simulation of Steady and UnsteadyIn viscid Transonic Flows by (ill Centered and C'ell Vertex Schtmts Proceedings of the5'A Int. Symposium on Computational Fluid Dynamics, Hfl. H. Daiguji, Vol.1, pp.172-177, Japan Society of CFD. 1<»«

This work was supported by grants A'o 8017 and 2

Fig.ltiXirbir.c cascade. Iso-Mach lines.a) method M 1 , M2 = 1.09, p2 - 0.5] pih) method M 2 , M2 - 1.16, p2 = 0.48;^

Fig.2:Radial cascade. Iso-Mach lines.Method M 2

a) pi = 0.85 p0, at - -71.22 degb) p2 = 0.92 p0, a, - -71.50 degc) p-i - 0.97 pa, ai = -76.30 deg

M

: ^ ^ ^ ^ •

C'TU SEMINAR 91 MATHEMATICS

MATHEMATICAL MODELLINGIN FLUID MECHANICS

J. Neustupa, J. Benda, S. Kracmar,M. Machalicky, S. Matusu

CTU, Fac. of Mechanical Eng., Dept. of Technical MathematicsKarlovo nam. 13, 121 35 Praha 2

Key words: fluid mechanics, viscous and inviscid fluids, multipolar fluids, mathematicalmodels. Navier-Stokes equations, variational inequalities, turbine profiles

This contribution contains a brief survey of results which were obtained by the authorsin the year 1993. This is also why none of the referred works has been published yet, theywill appear in various journals in the next years.

J.Benda dealt with a subsonic motion of an ideal compressible fluid in a plane profilecascade. He proved the existence and the uniqueness of a weak solution of a basic nonlinearboundary value problem by means of the method of monotone operators. The numericalsimulation was based on the finite element method. J.Benda proved the same rate of con-vergence of this method as for linear problems. The resulting nonlinear system of algebraicequations was solved by successive approximations. The convergence of an iterative processwas tested in dependence on the used net and the Mach number and the numerical resultswere obtained for subsonic flows in some profile cascades used in the engineering practice.The detailed description of the method can be found in [1].

The motion of a viscous incompressible fluid in a finite channel was studied by S.Krac-mar and J.Neustupa in [2] and [3]. The formulation of an appropriate mathematical modelwhich uses variational inequalities to simulate the flow with non-Dirichlet boundary con-ditions is discussed in [2]. The paper [3] treats the case of a steady flow. Solutions arelooked for in a convex set K which contains velocity fields u such that except others||(u,n)_||/,a(p) < C. (F is the part of the boundary of a flow field where the non-Dirichletboundary condition is prescribed, n is the outer normal vector, the index "—" means thenegative part, a £ (2,4) and C is a chosen fixed positive number.) The sequence of appro-ximations which converges to the weak solution was constructed and the uniqueness ofsolutions was proved under certain additional conditions.

S.Matusu studied the non-steady motion of a viscous compressible tripolar heat conduc-tive fluid in a bounded domain. She used the Galerkin method combined with the method ofcharacteristics to construct appropriate approximations at first. The equations of motion ofthe tripolar fluid contain dissipative terms of higher orders. They enable to derive estimates

| of the sequence of approximations which assure the convergence of a chosen subsequenceJ. to the weak solution. The details can be found in [4]. The global in time existence of at; measure valued solution of equations of motion of a nonnewtonian compressible fluid which• . has a constant temperature was proved by S.Matusu and A.Novotny in [5]. If the fluid is|i assumed to be bipolar, the existence can be proved even in the class of weak solutions -| see [6].f J.Neustupa dealt with the stability of solutions of the Navier-Stokes equations for com-\\ pressible fluids in unbounded domains. He proved that the uniform exponential stability of

• IIJ

CTU SEMINAR 94 MATHEMATICS '.

a given sufficiently smooth solution which may depend also on the time is a consequenceof the uniform exponential stability of the zero solution of a so called linearized problem.The solutions were assumed to belong to the functional spaces of Holder continuous anddifferentiable functions. See [7] for more details. Sufficient conditions for the uniform sta-bility at permanently acting disturbances of solutions of the Navier-Stokes equations forcompressible fluids in a bounded domain in the case of a constant temperature were derivedin [8]. Similarly as in [7], the stability was examined in Holder norms.

M.Machalicky has finished several versions of a program for smoothing discretely definedparts of surfaces of turbine profiles. The result is a polygon determining an approximativeB-spline curve whose curvature is continuous even in its end points if it is connected to asegment or to a part of a circle. M.Machalicky made up a program for the construction ofturbine profiles with line surfaces which enables an economically advantageous production.The program was used at the design of the low pressure part of the turbine "SKODA 200MW".

References:

[1] BENDA, J.: Numerical solution of an ideal fluid flow in a plane. To appear in Zeit-schrift fiir Angew. Math, und Mech. 74 (1994) 5.

[2] KRACMAR, S. - NEUSTUPA, J.: Modelling of flows of a viscous incompressible fluidthrough a channel by means of variational inequalities. To appear in Zeitschrift furAngew. Math, und Mech. 74 (1994) 5.

[3] KRACMAR, S. NEUSTUPA, J.: Existence and uniqueness of weak solutions of a •steady variational inequality of the Navier-Stokes type. To appear in Applications of |Mathematics. \

[4] MATUSU, S.: Global solution of real viscous compi'essible iripolar heat conductive fluid jon finite channel. Preprint 1993. <

[5] MATUSU, S. - NOVOTNY A.: Measurt valued solution of nonnewtonian compressibleisothermal fluid. To appear in Acta Applicandae Mathematical.

[6] MATUSU, S. - MEDVIDOVA, M.: Bipolar nonewtonian fluid. Preprint 1993.

[7] NEUSTUPA, .1.: Uniform stability at permanently acting disturbances of solutions ofthe Navier-Stokes equations for compressible isolhermic fluids. To appear in Acta Ap-plicandae Mathematical*.

[8] NEUSTUPA, J.: A principle of linearization in theory of uniform exponential stability ofsolutions of the Navier-Stokes equations for compressible barotropic fluids in unboundeddomains. Preprint 1993.

This research has been conducted at the Department of Technical Mathematics as a partof the research project "Numerical solution of inviscid and viscous flow problems" and hasbeen supported by CTU grant No. 8017

16

4.


STABILITY OF VIBRATING PLATESUBJECTED TO A CONFINED

FLUID FLOWC. Simerska, J. Horacek*

CTU, Far. of Mechanical Kng., Dept. of Technical MathematicsKarlovo nam. 13, 121 35 Praha 2

"Institute of Thermomechaiiics, Academy of Sciences of the Czech RepublicDolejskova 5, 182 00 Praha 8

Key words; fluidelasticity, differential-algebraic equations, finite difference method

Fluidelastic instabilities of elastic structures subjected to fluid flow in narrow gapsare studied very frequently in connection with engineering applications (nuclear reactortechnology, regulating valves in power stations, etc.). A similar problem of a plate-like solidbody in inviscid incompressible fluid flowing in a channel is studied here.

The elastically supported rigid plate is considered as the dynamic system with twodegrees of freedom (see [2]):

w2) + &i">i + ciwt + Fi = 0,

F2 = 0,

where ?t'i,2 are the deflections of the plate at two points A and B, m i - 2 are equivalent masses,FX2 are the external forces given by the perturbation pressure p(x,0,t) on the plate surface:

F, + F2 = hfoLp(x,0,t)dx,

and /, L],L are geometrical parameters ; h is the depth of the channel. Liquid with thedensity p and the mean velocity (/0 is flowing over the plate in a rectangular channel of thewidth H. Supposing 2D-potential flow and u>i, w2 <C H, the perturbation velocity potential4>(z, y,t) for the fluid must satisfy the equation

A<1> = 0. (3)

The perturbation pressure p is given by the relation

( 4 )

and the following boundary conditions for the potential (j> are considered:

IT,= 0,

T=0 dt= 0, (5a)

17

C'JT SEMINAR 94 MATHEMATICS

06Oy

dw , dw 0<f>dw , dw

y=0 ajj y=H= 0, (54)

where w is the displacement of the plate at a point ,T 6 < 0, L >:

w(x,t) = (x-L1) + . (6)

The problem formulated above can be considered as a system of differential-algebraic e-quations (see [3]) if we solve the elliptic problem, for example, by the finite difference methodin the spatial grid and under the assumption that the integrals in (2) are approximated bysome quadrature formula.

For a narrow channel (H <C L), instead of the described 2D-probIem for the fluid flow,a ID-problem for the potential d>(x,t) can be formulated from the continuity and Euler'sequations and solved by the classical methods of stability analysis.

The computation of the 2D-model proceeds in the following way. First the externalforces F\.F2 are calculated from the initial values of the potential <j>°. Then Eqs. (1) aresolved for unknowns w-\,w-i, iwj. »V These functions enter the boundary condition at thebottom of the channel, while the condition (5a) required at the outlet of the channel yieldsthe Newton condition of the form

L n ~ At. ' { 7 )

The boundary value problem is then solved for <f>. When <f> is found the values of theperturbation pressure (4) are calculated at the bottom of the channel as well as the newvalues of t\ and F2. The procedure is then repeated and Eqs. (1) of the mechanical systemare integrated.

The calculations of the displacements w\ and w2 of the plate in time for the 2D-modelwere done for various systems with several flow velocities Uo- By increasing the flow velocitylr

0 the system lost stability by flutter or by divergence.The solution of the 2D-model, which should be used for wider channels, possesses some

difficulties which have to be taken into account when designing the algorithm for differential-algebraic equations. The main problem stems from the fact that one cannot determine thecharacter of the particular ODE at each time level and choose an adequate time step At orODE method if it turns out that the ODE system is of a stiff type.

For narrow channels the results obtained of ID and 2D model were almost the same.

References:

[1] PAIDOUSSIS, M. P. - AU-YANG, M. K. - (EDS): Axial and annular flow-inducedvibration and instabilities, PVP- Vol.244, ASME 1992.

[2] HORACEK, J. - SIMERSKA, C : Eigenvibration and Stability of an Ellaslically Sup-ported Plate in a Cannel Conveying Fluid, to appear in ZAMM 74, issue 4, 1994.

[3] SIMERSKA, C : The Interaction of an Elastic Structure with the Fluid Flow. Proceed-ings of the 10th SANM Conference, Cheb, September, 1993.

This research has been supported by the Grant No. 27614 of the Grant-Agency-Academyof Sciences of CR.

18


NUMERICAL ANALYSIS OF THE FLOWIN CORRUGATED TUBES

Z. Skalak, P. Kucera

Academy of Sciences of the Czech Republic, Institute of HydrodynamicsPodbabska 13, 166 12 Prague 6

CTU, Faculty of Civil Engineering, Department of MathematicsThakurova 7, Prague 6

Key words: Navier-Stokes equations, blood flow, finite element method

The axisymrnetric tube w is supposed to be rigid, straight, infinite and periodical inthe axial direction. It has a circular cross section and square or circular corrugations on itswall. The fluid is Newtonian. No gravitation is considered. Let (0, T) be a time interval. Iniv x (0, T) we solve the system of the Navier-Stokes equations and the continuity equation(see [1]). We suppose the non-slip boundary conditions on the wall, and the zero initialconditions. The fluid is initiated to move by a known pressure gradient.

FEM with the isoparametric elements (Pi, P\) or (P2, Pi) is used. In the element {P2,P\)some degrees of freedom in centres of triangles are reduced and less number of equations issolved without the loss of accuracy (see [1]). We use the penalty function method for thecontinuity equation, the Newton-Raphson method for the convective term and the internalEuler method for the timo term. The system of linear equations is solved by the frontalmethod program. The mesh should be fine near the wall and around sharp corners (forsquare corrugations) especially if shear stress on the wall is computed.

The pat torn of the flow changes subslantionally with increasing Reynolds numbers instationary flows. For low Reynolds numbers the centre of the vortex is placed approximatelyin the middle of the corrugation (see Fig.2). For higher Reynolds numbers the vortex changesits shape and shifts in the direction of the flow and slightly towards the axis of the tube(see Fig.3,4). Secondary vortices develop in the sharp corners inside the corrugation in highReynolds numbers. The shape of the vortex also depends on the depth of the corrugation.The pattern of the flow in the main part of the tube isn't almost influenced by the existence

> a uwm

n . 1 SHDU sinrcsrs on M IMU rat TIC C I K U M COMUCMHM rii . i ucucnt no t m nc KCKKULM OMUMIMH

19


rig.3 «UCIT> ricu iti nc nxTMcuuui mmuuiiai rit-i tm.oc.ni riu* in JNI CSKUUI COMUUIIIM:• U « 1 U U .

-i-i-iflr-iiiiii;:? of the corrugations. In oscillatory and pulsatile;|:;: flows the vortex develops near the fixed wall and"li"lt; shifts gradually towards the centre of the tube.

When the pressure gradient changes its direction,the vortex leaves the corrugation (see Fig.5) anda new vortex with the opposite rotation developsnear the wall. Velocities inside corrugations arevery small in comparison with velocities aroundthe axis of the tube both for stationary and non-stationary flows. The pressure has singularities

n,.s uciocm ncu m IHC CIKULM COMMMIKM - osciiwto«< ruu around sharp corners for rectangular corrugationsand there exist regions ot high and low pressure near the wall. The shear stress on the wallreaches its peak slightly before the narrowest parts of the tube and is very small inside thecorrugation (see Fig.l). The numerical method described is stable and convergent in therange of physiological Reynolds and Wommersley numbers for the case of the blood flowthrough human arteries and artificial vascular grafts. So in this way we can get resultsuseful for the study of hemodynamics of blood vessels (see [2],[4]).

References:

[1] Van De VOSSE, F. N. - Segal, A. - Van STEENHOVEN, A. A. - JANSSEN, J. D.:A finite element approximation of the unsteady two dimensional Navier-Stokes equationsInt. J. Numer. Methods in Fluids, 1986, Vol.6, 424-443.

[2] SAVVIDES, C. N. - GERRARD, J. H.: Numerical Analysis of the Flow Through aCorrugated Tube with Application to Arterial Prostheses J. Fluid Mech., 1984, Vol.138,129-160.

[3] SKALAK, Z. - KUCERA, P. - CERTIKOVA, M.: Numerical analysis of the flowthrough a tube with square and circular corrugations on its wall Int. Sc. Con. FluidMechanics and Hydrodynamical aspects of biosphere, 20-21 September, 1993.

[4] NEREM, R. M. Vascular Fluid Mechanics, the Arterial Wall, and AtherosclerosisJ. Biomechanical Engineering, 1992, Vol. 114, 274-282.

This research has been supported by the Grant No. 2818 (Fund for Development ofUniversities), under the research project "Numerical simulation of pulsatile flow in vasculargrafts".

20

(TU SEMINAR 94 MATHEMATICS

NUMERICAL SIMULATIONOF PULSATILE FLOW IN THE AORTA

P. Burda, J. Kofenar*

CTU, Fac. of Mechanical Eng., Dept. of MathematicsKarlovo nam. 13, ]21 35 Praha 2

*Acad. Sci. Czech Rep., Inst. of Hydrodynamics, Dep. of BiomechanicsPodbabska 13, 166 12, Praha 6

Key words: Navier-Stokes equations, pulsatile flow, semiimplicit method, MAC method

Numerical analysis of flow of viscous incompressible fluid in corrugated tubes or tubeswith obstacles has been the subject of the series of papers in past two decades (cf. thereferences in [8]). The authors usually restrict themselves to the solution of some particularproblem. In the cast- of pulsatile flow, however, there are still many open questions. Soin our group, we decided to tackle the problem of pulsatile flow in a rather complex way.First, we need to know as much as possible on the theoretical properties of the mathematicalmodel. So the problem of the existence of solution was studied by our colleagues in [10].An investigation of the character of singularities of a related linear problem is in [6], [7].

i Numerical solution by the finite element method is done in [8], [9].; In the present paper we follow up with the results published in [l]-[5], where we analysedj various aspects of numerical solution of pulsatile flow simulating the flow in blood vesselsi in the vicinity of stenoses. In the present paper we focus our attention to the case of flow in

the tube with a shallow obstacle. On the other hand we admit higher velocities, to simulatemore faithfully the flow in the aorta.

We consider the problem governed by the Navier-Stokes equation

dV 1+ {V-V)V = — grad/> + / / A V , (1)

at p

where V is the velocity vector, p is the pressure, p the density, v is the coefficient of kinematicviscosity, t is time , and by the continuity equation

: ' div V = 0. (2)

>,' With regard to the axial symmetry, the problem is solved on a 2-dimensional domain,|j using cylindrical coordinates r, z,fy The time discretization is done by the semiimplicit scheme (cf. [1] for more details)ff% Vn — V" -I —- = ( -V n -V)V n + i/ AV" , (3)

Space discretization is done by a variant of MAC method, cf. [1]. Let us remark thatquite recently some error estimates for the velocity and pressure have been proved, cf. [11].

Some numerical results of the model wiih lower velocities were presented in [1] - [5].Here we give the results for the case of a tube with a shallow obstacle. On the other hand

21


the velocities are higher. Corresponding Reynolds number is R< =s 600. On the Figure 1we show the velocity vector field at, I = 17.0-r> sec.

Velocity Field Uectors PEB10»:15 t= 17.05 [s] SCflLE .5 x

PHflSE:Z89°

Fig. 1. Velocity vector field at / = 17.."5 sec.

References:

[1] BURDA. P., KORENAR. .J.. Numerical solution of pulsatile flow in a round tube withaxisymmrfric constrictions, Conun. Inst. Hydrodyn. 19, 1993,87-110.

[2] BURDA, P., KORENAR, J.. Numerical solution of Nanirr-Stokts equations for con-stricted pulsations, Conf. GAMM '93, Dresden, ZAMM 74. No. 6, 1994.

[3] BURDA. P.. KORENAR,.)., Constricted pulsations nunuricnlly, Proc. Conf. Numer-ical Mathematics in Theory and Practice. PIzen. 1993.

[I] BURDA. P.. KORENAR, .1., Numerical solution of pulsatile flow in a tube with ashallow obstuck, Proc. Fluid Meeh. and llydrodyn. Problems of Biosphere. Liblice,1993.

[!}] BURDA, P.. KORENAR, .J., Simulation of pulsatile flow in tlu symmetric model ofthe aorta, (in C:ech) Proc. Conf. Fluid Dynamics '93. Praha. 1993.

[6] BURDA, 1'., Cubic Finite Elements in Elliptic Probhms with Interfaces and Sintjular-ilits, Conf. MAFELAP S, London, 1993.

[7] BURDA. P.. Cubic version of FEM in tlliptic problems with inierfncfs and singulari-ties, to appear in Proc. Conf. FEM 50, .Jyvaskylii, 1993.

[8] SKALAK, Z., The oscillatory and pulsatile flow of a N( wtonian fluid through squarecorrugated tubes, 15-th Biennial Conf. on N'timer. Analysis. Dundee, U.K., 1993.

[9] SKALAK, Z., KUCERA, P., The oscillatory flow of a Newtonian fluid through tubeswith various corrugations, Proc. Conf. Numer. Math, in Theory and Practice, PIzen,1993.

[10] KUCERA, P.. SKALAK, Z., The mathematical model of the periodical flow in thecorrugated tube, Proc. Conf. Fluid Mech. and Hydrodyn. Problems of Biosphere,Liblice, 1993.

II1] 1IOU, T., 1.. WETTON, B., T., R., Second order conveigmce of a projection scheme forthe incompressible Navier-Siokcs equations, SIAM .J. Num. Anal., 30., 1993, 609-629.

This research has bi.en don< at the Dep. of Ma tlu matics of the Faculty of Mech. Eng. ofCTU Frcgnt, under tin project. ''Numerical simulation of pulsatile flow in vascular grafts",and has been supported by the grant No. 2X12 (Fund for Development of Universities).

22


GENERALISATION OF ELLIPTICMOTIONM. Kargerova

C'TU. Fac. of Mechnical Eng., Dept. of Technical MathematicsHorska 3 ,12800 P rah a 2

Key words: kinematics, geometry

Elliptic motion in the Euclidean space- has several characteristic properties:

1) It is a rolling of two circles with ratio of radii 1:22) It has infinitely many straight trajectories3) All non trivial trajectories are conies sections - ellipses.

In this paper we shall generalize the property 3). We shall describe equiaffine planemotions with all trajectories conic sections. Conic sections in equiaffine geometry are char-acterized as curves with constant equiaffine curvature. This means that for each point XeA-2we must have dh'x/(It = 0 where h'x denotes the equiaffine curvature of the trajectory ofthe point A'. Computation yields

|A", .Y"|2[451A", A (4 ' | + 9 |.Y\ A(5)|] + 40|A\ A " f

+ \X\ X"\ |A", A""| [-45 |A", A (4) | - 90 | X", X'"\) = 0.

From this formula we see that if |A", X"\ = 0 then also |A". A""| = 0. This means thatall points of the inflexion curve lie on the curve |A'\ X'"\ = 0. This condition yields that thedifferential equation of all trajectories is

A'" - aX' = 0.

For a — 0 we obtain two solutions and equiaffine plane motions g\ a.nd</2 c a n t>e

expressed in the following form:

/ I 0 0 \ffl = k(t/2 -t2) 1 - t/2 -t/2

\k'(t/2+t2) t/2 l+t/2/

for hyperbolic case and

Ifi for elliptic case; k is constant.

/ 1 0 0 \g2 = kt*/4 1 -t

\ 0 t l - t 2 /

23

(TV SEMINAR 91 MATHEMATICS

0 .5

10 15

1 4 .

Fig. 1 and 2 show polhodes of these motions and some of the trajectories. The fixedpolhode is a cubic curve and the moving polhode is a parabola.

References:

[1] BOTTEMA,O. ROTH, B.: Theoretical kinematics, Amsterdam, North-Holland 1979

[2] KARGER, A. NOVAK, .J.: Prostorovd kincmatika, SNTL, Praha 1978

,. i

This research has been conducted at the. Department of Technical Mathematics as a partof the research projfet "Mathematical Methods in Milling" and has been supported by GACR grant


MODEL OF SURFACE CREATEDBY DOUBLE ROTATIONAL MOTION

E. Kopincova


Key words: CAD/CAM, swept volumes, envelope of surfaces, characteristics

In mechanical engineering praxis we can find a lot of important surfaces which arecreated by moving a body or its boundary surface. These surfaces are created for exampleby the motions of a tool during a NC-tooling process. They can also be studied by collisiondetection of moving volumes. The computer can be used here only for checking and controlof tool paths or for the whole design and production of parts. Such modules of CAD/CAMsystems replace the real objects by its geometrical model. The process of geometric modelingis realized by a so-called sweeping operator. The object founded by this operator is calleda swept surface [I].

Let the boundary surface F of the moving body be given by the equation (1) and motionof this body be given by smooths piecewise differentiable function m(t).

f{x,y,z)=0 (I)

Then the equation (2) defines one parametric system of surfaces. The formulas (2) and(3) hold for coordinates of points of the envelope (F) of the system of surfaces (2).

f{x,y,z,t) = 0 (2)

StJ(x,y,z,t)-0. (3)

We will get the equations of two surfaces (4) from formulas (2) and (3) after the sub-stitution of the constant parameter t — c and St converges to zero. Their intersection is thecharacteristic line laying on the surface.

f(x, y,z,t) = 0, jtj(x, y,z,c + 6t) = 0 (4)

If we express the surface F by its parametric equation p=p(u,v) and if we mark d thetangential vector of the trajectory of the point C of the surface F by the motion m(t) thenthe formula (5) holds for all the points of the characteristic line (see [1]).

= 0 (5)1/ It t/ V

a This article deals with the creation of a geometric model of the envelope surface duringU the double rotational motion with skew axes. This double rotational motion can be substi-j ' tuted with the instantaneous helix motion for each value of the parameter t (see [2]). Theft; movement is applied on the surface of revolution. Its meridian is the curve of the degree


three at the maximum and it is given by its boundary conditions. A wireframe model iscomposed of characteristic lines which are computed for the given value of parameter ton the surface (2). The characteristics are approximated by polygons. Their vertexes arepoints on the surface (2) for which the equation (5) holds. The computing of these vertexcoordinates can be found in [3] under the condition of choosing a special coordinate frame.Well-selected segments of characteristics build up the boundaries of the patch of the facemodel of the envelope (F). This face model is used for the construction of contour lines.

The surface generated by the surface of revolution in orthogonal axonometric projectionis shown in the following figure. The wireframe model of the envelope contains 66 charac-teristics and the face model contains 208 patches. A few segments of one selected contourline on the envelope are also shown.

References:

[1] WANG, W. P. - WANG, K. K.: Geometric Modeling for Swept Volume of MovingSolids, IEEE CGA December 1986.

[2] LITVIN, F. L.: Teorija zubtschatych zaceplenij, Moskva, 1968

[3] KARGER, A. - NOVAK, J.: Prostorova kinematika a Lieovy grupy, Praha, SNTL,1978

This research has been conducted at the Department of Technical Mathetatics as a partof the research project Mathematical Methods in Kinematics of Machines and Robots andhas been supported by GA CR grant No. 101/93/0447 ( intern, no. 2837 88 ) .

I

26


SOME RESULTS FROM THEORYOF HOMOGENEOUS OPERATORS

S. Burysek, V. Buryskova

CTU, Far. of Mechanical Eng., Dept. of Technical MathematicsKarlovo nam. 13, 121 35 Praha 2

Key words: Hilbert space, homogeneous operators, polynomial operators, numerical range,convexity

The convexity of the numerical range of a couple of homogenous polynomial operators isproved. We deal with properties of the numerical range of a couple (5,7) of homogeneousoperators on an abstract Hilbert space X. The notion on the numerical range plays animportant role in localizing the spectrum and eigenvalues.

Definition: Let S, T : X —* X be homogeneous operators. We call the numerical rangeof the couple (S.T) the set W(S,Tj of complex numbers defined by

.r ||= 1, (Tx,x)

It is evident that for S linear continuous and T identity operator we obtain the well-known Ilaiisdorff's definition of the numerical range.

The main result of our work, a generalization of the well-known Hausdorff-Toeplitztheorem on the convexity of the numerical range, is the following theorem.

Theorem 1: Let the dimension of the space X be greater than one and let S,T : X —* Xbe continuous homogeneous polynomial operators of the degree k > 1. In the case when X isa real space suppose, further, that (Tx,x) > 0 for any x € Si(0). Then the numerical rangeW(S,T) of the couple (S, T) is a convex set. In the next theorem we give conditions for the

compactness of the numerical range W(S,T).

W Theorem 2: Let S,T : .Y —> A' be homogeneous polynomial operators. Suppose further& that the following conditions hold:f (1) The. operator S is strongly continuous.% (2) The operator T is positively defined and such that (Tx, x) is a real weakly lower% semicontinuous functional.

> 'f. (3) 0€ W(S,T).Tt Then W(S,T) is a convex, and compact set.

' X:*• ' 27

*


References:[1] CANAVATI, J. A.: A theory of numerical range for nonlinear operators J. Functional

Anal. 33 (1979), No. 3, 231-258.

[2] CONTI, C. - De PASCALE, E.: The numerical range in the nonlinear case. BolletinoU.M.I (5) 15-B (1978), 210-216.

[3] KVONG SOO KIM - YOUNGOH YANG: On the numerical range for nonlinear oper-ators. Bull. Korean Math. Soc. 21 (1984), No. 2, 119-126.

[4] ZARANTONELLO, E. H.: The closure of the numerical range contains the spectrum.Pacific J. Math. No. 3, 22 (1967) 575-595.

I

28

CTU SEMINAR 1)4 MATHEMATICS

STABILITY ANALYSISBY QUANTIFIER ELIMINATION

R. Liska, S. Steinberg*

CTU, Fac. of Nucl. Sci. & Phys. Eng., Dept. of Physical ElectronicsBfehova 7, 115 19 Prague 1

* University of New Mexico, Dept. of Mathematics and StatisticsAlbuquerque, New Mexico 87131

Key words: stability, difference schemes, computer algebra, quantifier elimination

This paper describes a new method for the stability analysis of time stepping differenceschemes used for numerically solving partial differential equations systems (PDES). Anynumerical solution has some error, so a very important property of the difference schemeis how are the numerical errors propagated as the solution proceeds from one time stepto another. If the errors are not amplified, the difference scheme is stable. The centralimportance of stability is expressed by the Lax-Ritchmyer equivalence theorem which statesthat, under certain natural assumptions, a scheme is convergent if and only if it is stable.

Difference schemes for initial value problems for linear time dependent PDES in severalspace variables are analyzed. The scheme approximating the PDES is built on a grid withconstant time and space steps. The stability analysis is done using the Fourier method,which proceeds by substituting Fourier components for the discrete function values in thedifference scheme and then constructing the amplification matrix for the transition fromone time step to another. The characteristic polynomial of the amplification matrix is thecharacteristic polynomial of the difference scheme. The von Neumann stability conditionrequires that all eigenvalues of the amplification matrix, i.e. the solutions of the character-istic polynomial of the scheme, are in absolute value less than or equal to 1 for all values ofthe wave numbers, i.e. the Fourier coordinates for each space coordinates.

The conformal map (z + l)J(z — 1) transforms the von Neumann condition into a Routh-Hurwitz problem whose solution results in a universally-quantified logically-connected setof polynomial inequalities. Thus the stability condition is transformed into a universallyquantified formula. The quantifiers can be eliminated from the formula by using a quantifier-elimination algorithm producing an analytic quantifier-free stability condition. For quan-tifier elimination, the cylindrical algebraic decomposition method developed by Collins [1]

i: and improved by Collins and Hong [2] can be used.| All steps of the outlined stability-analysis algorithm are exactly computable in a com-('. puter algebra system. For the initial experiments with the algorithm, the package FIDE,,i realized in the REDUCE computer algebra system, and the quantifier elimination by partialI cylindrical algebraic decomposition package QEPCAD [3], realized in the SACLIB computer;'•' algebra system, have been used. The initial results indicate that the method is only success-Is: ful for relatively simple difference schemes. Its limitation for larger problems lies in the huge| computational time and storage requirements of the quantifier elimination algorithm. Wei| are not aware of any other implementation of quantifier elimination algorithm that is better.!> For detailed description of proposed stability analysis by quantifier elimination method seeI [4] •

29


To provide a practical insight into the method, one example of the analysis of a schemefor the convection-diffusion equation «/ = auxx + bux is presented. The Adams-Bashforthdifference scheme

where A = a ht/2hx, B = bht/-ihx, a > 0,6 are constants, ht is the time step and hx is spacestep, is considered. The characteristic polynomial of the scheme is

where it, is the wave number or Fourier coordinate. After several transformations of thecharacteristic polynomial, a quantified formula equivalent to von Neumann stability condi- \tion is obtained:

V C x e [ - l , l ] 2(Cr- \)A2-A-2CxB2-2B2<0A

16(6* - 3C* + 3C, -l)A* + (12C2B2 - \2B2 + 1)A- 32(C* - 2Cr + l)(Cx + l)A2B2

-12(C2 - 2Cr + \)A3 + 16C?.B4 + 16C2B4 - 16CX£4 - 16/34 > 0

where Cx — cos(A> hx). After several steps, the quantifier free formula

2304/1B1' + 512£i; + 1216/42fl4 + 288AB4 + 36/43J32 - 108.42#2 - 27.452

+108.44 + 27A3 < 0 V (8A - 1 < 0 A 9A - 40B2 > 0)

is calculated. This formula is equivalent to the quantified formula and is the stabilitycondition of the Adams-Bashforth difference scheme. The second part after V is a simplesufficient stability condition. [

References:

[1] COLLINS, G.E.: Quantifier Elimination in the Elementary Theory of Real Closed Fields Iby Cylindrical Algebraic Decomposition. In Lecture Notes in Computer Science, Berlin. ISpringer-Verlag. 134 183, Vol. 33, 1975. j

[2] COLLINS, G.E. - HONG, H.: Partial Cylindrical Algebraic Decomposition for Quan- ftifier Elimination. J. Symb. Comp. 12(3), 299-328, 1991. j

[3] HONG, H.: Improvements in CAD-based Quantifier Elimination. Ph.D. Dissertation,: The Ohio State University, 1990.

' [4] LISKA, R. - STEINBERG, S.: Applying Quantifier Elimination to Stability Analysis j| , of Difference Schemes. Computer Journal 36(5):497-503, 1993.

# This research has been conducted at the Department of Physical Electronics of CTUp' and Department of Mathematics and Statistics of University of New Mexico as a part ofIf the research projects ''U.S.-Czech Mathematics Research on Symbolic Derivation, Analysis,f|:. and Programming of Finite Difference Schemes" (supported by National Science Foundation1 Grant No. INT-9212/,33), "Information Physics of Extreme Systems: Methods, Simulations| j | and Applications" (supported by the Universities Development Foundation Grant No. 0196)

and "Particlr Transport and Radiation Processes in Systems with High Energy Densities"(supported by CTU Grant No. M/,1).

' ^ f -


ON VARIANCES IN SPATIALSTATISTICS AND STEREOLOGY

V. Benes, B. Vesela


Key words: anisotropy, spatial statistics, stereology

Various problems in the material research, biology, medicine and geology force scientiststo quantify three-dimensional structures observing probes of dimension less than or equal tothree. The mathematical theory needed is called stereolog}'. There are two basic approachesto stereology which are often combined: either the structure is deterministic and the probesare considered random or the structure is modelled by spatial random processes when underthe assumptions of stationarity and isotropy the probes may be fixed. The first approachis called "design-based'" and makes use of the integral geometric notion of Minkowski func-tionals, while the second (model-based) approach [2] is based on the probability theorydeveloping properties of random processes of points, fibres, surfaces, geometrical particlesand tessellations. The estimation of paramelrs is based on spatial statistics which is muchdifferent from the classical statistics. Its special problems are dependent observations, edge-effects, systematic sampling and so on. When implementing stereology in practice eithersimple manual point counting methods are used or advanced systems of image analysis basedon mathematical morphology are available.

Basic stereological formulas relate first-order characteristics, i.e. intensities of inducedstructures. A lot of work has been done in 80's in studying such second-order characteristicsas second moment, measures and pair correlation functions. In our department the model-based approach has been developed since 1989 towards releasing the assumption of isotropyof the underlying stochastic models. The main achievements concern the following topics [1]:

a The germ-grain structures were modelled by means of marked-point processes and thedifferences between anisotropy of grains and that of spatial distribution of germs wereclarified,

b Second-order stereological formulas for anisotropic structures were developed usingthe Palm theory relating the structure of both projections and sections to the basicone.

c Methods of anisotropic sampling were systemized using the notion of projection mea-sure and techniques of integral Buffon transforms.

V, The recent research was devoted to random fibre and surface processes. Formulas for>f? variances of various intensity estimators were obtained in a comparable form using the two-

ipoint mark distribution. Counterexample for the validity of theorem of Rao-Blackwell typefor projection estimator appeared. Optimization of the estimation variances is studied indifferent ways:

1 With respect to the anisotropic sampling design and the shape of sampling window;this is easily solved for Poisson type processes otherwise it is an open problem.

3i

u•if.


2 With respect to the second-order characteristics of the process which leads to somegeneralized types of moment problems with unknown solutions.

The need of more models will be partly satisfied by simulation techniques, however theemphasis is placed on further theoretical results.

References:

[1] BENES, V.: On second-order formulas in anisotropic stereology VI Internat. Workshop"Stochastic Geometry, Stereology, Image Analysis", Valencia, +iis, to appear.

[2] STOYAN, U. - KENDALL, W. S. - MECKE, J.: Stochastic Geometry and Its Appli-cations Academie Verlag, Berlin, 1987

This rescarc.he is supported by the Grant Agency of the Czech Republic as a part ofproject 201/93/2172 " Anisotropy characteristics of random geometrical structures".

32

VTV SEMINAR 94 MATHEMATICS

STATISTICAL METHODSUSED IN BERNESE GPS SOFTWARE

L. Mervart , M. Cimbalnfk

CTU, Fac. of Civil Eng., Dept. of Advanced GeodesyThakurova 7, 166 29 Praha 6

Key words: statistical methods, gps

Global Positioning System (GPS) has become one of the most accurate and efficientmethods which is commonly used to determine the relative positions of points on the earth'ssurface. Using this method requires the use of advanced computation techniques to managethe amount of measured data. The Institute of Geodesy, TU Prague cooperates with theAstronomical Institute, University of Berne (AIUB). The Bernese Institute has been devel-oping the software for GPS analysis since 1980. Some of the results achieved during the lastyear are presented in this paper.

If small biases are neglected, the GPS measurements may be modeled by the followingobservation equation:

L'Fk - Sk + V nFk > (*)where k is the receiver index, / the satellite index, ol

k is the distance between the receiverand the satellite, F = 1,2 denotes the frequency, Xp is the corresponding wavelength and»}.'/>. is an unknown integer number of cycles, the so-called ambiguity. During the parameterestimation (e.g. least-squares adjustment) this ambiguity has to be replaced in a first step bya real-valued parameter. Under certain conditions some or all of the least-squares solutionsof the real-valued ambiguities can be related unmistakeably to the true integer values. Byintroducing these true ambiguities into a subsequent least-squares adjustment the solutionbecomes much more stable. The accuracy of the results can be improved by a factor of upto 4. Numerous methods have been proposed for dealing with the resolution of the initialphase ambiguity parameters. Most of these methods consist, generally, of two steps.

• Within the first stop the ambiguities are estimated together with other unknown pa-rameters. This first step leads to the real-valued ambiguity parameters; the a posterioristandard deviation of the unit weight and the covariance matrix of the parameters.

• The second step is based on the results of the initial adjustment. Different strategiesare used to find the integer values of the ambiguities.

•>

;. The strategy developed at AIUB uses the following information from the initial adjustment:

i x = (.i'i,... , .r,,)1 is the part of the solution vector which contains u real-valued (doubleI difference) ambiguities.i| Q is the corresponding cofactor matrix.'!• fTg is the a posteriori variance factor.

t From the a posteriori variance factor and the cofactor matrix the standard deviation m,- forII the ambiguity parameter ;r, or the standard deviation m,j for the difference between twof! parameters ,T,J may be computed:

| m, = <TOy/(h , vuj = <T0V/<?.. - 2 • Qn + Qjj . (2)

33


Choosing a confidence level a and using the Student's distribution we can compute theupper and lower range-width £ for the integer-valued alternative parameter xî or for thedifference x^j between two such parameters. Thus

•r,-£-m,< xAi < a\ + £ • mi , (3)x,j - £ • rriij < xA!J < i y + (, • rrtij . (4)

All possible combinations of integer values given by the first confidence range are used toform alternative ambiguity vectors x_Afl> k =• 1,...,7V to the initial ambiguity estimatesx. These alternatives are generated by forming all possible vector combinations using theinteger values within corresponding confidence ranges. Each of these alternative vectorsshould be introduced into a subsequent adjustment run. The integer ambiguities are treatedin these adjustments as known quantities. The resulting standard deviations a^ are used toassess the results. The integer vector T_h yielding the smallest standard deviation is selectedfor the final solution unless (1) its standard deviation is not compatible with <7o which meansthat the fraction a/,/<Xo is too high, or (2) there is another vector x^ which yields almostidentical standard deviation. It means that the fraction (Tq/ah is close to one.

The new approach is based on the experience that, if it is not possible to resolve thedouble difference ambiguities

nFkl — nFkl ~ nFkl ' nFkl ~ nFkl nFkl > \°I

it may be possible to resolve the difference

nFkl - nFkl nFkl ' W

which, as a matter of fact is a double difference ambiguity again. Let us assume thatx;, Xj are the (double difference) ambiguity parameters. For each parameter £; we canthen compute the a posteriori rms errors from the initial least-squares adjustment usingequations (2). All the rms errors m, and rriij are sorted together. Within one iteration stepthe Nmar best determined ambiguities (or differences between ambiguities) are resolved(rounded to nearest integers) unless:

• The corresponding rms is not compatible with <TQ (m, > amax or rtiij > <rmax)• or within the confidence interval (xi — £m;,Xj + fm,) or (xij — fm,j,Xij + £niij) is not

exactly one integer number.

References:[1] MERVART, L. - BEUTLER, G. - ROTHACHER, M. - WILD, U.: Ambiguity Resolu-

iion Strategies using the Results of the International GPS Geodynamics Service (IGS).Bulletin Geodesique, 1994 (in print).

[2] MERVART, L. - CIMBALNIK, M.: International GPS Service for Geodynamics. Mil-itary Topographical Institute, Prague, 1993 (in Czech).

This research has been conducted at the Department of Geodesy as a part of the researchproject "Solving the Problems of Geodesy using the Global Positioning System (GPS)" andhas been supported by CTU grant No. 8116/15270.

34


THE BAYESIAN INFERENCE WITHMODIFIED NORMAL DISTRIBUTION

L. Soukup

CTU, Fac. of Civil Eng., Dept. of Mapping & CartographyThakurova 7, 166 29 Praha 6

Key words: Bayesian approach, normal distribution

Bayesian inference is a very efficient tool for estimating unknown parameters from asample of observations. It is based on the well-known Bayes theorem. In the case of estimat-ing the value of the random vector i given by the observation vector y and overdeterminedoperator equation

A(x) = y , (1)

the Bayes theorem has the consequent form:

f[y-Ajx)\x)e{x)M)= ( 2 )

Meaning of the symbols used in this formula is as follows:i

e. ... prior probability density function of vector x, s

/ ... probability density function of observation vector y, j

g ... posterior probability density function of vector ,T, \

y ... vector of measured values, jj

X ... space of allowed values of unknown vector x.

It is not well known that the Bayes theorem was used for deriving normal distributionby C. F. Gauss almost two centuries ago (see [1]). For this derivation the most simple caseof equation (1) was assumed, i.e. .T was a scalar and for each component of y the pertinentfunction in (1) was identical. Furthermore, the prior probability distribution e was assumedto be uniform for the set of all real numbers. The domain of normal distribution is therefore

J the whole real axis as well. In fact, no density function e can exist under the mentioned \( | presumptions. From the formal view, it does not matter, because e can be eliminated fromS the fraction in formula (2).I- Function / in formula (2) is usually obtained by multiplication of normal distributionsj | ' , V7- m many applications a finite interval of expected values of vector x is known. This infor-H mation can increase the reliability of measurement results if some appropriate distributionI" / is designed. For the purpose of using the Bayesian theorem to consider the constrainedpi domain of the uniform probability density function e, such a distribution can be obtained|? by modification of normal distribution..& For this reason, Ciaiiss's original method was followed and, under slightly changed

, ' i'| assumptions, the probability density function of the error v of some component of y wasH finally found in the form:

»• 35

I


••fit :{-b,b)-* R:v->Cb ( 1 -i f - V2 \o> (3)

where n := \{~) a n d C6 , <7 are appropriate constants. The right side of this equationresembles the n-th member of a sequence the limit of which is exp( — \ (^) ). Hence, if n isa natural number, the function tpi, given by (3) converges to the normal distribution <p whilethe length of its domain reaches to infinity. The great advantage of the constrained normaldistribution is that the integral of its density function is analytically tractable. If n is anatural number, the integral can be expressed in polynomial form. This feature is significantfor dealing both theoretically and numerically with the constrained normal distribution.

The only disadvantage of this distribution is that the most probable value of the argu-ment of a posterior density function g is not the arithmetic mean as in the normal distribu-tion, but some slightly different value which is not very easy to evaluate. This bias can besimply reduced by increasing the size of interval (—6,6).

The use of the modified normal distribution in the Bayes theorem (2) allows the symbolicevaluating of a posterior distribution even if a non-uniform prior distribution is presumed.Using a properly designed prior distribution can increase the reliability of the results fromprocessing the observed data. This problem is a topic for future research.

Fig. 1: probability density function of the modified normal distribution (p4 (thick line) givenby (3) in comparison with the normal distribution ip (thin line) assuming a = 1

I

References:[1] GAUSS, C. F.: Theoria motus corporum coelestium in sectionibus conicis Solan am-

bientium, Liber II, Sectio III, Hamburg 1809; russian translation in: C. F. Gauss,Izbrannie geodezicheskiye sochinyeniya, Moscow 1957

This research has been conducted at the Department of Mapping and Cartography as partof the research project "Application of the Bayesian approach in geodesy and cartography"and has been supported by Internal grant of faculty of civil engineering No. 1158.

•S*

36


SKETCHES AND PRESENTATIONOF STRUCTURES

J. Adamek

CTU, Fac. of Electrical Eng., Dept. of MathematicsTechnicka 2, 166 27 Praha 6

An important type of presentation of data structures, generalizing equational presen-tation of algebraic structures and implicational presentation of relational structures, isthat of sketching of structures. This was introduced by C. Ehresmann [5]: A sketchS = (A,L.,C_,cr) is a small category A, with two small collections jL and C_ of diagramsin A, and a function CT assigning a cone to each ^"diagram and a cocone to each C-diagram.A model of S is a functor F:A —» Set such that for each diagram D £ L a limit of FD isF(aD), and for each diagram D £ C_a colimit of FD is F{aD). A category is sketched bya sketch S if it is equivalent to the category of models of S and natural transformations.

An important feature of the theory of sketches is the relationship between syntax (prop-erties of a sketch) and semantics (properties of the models). In [1] the basic result of Lair[6] that, a category can be sketched iff it is accessible was extended as follows: a categorycan be sketched by a limit-epi sketch (i. e., the only colimit specifications of the sketch arespecifications of some morphisms as epimorphisms via pushouts) iff it is accessible and hasproducts or, equivalently, iff it is accessible and has weak colimits.

Another syntax-semantics result is presented in [3] where quasivarieties are character-ized as categories sketchable by separated limit sketches. This solves the open problemof characterizing those sketches between product sketches (corresponding to varieties) andlimit sketches (corresponding to locally presentable categories) which correspond to qua-sivarieties. Furthermore, it is shown that product-mono sketches sketch precisely thosequasivarieties which have the property that every strong equivalence relation is effective.

Besides these new results, a survey of the known techniques is presented in the mono-graph [2] now in print. These include the techniques working with injectivity conditionsdeveloped in [4] where, inter alia, weakly locally presentable categories are characterized asthe small-injectivity classes in locally presentable categories.

", References:1 [1] A D A M E K , J . - R O S I C K Y , J . : On weakly locally presentable categories, C a h i e r s de

J; Topolog ie e t G e o m . Diff., accep ted for publ ica t ion

f> [2] A D A M E K , J . - R O S I C K Y , J . : Locally presentable and accessible categories, C a m b r i d g e| ; University Press, monograph in print

|; [3] ADAMEK, J.: How to sketch quasivarieties, manuscriptiv.

| [4] ADAMEK, J. - ROSICKY, J.: On injectivity in locally presentable categories, Trans-| actions Amer. Math. Soc. 336 (1993), 785-804»;

37


[5] C. Ehresmann: Esquisscs et types de structures algcbraiqv.es, Bull. Instit. Polit., Iasi14 (1968), 1-14

[6] LAIR, C : Categories modelables et categories esquissables, Diagrammes 6 (1981),1-160

[7] MAKKAI, M. - PARE, R.: Accessible categories, Contemporary Mathematics 104,Amer. Math. Soc. Rhode Island 1989

This research has been conducted at the Department of Mathematics as a part of theresearch project Algebraic and Categorial Methods in Computer Science and has been sup-ported by CTU grant No. 8010.

V 38

, i


NONCOMMUTATIVE PROBABILITYTHEORY AND ITS APPLICATIONS

J. Tkadlec

CTU, Faculty of Electrical Engineering, Department of MathematicsTechnicka 2, 16627 Praha 6

Key words: noncommutative probabilistic models, quantum logic, Boolean algebra, mea-sure theory, Jauch-Piron measure

"Noncommutative probability theory and its applications" is a research project conductedby V.Rogalewicz and J.Tkadlec. Let us first summarize the aims of the project:

1. To construct examples (and counterexamples) that illustrate differences between clas-sical and noncommutative probability theory.

2. To study various conditions imposed upon a noncommutative probability model andtheir influence on the structure of the space of probabilistic measures.

3. To clear up the connections between Jauch-Piron measures and concrete representa-tion (i.e., set-representations).

4. To develop close cooperation with experts from Geneva and from Sankt Peterburg.

5. To strengthen the reputation of Czech science and of Czech Technical University.

Results:

1. Various examples that illustrate differences between classical and noncommutativeprobability theory were constructed and presented. FY>r instance, in [6] there is anexample of Boolean orthomodular poset without any two-valued Jauch-Piron state.Some examples are constructed by using set-theoretic methods [7], some by usingmeasure-theoretic methods [6] and some by using combinatorial methods [3] that arebased on the theory developed in CTU and published in [1]. Two interesting examplesbased on this theory were presented by V.Rogalewicz in his lectures in Switzerlandand a very complex one in his lecture at Friedmann Laboratory in Sankt Peterburg.

2. Several results concerning the connection between algebraic properties of quantumstructures and spaces of measures on them were studied from different points of view.From one point of view, various generalizations of the notion of measure — partiallyadditive measures — such that there is sufficiently enough such "weaker" measures, arestudied [4]. From another point of view, there are given algebraic conditions that forcethe space of measures to be sufficiently large [7]. A measure theoretic characterizationof Boolean orthoposets is presented in [5].

3. The signification of Jauch-Piron measures is one of the very important questionswithin quantum logic theory. It is studied by many authors and also in this researchmany results are more or less connected to this question. Several results are presented

J- in [5, 6] (see also part 1.).; • *

•-' 39


4. According to the research project, V.Rogalewicz visited Universite' de Geneve, Groupede Physique Appiiqu.cc and Unive.rsitdt Bern (Switzerland, January 26 - February 24,1993). where he held three lectures and where he closely cooperated with N.Gisin.Both V.Rogalewicz and J.Tkadlec took part in the summer school "Lattices with or-thocoinplementations'" organized by Friedmann Laboratory (Sankt Peterburg, Russia,June 20-30, 1993). The}' held six lectures and had fruitful discussions with leadingRussian experts, e.g. with A.Grib, R.Zapatrin, P.Ovchinnikov, V.Tikhonov.

5. Results of this research project were or are presented in conferences and stays (notmentioned yet: J.Tkadlec, 3rd Winter School on Measure Theory, Liptovsky Jan,Slovakia, January 18-22, 1993) and/or published in renewed journals (see the listof references). We made a larger mathematical and physical audience acquaintedwith our research and with the work at Czech Technical University (special lecturein Sankt Peterburg). We took part in the organization of 'international QuantumStructures Minimeeting" (Prague. November 24-27, 1993). This "miniineeting" wasa preparation for the conference "Quantum Structures '91", of which we are membersof the organizing committee.

References:

[1] NAVARA, M. - ROGALEWIC'Z, V.: The pasting constructions for orthomodular pose.t- ;

s. Math. Nachr., 1991, 154, 157-168

(2] ROCiALEWlCZ. V.: Jauch-Piron logics with finiteness conditions. Int. J. Theor.Physics, 1991, 30, 437-44.r>

i[3] ROGALEW1CZ, V.: What does pasting manage in. OMPS? Int. J. Theor. Physics, I

1994, 33, to appear

[4] TKADLEC, J.: Partially additive measures and set representations of orthoposets. .). >Pure Appl. Algebra, 1993, 86, 79-94 j

[5] TKADLEC, .1.: Properties of Boolean orthoposets. Int. J. Theor. Physics, 1993, 32, to jappear 5

[6] TKADLEC, J.: Boolean orthoposets and two-valued Jauch-Piron states. Tatra Moun- 1tains Math. Publ., 1993, to appear f

[7] TKADLEC', J.: Boolean, orthoposets concreteness and orthocompletentss. Math. jBohemica. 1991, to appear |

This research has birn conducted at the. Department of Mathematics of the Faculty ofElectrical Engineering as a part of the research project "Noncommulativc probability theoryand its applications" and has been supported by CTU grant No. $132.

I

I40

•1

CTU SEMINAR 94 SECTION NAME

STATES ON VON NEUMANNALGEBRAS AND NON-COMMUTATIVE

MEASURE THEORYJ. Hamhalter


Key words: von Neumann algebras, states, homomorphisms

The theory of operator algebras was founded by J.von Neumann in 1929. Its origin wasmotivated by the development of functional analysis as well as quantum theory.

At the present time, the theory of von Neumann and C'-algebras represents a rapidlydeveloping discipline, whose applications range from the theory of representation of groups,spectral theory, non-commutative geometry and K-theory to quantum statistical mechanics,quantum field theory and axiomatic foundations of quantum physics.

Our recent research in this field is concentrated on properties of states (positive func-tionals) and homomorphisms defined on an operator algebra M and its projection latticeP(M). We summarize a few main results.

In papers [1,2,5,8,9] Jauch-Piron states on von Neumann and JBW-algebras are studied.(A state g of a JBW-algebra is called Jauch-Piron, if its null set is a sublattice in P(M).)Jauch-Piron states play an important role in the investigation of continuity of states andhomomorphisms of von Neumann algebras. Besides, they are relevant to the W— formalismof quantum theory as states having physical interpretation. A striking result in this contextis the fact that in many cases (pure slates, factor states) the Jauch-Piron property alreadyimplies a—additivity. Moreover, we succeeded in proving that any Jauch-Piron state on auniversally reversible JBW-algebra M extends to a Jauch-Piron state of its universal en-veloping von Neumann algebra W*(M). It allows us to use von Neumann algebra techniquesalso for the Jordan case. (Let us remark that the passage from von Neumann algebras toJordan algebras is far from being trivia] in this case.)

In paper [3] the traces on JBW-algebras are characterized as extensions of the subad-ditive states on projection lattices. (A state g of P(M) is called subadditive if g(p V q) <g(p) + Q(<]) for all projection p,q in M.) Since the trace plays the central role for determiningtypes of von Neumann algebras, the stated result has applications in structure theory.

Further we have investigated homomorphisms of von Neumann algebras. The mainresult [4] says that a homomorphism h between two von Neumann algebras M and JV isa lattice homomorphism (i.e. a lattice structure preserving mapping) if and only if k iscr—additive. (Algebraic properties of a homomorphfism are strong enough to impose thecontinuity property !) This surprising result completes previous known significant theoremsabout (7—additivity of homomorphisms. Coupled with the previous result of [7] it alsoconsiderably improves the classical Wigner theorem on automorphism of quantum systems[10]. It has been proved also that lattice homomorphisms are exactly homomorphismspreserving the set of all Jauch-Piron states. This result is relevant to the foundations ofquantum mechanics.

41

4

CTU SEMINAR <M SECTION NAME

Finally, our researrli has been focused on geometrical and extension properties of statespaces of operator algebras. The main result in this area is the theorem, that every state on :

a von Neumann algebra has its extension to an arbitrary larger orthomodular structure [6].This advocates the central position of the Hilbert space and operator algebras in quantumtheory. ;

References:

[lj BUNCEL.J.-J.HAMHALTER: Jauch-Piron states on von Neumann algebras, Math-ematische Zeitschrift, to appear. s

[2] BUNCE L.J. - HAMHALTER J.: Extensions of Jauch-Piron states on von Neumann |algebras, University of Reading, preprint. f

[3] BUNCE L.J. - HAMHALTER J.: Traces and subadditive measures on projections inJBW-algtbras and von Neumann algebras, Proceedings of the American MathematicalSociety, to appear.

[4] BUNCE L.J. - HAMHALTER. J. : On countably additive homom.orphisins betweennon Neumann algebras, in preparation.

[5] HAMHALTER J.: Pure Jauch-Piron states on von Neumann algebras, Ann. Inst.Henri Poincare, Vol. 58, No.2 (1993), 173-187.

[6] HAMHALTER J. : Gleason property and extensions of states on projection logics,Bulletin of the London Mathematical Society, to appear.

[7] HAMHALTER. J. : Additivity of vector Gleason measures, International Journal of jTheoretical Physics, Vol 31 (1992) 1-13. I

[8] HAMHALTER J.: States on projection logics of von Neumann algebras, International \Journal of Theoretical Physics, to appear. [

[9] PTAK P. : Jauch-Piron property (everywhere!) in the logico-algebraic foundations of jquantum mechanics, Int. J. of Theor. Phys, to appear. |

[10] WIGNER E.P.: Groups Theory and its Application to the Quantum mechanics of fAtomic Spectra, Academic Press Inc., New York (1995). ;

This research has been conducted at the Department of Mathematics as a part of theresearch project "von Neumann algebras and non-commutative measure theory" and has beensupported by CTU grant No. 8131. [

42

^ .,__


MATHEMATICAL METHODSOF QUANTUM THEORIES

P. Ptak


Key words: orthomodular structures, state space, noncompatibility relation, noncommu-tative probability theory

As first pointed out by Birkhoff and von Neumann (1936), it is the orthomodularlaw that plays the most essential role in the mathematical description of noncompatiblephenomena in quantum physics and elsewhere. This law usually replaces the distributivitylaw in the adequate mathematical model. For example, quantum mechanical experiments,measurement models, investigations in soft sciences (particularly in sociology) are oftenlinked with an orthomodular structure. This structure — a logic of the system in question— allows us to understand the behaviour of the events better and make predictions on thestates of the system in the future.

Mathematical questions studied in the theory of orthomodular structures generally re-flect the character of the area of where the potential solutions of the questions are likely to beapplied. The compatibility and noncompatibility problems lead to investigations of algebra-ic nature, the questions of interplaying physical systems lead to specific functional analyticproblems, the questions of state space representations are linked with measure theory andconvexity theory, stochastic questions usually find their interpretation in noncommutativemeasure theory, etc. The up-to-date theory of orthomodular structures overlaps with sev-eral fields of pure mathematics and ties them together. As an interdisciplinary theory, itcontains branches of pure mathematics as well as areas of applied mathematics and theoret-ical physics. Though having been over 70 years old, the orthomodular structure theory stillcontains significant open problems that may challenge both mathematicians and physicists.

In 1982, a group of mathematicians of the Department of Mathematics of the CzechTechnical University started intense investigation of orthomodular structures and associatedmathematical areas. So far they have succeeded in resolving a few significant problems.Recently, for instance, they have proved quite deep results which had remained unsolved

? for over ten years (see the references [1], [2], [8] and [9]). As regards the total research

5 production, they have published over 130 research papers (mostly in foreign journals) andp a monograph (Kluwer 1991). The high international standard of the group has also been)/;, confirmed by the appointment of P. Ptak, the scientific leader of the group, to the council ofM International Quantum Structures Association. Another member of this group, M. Navara,I' has become a member of the nominating committee of the latter association.| ; The research in the area of orthomodular structures is topical and has a promisingf\ perspective. Considerable research activity of the group (see a sample of recent publica-!r lions below) and undoubted mathematical expertise of its members guarantees a very good£ prospect for further research.

*. y 43

ft

CTU SEMINAR 9-1 MATHEMATICS

References:

[I] DE LUCIA, P. - PTAK, P.: Quantum probability spaces that are nearly classical, Bull.Polish Acad. Sci., Vol. 40 (1992), 163-173.

[2] FOULIS, D. - PTAK, P.: On tht tensor product of Boolean algebras and orthoalgebras,Czechoslovak Math. J. 1994, to appear.

[3] HAMHALTER, J.: Gkason property and extensions of states on projection logics, Bull.London Math. Soc, to appear.

[4] HAMHALTER, J. - PTAK, P.: Hilbert-space-valued states on quantum logics, Appli-cations Math., Vol. 37 (1992), 51-61.

[5] MAYET, R. - NAVARA, M. - ROGALEWICZ, V.: Constructions of orthomodularlattices with, strongly order-determining sets of states, to appear.

[6] MULLER, V. - PTAK. P. - TKADLEC, J.: Concrete quantum logics with coveringproperties, Int. J. Theor. Phys., Vol. 31 (1992), 843-854.

[7] NAVARA, M.: When is the integral on quantum probability spaces additive?, RealAnalysis Exchange, Vol. 14 (1989), 228-234.

[8] NAVARA, M.: There is a finite orthomodular lattice which does not admit any group-valued measure, Proc. Amer. Math. Soc, to appear.

[9] NAVARA, M.: Uniqueness of bounded observables, to appear.

[10] NAVARA, M. - PTAK, P.: Almost Boolean orthomodular posets, J. Pure Appl. Alge-bra, Vol. 60 (1989), 105-111.

[II] NAVARA, M. - PTAK, P. - ROGALEWICZ, V.: Enlargements of quantum logics,Pacific J. Math., Vol. 135 (1988), 361-369.

[12] PTAK, P. - PULMANNOVA, S.: Orthomodular Structures as Quantum Logics, KluwerAcademic Publishers, Dordrecht/Boston/London, 1991.

[13] ROGALEWICZ, V.: A remark on \-regular orthomodular lattices, Aplikace matem-atiky, Vol. 34 (1989), 449-452.

[14] TKADLEC, J.: Vector states on orthoposets and extremality, J. Math. Phys., Vol. 32(1991), 1117-1120.

[15] TKADLEC, J.: Boolean orthoposets and two-valued states on them, Reports Math.Phys., Vol. 31 (1992), 311-316.

This research has been conducted at the Department of Mathematics as a part of theresearch project "Orthomodular Structures as Quantum Logics" and has been supported byCTU grant No. 813S.

'I44


DISCRETE N-DIMENSIONALDYNAMICAL SYSTEMS

J. Gregor, E. Krajnik


Key words: discrete system, partial difference equation, convolution system

This contribution extends the work started in [1] and [2] where discrete systems de-scribed by the equation

[a,,3)x(a +ft) = y{a); a £ A (1)

{A, B are subsets of Z" and B is finite) have been analysed. An essential result describesnecessary and sufficient conditions for (1) to represent a convolution operator [3], [1]. When

S these conditons are met the sequence a, as a member of a convolution algebra, is invertible] there with an inverse h; the solution of (1) with zero initial conditions is then x = h* y.| New possibilities to compute the convolution inverse have been investigated. It turnsf out that the recently developed A'N)- transform is a suitable tool for this purpose [4], [5].

In the one-dimensional case, a finite-length approximation to the inverse is equivalent toinversion of a triangular Toeplitz matrix of order given by the length of the approximation.

' An extension of this result to dimension n = 2 is prepared for publication; approximationof a~l(fi) for /? € [0, m] x [0, m) can be achieved by inversion of a triangular, block-Toeplitz,

:' block-triangular matrix whose order is 2m x 2m and all blocks are T?I X m matrices.'.< The role of boundary conditions for the equation (1) have been studied and a general

system of boundary conditions has been formulated. If the solutions of (1) satisfy themaximum principle the uniqueness of the solution of interior boundary problems has beenproved. In several cases, the fundamental solution can be expressed by an Ar-dimensional

; integral. Using its asymptotic properties, the existence and uniqueness of the solution ofi, the corresponding exterior boundary problems have been proved.>! Previous results on singular systems have been extended in [6], The system (1) with

\B\ > 3 can equivalently be written as an equation with partial differences of order greaterthan one. Equivalence of such an equation with a system of first order equations has beeninvestigated and it has been shown that these 'canonical' first order systems are singular[6].

Studies on robustness of solutions yielded new results in characterization of convexcombinations of Hurwitz polynomials of one variable. It has been shown that both testingand constructive procedures for convex pairs of Hurwitz polynomials can be based on thezeroes of their even and odd parts. The concept of complementarity as a generalizationof the interlacing property of the set of zeroes of a polynomial originated new results for

45

I;


one-dimensional polynomials [7]. We hope that these results will prove useful in robustnessinvestigation of 2-D systems.

References:

[1] GREGOR, J.: Discrete n-dimensional dynamical systems, in Research Projects, CTU,Prague 1992, pp. 15-16.

[2] GREGOR, J., - VEIT, J: Discrete n-dimensional dynamical systems, in Workshop 93,CTU, Prague 1993. pp. 13-14.

[3] GREGOR, J.: Convolutionnl solutions of partial difference equations, Math. ControlSignal Systems. 4(1991), pp. 205-215.

[4] TARASOV, R. P.: A'"' -transform and digital signal processing algorithms in the algebraof formal polynomials, (in Russian), Zhurnal Vychislitel'noi Matematiki i Matema-tichcskoi Fiziki. vol. 31, pp. 505-521, 1991.

[5] KRAJNIK, E.: A'*' -transform: a new tool for homomorphic signal processing, in Cir-cuit Theory and Design - Proc. ECCTD'93, Elsvier, Amsterdam 1993, pp. 341-346.

[6] GREGOR, J.: On implicit linear N-D systems, Invited paper in Proc. IEEE Mediter.Symp. on New Directions in Control Theory and Applications, Tech. Univ. of Crete,1993.

[7] GREGOR, J.: On convex hulls of polynomials, in Circuit Theory and Design - Proc.ECCTD'93, Elsvier, Amsterdam 1993, pp. 1667-1670.

This research has been conducted at the Department of Mathematics as a part of theresearch project Discrete Dynamical Systems with Several Independent Variables and has-been supported by CTU grant. No. 8035.

K. • '• 4 6

1


THE PERIODICAL SOLUTIONSOF THE NAVIER-STOKES EQUATIONS

P. Kucera, Z. Skalak*

CTU, Fac. of Civil Eng., Dept. of MathematicsThakurova 7, 166 29 Praha 6*Institut of Hydrodynamics,

The Academy of Science of the Czech republic

In this contribution we prove one existence theorem for the system of the Navier-Stokesequations and the continuity equation. This study was inspired by the pulsatile flow ofa Newtonian fluid through the corrugated tube. Firstly we give the precise mathematicalformulation of the problem. Let us define

G= {x = (xi,x2,x3) €R3,X! €R,x22 + xl

where h is a L-periodical and positive function. We suppose the boundary dG of G to besufficiently smooth and

T, = { i =

Classical formulation:

' , We can write

.; dn = r, u r2 u r3.We solve the following system of equations

fs - j/Aa + «Vu + iVp = / inO®[0,r],\ divu = 0 in fi ® [0,7'],: «|r, =«|r2 ,p «|r, =0 ,| u(0) =u(T).

ig where u stands for velocity, p stands for pressure, p is density, v is viscosity, / stands for% volume force and [0, T] is a time interval.

t£ Weak formulation:

Definition 1. Let

n v = {<t> e [c°°(Si)}3,div<t> = o,supp(j>nr3 = 0}.• -it

*-•• 47

k

i.

I'


V, resp. H are defined as closures ofV in the norm of space [H''ll2(n)]3, resp. \L2(Sl)]3 and

Vff = {w G V; there existsg € H : ((w, v)) = (g, v)},

where

= / g, •Jn

Theorem 1. Let f € L2(0, T, H) and ||/||f,2(o,T.W) ê sufficiently small. Then there existsu € I2(0, T, Vk), u' e L2(0. T, / / ) so '

(u'. v) + f((«, i')) + b(u,u, v) = (/,u) for every')' € V,

«(0) = M ( 7 " ) .

References:

[1] TEMAM, R.: Navier-Stokes Equations North-Holland Publishing Company, Amstero-dam New York Oxford, 1979 ;

[2] FIJCIK, S. - MILOTA, J.: Matematickd analyza II. Statni' pcdagogicke nakladatelstvi,Praha 1978 |

This research has been conducted at the Department of Mathematics of the Faculty of &Civil Engineering as a part of the research project "Mathematical Methods in EngineeringProblems" and has been supported by CTU grant No. 8011.


PROBLEMS OF IMPLEMENTATIONOF SPECTRAL ELEMENT METHODS

M. Pultar

CTU, Fac. of Civil Eng., Dept. of MathematicsThakurova 7, 166 29 Praha 6

Key words: spectra! methods, finite element method

This work deals with problems of numerical solution of partial differential equations byspectral element method. The basis ideas behind spectral methods were presented aboutten years ago. The development of methods of such a type was motivated by the need forbetter accuracy in numerical simulation. The traditional monodomain approach of spectralmethods in combination with the technique of domain decomposition later gave a veryeffective method with a high order of convergence. In this context, the spectral methodsover a partioned domain are very similar to the h-p version of the finite element method.Both above mentioned methods are based on similar principles - the use of variationalprinciples combined with the use of polynomials of a higher degree. In recent years, thetechniques of using of a nonconforming mesh were developed and greatly extented the fieldof use of these methods, especially in complicated geometries.

In our work we have dealt with the so called "mortar" element method which is onepossible approach to the implementation of a nonconforming mesh. This method was ini-tially used for the solution of problems of the second order, is now used for the solution offourth and higher order problems and for the case of a sliding mesh [1]. This method is,as are all methods based on domain decomposition, very appropriate for implementationon parallel computers [2], [3] and the development of these methods is influenced by thedevelopment of computers of this type.

Recently, the method of the nonconforming mesh has been used, also, for the solution ofaxisymmetrical problems of flow. This problem is very close to the problem of examinationof the state of stress and deformation of the blood vessel walls and their replacement,especially in determination of the corresponding strain and the "blood vessel-replacement"contact. This problem was solved in collaboration with the Institute of Hydromechanics ofCSAV [4] and it would be very interesting to solve complex problems of this type.

Pi References:

i¥,i [1] PULTAR M.: Solution of partial differential equations by high order methods. Proc. of| the Sem. Applied Mathematics, Praha 1992§ [2] FISHER P.F. - PATERA A.T.: Parallel spectral dement solution of the Stokes problem.

J. Comp. Physics 92(1991), 380-421

[3] BEN BELGACEM F. - MADAY I.: A spectral element methodology tuned to parallelimplementation. Research Report Univ. Paris VI, 1993

49

CTl? SEMINAR 94 MATHEMATICS

[4] NOVOTNY R. PULTAR M.: A contribution to blood vessel simulation and replace-ment by elastic cylindrical shelles - some numerical resulte.s. Proc. of the Con I". FluidMechanics and Hydrodynamical Aspects of Biosphere, Liblice 1993

This research has been conducted at the Department of Mathematics of the Faculty ofCivil Engineering as a part of the research project "Mathematical Methods in EngineeringProblems" and has been supported by CTU grant No. SOU.

50


ON A THEORETICALENGINEERING PROBLEM

WITH AN INTEGRAL CONDITIONK. Rektorys, I. Zahradka

CTU, Fac. of Civil Eng., Dept. of MathematicsThakurova 7, 166 29 Praha 6

Key words: evolution equations, discretization in time, the Rothe method

Many years ago. the so-called problem of hydratational heat in a water dam was solved.My task was, at that time, to find the heat-distribution in the dam, governed by

where (he function g(t.) characterized the intensity of innner sources of heat. The problemwas relatively complicated: the time-space domain in which the equation was consideredchanged discontinuoiisly with time and, in addition, boundary conditions were discontin-uous and of different types on different parts of the boundary. The problem was solved,successfully by the method of finite differences.

However, it is well-known that, in practice, the function g is dependent not only onthe time but also on the temperature u to be found and on the quantity r of heat alreadydeveloped. This situation can be described by the equation

with an intergral condition

r(x,t)= I g(x,r, M(.T, r),r(.r, r))dT,Jo

v

I where x — [TJ, . . . , xn] (in dependence on the space dimension).a, This problem is rather complicated. My postgraduate student Dr. Ivan Zahradka solvedip it with success by the so-called method of discretization in time.!>• The aim of his work was, first of all, to present an existence and uniqueness theoremI for the weak, or very weak solution of problem (1), (2) (on a relatively very general domain,p with nonhomogeneous and discontinuous initial and boundary conditions). The essential*'. idea of the proof was the contruction of a sequence of the so-called Rothe approximations.I'; These approximations were shown to be uniformely bounded in the Hilbert space of abstract| functions /.^([O, T); W.^ ($2)), so that a subsequence could be found, weakly convergent to a

'• f, function u € ^([0,7']; W'2(l)(fl)). This function was then shown to bo the desired very weak

».t 51


solution of the problem. Uniqueness then yielded convergence of the whole sequence. TheRothe approximations were numerical approximations of the solution.

References:

[1] REKTORYS, K.: Solution of a problem of hydratational heat in a water dam. Proc. ofthe Czechoslovak Academy of Sciences, Praha 1956, pp. 1-73. (In Czech.)

[2] ZAHRADKA, I.: Solution of heat conduction in concrete massifs. Applications ofMathematics, Praha, to appear in 1994.

This research has been conducted at the Department of Mathematics of the Faculty ofCivil Engineering as a part of the research project "Mathematical Methods in EngineeringProblems" and has been supported by CTU grant No. 8011.

52

Section 2

NUCLEAR ENGINEERING

' l

CT(! SEMINAR 94 NUCLEAR ENGINEERING

I

A COMPUTER PROGRAMFOR STEAM GENERATOR PGV-1000THERMAL-HYDRAULIC ANALYSIS

O. Ubra, M. Doubek, Z. Zuna

CTU, Fac. of Mechanical Eng., Dept. of Thermal & Nuclear Power PlantsTechnicka 4, 166 07 Praha 6

Key words: multidimensional thermal-hydraulics, flow distribution, void fraction

A mathematical model is presented which enables steady state thermal-hydraulic anal-ysis of the horizontal steam generator PGV-1000. The model provides the capability tocalculate primary side flow distribution and pressure losses, heat transfer and some multi-dimensional thermal-hydraulic phenomena in the steam generator secondary system.For the mathematical simulation the steam generator is divided into three main regions:l.The area between the bottom of steam generator and upper tubes of the heat exchanger.This region is subdivided in horizontal and vertical direction as it is shown in Fig. 1,2.2.The region between the upper part of heat exchanger tubes and steam generator level.3.The steam region between steam generator level and outlet of the steam colector.

Fig. 1: Fig. 2

For the calculation of primary side flow distribution the heat exchanger is divided intogroups of tubes as it is shown in Fig.2 and the average flow velocity is evaluated for eachgroup. The outputs of the calculation are the velocity distribution in the header and theflow velocities in the tubes. Model representation of the primary side pressure losses takesinto account pressure losses in the inlet and outlet tubes, in both collectors and in heatexchanger tubes.The nodalization of heat exchanger tube bundles for steady state thermal calculation cor-responds to Fig. 1,2. The iterative method of calculation is based on thermal balance. The

55

CTU PRAGUE WORKSHOP 94 - SECTION NAME

calculation is performed for every node separately and a global balance is checked. Themain result, of this calculation is heat flux distribution in the steam generator shell side.This is dominant for the thermal hydraulic calculation of the secondary side. The globalheat flux is essential parameter for the assessment of secondary side pressure and steamoutput.A computer program for steady state thermal-hydraulic analysis of t he steam generator sec-ondary side provides the capability to determine average circulation rate in the first region,void fraction distribution, mass redistribution in the area between upper part of the tubebundles and submerged perforated sheet and steam generator level profile.To determine of the circulation rate average value a simple flow diagram is assumed. Two-flow mixture rises up through the area in tube bundles and above bundles steam and waterare separated and water flows back in the downcomer and in the opening between tube bun-dles. The average value of circulation rate is determined by the iteration method proceedingfrom pressure balance in upward and in downward sections.For the assessment of void fraction distribution the region between steam generator bottomand upper rows of heat exchanger is divided in vertical direction into 29 layers of equalheight 50 mm. The layers are subdivided into elementary volumes. The heat flux intoarbitrary volume is obtained from heat exchanger calculation. The feed water distributionis taken into account. The calculation of void fraction begins in the bottom of the steamgenerator and proceeds step by step over the layers to the top of the region. The appliedmethod is based on the theory of industrial steam boilers with natural circulation [1].Hydrodynamic processes in the region between upper rows of tube bundles and submergedperforated sheet depend on perforated sheet design, especially on the perforation degree andon the height of perforated sheet rim [2]. The aim of simulation is to assess steam overflow-ing from more loaded zone into less one and to determine steam layer thickness in differentlocation bellow perforated sheet. For determination of the local value of steam generatorlevel height and for assessment of the steam generator level profile the steam-water mixturezone above the perforated sheet should be analyzed.The complete mathematical model for steam generator PGV 1000 thermal-hydraulic study-is formulated in [3]. Results of steady-state calculations for different input data correspond-ing to the reactor power range 0 - 107give quite reasonable data and program operatingexperience are good. Some results of the model were compared with experimental datapublished by Gidropress. For more complete verification the measurement on experimentalfacility and on real power plant in the Czech Republic is planned.

References:

[1] LOKSHIN, V. A. PETERSON, D. F. - SVARC, A. L.: Gidrauliceskij Rascot Kotei-nych Agregatov Energia,Moskva, 1978

[2] STERMAN, L. S. STJUSHIN, N. G. - KUTHEPOV. A. M.: Gidrodimmika i Teploob-men pri Paroobruzovann Vyssaja Skola,Moskva,1978

[3] DOUBEK, M. UBRA, O. ZUNA, Z.: Steam Generator PGV-1000 Research ReportZ-490.CTU,Pral'.a,HW3

This research has been conducted at the Department of Thermal and Nuclear PowerPlants as a part of the research project "Thermal-hydraulic Analysis of the Two-phase. Flowin the SG Secondary Side" and has been supported by CTU grant No. 8123.

'- 56ft

CTU SEMINAR 94 NUCLEAR ENGINEERING

TEXTBOOKS FOR TRAININGAND EXAMINING THE STAFF

OF RESEARCH NUCLEAR REACTORSJ. Zeman, K. Matejka, J. Fleischhans

CTU, Fac. of Nucl. Sci. & Phys. Eng., Dept. of Nuclear ReactorsV Holesovickach 2, 180 00 P rah a 8

Key words: examination, database, nuclear safety, safety culture

There is a specially trained staff needed to operate the nuclear facilities (including ex-perimental and research reactors). Special examination by the State supervising commissionfor nuclear safety is required. After successful pass in this exam SUJB issues the licensefor highly qualified workers as a reactor operator, an operator-in-chief, a check-up physicist,etc.

With increasing general requirements on security and reliability of nuclear devices sim-ilar regulations for research reactors were raised. One of suitable possibilities is improvingthe quality of the staff training control).

Since 1990 the KJR FJFI operates one of three experimental reactors in the CzechRepublic and studies problems connected with the operators training. In cooperation withSUJB the Department prepared a set of textbooks and tests for education and testing ofthe nuclear reactor staff.

The aim of these texts was a unification of the content and the demands required bydifferent experimental reactor bases. The basic knowledge should be enlarged especiallyin the fields of reactor physics, technique and ensuring the nuclear reactor safety. As toexaminations, the set of testing questions for individual devices and individual positionsshould make these tests more objective and emphasize individual specific positions.

The theoretical level and requirements of these texts are aiming at not only graduatedworkers but also on capable high school graduates.

For nuclear devices control the essential knowledge of nuclear and neutron physics andtheory of nuclear reactors is required. This theoretically the most difficult part was preparedon the basis of pedagogical experience of the department, and practical requirements of thereactor staff. A special treatment was given to safety analysis.

> For the first time in the Czech Republic the educational course on training VR-1 reactorI was included in the preparation of the nuclear reactor staff. This course should be passed• not only by the beginners in the staff but also by those tested for the license prolongation.f. The content of the course aims at the practical knowledge of the basic physics and its•| interpretation in different operational conditions and situations. That is why the courseI' consists of individual lectures, developed and tested at the VR-1 reactor.C, To improve general knowledge of the staff a special overview of the different types offe nuclear experimental reactors, fuels, control systems, equipment, etc. is included.& Those parts connected with the safety and operation of experimental nuclear reactorsf. are based on our legislative intimations and are developed into practical applications. The| role of the State supervising commission for nuclear safety is emphasized. The comparison of

I 57

1


the operation organization at different reactors provides better overview and deeper generalknowledge.

The examinations of selected workers are made by both theoretical and practical tests.Consist of the theoretical one is divided into written and oral parts. Both of them aresupplied by special set of questions for all staff categories. These questions are stored in acomputer database, and a special program randomly selects questions for the test. This setcovers the whole area of required knowledge and is organized so as to provide the generalcomplete overview of the knowledge in the written part and deeper requirements in selectedproblems in the oral part.

The textbooks and question files are divided into six relatively independent parts. Oneof them, written in three volumes, consists of technical description of all three experimentalreactors in the Czech Republic.

This work is of pedagogical-scientific character and its results will be an importantcontribution to the higher level of selected workers knowledge and to nuclear safety culture.

This research has been conducted at the Department of Nuclear Reactors

58


PROGRAM DYNAMIKA FOR THEREACTOR KINETIC CALCULATIONS

S. Krops

CTU, Fac. of Nucl. Sci. k Phys. Eng., Dept. of Nuclear ReactorsV Holesovickach 2, 180 00 Praha 8

Key words: nuclear reactor, kinetic, calculation, computer program

Mastering reactor dynamics is very important for all operators of the nuclear reactor.It's essential for for reaching the high level of the nuclear safety.

Nuclear reactor working on low power an is unstable and strongly non-linear system.Its dynamics is not affected by any feedback. When the reactor active core is small, an onepoint kinetics model can be used to describe the reactor behavior.

This model consist of a system of seven differential equations which can be solved onlyin some special cases of reactivity changes. When the reactivity is a complicated functionof the time, (lie only possibility to find solution to this system of equations is to use someof the numerical methods.

The "prompt jump" approximation is used in the computer program DYNAMIKA tofind solution to one point kinetics equations. It allows to solve many different zero power

• reactor dynamics problems. The limitation of this approximation is that the model is valid; only for reactivity smaller then \fl and the reactivity should be even smaller than 0.5,3 to) obtain a small error of the result.5 Program DYNAMIKA runs at the PC-AT compatible computers. It is written in the

language TURBO PASCAL 6.0. This program is written in "user friendly" form and it iseasy to model behavior of the reactor for different reactivity changes. The advantage of thisprogram is that it is possible to simulate experiments before they are applied to the realreactor and tc find the best parameters of experiment quickly.

The calculated values are usually in a good correspondence with the results of experi-ments.


I4

I*•• 5 9

'ft

Ikis

CTV SEMINAR 94 NUCLEAR ENGINEERING

AN EXAMPLEOF THE LABORATORY EXERCISE

ON THE FNSPE VR-1 REACTORJ. Fleischhans


Key words: training reactor, reactor dynamics, laboratory exercises

More than 25 laboratory exercises were prepared for students by the Department ofNuclear Reactors FNSPE staff. Most of them were presented in a special textbook lastyear.

In this paper we shall demonstrate one of the typical works, the STUDY OF THEREACTOR DYNAMICS. This work consists of the three separate measurements:

• asymptotic period measurements,

• reactor power response to the periodical stepwise input reactivity oscillations,

• reactor power response to the pile-shape input reactivity oscillations.

A theoretical reactor power response is calculated before the measurement is started.The computer program for these calculations is mentioned in the previous paper. After asafety analysis, a short program for the control rod movement is loaded into the controlsystem computer and started. The reactor power is then recorded on the multiscaller andthe obtained result is compared with the theoretical curve. A very good agreement betweenthe theoretical and experimental curves is usually reached.

61


18000 -

16000-1

^ HOOO-I

v>W 12000 -.

a. IOOOO-i

8000

6000 -.

V

200 400

TIME (s)600

ig. 1: Typical reactor power response to the periodical input reactivity oscillations

References:

[1] KROPS, S.: Program DYNAMIKA for the reactor kinetic calculations CTU, FNSPE,Dept. of Nuclear Reactors, Prague, 1993


« • • ' 62


SOFTWARE FOR NUCLEAR SAFETYCRITICAL APPLICATIONS

K. Matejka, J. Fleischhans, M. Kropik, T. Sejba

CTU. Fac. of Nucl. Sci. & Phys. Eng., Dept. of Nuclear ReactorsV Holesovickach 2, 180 00 Praha 8

Key words: training reactor, digital control, nuclear safety, software requirements, softwaredevelopment, software verification

The department of Nuclear Reactors of the FNSPE began research work on the inno-vation of the microprocessor based control and safety system ol the school nuclear reactorVIM SPARROW at the end of 1991. This article deals with development of the safety crit-ical software for this control and safety system. This safety critical software was developedaccording to the IAEA recommendations and IEC-880 [1] requirements.

In the first place, safety critical parts of the computer control system were determined.Measuring and safety channels of the advanced nuclear reactor control system [2] werefound as safety critical in the requirements of safety system. During the establishment ofthe project [3], it was necessary to consider the whole software life cycle. The softwareproject was divided into a number of phases. Each phase is to some extent self-contained,

| but will depend on other phases. For safety critical applications, these phases are formalized\ and none of the identified phases shall be. omitted. Each phase is terminated by a criticalj review and is followed by verification of t,his phase according to a quality assurance plan.j The quality assurance plan contains all quality assurance procedures required during the

whole software life cycle.The next phase of software development was to create software requirements. The

software requirements were derived from the requirements of safety system and are partof a computer system specification. The computer system specification is a description ofthe combined hardware/software system and states objectives and functions assigned tothe computer system. The software requirements describe the product, not the project.They describe what has to be done, and not how it has to be done. After the softwarerequirements were set, thorough verification followed.

The software requirements specification was followed by design of software. Programs: structure was based on a decomposition into modules, simple and easy to understand. In the

software design phase algorithm of the control and data flow, and requirements for accuracy,f; of the calculations and exceptions behavior were established. Procedures, data structures|v and communication used in the program were defined. Requirements for critical timing of£• procedures were also given.S Programming languages and development tools were also selected in this phase. Asf|; the main programming language was used 'C , for small, time critical parts, assembler. Ac-§: cording to the diversification of the safety critical hardware (different microprocessor in theijf: computers) [2], different software development tools were selected. For measuring channelIj' computer with the microprocessor NEC V25 it was compiler, linker, and debugger Borland

C++ 3.1 and ROMable locator Paradigm Locate, for safety channel computer with the mi-croprocessor Z280 it was C-compiler, assembler and linker Softools. The verification of thisphase checked if the design of the software is in accordance with the software requirements.

63

CTU SEMINAR 9-4 NUCLEAR ENGINEERING

Code flow of the program for measuring channel is described now as an example. Afterinitialization, the program decodes data, if there are any, from the communication channel.Then it checks the given status and executes either measuring of the neutron flux or testingitself. In the measuring part the program enables or disables generating of the safety signalto control safety circuits. Then it sends gained data about neutron flux and period tothe communication channel. If any exception occurs, the generating of the safety signal isstopped and the program goes to the main loop, disabling safety signal generation. Twointerrupters are used. The first one to get input data from frequency counters (neutron fluxmeasurement), the second one to control serial data communication with the communicationchannels.

Finally, coding of the program was made. It was important to ensure good readability ofthe source text, to give good comments, to fulfil demands of the software design specificationand to avoid tricks and recursive structures. After coding the program was verified bythe inspection of the source code. The inspection checked that all functions specified insoftware design were implemented, definition and initialization of data is correct, commentsare sufficient, etc. This inspection, according to IEC-SSO, should be supported by automatictools, but these tools were not available. Another important step in the coding verificationwas procedure testing. The purpose of procedure testing was to show that each procedureperforms intended function and does not perform unintended functions. Critical timing wasalso checked.

Hardware/software integration as the combination of verified hardware and softwaremodules into a system that is capable of performing specified functions is the next step tobe taken. Hardware/software integration will be also verified. Then the final task will bevalidation of the advanced nuclear reactor control system to ensure compliance with thefunctional and performance requirements. The mentioned tasks are planned for the year1994.

References:

[1] IEC-880 Software for Computers in the Safety Systems of Nuclear Power Plants. CEIGeneve, 1986.

[2] KROPIK, M.: ANRCS. FNSPE, 1991.

[3] SEJBA, T.: Software Project of ANRCS. FNSPE, 1993.

This research ha.* been conducted at the Department of Nuclear Reactors FNSPE as apart of the research project "Advanced Control and Safety System of the Nuclear Reactor"and has not been supported by any CTU grant.

st,% I1 I

I i

C H ! SEMINAR 04 Nl'CLEAR ENGINEERING

PIXE ANALYSIS - EQUIPMENTAND TECHNIQUES

J. Krai, J. Voltr, V. Potocek, R. Salomonovic

( T l ; . Fac. of Nnrl. Sci. & Phys. Eng., Dept. of Physical ElectronicsV Holesovickach 2, 180 00 Praha 8

Key words: ion brain equipment, ion beam analysis, PIXE

An equipment for PIXE analysis has been developed as a part of an ion beam analyticalequipment with energetic light ions from 2.5 MV Van de Graaff accelerator of Nuclear Centreof Charles University. The equipment- has been equipped with a large target chamber withtwenty position carousal sample holder. The x-rays emitted from the proton bombardedsample are deter toil by a Si (Li) detector and analysed with a multichannel analyser. Theanalysis may be performed both in high vacuum and in a gas atmosphere with pressureup to the ambient one. When operated with external beam, extracted from high vacuumto atmosphere through a thin Kapton foil, the vacuum in the accelerator is preserved by aprotective system [I], Analyses of insulating samples are performed usually in nitrogen ofslightly enhanced pressure (cca 15 Pa), to suppress charging the samples. Current, densityprofile is measured during the analysis by two perpendicular wire probes, crossing the beamin front of the target chamber [2]. Routinely, analyses of thin broad homogeneous samplesof aerosols collected on thin membrane filters are performed. Samples both from our ownsamplers and from cooperating laboratories have been analysed. A study of two differenttypes of used filters and an observation of temporal development of aerosol's element com-positiijn during a day are described in another contribution [3]. One possible form of asample is dry residue of liquid solution drop of a material studied after its evaporation on asupporting foil. In such a way samples of various materials may be prapared, including bothbiological and geological ones. Samples of such a kind have also been analysed. Namely, dryresidues of reference water solutions of metals on thin (1.5 m) Mylar foil have been used forcalibration of the equipment. At the same time several absorbers in front of detector weretested as for their influence on the spectrum detected. Attention has also been paid to theinaesurement of thick samples and to their quantitative analysis. Special thick targets withsample of liquid fixed on a. gel substrate has been studied. External ion beam of verticaldirection on the target offers the unique possibility of liquid sample analysis. Some testswith liquid samples analysed with external beam in air have been done. However, ratherhigh stopping power of air makes proton energy on target surface too low and spectrumbackground contains strong peak of argon. Then, to prepare more convenient conditions forliquid sample analysis with external beam, a special arrangement for analysing in heliumatmosphere has been prepared. It presents a cell rinsed out with helium flow.

! , References:

ff. .y>' [1] KRAI,, J. - VOLTR, .J.: Ion beam equipment modification for external beam operationA to be published in Nucl. Instr. and Meth., Sec. 13, 1994i., [2] 'VOLTR, J.: Ion beam profile measurement presented in this workshop'£•r 65

• "<---{• j-»r»

CTC SEMINAR 91 NUCLEAR ENGINEERING

[3] POTOCEK, V. KRAL, J. - VOLTR: Elements concentrations in Prague aerosol asmeasured by PIKE, presented in this workshop

This research has been conducted at the Department of Physical Electronics, Faculty ofNuclear Science ami Physical Encgineering as a part of research project "Development ofPIXE analysis methodology'' and has been supported by CTU grant No. 8058. The study ofsamples fixed on a gel substrate has been performed in the frame of a contract with AKDARB- PR A HA s.r.o.

• I<h

K ^ 66

» * . • : : • "

C'TU SEMINAR 94 NUCLEAR ENGINEERING

DEVELOPMENT AND TESTINGOF COMPOSITE ION-EXCHANGERS

F. Sebesta, J. John, A. Motl, J. Steinerova

C'TU, Fac. of Nucl. Sci. & Phys. Eng., Dept. of Nuclear ChemistryBfehova7, 115 19 Praha 1

Key words: composite ion-exchangers, inorganic ion-exchangers, radioactive wastetreatment

Characteristics of composite ion-exchangers composed of powdered inorganic ion-ex-changer (active component) and binding polymer (polyacrylonitrile - PAN) have been givenearlier [1.2]. The list of composite ion-exchangers then prepared contained some 10 types ofabsorbers differing by their active components [2]. The results of studies of properties andpossible applications of composite ion-exchangers developed have been presented in earlierpapers [1-3]. This contribution summarizes the results obtained in 1993.

New types of composite ion-exchangers have been prepared following the procedure de-veloped earlier. These exchangers contain zirconium phosphate (ZrP-PAN), titanium phos-phate (TiP-PAN), zirconium oxide (ZrO-PAN), polyantimonic acid (CSbA-PAN), tin(IV)autimonatt- (SnSbA-PAN), titanium antimonate (TiSbA-PAN) or a mixture of nickel he-xacyaiioferrate and manganese dioxide (NM-PAN), or zirconium oxide and zirconium phos-phate (ZrOP- PAN). These new absorbers have been prepared for testing not only in ourlaboratory. Their possible use for treatment of selected types of liquid radioactive wastewill be tested in the framework of activities of "Novel Absorber Evaluation Club" (AEATechnology, U.K.). In Los Alamos National Laboratory (University of California, U.S.A.)the new absorbers will be tested as a part of the project "Tank Waste Remediation System(TVVRS)" in Hanford area.

The main activities were dedicated to the study and further applications of compo-site ion-exchangers developed earlier. Development and testing of prototype radionuclidegenerator l3 'Cs - 13""Ba were completed. The generator contained ~ 355 MBq (9.6 mCi)of lr)'Cs sorbed on NiFC-PAN composite ion-exchanger. The parameters achieved enableapplication of the generator in several industrial processes (measurement and regulation offlow-rate, monitoring the process of mixing of liquids, etc.). High radiochemical purity ofi3imga generat,eil (D/ > 10') makes this generator prospective even for contingent medical

•: applications.• The most prospective composite ion-exchanger NiFC-PAN was applied to pilot-plant•\i, scale removal of 1 1 7Cs from waste water ( ~ 50 m 3 ) from migrat ion expe r imen t s performed;. in model deep underground rock Grimsel Test Site laboratory. T rea tmen t of waste water% was performed in col laborat ion with N A G R A (Swiss National Coopera t ive for t h e S to rage| of Radioact ive Was te ) . T h e results of removal of 1 3 7Cs ( D / = 200 1000 for t r e a t m e n t of)J' more t han 10.000 B V of waste water ) again proved the advantages of applying th is compos i t eIp ion-exchanger for t r ea tmen t of radioactive waste water.if Industr ia l appl icat ion of N i F C - P A N composi te ion-exchanger has been proposed [4] in:: an upda t ed proposal for lowering the activity of water from the long t e rm s torage pool a t| N P P A- l (Slovak Republic) . Six o ther (all of t h e m foreign) companies took pa r t in t h e

67


tender. Two out of three proposals selected for more detailed evaluation are based on theapplication of NiFC-PAN composite ion-exchanger.

Four composite ion-exchangers were tested for separation of radium and thorium fromdistilled water and saline solutions as a part of Sudbury Neutrino Observatory project. Thisstudy was conducted in collaboration with University of Oxford (U.K.) [5].

On the basis of Memorandum of Understanding between Los Alamos National Labora-tory (U.S.A.) and CTU Prague, Department of Nuclear Chemistry, nine samples of compo-site ion-exchangers were prepared and submitted for a screening study of the separation of14 elements from simulated solutions for Hanford HLW Tank 102-SY. The results achievedare promising [6] and indicate the possibility of industrial application. Good results are cur-rently being achieved in tests of another five composite ion-exchangers in Novel AbsorberEvaluation Club. An indication of the quality of these results may be the discussion of pos-sible applications of some types of composite ion-exchangers in the framework of activitiesof AEA Technology (U.K.).

References:

[1] SEBESTA, F. - MOTL, A. - JOHN, J.: Composite. Ion-Eichangers, their Developmentand Use Workshop '92, Part B, Sect. 1, pp. 25 - 26, CTU Prague, 1992

[2] SEBESTA, F. - MOTL, A. - JOHN, J. et al.: Composite I on-Exchangers and theirPossible Use in Treatment of Low/Intermediate Level Liquid Radioactive Wastes In:Proc. 1993 Int. Conf. Nucl. Wastes Management and Environmental Remediation,September 5-11, 1993, Prague; Vol. 3, pp. 871 - 878, ASME, New York, 1993

[3] SEBESTA, F. - JOHN, J. - MOTL, A. - STEINEROVA, J.: Development and Testingof Composite Ion-Exchangers Workshop '93, Part C, Sect. 12, pp. 75 - 76, CTU Prague,1993

[4] SEBESTA, F. - PETR, J. - HLADKY, E. - BRZOBOHATY, J.: Proposal to a Tenderfor Technology of Lowering the Activity of Water from the Long Term Storage Poolat NPP A-l Faculty of Nuclear Sciences and Physical Engineering, CTU Prague, July1993, 32 pp. (in Czech)

[5] SEBESTA, F. - JOHN, J. - MOTL, A.: Preparation and Characterization of Samplesof Composite Absorbers for the Sudbury Neutrino Observatory, Research Report forthe University of Oxford, Nuclear Physics Laboratory Faculty of Nuclear Sciences andPhysical Engineering, CTU Prague, June 1993, 60 pp.

[6] MARSH, S. F. - SVITRA, Z. V. - BOWEN, S. M.: Distribution of H Elements on60 Selected Absorbers from Two Simulant Solutions for Hanford HLW Tank 102-SY

i LA-12654, Los Alamos National Laboratory, October 1993, 96 pp.

j;,; This research has been conducted at the Department of Nuclear Chemistry as a part ofjj;. the research project "Development and Testing of Composite Ion-Exchangers" and has beenI supported by CTU grant No. 8109.

68

CTU SEMINAR 9-1 NUCLEAR. ENGINEERING

RADIATION INFLUENCINGOF CATALYTIC ACTIVITY

AND REACTIVITYOF TWO-COMPONENT MIXED OXIDES

V. Miicka, M. Pospisil, R. Silber

CTU, Far. of Nuci. Sci. k Piiys. Eiig., Dept. of Nuclear ChemistryBfehova 7, 115 19 Praha 1

Key words: catalytic activity, hydrogen reduction, ionizing radiation

This paper describes some results of systematic research of mixed oxide catalysts. Itis aimed at the study of influence of genesis and ionizing radiation on the catalytic activityand chemical reactivity'of selected two-component oxide systems based on nickel oxide. Forthis piirpose, two series were prepared of NiO-ZnO mixed catalysts differing in their originand NiO-FÔ.-j mixed oxides. With all these series of various composition in the range0-100 wt.%, the basic physico-chemical properties were investigated. The catalytic activitywas studied with both NiO-ZnO mixed systems using as a test reaction the decompositionof aqueous solution of hydrogen peroxide (1.2 mol/1), whereas with the third series the effortwas concentrated on the study of chemical reactivity during the reduction with hydrogen.

The NiO-ZnO mixed catalysts were prepared by calcination of mixtures of basic nickelcarbonate and zinc nitrate (N-samples), and of mixtures of basic zinc carbonate and nickelnitrate (series Z). The precipitated carbonates in required volume of the nitrate solutionswere evaporated, dried, pulverized, and calcinated in air for 3 h at 470°C. The catalyticactivity of all samples was mesured at different temperatures from 25 to 40°C before andafter their irradiation with gamma-rays of 60Co (doses of 328 kGy or 3.7 MGy) or withaccelerated electrons (4 MeV) using a dose of 588 kGy.

According to structure analysis, the N-samples consist of a solid solution containingabout 30 wt.% of ZnO in the structures of NiO, whilst in the Z-samples the concentration ofthe ZnO in the solid solution decreases after reaching a maximum value at 35 wt.% of ZnO.The different non-monotonic and non-linear dependences of the composition of both N- andZ-samples give evidence that the mutual influence of the catalyst components seems to begoverned significantly by the character of the mixture of precursors used for preparation of

y. the catalysts. A great difference between the two series was also observed in their specific,"•' catalytic activities. The highest values of this parameter was found at 8 and 50 wt.% of ZnO;"j in the case of Z-samples, whereas a maximum catalytic activity of the N-samples was foundi: only in the central range of their composition. Furthermore, the activity of the N-samples|' decreases after their irradiation with the lower doses of gamma or electron radiation. This> difference gives evidence that the nature of precursors used and the conditions of preparationjj^ are extremely important also for the radiation sensitivity of the mixed oxides catalysts.Ui, The samples of NiO-Bi2O3 series were also prepared by thermal decomposition of cor-$' responding basic carbonates of both metals for 3 h at 600°C in air. The X-ray diffraction| | proved the presence of alpha, beta and gamma phase of Bi2O3 in the mixed system. The

69

CTU SEMINAR 94 NUCLEAR. ENGINEERING

specific surface area, the size of coherent regions, as vvel as the specific surface oxidationability of nickel oxide were found to be profoundly influenced by the second component.From all the physico-chemical parametres followed, it was only the oxidation ability whichappears to be sensitive to pre-irradiation with gamma rays of 6uCo at a dose of 1 MGy. Thechanges of this parameter, observed only with the samples containing an excess of nickeloxide, differ in dependence on conditions of the irradiation. It was performed partly in air,partly with the samples suspended in distilled water.

The kinetics of hydrogen reduction was studied by isothermal thermogravirnetry in therange 320-440°C and also in the non-isothermal regime at a heating rate of 10°C.inii]~' up to440°C. As it was found, the reduction of the system under study proceeds in two consecutivesteps and its rate is a non-monotonic function of composition of the samples. Accelerationof the reduction of thermodymanically more stabile IÔs by the admixture of nickel oxideseems to be due to the trapping effect, i.e. the binding of liquid bismuth into the compound ;or alloy with mettaiic nickel. Reduction rate of the samples with prevailing content ofNiO is enhanced by their pre-irradiation in air and, on the contrary it is lowered after thesame irradiation in water suspension. The positive radiation effect can be attributed to theincreased concentration of the charge defects generated by ionization. The negative effectis correlable with the increase of the content of strongly bound, ionogenic forms of oxygen,retarding the donor adsorption of hydrogen.

The partial results presented in this paper have already been published in more detail •,in the Radiation Physics and Chemistry, or will be published in the same journal. •'

This research has been conducted at the Department of Nuclear Chemistry as a part of, .'. the research project "Application of radiation and nuclear chemical mtthods in heterogeneous ^\ catalysis" and has been supported by CTU grant No. 8108. *

70

-—-pV,wt »•iif^.-.-i^'.Sf^


GAMMA MONITORING ARROUND THETRAINING NUCLEAR REACTOR VR-1

A. Kolros


Key words: nuclear reactor, gamma monitoring, scintillation detector, computer programPROBE

The facility for environmental monitoring was instalated at the nuclear training reactorVR-1 SPAROW side. This facility can measure level gamma radiation in the wide rangedose and dose rate (from natural background). This facility was presented by CEZ PRAHA.

The facility consists of:

- Dose rate meter type NB 3202 (produced by: TESLA VUPJT Pfemyslenf, CZ),Wide-area LED display,

- Computer PC 286,- Computer program PROBE v. 1.98.

« The basic part of facility is the measurement unit type NB 3202. This unit is designedj to continuous dose and dose rate measurings with very high sensitivity and low energy| dependence in a wide energy range. Specifications NB 3202:s

Measured value : tissue dose rateDose rate range: 30nGy.h~HolOGy.h~1

Dose range: up to 10 GyBasic measurement error: < ±15%Energy dependence (toleration): 20keVto80keV(±40%)

80keVto3MeV(±15%)Temperature range: -Z5°Cto + 55°C

Measurement unit contains a combined plastic scintillation detector with ZnS layer andNal/Tl inside. Electronic part contains microcontroller type 8751, high voltage power suply,

; photomultiplier, current-frequency convertor, thermometer. Light source (LED diode) and•• temperature senzor are used to perform long term correction.i', Output value dose rate and other output values are the best calculation immediate.4 value . Measured data (dose rate, dose, time derivation of dose rate, statistical errors) arejs transferred to the control computer PC 286. For communicating PC with NB 3202 unit,jjii work and archives datas the computer program PROBE is used.I The facility is located in the MFU TROJA building. The measurement unit is located|. on the roof, 8 m up the level ground and at the distance about 150 m from the reactor. Data§i. on the display in the hall building are actualy every 10 seconds. Every 30 minutes are data% stored on hard disk PC. The group is used from July 1993. Tab. 1 represents measurementI ' data, Fig. 1 represents time dependence dose rate gamma.

•f' 71

I


Tab. 1: Output value from program PROBE

D

pGy/hod

0,0998

0.1001

0.1

0,1

0.0996

16

*

0,36

0.33

0.31

0,35

0,28

6'ftQy/boffi

-O.0OW

-0.0002

-0,0002

-0,0001

-0,0004

%

38

59,1

45,1

93,4

26,5

D

*Gy

0,1408

0,1533

0.1658

0,1783

0,1908

sD

%

0,29

0,28

0,27

0.26

0,25

TH

hod

1,9664

2,1658

2,3471

2,2798

2,4792

time

13:00

13:15

13:30

13:45

14:00

ditc

10/01/93

10/01/93

10/01/93

10/01/93

10/01/93

S?ft

D - dose rate sDD - time derivation dose rate sDD - dose (start point) sDTH - average time measure

- error dose rate- error time derivation dose rate- error dose

Fig. 1: Time dependence dose rate gamma (August 1993)

0.16 T

i : 0.14

I- 0 . 1 2 -

o.io -

0.08

01.08 06.08 11.08 16.08 21.08 26.08 31.08date

In the night from 5.8.93 to 6.8.93 there was a thunderstorm with a heavy rain. Thiscaused strong grow of the dose rate gamma with successive fall. Little oscillation timedependence ±5% around the average value is caused probably by temperature.

Facility is part of outside dosimetric system of the training nuclear reactor VR-1 andgives information to the both laymen and the scientific, public.

References:

[1] Technicky popis a pokyny pro provoz mtfict ddvkovt'ho pftkonu NB 8202 TESLAVUPJT Pfemysleni, CZ, 1993

This research has bren conducted at the Department of Nuclear Reactors

^

Section 3

PHYSICS

«8'''!»SI^4^*'S*!!S!^^

CTU SEMINAR 94 PHYSICS

NATURAL FREQUENCY

OF AN AIRCRAFT TIREE. Vesela

CTU, Fac. of Mechanical Eng., Dept. of PhysicsTechnicka 4, 166 07 Praha 6

Key words: aircraft tire, natural frequency, vibrational system, time behavior of displace-ment

The following methods were used to analyze the natural vibrations of an airplane tiretogether with finding the natural frequency. First, the assumptions were stated (as forexample an adiabatic process the air in the tire follows, neglection of the mass of both thetire and air with respect to the mass of the load, only small deformations were supposed andthe constant determining the shape of the tire lies within the interval which occurs in therase of real airplane or car tires), and with res pect to them the non-linear motion equationwas found.

Time evolutions of vibrations, velocity and acceleration together with the natural fre-quency of the system were found for botli the original differential non-linear motion equation(using numerical methods from the Czech computer software Famulus) and its simplifiedform which was discovered to describe the real process under certain conditions. This e-quation was again solved using both tlie numerical methods and the method of successiveapproximations. This last method gave a closed analytical relati on describing the naturalfrequency as a function of all the parameters determining the behavior of the system.

The three- methods mentioned above were mutually compared and evaluated. Numericalvalues of experimental investigation of a given aircraft tire complete the work.

The vibrational motion of a given non-linear torus-shaped mechanical system was solvedusing various methods. Each method has a certain number of advantages and disadvantages.

The analytical solution brings a closed form and shows the mutual dependence of allthe parameters determining the problem in a general form.

The numerical solution, which uses the FAMULUS system, can describe only one spe-cific problem (or one set of problems - if we define the shape constant k as a variable, aswe did). To a certain extent, the mutual relation of the parameters may be found, too,but a certain amount of invention in formulating the problem when a computer is used isnecessary. On the other hand, computers are very fast, and there are no substantial troublesin preparing the program which allows any quantity in whic h we are interested to be foundas a function of the wide variety of chosen parameters. Moreover, it is possible to make theprogram even more user-friendly.

Comparing the amount of mathematical work necessary to obtain the general formu-la (which, in fact, describes the problem under certain conditions necessary to find thesimplified form of differential equation, allowing us to use the method of successive approx-imations) with that needed to create the computer program and with the wide variety ofinput parameters it may offer, including the real motion equation but excluding the closedanalytical formula, the most suitable method for a particular case must be chosen.


Both methods lead to nearly equal results which are comparable with the data obtainedexperimentally. The paper should clarify which method is best for a given problem anddesired results.

76


COMPUTER AIDED SEMINARSOF PHYSICS AND SW FAMULUS

E. Vesela, J. Kvarda*

C T U , Fac. of Mechanical Eng. , Dept . of PhysicsTechnicka 4, 166 07 P raha 6

*CTU, C o m p u t i n g Center, International Center for Scientific Compu t ingZikova 4, Praha 6

K e y w o r d s : software. Famulus, seminars, physics

A new subject Compu te r Aided Seminars of Physics will be opened at our faculty.O u r lectures will be followed by special and very complex problems to be solved using t h eCzech compute r system FAMULUS 3.5. This software allows us not only be t t e r and deeperunders tand ing of any par t icular problem solved by means of computer , bu t it is possible tobe acqu in tan ted with many interesting figures concerning the problem, and from th is pointof view, to know more about t he world about us.

As far as t h e software itself, it is especially the wide MENU which m a y be int roducedand within which i t is qui te easy t o make any new choice of pa ramete r s character izing t h eproblem. In this way, t he usage of a computer program is not only very easy but very friendlyand comfortable and t h e wide variety of solutions of a problem can be demons t ra ted ,

i T h e not iceable advantage is represented by a stable display of any given choice of inputpa ramete r s of t h e problem, which means a continuous vision check of the problem jus t beingsolved. Moreover, t h e au toma t i c choice of scale may be easily used, which allows reasonableusage of t h e whole area of the screen. The results may be shown in form of tables too . Asa whole, t h e program is very comfortable, no other activities connected with any controlof t h e compu te r are necessary here, and the program c an offer a wide variety of graphsdescribing t h e problem.

!, T h e compute r program "Project i le Motion" can serve as an example . It allows thechoice of the shape of the body (a sphere, hemisphere, discus or any a rb i t ra ry shape) ,

.•• t hen the choice of numerical values of parameters describing the problem (init ial velocity ,.': angle of depar tu re , initial height , characteristic cross-sectional a rea of a body if it has any| a rb i t ra ry shape and a mass of a body) . The computer program involves t h e correspondingj coefficients of air resistance (drag coefficients), bu t of course, they m ay be changed as well.| | T h e in t roduced M E N U enables t he choice of both the type of solved problem (graphsf,< of bo th coordinates as functions of both t ime and displacement, velocity as a function ofI?, displacement and t ime) and of the drag force as a function of displacement.ft- Then, we can decide between the solution of the problem with air resistance (the real| | case) and the solution that shows both the result under air resistance and the ideal one, inP" a free space. One more choice allows us to see the display of the case where the scale is$& found with respect to the ideal case or the case with the scale found that of air resistance.-1 The following picture shows the MENU with one of the possible choices. The nextj | figure shows the solution of the motion of a sphere in both a free space and air.' | From the point of view of the laws of physics, the problem is solved under the nextf assumption: the main axis of the body changes its position in such a way that it follows the

f * M

(TU SEMINAR 91 PHYSICS

vector of the? instantaneous velocity of a body - that means it is constantly tangent to thetrajectory.

The introduced menu allows a wide variety of initial condition and it is possible toinvestigate many interesting real problems. The computer program was prepared in such away that it is user-friendly.

| S°dw

Sphere C

r

rhom

Init.Values

= O.4-7

= 0.0Z0 »

= 7800 V<,/,= 0.Z6138 kg

Projectile Moti

Problen ••*:»«».»*

phi =

t*3 h =Real"Takle

on

<*'„« Solution

* ideal graphs

Clear End

<•) '

%

Projectile Notion

Sphere C = 0.47 v =

r = a.OZa m phi =

rho - 7S00 ks/'n'-S h =

m = 0.26138 kg

"c-cmx i nue

78

i-^^^^^ Sus-treT •• ••

( T C SKMIXAR ill PHYSICS

COMMENTS ON TIME, TENSEAND PHYSICS

P. Zamarovsky

( T l \ Fac. of Mechanical Eng., Dept. of PhysicsTechnicka -1, 166 07 Praha 6

Key words: time, tense, horizon

For most physicists time and space represent two components of one universal space-time. Their connections are so close that we cannot in tiie general case unambiguouslydistinguish between them. Hidden in the shadow of the conception of relativistic spacetimeremained the simple fact that we can find fundamental differences between space and time.Perhaps the most striking feature is the "flow of time"', which we cannot describe by physics.

This "flow" is projected more or less consciously to our speaking and thinking. In lan-guages of the so-called "tensed camp" (most indo-european languages) we use grammaticalforms - "tenses" - to express events in temporal reference frames connected with the moment"now". For the subject, this moment plays the prominent role: it divides events into three"classes of existence". To the "strongest" class belongs everything which is present now,the class of past is less real, and the future exists even more weakly. On the other hand, weoften use also other temporal determination in a "fixed" reference system, given by "usualdata", these we will call tenseless time (data). Tenseless time represents an abstractionfrom (i.e. negation of) the moment "now", a negation of the subject. In accordance withit everything lies in the same class of existence, we observe hidden determinism introducedby this approach.

The aim of this remark is my objection to the traditional affirmation that only "tense-less"1 time has any physical meaning, "tense" being only subjective or even unreal. I want topresent my hypothesis that ontological problems which quantum mechanics have introducedhave come from the sipmle fact that the Newtonian concept of tenseless time, resp. space-time, was uncritically adopted. From the gnoseological view, tenseless concepts belong toa mechanical world scheme which supposes the possibility of perfect objective description.Our tenseless concepts quietly survived the fail of Newtonism and nestled down in newphysics. The ontological crisis in physics was then "rescued" by another way, by introduc-tion of unnatural, "artificial" methodological steps. In quantum mechanics the movementof "real" objects was substituted by the evolution of unobservable wave functions. The"tenselessness" of the time of development of such functions was paid by separation of thewhole quantum model from macroscopic phenomenology, then denounced as "naive". Thestep from theoretical description to real observation is given by the "act of measurement",whicli reduces the wave function. So this act defines the moment of measurement as themoment "now". This "step" to reality substitutes the hypothetically objective (tenseless)time of waves with the tense of the real world where the observer or subject is present.

The tensed view is being rehabilitated and finds its role in many scientific branches.It forms a base for the definition of "horizons", i.e. bounds, where (subjectively taken)existence changes its modality. Such "horizons" (of not only temporal or spatial nature)

79


arc introduced in Eclmunt. Husscrl's phenoinenologj- and in mathematics in alternative sottheory. Horizons also play a significant role in relativistic cosmologies.

This research has been conducted at the Department of Physics as a part of the researchproject "The Study of Physical Background of Chronometry".

SO


NONLINEAR MODELS IN QUANTUM

PHYSICSG. Chadzitaskos, K. Kostal

CTU, Faculty of Mechanical Engineering, Department of Physics,Technicka 4, 166 07 Praha 6

Key words: quantum theory, stochastic mechanics, quantum groups, nonlinear Schrodingerequation

The investigation of nonlinear models in quantum physics carried out at the Depart-ment of Physics of the Faculty of Mechanical Engineering has been concerned with thequantization on a discrete finite space, the realization of quantum algebras and with thethermodynamic interpretation of the solution of the nonlinear Schrodinger equation for asystem of N particles.

I. The quantization on a discrete finite space was studied in connection with the orderingproblem and the Feynman path integral in a discrete space is constructed in [1], wherethe connection between operators in quantun mechanics and matricies which correspond tofunctions in classical mechanics is derived . The *-product for discrete symbols and matriciesas discrete symbols are also introduced. The finite-dimensional quantum mechanics yields a

| convenient operator basis for representations of g-deformed Heisenberg-Weyl algebras whenq is a root of unity, i.e. qM = 1 [2]. Two free parameters appear when the representationsare constructed. The necessary conditions for the representation to be irreducible are shown.Contributions at the Colloquium on Quantum Groups (Prague, June 1993) and at XIIth

Workshop on Geometry and Physics (Bialowieza, July 1993) were presented on this topic.In [3j a new definition of coherent states over Zn x Zn phase space was given with theanalogy for R2 phase space.

II. The stationary nonlinear Schrodinger equation with a logarithmic term (NSE) reads

where tp is a complex function, H denotes the Hamiltonian operator for a system of Nparticles, K a constant and 9 a positive parameter [4,5,6]. We assume that

W0n = £ n 0 n , n = 0 , 1 , 2 , . . .

and that the eigcufunctions jj>o,t{>t,4'2,- • • corresponding to the eigenvalues E0,Ei,E2,-;respectively, of the Hamiltonian H form a complete set of orthonormal functions. Theenergy eigenvalues are numbered in such a way, that EQ < Et < Ei < . . . . Then thesolution of the NSE can be expanded in a series of these eigenfunctions:

•'. Substituting this expression into the NSE, we obtain the NSE in the energetic representation:

'4

81

V. 2î °n C"1 Wn + K 2^°^ =-9 2^, an^n In / ,f 1 n n n


where / = i/'*V' is the density of the joint probability distribution of the coordinates ofN particles. Using this equation, we can easily express the density / as a function whichdepends explicitly both on 6 and the energy values EQ,EI,E2, Since / and all theeigenfunctions apearing in the above expression for ifi are normalised to unity, it can beeasily proved that also £ n Pn = £ n a'nan = 1.

These conditions, together with the equation

n

which follows from the NSE, enable us to find the expressions, depending on 6 and theenergy values, for the probabilities Pn , namely

/>„ = • ! « - * , where Z = ] T V ^ .n

If we put. 0 = k'J' (k is the Boltzmann's constant, T the thermodynamic temperature), thisprobability distribution we derived from the NSE can be interpreted as Gibbs distributionfor quantum canonical ensamble. Accordingly, we can interpret the NSE as an equation ofmotion, which involves both the quantum mechanical and the thermal motion of particles.

References:

[1] CHADZ1TASKOS, G. - TOLAR, J.: Feynman path integral and ordering rules ondiscrete finite space, Int. J. Theoret. Phys., 32 (1993), pp. 517-527.

[2] CHADZITASKOS, G. - TOLAR, J.: Quantization on Zn and coherent states overZn x Zn, (to be published).

[3] CHADZITASKOS, G. - TOLAR, J.: Quantum mechanics on Zn and q-deformedHeisenberg-Weyl algebra, Quantization and coherent states methods, 1993 (to be pub-lished).

[4] KOSTAL, K.: Stochastic mechanics based on differentiable random functions, SelectedTopics in Mathematical Physics and Quantum Field Theory, World Scientific, Singapore1990, 251-264.

[5] KOSTAL, K.: Thermodynamic interpretation of the nonlinear Schrodinger equation, acommunication presented at the meeting of Czech and Slovak mathematical physicist,Opava, April 1993.

[6] KOSTAL, K.: Thermodynamic interpretation of the nonlinear Schrodinger equation,i' (to be published).

I;' This research has been conducted at the Department of Physics of the Faculty of Afechan-*§?, ical Engineering as a part of the research project "Nonlinear models in quantum physics"| ' and has been supported by CTU grant No. 8002.

82


SOUND PROPAGATION IN KLADNOSANDSTONES

K. Malinsky

CTU, Fac. of Electrical Eng., Dept. of PhysicsTechnicka 2, 166 27 Praha 6

Key words: ultrasound, mining

A precise method for measuring sound velocity in rocks was developed in the departmentof physics, faculty of electrotechnical engineering, CTU Prague [1]. The device was usedin crystalline rocks in Pfibram [2]. The situation in the Kladno coal-mining region hasproved entirely different for extremaly high attenuation of sound in coal, where ultrasonicmeasurements are quite impossible, and for high but measurable attenuation in sandstonesabove the coal layer.

The Kladno sandstone is highly inhomogenous but rather fine-grained, with grainsless than 3 mm. Their shape is more or less spherical, unoriented. The wave vector forultrasound used is k = 60 m"1, so that the condition Ic.a < 1 is well fulfilled (a is the grainsize). It leads to the possibility of considering the long-wave approximation only.

The sandstone in the place of measurements is far from firm consistency. Thus, it ispossible to neglect the binding layer and assume the rock to be a mixture of quartz grainswith water in voids. The acoustical constants of such a mixture have been studied elsewhere[3]. A quasi-static and extended quasi-static approximation was used [4]. (The stress field inthe scatterer is given by the static field produced by the displacement of the incident wave,which is valid in the low frequency regime.) In this case, the solution of the wave equationfor sine waves may be expressed using integrals from Green functions with assuming onlythe statical part of the entire Green function. For this case, the formulae calculated in [5]may be used.

The propagation of sound in a system of scatterers depends on the degree of coherencebetween the particular scattered signals. In our case, the scatterers are spread through thewhole space between the transmitter and receiver of ultrasonic waves, i.e., the scatteringis incoherent (with the only exception for scattering in the straight direction that maybe assumed as coherent). While in coherent, scattering the intensity of scattered wavefrom N scatterers exceeds /V2-times the intensity from one scatterer, the contribution fromincoherent scatterers is proportional to their number (density).

5, The relation between the phase delay of the detected ultrasonic wave and elastic prop-; erties of the rock in conditions described is rather simple and may be expressed in termsff< of velocity and elastic moduli. In this way, the elastic modulus of the rock and its time$ changes may be determined from acoustic measurements.

I References:| j [1] MALINSKY, K. - PLOCEK, J.: Device for on site sound velocity measurements inf: rocks. Acta polytechnic* 6 (III,I) 1991, 55

[2] MALINSKY, K. PLOCEK, J.: In-situ sound velocity measurements in rocks. Acta, .£ Montana 84 (1992), 203

V*' 83

1k


[3] MALINSKY, K. - PLACHY, M.: Concentration of sand-water mixture measured byultrasound. CTU Prague Workshop 92, 6-15

[4] PER, Y. H. - MOW, C. C : Diffraction of elastic waves and dynamic stress concentra-tion. New York, 1971

[5] ESHELBY, J. D.: Static strain fields of spheroidal inclusions. Proc. Roy. Soc. LondonA 271 (1957) 376

This research has been conducted at the Department of Physics as a part of the researchproject "'Ultrasound as a Means for Evaluation of Strains in Rocks" and has been supportedby CTU grant No. 3814.

V •' 84

ft

I

I


DYNAMIC MODEL OF THE RAILPLASMA ACCELERATOR

J . Maloch, P. Konicek


Key words: railguns, electrothermal guns, electromagnetic launchers

The main field of rail plasma accelerators application is accelerating of macroscopicobjects to hypervelocities. In the railgun the plasma is driven by electromagnetic force Fem

acting on the charged particles forming the plasma armature. During the initiation phaseof electrical discharge, the thin metal wire connecting railgun electrodes rapidly vaporizesto form the plasma armature. Electrothermal heating throughout the drive of the armatureproduces the pressure acceleration force Fe(.

The projectile dynamics in the railgun is also influenced by retarding forces acting onthe plasma and the projectile (see Fig.l).

The plasma armature experiences the viscous drag from the plasma-discharge tubeboundary layer and the ablation drag due to electrodes and discharge tube material beingablated and accelerated up to the projectile velocity. The total force Dpi acting on thearmature was derived in [1]. Thus we can write

Dpl = DV + Da = fr>y "»•),.

where fip is the plasma-bore wall viscous drag coefficient, v is the armature velocity, mo isthe initial plasma mass, D is the discharge tube diameter, a is the ablation coefficient, / isthe discharge current and Up is the breech voltage.

There is also retarding force in the railgun Dp acting directly on the projectile due to] its mechanical friction in the bore. For Dp we have [2]

Dp = ^ ^ V e m + Fe«], (2)

where (tk is the mechanical friction coefficient, k\ is the axial-radial pressure transformationI coefficient, Ok is the bore perimeter, lp is the armature length, A = irD2/4.j There exist also drag forces associated with the compression of the gas in the bore inI' front of the moving projectile. The first is due to viscous drag in the compressed gas-bore% walls boundary layer. The second arises from the accelerating of this gas and from the|'j. accelerating of the shock wave which propagates in front of the projectile. The velocity of

the shock wave is greater than that of the projectile which causes the mass of the compressedgas to increase. The total retarding force associated with these phenomena is [2]

i

r\ r\ i r\ f ' * JO 2 . / ' * I A 2 » A 1 /»i\

i?me = Z). + Dc = -^ / tôOkV 2 ! + - ^ - ^ {Av* + Ax-J , (i)

where fiv is the compressed gas-discharge tube walls viscous drag coefficient, p0 is the densityof uncompressed gas, x is the position of the projectile and 7 is the Poisson coefficient ofthe gas.

85

CTU SEMINAR 9-4 PHYSICS

In Fig.2 we see t he calculated dependence of t he projectile velocity versus its position inthe discharge channel. Curve 1 is calculated without considering any retarding force, curve 2is calculated considering the retarding forces on the plasma, curve 3 is obtained taking intoaccount projectile mechanical friction too and curve 4 is the experimentally measured oneusing conventional two-stage railgun.

References:

[1] KONICEK, P. - MALOCH, J. - SABLATURA, J.: Influence of Ablation to Projec-tile velocity in the Rail Plasma Accelerator 16 th Symposium on Plasma Physics andTechnology, Prague 1993

[2] MALOCH, .1. KONIOEK, P.: Plasma Accelerator as Linear Ultraspced Driver Kon-ference JCSF Zilina 1993

This research has been conducted at the Department of Physics as part of the researchproject "Plasma Accelerator as Linear Ultraspecd Driver" and has been supported by Uni-versity Development Foundation grant No. 1033 (3815).

s//y/yy/ys//y//y//s//y///yy///y/^^

v[m/s]

800-700-600:

500-400:

300-200100

100 200 300 400 500 600 700 x[mm]

86

! S * K ^ ^ >•-. :. .


DIAGNOSTICS AND DYNAMICSOF THE Z-PINCHJ. Hakr, J. Kravarik, P. Kubes,

P. Kulhanek, J. Pichal


Key words: z-pinch. optical diagnostics, plasma discharges, plasma turbulences, plasmainhomogeneities

The Z-pinch plasma implosion is connected with interesting characteristics during thetime of maximal compression - extraordinary stable configuration, production of the highenergy electron and ion beams and hot-spot microsources of X-ray radiation with widepossibilities of applications. Considerable effort is devoted to understanding the physicalprinciples for more complete utilization of extreme pinch properties.

In these experiments a discharge at low energy of 0.5 kJ and relatively high pressure(1-50) kPa of nitrogen and argon were used, where the maximum current (50 kA) is reachedat a time 10~6 s. The conical electrode configuration induces, besides the radial implosion, anaxial one with two important advantages - the possibility of dynamic study of the compressphase and separation of the high energy plasma and electrodes.

The diagnostics were realised1) by a schlieren configuration with various diameters of disk screen in the schlieren

lens focus and a schlieren interferometry with ruby laser pulses in Q regime with 40 nspulse-length

2) by pin-diode signal, Faraday rotation and spectroscopic continuum radiation mea-surements

for plasma density, temperature and magnetic field determination. The low energy andhigh pressure of the discharge provide sufficient conditions for distinct diagnostic imaging.

In 1992 these important results were obtained: the plasma temperature and densityvalues in the current layer, the existence of jets and a dense central structure - plasmoid,the presence of electrode and filling gas ions in the jets and in the central structure and thevalue of the plasma velocity near the plasma jets.

The results obtained from diagnostics in 1993 can be summarized in these conclusions:-the plasma density in the jets has the same value as in the neighbouring current layer

||" -the continuum radiation has the same intensity as the plasmoid, jets and current layer-the plasmoid is homogeneous with a sharp density gradient on its boundary-in the argon filling, a compact plasmoid is formed with diameter 1-2 mm during aU

the life-time of 10~6 s-negative results were obtained from pin-diode signals and Faraday rotation measure-

jfe ments (this means that in the discharge short light pulses are not present of duration ap-proximately 1 ns and magnetic field higher than 10 T).

This experimental knowledge enables us to make calculations and conclusions:The low plasma jet density and temperature provide a powerful reason for a turbulent

structure. Magnetohydrodynamic turbulences are created as a consequence of the ion a-

87

* . ' • •


coustic instability in the current layer near the jets at the plasma deceleration time. Thecharacteristic turbulence parameters - low collision frequency and energy dissipation, highconductivity, diameter 0.1 mm, velocity 10 km/s, stochastic magnetic field about 3 T andcurrent some kA with kinetic, magnetic and electric energy density about 3 MPa.

The filaments are probably the stationary and stable phase of the magnetic line recon-nection instability. The shear magnetic field in the filaments is estimated as 5 T and thecurrent 2 kA. The conductivity of 100000 Sm/m (two orders higher than that for measuredtemperature and density) can be explained as due to plasma magnetization and ion andelectron separation inside the volume of the filaments.

Turbulences in the jets are exposed to the kinetic pressure of the neighbouring currentlayer and they are accelerated into the central part with the same kinetic energy density.In this area the plasma with the same temperature and density 3-4 times higher than thatin the plasma jet is observed.

A compact plasmoid is formed at argon filling of the discharge chamber, while at nitro-gen filling, an expanding plasmoid like cauliflower is observed. This interesting phenomenoncan be caused by the argon ability of more intensive radiation release. The plasmoid is rela-tively cold and high density configuration, separated from the electrodes and composed fromthe magnetohydrodynamic turbulences with kinetic, magnetic and electric energy densities10 times higher than the plasma pressure nkT. A life-time of 10~6 s can be a consequenceof such phenomena as high conductivity, magnetic field streamlines frozen into the plasmaand a double layer electric field. The low boundary for the conductivity of the plasma witha length of some mm and velocity 10 km/s can be estimated as about 100000 Sm/m.

In 1994 the GACR grant (1993-1995) will continue- complex diagnostics for measure-! ment of temperatures, densities and magnetic fields on the IPP Z-pinch gas puff device

is planned as a cooperation between the Institute of Plasma Physics and the Institute of'• Physics CAS and the Department of Physics FEE CTU and the Department of Electronics

FNSPE CTU in Prague. The proposal of the CTU grant is prepared for continuation of theFEE Z-pinch device- diagnostics.

: References:

I [1] KUBES, P. et al.: Proc. 3rd Int. Conf. Dense Z-pinches, P 38 London 1993

I [2] KUBES, P. et al.: Proc. 16th Symp. Plasma Physics and Technology, p. 170. Praha,? 1993

f [3] KUBES, P. et al.: Contr. Papers 20th Fusion and Plasma Physics II, p. 535. LisboaI 1993.I [4] KUBES, P. et al.: Proc. I. XXI Intern. Conf. Phen. Ion. Gases, p. 381. Bochum1 1993.

fe [5] KUBES, P. et al.: IEEE Trans. Plasma Science, Vol. 21, No. 5. 1993.

This research has bf.rn conducted at the Department of Physics as a part of the issearchproject "Diagnostics and Dynamics of the z-pinch" and has bicn supported by CTU grantNo. 8100.

88


i

m

OPTIC DIAGNOSTIC DEVICESFOR PULSE DISCHARGE PLASMA

J. Kravarik, J. Hakr, P. Kubes,P. Kulhanek, J. Pichal


Key words: plasma diagnostics, pulse laser, pulse discharges

Two devices for plasma optic diagnostics are described in this paper: 1) experimentalset-up used last year in the Department of Physics FEE CTU and in the Department ofPlasma Physics at the University of Ferrara in Italy, 2) a high time resolution device forextremely rapid discharge phenomena.

In the optic diagnostics of pulse discharges there are two conditions to fulfill: a suf-ficiently short and intensive pulse for the photoregistration of rapid variation of the lightfield and the most precise setting of the moment of exposure. In special cases a sequence ofseveral time shifted pulses for plasma motion imagination can also be used.

For z-pinch plasma schlieren and interferometric diagnostics Q-switch ruby laser pulsesare used with halfwidth 40-60 ns and energy 0.5 J [1]. The diagnostic apparatus is transfer-able and this advantage made a diagnostic measurements possible in Ferrara on the 35 kJplasma focus device [2j. The scheme of the experimental set-up is presented in Fig.l.

I!to laser

SY

OE 1 J-CB

to H.V. Maxwell generator

Fig. 1: Bubble pinch experiment set-up in Ferrara: RL-ruby laser; T-telescope (10 timesmagnification); IE,OE- inner and outer plasma gun electrodes, B-bubble (special watersolution); O-schlieren lens; S-little circle screen; F-laser wavelength filter; FC-photocamera;SY-synch-signal generator; CB-condensator battery 60 F; 35 kV.

The current layer accelerated in the gun is compressed in front of the inner electrodein the radial direction and the bubble is pressed to the coaxial axis. This experiment isan alternative of the liner inertial fusion study [3]. Diagnostics in various gases (hydrogen,deuterium, helium and argon) was used and both the interesting schlieren pictures withhigh density filaments and the verification of the theoretical calculations were obtained.Two conclusions for further experiments can be suggested - increase of the current in frontof the gun and the axial stop segment for the current sheath is necessary. The diagnostic

89


equipment, used enables distinct imaging of the schlieren field for plasma velocities lowerthan 20 km/s.

The short time and high velocity plasma inhomogeneity imagining in a nanosecund andsub-nanosecund length of the laser pulses is neccesary for a detailed study. These parameterswill be acquired in new equipment.

The neodym YAG laser as a source of light pulses consists of two components - anoscillator and an amplifier. The gigantic pulses with 10 ns halfwidth and energy 100 mJ areformed in the oscillator neodym rod and amplified 5-6 times in the second rod. The basewavelength of the radiation (1064 nm) is converted in the second harmonic generator (KDPcrystal) into 532 nm radiation with S ns pulse length. Moreover, if the cell with specialcolouring matter solution is placed into the oscillator resonator, the mode-locking regimewill be realized. Several short pulses (300-500 ns) are generated in this case and after theamplification and conversions it is possible to use these pulses for the diagnostics. Anothermodification is prepared - a selection of one pulse with the highest amplitude only and itsmultiplying into 2-4 pulses with variable time shift with the help of the sequence of mirrors.The scheme of this set-up is shown in Fig. 2.

MAM

M2

Fig. 2: Scheme of laser device for nano and sub-nanosecond pulse generation: H-bodyof laser; YAG-O-neodym oscillator 6x60 mm; YAG-A-neodym amplifier 6x60 mm; FT-xenon tube; (Both neodym rods are placed in focus points of two elipse reflex cavity); PC-Pockers' cell (DKDP); C-colouring matter, P-polarizator; Ml, M3, M4, M6, M8 -mirrors(lOOrefractivity); SHG-second harmonic generator, L-auxiliary semiconductor laser.

References:

[1] KUBES, P. - HAKR, J. - KRAVAR1K, J. et al.: Interrupted Z-pinch in Argon. Proc.16th Symp. Plasma Physics and Technology, p. 170, Prague 1993.

[2] BORTOLOTTI, A. - LINHART, J. G. - KRAVARIK, J. - KUBES, P.: Plasma DrivenImplosions of a Bubble-Liner. Proc. 3rd Int. Conf. Dense Z-pinches B2, London 1993.

[3] BILBAO, L. et al.: Dynamics of Thin Liners Driven by a Quasicylindrical Z-pinch.Kerntechnik 57, No. 5, p. 330, 1992.

This research has been conducted at the Department of Physics as a part of the researchproject "Optic Diagnostic Devices for Pulse Discharge Plasma" and has been supported byFDDU grant No. 3812.

\A I

90


ABSORPTION OF FEMTOSECONDLASER PULSES IN SOLID TARGETS

J. Limpouch, L. Drska, A. Andreev*

CTU, Fac. of Nucl. Sri. & Phys. Eng., Dept. of Physical ElectronicsBfehova 7, 115 19 Prague 1

*Vavilov State Optical Institute, Russian Academy of ScienceBirzheway 12, Skt. Petersburg, Russia

Key words: laser interaction, laser plasma, femtosecond pulse, numerical simulation, laserabsorption

The interaction of sub-picosecond laser pulses with solid targets is investigated heretheoretically: via analytical models and via numerical simulations. This study involves thefollowing two types of problems:

1. Numerical simulations of laser interactions with solid-state density plasmas in theregime of anomalous skin-effect.

2. Analytical study of the absorption of p-polarized obliquely incident wave for very shortscalelengths of plasma density profile.

1. For a sufficiently short (T>-IVMA/~ 200 fs) intense laser pulse incident normally on solidtarget, the collisionless absorption in regime of anomalous skin effect seems to be dominant[]]. The interaction of femtosecond laser pulses with solid-state density plasmas in regime

f of anomalous skin effect is studied here by solving Fokker-Planck equation in diffusion; | approximation. The aim is to examine in detail the impact of collisionless absorption and of! temperature gradient in the skin layer on the electron distribution function. The absorption| efficiency and the heat flux limiter are then determined by the shape of electron distribution.s Our Fokker-Planck code, described in detail elsewhere [2], has been applied for numer-ic ical simulations of interactions of very short TFWHM = 36/.S Nd-laser pulses of intensities£ in range 1017 W/cm2 - 3. 1018 W/cm2 with solid targets. The model and the results areV presented in detail in [3].I';; The obtained electron distributions are consistent with our self-similar analytic solutionJg£ for the symmetric part of electron distribution /o(v) in case when full inhibition of energyfji flow out of the skin layer is present. As an example, the anisotropic part f\ of the electron

distribution is presented in Fig.l together with the theoretical function calculated a sim-plified analytic formula from the electron distribution fo(z = 0, v) at the plasma-vacuumboundary. The resulting distribution /i is quantitatively consistent with the theoreticalprofile, but the velocity extremes of f\ are shifted to lower velocities, partly because of thegradient of electron temperature in the skin layer and partly due to electron slowing downby the self-induced electrostatic field.2. Previous numerical simulations have shown that p-polarized obliquely incident laserwave may be absorbed with considerably higher efficiency than the s-polarized wave. Inplasma with the density scalelength L much less than the laser wavelength A, resonant

*! 91

CTU SEMINAR 94 PHYSIOS

Fig. 1: Anisotropic part of electron distribution at the laser pulse maximum Im =lO18W/cm2, compared with the theoretical function, denoted by • .

absorption is efficient in a broad range of angles of incidence with maximum shifted to largeangles of incidence 0 ~ TT/2. While for the simpler case of s-polarization accurate analyticalformulas for absorption efficiency exist for certain density profiles and any ratio L/X, similarformulas for p-polarization are known only in the limit of geometric optics L/X ^$> 1. Herethe analytical solution for the absorption efficiency of p-polarized wave is presented in limitL/X <C 1 for Epstein density profile and any ratio of electron collision frequency to laserfrequency for the first time. For a detailed description of the model and the results see [4].

References:

[1] LIMPOUCH, J. - ANDREEV, A. - SEMAKHIN, A.: Conversion of ultrashort laserpulses into X-ray emission in high-density laser plasma. In Iodine Lasers and Applica-tions. Proceedings SPIE, 1993, Vol. 1980, p. 75-86,.

[2] DRSKA, L. - LIMPOUCH, J. - LISKA, R.: Fokker-Planck simulations of ultrashort-pulse laser-plasma interactions. Laser and Particle Beams 1992, 10, (3), 461-471.

[3j LIMPOUCH, J. - DRSKA, L. - ANDREEV, A.: Anomalous skin-effect regime of in-teractions of femtosecond pulses with dense plasmas, submitted to Laser and ParticleBeams

[4] ANDREEV, A. - LIMPOUCH, J. - SEMAKHIN, A.: Absorption of enegy of shortlaser pulse at oblique incidence on strongly non-uniform plasma (in Russian). IzvestijaAkademii Nauk, seria fizicheskaya, 1994 (in print)

This research has been conducted at the Department of Physical Electronics of CTU asa part of the research projects "Information Physics of Extreme Systems: Methods, Sim-ulations and Applications" (supported by the Universities Development Foundation grantNo. 0196) and "Particle Transport and Radiation Processes in Systems with High EnergyDensities" (supported by CTU grant No. 8141).

92

CTU SEMINAR <M PHYSICS

PARTICLE TRANSPORT COEFFICIENTSFOR EXTREME SYSTEMS

L. Drska, M. Sinor, J . Vondrasek

CTU, Fac. of Nucl. Sci. & Phys. Eng., Dept. of Physical ElectronicsV Holesovickach 2, 180 00 Praha 8

Key words: high-parameter plasmas, transport coefficients, stopping power

The problems of kinetic behaviour and charged particle transport are of interest inmany areas of research and applications of systems with extreme parameters. In our studythese problems are treated in consistent way from first principles.

Interactions of atoms/ions and electrons are considered in the cluster model approxi-mation. Two types of clusters are introduced: (i) the cluster of randomly distributed ionspheres and (ii) the cluster of free electrons distributed in ion spheres according to the SelfConsistent Average Atom Model (SCAAM) [1]. In the model, there exist interactions be-tween (i) ion cluster and other ion clusters, (ii) free electron cluster and other free electronclusters, (iii) ion cluster and free electron clusters, (iv) free electron cluster and ion clusters.

The atomic structure data obtained by SCAAM and the cluster interation model arethen used in the BBGK V formulation of the kinetic theory of ions and free electrons in theplasma. Truncating BBGK Y equations hierarchy after second equation lead to the transportequation with collision integral in the extended Balescu-Lenard form. The collision integralcan be transformed to the Landau-like form. In this expression formulas for stopping powerand diffusion coefficient can be identified.

The kinetic equation for elections with the derived collision integral is utilized forexamination of electron relaxation rates and transport coefficients (thermal and electricalconductivity) for plasma close to the local thermodynaniir equilibrium. The conductivitycoefficients are obtained as solution of the stationary linearized kinetic equation [2].

Presented unified formulation is useful for estimation of the influence of ion strippingprocesses, which form the charge state of heavy ions in dense plasma, on the stoppingpower. In order to calculate the energy losses of heavy ion moving through a hot matter, itis essential to specify (i) realistic stopping power formula, and (ii) model for the projectilecharge state. For the stopping power calculation formula derived from extended Balescu-Lenard collision integral can be used. The charge state of heavy ions is introduced as anequilibrium ionization state of this ion in the target plasma al the effective temperature.The charge state, atomic structure and interaction potential is calculated by SCAAM. Theeffective temperature is derived from energy (velocity) of heavy ion and the mean kineticenergy of electrons in the plasma.

The model shortly described in the previous sections has been used for some calculationsrelated to light/heavy ion beam driven fusion. As a typical example of the results stoppingpower of fast bismut ions on lead is presented on Fig.l. Fig.2 demonstrates the stoppingpower of bismut ions on aluminium at various densities and temperatures.

93


TottlEtodronie p«t I

u«f » ur vTEn«fgy(»V)

Fig. 1: Stopping power as function of energy for 10 GeV Bi ions on Pb (p — 11.2 g/cm3,kT = 100 eV).

^ rr1?" % « r i o ' > » i o *

En»rgy(l»V)i «

Fig. 2: Stopping power as function of energy for 10 GeV Bi ions on Al.

References:

[1] DRSKA, L. - SINOR, M.: Average Atom Model and EOS Calculations: DFT Approach.Laser and Particle Beams 1992, 10, (2), 277-298.

[2] DRSKA, L. - VONDRASEK, J: Some Aspects of the Unified Model of Non-Ideal High-Parameter Plasmas: Electron EOS and Conduction Coefficients. In: Proc. Symposiumon Physics of Target Implosion, edited by K. Niu. Report IPPJ-859.Nagoya University,Nagoya 1988, p. 164-184.

This research has been carried out at the Department of Physical Electronics as a partof the research projects "Information Physics of Extreme Systems: Methods, Simulationsand Applications" (supported by the Universities Development Foundation Grant No. 0196)and "Particle Transport avd Radiation Processes in Systems with High Energy Densities"(supported by CTU Grant No. 8141).


RADIATIVE CHARACTERISTICSOF EXTREME SYSTEMS

L. Drska, M. Sinor


Key words: atomic structure, high-parameter plasmas, radiative properties

Radiation characteristics represent physical data having key role in understanding ra-diative properties of laboratory and astrophysical plasmas. This contribution is devoted tothe opacity code RACHEL (RAdiation Characteristics EvaLuation), which is a part of thepackage MIRIAM [1] for the simulation of puised-source-driven high-parameter non-idealplasma systems. The most important characteristics of the RACHEL code [2], the mainstrength of which should be in a reasonably consistent physics model with relatively detailedevaluation of non-ideal plasma effects, are as follows:

• Atomic data are obtained by the modified version of the self-consistent-fiekl quantum-mechanical ion-sphere average-atom model SCAAM [3], which is based on the finite-temperature density-functional theory.

• The bound-bound transitions are calculated for all lines between pairs of single-electron states obtained from average atom. The transitions between two single-electron states from each configuration of the diverse ion states give rise to a cluster oflines. If we suppose, that lines in the cluster merge together, than statistical methodcan be adopted for description of the shape of the cluster of lines. The final profile ofthis cluster is formed by individual line profiles, which have Voigt forms with Gaussianwidths given by Doppler broadening. Lorentz widths of the profiles are determined bynatural broadening, electron impact broadening with contributions from elastic and

: inelastic scattering, and Stark broadening calculated in the nearest neighbor dipoleand quadrupole approximation. '•

• The photoabsorption cross section is evaluated with the use of the standard formulabased on the dipole matrix elements. The free-electron wave functions are obtained

;• as a solution of the Schrodinger equation with the self-consistent field average-atompotential. The description of the photoabsorption-edge broadening is based on the

| statistical method analogous to the one accepted for bound-bound transitions.

t • Inverse Bremsstrahlung is, as in the case of photoefFect, evaluated using the free-f" electron wave functions. The computation of the dipole matrix elements with theseI wave functions represents one of the alternatives of obtaining free-free cross section| in the RACHEL code. But this method is, as a rule, relatively time consuming due|. to the large number of partial waves, which must be taken into account. The secondI choice is based on the zero-frequency approximation, in which free-free absorption cross| section is expressed in terms of the elastic scattering amplitudes. This approach canI be justified by the dominant free-free contribution to the opacity at low frequencies.

"I'•? 95


At present, several groups in different countries are developing radiative opacity codes.In view of the complexity of the physics and the numerical modeling involved, there isconsiderable interest in a detailed comparison of results calculated with different codes.To the structured comparison of opacity codes the workshop WORKOP-III:94 is devoted,which will be held at MPQ/Garching, Germany. We have been also invited.

As a small example of data, which can be obtained with RACHEL opacity code, thereis shown Rosseland group mean opacity for gold in Fig. 1.

Fig. 1: Rosseland group mean opacity for gold at density 1.93 g/cm3 as a function oftemperature.

References:

fl] DRSKA, L. - SINOR. M. - VONDRASEK, J.: Program Package MIRIAM and Atom-ic Physics of Extreme Systems. In: Physics Computing '92, Eds: R. A. de Groot,J. Nadrclml. (World Scientific, Singapore 1993), p. 324-325.

[2] DRSKA. L. SINOR, M. VONDRASEK, J.: Particle Transport and Radiation Char-acteristics of Hot Dense Matter. Presented at ECLIM 22: 22nd European Conferenceon Laser Interaction with Matter, Paris, May 10-14, 1993.

[3] DRSKA, L. - SINOR, M.: Average Atom Model and EOS Calculations: DFT Approach.Laser and Particle Beams 1992, 10, (2), 277-298.

This research has been carried out at the Department of Physical Electronics as a partof the research project* "Information Physics of Extreme Systems: Methods, Simulationsand Applications" (supported by the Universities Development Foundation Grant No. 0196)and "Particle Transport and Radiation Processes in Systems with High Energy Densities"(supported by CTU Grant No. Sljl).


I

I§

INFORMATION PHYSICS OF EXTREMESYSTEMS

L. Drska

CTl\ F'ac. of Nucl. Sci. & Phys. Eng., Dept. of Physical ElectronicsBfehova 7, 115 19 Prague 1

Key words: computational physics, physics of high energy density

Many very important systems for the development of high technology, which are s-tudied by contemporary physics, have to be considered as a subject of complex systemstheory. Their realistic models are nonreducible and highly complicated. The use of moderncomputers and new information technologies is the key to the solution of this problem.

Physics of extreme systems - systems with extreme parameters (density, temperature,energy density etc.) - represents a typical case when combining the knowledge of physicsprinciples with computer science (informatics) tools and techniques is essential.

The projects in this field, summarized in this contribution, have included the followingtopics :

• Application of computer algebra and integrated computing system to the developmentof the theory and tools for intelligent scientific computing : semiautomatic solution ofsystems of PDE [1] [2].

• Using these tools to the study of a challenging physical problem : interaction ofpowerful femtosecond laser pulses with dense plasmas [3] [4].

RELATIVISTIC

—n—

10" H>* t o "

Particle density (rn3)10" 10"

Fig. 1: Plasma states studied in the project : collisional, strongly coupled, and degeneratesystems.

97


• Development of DFT based models and numerical codes for atomic physics of col-lisional, strongly coupled, and degenerate plasma systems - Fig. 1 - and their realapplication : radiative characteristics and charged particle energy transport coeffi-cients of dense and hot matter [5] [6].

• Search for new applications of physics of extreme systems extending their traditionaluse: fusion burning in magnetized plasma channels, laboratory astrophysics [7] [8].

Computer science methodologies mastered in this project proved to be inspirative alsofor educational process both in undergraduate and postgraduate study. Their marriage withinformation pedagogy tools resulted in development projects described in [9], [10].

References:

[1] LISKA, R. - STEINBERG, S.: Stability Analysis by Quantifier Elimination. In: CTUWorkshop 94, Prague 1994, Section 1 : Mathematics.

[2] LISKA, R. - DRSKA, L. - LIMPOUCH, J.: Ultra-Short Laser-Plasma Interactions byFokker-Planck Simulation Code Developed by Computer Algebra Tools. In: 48th AnnualMeeting of the Physical Society of Japan, Sendai 1993.

[3] LIMPOUCH, J. - DRSKA, L. - ANDREEV, A.: Absorption of Femtosecond LaserPulses in Solid Targets. In: CTU Worksshop 94, Prague 1994, Section 2 : Physics.

[4] LIMPOUCH, J.: Laser Target Interaction in the Regime of Anomalous Skin Effect. In:CECAM Workshop on Short Pulse Laser-Plasma Interactions, Orsay 1993.

[5] DRSKA, L. - SINOR, M.: Radiative Characteristics of Extreme Systems. In : CTUWorkshop 94, Prague 1994, Section 2: Physics.

[6] DRSKA, L. - SINOR, M. - VONDRASEK, J.: Particle Transport Coefficients forExtreme Systems. In : CTU Workshop 94, Prague 1994, Section 2 : Physics.

[7] DRSKA, L.: ICS Techniques and Atomic. Physics of Extreme Systems. In : Workshopon Nuclear Detonation Waves in Magnetized Plasma Channels, Prague 1993.

[8] DRSKA, L.: Laboratory Nuclear Astrophysics - A Challenge for ICF Systems ? In :' European Research Conference on Nuclear Astrophysics, Knossos Royal Village, 1993.

[9] DRSKA, L. - LIMPOUCH, J. - SINOR, M. - VAGNER, S. - VONDRASEK, J.:4 Coordinated System of Programs and Physics Education. In: CTU Workshop 94, Prague• 1994, Section 19 : Education Development at the CTU.

I [10] DRSKA, L. - LIMPOUCH, J. - LISKA, R. - SINOR, M. - VONDRASEK, J.: A'§; Computerized Course of Computer Algebra. In: CTU Workshop 94, Prague 1994,| ; ' Section 19 : Education Development at the CTU.

| lH This research has been carried out at the Department of Physical Electronics as a part

of the research and development projects "Information Physics of Extreme Systems : Meth-ods, Simulations and Applications" (supported by the Universities Development FoundationGrant No. 0196), "Particle Transport and Radiation Processes in Systems with High En-ergy Densities" (supported by CTU Grant No. SHI), and "Facility for the Application ofIntegrated Computing Systems" (supported by the Grant V 307 of the Czech Ministry ofEducation).

98


LASER PATTERNING OF THIN FILMSK. Hamal, M. Jelinek*, M. Cech,

J. Lancok, V. Olsan*


*CAS, Institute of Physics,Na Slovance 2, 18040, Prague 8

Key words: laser applications, laser writing, laser patterning, laser ablation, laser deposi-tion, thin films, laser lithography

After the development of technology of deposition of high quality thin films the nextlogical step is the creation of micron scale structures into layers with the goal to extend thefield of possible applications. Patterned thin films of high temperature superconductors arenecessary for fabrication of superconducting ceramic antennas, microstrip bandpass filters,resonators, SQUID-s, fast AD and DA converters, logical circuits, transmission lines andbolometers [1]. The patterned and modified hard carbon films are used for creation of ad-vanced electronic device structures, for electronic packaging, selective hardening treatment,for development of backward-wave oscillators operating in excess of 500 GHz, for study oflaser-induced phase transitions [2], and study of morphological and structural film changes.Patterned ferroelectric films are used for production of special devices, waveguides [3], etc.One of the method used for film patterning is laser ablation by focused laser beam. Thelaser ablation has a number of advantages over other techniques. It is a clean, dry processthat requires no organic solvents. In addition, it is quick, extremely flexible, and offers goodspatial resolution without film degradation. The laser patterned structures are influenced byparameters of the laser used (pulsed or cw regime, vvavelenght A, pulse duration r, repetitionrate), parameters of the film and substrate (optical transmittion, thermal conductivity, filmthickness), laser surface fluence, and rate v of film motion compared to the focused laserbeam.

For film patterning and study of processing parameters a unique workplace was devel-oped consisting of massive inicrofabrication apparatus with a IBM/PC computer controlledtwo stepper motors in x and y axes, lasers, and optical monitoring system for visualisationof created structures. As source of laser radiation a cw Ar+ ion laser (with multiline regimeA = 488 - 514.5 nm, Po,,< = 3 W), and pulsed lasers (NdrYAG and ruby) can be used. Pulsedlasers parameters:

1) Nd:YAG (oscillator + amplifier, A = 1.06 fim, r = 10 ns, Ev = 200 mJ)2) Ruby laser (A = 0.694 fim, r = 20ns, Ev = 500 mJ).For patterning experiments the following high quality thin films were deposited by laser

ablation technique using KrF excimer laser:1) epitaxially grown superconductive YBaCuO films and buffer layers on crystalline,

polycrystalline and technological substrates2) epitaxially grown ferroelectric films (PZT, PLZT, PMN and SrTiO3:Cr+) on sapphire

or SrTiO.t3) high quality hard carbon films on Si or fused silica substrates.

99


Fig. 1: SEM plan view of Ar+ ion laser patterning: a) grained YBaCuO/polycrystallineSrTiO3 (P=2.6xlO5 W/cm2, v=25 ftm/sec, 200x magnification); b) smooth epitaxial Y-BaCuO/(100) SrTiO3 (P=6xlO5 W/cm2,v=2.5 ftm/sec, 860x magnification)

The laser patterning was applied on all three kinds of films. From preliminary experi-ments it follows that using cw Ar+ ion laser it was possible to modify only YBaCuO layers,and lines of a 10-pm-wide were cut (see Fig. la). It is seen that the neighbourhood of the cutline is influenced by redeposited material or by thermal changes. Fig. 1b reveals the crackin the direction of the modified laser line. For higher scan velocities (v=50 /im/sec), thecracks started to be more complicated. For ferroelectric and carbon films the successful re-sults were not reached even for high power densities (P=1.3xlO6 W/cm2) and small steppingrate (v=2.5 /jm/sec), probably owing to films optical transparency or thermal conductivi-ty. Using focused Nd:YAG laser, the structures into all kinds of samples were successfullycut. The power density in this case was P=6xlO8 W/cm2. In pulsed patterning regime thestructures into all films is possible to create, but in some cases the substrate can be alsodamaged. Therefore further study and optimisation of all conditions having influence onfilm patterning is necessary to be done in the future.

As the conclusions, the system for laser paterning of thin films was built and firstsuccessful experiments with patterning of superconductive, ferroelectric and diamond-likefilms were done.

References:[1] JELINEK, M. - JANU, Z.: Laser creation of microstructures in thin film superconduc-

tive layers Czech. J. Phys. A42, 262, 1992

[2] PRAWER, S. - KALISH, R. - ADEL, M.: Pulsed laser treatment of diamondlike carbonfilms Appl. Phys. Lett. 48(23), 1585, 1986

[3] HARUNA, M. - MURATA, Y. - NISHIHARA, H.: Laser-beam direct writing of TiO2-channels for fabrication of Tv.LiNbQj waveguides Jpn. J. Appl. Phys. 31, 1593, 1992

This research has been conducted at the Department of Physical Electronics of CTU andInstitute of Physics CAS as a part of the research project "Laser Thin Film Lithography"and has been supported by the grant of Dynamic Development Fund No. 0739.

100

CTII SEMINAR 94 PHYSICS

SYNTHESIS OF Ni SILICIDES INDUCEDBY EXCIMER LASER PULSES

R. Cerny, P. Pfikryl*, K. M. A. El-Kader**, V. Chab**

GTU, Faculty of Civil Engineering, Department of Physics

Thakurova 7, 166 29 Praha 6

"Institute of Mathematics, Czech Academy of SciencesZitna 25, 115 67 Praha 1

**Institute of Physics, Czech Academy of SciencesCukrovarnicka 10, 162 00 Praha 6

Key words: silicides, nickel, excimer laser, TRR, SEM, AES

The laser synthesis of MS (metal-semiconductor) and MIS (metal-insulator-semiconduc-tor) structures until now has been analyzed [1,2] by the methods common in thin filmstechnology (RBS, AES, electron microscopy, STM). To obtain information about the dy-namics of a synthesis, time resolved methods have to be used. For the clean Si and Ge, timeresolved reflectivity measurement (TRR) is a widely used technique to study the dynamicsof thermodynamic phenomena under the laser pulse irradiation [3]. It has been, however,very rarely used to study the composed systems because of the complex of effects which

: could influence the monitored reflectivity during the pulse processing.

•.,. I In this paper, we study the changes in the Ni-Si and Ni-SiCvSi structures due to the' ! XeCl excimer laser irradiation both theoretically using a mathematical model and experi-

mentally performing TRR. measurements in combination with scanning electron microscope(SEM) observation and Auger electron spectroscopy (AES).

The samples were irradiated in a stainless steel vacuum chamber. The XeCl excimerlaser pulses (308 nm, trapezoidal tailed shape, 28 ns FWHM) were transmitted into thechamber through a silica, window by optical path built up from silica fused optical elements.The energy density on the sample was varied by focusing and defocusing the beam in theinterval from 0.5 J.crrT2 to 1.0 J.cm"2 . The Si(]00) wafers were used as a substrate. Nilayers were evaporated in situ from a tungsten basket onto the Si surface covered withnatural SiC>2 layer or on a clean surface prepared by repeated heating of the substrateup to 1200 "C. The deposited layers were relatively thick and the estimated thickness was~ 500 nm±20%. The samples were fixed on the simple manipulator allowing an accurate

;., adjustment of the TRR cw HeNe laser probing beam in the centre of the XeCl laser pulsespot. The intensity of the reflected HeNe laser beam from the surface was measured by fastphotodiode, amplified, captured by a memory oscilloscope and stored by PC computer (see

£_.-, [4], for details). The selected spots and associated area were studied by AES spectroscopyfjj.1 and Jeol scanning electron microscope to estimate the chemical composition and morphology£ ' of the irradiated surface.*•£ In order to achieve first estimates of the basic parameters of the heating and cooling pro-jjjj1, cesses induced by the XeCl excimer laser, we have chosen a simple thermal model neglectingSj, the heat loss within the sample due to the chemical reactions. A detailed description of the

••• -y *•_ model for one-component systems has been published elsewhere [5,6]. Now, we assume a• p',( two-layer system Ni-Si with an ideal thermal contact on the Ni-Si interface and neglect the

, T 101

s^fe^

CTU SEMINAR 1)4 PHYSICS

ambivalent diffusion during the process. Therefore, we obtain a higher estimate to the realtemperature field within the sample, a lower estimate to the melting threshold etc.

For Ni-Si system, the most promising results were obtained for the energy densitiesaround 0.5 J.cm"2. A consequent analysis of the irradiated layer using AES and reflectivitydata has clearly shown that the top most layer was fully reacted. Although it was notpossible to determine the exact composition of this layer, there was a strong indication ofthe presence of a silicon reach form of compound. In addition, the measured TRR spectraallowed us to estimate the time range of reaction to be ~ 30ns. The electron microscopeimage of the processed surface does not exhibit any damages or morphological changes.

The presence of S1O2 (~ 4nm prepared by chemical etching) between the Ni and Silayers significantly prolongs the reaction time from 30 ns for simple Ni-Si system to ~ 80- 100 ns. Also a higher energy density of laser pulse (0.7 - 0.8 J.cm~2) was necessary toachieve a successful reaction between Ni-Si. SiO2 layer protects effectively from the Ni-Sireaction in the system until its temperature reaches a value high enough for the desorption.The generated vapor of desorbing SiO causes an increasing pressure at SiO2-Ni interface [7]which ruptures consequently the solid Ni layer. Clear evidence of this effect, is shown in theelectron microscope image. The removal of SiO2 layer necessary to begin the Ni-Si reactionallows us to conclude that this reaction arises at a minimum temperature of ~ 1000 K. Inthis way, a sequential character of Ni-Si reaction is overruled.

The applied energy densities together with the character of measured TRR spectra giveus evidence of a solid state reaction in both systems. To confirm this statement, model cal-culations of temperature fields within the system were performed. Computed time evolutionof the surface temperature shows there is no molten layer under 0.8 J.cm~2, which supportsthe solid state reaction model. The calculations of the Ni-Si interface temperature displaythat a minimum energy density of 0.75 J.cm"2 is necessary to reach the decompositiontemperature of SiC>2 layer. This is in a good agreement with our experiments, too.

References:

[1] VON KAENEL, H.: Mat. Sci. Rep. 8(1990), No. 5

[2] D'ANNA, E. - LEGGIER I. G. - LUCHES, A: Appl. Phys. A 45(1988), 325

[3] JELLISON JR., G. E. - LOWNDES, D. H. - MASHBURN, D. N. - WOOD, R. F.:Phys.Rev.B 34(1986), 2407

h [4] DOHNALEK, Z. - CHAB, V. - T,UKES, I. - SASIK, R.: Proc. of LAMP'92, Nagaoka,[. Japan, June 1992, 275

v, [5] CERNY, R. - SASIK, R. - LUKES, 1. - CHAB, V: Phys. Rev. B 44(1991), 4097

ft

% [6] LUKES, I. - SASIK, R. - CERNY, R: Appl. Phys. A 54 (1992), 327

II ' [7] ENGEL, T.: Surface Sci. Rep. 18 (1993), No. 4

This research has been conducted at the Department of Physics, Institute of Mathematicsand Institute of Physics and has been supported by the Grant Agency of Czech Republic,under grant No 202/93/2383. \

102 j


NEUTRON DIFFRACTION ANALYSISOF BaCuO2 AT 7 KM. DIouha, S. Vratislav, Z. Jirak*

CTU. Fac. of Nucl. Sci. k Phys. Eng., Dept. of Solid State EngineeringV Holesovickach 2, ISO 00 Praha 8

•"Institute of Physics,Na Slovance 2, 180 00 Praha 8

Key words: neutron diffraction, structure analysis, barium cuprate

One of the frequently present compounds in the process of preparation of new high -temperature superconductors is barium cuprate BaCuOj. The present research activity incuprates was stimulated by the discovery of high - temperature superconductivity. It meansthat many new cuprate systems were prepared and simultaneously the structure of manyold systems was reinvestigated. Neutron powder diffraction has proved to be importantfor understanding the structure of the oxide superconductors and related compounds. Thereason is the lack of suitable single-crystals and the need to locate oxygen atoms in thepresence of heavy metal atoms such as barium and bismuth.

The BaCuO2 cuprate was investigated at room and low temperatures by neutron pow-der diffraction. Experiments were performed at the KSN-2 diffractometer situated at theresearch reactor LVR-15 in Rez near Prague. The Cu(200) monochromator was producedA = 0.1364 nm and the resolution of the 6d/d = 7.5xlO~3 was achieved. The angle rangewas limited to 20 = 55°. The diffraction patterns recorded were refined using the Rietveldprofile method (code RIETV-FN). In the refinement process 136 diffraction lines were usedfor both the room and the liquid helium temperature measurements. Barium cuprate wassynthesized by the standard ceramic technique at 800°C and quenching to room tempera-ture. Then this compound was annealed at 200°C. The phase analysis were carried out ona diffractometer DRON-3 using CuKa radiation.

The structure of BaCuO2 was determined by a single crystal structure analysis (X -! rays) [1] and neutron powder diffraction [2]. Preliminary results of our room temperature

investigations were given earlier [3]. It was found that in a cubic cell of space group Im3m| and that there are four different eqiuvalent positions for barium, four for copper and sixt for oxygen. Our structure model was based on these assumptions. We have confirmed|.! space group Im3m with a = 1.82890(5) nm and a = 1.82806(5) nm for the room and low§3 temperature , respectively. Atomic co-ordinations x, y, s, occupancy numbers n , tempera turej£ coefficients B, and atomic positions were determined. Two copper and nine oxygen positions|i are not fully occupied. Our results which we obtained by the Rietveld refinement process§? with some C u - 0 atomic distances are summarised in Tab . l . The excess oxygen above two| i in BaCuOj+x was located by refining the A1-A3 and the A5-A10 site occupancy and it& corresponds with chemical formula of Bao.g2Cu1.07O2.31. The room and the low tempera ture

. I ' measurement are in reasonable agreement, the latter being aimed to determine the A site» coordinations more accurately.

• f[

*•• 1 0 3

CTU SEMINAR !)-l PHYSICS

atomBalBa2Ba3CulCn2C»3Cu4Cu5010203AlA2A3AlA5A 6A7A8A 9A10

.c.0000

.3608(6)

.1785(1)-.3551(8).1211(7).7917(4).0000.2500

.0751(7)

.645-1(3)

.4M5(-1).0000.0000

.0628(5).0000.0000

.0734(7).0000

.0914(11)

.0366(12)

.0539(10)

y.6888(5).3608(6).1785(4).2500.0000.0000

.5664(11).5000

.8118(9)

.6451(3)

.2332(6)1.0000.6472(5).8537(4).3331(5).5000.5000

.6423(6)

.4517(8)-.5720(9)

.5000

~.1527(5).0000

.1785(4)

.1540(2)

.1241(7).0000.0000.0000

.0751(7)-.1591(10).2332(6).0000

.1663(11).0000.0000.0000.0000.0000.0000.2500

.2955(8)

#(10-2nm)3.9(6)1.9(7)2.3(5)3.4(3)3.3(3)3.2(5)•r'-l(7)

5.0(6)3.3(5)3.0(5)2.2(4)4.2(6)3.5(6)7.1(7)2.9(6)3.1(5)3.9(6)5.3(5)2.6(4)2.3(4)3.7(6)

n1.01.01.01.01.01.0

0.88(2)0.71(3)1.01.01.0

0.46(5)0.18(3)0.13(3)1.0

0.13(4)0.18(3)0.14(4)0.24(4)0.36(3)0.18(2)

We have demonstrated the strtictural analogy of the BaCuO^ framework with zeo-lite structures, i.e. altunino-silicate framework in paulignite or faujasite. We intend toprepare such compounds to modify the barium cuprate by substitution of application inchemisorption, activated absorption, and activation in catalytic reactions may be anticipat-ed. Structure parameters of this new materials will be investigated by means of the X-rayand neutron powder diffraction method.

Results of our structural analysis of barium cuprate are prepared to print.

References:

[1] PAULUS, E. F. FUKSS, H. YEHIA, 1. - LOCHNER, U.: The Crystal Structure ofBaCuO2. Journal of Solid State Chemistry, 1991, 90, 17

[2] WELLER, M. T. LINES, D. R.: Structure and Oxygen Stoicheimetry in BuCuO2. J.Chem. Soc, ('hem. Commun., 1989, 484

[3] DLOUHA, M. - VRATISLAV, S. JIRAK, Z.: Workshop 93 - Physics, p.105, 1993,CTU Prague

This research has been conducted at the Department, of Solid State Engineering as partof the research project "Nentronograpkic Structure and Texture Analysis" and has been sup-ported by CTU grant No. StO3.

104

CTU SKMINAR 9-1 PHYSICS

OPTICAL PROPERTIESOF NOMINALLY PURE

AND CR-DOPED PLZT CERAMICSZ. Bryknar, L. Jastrabik*, A. Konakova

CTl1, Vac. of Nucl. Sci. & Phys. Eng., Dept. of Solid State EngineeringV Holesovickach 2, 180 00 Praha 8 I

"Czech Academy of Science.Inst.it ute of Physics,Na Slovance 2, 180 40, Prague 8

Key words: luminescence, optical absorption, PLZT, ceramics

The interesting properties of the PLZT (Pb,ZrxTii_xO3: La) transparent ferroelectricceramics have made it a popular subject of study in connection with its important applica-tions and diffuse phase transition problem [1—3]. It is known that suitable modifiers affectthe properties and improve the practical characteristics of ferroelectric crystals and ceram-ics. On the contrary, the phase transition and temperature-dependent soft phonon modescould lead to specific states of impurities and create unusual optical properties. However, 'Jthe microscopic nature of these mutual interactions has not been sufficiently investigated so |far. I

This is the first presentation of the optical absorption, emission and excitation lumi- 3nescence spectra of transparent PLZT 10/65/35 and 8/65/35 ferroelectric ceramics, both |undoped and with Cr2O3- f

Thin plates of thicknesses < 0.3 mm of pure as grown PLZT ceramics were transparent fup to 365 nm (3.4 eV), where O2~ —> Cr 4 + absorption edge charge transfer transition occurs. 1It is believed that the additional absorption spectrum of PLZT:Cr is characteristic of Cr 3 + [Iions in octahedral sites of nearly O\ symmetry. The states of Cr 3 + in crystal field theory fare classified by irreducible representations of 0^ group. For the 3d3 configuration of Cr 3 + ionly 4 F , 2G and 4 P levels can be taken in consideration. Their splitting in an octahedral -|crystal field (Tauii.be-Sugano diagram) is shown in the insert of Fig.1. It can be seen that \all the existing visible absorption transitions are parity forbidden and therfore they are

. ;•. very weak in accordance with our results. In our opinion, a more pronounced A absorptionf. belongs to the spin allowed 4A2 —»4T2 transition (15 400 cm"1) and it is masked by bandgap1^ absorption C: l A 2 -» 4 Ti at 21 100 cm" 1 . The very weak shoulders R at 13 640 cm" 1 and$?'. more pronounced B4 at 19 400 cm" 1 we attributed to spin- and parity-forbidden 4A2 —>2E,|fe and 4A 2 —>2T2 transitions, respectively. The value of the crystal field 10 Dq = 15 400 cm" 1

H was found from energies of the 2 E, ""Ti and 4T2 states, taken with respect to 4A2. Wep ' calculated from equations for Racah parameters B ~ 560 cm" 1 and C c; 3173 cm" 1 .H": The complex emission spectrum of PLZT 10 doped with 5 x 10"3 wt % CT2O3 under; | f excitation 340 nm is shown in Fig. 1, curve 1. The spectrum consists of an R-Iine, which in•| • various samples peaked at, 735.7 — 736.9 nm (13 589 — 13 567 cm" 1 ) , and of broadband

• |>< D-emission with a maximum at 688 nm (1.8 eV).

L f 105


350 400Wavelength ( nm ]

500 650 700 750 800

30 2B 25 24 22 20 13 15 ^ 14Wcvenumber (1C3crr"1]

13

Fig. 1: Excitation and emission spectra of PLZT 10: 5 x 10 3 wt % Cr O.-i at T — 77 K.Curve 1 — emission under excitation at 340 nm; curve 2 — excitation for emission observedat 735 nm; curve 3 — excitation spectrum for emission observed at 680 nm. Tanabe-Suganodiagram of Cr3+ ions in an octahedral crystal field is shown for C/B = 4.5 ( in insert ).

The excitation spectrum of the R-line is plotted in Fig. 1, curve 2. It has a strongmaximum at, 392 nm (25 500 cm"1) and it is probably connected with charge transfer of theelectrons from the tightly bound O2~ electronic configuration. The electrons are removedfrom the oxygen ions and transferred to the Cr3+ ions. This transition can be representedby the following formula: O2~(2p)6 -f Cr3+(3d3) -> O"(2p5) + Cr2+(3d4), the emissionoccurring after hole capture. The further shoulders in excitation spectra at 465 nm (21 500cm"1) and 520 nm (19 200 cm"1), coinciding with the C- and B- absorption bands, are dueto 4A2 ->4T1 and 4A2 ->

4T2 transition of Cr3+, respectively.The temperature dependence of the inhomogeneously broadened R-line luminescence of

Cr3+ ( % -+4A2s), which peaked at ~13 610 cm"1 at 77 K in PLZT 8/65/35, reveals a linesplit in the vicinity of 183 K. This is tentatively attributed to an unknown low temperaturelattice reconstruction or to a phase transition.

References:

[1] HAERTLING, G. II.: Ftrroclcctrics 131, 1 (1992)

[2] ISUPOV, V. A.: Ferroelectrics 131, 41 (1992)

[3] HAERTLING, G. H.: Ferroelectrics 75, 25 (1987)

I

This research has been conducted at the Department of Solid State Engineering as apart of the research project "Optical properties of alloys and defects in ferroelectric andferroelastic materials" and has been supported by grant No. 0503 from the "fond rozvojevysokych skol"'.

106


LUMINESCENCE OF DEFECTSIN MERCUROUS CHLORIDE CRYSTALS

Z. Bryknar, A. Konakova, P. Jirousek,J. Krai*, V. Potocek*

CTU, Fac. of Nucl. Sci. & Phys. Eng., Dept. of Solid State EngineeringV Holesovickach 2, 180 00 Praha 8

*CTU, Fac. of Nucl. Sci. k Phys. Eng., Dept. of Physical ElectronicsV Holesovickach 2, 180 00 Praha 8

Key words: luminescence, emission spectrum, excitation spectrum, mercurous chloride

5

.1

Mercurous chloride crystals HgaClj are highly promising for applications in opto-electro-nics because of the high value of birefringence, transparency up to 20 //m, and favourableacousto-optic figures of merit. The anisotropy of the physical properties follows from theirstructure. Crystals are formed by linear chains of molecules Cl-Hg-Hg-Cl oriented parallello axis c, this direction being the direction of optical axis. The intramolecular bondingHg-Hg is covalent and the bond of this core with the chlorine ions is ionic with a partiallycovalent character.

The aim of this work was to study the formation of the luminescence centres responsiblefor infra-red (IR.) emission and to gain more information about their properties which wouldhelp to understand the origin of IR emission bands.

Hg2Cl2 crystals were prepared by crystallization from the vapour phase. Using PIXE(Proton Induced X-ray Emission) analysis the following impurities in the crystals withconcentration higher than 1 ppm and atomic number Z > 15 were found : Br — 539 ppm,As — 60 ppm, C>e — 53 ppm, K — 3 ppm, Cr — 2 ppm, Mn — 2 ppm, and I — 1 ppm.

1.6 1.8 2.0Energy (eV)

2.2

Fig. 1: Normalized Hg2Cl2 emission spectra at 20 K for a crystal exposed at RT to unfilteredhigh-pressure xenon lamp (500 Watts) light at the distance of 6 cm for 0.5 min. Emissisonwas excited by photons (1) 4.28, (2) 3.87, and (3) 3.35 eV.

107


Normalized Hg2Cl2 emission spectra (Fig. 1) are shown for the sample exposed at RTto UV light. The emissions were excited with photons from the 3.35 — 4.27 eV spectralrange; the excitation photon energies are indicated in the figure. The irradiation of crystalswith UV light at RT enhanced the intensity of all displayed emission bands so that newluminescence centres were created. The excitation spectra of these new centres are shownin Fig.2 and are compared with the spectral photosensitivity of Hg2Cl2 crystals.

3.0 3.2 3.4 3.6 3.8Ensrgy (eV)

4.0 4.2

Fig. 2: Comparison of UV light induced excitation spectra of the infra-red emission withthe Hg2Cl2 spectral photosensitivity after ref. [1]. Curve 1 — induced excitation of emissionwith hi/ < 1.73 eV, curve 2 — induced excitation of emission with \iv < 1.23 eV.

It can be concluded from the results, that the centres responsible for IR Hg2Cl2 emis-sions are excited (i) via excitons, (ii) directly from their own excitation bands, (iii) theexcitation energy is transferred between different kinds of defect centres.

It is concluded that the IR luminescence of Hg2Cl2 originates from the structural defectsof the crystals and is not of an intrinsic nature. As the crystals contain a high concentrationof bromine, we suppose that luminescence centres are built up from Hg, Cl, and possiblyfrom Br. Therefore serious candidates for the IR luminescence centres are chlorine and/orbromide-chlorine complexes of mercury, e. g., HgClJ and HgCl^" into which Hg(II) can becomplexed [2], however, supposedly some chlorine ions can be substituted by bromide ions.Consequently, a great variety of the IR emission spectra of Hg2Cl2 is to be expected. Amore exact explanation of the nature of the IR Hg2C-l2 luminescence has not been possibleuntil now .

References:[1] BRYKNAR, Z. - HOLOUBEK, M. - WALTER, J.: Proc. Int. Conf. Defects in Insul.

Mat., eds. O. Kanest and J.M. Spaeth, Nordkirchen 1992, (World Scientific, Singapore1993), 1154

[2] FUJITA, S. - HORII, H. et al.: J. Phys. Chem., 82 (1978), 1693

i

This research has been conducted at the Department of Solid State Engineering as apart of the research project "Photochemical processes and radiation defects in halides andcomplex oxides single crystals" and has been supported by CTU grant No. 8137.

.<•# 108


GaAs PARTICLE AND GAMMA-RAYDETECTORS

Z. Tomiak, B. Sopko, I. Macha, H. EVank

CTU, Fac. of Nucl. Sci. k Phys. Eng., Dept. of Solid State EngineeringV Holesovickach 2, 180 00 Praha 8

Key words: GaAS detectors, bulk material, Schottky and ohmic contacts, semiconductortechnology

Gallium arsenide is one of the most familiar materials of III-V semiconductor com-pounds. The main properties of GaAs are as follows:The energy gap at room temperatureis 1.4 eV. The mobilities ot electrons and holes at room temperature are about 8000 cm2

V'^'1 and about 400cm2 V~1s~1, respectively. The atomic number Z of Ga and As are31 and 33. Duo to these physical properties, GaAs is a suitable material for room tempera-ture detectors. Futhermore, GaAs is highly resistant against any radiation, for example fivetimes more than silicon under neutron bombardment [lj.The epitaxial growth was the onlymeans available to produce high quality layers of sufficient thickness, generally limited toless than 100/im. Since then, high quality semi-insulating GaAs material grown by the liquidencapsulated Czochralski (LEC) method has been developed. It appears that, for the timebeing , only the undoped semi-insulating LEC material is likely to satisfy the requirementsfor the particle and gamma-ray detectors [1].

Principles of operation

A charged particle entering a surface barrier detector produces one free electron-holepair for each 4.51 eV of the energy absorbed in GaAs. The particle is brought to rest almostinstantaneously, losing almost all its energy in the production of low energy electrons by

s." impact ionisation. Gamma rays do not quite fit this pattern. At each interaction theyproduce an energetic electron, either by photoelectric or Compton process. These secondary

; electrons lose their energy rapidly by the further impact ionisation until their remainingkinetic energy is insufficient to excite an electron-hole pair. The number of electron-holepairs produced is proportional to the energy lost. Therefore, detectors can give a linearrelationship between the size of the current pulse generated and the particle energy providedinto the depletion region [2]. The electric field in the depletion region of detector, generatedby built-in and the applied bias voltages, produce a nonuniform space charge density,thevalue of which depends on the electric potential. In a n-type SI GaAs detector the space

,:;. charge density arises from ionized shallow donors and ionized shallow acceptors, ionized;1| deep level and electrons in the conduction band.

| | : Detector fabrication

The GaAs detectors were made using wafers both from Cr-doped SI GaAs and fromundoped very high purity GaAs. The material, as supplied, was by cleaned using organicsolvents and a deionised water and de-oxidized using hydrochloric acid. The dielectric silicondioxide layer was deposited on one side of wafers. The ohmic contact was made on the otherside. No implantation has been used to lower the resistivity of the bulk material behind

•i#• 109

T


the ohmic contact to avoid the subsequent thermal annealing. The wafers were loaded inthe evaporation chamber and the AuGe, Ni, An were then sequentially evaporated ontosurface of wafers to obtain metal thickness of about 350 nm for AuGeNiAu contacts. Thiscontact system is based on solid-state reactions at low temperature. The metallized waferswere annealed in a rapid thermal annealer, the so called Hot-plate furnace, under a flow offorming gas at 400° C for 1 min.[3],[4]. During the heat treatment, a conducting layer wascreated on the top of the wafer surface, highly doped by Ge. The opposite side of wafers,covered with the dielectric layer, was spun with photoresist (Shipley) before exposure withthe appropriate photomask. The silicon dioxide within the opened resist windows was etchedout until the surface GaAs was reached. The Schottky contact, was made by the gradualevaporation of 30 nm Ti followed by 50 nm Pt and 200 run Au. Lift-off of photoresist andexcess metals was achived using warm acetone. The finished devices were cut from thewafers. The t3rpical size of chip device area was 8 x 8mm2 and thickness about 200//rn.

Electrical tests

We have looked at I-V characteristics and the value of capacity at zero bias voltage.The forward current rises slowly with the voltage. This does not come surprise, as it isgiven by the high resistivity of the basic material. The reverse current is about hit A/mm2

at reverse bias 50V. The breakdown voltage is about 1801'". The capacitance was measuredat zero bias only with the frequency varying from 400 Hz to 20 kHz. The value of capacity-depends on the frequency (oO pF at 400 Hz, 30 pF at 20 kHz).The values measured do notcorrespond with the totaly depleted diode capacity, taking into account, the diode surfaceand the thickness of GaAs (20 pF). It can be concluded that the diodes are not fully depletedat zero bias. All the other tests, especially the test with the radioactive sources, have notyet been finished and still continue. We have to make the measurements of the capacityvoltage dependance to obtain the knowledge concerning the depletion layer thickness andthe charge collection efficiency.

References:

[1] BERT1N, R.: A Preliminary Study of GaAs Detectors for High-Energy Physics, N'ucl.Instr. Meth., A 29/,. (1990), 211

[2] BEAUMONT, S. P.: Charge Transport Properties of SI LEV GaAs Solid-State Detec-tors, Nucl, hist. Meth, A 326 (1992), 313.

[3] TOMIAK, Z.: Zpiisob vytvofr.vi ohmickc'ho kontaktu pro polovodicove souedstky, PatentPV 4443-86, Praha 1.986.

[4] TOMIAK, Z.: Sle'vacipcc pro vylvohnt ohmickeho kontaktu, Patent PV 7623-86, Praha1986.

This research has been conducted at. the Department of Solid State Physics, CTU Pragueas a part of the. research project Semiconductor Detectors and has been supported by CTUGrant No. 8138.

*. *' 110


APPLICATION OF RADIATIONDAMAGE IN SEMICONDUCTORS

B. Sopko, I. Macha, I. Prochazka, K. Hamal,H. Frank, M. Virius, B. Lonek, P. Hazdra*

CTU, Fac. of Nucl. Sci. & Phys. .Eng., Dept. of Solid State EngineeringV Holesovickach 2, 180 00 Praha 8

*CTU, Fac. of Electrical Eng., Dept. of MicroelectronicsTechnicka 2, 166 27 Praha 6

Key words: semiconductor technology, radiation detectors, photon counting microstripgas detector

i

The. latest results in the de .elopment of silicon pixel (PAD) detectors and of SinglePhoton Avalanche Diodes - SPADs and microstrip gas detectors (MGD) at the CTU Pragueare presented. For several years we have cooperated with the Czechoslovak Academy ofSciences, CTU and CERN on silicon PAD detectors and MGD for high energy physicsand complex detection systems construction [1]. PAD Detectors - A planar process on highresistivity Si was used for PAD detector fabrication [3]. A new a 'plication of PAD detectorswas found for the detection of radon and neutrons. For this purpose a new package has beendeveloped using metallized plastics, as shown in Fig. 1. ,<-

si detector1 0 '

l 0 '

1 0 * •

total! - C>i cnwr^rt An

to" to" io" 10" 10"Flutncc (ncm'l

Fig. 1: Package of PAD detectors Fig. 2: Current density vs. neutronfluence

An average diode leakage current of about 3 nA/cm2 was reached for depletion voltagegreater than 40 V on 4500 fi.cm WACKER silicon as the starting material. The systempresented was tested on the muon beam of the CERN LHC collider.

SPAD Detectors - In our design we concentrated our efforts on diode structure designand manufacturing technology to increase the diode active area diameter up to 100 mi-crons while still maintaining an acceptable dark countrate at room temperature and a fastresponse, as well. The SPAD we developed is a special diode structure fabricated using con-ventional planar technology on silicon. The single photon sensitivity is achieved by biasingthe diode above the junction breakdown voltage. In this stage, the first absorbed photonis capable of triggering the avalanche multiplication of carriers and a fast risetime currentis generated. The photon counting package consists of the in house manufactured SPADand the gating and quenching electronics [2]. The detection sensitivity of SPAD presented

111

CTV SEMINAR 94 PHYSICS

Fig. 3: (Left) Cross section of the microstrip gas detector. (Right) The strip pattern.

is 10~3 at the wavelength of 1.3 ftm and 10~5 at 1.5 fim. The SPAD detectors developed byus are used especially for the tracking of geodetic satellites. A ranging precision of about0.7 cm when measuring satellites at a distance of 20000 km was achieved.

Further investigation of radiation resistance resulted in evaluation of the dependence ofleakage current on radiation dose as shown in Fig. 2. The increase of dark current adverselyaffects the detector response.

Microstrip gas detectors are advantageous for these reasons:

1. Cheap construction material

2. High radiation resistance

3. Internal amplifying effect

4. Possibility of realization of large area detectors

5. Savings in electronic circuits

On Fig. 3 there is a sketch of the construction of these detectors, where the microstriplines of anodes and cathodes arc realized by vacuum evaporation of Ti and Al on glass.

References:

[1] PAVLU, .). - SOPKO, B.: Last Results in the Development of Silicon Strip avd SPADDetectors in Czechoslovakia, Experimental Apparatus for High Energy Particle Physicsand Astrophysics, edit. Gusti P., Navarria F., Pelfer P.G., World Scientific, Singapore,1991, pp. 219- 227

[2] PROCHAZKA, I. HAMAL, K. - SOPKO, B. MACHA, I.: Novel Contribution inBranch of Ultro-Fa.it Condensed Matter Speclrascopic Photon Counting System, ESS-DERC'92, Microelectronic Engineering, 19, 1992, pp. 643 - 64S

[3J SOPKO, 13. PAVLU, J. MACHA, 1. - PR.OUZA, Z. SPURNY, F. - KITS, J. -LATAL, F.: Dosimetric Parameters and Application of Czechoslovak Long Base SiliconDiode, First European Conference on Radiation and its Effects on Devices and Systems,Montpellier ( France ), September 1991, pp. 81 - 83

This research has been conducted at the Department of Solid State Physics, as a partof (he research project "Application of Radiation Damages in Semiconductor Devices" andhas been supported by CTU Grant No. 8068.

112


ANALYTICAL SENSITIVITIESFOR NEUTRON CAPTUREGAMMA-RAY ANALYSIS

S. Pospfsil, J. Kubasta, I. Stekl, M. Vobecky*

CTU, Fac. of Nucl. Sci. & Phys. Eng., Dept. of PhysicsBfehova7, 115 19 Praha 1

*Inat. of Analytical Chemistry, Ac. of Sc. of Czech Rep.Videnska 1083, 142 20 Praha 4

Key words: neutron reactions, capture, HPGe detector, detector response

A computer program was created for predicting net peak areas and their errors ingamma-ray spectra from measurements by PNCGA method [1]. The program is designedfor use in high-resolution analytical prompt 7-ray spectroscopy. It could be useful forlarge volume bulk sample measurements, bore-hole analytical measurements and for reactorneutron beam measurements.

Overall form of the gamma-ray spectra from radioactive capture is determined by: a)gamma rays from the measured sample (full energy peaks, escape peaks, Compton continu-um); b) gamma rays from the surrounding materials; c) gamma rays scaterred by surround-ing materials (producing continuous background). For the given experimental arrangementand samples with similar basic elemental matrix the shape of continuous part of spectrumis only slightly dependent on the measured sample. From the measurement in the definedexperimental arrangement and with a sample of known elemental composition the detec-tion efficiencies for FE, SE, DE peaks and the continuous background shape are obtainedas functions of E1. The continuous background shape is used to determine spectral peakuncertainties. Then the shapes of spectra of other samples can be predicted as follows.

Generally, the amount of gamma pulses N~, registered in the peak of energy Ey is givenby the following equation:

JE,, JV(1)

where $(£.'„, f) - neutron flux density; NA - Avogadro constant; c(f) - concentration ofelement; p(r) - sample density; <r(En) - capture cross section; I-,(E*,) - transition intensity innumber of photons per 100 captured neutrons; Ar - atomic weight; e'(E^, r) - peak detectionefficiency for photon with the energy Ey originated at the point of the coordinates r.

Under acceptable assumptions: a) the sample is homogenous; b) the elements are u-niformly distributed in the sample; c) the neutron field is sufficiently thermalised; d) theintensity of transition and the thermal cross section is known, the relation (1) can be sim-plified into the following form:

AT, = cPNAS f ^th(f)i'(Ey,f)dV, (2)Jv

113

if

1

[2]

[3]

[4]

Kt

(TU SFMIXAR 9! PHYSICS

whore S is the sensitivity factor defined by the equation 5 = <7(fc/-,//lr. For a given experi-mental arrangement the real detection efficiency f(/?-,) defined as a function of energy((E-,) — fv <&tl,{r)<"(Ey,r)dV can be introduced and its shape can be modeled on the basisof a calibration measurement, in the defined arrangement with a sample of known elementalcomposition. The net peak area is calculated by the program using the equation (2), thecalibrated real detection efficiency, the thermal cross sections and relative atomic weights,and the table of intensities of gamma transitions [2], [3] compiled into dBASE format datafile.

Two different experimental arrangements have been calibrated. The first one consistsof a large volume (40 1, 70-100 kg) metal ore or a brown coal [4] sample, a portable neutronsource 252Cf and a HPGe detector. The other one has been arranged on the reactor thermalneutron beam and small (5g) artificially prepared samples have been viewed by Ge(Li)detector. Calibration samples with added defined amount of sodium chloride have beenmeasured to obtain data from chlorine peaks for the efficiency calibration in both cases.

The large volume metal ore standard samples with chemically analyzed content of Crand Fe have been measured and the analytical peak areas have been compared with thevalues calculated by the program. A good agreement between measured and predictedvalues was obtained. For the samples which differ in the elemental composition and densityfrom the calibration sample more significantly, the differences in predicted and measuredareas are up to 50%. However, even such a result is sufficient to estimate and to predictroughly the interference contributions to the analytical peaks and the detection limits.

In the reactor beam experiments Cr and Fe contents have been investigated in thesamples prepared from salts of these elements. The comparison of the prediction and theexperiments has been performed with good results. The detection limits for ten otherelements in the given arrangement have been calculated using the program.

Conclusions: The presented computer program could serve as a useful tool in manyactivities dealing with analytical measurements by the PNCGA method. The most sig-nificant advantages of the program are the simplicity of the model and the speed of thecalculation.

References:

[1] CHRIEN, R. E.: Practical Uses of Neutron Capture. Gamma-rays Spectroscopy Perga-mon Press, OECD 1984, p.187-213.

LONE, B. M. LEAVITT, R. A. - HARRISON, D. A.: Prompt Gamma-rays fromThermal Neutron Capture At. Data and Nucl. Data Tabl., 26, 1981, p.511-559.

KRUSCHE, B. - LIEB, K. P.: Gamma-Ray Energies and MCl Level Scheme fromReaction 3sCl(n,t). Nucl. Phys., A386 1982, p.245-268.

JANOUT, Z. - KONICEK, J. - POSPISIL, S. et al.: Fast Non-Destruktive Determi-nation of Iron and Sulphur Content in Coal by Means of Neutron Radiative Capture.J. Radioanal. Nucl. Chem., Letters 136, 6 (1989), p.423-435.

This research has been carried out at the Dept. of Physics FNSPE as a part of theresearch project "Spin and Resonance Effects in Nuclear Interactions" and has not beensupported by any grant.

114


SEMICONDUCTOR DETECTORSFOR NUCLEAR INSTRUMENTATION

S. Pospisil, A. Gosman, K. Hamal, Z. Janout, C. Jech*, J. Konicek, J. Kubasta,I. Macha, I. Prochazka, J. Ridky**, B. Sopko, Z. Tomiak, I. Wilhelm***

CTU, Faculty of Nucl. Sci. & Phys. Engineering, Dept. of PhysicsBfehova7, 115 19 Praha 1

*Acad. of Sciences of Czech Republic, The J. Heyrovsky Inst. of Phys. ChemistryDolejskova 3, 180 00 Praha 8

**Acacl. of Sciences of Czech Republic, Institute of PhysicsNa Slovance 2, 180 40 Praha 8

***Charles Univ., Faculty of Mathematics and Physics, Nuclear CenterV Holesovickach 2, 180 00 Praha 8

Key words: Si detectors, GaAs detectors, scintillating fibres, radon, thoron, daughterproducts, alpha particles, beta particles, photons, radiation detection, detector response,Doppler effect

The project is a continuation of the research which started in 1991 under CTU grantNo. 8054 [1] and which was extended in 1992 as a CTU Grant No. 8101 [2]. The researchin 1993 has included five R k D activities.

I. Si detectors. A new type of Si detection chip has been developed for two practicalapplications (electrostatic collection of Rn and Th daughter products [3]; small thermalneutron detector for Neutron Boron Capture Therapy [4]). Results of the beam test of pixelSi detectors obtained in frame of 11D19 collaboration in CERN were accepted for publication[5].

II. Radon decay products monitoring. Two types of electrostatic collection cham-bers for measurement of Rn and Th daughter products in ambient and soil air have beendeveloped and tested (see this proceedings [3]).

J III. GaAs detectors. A series of GaAs detection chips was manufactured using' improved quality substrate material (undoped material with significantly higher mobility of• electrons which is equal to 6500 an2V~1s~l) and their response and resolution have been

tested with beta and alpha radiation and energetic protons, as well.L IV. Scintillating fibres. A special detection elements consisting of scintillation fibres| | in lead matrix intended for use in calorimetric detector of high energy particles has beeni| tested with electrons, gamma radiation and fast neutrons. Special attention was paid toH the understanding of the origin of signal produced by fast neutrons. Light transfer fromgj? scintillator fibre into small photosensitive semiconductor reading elements has also beenj$y intensively investigated.H V.Doppler broadened lineshapes. The analytical results of the investigation of the

§ Doppler broadened spectral lineshapes were presented on International Conference [6].

„ VI. Conclusions. The work carried out and results obtained within the framework of• §| (ITU grants 8054 and 8101 represent a starting point for further work in this direction. For

j | the coming period 1993-96 the continuation of research project is covered by the five grants-||' awarded by the Foundation for Dynamical Development of Universities and by the Grant

I,ff


Agency of the Czech Republic ("The Development of Plastic Scintillating Detectors forExperiments on LHC in CERN", FDDU 1993; "New Methods for Measurements of Radonand its Progeny in the Air", GA CR No. 202/93/0392, 1993-95; "The Development ofOrganic Scintillating Detectors for Research in Particle Physics", GA CR No. 202/93/0532,1993-95; "Experimental Study of Dense and Hot Nuclear Matter in the Relativistic HeavyIon Collisions", GA CR No. 202/93/1144, 1993-95; "Participation on Experiment DELPHI- Study of e+e" interactions on LEP Accelerator", GA CR No. 202/93/476, 1993-95).

References:

[l] JANOUT, Z. et al.: Instrumentation and Techniques for Measurement of Neutrons andRadon with its Progeny, CTU grant No. 1991/8054, CTU Prague, Workshop 92, PartB-Physics, 63-64

[2] POSPISIL, S. et al.: Detection Structures on Silicon and their Utilization in Nuclearand Subnuclear Instrumentation, CTU Prague, Workshop 93, Part B-Physics, 103-104

[3] JECH, C. - JANOUT, Z. - KONICEK, .1. - POSPISIL, S.: Detection of Radon andThoron Daughters using Electrostatic Collection, published in this book of abstracts,CTU Prague, Workshop 94

[4] POSPISIL, S. et al.: Si Diode as a Small Detector of Slow Neutrons. Rad. Protect.Dos. 46, 2 (1993) 115-118

[5] HEIJNE, E. H. - KUBASTA, J. - POSPISIL, S. et al.: Analysis of Detection Efficien-cies of Pixel Detectors, will be published in NIM-A PSD3, London, Sept 1993 i

[6] POSPISIL, S. - KUBASTA, J. - TELEZHNIKOV, S. A.: Doppler Broadened Line- rshapes Produced at Isotropic Velocity Distributions, 8-th International Symposium on jjCapture Gamma-Ray Spectroscopy and Related Topics, Sept 20-24, 1993, Fribourg, fSwitzerland. Proceedings will be published by World Scientific, Singapore j

i

This research has been conducted at the Department of Physics FNSPE CTU as a part \of the research project "Spin and Resonance Effects in Nuclear Interactions" and has been ;supported by CTU grant No. 8101 "Detection Structures on Silicon and their Utilization inNuclear and Subnuclear Instrumentation".

116

VTV SKMI.NAK91 PHYSICS

DETECTION OF RADON AND THORONDAUGHTERS USING

ELECTROSTA'FICC. Jech*, Z. Janou t , J . Konicek, S. Pospisil

CTT, Fac. of Nucl. Sri. & Phys. Eng., Dept. of PhysicsBfehova 7, 115 19Praha 1 J

"Institute of Phys. ('hem. k Elect rochem. JH, AS CR, •;DoK-jskova 3, 180 00 Praha 8 -:

Key words: radon, thoron, decay, alpha particles, dught.er products, electrostatic collec-tion, air !

As part of current development of methods for measuring radon with the technique ofelectrostatic collection experiments [1,2] with a very simple arrangement were carried outwith the aim of detecting both radon and thoron daughters in ambient and soil air. In ourprevious studies a high positive potential was applied to the walls of the collection chamberto achieve the collection of radon daughters on grounded detector surface [3]. This madepossible to proceed with the activity measurement already during the collection period.

We have found now, for many purposes more practical, to collect radon daughters on »an electrode held at a high negative potential while having the chamber walls grounded. -To avoid detector damage, activity measurement is carried out only after the completion of |»collection using a PSDA instrument. For such an arrangement a charged capacitor (with .1a good dielectrics) is used to maintain the necessary collection potential even for extended |collection periods (up to 24 hours). I

Experiments with such a collection set-up were carried out with the aim to investigate fthe feasibility of detection of both radon and thoron daughters in ambient air using a 10 liter |chamber and in measuring radon and thoron diffusion from the soil using a 0,5 liter chamber j[4]. For sufficiently long collection periods (e.g.24 hours) the enrichment of thoron daughters jactivity was achieved. So then comparable activities of radon and thoron daughters are |collected. This makes a separate determination of volume activity of radon and thoron jpossible. Radon and thoron daughters are resolved on basis of their decay characteristic jand/or on a spectrometric analysis of their alphas, as can be seen in Fig.l. Detection limit

fe for determining volume activity of radon in ambient air was estimated to be 50 Bq/m3 forj; , ; 10 1 electrostatic collection chamber.

%fc References:

f [l] HOWARD, A. J. - JOHNSON, B. K. - STRANGE, W. P.: A high-sensitivity detectionsystem for radon in the air, Nucl. Instr. & Meth. in Phys.Res. A293 (1990) 589-595

j | [2] JECH, C. - JANOUT, Z. - KONICEK, J. - POSPISIL, S.: Monitoring of radonj p and of its progeny. 9th Czechoslovak Spectroscopic Conference (with Internationalfe|; Participation), Ceske Budejovice, Czechoslovakia, June 22-24,1992. Abstracts from the| | j Conference, Prague, Czechoslovakia, May 1992,S9

»:"' 117

CTU SEMINAR !M PHYSICS

[3] POSPISIL, S. et al.: Semiconductor detectors for Nuclear Instrumentation, CTU grantNo 1992/8101, CTU Prague Workshop 93, Part B-Physics, 103-101, Prague, Jan 18-21,1993

..[4] JECH, C. - JANOUT, Z. - KONICEK, J. - POSPISIL, S.: Current Developments ofRadon Detection Methods Book of Abstracts from the 8th Seminar on SpectroscopicMethods in Environmental Monitoring, Nov. 15-20,1993, Liblice, Czech Republic, Spek-troskopicka spolecnost .Tana Marca Marci

10

50

RaC

100 150

Channel

Fig. 1

200

This research has been conducted at the Department, of Physics FNSPE CTU as a partof the research project "Spin and Resonance Effects in Nuclear Interactions'' and has beensupported by CTU grant No. 8101 ''Detection Structures on Silicon and their Utilization inNuclear and Subnuclear Instrumentation".

118


SOME CONNECTIONSOF DETERMINISTIC CHAOS

J . Jelen


Key words: chaos, determinism, randomness, dissipation, self-organization, synergetics

Deterministic chaos means irregular, erratic and unpredictable behaviour of dynamicalsystems described by nonlinear differential or difference equations in which the nonlinearcharacter of the process leads to a sensitive dependence on initial conditions. A differenceof two initially close states increases exponentially with time. This means that at least oneof the Ljapunov exponents is positive. The Kohnogorov entropy of the system, which givesthe rate of forgetting about initial conditions, is also positive.

Chaotic behaviour is quite common in nature. It may appear whenever nonlineardynamical models are applicable.

The role of chaos has been extensively studied in many branches of physics (turbu-lence, plasma, quantum optics, superconductivity, astrophysics...). meteorology (weatherforecast... ), biology (population dynamics, evolution...), electrical engineering (nonlinearcircuits...), cybernetics and informatics (information processing...), mechanical engineer-ing (nonlinear vibrations... ) etc. but also in sociology and economics (nonlinear models).

Thus, cooperation of specialists in different fields is very useful and desirable. In theframework of the project we cooperated with some institutes of the Czech Academy ofSciences. Selected problems of deterministic chaos and synergetics have been included insome elective courses for CTU students.

This short contribution is intended to remind two fields where the deterministic chaostheory reveals far reaching connections.

Considered as a part of synergetics, deterministic chaos sets up the way to self-orga-nization and evolution. It enables the creation and preservation of dissipative structures.In dissipative dynamical systems the chaotic behaviour takes place on the so called strangeattractors. Their geometric nature is fractal and it is possible to characterize them bynon-integer metric and information dimensions. The loss of energy (that is, its dissipationto microscopic degrees of freedom) is compensated by an input of valuable energy from

;•• outside (that is, by an input of negative entropy). Methods and mathematical concepts ofI deterministic chaos together with nonequilibrium thermodynamics are the proper tools in£ the theory of dissipative structures.; The task that the process of self-organization and evolution solves is the problem of| making two contradictory requirements compatible: the preservations of individuality and| identity of the system and its openness to the environment.I The adequate ratio of order and chaos is the solution to this problem. The boundaryI between them is, of course, an extremely delicate matter. Flows of entropy and informationI are relevant here.| Even our Earth with the life on its surface and every living organism may be considered || as very complex dissipative systems. |

•} 119 I


The second aspect of deterministic chaos we want to mention here is the relation betweendeterminism and randomness. These contradictory concepts seem to be fully incompatible.

The evolution of a system can be described in a fully deterministic way (uniqueness ofsolutions of differential equations). However, it makes good sense only if its state is describedabsolutely exactly. Unfortunately, real numbers, which are necessary in such descriptions,contain an infinite amount of information and they are inaccessible to human beings.

Finite exactness in the specification of a state is not sufficient for predictions. Theexponential divergence of neighbouring trajectories in the phase space may prevent long-term predictions of the states in the future.

If the phase space of a problem has three or more dimensions, a chaotic motion ispossible. Trajectories may create knots on themselves and may be as tangled as spaghetti.When the measurements are of finite accuracy and made in discrete moments of time, thechaotic trajectory reduces itself to a sequence of macroscopic states, incompletely specifiedfrrm microscopic point of view. Such a sequence is long-term unpredictable on the base ofthe previous measurements. It may be as random as coin tossing. Deterministic law doesn'tprevent random behaviour. By the way, coin tossing obeys the deterministic Newton's law.

In symbolic dynamics the theory of deterministic chaos meets the theory of algorithmiccomplexity. Almost all sequences are algorithmically random, i.e. they are informationallyincompressible.

Despite this fact there is no general way to prove that a given sequence is random. Thisimpossibility results from GSdel's work in mathematical logic. It follows from the theorem ofincompletness of any formal system which is rich enough to describe arithmetics. In such asystem there exist statements which are true but improvable. At this point, the deterministicchaos theory touches very deep philosophical problems.

Another wry important place where deterministic chaos has much to say to the very *ifoundations of natural science is the so called quantum chaology. It lies on the boundarybetween the classical description of nature and the quantum theory. Better understandingof the situation at this border may contribute to a deeper comprehension of the notion of ireality. '

References:

[1] JELEN, J.: Some aspects of the notion of entropy (in Czech), the 11th Conference ofCzech and Slovak Physicists, Zilina, August 1993, in press

[2] JELEN, J.: The Concept of Entropy in Ecology (in Czech), Second International Con- „ference on Ecology, CTU Prague, September 1993, Vol. 2, p. 64 E

[3] JELEN, J.: Various Concepts of Entropy and Information in Physics Workshop 93, jCTU Prague, .January 1993, Part B, p. 95 |

[4] JELEN, J.: Determinism and Randomness (in Czech), in: Kapitoly z filosofie vedy J(Chapters in Philosophy of Science), Ed.: L. Adamova, CTU Prague 1993, p. 40-57 jf

4i

This research has been conducted at the Department of Physics as part of the research |project "Selected Problems in Synergetics" and has been supported by University Develop- ;|meat Foundation grant No. f?f/,? (3807). I

I

-•r'• 120


A THEORETICAL METHODFOR DETERMINING

THE VISCOSITY OF GASESR. Cerny, F. Vodak

CTU, Faculty of Civil Engineering, Department of PhysicsThakurova 7, 166 29 Praha 6

Key words: viscosity, thermal conductivity, gas, balance equations

Most of the theoretical methods for determining the viscosity of gases use the kinetictheory to deduce approximate formulas. The elementary gas model assumes all moleculesto be noninteracting randomly moving rigid spheres [1]. If the effect of intermolecular forcesis taken into account, the theory of Chapman and Enskog [2] is usually employed. Anothercategory of methods for the gas-viscosity estimation is based on empirical approximationsusing critical quantities of the gas. These methods are called corresponding - state methods

Ml.The kinetic theory of gases also leads to the relation between viscosity and thermal

conductivity. The elementary gas model gives an approximation for monoatomic gases inthe form [1] / = —, where k is the thermal conductivity, cv the specific heat at constantvolume, i) the viscosity. Eucken proposed a modification to this equation for polyatomicgases by separating the translational- and internal-energy contributions [5].

All the- methods described above are based either on kinetic theory or empirical ap-proximations. In this paper, we have chosen a different treatment, and derive the relationbetween viscosity and thermal conductivity from the macroscopic balance equations.

We study laminar flow of a viscous gas in the laboratory coordinate system (zi, 221 £3)1assuming there exists a coordinate system (x'^x'.^s) moving with the velocity vm = (0,0,v)with respect to our laboratory system ( . T I , ^ , ^ ) , in which all the studied processes have asteady-state character. For simplicity, we also assume that the problem is one dimensionalalong the .C3-axis and neglect the influence of viscous dissipation in the balance of internalenergy. The transformation of the basic system of balance equations into the coordinatesystem (x\,x^,:) can then be carried out as follows:

| P^ dz~ dz\^dz) dz

I „ dT

| *r~% + * (4)

i J where Y is the reduced velocity of the gas, Y = v^ — v, p is the pressure. From equation[* (1), it follows immediately that pY = A, A = const. Substituting this into (4), we obtain..r"

121


the relation between the temperature T and the reduced velocity, Y = e.T = Pif T. Thus,

taking into account that for most of the gasesand internal energy balances in the form:

k dc,,cl dT << k,,f= , we obtain the momentum"dT

dT Tdc d /4 dT\ 8?idTd(. T d (\ dc\ AR dt

dz dz \cT dz J cx dz'where

Combining equations (5) and (G), and assuming in the first approximation small changes ofthe state parameters and small velocities, which leads to the condition ^ —• 0, we find thatthe solution for an arbitrary temperature field can exist only under condition that

where cx is defined by (7).Equation (8) is the new relation between viscosity and thermal conductivity which has

been derived from the macroscopic transport equations.The new by developed method for determining the viscosity of gases was tested on

three arbitrarily chosen nonpolar gases, O2, N2, and CH4, in wide temperature and pressureranges, T € [100 K, 1500 K], p € [105 Pa, 107 Pa], Five other gases, C2H6, C3H8, C4Hi0, CO,and CO2, were tested for T € [300 K, 800 K], p = 105 Pa. The results obtained using relations(26), (29) were compared to the experimental data from [6]. The comparison showed thatfor all the three gases, O2, N2, and CH4, the differences between the computed and measuredvalues of viscosity were less than 5% which is within the margin of experimental errors. Asimilarly good agreement was achieved for five other gases, C2H6, C3H8, C4H10, CO, and

'j CO2, for p = 105 Pa. Also here, the differences between computed and measured values ofviscosity were less than 6%.

; References:

I [1] REID, R, C. - PRAUSNITZ, J. M. - SHERWOOD, T. K.: The Properties of Gases• and Liquids, 3rd Edition. Me Graw-Hill, New York 19771 [2] CHAPMAN, S . - COWLING, T. G.: The Mathematical Theory of Non-Uniform Gases,f': 2nd Edition. Cambridge University Press, Cambridge 1952I [3] YOON, P. - THODOS, G.: AIChE J. 16:300 (1970)I [4] JOSSI, J. A. - STIEL, L. I. - THODOS, G.: AIChE J. 8:59 (1962)f' [5] EUCKEN, A.: Phys. Zeit. 14:324 (1913)I [6] LIDE, D. R. (ed.): CRC Handbook of Chemistry and Physics, 72nd Edition. CRCI Press, Boca Raton 1991

j | Tkis research has been conducted at the Department of Physics and has been supported-,.. I by Faculty of Civil Enginnring grant No 1103.


NONLINEAR MODELS IN QUANTUMPHYSICS

J. Tolar*, M. Havlicek**, L. Hlavaty*, P. SCovicek**, C. Burdik***

*CTU, Faculty of Nuclear Sciences & Physical Engineering, Department of PhysicsBfehova7, 115 19 Praha 1

**CTU, Faculty of Nuclear Sciences & Physical Engineering, Department of MathematicsTrojanova 13, 120 00 Praha 2

***Charles University, Faculty of Mathematics & Physics, Nuclear CentreV Holesovickach 2, 180 00 Praha 8

Key words: quantum theory, nonlinear integrable models, quantum groups

Mathematically rigorous investigations of nonlinear systems in classical and quantumphysics carried on our research of 1991-92 in the following three main areas:

I. General quantum theory on nonlinear manifolds: [1] For the generalized two-solenoidAharonov-Bohm effect the scattering cross section was calculated in the asymptotic region.[2, 3] Quantization on discrete finite space was studied in connection with the orderingproblem; a new definition of coherent states was given.

I II. Lie algebras, quantum groups and their representations describing new symmetriesI of nonlinear integrable quantum models: [4, 5] The dressing transformations for quantumj groups and quantum orbits for SUq(2) were derived. [6] Quantum Grassmann manifolds were•\ investigated as important models for representation theory. [7-10] Quantum supergroups'', and quantum braided groups were studied as new algebraic structures important in quantum.; physics. [11-13] Bosonic realizations were constructed for U<,(sl(n + 1,C)) and Uq(so(2n+1)).': [14] The duality between the quantum algebra U<,(sl(n)) and the Hecke algebra //m(</2) was

exploited to construct representations of Ug{sl(n)). [15-17] Universal /2-matrix was applied; in the theories of quantum groups and of nonlinear integrable models. [19-21] The results

on graded contractions of B2 were further extended to A3. [22] A series of papers onquantum groups were summarized in the habilitation dissertation. [23] Introductory noteson quantum groups were prepared for the students.

References:

[1] STOViCEK, P.: Scattering on hvo solenoids, Phys. Rev. A, 1993 (in press).II-

[2] CHADZITASKOS, G. - TOLAR, J.: Fcynman path integral and ordering rules ondiscrete, finite space. Int. J. Theoret. Phys., 32 (1993), pp. 517-527.

[3] CHADZITASKOS, G. - TOLAR, J.: Quantization on Zn and coherent states overZn x Zn, (to be published).

[4] JURCO, B. - STOVICEK, P.: Quantum dressing orbits on noncompact groups, Com-mun. Math. Phys., 152 (1993), pp. 97-126.

123


[5] ST OVICEK, P.: Quantum line bundles on S2 and method of orbits for SUq(2), J. Math.Phys., 34 (1993), pp. 1606-1613.

[6] STOVICEK, P.: Quantum Grassmann manifolds, Commun. Math. Phys., 1993 (inpress).

[7] HLAVATY, L.: On quantum supergroups, Group Theor. Methods in Physics (edited byM. A. del Oimo, M. Santander, and J. Mateos Guilarte), C1EMAT 1993, pp. 127-130.

[8] HLAVATY, L.: Examples of quantum braided groups, Proc. of XIII Winter SchoolGeometry arid Physics, Zdi'kov 1993, (to be published in Rend. Circ. Math. Palermo.)

[9] HLAVATY, L.: Introduction to quantum braidtd groups, Proc. of III Wigner Sympo-sium, Oxford 1993 (to be published).

[10] HLAVATY, L.: Quantized braided groups, (submitted to J. Math. Phys.).

[11] BURDIK, C. - NAVRATIL, 0 . - THOMA, M.: The realizations of the Lie algebra G2,Czech. J. Phys. 43 (1993), pp. 697-776.

[12] BURDIK, C. - CERNY, L. - NAVRATIL, O.: The q-boson realizations of the quantumgroup Uq{sl(n + l .C)), J. Phys. A: Math. Gen., 25 (1993), pp. LS3-L88.

[13] CERNY, I,.: Bosonic realization of the quantum group Uv(so(2n -f 1)), diploma thesis,CTU-FNSPE, Prague 1993 (in Czech).

[14] BURDIK, C. - KING, R. C. - WELSH, T. A.: The explicit construction of irreduciblerepresentations of the quantum algebras Uq(sl{n)), Proc. of III Wigner Symposium,Oxford 1993 (to be published).

[15] BURDIK, C. - HELLINGER, P.: The quantum double for a nonstandard deformationof a Borel subalgebra of sl(2, C), preprint PRA-HEP-93/2, Prague 1993.

[16] HELLINGER., P.: Quasi-triangular Hopf algebras, diploma thesis, Charles University,Prague 1993.

[17] TOMASEK, R.: Integrable models in statistical physics, Yang-Baxter equations and theBethe ansatz, diploma thesis, Charles University, Prague 1993 (in Czech).

[18] LEVINSKY, R.: On noncommutative differential calculus and the quantum group jGLJ

a<p(2), diploma thesis, CTU-FNSPE, Prague 1993 (in Czech). \

[19] de MONTIGNY, M. - PATERA, J. - TOLAR, J.: Graded contractions and kinematicalgroups of spacetime, Journal of Mathematical Physics, 1993 (in press).

[20] TOLAR, J. - TRAVNICEK, P.: Z2 x Z2-graded contractions of the Lie algebra A3, (tobe published). j

[21] CHADZITASKOS, G.: Quantum mechanics on Zn and q-deformed Heisenberg-Weyl" algebra, Quantization and coherent states methods, 1993 (to be published).

[22] BURDIK, C.: Quantum groups, habilitation thesis, Charles University, Prague 1993 (inf Czech).

| , [23] HLAVATY, L. - TRAVNICEK, P.: Quantum groups for beginners, lecture notes, FN-| SPE CTU, Prague 1993 (in Czech).if

H This research has been conducted at the Departments of Mathematics and Physics of4 . the FNSPE as part of the research project "Nonlinear models in quantum physics" and has$p been supported by CTU grant No. 8002.

I* 124

CTU SEMINAR !H PHYSICS

N-N ELASTIC SCATTERINGAND TRANSMISSION EXPERIMENTS

P. Bach10, J. Ball2, L. S. Barabash3, R. Binz4, J. Bystricky5, P. A. Chamouard2,Ph. Chesny2, M. Combet2, Ph. Demierre1, J. M. Fontaine2, G. Gaillardlb,J. P. Goudour6, R.Hess1, Z. Janout3c, Z. F. Janout", V. A. Kalinnikov3,

Yu. M. Kazarinov3, B. A. Khachaturov3, A. Klett4, R. Kunne2, C. D. Lac2e,J. M. Lagniel2, F. Lehar5, M. C. Lemaire5, A. de Lesquen5, E. L. Lomon1^,

D. Lopiano7, M. de Mali5, V. N. Matafonov3, G. Milleret2, F. Perrot-Kunne5,I. L. Pisarev3, A.A.Popov3 , D. Rapin1, L. van Rossum5, E. Rossle4, J.L. Sans2,

H. Schmitt4, Ph. Sormani'8, H.Spinka7, Yu. A. Usov3, B.Vuaridel1

1) DPNC, Univ. of Geneva, 24, q. Ernest-Ansermet, 1211 Geneva 4, Switzerland

2) Laboratoire National SATURNE, CE Saclay, 91191 Gif sur Yvette, France

3) LNP - JINR, Dubna, 101000 Moscow, P.O.Box 79, Russian Federation

4) Faculty of Physics, Freiburg University, 7800 Freiburg im Br., Germany

5) DAPNIA, CE Saclay, 91191 Gif sur Yvette Cedex, France

6) C.E.N.B., Doinaine du Haut-Vigneau, 33170 Gradignan, France

7) ANL-HEP, 9700 South Cass Ave., Argonne, IL 60439, USA

Present addresses :a) College Rousseau, 16A, av. du Bouchet, 1209 Geneva, Switzerlandb) Schlumberger hid., 87, rte de Grigny, 91130 Ris Orangis, Francec) FJFI, Czech Tech. Univ., Brehova 7, 11519 Prague 1, Czech Republicd) Comp. Center, Czech Tech. Univ., Zikova 4, 16635 Prague 6, Czech Republice) Inst.Nat.des Telecom. 9, rue Charles Fourier, 91011 Evry, Francef) Center of Theoretical Physics, MIT, Cambridge, MA 02139, USA

• g) Brainsoft Consulting S.A., Cusinand 46, 1285 Athenaz, Switzerland

It is essential to have a clear understanding of the nucleon-nucleon interaction as it; impacts on a variety of topics in particle physics as well as in nuclear physics. A knowledge\ of the nucleon-nucleon (NN) interaction is essential in calculating the scattering of nucleons- from nuclei. The elastic NN scattering is the basic reaction necessary to understand the§ nuclear force. Spin effects of the nucleon constituents can be investigated (see ref.fl]).| Here we treat a part of the NN program at SATURNE II carried out by the present|!, large international collaboration. Results concern np and pn elastic and quasielastic scat-% tering and transmission measurements at Saclay. Polarized proton and neutron beams in'%. conjunction with poiarized proton and deuteron targets (PPT or PDT) were used in theseH measurements. The study aims to reconstruct unambigously the five complex amplitudes% of the np or pn reactions over the energy domain of 0.8 to 2.7 GeV. Data taking for the npP part is completed. The pn part started recently.

f| The beam line, the PPT and PDT, the experimental set-up, the trigger and MWPC% electronics, the data acquisition and OFF-LINE analysis are described in ref.[2]. We use the

f•

, :F 125


NN formalism and the four-spin notation of observables from ref.[3]. The beam polarizationPg was oriented in the normal (r7), sideways (s) and longitudinal (k) directions. The PPTpolarization Pf was oriented along n and /\ The polarization of recoil particles was mea-sured in the n and J5T directions. Our collaboration also determined the total cross sectiondifferences A<TT in np transmission [4]. Polarized neutrons with maximal energy of 1.15GeV are produced by break-up of vector-polarized deuterons on a Be target. The singlescattering observables[5] AMno, Aooon, Aoonn, Aookk, Aoosk were measured with a high accu-racy. As examples see Figs 1,2,3. The rescaUering parameters Donon, Do,»ok* A'ormo, A'c,s"so,KOs"ko, NO,M-, N^^ were measured simultaneously with lower statistics. Each observablehas been measured at 6 to 8 energies. This complete set, together with known differentialcross sections makes it possible to reconstruct all np scattering amplitudes directly fromobservables. Results above 0.8 GeV were determined for the first, time.

Fig. 1

Fig. 3 -aV-J-3frJ

0 ' ' w ' 90 120' ' 150'

1 5 0 I S O

It is possible to reach an energy above 1.1 GeV for the np system using incident protonsscattered on target, neutrons. A 6LiD PDT was used for simultaneous measurement of paand pp quasielastic scattering. First measurements of AOOnO-, Aoot,H, Auonn. Doncm, and A'OBnowere performed between 1.1 and 2.4 GeV.

References:[1] LECHANOINE-LELUC, C. - LEHAR, F. Rev. Mod. Phys. 65 (1993) 47[2] BALL, J. et al.: Nucl.Instrum.Met.hods A327 (1993) 308

[3] BYSTRICKY, J. - LEHAR, F. - W1NTERNITZ, P.: J. Phys. (Paris) 39 (1978) 1

[4] BALL, J. et al.: Zeil.scjnift fiir Physik C, to be published

[5] BALL, J. et al.: Nucl.Phys. A559 (1993) 477, 489, 511

126


NARROW STRUCTUREIN pp SCATTERING AROUND 2.11 GeV

J.Ball1, L. S. Barabash2, M. Beddo3, A. Boutefnouchef, J. Bystricky5,P. A. Chamouard1, M. Combet1, Ph. Demierre6, J. M. Fontaine1,

V. Ghazikhanian4, D. Grosnick3, R. Hess6, Z.Janout20, Z.F.Janout f i\V. A. Kalinnikov2, T. Kasprzyk3, Yu. M. Kazarinov2, B. A. Khachaturov2,

R. Kunne1, J. M. Lagniel', F. Lehar5, J. L. Lemaire1, A. de Lesquen5,E. L. Lomon6c, D. Lopiano3, M. de Mali5, V. N. Matafonov2, G. Milleret1,

F. Perrot-Kunne', I. L. Pisarev2, A. A. Popov2, D. Rapin6, J. L. Sans1,H.Spinka3, Yu.A.Usov2, B.Vuaridel6, C. A. Whitten4

1) Laboratoire National SATURNE, CE Saclay, 91191 Gif sur Yvette, France2) LNP - JINR, Dubna, 101000 Moscow, P.O.Box 79, Russian Federation3) ANL-HEP, 9700 South Cass Ave., Argonne, IL 60439, USA4) UCLA. 405 Hilgard Ave., Los Angeles, CA 90024, USA5) DAPNIA, CE Saclay, 91191 Gif sur Yvette Cedex, France6) DPNC, Univ. of Geneva, 24, q. Ernest-Ansermet, 1211 Geneva 4, Switzerland

a) Present address: Faculty of Nuclear Sciences and Physical Engineering, Czech TechnicalUniversity, Brehova 7, 11519 Prague 1, Czech Republic

I)) Present address: Computing Center of the Czech Technical University, Zikova 4, 16635Prague 6, Czech Republic

c) Present address: Center of Theoretical Physics, MIT, Cambridge, MA 02139, USA

A structure in the energy dependence of pp elastic scattering observables and amplitudesat fixed angles has been suggested by a direct reconstruction of the pp scattering matrix at11 energies between 0.83 and 2.7 GeV [1]. Anomalies in the pp analyzing power around Tkin= 2.1 GeV were first observed in the ANL-ZGS measurements [2]. At the same energy, theexistence of a dibaryonic resonance in the ' So partial wave was predicted [3]. The predictedstructure, as well as another one near 2.54 GeV, is also suggested in the total cross sectiondifference Aox [4]. Additional evidence for this structure is suggested by the measurementof the analyzing power and j ^ of the reaction pp — di:^ centered around a mass of 2.7 GeV[5].

The present large international collaboration checked evidence for the structure in a dedi-cated experiment. It used the SATURNE II polarized proton beam and the Saclay polarizedproton target (PPT). The experimental set-up is described in ref.[6]. Here we use the N-N formalism and the four-spin notation of observables from ref.[7]. The beam and targetpolarizations PB and Py were oriented perpendicular to the scattering plane.

The angular dependence of the pp elastic scattering analyzing powers Aoono = A^m andthe spin correlation parameter Aoonn were measured from 60° to 97°CM at 14 energiesbetween 1.96 and 2.23 GeV. The observables Dmm and A'onno were simultaneously measuredwith lower accuracy. The Aoono energy dependence at fixed angles shows two well pronounced

—-127


maxima, at 2.04 and 2.16 GeV, separated by a minimum at 2.11 GeV. Fig. 1 shews theenergy dependence of Aaom, averaged from 60" to $7°CM together with former data [8](connected by a solid line).

i

0.15

0.10-

005 -

as

OA

as

Y U** 1 .: T: *

ôonnP-P

90° CM '

} j ;-

2.0 22Tkln(G«V)

Fig. 1 Fig. 2

A rapid decrease of the Aoonn energy dependence at. 90°CM is observed in this energyregion[9,10] (Fig. 2). This agrees with the behavior of Aoonn predicted on the basis of anexotic six-quark structure[3] (solid line in Fig. 2). ABOnn{90°CM), together with the knowndifferential cross section, allows the determination of the absolute value of the pure spin-singlet amplitude. The energy dependence of this amplitude shows a shoulder centered at2.11 GeV, corresponding to a possible resonance with a total mass of 2.735 GeV and anestimated width of 17 MeV.

The obtained results need a confirmation by further measurements. It is desirable tocheck the suggested spin-singlet resonance in the ' 5 0 partial wave as well as the next one inthe J£)2 wave at Tkin around 2.5 GeV.

References:

[1] LAC, C. D. et al.: J. Phys. Fiance 51 (1990) 2689[2] SPINKA, H. et al.: Nucl. Instrum. Methods 211 (1983) 239

[3] GONZALES, P, - LAFRANCE, P. LOMON, E. 1.: Phys.Rev. D35 (1987) 2142

[4] AUER, I. P. et a.l.: Phys. Rev. Lett. 62 (1989) 2649

[5] YONNET, J. et al.: Proceedings of the 7th International Conference on PolarizationPhenomena in Nuclear Physics, Paris, edited by A.Boudard and Y.Terrien, ColloquePhys. 51 (1990) C6-379

[6] BALL, J. etal: Nucl.Instrum.Methods A327 (1993) 308[7] BYSTRICKY, J. - LBHAR, F. - WINTERNITZ, P.: J.Phys. (Paris) 39 (1978) 1[8] PERROT, F. et al.: Nucl.Phys. B294 (1987) 1001[9] BALL, J. et. al.: Phys.Lett. B, to be published[10] LEHAR, F. et al.: Nud.Phys. B294 (1987) 1013

128

Section 4

DEVELOPMENT

OF CTU STUDY

CTU SEMINAR 94 DEVELOPMENT OF CTU STUDY

INTERACTIVE EDUCATIONALPROGRAMS FOR MULTIMEDIA

SYSTEMSR. Sykora*, Z. Zochova*, G. Dohnal,

L. Kolek, S. Vavra, C. Zlatnik

CTU, Fac. of Meclianical Eng., Dept. of Technical MathematicsKarlovo nam. 13, 121 35 Praha 2

*CTU, Publishing House, Audiovisual and Technical CentreTrojanova 13, 129 00 Praha 2

Key words: educational program, video-computer program, multimedia system, graduatedhelp, selfregulative branching nodes

Dealing with complex application type tasks forms a significant part of the teaching ofmany subjects at Technical Universities. Independent solution of complex tasks representsvery hard problem for a great numbers of students. In these situations, control of theteaching process can increase success by means of a program of teahging, which stimulatesand forms an independent and creative approach to solving tasks on the part of students.Programs of this type must be based on interaction witli the student and have to proceedfrom pedagogical and psychological theories.

Our presumed conception of teaching programs is supported by qualitative analysisof subject matter and by experimental research into teaching programs at the faculty ofMechanical Engineering CTU.

Pedagogical basis of the conception:a. Program Teaching - the application of internal and external feedback as a significant

method of effective control of the teaching process and principles ofteachers working at theirown pace and respondingactively.

b. Problem Teaching - transferring a problem from the end of teaching to its beginning,teaching to intensification of motivation and increase in memory retention.

Psychological basis of the conception:a. Rubinstein's Theory of Transfer - use of the transfer of solving principle from the

easier task to the harder task.b. Kulic's Theory of Mistakes - formation of positive conditions for reasonable correction

of mistakes, and use of the principle of selfregulation.For effective teaching control we have formed a methodology based on the integration

of priorities and the elimination of the imperfections of the above mentioned psychodidacticsystems.

a. Selfregulative branching nodes method - this finds its function in placesin a program,where the student and the information bearer are able to find the mistake, but they are notable to identify and interpret it.

b. Method of teaching with graduated help - If the student is not able to deal withthe complex of problems with what he is faced, or if he deals with it badly, he receives asuccession of hierarchically ordered help.

131

i3


The above described methods of teaching management can be applied in teaching pro- '•grams presented by computer. However, the replacement of our videoprogram by a teachingcomputer program above could impact many important factors in the teaching process. Thequalitative analysis of priorities and imperfections of the two media lead us to the interactivesystem: computer - videoplayer - student. The goal of forming a teaching program basedon this system is to apply the first or second medium in a place where the effect can beoptimal. The control element of this system is the computer.

The interactive system has been created in several variants. The latest consists of a :

16-bit PC and a VHS videoplayer. The technical device completing the whole system is theinterface which transmits the control signals between the computer and videoplayer.

The work of the system is controlled by the computer program. This program consists «,of a sequence of separate blocks determining which part of the teaching program should be | fpresented by the videoplayer and which should be presented by text from the graphic com- v.;;puter output. The basic elements of this interactive videoprogram are separate sequences :•?recorded on videotape with indicated codes and recordings of text and graphs contained %in the microcomputer's memory. The course of the interactive program is controlled by a V*computer program in connection with signals coming from the videoplayer and computer >£keyboard. The technical solution will centre on the creation of an interface for IBM PC '•!standard and on the chosen type of videoplayer, the desirable program equipment including icomputer control programs for the multimedia system. ;.

The methodology of graduated help and selfregulative branching nodes were applied Hin interactive educational video-computer programs: "Application of the First Order Li- inear Differential Equation (Rectilinear Movement)", "Linear Analytic Geometry in Space - MApplications11, "Linear Regression". j ;

Our purpose is to focus on the identification of mistakes and to reinforce the diagnostic |jfunction of our program to the intensification of adaptability of teaching control. For thispurpose we have built workplaces in the Faculty of Mechanical Engineering and in two highschools in Prague, where the multimedia programs will be presented.

The aim of the program is not only to teach mathematical problems, but to teach thetransfer of mathematical knowledge to other situations, and to generalize the problems. Theprograms instruct the students in analytical and synthetic thinking.

References:

[1] KOLEK, L. - SYKORA, R. - VAVRA, S. - ZOCHOVA, Z.: Koncepce tvorby videopro-gramu. Alma Mater 1/4 1990-91

[2] KOLEK, L. - SYKORA, R. - VAVRA, S. - ZOCHOVA, Z.: Interactive Programs forMultimedia Systems. Proceedings of the International Conference on Trans-EuropanCooperation in Engineering Education, Prague 1992, pg.234-236

This research has been conducted at the Department of Mathematics Faculty of Mecha-nical Engineering and at the Audiovisual and Technical Centre CTU as a part of the researchproject "The Creation of Interactive Educational Programs for Multimedia Systems" and hasbeen supported by the Ministry of Education, Youth and Physical Training Grant No,2-III-12-92/93.

|

132 \

("IT SEMINAR 9-1 DEVELOPMENT OF ("IT STUDY

MULTIMEDIA PROGRAMMESFOR LANGUAGE TEACHING

IN AUDIO-VISUAL STUDYAT THE CTU IN PRAGUE

M. Tlalkova, L. Mikysa*

CT1', Fuc. of Electrical Eng., Dept. of Foreign LanguagesZikovat, 166 27 Praha G

*CTT, Publishing House, Audio-visual and Technical CentreTrojanova 13, 120 00 Praha 2

Key words: programme, multimedia, teaching, language, audio-visual, computer

A workplace where students can stud}' using multimedia programmes has been installedat the Faculty of Electrical Engineering of the Czech Technical University in Prague. Twomultimedia English teaching programmes are now available there. Both programmes are forintermediate students of English. These are 'Power Generation" and "'Telecommunications,Part I" intended for students from the respective specializations of study. The workplace isequipped with a PC/AT personal computer with an EGA-card and colour monitor and witha TV-set and video cassette recorder which is controlled by the computer through a specialinterface card. This arrangment enables the presentation of the subject to be taught not onlyin written form but also by sound and picture. Sound is especially important in languageteaching programmes. Although the utilization of the computer-controlled video cassetterecorder has some disadvantages, it enables multimedia programmes to be provided at lowcost even if the number of copies of the programme is small. The multimedia programmeconsists of a text file with the corresponding video record and possibly other files which areinterpreted by a special interpreting programme common for all multimedia programmes ofthis kind. The interpreting programme uses a hypertext technique applied not only to thetext but also to the graphics and parts of the video recording. The utilization of a simplewindows technique, context oriented help and mouse facilitates work with the programmes.

The programmes "Power Generation" and "Telecommunications, Part I" are of similarstructure. Both programmes consist of several parts which can be selected through the mainmenu. Although the order of individual parts can be selected arbitrarily, it is recommendedto follow the order of items in the main menu. If the student wants only a brief survey ofthe programme, he can switch off its video part.

A typical path through the programme is as follows: the student is introduced to theterminology of the subject by several short articles in English. He can read the text on thescreen of the monitor and at the same time listen to a native American speaker reading thetext. Technical terms and some other words in the English text, which is displayed on thescreen of the monitor, are emphasized by different colours. Translation of these words canbe easily obtained by placing the cursor on these words and pressing down the button onthe mouse. The Czech equivalent of the word accompanied with some examples of its usageis then displayed in the lower part of the screen. It is possible to get the Czech translation

133

CTU SEMINAR !M DEVELOPMENT OF CTU STUDY

of the whole English text. In the Czech translation, which is displayed simultaneously withthe original English text, some words may also be emphasized by colour. Placing the cursoron them and pressing down the button on the mouse, the student can get some commentsconcerning the translation technique or some interesting grammar phenomena.. If a printeris connected to the personal computer, it is possible to print out the original English text,its Czech translation, the translation of the selected individual words with examples of theirusage or comments concerning the translation or grammar. Each of the short articles inEnglish is accompanied with a cloze test. The cloze test makes use of the same article withsome words missing, giving the first, character of the word. The task is to fill in the missingparts of these words. At the end of the test an evaluation is done and all the parts of wordswhich were missing are displayed in the correct form in green or red. (Ireen means thecorrect answer and red the opposite. If the cursor is placed on any part of a word displayedred, and the button on the mouse is pushed down, the part originally filled in by the studentis displayed for a short while. In this way the studeni can check his mistakes. The numberof filled in words and the percentage of successful answers is registered and displayed in thelower left corner of the screen.

A selected vocabulary of fundamental terms with examples of their usage form thenext part of the programme. The written form of each term with its Czech equivalent, andexamples of usage are displayed on the screen and. simultaneously, the corresponding partof the video record of the speaker reading the displayed text is provided. Individual termsor the survey of terms can be selected from the menu. If the survey of terms is selectedand the video part is switched on, all terms included in the vocabulary are automaticallysequentially displayed.

The next, part of the programme is an exercise in which the student fills in technicalterms used and explained in previous parts of the programme. The evaluation of this Aexercise is similar to that described above. In the next exercise the student selects the Scorrect form of verbs in displayed sentences using the multiple-choice technique. The next |part of the programme is a dictation, which has three forms: dictation of individual words, $dictation of individual sentences, and dictation of short articles. In the second and third |cases the dictated text is displayed on the screen with some words missing. The task is |to fill in the missing words according to the dictation. The evaluation can be done either |immediately after each word written or at the end of the dictated part. The next part of the |programme is listening comprehension. A video record where the speaker is saying short |statements is provided. Then a question is displayed on the screen and the student answers |it using the multiple-choice technique. The next part of the programme is an alphabetical |list of vocabulary used in the texts. It is possible to display the examples of usage of the ';individual words by using the cursor and the push-button on the mouse. The last, part of '!

the programme is a vocabulary test with immediate evaluation. |The workplace was installed in the audio-visual study last year and since then many |

students have been using the programmes described here. Further multimedia English ]teaching programmes are being prepared. \'.'

This re.ifnirh has been conducted tit Ihr Audio-visual and Technical Centre of the CTU. j

134


A COMPUTERIZED COURSEOF COMPUTER ALGEBRA

L. Drska, J. Limpouch, R. Liska, M. Sinor, J. Vondrasek

CTU, Fac. of Nucl. Sci. & Phys. Eng., Dcpt. of Physical ElectronicsBfehova7, 115 19 Prague 1

Key words: computer algebra, computer aided instruction, hypermedia

In computer algebra ( symbolic and algebraic computation o« computer ) keyboardand display replace the traditional pencil and paper in doing mathematical computation.Integrated computing systems are interactive program packages which include consistent fa-cilities for computer algebra, numerical computing and high-quality computer visualization.

Integrated computing systems [1] ( Mathematica, Maple, Reduce, Axiom, etc.) arepowerful tools for mathematics, science and engineering and have too a high applicationpotential for economy and humanities. They find also their way in education process andnowadays they represent a novel effective strategy to teach mathematics, physics, chemistry,

• foundations of high technology and other disciplines [2].'• To support progressive approaches to master and effectively use integrated computinge systems as a very important product of information technology, a hypermedial presenta-," tion/educational program "Computer Algebra and Integrated Computing System51 has beenI developed. The program consists of following chapters:

| Introduction. Brief explanation what computer algebra (CA) is and why is it useful isi given. The short history of CA is outlined.i*

I Algorithms for algebraic computation. Theoretical background of CA systems is ex-\ plained. Algebraic structures as number domains and algebraic expression domains

which are used in CA are introduced. Arithmetic and simplification of the algebra-ic structures are discussed. Algorithms for calculating of greatest common divisor,resultant, solution of equations, derivation, series summation, integration, solutionof ordinary differential equations, polynomial factorization and quantifier eliminationare described. Several basic algorithms are explained in detail, others are only briefly

; introduced.

; Integrated mathematical systems. IMS Axiom, Derive, Macsyma, Maple, Mathemati-;*;' ca, Reduce are described. Special features of programming in IMS are mentioned.Kp- Basic capabilities of IMS. Capabilities of IMS Derive, Maple, Mathematica and Reducep are demonstrated on various simple examples. Examples include algebraic and graph-s'* ical facilities of IMS.

kApplications of computer algebra. Application areas of computer algebra are outlined.

Four case studies (perturbation methods, general theory of relativity, collision integralsin plasma physics, numerical solving of partial differential equations) are presented toprovide a deeper insight into methods where CA can be used and to demonstrate itspower.

135


I

Another sources for study. Basic ('A and IMS literature is given. Electronical informa-tion sources from this area arc presented.

The presentation/educational program has been realized in the hypermedial systemEncyklopedie which allows to combine textual and graphical information in hypermediadocument. The document is composed of cards, cross-referenced by links, which alloweasy moving and navigation in the document. An example of a card showing parametricalplotting in Mathematica is provided in Fig. 1. The document has been prepared in Czechlanguage, its translation into English is planned.

• paranetricku zadana piocha

dbell - ParaaetrlcPlot:3D[<Sin[t], SinlZtJ 5in(u], Sin[2t] Cos[u)),

(t,-Pi/2,Pi/2>, (u,0,2 Pi), Ticks -> Hone ]

Fig. I: A part of one card showing parametrical plotting in Mathematica.

References:

[1] HARPER, D. WOOFF, C. HODGKINSON, D.: A Guide to Computer AlgebraSystems. John Wiley & Sons, Chichester, 1991.

[2] DRSKA, L. - L1SKA, R. SINOR, M.: Computer Algebra and Integrated ComputingSystems in Education of Physical Sciences. In : Physics Computing 92 : Proceedingsof the 4th International Conference, edited by R.A. de Groot and J. Nadrchal. WorldScientific, Singapore 1993, p. 320 321.

This research has been conducted at the. Department of Physical Electronics of CTU asa part of the research project "Facility for the Application of Integrated Computing Systems"supported by the grant V SOI of the Czech Ministry of Education.


I

COORDINATED SYSTEMOF PROGRAMS

FOR PHYSICS INSTRUCTIONL. Drska, J. Limpouch, M. Sinor, S. Vagner,

J. Vondrasek

CTU, Fac. of Nucl. Sci. & Phys. Eng., Dept. of Physical ElectronicsBfehova 7, 115 19 Prague 1

Key words: computer aided education, hypermedia, physics instruction

Computers can have powerful effect on the way we teach physics. This contributionintroduces a systematic approach to effective applications of computer aided education inundergraduate physics curriculum - the Coordinated System of Programs (CSP) for theMS DOS environment. The scheme of the system is shown in Fig. 1. Its most importantcomponents are described in Tab. 1.

Windows MS DOS Environment Utilities

Courseware Hypermedia documents

Quattro Pro to*** Turbo Pascal

Fig. 1: Structure of the CSP for MS DOS Environment

Application of the CSP should support the complex use of the computer technology(general, educational and professional) with expected positive effects on the process of ac-quisition of fundamental physicist's skills and allow to develop research - based instructionalstrategies (Overwiev, Case Study (OC3) physics etc.).

137


tft.

Teacher / Author level subpackage

- GENIE: Authoring system for courseware development [J]

- ENCYCLOPEDIA: HyperCard system for hypermedia documents preparation

and browsing [2]

Student / User level subpackage

- Quattro Pro: Electronic spreadsheet for prompt formula evaluation and

numerical data processing

- Famulus: General program for numerical simulation and computer

visualization

- Derive: Small computer algebra both for tutoring and students

computation

- Turbo Pascal: Standard high-level programming language with integrated

development environment

Tab. 1: Key components of the CSP

The most effective practical implementation of the CSP in the education process repre-sent, fully computerized elective courses with maximum work done in the computer labora-tory, which support and extend the conventional introductory physics course. The curriculafor two versions of such courses have been elaborated [3], one of them is currently tested inreal conditions.

References:[1] DRSKA, L. - JERIE, T. - LISKA, R. - SINOR, M. - TUREK, J. - VONDRASEK, J.:

The Authoring System GENIE and Its Applications. In: CALISCE 91 : Proceedings ofthe International Conference on Computer Aided Learning and Instruction in Scienceand Engineering. (Presses polytechniques and universitaires romandes, Lausanne 1991),p. 251-256.

[2] DRSKA, L. - SINOR, M. - VONDRASEK, J.: Coordinated System of Programs forUndergraduate Physics Instruction. In: Physics Computing 92. Eds.: R.A. de Grootand J. Nadrchal. (World Scientific, Singapore 1993), p. 322-323.

[3] DRSKA, L. - LIMPOUCH, J. - SINOR, M. - VAGNER, S. - VONDRASEK, J.: CSP/ Famulus Courseware Projects for University Physics Teaching. In: Internationa]Workshop Famulus 94: Computational, Modelling, and Presentation SW System andIts Use in Education, Prague 1994.

This research has been conducted at the Department of Physical Electronics with partialsupport of the research project "Facility for the Application of Integrated Computing System-s'' (Grant V S07 of the Czech Ministry of Education) and TEMPUS project "New Curriculaand Courses in Engineering Education" (JEP 2262).

138


FIRST CONTACTS WITH INTERNETA. Cepek

CTU, Fac. of Civil Eng., Dept. of Mapping & CartographyThakurova 7, 166 29 Praha 6

Key words: Internet, education

About a year ago I peeped for the first time into the world of computer networks. Withina couple of days I was able to enter the Cyberspace. All dreams of mediaeval alchemists,fumbling on their way to the philosophers' stone, are fading compared with the presentreality- a living ocean of information flowing through computer networks all over the Worldlying at our fingertips and at our service. My previous feelings, which were not in any case |exceptional, were intensified by the simple fact that I was born in a country living its apoor existence in a gloomy shadow of an iron curtain. The civilized world had a period of Iabout, twenty years to adopt the phenomenon of computer networks as an integral part of |its culture. Our universities joined the European Academic & Research Network (EARN) ;|towards the end of 1990; our first link to Internet was around February 1992. II

Since my very first contacts with Internet I have been absolutely sure that it is essential ; |; for our students to enable their access to the network and to introduce them to the field of j |

networking. Therefore in the autumn of 1992 I included "Internet" within the curriculum Hof a seminar entitled "Introduction to data processing1'. During the following months, mymain source of information concerning Internet was a series of excellent courses held by theEducational association Omicron at the Department of computers within the Electrotech-nical faculty. Soon it became clear to me that introducing new endusers to Internet wouldcover (at least.) one whole semester. At the first meeting with my students in October, Icould tell them that the whole semester would be focused on Internet (this statement wasapplauded). As for next year, it has been definitely decided to change the subject of the

' » seminar to "Internet resources".; As the first run of any seminar is more or less experimental in nature, I have set an• upper limit on the number of students enrolling to ten and I personally informed those

students whom I wanted to get for my seminar (these are forming majority) about myplans. Starting from next year the seminar will be open paralelly in both semesters and I

i am not intending to limit the number of students (saying this I can just hope that we will• manage to get a new server at, our department). In the future I can rely on the help of my| colleagues who are representing two extra students of the seminar today.| I started our seminar with a short description of the ten following themes

I|; • e-mail (electronic mail)

1I • mailing lists (e-mail conferences)

| • Gopher, Veronica, Jughead

• FTP (File Transfer Protocol)

• Archie139


• Telnet, Hytelnet .

• Whois, Netfind

• Netnews (Usenet)

• World-Wide Web (WWW)

• electronic journals and libraries.

Each of the students was to choose one of these topics and to prepare a lecture thereby beingresponsible for introducing his/her colleagues into the topic. The sources of information Vwhich I could supply my students with were manuals [1,2,3], various texts obtained from ••*•the network and tutorial hours, five days a week. During our introductory meeting I briefly ''•mentioned the history of Internet and explained the functions of e-mail and some basicrelated terms (TCP/IP, IP address, nameserv, . . . ) . On our second session, which againfocused on e-mail, the lecture was read by the first of the students; in fact we were only ^revising the first week. It was just a warm up round, for by following session we were ]running at full speed. The lectures are continuing still, and when all of the ten lectures are "*'read I am going guide the students practice of networking.

Since the discussed seminar is intended for endusers, I am putting much stress onpractical skill. We have learnt a lot from experiments with one demonstrational mailinglist demo-lficsearn. bi tnet which was set up for practical education of students and ismaintained by Mrs. Ingrid Ledererova, (here I would like to thank her and other colleaguesfrom the Computer Center of the Czech Technical University for all they have done forour academic society). To make active use of Internet resources it is necessary to master acertain minimum knowledge enabling later selfeducation (anything you want to know aboutInternet is there). One of steps on this way is the ability to take an active part in interestconferences. The above mentioned demo-1 list is supplied with a standard bitnet conferencearchive. The more that students will use this in the future, the higher the educational profitwe may expect.

• At this time (November 1993), the semester is not over yet. Nevertheless I can say thatthe first course of my seminar has surpassed all my expectations. Most of all I am satisfiedwith the active role of my students in the seminar. Today I can not say what gave me thecourage to initiate a seminar in which I only had an advantage over my students that you

;r could measure in weeks. I am convinced that it is just a matter of time before networkingi becomes a standard subject of education, as for example, programming is nowadays. I•. would be happy to answer all comments and suggestions on the given topics sent to my*;' e- mail address cepekOaci. cvnt. cz. If anybody wants to hear the opinions of my students,| i please write to demo-lCcsearn. b i tnet .

<% References:

| | [1] VRABE.C, V. — BILY, M.: Elektronickd posta a elektronicke konference v siti Internet,W Vyukove sdruzeni OMICRON, Praha, bfezen 1993.

f| [2] Informacni sluzby v pocitacovych sitich European Academic & Research Network (Guide.... U to Network Resource Tools, EARN), Vypocetni centrum CVUT, Praha 1993.

•i | [3] HAMPL, M. - VLACHOVA, Z. - BURE§, P.: Pocitacovd sit Stavebni Fakulty CVUT,Y« . H Vypocetni a Informacni centrum Stavebni fakulty, Praha, zafi 1993.

' rt j-

140


THE INTRODUCTION OF A MODERNDATA ACQUISITION SYSTEM

INTO THE STUDENTS EXPERIMENTALTRAINING

J. Nozicka

CTU, Fac. of Mechanical Eng., Dept. of Fluid Mechanics k ThermodynamicsTechnicka 4, 166 07 Praha 6

Key words: data acquisition system

All students of the Faculty of Mechanical Engineering of the Czech Technical UniversityPrague have to pass some experimental training included in the course of Thermomechanics.This one is lectured by the Institute of the Fluid Mechanics and Thermodynamics in thethird study year. The aim of this practica is not only to illustrate some thermodynamicalphenomena, but to acquaint the students with the experimental methods and techniquesused in thermodynamics, as well.

Because of the extension of modern electrical methods of measurement which in recentyears appeared in our country, such methods should be introduced into the practica.

Two experiments were equipped by the measurement mentioned. The aim of the firstone is to determine the efficiency of a simple heat exchanger. In the second one the mixingof two air flows is to be studied.

The experiments described require the calculate of the mass flow rates and the enthalpychange by the pressure drops on the calibrated nozzle and temperatures measured. This isensured in a common way by the glass thermometers and liquid manometers. Parallelly, anelectrical measurement, controlled by a computer, is installed. Thank to this, both methodscan be compared and the advantages of modern methods are evident. This is emphasizedby the real time evaluation of experimental data.

This was made possible due to the cooperation of the Institute of Fluid Mechanicsand Thermodynamics with the Prague office of the firm FCC FOLPRECHT ltd. This firmsupplied the institute with the modern data acquisition system ADVANTECH, based ona multichannel labcarb PCL 812, built in the personal computer of the PC-XT or highercategory. Some auxiliary devices ( multiplexer - amplifier card, terminal boards ) weredelivered by the firm as well. For pressure measurement low range pressure transducersROSEMOUNT 1151 DR2 and DP3 were used. Temperature measurement is ensured byNiCr-NiAl thermocouples, connected to the data acquisition system using a special CJCcircuit developed and built at the institute. The scheme of experimental plant is on the fig.1. In the upper side the heat exchanger is shown, supplied by a centrifugal fan. Temperaturein front of and behind the exchanger and the pressure drop, line pressure and temperatureon the vane are measured. The lower part of fig. 1 shows the mixing of two air flows, oneof which is heated. Pressure drop on the nozzle and temperature behind and in front ofthe mixing area are measured. In the central part of fig, 1 the wiring diagram of dataacquisition system is plotted.

141


Because computer-controlled measurement has been successfully introduced into thepractical training, it has been decided to automize another experimental plant, in this casefor the practical training of Mechanics of Fluids. This should be realized in the beginningof next year.

m

p.

pressure transducers [ I

B -t \ 1 — -

Fig. 1: Experimental plant scheme.

142

^ > » e K < S ! ^ ^ - . '


LABORATORY FOR MICROPROCESSORAPPLICATIONS

IN INSTRUMENTATIONJ. Fischer, T. Jak), P. Kocourek,

J. Novak, M. Sedlacek

CTU, Fac. of Electrical Eng., Dept. of MeasurementsTechnicka 2, 166 27 Praha 6

Key words: microprocessor applications, teaching methods, intelligent sensors, open lab-oratory, digital signal processing, measurement

In 1993 we acquired a grant from the Fund for Dynamic Development of Universitiesfor a laboratory project on microprocessor applications in instrumentation. We set upa universal and open laboratory (in the sense of modularity, standards acceptance andgeneral access). The backbone is formed by a LAN (local computer network), composed offile server and print server stations and ten diskless workstations, compatible with widelyused standard IBM PCs. LAN (Ethernet and Novel Netware 3.11) technical equipmentand software enable us to share expensive or relatively rarely used accessories (file system,printers and in the near future also a modem). The laboratory's LAN is a part of the FacultyInformation System and is linked throught it to INTERNET and BITNET internationalnetworks. Thus, any user has access to all services (background research, information databases, software, etc.) provided by these systems.

Because practical teaching in laboratories is expensive and fully specialized laborato-ries would not be extensively used, our laboratory is intended for use in a whole group ofinterrelated courses. This lends to more cost-effective use of funds. The courses using thislaboratory are Information Transmission (the laboratory is used for introducing students tomodern information systems), Microcomputers and Microcomputer Programming (studentsare introduced to microprocessor technology), Microprocessors in Instrumentation (use ofmicroprocessors in measuring instruments and intelligent sensors), Signal Processing in Mea-surement (dealing with DSP algorithms), and Design of Measurement and Data. AquisitionSystems (development of automated measurement and data aquisition systems).

At present the laboratory is comparatively poorly equipped with measuring instru-ments, because of lack of funds from grants and from our Department. Students have accessto power supplies, two analog oscilloscopes, logic probes, universal measuring instrumentsand one logic analyser. A desirable level of equipment for one workplace, allowing indepen-dent work by students, is shown in the Fig. 1.

As follows from the picture, each workplace should have its own computer and corre-sponding software, development module with microprocessor (SAB80C537), non-solderingcontact field, oscilloscope, multimeter, function generator and logic probe.

The chosen plan for the teaching room is advantageous from the point of view of costand serviceability. The modular structure and the concentration of software at the serverallows for easier maintenance of hardware and software.

143


o o oCD

oQ

oo

o

Oo

o

7

o oo o

Oo II

Fig. 1: Student's workplace

The open conception of the Laboratory is very important from the point of view ofuse by students and teachers. The basic idea was to allow maximum use of the laboratoryfor class teaching, and especially for independent study. The laboratory is freely accessiblewhen not used for teaching. It is used for work on project preparation for various coursesand for working on research projects. The qualified supervisors of the Laboratory are almostalways available to students. This model of teaching helps to support the competitivenessand creativity of students.

The course in "Microcomputers and Microcomputer Programming" provides an exam-ple of the use of this laboratory:

The course aims at developing software for intelligent measuring modules and instru-ments. Students are introduced to microprocessor technology. They study the architectureof a microprocessor, its functions and instruction set, interrupt system and DMA, micropro-cessor programming and C language, basic programming techniques and special operationalsystems. The typical features of the use of microprocessors in instrumentation are empha-sized. Instruction is based on the Intel 8051 Assembler. Students are introduced to "C"language, the operational system kernel for real-time work, parallel proceses and their syn-chronization and communication. The Laboratory is used mainly for mastering assemblerand G language and for programming of periferal units. Students also learn about smallmultitasking operational systems.

References:

[1] FISCHER, J. - KOCOUREK, P. - NOVAK, J.: The teaching of applications of mi-crocontrollers in instrumentation. Submitted paper to World Congress of IMEKO'94,Torino.

This research has been conducted at the Department of Measurements as a part of theresearch project "Laboratory for information systems and microprocessor application" andhas been supported by CTU grant No. 1234.

141


COMPUTER ASSISTED LEARNINGOF STATIC AND DYNAMIC ANALYSIS

OF STRUCTURAL SYSTEMSJ. Maca, P. Konvalinka, Z. Bittnar

CTU, Fac. of Civil Eng., Dept. of Structural MechanicsThakurova 7, 166 29 Praha 6

Key words: computer assisted learning, structural analysis, finite element method, pro-gramming, static analysis, dynamic analysis

At the present time a large number of computer programs for complex three-dimensionalanalysis of structural systems exist. After the computer model and input data is prepared,the analysis process is completely automated. Therefore, it is now possible for students andprofessional engineers to perform structural analysis and design using computer programswithout a complete knowledge of the approximation which have been incorporated in the

., computer program. The major reason for the misuse of computer programs for structuralI analysis is the lack of understanding of the engineering fundamental of equilibrium, force-| -deformation requirements and compatibility equations.j The basic purpose of the CAL (Computer Assisted Learning) program is to bridge the~ gap between traditional methods of teaching structural analysis and the use of automated: programs. As a result of using CAL it is hoped that students will understand the theory

and approximations which are used in modern structural analysis, and they will not useprograms as black boxes.

[ CALcz is the modified and extended version of CAL-91 program, which has been de-' veloped by Professor E.L.Wilson in Berkeley, University of California. The philosophy of•; the CAL program is to use a special language which was designed to subdivide structural

analysis into a sequence of logical steps. The use of such an approach requires that theI students understand basic structural theory and behavior without the need to perform a!; large number of time - consuming hand calculations.? With the aid of CALcz commands it is possible to solve the following types of problems:8§ A - STATIC ANALYSIS

I? 1. slope - deflection method (frame element)2. direct stiffness method (2-D and 3-D beam and truss analysis)3. direct stiffness method (grid element on the elastic foundation)4. force method for beam analysis5. FEM - plane stress/strain element, plate bending element

K .**' 145


B - LINEAR STABILITY ANALYSIS (2-D beam structures)

C - DYNAMIC ANALYSIS

1. eigenvalue analysis2. mode superposition analysis3. step-by-step analysis4. analysis in the frequency domain

It should be remembered that the basic purpose of CAL is educational. Since CAL isdesigned for the solution of small problems (under 100 degrees of freedom) it has limitedvalues for the solution of large practical problems.

References:

[1] WILSON, E. L.: CAL-91. Computer Assisted Learning of static and dynamic analysisof structural systems University of California, Berkeley 1991

This research has been conducted at the Department of Structural Mechanics as a partof the research project "The Use of Artificial Intelligence Methods for Structural Analysis"and has been supported by CTU grant No. 13250.

146


ADVANCED FORMSOF EXPERIMENTAL MECHANICS

EDUCATIONS. Holy, J. Benes* ]

CTU, Fac. of Mechanical Eng., Dept. of Elasticity & Strength of Materials :

Technicka 4, 166 07 Praha 6 j*Academy of Sciences CR, Inst. of Thermomechanics, Dept. of Solid Mechanics f

Dolejskova 5, 182 00 P raha 8

K e y w o r d s : education, mechanics, computational & experimental methods

Introduction: Education of professional fellow-workers by higher education inst i tut ions \(HEI) and Academy of Sciences (AS) is provided separately. While HEI cover all levels of ihigher education studies from basic level up to the postgraduate one, academic inst i tutes 5devote themselves mostly to postgraduate s tudents . T h e project, recently proposed and >;in 1993 supported by a grant from the Fund of The Dynamic Development of the Higher IEducation, is aimed at creating conditions for systematic cooperation between HEI and J|AS, and particularly CTU FME and IT, at preparing of s tudents in the branch "AppliedMechanics". In this way conditions for bet ter research activities could be also achieved inboth insti tutions.

Background: In spi te of the great success of computat ional methods it is also necessaryto develop experimental approaches in the field of solid mechanics. Laboratory equipmentat. HEI does not generally allow the students to follow experiments on the high level andteachers to demost ra te it and take part in current experiments. Tha t is why IT AS supplieslaboratories and their equipment for both educational and research purposes. This jointlaboratory will serve for common scientific and pedagogic activities of workers from bothCTU F M E and IT AS.

Results: T h e laboratory was established in 1993 in IT AS by means of collaborationof fellow-workers from both institutions under the s ta tus Joint Laboratory of ExperimentalMechanics. Three different programs nave star ted: diploma projects, postgraduate studiesand international scientific exchange.

: - Conclusion: According to the experince gained the project will enable:

j / r 1) larger diversification of the education process in solid mechanics,s£ 2) mobility of fellow-workers from the relevant institutions,§» 3) selection of s tudents qualified for research and their participation in the teams inter-•jfe ested in either basic problems or problems for industry,! | 4) effective utilization of both financial input and human potencial,fr 5) modernization and improving quality of education process given by:

• f%, a) practice in the laboratory, first for the field of study "Applied Mechanics", later'|v for other applications,| j b) usage of the laboratory for postgraduate studies,

' %. -r 147


c) application of the newest approaches in computational mechanics, diagnostics oflimit states etc.,

d) support of interdisciplinary studies, e.g. biomechanics, mechatronics, robotics,e) connection of research capacities of the relevant institutions for solving complicat-

ed tasks with the possibility of student participation, particularly postgraduatestudents.

The above-mentioned education is used at CTU FME for the following subjects:Strength of Materials, Fundamentals of Experiment in Engineering, Experimental StressAnalysis, Thermoelasticity, Impact Mechanics, Contium Mechanics, Airplane StructureAnalysis, Computational Mechanics, Theory of Thin-Walled Structures, Composite Ma-terials Mechanics, Fatigue of Structures and Reliability.

References:[1] HOLY, S. - BENES, J.: Application of Advanced Forms of Experimental Mechanics Ed-

ucation, Grant No. 0715, Fund of Dynamic Development of Higher Education Ministryof Education of the Czech Republic, 1993

[2] LAERMANN, K. H.: The Future Role of Experimental Mechanics Under InternationalAspects Proc. 2nd Europ. Symp. IMEKO TC 15 "Testing Equipment for ExperimentalInvestigations of Mechanical Properties of Material Structures" Moscow 1989

[3] HOLY, S.: An Invisible Danger of Schematization and Its Deleting by Means of Ex-periment 4. Deutsch / Tschechisches Symp. ueL-r Experiment. Festkoerpermechanik .;"Experimental Mechanics Methods in Nondestr. Testing of Structures", Bad Honnef, ,jJune 1993 |

[4] Benes, J. - Novotny, T. - Vesely, E.: Transmited Pulse Analysis Employed for Deterem- )ination of the Status of Machine Parts ibid. \

[5] HOLY, S.: Application of Experimental Stress Analysis for Minimization of Structure JFailure (in Czech) Proc. 30th Conf. on Exper. Stress Analysis, EAN 92, Praha 1992, |pp. 73-76 ]

This research has been conducted at the Department of Strength of Materials, FMECTU together with the Department of Solid Mechanics, IT AS CR as a part of the researchproject "Advanced Forms of Experimental Mechanics Education" and has been supportedby CTU grant No. 0715/2816 of the Fund of Dynamic Development of Higher Education, '•Ministry of Education CR, 1993. i

148


UNIVERSITY STUDIES OF VISUALLYHANDICAPPED STUDENTS

I. Nemecek

CTU, Fac. of Nucl. Sci. & Phys. Eng., Dept. of MathematicsTrojanova 13, 120 00 Praha 2

Key words: visually handicapped, Braille, computer, TEMPUS

The problem of higher education of blind and partially sighted is quite difficult andcomplex, because traditional teaching methods strongly depend on visual perception. Thepossibilities of university studies for visually impaired would be very limited without ad-vanced technology.

The main aim of the TEMPUS project JEP 2423 "New vocational and study possibil-ities for visually handicapped people" is to establish the support center and services thatenable access to the higher education for visually disabled students.

The project has been running at the Department of Mathematics , the Faculty of Nu-clear Sciences and Physical Engineering, since the year 1991 in cooperation with Universityin Karlsruhe, California State University in Northridge, Royal National Institute for theBlind, Komenius University in Bratislava and Czech Union of the Blind.

Special equipment of the centreIn the first year of the project the special classroom was built at the Department of

Mathematics in Trojanova street no. 13. The classroom is now equipped with: PCs connect-ed to the network with software Novell Netware 3.11, Two 80-character Braille displays, 1Braille printer, 4 large monitors (19") for partially sighted students and special enlargement,software (Zoomtext, Visulex LP DOS), 3 Czech speech outputs, 1 English speech output, 3CCTV magnifiers, 2 OCR systems, 1 optacon, 1 CD ROM drive.

How does this equipment help visually handicapped students ?Braille display is the device which enables to transfer 1 line (or a part of it) from PC

display to the Braille line consisting of special cells. Every cell consists of 8 pins and candisplay one character in Braille. The active line can be selected by special keys on theBraille display. Thus blind people can read the contents of PC display by their fingers.

Braille printer (INDEX EVEREST) prints the text stored in PC's in Braille.Large monitors with special magnifying software help partially sighted students to work

with computers both in text and graphics modes. A part of the screen can be magnified upto 16 times.

Speech outputs can read and pronounce the selected text from the PC display. Gen-erally, speech outputs are useful for reading while Braille displays are more suitable forprogramming.

CCTV magnifiers enlarge printed materials and display it on the monitor. Suitablemagnification and colours can be selected.

OCR systems enable to transfer printed material into digital form. Blind students canread transformed text by Braille displays, speech outputs or print it in Braille.

149

, ._ 4

CTU SEMINAR 94 DEVELOPMENT OF CTU STUDY :

Preparing study materials for visually impairedThere are several methods how to prepare materials in digiial form depending on the

form in which study materials arc available. '

t. The text is only handwritten. Then we must write it with some text editor. If there •are no mathematical or special symbols in the text, plain ASCII format is suitable.But this situation is very rare. We prepare text with mathematical symbols in TgX.Then we convert the text by the conversion program into the form similar to T£Xbut ';better readable for the blind. There are also problems with graphics. As we have nothad a system for creating tactile graphics yet, we must, omit the graphics from the :text, if possible. If not, we include a detailed description of the picture into the text.

2. The text is in printed form. Then we can use OCR systems and convert the text ,into ASCII form. Then we must correct mistakes, include unread text (especially :formulas), graphics if necessary, and reformat, the text as mentioned above.

3. The text is in the digital form. Then it is necessary to reformat text into the formsuitable for the blind. It depends on (he form of the text, but a lot of work must be ",done manually. ;

Other activities •

Besides a technical support and preparing study materials, several courses are orga- »nized for visually impaired students in the special classroom. Courses on basic work with ;computers, operating system DOS, programming in Pascal, word processors (Word Perfect J5.1) were offerred to 16 students from universities and secondary schools in the year 1993. |More than 20 students visited the centre and used its services. s

Special software (speaking editor, special utilities etc.) has being developed at the ;Department, of Mathematics in cooperation with student of software engineering (two of jthem are visually impaired). (

Special counselling is offered to handicapped students. \One computer with voice output and a printer has been installed at the students hostel |

and several computers will be installed in the library for the blind. j

Problems to be solvedThe problem of education of blind and partially sighted is, however, more complex then

to build the support centre, enable access to the literature and provide special courses. It ]includes special counselling, home equipment of the students, organizing tutorial assistance (for preparing study material, solving the problem of exams, building contacts between differ-ent faculties and organizations of visually impaired, organizing exchange of study materials,building contacts to companies which could employ visually handicapped people.

Last, but. not least, we must ensure the continuity of the project, because the TEMPUSproject will finish in the year 1994.

References:

[1] PROCEEDINGS: Sustem of University Studies of Visually Handicapped Students, 1992

[2] PROCEEDINGS: University Studies of Visually Handicapped Students, 1993

K ""' 150

^


INFORMATION SUPPORT FOR THEENVIRONMENTAL ENGINEERING

STUDY BRANCHJ. Vlcek, F. Drkal*, P. Moos**

CTU, Fac. of Civil Eng., Dept. of Applied InformaticsThakurova 7, 166 29 Praha 6

*CTU, Fac. of Mechanical Eng., Dept. of Environmental EngineeringTechnicka 4, 166 07 Praha 6

**CTU, Fac. of Transport Eng.,Konviktska 20, 110 00 Praha 1

Key words: environment, heterogeneous system, informative representation, branch ofscience and branch of study, exchange of information, professional literature, seminars

Much practical attention has been paid to the environment at all levels, from individualbiological and social features to those which involve the whole of civilization. The reasonis that the environment is endangered in all its dimensions. No adequate theory and noadequate verifiable and applicable information is available for dealing with these problems.A technical university should be able to provide theoretically - based, informatized tools forengineers, so that they can solve practical problems.

In order to meet the demand of scientific methodology concerning the independenceand separability of branches of science and fields of activity, the invironment may be de-fined as a heterogeneous system consisting of heterogeneous elements with "hard" or "soft"links between them. The behaviour of the whole system exhibits negative features, as the

• , environment has been damaged so greatly that all civilization is now at- stake. The conceptand the definition of the system (covering its three main components and the developingcomponents related to the size of the system (and to its genetic code) make it possibleto create a model of the environment in any dimension, from the microlevel up the thelevel of regions, nations, geographical areas or biological or botanical species, technological

.'• processes and technical constructions. Systems analysis and systems design will help solveenvironment-related problems formulated as systems.

; The applicability of a systems-based model of the environment depends on its level of| i informative representation by means of technical instruments and appropriate measuringf'f methods while at the same time the basic impaco of man on the environment must be| j respected.

The branch of science thus formulated becomes a research task to be dealt with by abranch of study. The heterogeneity of the subject matter and the high demands placedon the methodology of this branch of science make high demands on the methodology of

?|f the branch of study called "The Environment". Efficient methodological tools are basedon an interfaculty, interdisciplinary form of study which makes it possible to cope with theheterogeneity of the subject. This requires compatibility among the contributions made byeach discipline and by the whole branch of study concerned. The compatibility and mutualcomplementation of individual contributions can be achieved by means of study materials

151


consistently conceived, and also by means of an exchange of information in the form ofworking seminars.

The Environment as a field of research, and information support for it, have involved allcomponents of the field of study: definition of the subject and its methods at the interfacultylevel. This has led to the preparation of two monographs: Technology and the Environment,and Methodology of Environmental Studies. Meetings of the research workers involved haveculminated in a joint seminar with other higher educational facilities in Prague preparingor already implementing environmental studies in cooperation with their major user, thePrague Municipal Council.These meetings provide a sort of information support for suchstudies, consisting in a direct exchange of information. Such seminars also raise the objectiveand complex character of the field of study.

This project has been supported by Ike Fund for the Dynamic Development of CzechUniversities grant No. R 0040.

>.'

152


MODERNIZATION OF PhD. STUDIESIN RADIOELECTRONICS

K. Novotny, M. Mazanek, Z. Skvor,F. Vejrazka*, Z. Hrdina*, J. Sykora*

CTU, Fac. of Electrical Eng., Dept. of Electromagnetic FieldTechnicka 2, 166 27 Praha 6

*CTU, Fac. of Electrical Eng., Dept. of RadioelectronicsTechnicka 2, 166 27 Praha 6

Key words: radioelectronics, PhD. stvidies

The main purpose of this project was the creation of a complex structure of dissertationstudies in the field of radioelectronics, which by its level and content would correspond withEuropean standards.

The project was divided into two parts. First, curricula for dissertation studies, werecreated, containing two groups of subjects. In the first group there are five obligatorysubjects. The second group consists of a large number of optional subjects according tothe specialisation of the dissertation. The majority of the subjects include laboratory work,some of which will be done outside the faculty (Czech Academy of Science and others).

The second part of the project was the establishment of contacts with foreign insti-tutions specializing in radioelectronics. These contacts should in future help to provideregular stays for our postgraduate students at European institutions. From the first con-tacts it was immediately evident that stays in foreign countries fully financed by our sidearc unachievably expensive and can be realized only in exceptional cases.

At the present time, the only attainable way is through reciprocal visits, where roomand board is covered by the inviting party. However, not even these kinds of international

; contacts at the post-Masters level are without problems. Foreign doctoral students whof express interest in staying at our faculty expect to have at least as good working conditions; as they have at their home universities. With our very limited facilities, at the present time,

we are not capable of providing such conditions for the entire range of radioelectronics.Therefore in preparing this project, we focused on some narrower areas. First of all we

i equipped our worksite with top-level software ( Microwave Harmonica and SCOPE), which| makes possible proposal and optimalisation of microwave and optical circuits and systems| used in radioelectronics, and also with software for studying special problems in wave prop-I agation and electrodynamics in general (The 3D Electrodynamic Wave Simulator from the|- Institute of Technology, Zurich).g. An experimental group of PhD students was formed and prepared. Six from them took|f part in the projects COST 235 (Radiowave Propagation Effects on Next-Generation Fixed-<k Services Terrestrial Telecommunications Systems) and COST 227 (Terrestrial and Space0 Networks). Two postgraduate studentships abroad have been funded from the budget of

grant No. 3818.A five-week study visit took place at the University of Bradford. Our student (received

by Prof. Gardner) spent that time studying a TERRA intelligent data transmission terminal;„ in the framework of European community collaboration. We intend to make use of this

153

^

CTU SEMINAR 94 DEVELOPMENT OF CTU STUDY '

terminal in future in order to enable our students to take part in international researchprojects. The host university made use of our student's knowledge of localization. This 'study visit has been strongly related to European research project COST 227. '

The second (two week) study visit took place at TU Zurich. The main objective was ;to gain experienceof using special software which will be used in the COST 235 project. An ;training, knowledge and experience received will be transferred to other Ph.D. students.

Achieved results:- Creation of a study structure and curricula of obligatory subjects in Radioelectronics -,

for the first two years of courses.- Establishment of a working place for mathematical modelling and optimization of 8

microwave devices and computation of common problems in wave propagation and electro- |dynamics. |

- Transfer of experiences of using the TERRA terminal and opportunities for interna-tional cooperation of PhD students within the frameworkof the EC.

- Promise of Prof.John G.Gardiner BSc MSc PhD DSc from the University of Bradfordto participate in rigorous examination of PhD students.

This research has been conducted at the Department of Electromagnetic Field and theDepartment of Radioelectronics and has been supported by CTU grant No. 3818.

154

•

^-^^:®^^ %


DEVELOPING A NEW PhD COURSEIN A SUGGESTED DISCIPLINE

PHOTONICSE. Kostal, K. Novotitf*, J. Schrofel**, M. Klima

CTU, Faculty of Electrical Engineering, Dept. of RadioelectronicsTechnicka 2, 166 27 Praha 6

*CTU, Fac. of Electrical Engineering, Dept. of Electromagnetic FieldTechnicka 2, 166 27 Praha 6

**CTU, Fac. of Electrical Engineering, Dept. of MicroelectronicsTechnicka 2, 166 27 Praha 6

Key words: postgraduate study, photonics, teaching, technical university, optical informa-tion processing

Supported by general interest from students this grant is the first step towards estab-lishing Photonics as a new scientific discipline which will result in formulation of curriculafor a course leading to a doctoral degree. This idea is fully compatible with recent worldwideprogress in technical disciplines [1]. The main aim is to create a study structure based uponthe existing PhD. disciplines of Radioelectronics and Microelectronics. A small experimen-tal group of PhD. students has been formed and educated. A mobility scheme in generalhas been agreed with our partner PSIZ, and the first two visits ( one PhD. student, onestaff member ) have already taken place. Two seminars related to this field were held [2].Concurrently the coordinator of this project is participating in another project No.3855-V324 "The development of optoelectronic study". These two projects differ, especially inthe field of activity and goals. Project No.3855 concentrates on optoelectronics and under-graduate study is stressed. However, significant financial restrictions resulting in a lack offunds for student scholarships eliminated the most important proposed activities especiallystudy stays planned for this year. Nevertheless we keep discussing these activities with ourcooperating partner at PSIZ and the program will be launched next year ( depending onavailable funds ). The minimum accomplished exchange program was mostly sponsored bythe Swiss side.

In spite of these difficulties the main aim of the grant has been achieved. PhD. stu-dents are participating fully in research cooperation with the PSIZ, while personal contactshave mostly been replaced by e-mail communication. We have succeeded in involving theCzechoslovak Society for Photonics and the European Optical Society in our activities.A seminar backed by the Czechoslovak Society for Photonics was held at FEE CTU onSeptember 17, in which PhD. students took active part.

There have already been 10 PhD. students participating in the above mentioned exper-imental course (5 from the Dept. of Radioelectronics, 3 from the Dept.of Microelectronics,

, If 2 from the Dept. of Theory of Electromagnetic Field ). Because the discipline Photonics1 has not yet been officially established, this course has been incorporated into the existing

*-• 155'ft

M -Ml


Radioelectronics and Microelectronics disciplines.

Summary of achieved results:

- definition of a study structure and curricula for Photonics for the 1st and Ilnd yearsof study

- fundamental innovation of the offered subjects for the postgraduate course in Pho-tonics in the current school year, based upon the introduction of new subjects i.e.Research work management, Photonics Laboratories

- participation of PhD. students in international research program- participation of PhD. students in CTU research grants No.8042,8124- an experimental laboratory setup has been partially established and is currently being

used by PhD.students- improvement of laboratory facilities after the release of funds (see a budget report)- doctoral students use professional software packages for circuit and signal analysis of

optical elements and networks- an organizational structure and timetable has been prepared for doctoral student

involvement in the research grants running concurrently i.e. Nos: 8042, 8124, 1818,3855 etc.

References:[1] CATHEY, W. T.: Guest Editorial - Special Issue on Optoelectronics Education; IEEE

Transactions on Education, Vol.35, No.2, p. 101, May 1992

[2] KL1MA, M.: Research activities in cooperation between the PSIZ and DR FEE CTUPrague, invited paper, Zurich , July 1993

[3] PALAIS, J. C. - GALLAGHER, N. C. - STARK, H.: Photonics Enrichment of the EECurriculum; IEEE Transactions on Education, Vol.35, No.2, pp.103-108, May 1992

[4] BOERO, F. - CHIVIAN, J. S.: A B.S. Degree in Photonics; IEEE Transactions onEducation, Vol.35, No.2, pp.122-125, May 1992

This research has been conducted at the Department of Radioelectronics, Microelectron-ics and Theory of Electromagnetic Field as a part of the research project "Developing a newPhD course, for new suggested discipline Photonics" and has been supported by CTU grantNo. 3811.

156


DEVELOPMENT OF NEWSPECIALIZATIONS OF PGS

IN MATHEMATICS,

SOLID AND FLUID MECHANICSV. Stejskal, K. Kozel*, J . Jezek**

CTU, Fac. of Mechanical Eng., Dept. of MechanicsKarlovo nam. 13, 121 35 Praha 2

*CTU, Fac. of Mechanical Eng., Dept. of Technical MathematicsKarlovo nam. 13, 121 35 Praha 2

**CTU, Fac. of Mechanical Eng., Dept. of Fluid Mechanics & ThermodynamicsTechnicka 4, 166 07 Praha 6

Key words: post-graduate study, mathematics, solid mechanics, fluid mechanics, list oflectures, new methods

The contribution deals with the solution of the grant project No. 1110. The main aims) are:

J (a) Cooperation of courses of PGS (postgraduate study) in the following three direc-

;-| tionsa) solid mechanics/?) fluid mechanics7) mathematical and physical engineering (part mathematics).

1 (b) Support of theoretical part of solid and fluid mechanics by a modern applied: mathematics and numerical mathematics.

(c) Development of new numerical methods solving some problems of fluid and solidmechanics.

The results of our solution are:

(a) The lists of complete system of lectures in the three parts of PGS. The items ofthe list are abstracts of the lectures, syllabi, list of lecturers and references. Thelist contains about 20 lectures in mathematics, 11 lectures in solid mechanics and14 lectures in fluid mechanics.

(b) Cooperation in a choice of lecturers among all three parts of PGS. The majority oflecturers are members of staff of Faculty of Mechanical Engineering, about 20 %lecturers are from institutions collaborating with our Faculty, e.g. University ofWest Bohemia, Institute of Therrnomechanics of The Czech Academy of Sciences,etc.

157


(c) New numerical methods:a) New method for numerical solution of 2D incompressible laminar Navier-Stokes equations. The system was solved by an artificial compressibility methodusing H-grid and multistage Runge-Kutta finite volume method. We have devel-oped new method and achieved first results for several Reynolds numbers. Theresults are considered in the form of isolines of value of velocity of the flowfield.fl) New method of assembly of equations of motion of a multibody system. Themethod is an extension of composite rigid body inertia method to flexible bodies.The residual algorithm for numerical solution is proposed.7) New method of solution of eigenvalues and eigenfunctions of Orr-Sommerfeldequation for the case of wall flow.

Within our project an international conference of departmens engaged in teaching offluid mechanics was organized with participation of teachers from France, Germany andSlovak Republic. Problems of PGS of fluid mechanics were discussed during the conference.

This research has been conducted at the Department of Mechanics. Department of Tech-nical Mathematics and Department of Fluid Mechanics and Thermodynamics as a part ofthe research project "Development of New Specializations of PGS in Mathematics, Solid andFluid Mechanics" and has been supported by grant No. {110.

*. 158 f-1 1


EDUCATION OF EMC EXPERTSJ. Svoboda, B. Simak, M. Vondrak, T. Zeman

CTU, Fac. of Electrical Eng., Dept. of TelecommunicationsTechnicka 2, 166 27 Praha 6

Key words: electromagnetic compatibility (EMC), curricula, multimedia programme

A course of stadies electrical and informatic technologies involves an undersanding ofprinciples of Electromagnetic Compatibility (EMC). This can be attained only with goodfacilities and adequate funding.

The project "Education of EMC experts" started in 1992. The goal of the second stageof the project is to use the staff and facilities of CTU to implement project aims. Our team isworking not only on the development of new subjects but also on proposals for the learningstructure for a wide range of problem-solving. The education center concentrates on EMCproblem-solving at CTU. The center provides facilites and courses not only for specialists,but also for the whole technical community. Our main activities are concentrated on thefollowing points:

1. Collecting study materials2. Creationg new curricula3. Preparation of EMC technical handbooks

I 4. Software support for EMC education'i 5. Construction and expansion of hardware and software for multimedia based workinigJ places' 6. Construction of an EMC laboratory for teaching measuring and testing technology

7. Consultations, publications, conferences: Results:

• J We are collecting information, study materials, standards and requirements for EMC.;:<< We have obtained the EMC teaching materials produced by Hewlett Packard and Rohde5? Schwarz and the proceedings of EMC Symposium 93 in Wroclav. We can cooperate with

other universities at home and abroad. We have created databases of EMC firms and' specialists. We also organized the workshop EMC 93 [1].

This year we have completed curricula for "Basics of EMC" and "Teleinformatics andEMC" and these new subjects have been taught at CTU. We have prepared a curriculumfor "EMC of Electronic Systems" for courses taught to PhD students.

f Based on the results of our work in the first stage of the project we recently published'\ "Basics of EMC" [2] the first Czech language overview of EMC problem-solving.L The computer learning program "Basic Measuring Methods in EMC" has been madeg*f with support authoring system GENIE and has been used in "Teleinformatics and EMC".^ In the TESTCOM institute labs we created a short videoprogram on "Overvoltage EMC£ Testing of Telecommunications Equipment". We converted two Hewlett Packard video-§- programs ("Basics of EMC" and "Using an EMC Spectral Analysator") from NTSC TVfc_ standard to PAL.M We have extended multimedia work place. We can create multimedia based learningP programs. We have worked not only on creating learning programs, but also on good quality|£ of presentation equipment with multimedia support (video, sound, CD, camera, . . . .). This

159


involves establishing a complex system with powerful computer, audio and video convertors,tape and computer controlled video recorder, view frame with a good overhead projectorand good color TV network. We have brought together a selection of special multimediacomponent facilities:

A) facilities for creation and preparation of applicationsB) facilities for presentation of multimedia educational programsC) mobile facilities (with lower quality performance)Owing to limited funding for this project, it is not possible to use all these facilities

simultaneously, and some components are available in very limited quantities.The first stage was a base for minimal equipment of EMC labs. In this stage we

completed the installation of the .shielded chamber, which was a necessary condition forbasic EMC measuring a testing. We have taught classes in this chamber this year. Thischamber has only a basic equipment, which enabling some types of tests for use in practicalapplication. We have a cooperation agreement between EMCaTEL and the Czech Societyfor Quality under which we test Czech products applying for the CZECH MADE attestationof quality. We need to obtain an official accreditation.

Next stage of the project:Our group will continue with its work. The information from EMCaTEL databases will

be distributed by computer net on CTU (special server). We wish to transmit and receiveinformation using special telematics services such as VIDEOTEX and TELETEXT.

Our research project deal with methods for testing electromagnetic compatibility ofteleinformatics equipment.

The group will continue to produce learning programs and handbooks. Also we are :preparing Workshop EMC !)4. |

References: I

[1] SVOBODA, J. - SIMAK, B. - ZEMAN, T. - VONDRAK, M.: Experience with CAD |Program Production in tht Field of Teleinformatics and EMC, Proceedings of Workshop <jEMC 93. CVUT. Praha 1993 f

[2] SVOBODA, J. VACULIKOVA, P. - ZEMAN, T. - VONDRAK, M.: Zdklady clektro- Imagneiickc kompatibility. Skriptum CVUT Praha, 1993 '

iThis research has been conducted at the Department of Teh communications as a part of i

research project "Education of EMC experts" No. 3831 and has been supported by a Ministry \of Education grant . \

i

-"•4

160

("IT SEMINAR 94 DEVELOPMENT OF CTU STUDY

ELECTRIC TRACTIONAS A NEW TOPIC

IN POSTGRADUATE STUDIESAT FEE-CTU

J. Kadlec, J. Zdenek, J. Gerlich

CTU, Far. of Electrical Eng., Dept. of Electrical Machines, Apparatus & DrivesTechnicka 2, 166 27 Praha 6

Key words: education, postgraduate studies, electric traction, traction vehicle, controlsystems

The aim of this paper is to present the basis for setting up a postgraduate course inElectric Traction at the FEE-CTU. Setting a basis for this was the main aim of our project,supported by Fund of Dynamic Development of Universities in 1993. Building up a newstudy discipline is longer-term matter than the one year spent on preparing the basis forthe subjects described below. Hie present state of preparation enables this study branchto be opened for next year (summer term 1994), and the full course can be provided fornext school year 1994/9.5. The introduction of Electric Traction at FEE-CTU rest on twoarguments. Firstly. FEE-CTU has not provided postgraduate courses for engineers in thisarea before. There were only theoretical possibilities in the limits of former research branchNo. 26-04-9, where some questions of electric traction are dealt with. Postgraduate studentsdid not in practice take up this option. Secondly, the undeniable fact of the splitting of ourfederal republic provides a reason for setting up such studies here. The most importantdepartment for education in this area is now located abroad (University of Transport andCommunication in Zilina). Our efforts in 1993 constitute the first stage of building upthe course of study. This has mainly involved preparations for education in the followingfour special subjects: "Electrical Equipment for Traction Vehicles'', "Dynamics of ElectricTraction", "Control of Electric Traction Drives", "Traction Vehicle Control Systems". Syl-labuses for these subjects have been developed firstly by using the experience of projectparticipants. Each of them has been engaged in problems of electric traction. Secondly wehave held many discussion with specialists from institution at home and abroad (Prague,Plzeii, Zilina, Baden). Last (but not least) we have dealt with professionals from the GeneralDirectorate of Czech Railways. A detailed description of the proposed curricula is beyondthe scope of this paper, but the proposals are available on request. The full version willbt available at the Department of Research and Development FEE-CTU. We will mentiononly the main ideas which form the basis of our proposed syllabuses. Bearing in mind thevarying knowledge of students on admission, we have proposed two limits. On the onehand we assume that we will have students graduated from a branch of power engineering(e.g. at FEE-CTU) without detailed knowledge of traction problems. On the other handthere will also be students with specialist knowledge in traction or transport (e.g. graduatesfrom UTC-Zilina). For reasons mentioned above, about a quarter of the prepared syllabusesdeals with common introductory subjects. "Electrical Equipment for Traction Vehicles" em-

161

II


phasizes the basic classification of this equipment for dependent and independent tractionvehicles. For dependent vehicles the equipment is classified according to the supply system.Next, the equipment is described from point of view of control, construction and progress."Dynamics of Electric Traction"' (besides providing an introduction to traction mechanics)deal with adhesion (the most important phenomenon) and other working conditions of trac-tion drives. Next we define the operating cases and their power consumption with a surveyof various types of driving vehicles. Along with this we discuss high velocity problems inthe design of modern electric railways and traction vehicles. "Control of Electric TractionDrives" centres on an explanation of different strategies for the control of traction driveswith respect to type, power and complexity of energy converters used. For example wepresent so called "shifted control of multi-phased chopper converters" and "control of four-quadrant converters11. We always present the state-of-the-art in design of modern tractiondrives from leading world producers (ABB, Siemens, GEC-Alsthom, Skoda, AEG). The finalsubject "Traction Vehicle Control Systems" concentrates mainly on the use of microproces-sors for control and regulation of the electric traction vehicles (or trains). In addition tothis general introduction we characterize the latest structure of multi-microprocessor controlarchitecture. We show this situation by detailed description of control systems producedby ABB and Siemens. Considerable funds have been spend on buying vocational literaturein order to fill the information gap. We select titles which will provide an overview of thelatest state of electrical traction drive design. We buy some technical standards (controlcommunication protocols, EMC of traction equipment, etc.) valid for the EC, and also somespecialized and less specialized publications dealing with traction vehicles. Seminars willbe held on special subjects and will deal with situation encounteres in the Czech Repub-lic. For this purpose technical documentation has been obtained from the producers Skodaand CKD. Course organization complies with the general requierements of the AccreditionCommittee from the Ministry of Education of the Czech Republic. One recommendationwas that the number of postgraduate courses should not be extended, which lead to thefollowing decission. The current branch of Electrical Machines, Apparatus and Drives willbe changed (including its name) and Electric Traction will be taught in this new course.This solution has not yet been approved. Nevertheless the authors believe that there are nomajor barriers to the introduction of the new postgraduate courses in the branch of ElectricTraction for new school year 1994/95.

References:

[1] JANSA, F.: Vozidla elektricke trakce, NADAS, Praha, 1985

[2] FILIPOVIC, Z.: Eltktrischt Bahnen, Springer-Verlag, GmBH&Co, Berlin, 1992

[3] ROSE, H.: Lexikon der Lokomotiven, Transpress Verlag GmBH, Berlin, 1992

This research has been conducted at the Department of Electrical Machines, Appara-tus & Drives as a part of the research project "Building up Electric Traction as a part ofpostgraduate studies at the FEE-CTU" and has been supported by FDDU grant No. 0463.

162


THE CONSULTING CENTRE FORSTUDENTS AND PUBLIC RELATIONS

P. Novotny, M. Molhanec, M. Fenclova

CTU, Fac. of Electrical Eng.,Technicka 2, 166 27 Praha 6

Key words: students consultancy, students orientation, profession consultancy, graduatesemployment, rate, psychological consultancy, relaxation, creativity, psychohygiene

The aim of the development project THE CONSULTING CENTRE FOR STU-DENTS AND PUBLIC RELATIONS ( CCSPR ) is to continue in the work of theprevious CONSULTING PUBLIC RELATIONS CENTRE existing at FEE since 1990 , andto assure its further development.

According to the CCSPR FEE CTU Status its activity is focused on three subjects:

• 1 The study orientation of both high-school students before entering the universityand university students during their studies, including the outline of possible changesof branches of study etc.

• 2 Profession (career) consultancy in the possibility of asserting selected branches ofstudy on the labour market, and in concrete assistance in searching jobs.

• 3 Psychological and social-psychological consultancy for university students.

The main task of CCSPR is to contribute to the optimization of university studies,education, and academic and professional adaptation.

The analysis of present results of the work of CCSPR

• 1 study orientation

Except routine consulting activities in cooperation with the Pedagogical Departmentat FEE, and the organisation of promotional campaigns such as " The Open DoorDay " there has been developed the expert " Consulting informational system" (CIS)for the choice of the structure of study specializations, the authors of which are thestudents of the faculty.

The database of know-how for the choice of branches of study for the empty expertsystem FELEX has been worked out by the specialists of the Department of ControlEngineering . It is evaluated according to contents of study of the branch " TechnicalCybernetics".

• 2 profession (career) consultancy

A basic part of this type of consultancy is the database system for the interactivesearching of vacancies called "Informational system of vacancies " ISV. It has been

163

CTU SEMINAR 94 DEVELOPMENT OF CTU STUDY ;

worked out in cooperation with the experts from the group of Automatic technolog-ical control systems at the Department of Electrotechnology and the Department ofElectrical Machines, Apparatus and Drives. This system works on the basis of dataincluding ten thousands of vacancies recorded at all job centers in the Czech republic . ;The data are obtained from the Ministery of Labour and Social Affairs. By means ofthis programme vacancies can be overviewed , classified according to various criteria,completed, and the results can be printed out. The programme can be run on IBM IPC compatible with hard disks (or network disks), with any grafic card. -jf

At present the possibility of data transmission from the ministery to FEE by means ij,of a modem is verified. The transmission itself is organized manually. In future the : |automated data transmission is expected to be developed. According to the verbal Jagreement with the workers of the ministery it is supposed that this transmission -»of the data of vacancies will become the main means of communication between theministery and universities. Data files will be distributed to each university in theCzech republic through the academic network CESNET covering the whole republic.At the same time the system CIS, developed at FEE, will be opened to each universitythrough this network. The exchange of data providing vacancies and requirements forspecialists from the universities in CR , and its coordination will be enabled.

The statistical processing of the avalability of vacancies on the labour market willpresumably enable to create future trends of the requirements for the number of grad- fuate students from different study branches and specializations within further several fyears. The results of the assessment can be exploited for the determination of thenumber of students beginning from the first year of the study, which will result in theflexible development of individual branches and specializations.

• 3 psychological consultancy

Psychological consultancy is being developed only now due to the previous lack ofpersonel. About 30 students from the first three years of study have been examinedby the psychologist employed at FEE, at the Department of Economics, Managementand Humanities. Psychological probes were provided to about 70 students of the 4thand 5th years by the experts in the Pedagogical and Psychological Advice Center atthe Faculty of Physical Training and Sports in Prague. There were used Raven andAmthauer IQ tests , the tests of individual rate , Eysenack and Cattel personalityquestionnaires, tests of efficiency, motivation and anxiosity, memory tests, tests ofsocial relations and partner relation tests. The results of all the tests were consultedindividually.

To assure further continuation and development of the work of our Consulting Center,* including the Psychological Laboratory, CCSPR Project for the year 1994 has been applied, for the grant.

ij This research has been conducted at the Department of Pedagogical at FEE as a partt*' of the research project "The Study and Career Consultancy on Universities" and has been>, supported by CTU grant No. 3819.

*.'•"' 1 6 4

I

Section 5

FLUID MECHANICS

^

CTU SEMINAR 94 FLUID MECHANICS

AERODYNAMIC INVESTIGATIONSOF THE WEAVING REED

V. Tesaf

CTU, Fac. of Mechanical Eng., Dept. of Fluid Mechanics &; ThermodynamicsTechnicka 4, 166 07 Praha 6

Key words: Weaving, shuttleless loom, reed, jet, cascade

The reed is one of the basic weaving tools of the loom, in which the tools act on threadsto weave them into the fabric. In principle, the weaving process consists of periodicalinsertion of the weft thread in the transverse direction between the longitudinally orientedwarp threads. The reed consists of thin metal lamellae, the blades, which are permanentlyinserted between the warp threads and move periodically towards and away from the headof the fabric. Its task is to beat the inserted weft against the fabric head. In its basic form,the reed blades are produced by rolling steel wires into thin flat strips with rounded edges.

In the modern shuttleless looms, the weft insertion is achieved by the action of a fluidjet. The jet is blown along the reed into the space formed momentarily between the warpthreads. An important problem of the air jet looms is the fact that the jet gradually loses itsmomentum as it moves along the reed. One of the possible ways how to alleviate this problemis the use of a system of auxiliary jets issuing from the "relay-race" nozzles. These are hollowneedles, momentarily inserted between the warp threads at intervals along the insertionpath of the weft. The auxiliary jets adds momentum to the air Row which compensates forthe loss. Since these nozzles cannot be placed directly in the path of the weft and mustbe placed somewhat sideways, their exit channels are to be inclined towards the path -and this means they are inclined towards the reed. The reed is a rather complex periodicstructure, consisting of individual blades. Consequently, the flowfield generated by the main

' > and auxiliary jets hitting upon the reed blades and partly passing between them is complexas well. The phenomena taking place in this complicated and little understood flowfield

; have primary influence upon the dynamics of the weft motion. It is recognised that oneof the conditions necessary for further increase in fabric manufacturing productivity using

; air jet looms critically depends upon better understanding of the aerodynamic phenomena§ taking place during the weft insertion process.5 For achieving smooth motion of the weft along the reed, it is essential that the weft doesit not come into contact with the edges of the reed blades, despite the fact that the auxiliaryI, jets tend to move the reed towards them. Early visualisation studies have explained the| | apparent paradox by the "reflection" of the jet [1] - as shown schematically in Fig.l. A partf of the impinging jet is transmitted through the reed and its flow direction is changed togj correspond to the direction of the passages between blades. The rest of the jet then behaves|s: as if reflected from the reed to compensate for the change in the lateral momentum of the§| diverted transmitted part.W Interesting results were obtained experimentally for the transmission loss in the flow$ passing through the reed. Since the reed passages have a pronounced direction, detailed

• I; studies of the transmission loss were also made with oblique angles of the incident flow. This, |i has led to the discovery of a surprising phenomenon, which is important for the generated

- • I••f 167


diverting effect of the reed passages. Especially in the range of Reynolds numbers (relatedto the blade chord) from Rei = 0.5 103 to Ret = 5 103, which is just about the rangeof usual operating conditions in the loom, it was discovered that the exit flow direction iscompletely different from the expected direction parallel to the reed passages.

In principle, the reed might be viewed upon as an non-conventional profile cascadeexhibiting unexpected, variable flow turning properties. The experimental procedure usedby the author made it possible to evaluate the lift and drag coefficients of such a cascade.

Impingingjet

Reflected* jet

IlllllllllReed

Transmitted flow

Fig. 1: The "reflection" phenomenon: the part of the jet which does not pass through thereed returns away from the reed. In the jet loom, this is used to generate the lift force onthe weft.

pipe

ifI

Fig. 2: The discovered extraordinary flow-turning properties of the reed were investigatedwitli the reed attached at an oblique angle at the end of a pipe.

References:

[1] TESAR, V.: "Reflection" of a Fluid Jet from a (Perforated) Wall: a Flow VisualisationStudy FLOW VISUALISATION V, Proceedings of the Fifth International Symp. onFlow Visualisation, p. 640, Praha 1989

•r 168


TEST EQUIPMENTFOR MEASURING ENERGY LOSSES

IN WET STEAM FLOWV. Petr, M. Kolovratnik, J. Jilek

CTU, Fac. of Mechanical Eng., Dept. of Thermal k. Nuclear Power PlantsTechnicka 4, 166 07 Praha 6

Key words: energy losses, wet steam, measurement, convergent-divergent nozzle

Expansion of a pure steam in a convergent-divergent nozzle from a superheated stateat an inlet into a wet steam region is characterized by spontaneous formation of tiny waterdroplets within condensation shock. The metastable state of steam in front of the conden-sation shock undergoes transition to near-equilibrium state of wet steam flowing past thecondensation shock.

Assuming further the flow of wet steam in the convergent-divergent nozzle operating atnon-design conditions (i.e. with increased back-pressure), the wet steam will pass throughthe aerodynamic shock wave. Within the front of the shock wave a stepwise change ofpressure, velocity and temperature of the vapour phase only is taking place, while the newequilibrium state of the wel steam will be reached in the relaxation region past the shockwave.

Both phenomena i.e. transition from metastable to near-equilibrium state within thecondensation shock and relaxion phenomena i.e. mass, heat and impulse exchange betweenthe liquid and vapour phases occurring past the aerodynamic shock wave, are stronglyirreversible. These irreversibilities are characterized by the corresponding entropy increasesresulting in the energy losses.

It is the aim of the present research program to compare the theoretical prediction ofthese energy losses [1] with experimental results. The research program in 1993 was aimedat improvement of the test equipment consisting of the convergent-divergent nozzle as it isseen in Fig.l. Superheated steam is corning from the boiler through the separator 1 into thenozzle inlet vane 2. Then passes through the convergent-divergent nozzle 3 and nozzle outletvane 4 into the mixing-type conderser 5. Control valves Vi and V-i enable the desired inlet andback-pressures to be settled. The nozzle is equipped with pressure probes pt<s (inlet total),Pi (total current) and p, (static current) connected through tranducers with PC. Inlet steamtemperature t0 is measured by means of thermocouple. Mean radius of droplets formingthe liquid phase of wet steam is determined by means of the monochromatic light beamattenuation I/Io when passing through the wet steam (6-light source with monochromator,7-photodiode).

Variation of ps(«), Apt(z), ///o(z) along the nozzle axis is measured by moving thenozzle profile with hydraulic cylinder 8.

-if»- 169

1•I

CTU SriMINAR 94 FLUID MECHANICS

max O.SHPa, 180 C_ .

O —>•—*• I t

Fig. 1: Test equipment of convergent-divergent nozzle

In order to prevent the pressure probes from steam condensation, the measuring systemis equipped with air purge controlled by electromagnetic valve system 9.Measurements and final discussion of the results will be the aim of the research programfor 1994.

References:

[1] PETR, V.: A survey of relaxation losses in a turbine blading operating in wet steam.Proceedings Inst. Mech. Engrs: "Turbomachinery-Efficiency Prediction and Improve-ment", Cambridge, 1987

This research has been conducted at the Department of Thermal and Nuclear PowerPlants as a part of the research project "Experimental proof of energy wetness losses occur-ring in steam turbines" and has been supported by CTU grant No. 8023.

170


ON OPTIMAL PARAMETERSOF SHOCK WAVE SYSTEMS

A. Polak, P. Safafik*

University of Cincinnati, College of Eng., Dept. of Aerospace Eng. and Eng. Mechanics

797 Rhodes Hall, Cincinnati, Ohio 45221, USA

*(TU. Fac. of Mechanical Eng., Department of Fluid Mechanics & ThermodynamicsTeclmicka 4, 166 07 Praha 6, Czech Republic ]

Key words: aerodynamic optimization, supersonic flow, shock waves

The shock wave theory assumes a discontinuity in flow parameters across the shock sur-face and is based on the consequential principles of balance of mass, momentum and energyacross this surface. This theory offers an oportunity to formulate and solve optimizationtasks for shock wave systems. In the principal work by Oswatitsch [1] the optimizationproblem is formulated for n shock wave system in a supersonic inlet when the last shock isnormal. The task set forth is to determine, for given n and an upstream Mach number Mj,the shock configuration producing the maximum overall total pressure ratio pOn+i/Poi- i

In this short paper we consider further optimization problems for a system of shock jwaves, as were presented and solved in [2]. The optimization criterion is that overall ratio ]of total pressures is maximum.

5 The two-dimensional flow geometry with pertinent parameters to be considered in thetask formulation is exhibited in Fig.l. The oncoming supersonic stream 1 deflects fromhorizontal surface by an angle 8\ and the first oblique shock wave is inclined relative to the

: oncoming stream at an angle ff\. The resulting increase in static pressure from p\ to p2 isgiven by the parameter ft = pz/p\. The total pressure and Mach number decrease fromPel to ;>,,2, and Mt to M%, respectively. Subsequent deflections S2, ...,<S;, ...,<5n produce shockwave system under condition M-i > ... > Mi > ... > Mn.

In the analysis we assume the fluid to be a perfect gas with a ratio of specific heatsK = 1.4. The oblique shock relations substituted into the optimization criterion - minimum

J entropy increase in shock waves - give the system of equations satisfying the criterion of£ the formulated optimization tasks. Further limitations, conditions and descriptions must

be given in the formulation. We have solved the following three cases of the optimizationf: tasks :H' Case (a) : Given pn+i/px and Mi.| | Independently of the value Mi from pn+\jp\ = ft • ft •... • ft •... • ft, = const the system§jj; of equations is derived which combined with the criterional system gives a solvable system

valid only when ft = ft; = ... = ft = ••• = fti = £ = \/pn+i/pi- The limit case of thisoptimization task is identical to Oswatitsch's solution [1]. Remaining flow parameters areobtained from formulas for oblique shock waves. A sample calculation is presented in [2],

Case (b) : Given Mi and M>1+iIndependently of the values Mi and A/n+i from description of shock wave parameters

the system of equations is derived which combined with criterional system gives a solvable

s . ,.. % system valid only when ft = ft. = ... = ft = . . . = £ „ = £ = 3 ( F s - l ) + ^ 9 • (Ps- 1)2 + Ps,.; ,t_; §1 where Ps = i/(M,2 + 5)/(M*+l + 5). The advantage of multiple wave system is verified

*-.'•'*: i7i


If

from S, the ratio pOn+ilpa\ to single wave case (pO2/Poi)n=i, and sliown in Fig.2. For n = oothe solution is identical to Prandtl-Meyer supersonic compression. Lower bound of A/j isdetermined for given values of A/i and Mn+j. A sample calculation is presented in [2],

Case (c) : Given 6\ and 82

This case is applicable when the shock wave generator geometry is given and optimalparameters are to be determined. The case was solved for n = 2. From conditions onshock waves the system of equations is derived which combined with the criterional systemgives the system solvable by means of the computer only. A double iteration procedure wasdeveloped and applied. A sample calculation is presented in [2].

The various optimization tasks using the same criterion produced substantially differentresults. The formulation and solution of the optimization tasks seem to be a topical approachto aerodynamic problems and offer a wider variety of views into aerodynamic processes.

n 5

Fig.l Fig.2

References:

[1] OSWATITSCH, K.: "Pressure Recovery to Missiles with Reaction Propulsion at HighSupersonic Speeds (the Efficiency of Shock Diffusers)", NACA TM-1140, June 1947.

[2] SAFARIK, P. - POLAK, A.: "Optimal Shock Wave Parameters for Supersonic Inlets",(the paper submitted to the Journal of Propulsion and Power for publication).

172


SIMILARITY SOLUTIONOF THE PLANE JET

USING ADVANCED TURBULENCEMODELS

V. Tesaf, J. Lain

CTU, Far. of Mechanical Eng., Dept. of Fluid Mechanics &• ThermodynamicsTechnicka 4, 166 07 Praha H

Key words: Jet, turbulence models, plane turbulent jet. similarity solution

The shear flow generated by outflow of fluid from a slit nozzle into an unboundedspace containing the same fluid is called the plane submerged jet. It is of importance formany practical applications, where the jet is usually turbulent. An interesting feature isthat beyond several nozzle widths from the nozzle the jet flow attains an asymptotic state.This is manifested by mutual similarity of the velocity profiles - as well as profiles of otherparameters - which, when transformed into suitable similarity co-ordinates, change into justa single curve. This fact makes applicable the idea (first used by Blasius, 1908, for solutionof laminar boundary layer) of similarity solutions: the partial differential equation which

> describes the flowfield, when re-formulated using the similarity co-ordinates, transforms intoan ordinary differential equation. This, of course, is much easier to solve and analyse. Thisapproach has been a standard one for solutions of the turbulent jet flow problem with simple,algebraic turbulence models - the well-known examples are solutions due to Tollmien (1926)and Gortler (1942) ..e.g. ref. [1].

• % In fact, the similarity approach is so much associated with these simple solutions thatthe idea of applying it with the present-day, advanced turbulence models seemed almost. j

,; absurd. Nevertheless, since available experimental results (such as the mutual similarity v

of measured velocity profiles) [2] clearly demonstrate the objective existence of similarity•;:'•' in the flowfield, there is no reason why the approach should not be applicable also with%} turbulence models of any complexity and, in fact, might offer an interesting possibility for;1 study of the more subtle features of these models.: |. The present authors applied the similarity solution approach for plane turbulent jetflf flows calculated with the one-equation and the two-equation models of turbulence [3]. These•|f' models use the transport equations to describe (or simulate) the distribution of individualfgi turbulence parameters. It is then possible to take into account both the advective as wellS , as diffusive transport phenomena which govern the spatial propagation of turbulent fluctu-gj: ations - in contrast to the classical algebraic turbulence models in which the fluctuations

should be governed solely by the local parameters of the flowfield. This may lead to bettersolutions of the turbulent flowfield. In the case of jets the better modelling is expectedespecially for the flow near the jet axis, where the algebraic models (in which turbulentviscosity is proportional to the local value of the gradient) predict nearly zero turbulence,while experiments witness that turbulence intensity at the axis is nonzero, the fluctuationsbeing propagated towards the axis by the diffusive transport.

•- 173'ft

CTU SEMINAR 9-1 FLUID MECHANICS

The mean flow results for t tie one- and two-equation model are practically equal. Theyboth compare very well with experiments. For the one-equation model, the solution containsa parameter associated with the mixing length magnitude. The parameter and, in turn, thecorresponding constant of the mixing length distribution could be determined from thecomparison of the calculated and experimental velocity profiles. The two-equation modelwith the standard set of model constants avoids even this empirical input.

0*0

— generation

— — convection

— — diffusion

— dissipation

2.50

V •n

Fig. 1: Left: The profiles of time-mean velocity and turbulence kinetic energy, practicallycoincident for both one-equation and two-equation model. Fig. 2 : Right: distributionof individual terms in the transport equation for the turbulence energy across the jet crosssection.

As far as the limited available experimental evidence [2] admits to conclude, the ad-vanced models also very well describe the profile of turbulence energy. Of particular interestare the values of individual terms in the turbulence energy transport equation obtained fromthe solution.

References:

[1] TESAR. V.: ''Stcnovy proud v soubezne'm proudeni - konfrontact dvon zdkladnieh mod-elu turbulence" (Wall Jet in Concurrent Flow - Confrontation of the Two Basic Tur-bulence Models, in Czech) ACTA POLYTECHNICS - Prace CVUT v Praze c. 4 (II,2) 1985, Praha

[2] RAMAPR1AN, B. R. - CHANDRASEKHRA, M. S.: Measurements in Plane TurbulentJets" ASME, Journal of Fluids Engineering, Vol. 107, 1985,p.p. 264-271

[3] TESAR, V.: "Mezni vrstvy a turbulence" (Boundary layers and Turbulence, in Czech)Textbook FS-CVUT, published by Edicni stfedisko CVUT, Praha 1991

This research has been conducted at the Department of Fluid Mechanics and Thermo-dynamics, Faculty of mechanical Engineering, as a part of the research project "Numericalsolutions of turbulent jets' and has been supported by GACR grant. No. 101/93/0^44-

174


COHERENT STRUCTURESIN TRANSITIONAL WALL JET

J. Lain

CTU, Fac. of Mechanical Eng., Dept. of Fluid Mechanics & ThermodynamicsTechnicka 4, 166 07 Praha 6

Key words: wall jet, transition, hydrodynamic stability, Orr-Sommerfeld equation, coher-ent structure

The wall jet is one of the basic shear flows. A practical application of the wall jetis for instance the creation of the cooling layer between hot fluid and a wall. The walljet is theoretically interesting for turbulence research because it combines two instabilitymechanisms - inviscicl and viscous. The former is due to inflexion point in the mean velocityprofile, the latter due to proximity of a wall. The entrainment into the shear layer and thetransition are phenomenons which determine behaviour and development of the flow. Thesephenomens are influenced by the stability of the flow.

The hydrodynamic stability has gained much attention of fluid mechanics scientistsespecially for the possibility of explaining some features of the laminar to turbulent transi-tion, or even the turbulence. The big obstacle in the hydrodynamic stability theory is thenonlinearity of the basic equations of fluid motion. So the first theory of hydrodynamic sta-bility, called linear, has used the linearized equation for disturbances under the assumptionof infinitesimally small disturbances. The great gain of the linear stability theory is theOrr-Sommerfeld equation. The linear theory can predict the loss of stability of a laminarbasic flow, eventually the first stage of the instability growth, the so-called linear part, whenthe disturbance is very small. When the disturbance becomes finite, the linear theory willnot more be valid.

To explain the next stages of the disturbance development the nonlinear stability theoryhas been created. When the disturbance becomes finite, it can significantly influence thebasic flow. Experimental evidence leads to the conclusion that the coherent structures aremanifestation of the hydrodynamic instability. The coherent structures were first recognizedexperimentally and has been observed in transitional and turbulent domains of shear flows.The coherent structures are important especially for their qualities which are different fromthat of the stochastic fluctuations of the turbulence. They are organised and are sensibleto the boundary respectively initial conditions. So they can be managed through theseconditions. And because they can be an intermediary in the energy transport between themean flow and the turbulence, also the turbulence can be managed through the coherentstructures managing. Turbulence managing is a new field in fluid mechanics research thatcan have broad use in all fluid flow applications. The nonlinear theory supplies a theoreticalinstrument to describe the coherent structures quantitativly.

This work deals with the usage of the nonlinear theory of hydrodynamic stability todescribe the coherent structures development in the transitional domain of the wall jet. Thetheory rises from the basic equation of the fluid motion where the variables are split intothe mean and disturbed parts. The basic equations with the splitted variables undergo theconditional averaging which filters some harmonic component of the disturbances with all

175

("TV SEMINAR 91 FLUID MECHANICS

its higher harmonics. The experimental evidence shows that the first harmonic of the mostamplified frequency becomes dominant in the first stages of the transition. The experimentalresults also conclude that the disturbance form is very closed to the eigenfunction fromthe linear stability theory. So the form assumption for the disturbances is taken as theeigenfunctioi) of the Orr-Sommerfeld equation and the spatial amplification theory is usedfor the disturbance which develops in spare. At each space coordinate the eigenfunctionis calculated for the actual mean velocity profile and ditnensionless frequency so that thephysical frequency of the disturbance remains constant. For the mean flow the thin shearlayer simplification is used. As the mean flow velocity profile the Glauert solution of thelaminar wall jet is assumed. After the integration of the basic equation for mean and idisturbed flow across the shear layer, a system of ordinary differential equations describing .the mean flow and disturbance development in space is obtained.

To provide a numerical calculation of the equations obtained from the nonlinear theoryone needs at first an algorithin to solve the eigenfunction of the Orr-Sommerfeld equation.To solve the Orr-Sommerfeld equation the Keller's box scheme was used. To solve theeigenproblem the Newton's method of approximations was used as in [5].

The qualitative comparison of results with experimental data looks very well. Espe-cially the form of the disturbance and the tendency of its development. The quantitativeagreement is to reach only for the first stage of the nonlinear domain, because in the real flow •;the subharmonic frequency disturbance development follows. Subharmonic (the componentof the disturbance with a frequency one half of the fundamental frequency) development isthe next aim of this work. I

References: ,1

[1] BAJURA, R. A. - CATALANO, M. R.: Transition in a two-dimensional plane wall jet. |J. Fluid Mech., Vol. 70, 1975, pp. 773-799 1

[2] MELE, P. MORGANTI. M. - SCIBILIA, M. F. - LASER, A.: Behaviour of wall jet |in laminar-to-iurbuUnl transition. A1AA .]., Vol. 24, No. 6, 1986, pp. 938-939 f

[3] LIU, J. T. C : Contribution to the understanding of large-scale coherent, structures in |developing free turbulent shear flows. Adv. in Appl. Mech., Vol. 26, 1988, pp. 183-305 t

[4] LIU, J. T. C : Coherent structures in transitional and turbulent free shear flows. Ann. •Rev. Fluid Mech., Vol. 21, 1989, pp. 285-315

[5] CEBECI, T. - CHEN, H. H.: Numerical method for predicting transition in three- idimensional flairs by spatial amplification theory. AIAA J., Vol. 30, No. 8, 1992, pp. ;1972-1979 i

\This research has been conducted at the Department of Fluid Mechanics and Thermo-

dynamics as a part of the research project "Hydrodynamic Stability and Phase TransitionKinetics" and has been supported within the framework of the Czech government program."Education Development".

176


LAMINAR FLOW IN SPIRAL DUCTOF RECTANGULAR CROSS SECTION

J. Sestak, M. Dostal, R. Zitny, F. Ambros

CTU, Fac. of Mechanical Eng., Dept. of Chemical & Food Process Equipment DesignTechnicka 4, 166 07 Praha 6

Key words: laminar flow, spiral channel, secondary flows, friction factor, CFD, FLUENT

Laminar fluid flow in a. spiral duct is of great practical importance, because the spiral ge-ometry (usually with rectangular cross section) is frequently encountered in heat exchangersand membrane filters. Some process characteristics are closely related to the spiral channelcurvature, because centrifugal forces induce secondary flows, which enhance heat transfer ormembrane rinsing. On the other hand, secondary flows increase the pressure drop along thechannel axis, characterized by the friction factor A. In the previous workshop contribution(Sestak [1]) a critical review of existing friction factor correlations and also a new corre-

: lation for rectangular cross-section geometry was presented. The conclusion was obvious:There is a lack of reliable experimental results in a sufficiently broad range of geometricalparameters, which could substantiate (or discard) suggested correlations.

The "true1" experiment in laboratory is expensive, difficult (the results obtained so farare rather inaccurate) and gives no information about velocity profiles or associated quan-tities (e.g. residence time distribution). Therefore we turned to the numerical experiments,using comercial CFD package FLUENT, which is capable to solve incompressible flows,described by three dimensional Navier Stokes equations, using control volume approach.

Although Fluent is equipped with its own preprocessor for definition of geometry and, computation grid, we developed a special preprocessing programm, which enables to create{ an optimal nonuniform grid in a rectangular channel. The assumed channel consists of two

regions: the straight inlet section and the following spiral section defined by the geometryof the Archimedean spiral: r{(j>) = r0 + a<t>, 0 < <f> < (j>max •

To decide whether Fluent is the proper tool for the spiral flow simulation, we shall•; compare the results with the numerical solution published by Ghia and Sokhey [2]. Thisf solution describes the developing laminar flow in curved ducts with the rectangular cross-t; section by means of finite difference method applied to the Navier Stokes equations simplifiedjjj, by parabolization.j | The comparison was performed for the following set of parameters:| R/D = 14.5; Re = (wDp)/ft = 206; De = Re.^D/R = 55 , where D is hydraulic§' diameter (Z?=width=height), R is the radius of curvature and Tv is the mean axial velocity.

As a boundary condition the uniform (flat) axial velocity profile was assumed at the entry.The grid prepared for Fluent was rather coarse (5 * 10 * 60 cells), so that the number of

iterations was relatively small - 633( to attain residuals of moment equations below 10"6).The comparison of axial velocity profiles in different cross sections is given in the fol-

*'- | lowing figure (1).

V*


ftI)

-o.a

-ej

j

. 0

1 2

Fig. 1: Axial velocity profiles (points - Fluent, full line - Ghia, Sokhey)

It is clear that the results computed by Fluent and Ghia, Sokhey compare rather well,which is not true for the velocity profiles in the cross-section (Dean vortices), see fig. 2. Thesame discrepancy occurs when comparing axial presure profiles (in Fluent it was computedby a special postprocessing program, averaging pressures in cells for every cross-sectionplane). Possible explanation may be that, the grid used in Fluent was too coarse andthe departures observed are nothing else than approximation errors (more than that, thesimulation reveals an obvious Fluent error when transferring data, making approximately20 percent of computed pressures in boundary cells unaccessible). Nevertheless it is stillpossible that either the solution by Ghia is a little bit distorted by the parabolization ofN.S. equations.

:

M M 1

Fig. 2: Axial pressure profile Fig. 3: Secondary flow in cross-section

The final decision has been postponed until the new version of Fluent will be installed,because it should improve efficiency of simulation using multigrid method, thus enablingmuch finer meshing with resonable run-time demands.

References:[1] SESTAK, J.: Pressure drop prediction in a spiral channel Workshop 93 - Fluid mechan-

ics, CTU Prague, January 18-21, 1993

[2] Ghia, K. N. - Sokhey, J. S.: Laminar incompressible viscous flow in curved ducts ofrect. cross-section Transaction of the ASME, J. of Fluids Eng.; (1977), pp.640-648

This research has been conducted at the Department of Chemical and Food ProcessEquipment Design, Faculty of Mechanical Engeneering CTU and has been supported byCTU grant No. 8083.

178

^ ^

CTV SEMINAR 94 FLUID MECHANICS

MACRO-INSTABILITY MEASUREMENTIN AGITATED SYSTEMS

P. Smolka, O. Bruha, I. Fort*, T. Makovsky*

CTU, Far., of Mechanical Eng., Dept. of PhysicsTechnicka 4, 166 07 Praha 6

*(TU, Fac. of Mechanical Eng., Dept. of Chemical & Food Process Equipment DesignTechnicka 4, 166 07 Praha 6

Key words: mixing, (low, instabilities, turbulence

The objective of this paper is an experimental study of a turbulent macro -instability ina mixing process. By instability we mean the time-limited occurrence of a certain characterof turbulent flow whose extent exceeds the scales of common turbulent vortexes [2],[3]. Inthe final stage it usually manifests itself by the level swelling-up in the region in front of thebaffle in a. vessel, and the occurrence, interval of this instability is within the range of severalup to tens of seconds. As this phenomenon may bring about rather big dynamic effects onthe parts of industrial agitating equipment and may also influence the entire mixing process,its study is of considerable importance both from the point of view of the equipment designand the optimization of mixing as well.. Investigations of macro-instabilities have explainedtheir occurrence as a consequence of the existence of "double-loop" flow patterns in anagitated system in addition to the classical "single-loop" one. This knowledge was obtainedby mixing water in a cylindrical vessel with four baffles and six-blade impeller rotating topump water towards the bottom [ I ], [•!]. According to the results presented, the frequency ofturbulent macro-instabilities depends approximately linearly [2] on the frequency of impellerrevolutions. The aim of this work was the investigation of regularities of the turbulent macro-instability occurrence in a mixed liquid as a function of impeller frequency of revolutions,liquid viscosity and type of baffles in the mixed system. A cylindrical vessel with an axial jhigh-speed impeller served as an experimental equipment, the manifestation of the turbulentmacro-instability being considered the shift-over between the single-loop and double-loop(low patterns. To identify the transition from one to another of the above mentioned flow

> patterns, a special measuring technique was designed. The experiment was carried out; in a cylindrical vessel of diameter D = 300 mm filled with liquid to the height H=D. The

;. impeller off-bottom clearance was set at three positions, H2=0.2 D, 0,35 D and 0.5 D. Three§: different charges were used for the measurements: water and saccharose solutions of massif concentrations 27mixing numbers, calculated from the relation

I Re -p. '/

|t; lays in the range from 4200 to 66 600. It is evident that all the measurements wereif carried out in the turbulent flow of the mixed liquid . To indicate the shift-over from thep single-loop to the double-loop patterns, a device was developed, which is a circular target§3 attached to a swinging arm. The transition of the single-loop pattern to the double-loop one

> gj" causes the arm deflection through the mediation of the target and this is transferred to a line, % recorder in terms of an electric resistance sensor. From the record obtained and with help

*-• ' 1791

i

w


of flow visualization (light knife method) , it was found that the change of the single-loopof flow to the double-loop one, accompanied by the turbulent macro instability, manifested :

itself in the record as a conspicuous change of displacement of the recorder tip. These >displacements, when indicating the turbulent macro-instability, differ from those brought •about by common turbulence by the following properties: they have larger amplitude , ;they have a character of mostly unidirectional deviation and their changes have a step ;

character. The measurements proved that within the impeller frequency of revolutions200-400 min-1, the dependence of turbulent macro-instability frequency on the impeller %frequency of revolutions may be considered linear for all the impeller off-bottom clearances. ,'In the examined range of viscosities an expressive effect of the mixed liquid viscosity was |not proved on the turbulent macro-instability frequencies in the given range of impeller |frequencies of revolutions. !l

References: $\

[1] BRUHA, O. - FORT, I. - SMOLKA, P.: Large Scale Unsteady Phenomenon in a Mixing §Vessel Proc. of Workshop 93, sect. 6, p.59-60, Prague 93 §

[2] HAM, S. - BRODKEY, R. S.: Local Heat Transfer in a Mixing Vessel Using a Heal |Sensor Ind.Eng.Chem.Res., 1992, 31, pp.1384-1391 §

[3] WINARDI, S. - NAGASE, Y.: Unstable Phenomenon of Flow in a Mixing Vessel with §a Marine Propeller Jour. Chem. Eng. of Japan, Vol.24, No.2, 1991, pp.243-249 f

[4] KRESTA, S. N. - WOOD, P. E.: The Flow Field by a Pitched Blade Turbine: Changes fin Circulation Pattern due to Off-bottom Clearance Canad.Jour.Chem.Eng. 1993 I

This research has been conducted at the Department of Physics, Faculty of Mechanical fEngineering and has been supported by CTU grant No. 8021.

180

CTV SEMINAR 94 FLUID MECHANICS

OPTIMIZATIONOF MIXING EQUIPMENT:

PROCESS AND DESIGN PARAMETERSF. Rieger

CTU, Fac. of Mechanical Eng., Dept. of Chemical & Food Process Equipment DesignTecluiicka 4, 166 07 Praha 6

Key words: mixing equipment, agitator, power consumption, mixing time, suspension,flow, draught tube

Our research on mixing equipment optimization was subdivided into three parts. Thefirst part was devoted to power and homogenization characteristics, the second part dealedwith mixing of suspensions and the third part was concentrated on the flow in vessels witha draught tube.

In the first part:- We finished measurements of homogenization in unbaffled vessels. It was found that

the product of mixing time t and the agitator speed n is constant for given agitator geometryin the turbulent region. The experimental results for three and six pitched blade turbinesand for the disc turbine were presented on CHISA Congress [1].

- Power consumption and homogenization time measurements were also carried out forturbines with the profiled pitched blades. The research on this topic will continue.

- The method for industrial mixing equipment calculation from experimental powercharacteristics was suggested and applied on proposal of equipment series with close clear-ance agitators.

- The results of earlier power consumption measurements with non-Newtonian fluidmixing were published [2].

In the second part: - The dimensionless equation for the agitator speed calculationsuggested on the basis of laboratory experiments with glass ballotine suspensions was verifiedby measurements on the vessel with diameter D = lm and with particles of smaller density

I| - The dimensionless criterion proposed for comparison of the agitator efficiency atf mixing of suspensions was applied for selection of the optimum relative agitator size. The|i equipment characterized by the ratio of vessel to agitator diameter D/d = 3 was found more| | efficient than equipment with ratio Did = 2 [4].If - The results of the geometrical parameters optimization for the tall vessels with afjfi draught tube were presented [5]. The following optimum parameters were recommended:H the conical bottom angle a = 45" and the draught tube height above bottom equaled to 0.17H of its diameter.I'; - The measurement of power consumption [3] showed the constant power number for

v Wl dilute suspensions of light particles and the power number dependent on state of suspension1 f| for concentrated suspensions of heavy particles. The research in this field will continue.

.-¥ 181

k

f


The third part of the research project dealed with flow in vessels with a draughttube. This arrangement is frequently used in mixing equipments and was also used inmeasurements of the agitator operating characteristics [6]. The flow in vessels with a draughttube was analyzed numerically using the specialized program product. FLUENT. The firstresults were obtained and the research on this topic will be continued.

References:[1] NOVAK, V. - RIEGER, F.: Mixing in unbaffled vessels. 11th CHISA Congress, Prague

1993

[2] NETUSIL, J. - RIEGER, F.: Power consumption of screw and helical ribbon agitatorsin highly viscous pseudo-plastic fluids. Chem. Eng. J. 52 (1993) p.9

[3] RIEGER, F. - SINEVIC, V.: Mixing of suspensions. 11th CHISA Congress, Prague1993

[4] RIEGER, F.: Efficiency of agitators while mixing of suspensions. Proceedings of 6thPolish Conference on Mixing, TU Cracow 1993, p.79

[5] JIRICKOVA, E. - RIEGER, F.: Optimization of tall vessels with draft tube for mixingsuspensions. 11th CHISA Congress, Prague 1993

[6] RIEGER, F. - WE1SER0VA. H.: Determination of operating characteristics of agita-tors in tubes. Chem. Eng. Technol. 16 (1993) p. 172

This research has been conducted at the Department of Chtmical and Food ProcessEquipment Design, Faculty of Mechanical Engineering CTU and has been supported byCTU grant No. 8025.

» . 182

*

• sV--<* ~n*Kr**>=*i'*-


FLOW OF LIQUID IN AGITATEDFERMENTOR WITH

COUNTERCURRENT IMPELLERSI. Fort, V. Strejc

(•TU, Fac. of Mechanical Eng., Dept. of Chemical & Food Process Equipment Design jTechnicka 4, 166 07 Praha 6 |

Key words: agitated fermentor, flow of liquid, countercurrent impellers

Mechanically agitated ferinentors with high height / diameter ratio are equipped withtwo or more impellers on the same shaft. A standard arrangement of fermentor consists ofbaffles at the vessel wall to avoid central vortex at the liquid surface as well as insufficient >.mixing ( blending ) in liquid phase. Aplication of the radial baffles may cause problems withsanitation after a fermentation process is finished and, moreover, may cause an additionalturbulent stress - source of the mechanical damage caused by microorganisms produced. Theaim of this study was to design and to test a pilot plant mechanically agitated fermentorwith two high - speed axial countercurrent impellers ( see Fig.l ) pumping liquid in the 3same direction. Two impellers with six inclined plane blades of the same diameter d ( seeFig. 2 ) rotated at the same level of frequency of revolution in clockwise or counterclockwisedirection, respectively, both pumping liquid downwards towards to the bottom of fermentor.

* The following requirements for the flow pattern of agitated batch were defined:

1) Single continuous circulation loop in the whole system,2) Negligible contribution of tangential ( peripheral) component of the macroflow at the

vicinity of the liquid surface ( i.e occurence of the central vortex ).

Three distances between countercurrent impellers #3 as well as three values of theirangles of inclination a ( see key of Fig. 1 ) were tested. Three experimental techniques for

•: the test used were introduced:

1) A "Light knife" for the determination of the existence of the two - loops or one - loopliquid circulation.

| | 2) Observation of the peripheral (tangential) circulation of the "Flow follower" for deter-s| mination of the flow pattern without the existence of the above mentioned componentps of t he circulation a t t h e liquid surface.H 3) T h e torsion dynamomet r for determinat ion of the power input, of t he countercurrent

Isk, impellers tes ted.

S From the exper iments m a d e on the pilot plant equipment following results follow:

>, ! | 1) O n e circulation loop of agi ta ted batch appears up to relative axial ( ve r t i ca l ) d is tance••, ' ||: between impellers H3 = 2d. However, t he flow pat te rn a t this d is tance is not s tablei ' f| and , tlerefore, max imum dis tance between impellers H3 = 1.5d is recommended.

«.:*'* 183


2) Minimum, i.e negligible, peripheral circulation of agitated liquid appears at the con-figuration of the angles of impeller inclination ai + Q2 = —5°, i.e. when the absolutevalue of the upper impeller angle of inclination is about 5° greater than the lower one.

3) Power input of the two countercurrent impellers with inclined plane blades is practi-cally the same as power input of the same impellers in the standard arrangement ofthe agitated fermentor with baffles [ 1,2 ].

In conclusion the best configuration of the agitated fermentor with two countercurrentaxial high - speed impellers of the same diameters as well as the frequencies of revolutioncan be recommended:Lower impeller «j = 40°, H2 = d; upper impeller o2 = —45", H3 —1.5d, H — Hi — Hi = 2«f; flow of liquid under the turbulent regime of flow.

. • : ' . ; •

Fig. 1: Pilot plant agitated ferrnentor Fig. 2: Impeller with six inclined plane(D = 292mm, rf, = d2 = D/'i, H2 = d, blades (A = 0.2d).H3 € (d; 2d), H - H2 - H3 = 2d,a, € (25°; 45"), a2 6 (-45°; -25°)).

References:

[1] Medek, J. - Klohna, J. - Hruban, M.: Some Posibilities of Innovation of Mixing E-quipment I (in Czech). Chem. Prum, 1985,35,61-66.

[2] Novak, V. - Rieger, I". • Marisko, V. - Masi'n, L.: Power Input and Blending Efficiencyof Multistage lmptllf.ru ( in Czech ) . 36th National Conference CHISA, Strbske pleso1989.

''A -/- -

This research has been conducted at the Department of Chemical and Food ProcessEquipment Design as a part of the research project " Turbulent Characteristics of AgitatedBioreactors " and has been supported by CTU grant No. 8026.

184


TRANSIT TIME METHOD IN LAMINARFLOWS

R. Zitny, J. Sestak, F. Ambros

(TU, Far. of Mechanical Eag., Dept. of Chemical & Food Process Equipment DesignTechnicka 4, 166 07 Praha 6

Key words: flow-rate measurement, transit time method, correlation method, residence Itime distribution |

The basic principle of flow velocity measurement by using transit time method (and %more specifically using correlation method) is seen on the following picture: >|

j ihaatpulsa

thermistor 1TX(t)

thanistor 2

Fig. 1:

Mean velocity (and fluid flowrate) is computed according to u = L/At where L isthe distance between the detectors and t\, h are the mean times of responses. Thetransit time At can be evaluated by means of cross-corelation method, which assumesthat the At is the time, corresponding to the maximum of the cross correlation function:

The transit time computed in this way exhibits a systematic error due to the axialdispersion of the trace]' in the turbulent flow or to the nonuniform velocity profile in thelaminar region. The turbulent flow analysis was presented on the previous workshop (Zitny[1]) whereas this contribution is devoted to the laminar flow region only. We describe severalpossible arrangements of experiments theoretically with the aim to obtain the flowmetercharacteristic (relation between actual flowrate and the transit time measured).

The transient temperature field for fully developed newtonian laminar flow in a pipe isdescribed by the well known Fourier Kirchhoff equation:

^ + ^ ( l - ^ - = - - ( p - ) + — + - (1)

T = (at)/(R2); p = r/R; £ = zjR; Pe = (2uR)/a where R denotes the pipe radius, a-thermal diffusivity, A thermal conductivity and Q volumetric heat source. Later on we shallassume the electrical resistive heating which generates just one short pulse characterized byuniform Q in a short heated section of the tube.

To simulate the experiment, several versions of the control volume method (rectangulargrid, flux corrected transport) had been used for the solution of (1). Mean transit time isobtained by using the standard FFT algorithm. The results are presented as a flowmeter

<•' 185t

^


V : 1

characteristics: transit time versus Peclet number. As an example, the depence of thecharacteristics upon the heat pulse duration is shown on the following figure, which displaysdata obtained by detectors located on the tube axis at distances £1 = 20, (,'2 = 50 from theheating section of the length £>, = 1:

Fig. 2: Flowmeter characteristics for differ-ent axial positions of thermocouples

Fig. 3: Kebort and Cejnar experimentaldata, and flowmeter characteristics

The most important conclusion is that the flowmeter characteristics are nonlinear; onlyfor very small Peclet numper (small velocities) the radial diffusion flattens the temperatureradial profile, so that the model of axial dispersion can be applied for error estimation.

Instead of a single pulse, sequence of randomly generated heat pulses PRBS - (PseudoRandom Binary Signal) is frequently used. This method was used by Abesekera and Beck[2] but recalculated flowmeter characteristics reveals the fact that their experiments werein fully convective region (Pe > 3000) and no wonder that the reported characteristics areperfectly linear. Nevertheless our numericall simulation indicates, that the PRBS methodis inappropriate especially for very small velocities when Taylor Aris dispersion dominates.

The experimental data which fall at least partly into the transition Peclet region weremeasured by Kebort [3] and Zitny [4]; corresponding characteristics are presented on thefigure 3. A further experimental program, which should map the transition region in moredetails, continues.

References:

[1] ZITNY, R. - SESTAK, J. - AMBROS, F.: Transit time method for flowratt measure-ment Workshop 93 - fluid mechanics, CTU Prague, 1992, p.55-56

[2]

[3]

ABESEKERA, S. A. - BECK, M. S.: Liquid flow measurement by cross-corelation oftemperature fluctuations Trans, of Inst. of Measurement and Control, Vol.5, (1972),p.435-439

KEBORT, P.: Flowrate measurement by corelation method (in czech), M. Sc. thesis,CTU Prague, 1992

[4] ZITNY, R. - SESTAK, J. - AMBROS, F.: Transit time method for flowrate measure-ment Conference on Fluid Mechanics and Hydrodynamical Aspect of Biosphere, UHCSAV, Liblice, 20-21.September 1993

This research has been conducted at the Department of Chemical and Food ProcessEquipment Design, Faculty of Mechanical Engeneering CTU and has been supported byCTU grant No. 8O84.

186

^


MICROMIXING AND ITS EFFECTON POLYMERIZATION

J. Votava, P. DitI

C'TU, Fac. of Mechanical Eng., Dept. of Chemical & Food Process Equipment DesignTechnicka 4, 166 07 Praha 6

Key words: micromixing, chemical reaction, reactors

Mixing influences the yield of complex chemical reactions (namely reaction with orderhigher than one). Polymerization is au important representative of these reaction types.Polymers are finding increasing use throughout our society. Well over 50 billion kilos ofpolymer are produced each year and it is expected that this volume will double in thecoming years as higher strength plastics and composite materials replace more metal carparts and other products. Consequently, the field of polymerization engineering will takean even more prominent place in the chemical engineering profession.

Chemical reaction is a molecular level process and only mixing on the molecular scalecan affect its course directly. Mirromixing affects the course of fast and instantaneouschemical reactions, changing their conversion and selectivity. These effects were observedin reactive mixtures of gases and liguids in both turbulent and laminar flows. Micromixingcan change product properties and hence product quality. It was observed in precipitationprocess where the size distribution of precipitating particles depends on mixing. Analogicallymixing can control the molecular weight distribution of polymer molecules. Mixing problemsmay be arbitrarily classified in accordance with operating modes, chemical process, numberof phases involved, flow regimes, fluid properties and operation purposes. This is illustratedin Fig. 1.

This report focuses on the effects of mixing of incompressible single phase fluids onthe course of homogeneous chemical reactions. This contribution summarizes the results ofour current research focused on the micromixing effects on the yield of a complex chemicalreaction (polymerization) occurring in low and higher viscosity bulk liquid systems. Further,it reports the achieved experimental results and compares them with previous ones obtained ifor low viscosity systems. The role of mixing and micromixing was investigated through the jcompetitive consecutive chemical reaction, having the following stoichiometry

A + B - R

A + FJ — S

where k\ << fa. The azo coupling between 1-naphtol (reactive species 1-naphtolat.e ion)and diazotised sulphanilic acid (reactive species 4-sulphophenyl-diazonium ion) in alkaline-buffered aqueous solution was used in our experiments. Higher viscosity was attained byadding a glycerol. This chemical reaction plays the role of chemical probe. The variousfeeding conditions such as feeding time, diameter of fowling pipe, initial concentrations ofthe incoming components, and feed location were investigated in an endeavour to obtain theproper operating scale-up conditions. All measurements have been performed in cylindrical

187

• w.


tanks of 0.15, 0.19 and 0.30 m in a diameter mixed with standard Rashton turbine, anchorand helical ribbon agitator at different rotation speeds.

The system of governing equations includes the continuity equation, Navier-Stokes equa-tions, constitutive mass transfer equation, reaction kinetics equations, initial and boundaryconditions may not be analytically solved due to the geometrical complexity of the system.Inspection analysis of governing equations may offer guidance in micromixiiig problems.

Objectives from a theoretical viewpoint. To observe behaviour of chemical reaction underthe mixing conditions. To make theoretical analysis. To make experiments in low viscositysystems. To prepare experimental method for investigation of micromixing for systems withhigher viscosity. To investigate micromixing effects of the feed.

Objectives from an industrial viewpoint. Product distribution is strongly affected bymixing on the molecular level. Hence it is necessary to recognize the micromixing influencethat determines conversion efficiency of raw materials to useful products. From this pointof view the scale-up effect is dramatically significant.

Fig. 1: Classifications of mixing (macromixing and micromixing)

References:

[1] VOTAVA, J. - DITL, P.: Selected Micromixing Effects in Mixed Reacting Systems ofLow and Medium Viscosities. CHISA 93, Praha Czech Republic

[2] VOTAVA, J.: The Effect of on Micromixing and scale-up at Complex Chemical Reac-tions PhD Thesis, CVUT v Praze, strojni fakulta, 1993, 140 p.

This research has been conducted at the Department of Chemical and Food ProcessEquipmeri Design as a part of the research project "Intensification of Bioreactors and Poly-merizators" and has been supported by CTU grant No. 8082.

I

188


EVALUATION OF ENGINEWORKING CYCLE

M. Takats

CTU, Fac. of Mechanical Eng., Dept. of Automobiles, ICE k Rail VehiclesTechnicka 4, 166 07 Praha 6

Key words: working cycle, thermodynamics, gas engine

The 1993 research effort has concentrated mainly on the evaluation of measurements ofthe in-cylinder pressure history of a running engine. Pressure traces have been sampled bymeans of Keithley DAS 58 aquisition board and stored into files. A number of softwareproducts are available for further evaluation of such records, but they are very expensive,their source code is not available and usually an evaluation of charge temperature and rateof heat release is applied only to the average engine cycle (with average peak or indicatedmean effective (IME) pressure). Hence an evaluation of cycle to cycle variation of someimportant features is not possible. A decision was made to develop a program for fastanalysis of a great number of recorded cycles.

Program EVALINDI can handle as many individual records as represented by ap-proximately 130 engine work cycles sampled at each 2° crank angle. During evaluation azero pressure level is estimated. Traces of charge temperature (with regard to change ofworking gas composition during combustion), rate of heat release (using Woschni's-equationto compute the wall heat transfer) are computed and plotted on the screen. A polynomalapproximation of specific enthalpy as a furr-'~>n of temperature is used. So-called dissoci-ation is omitted at thij time (content of faJj, such as CO or H2, in combustion productshas 110 influence when A >• 1). Simultaneously, the rate of pressure change (dp/do) and thelnp(inv)-curve are displayed.

An example of almost standard (slightly modified to fit the format prescribed) graphicprinting is presented in the Fig.l. Results of the statistical evaluation (if requested) areprinted in the footnote (using Czech language/characters). Values have been measuredduring engine run near the lean misfire limit (but misfiring has not occurred).

A special file containing records of maximum pressure, maximum dp/da, correspondinga values and IMEP (one line for each cycle) can be created. Another file with weightedaverage values of actual pressure (one line for each position within one cycle - total 360lines) can also be demanded. Finally a script file for AUTOCAD (to create 3-D pictures)can be requested.

Evaluation of 130 cycles is completed within one minute (using a 486-machine). Lo-cation of TDC can be estimated using a trial and error procedure. Further evaluation ofaverage cycle or cycles with extreme fluctuation of properties (greatest or lowest peak pres-sure or IMEP) can be made, such as Fourier analysis or two zone model for thermodynamicanalysis (including dissociaton).

189

CTl.T SEMINAR 94 FLUID MECHANICS

SOUBORDAS58 Jmeno : G6. Datum mefonf: 11/23/93, Cas mefeni: 13:46:30, Pocet z&rnamfl: 4O000M0T0R/RE2IM. Vrtanf: 102 mm, Zdvih: 110 mm, Stupen komprese: 11 Otacky: 1800/minyl = 1.47VYHODNOCENI Pocet hodnocemteh cyklu: 10, Poloha 1 . HU: 927pmax/poloha HU 32.19/2007..36.75/3807..40.25/1647 pi/poloha HU 6.245/2727..6.899/4167..7.535/1287

Fig. 1: Example of EVALINDI output

This research has been conducted at the Department of Internal Combustion Enginesas a part of the research project "Electronicaly Governed Lean Burn Gas Engine" and hasbeen supported by CT'V grants No. 8008.

190

C'TU SEMINAR 94 FLUID MECHANICS

ZONE MODELS OF INTERNALCOMBUSTION ENGINE CYCLE

APPLIED FORTURBULENCE MODELLING

J. Macek

CTU, Far. of Mechanical Eng., Dept. of Automobiles, ICE & Rail VehiclesTechnicka 4, 166 07 Praha 6

Key words: mathematical modelling, internal combustion engine, thermodynamics of cy-cle, internal aerodynamics, zero dimension model, turbulence inside cylinder, K-epsilonmodel

The detailed description of burning and gas-wall heat transfer inside an ICE cylindercannot be conducted without taking turbulence into account - [1], [2]. The source of itsenergy provides a bulk flow in the cylinder excited by a piston movement (especially whena deep bowl combustion chamber is used), an inlet air flow or a fuel (mixture) injection.

These sources of kinetic energy A', its transformation into turbulent, kinetic energyk and finally dissipation of rate e have been studied by the author's department usingLDA experiments - [3] and developed into a very detailed CFD model - [4], up to nowlimited only to the 2D or rotational symmetric 3D cases. The immediate use of partialresults obtained nevertheless needs "extrapolation" based on the zero-dimension, ordinarydifferential equation-based simple models, previous]}' mentioned [1] and presented [5].

The main new idea has been to take all shear areas, including mixing of non-uniformvelocity streams (not only boundary layers), into account. The assumption of the velocityfield pattern is a necessary prerequisite (e.g., the solid body rotation law in the case of allvortices). These hypotheses have been based partially on more detailed computations andmeasurements already described.

The change of a bulk flow kinetic energy provided by the external work source (in mostcases by the piston) is calculated for all flows in every time step of differential equationsintegration. This set has been created by an amendment of the existing set of mass compo-nents and energy conservation equations. The equation of momentum conservation providesthe velocity change after stream mixing and the resulting kinetic energy of the bulk flow canthen be computed. The examples of main bulk flows can be seen at Fig. 1. The differencebetween the external work imposed and kinetic energy obtained determines the generatingterm of turbulent kinetic energy. Its dissipation is calculated using a boundary layer modelwith estimated length scale - e.g. [6].

The modelling of a bulk flow angular momentum created during inlet stroke is describedin more details in [6], including the swirl (the "tangential" vortex). Similarly, estimating asquish flow velocity from the condition of pressure uniformity in both subvoluines (zones)Vj and 14 of a cylinder, the rate of kinetic energy and the angular momentum increment iscomputed from the assumed velocity field.

191


The first computations using CFD code [4] have shown the nonuniform velocity fieldof the squish bulk flow. This fact is respected in the scheme at Fig. 2. The geometry of acylinder head and that, of a piston determines the maximum possible radius of the squishvortex and the location of its centerline C The real vortex radius depends on a mass trappedin it.

The conservation of angular momentum includes the rates of angular speed, radius(especially during compression) and mass trapped in the vortex which are changed as aresult of angular momentum flow squished from the gap above the piston perimeter. Inthe case that the mass trapped in the swirl is bigger than the maximum mass possible, themass excess is expelled to the space outside of the vortex with the mean kinetic energy thuscreating one of the sources of turbulence.

1

t.-.

•.- . • • ] • ' •. v '•-,

-•-• p

111. J ' '

_dv

j

I

: u 1

• • ' / / / ,

I

•g~ '

';. | 'Mi

Fig. 1: Flows in the cylinder Fig. 2: Squish vortex model

References:

[l] MACEK, J.: Models of Thermo-Aerodynamics for Internal Combustion Engines. Work-shop CTU '93. Part B. Praha : CVUT, 1993; pp. 49-50.

[2] MACEK, .].: Vyznam modelovdm turbulence ve spalovacirh motortc.h a jeho soucasnystav. Kol. DYNAMIKA TEKUTIN. Praha: UT AV CR. 1993. pp. 35 - 36.

[3] HATSCHBACH, P.: Porovndni sroaboveho a tangencidlntho saciho kandlu TATRAmerem'm ryr.hl. pole vt vdki pomoci LDA. Report K221 Z 93-13. Praha: CVUT, 1993.

[4] BENDL, F. - KOZEL, K.: Program pro resent Eukrovych rovnic v rovine. Code libraryHP 9000. Praha: AVIA, a.s. 1993.

[5] TAKATS, M. MACEK, J.: Vehicle Lean Mixture Gas Engines. 20th Int. Congresson Combustion Engines. London: CIMAC. 1993. FISITA Session, pp.1-20

[6] MACEK, .J.: Pri/spevek k vytvdftni zonovych modelu pracovniho procesu spalovacichnwiorn. XXIV. konf. kateder a pracovistf SM. Liberec: VSST. 1993. pp . 11 /1-11/8

This research has been conducted at the Department of Int. Comb. Engines as a partof the research project "Thermo-Aerodynamics of Internal Combustion Engines - The Baseof Improved Economy and Environment Protection" and has been supported by CTU grantsNo*. 8085. 8008 and GA CR grant No. 101/93/0237.

192


PIPE DIAMETER EFFECTAND DRAG REDUCTION

BY SURFACTANT ADDITIVESJ. Pollert, P. Komrzy, A. Vozenilek

CTU, Fac. of Civil Eng., Dept. of Hydraulics & HydrologyThakurova 7, 166 29 Praha 6

Key words: drag reduction, surfactant, turbulent pipe flow

INTRODUCTIONIn many closed loop heating systems, such as hot water district heating systems, a

drag reduction additive could reduce pumping costs, or increase the potential distributiondistance without adding more pumps. For these applications ideally the drag reductionsurfactant additive would provide good drag reduction over most of the closed-loop system.The drag reduction additive must be able to maintain its activity over the temperature rangeexperienced in the application and be able to withstand the continuous shearing caused byrecirculat.ion (1).

Low molecular weight surfactant molecules form aggregates or "micelles" made up ofmany molecules. Rod like micelles or possibly networks are very effective in reducing tur-bulent friction up to a certain shear stress, whereupon the micellar bonds or the networksare broken and the fluid becomes Newtonian, with no friction reduction whatsoever. If thestress is relaxed, the bonds reform and the friction reducing ability reappears. This is incontrast, to polymer solutions where, if the polymer molecule is degraded or broken, thefluid loses its drag reducing ability permanently (2).

EXPERIMENTALThe test sections for the drag reduction measurements consist of straight stainless

steel tubes of different diameter (4, 6, 10 and 20 mm) each of length 5 m. Other parts ofrecirculation test pipe loop were constructed from PE smooth tubes. The entrance length tothe first pressure tap was at least 150 times the diameter of each tube used in order to insurethat the turbulent flow was fully developed. The pressure measurements were made usingHottinger Baldwin differential pressure transducers with distance between pressure taps 1in. The flow rate of the test fluid was measured by a Krohne magnetic-inductive flowmeter.All data including temperatures, were collected into a Multipoint Measuring InstrumentUPM 60. All surfactant additive experiments were carried out at three temperatures - 20,40 and 60 C. Duration of each concentration test was 15 hours.

The surfactants used for the tests were HABON G and ETHOQUAD T/13 with natriumsalicylate (1:2.5 molar ratio). Both surfactants are good candidates for use as drag reducersin district heating systems. Habon G, a product of Hoechst Co., FRG, has 53.5 % activesurfactant, 10.2 % isopropanol and 36.3 % water. Concentrations of 0.05 % and 0.1 %by weight were tested. Ethoquad T/13 Acetate, a product of Akzo Chemicals Inc., U.S.A.contains 50 % active surfactant, 36 % isopropanol and 14 % water. The tested concentrationwas 0.2 % by weight (active part of T/13).

193

e r r SEMINAR O-I FLUID MECHANICS

RESULTS AND DISCUSSIONOne of the most interesting issues which has surfaced during studies of drag reduction

In- polymers is the "diameter effect". This refers to the fact that for a given fluid andReynolds number, the friction (except in the maximum drag reduction asymptote regime),is a (unction of the diameter of the pipe. i.e. for a given polymer and concentration the dragreduction is greater in small pipes. This is. of course, not the case with Newtonian fluidsfor which the pipe diameter is already taken fully into account in the Reynolds number.

For both surfactants at all concentrations which were studied, the results fall into twodistinct groupings; one of 1he smaller size pipes: 1 and 6 mm and the other, the largerpipes 10 and 20 mm. In the smaller pipes the critical wall shear stress was reached at lowReynolds number and sharp changes in drag reducing effectiveness in a narrow range ofReynolds number were not observed. But in the cases of the 10 and 20 mm pipe sizes itwas possible to sec typical surfactant drag reduction additive behaviour, i.e when the stresscauses breakdown of the network structure of the rod-shaped micelles and when the shearstress exceeds a critical value.

It is not clear why drag reducing data fall into two groupings. One possible explanationis related to the differences in the shapes of the velocity profiles with surfactant and withoutsurfactant. Velocity profiles in drag reducing miccllar solution systems are quite flat in thecentral region. In the smaller 4 and (S mm tubes, the size of the micelles may be large relativeto the distance from the wall at which the expected steep portion of the profile should lie,thus interfering with the development of the profile.

Alternatively, the groupings may be caused by the high wall shear stresses in the smalltubes in which the critical wall shear stress for mechanical degradation of the Habon Gmicellar network may have been exceeded at low Reynolds numbers in the 4 and 6 mmtubes. Estimates of the critical wall shear stresses for the 0.05 % Habon G measurementsat 20 C show all values lying within +/- 60 % of 2.0 Pa while for the 0.1 % Habon G dataat 10 C all values lie within -+/- 40 % of 3.0 Pa. Since estimation of the critical shear stressvalues is subject to considerable uncertainty, these values can be considered nearly constant.

CONCLUSIONSI. For the surfactants, the influence of pipe diameter on drag reduction is opposite to

that of polymers, i.e. with increasing diameter drag reduction increased for the surfactants.2. During experiments in a closed loop pipeline system no mechanical or aging degradationeffects were observed as are found with polymer additives.

References:

[II CHOU. L. C. - CHRISTENSEN, R. N. - ZAKIN, J. L.: The Influence of ChemicalComposition of Quart ernary Ammonium Silt Uationtc Surfactants on their Dray Rt-ducing Effectiveness. P. of hit.Conf.Drag Reduction in Fluid Flow, Ellis Horwood Ltd.,pp.141-149, 1989

[2] POLLERT, J. - SELLIN, R. H.: Mechanical Degradation of Drag Reducing Polymerand Surfactant Additives: A Review. P. of Int.Conf.Drag Reduction in Fluid Flow, EllisHorwood Ltd., pp.179-189, 1989

This research has been conducted at the Department of Hydraulics and Hydrology asa part of the research project ''Savings of energy in heating/cooling systems by means ofsurfactant drag reducing solutions" and has been supported by CTU grant No. 8006.

194

e r r SEMINAR <» FLUID MECHANICS

POWER ECONOMY IN HEATINGAND COOLING SYSTEMS

(MEASURING OF THE COEFFICIENTOF HEAT TRANSFER)

J. Ota, V. Sykora, J. Melichar

CTl', l*;ie. of Mechanical Kng., Depl. of Compressors, Refrig. fc Hydr. MachinesTeclinicka 4, 166 07 Praha 6

Key words: additives, coefficient, of heat transfer, liquid heating systems, air conditioningsystems

The use of additives as a component to the circulating water of heating and air condi-tioning systems yields advantages in reducing the flow resistance, neverthless the additivescan also affect the coefficient of heat transfer in heat exchangers in the heat transfer process.

The aim of work for this year was to design, construct and verify a suitable apparatus(alphameter) for measurements of the coefficient of heat tranfer in a circular channel. Basedon a preliminary analysis of two projects, a type with a smaller heat input was chosen. Ameasurement of the temperature profile in a pipe wall along the flow direction after theplace of ouier heating was used for the determination of heat transfer intensity.

The pattern of the temperature profile depends above all on the geometry of the pipe,the thermal conductivity of the pipe material and on the coefficient of surface heat transfer(alpha). An analytical solution suggests that the coefficient of surface heat transfer alphacan be determined by measuring any two different temperatures in two points at a defineddistance. To propose an optimum temperature pickup layout in the alphameter tube walla preliminary calculation of the temperature field has been performed using a unidimen-sional mathematical model and the program FLUENT, under which the ta.sk was solvedby a method of finite elements (the program FLUKNT moreover displays the temperatureprofile in the wall). Further consideration concerned above all the influence of temperaturemeasurement error in two different points of the apparatus. The relative error (related tothe nominal value) and the absolute error of the alpha determination as a function of thelongitudinal distance are traced in the fig. 1 under a presumption of an error of both of thethermometer pair + - 0.1 and + - 0.15 °C.

The result of the analysis was a finding that the function had a favourably flat optimumin 1/4 to 1/3 of the measurable temperature profile. That also suggests that the determi-nation of further temperatures of the temperature profile has rather a checking importanceand the alpha measurement proper should be based on a temperature measurement in onlytwo optimally-spaced points.

The apparatus was constructed this year in two alternatives: with a thick-wall stainlesssteel tube 14/2.5 and with a copper-clad thin-wall stainless steel tube 12/1. In the latteralternative a copper tube of 2 mm wall thickness wa.s soldered on the stainless tube in orderto improve the axial thermal conductivity. With both said alternatives a measurement wasmade for apparatus gauging with distilled water.

195

CTU SEMINAR .94 FLUID MECHANICS

Next measurements were made with an additive HABON G made by HOECHST atconcentrations of TOO, 1400, 2100 and 2800 ppm. The coefficient of heat transfer featureda slight decline with increasing concentration. According to the measurements the dropattained approximately 15% at a solution temperature of 17 °C.

After a certain operation time a considerable quantity of fine desorbed gas particles wereobserved, probably generated in the pump impeller chamber. This finding is important,because for theoretical reasons it is necessary to have a defined materially homogenous flowstructure for comparability of the measurement results. Important from the applicationpoint of view is also the problem of pump type choice as well as general layout of the collectorand pump in the system. It is therefore recomrnendable to consider this phenomenon atleast qualitatively.

For systematic data processing it seems necessary to prepare a computing programcomprising mass properties and conversion of data formates from the program controllingthe measuring central station. Measurements of 13 temperatures were implemented using aPC-based central measuring station.

»„ - 20 "cM ' * 0.1 * C ; * 0.15 -C

MEASUREMENT— — FLUENT

This research has been conducted at the Department of Compressors,Refrig. and Hydr.Machines as a part of the research project "Reducing energy costs in district heating-coolingsystems by surfactants drag reducers of micelar type " and has been supported by CTU grantNo. 8006.

196


THE SHIELDED THERMOCOUPLEAS A SIMPLE TEMPERATURE PROBE

J. Nozicka

CTU, Fac. of Mechanical Etig., Dept. of Fluid Mechanics & ThermodynamicsTechnicka 4. 166 07 Praha 6

Key words: shielded thermocouple, temperature measurement

The measurement of the total temperature of the gas flow is quite a complicated task,if the flow speed is higher than 50 m/s. The temperature probe in this case indicatesthe so-called probe indicated temperature 7j, which is usually lower than the stream totaltemperature Tt and the stream line temperature T. To design the probe indicating thetemperature being very close to the Tt - the so-called direct reading probe - costs a lot ofeffort. Moreover, the probes mentioned often have some disadvantages, as for example largedimensions, high manufacturing costs, high radiation or angular sensitivity.

Another possibility is to use a very uncomplicated temperature sensor and determineits qualities by an exact calibration. If the probe shape is simple enough, the calibrationdata can be sampled with a high accuracy.

The simplest possible temperature sensor is the separate shielded thermocouple. Undercommon conditions it requires no additional support or shaft, is small and can be perfectlyused for the temperature profile traversation.

Because similar probes are expected to be used in the research institute of the IBS VelkaBite, there now is the possibility to compile some previous results of shielded thermocouplemeasurement and to complete them with some new results which have appeared. Calibrationdata were evaluated by the author's method of model calibration for 7 various diameters ofthermocouples between 0.2 and 6 mm. The influence on the free stream Mach number upto 0.85, on the angle of attack and heat conduction and radiation was investigated as well.

Fig. 1 shows the dependence of dimensionless temperature measurement error Z on thefree stream Reynolds number, determined for two basic thermocouple positions, i.e. paralleland perpendicular to the free stream velocity vector. Dependence shown was obtained byrecalculating the data measured by various values of stream Mach number to the value ofMach number equal to zero. Due to it, the influence of the Mach number can be estimatedas well. In fig. 2 the influence of an angle of attack is illustrated. Some intervals of angularinsensitivity for both parallel and perpendicular position are evident. This phenomena couldbe very useful for such measurements, where the exact position of thermocouple with respectto the stream can't be guaranteed.

The results of heat radiation sensitivity are very interesting. Although equipped withno radiation protection, due to a good heat convection between the stream and the ther-mocouple, the error due to radiation is comparable with that of the probe with a radiationshield.

All the qualities mentioned confirm the assumption that a separate thermocouple canbe used as a total temperature sensor for high subsonic velocities as well.

197


Re.

Fig. 1: Z=f(Re)

0,6

Fig. 2: Z=f(alfa)

198

FLUID MECHANICS

SIMULATION OF FLOW PATTERNSIN COMBINED SEWER OVERFLOWS

P. Komrzy, K. Svejkovsky, Z. Konicek*

CTI'. Fac. of Civil Kng., Dept. of Hydraulics k HydrologyThaktirova 7. 166 29 Praha 6

*(..TU, Fac. of Civil Eng., Dept.. of Sanitary EngineeringTliakurova 7. 166 29 Pralia 6

Key words: flow patterns, cross circulation, combined sewer overflow(CSO), swirl CSO,vortex ('SO, helical hend CSO. model suspension, physical model, simulation program

Tlie development of new designs of combined sewer overflow structures, providing boththe hydraulic control and the effective retention of the pollutants, is of great importancewith respect to reducing the environmental impacts of CSOs. The swirl, vortex and helicalbend CSO structures are mentioned elsewhere (1.2,3).

This paper compares the hydraulic behaviour of the swirl-vortex and helical bend com-bined sewer overflow chambers. The separation process is produced under the hydrauliccondition of a cross circulation flow in the swirl-vortex and helical bend CSOs.With a con-stant weir crest height in the swirl CSO the vortex flow conditions can be obtained bychanging the inflow to outflow ratio. The hydraulic conditions and the trajectories of float-able and settleable material were studied using the computational simulation programmeFLUENT at the University of Sheffield. '1 he laboratory models (Fig.l) were tested in thehydraulic laboratory of the Faculty of Civil Engineering CTU Prague, using a suspendedsediment model.

The computational fluid dynamics software package called FLUENT was used whichallows one to solve the Navier-Stokes equations governing t he fluid, for laminar and turbulentflow in three dimensions using the finite difference method. FLUENT describes the velocitydistribution inside of the CSO separators and predicts the trajectories of floatable andsettling particles under various flow conditions.

The example of flow patterns and the particle trajectories in vortex conditions arepresented in Fig 2. and Fig '3. The simulation of velocity distribution and the particletrajectories in the helical bend CSO are demonstrated in Fig 4.

This paper shows the possibility of demonstrating the How conditions and the trajec-tories of particles in different types of CSO structures using the FLUENT version 4.11.simulation program. The particle tracking of suspended solids also demonstrates the possi-bility of modelling the efficiency of CSOs.

References:

[1] FIELD, It.: Design of a Combined Sewer Overflow Regulator/Concentrator, JournalWPCF,Vol.46, No.7, July 1974, pp. 1722-1741

[2] KONICEK, Z. - MARSALEK, J.: Comparativt Study of Swirl, Vortex arid Helical BendSeparators, 6th. Int. Conf. on Urban Storm Drainage, ICUSD 1993, Niagara Falls,Ontario

199

('] "U SEMINAR 94 FLUID MECHANICS

[:l] SULLIVAN. R. U. UKE. J. E. PARKINSON. F. Z1EL1NSKI, P.: Drsujn Manual- Swirl and Hi Ural Bind Pollution Control Dccicts. Repl. EPA -600/8-82-013, U.S.EPA, Washington D.C.CSA

This nsrarrh has bun roiirlurlol at tiu Pfpaiimeiil of Sanitary Enyinctriny as a part oftin research projtrt "homphrni nsciii odloku dtsloct/rh odpadnirh rod ; rm:.itskr.ho pouodi"and has bttn supported by (TV qrnnt No. Sill.

Fig. 1: Solid-liquid separators listed Fig. 3: Trajectories of SS in vortex CSO

Fig. 2: How patterns in vorli-x CSO Fig. 4: Trajectories of SS and flow patterns in helical bend CSO

200


GROUND WATER FLOWIN A MULTILAYERED CONTINUUM

I. Kazda, P. Valenta

CTU, Fac. of Civil Eng., Dept. of HydrotechnicsThakurova 7, 16'6 29 Praha 6

Key words: ground water flow, finite element method, numerical modelling

The construction and performance of hydraulic structures usually influence groundwater flow in extensive regions the area of which can amount, to several square kilometres. Inthe investigation of the seepage flow patterns in similar large domains a numerical methodis to be used making it possible to consider all essential features of the hydrogeologicalstructure of the given territory.

For the numerical solution of the mentioned problems the so-called multilayered modelshave proved useful starting from the fact that it is very often possible to approximate thegeological structure of an extensive region by a system of alternating aquifers and aquitards.The model starts from the point that it possible to substitute with sufficient accuracy theground water How in an aquifer by horizontal flow and that in aquitards only the verticalcomponents of the seepage velocities can be considered [liazda 1900]. The multilayerednumerical model realised at with the help of the finite element method thus forms layersof plane elements corresponding to the aquifers, and the vertical one-dimensional elementsconnecting the nodes of the adjacent aquifers model the aquitards.

Multilayered models have proved useful in practice but for the solution of local under-ground flow in the vicinity of tectonically fractured zones with marked discontinuities it isnecessary to apply a three-dimensional flow model.

A part of the solution of Grant No. 8072 of the year 1993 was also represented by nu-merira) modelling of three-dimensional seepage flow in domains formed by several geologicalstrata with markedly different permeability. The model realised by means of the finite ele-ment method use solid isoparametric elements of the shape of hexahedrons with twenty oreight nodes. The twenty noded elements that have a quadratic approximation polynomialproved to have a great numerical accuracy as well as a suitability for the application of spe-cial finite element techniques. Their drawback, however, is the toilsome preparation of inputdata and the demanding requirements concerning the capacity of the internal memory andthe speed of the computer applied. For these reason a program has been elaborated makinguse of three-dimensional elements with eight nodes. Although these elements have only atrilinear approximation polynomial, their imposing is easier that in the case of twenty-nodedelements.

For the preparation of three-dimensional meshes it is necessary to use to a maximum ex-tent the generation of input data. Subroutines have been elaborated both for twenty-nodedand for eighty-noded elements making possible the generation of the mesh by individualcolumns or by whole layers. In addition a transformation code has been elaborated whichwill automatically yield from the input, file for an eight-noded element mesh a new inputfile giving a twenty-noded element mesh.

201


For every actual problem several verifying comparisons have to be carried out first.An eight-noded element mesh is sufficient for these computations; after verifying the pre-sumptions applied for the elaboration of the numerical model the input file for the finaltwenty-noded element mesh is conveniently formed by means of the transformation code.

The first study carried out with the help of three-dimensional elements was a sensitivitystudy to verify the fundamental presumption used for multilayered models (see above). Ithas been proved that the flow in an aquitard can be considered as vertical flow only if itshydraulic conductivity is at least by three orders of magnitude lower than the hydraulicconductivity of the adjacent aquifers.

Further investigation were concerned with the numerical modelling of different discon-tinuities in an aquitard and and their influence on seepage flow in the adjacent aquifers. Itwas shown that the eleborated numerical models are sufficiently robust and make possiblethe modelling even of complicated cases with sufficient lucidity and accuracy.

Numerical experiments have shown that graphic presentation must be used for resultevaluation. For this reason special software integrated with AutoCAD has been elaboratedmaking it possible to characterise the resultant seepage pattern by means of space presen-tation with the help of total head contours or the drawing of seepage velocities in the givendomain section.

References:

[1] KAZDA, I.: Finite element techniques in groundwater flow studies. Elsevier, Amster-dam 1993

This research has been conducted at the Department of Hydrotecknics as a part of theresearch project "Solution of Environmental and Technical Problems in Groundwater andRiver Water Abstraction Development" and has been supported by CTU grant No. 8072.

202

Section 6

THEORY OF CONSTRUCTIONS

CTU SEMINAR 94 THEORY OF CONSTRUCTIONS

CIVIL ENGINEERING PROSPECTINGP. Broz, M. Hrabanek

CTU, Klokner Institute, Dept. of StructuresSoh'nova 7, 166 08 Praha 6

Key words: balance structure value, break-down, Capo-test equipment, elaborator capa-city, hardness tester method, interim stage, neutralization depth, pH-value determination,pull-out procedure, re-development, reinforcement corrosion, residual life

1. Reinforced concrete beams built in the cooling stack - their evaluation according toenvironmental characteristics

Technical ispections and loading tests of four reinforced concrete beams have beenperformed in our Institute this year.The two sets of results are given in the table, as follows :

Beam notationlength (mm)height (mm)width (mm)mass (kg)compression strength of the concrete (MPa)(the accuracy of this value is not guaranteed)strength magnitude of guaranteed accuracyconcrete classneutralization depth values :mean (mm)minimum (mm)maximum (mm)protecting layer thickness at maximumneutralization depth point (mm)stress value gauged by non-destructivereinforcement corrosion test :meanminimummaximum

Al4980234108.5325

5242.1

B40

6.8/6.24/2

12/11

23/33

0-170220

A24990232104.5320

4541.2

B40

6.1/5.43/2

10/11

20/52

-20-170120

Bl5180420122610

4641.2

B40

3.3/3.32/17/6

0-150

80

B25200425113560

5242.9

B40

3.0/3.31/25/6

13/32

0-120160

ASTM C 876 mV probable corrosion> -90 10%<-200 90%

load-carrying capacity (kN)deflection (mm)maximumpermanent

43

30.613.24

40

46.1221.00

116

30.3517.50

68*)

20.8614.91

205

^ T f f ' < 6 ^ ^


*) Prior to the experiment, a crack had occurred in the beamInformative pll-value of water : 7.1 - 7.2

2. Inspections and maintenance of extra engineering structures

Generally speaking, civil engineering prospecting is sought mainly for the followingpurposes :

- modernization of a building structure- re-development of building structures- structural repairs, change of owner- determination of causes of construction failures- a new structure close to the current structure

Basic economic data should also form part of the investigation. Any decision on re-construction, modernization, repair etc. should always take into consideration economicfactors, above all the cost of structural re-design or modernization with regard to addedvalue. The technical survey, as an implement, yields, an estimate of residual life and thusof the balance structure value.

From a practical point of view, prospecting has come to be divided into three stages :- interim- detailed- complementary

For instance, at Prague airport we performed extended relevant preventative overhaulsof steel structures in hangars, as follows :

1. Implementation of detailed visual overhaul of all steel structures, i.e. flooring andwalkway level.

2. After inspection of the structure, detailed overhauls wore performed, each dealing withone construction type : the truss, purlin, wind bracing, bearer above the gate, togetherwith measurements of their main dimensions. These elements were chosen at random,where possible including places accessible to a vehicle with an inclined elevator

3. In the office, the measurement of elements was later evaluated, and in unclear casesthe operation was repealed.

4. We paid attention to the condition of roof slabs, except, when it was a case of corrodedreinforcements.

5. Following both visual inspection of the whole structure and the detailed overhaulof single elements, the state of the steel structure of the building in question wasdetermined.

6. Some elements of other steel structure sections were measured approximately, in orderto check the identity of steel structure segments.

This research ha* been conducted at the Department of Structures as a part of theresearch project "Technical luapictions and Re-development of Building Structures" and hasbeen supported by CTU grant No. 8148.

206

^

CTU SEMINAR 9-1 THEORY OF CONSTRUCTIONS

THE STEEL FRAME, FOUNDATION

AND SOIL INTERACTIONF. Wald, M. Juchelka, J. Zalesky,

M. Drdacky, M. Pultar

CTli, Fac. of Civil Eng., Dept. of Steel Structures,Thakurova 7, 166 29 Praha 6

Key words: steel structures, semi-rigid design, column base, foundation, soil influence

The deformability of the column-bases consists of the deformability of the steel connec-tion part (mostly the plate and bolts), of the deformability of the concrete block and of thesubsoil deformability Fig. 1. The subsoil contribution could significantly affect to the overallframe behaviour [5]. The current knowledge of subsoil interaction was based on engineeringsimplified estimate. The stiffness of the column bases has a similar influence to the momentredistribution as the beam-to-column connection stiffness [2].

Fig. 1: The column base components

The presented works are pilot studies of a frame's sensitivity to different soil influence.Three simple models of soil deformability were compared - Tsythowich's method, Terzaghi'smethod and Jianguo's method [6], see Fig. 2. The methods form practical analytical toolfor structural analysis. These simplified methods are based on assumptions. Firstly thatthe subsoil consists of one kind of soil only, secondly the incompressible base is very deepand thirdly the bearing capacity is high enough for the linear stress-strain relation to bevalid. The Terzaghi method takes into account changes in the soil

Moment, kNmSteel Part [6]

Terzaghi [1] Subsoil PartTtytovichfl]

Steel Part &Mean Value for Subsoil

5 Rotation, mrad

Fig. 2: The moment-rotation diagram for clay subsoil (ML) and unstiffned base plate [1]

207

-,..•_.,..*..„,..».....* .r, • . - - • *

CTU SEMINAR !M THEORY OF CONSTRUCTIONS

The pilot tests results are shown in Fig. .3 the column base in situ represents theinfluence of the subsoil of column base designed according to a rigid column-base model.The simplified linearized model expresses the importance of the rigidity of the column-baseeach part contribution Fig. 2. The summarisation of contribution's is only possible on aprobabilistic basis only. The generalisation of each contribution is bound to the varietyfound within foundation detailing and within subsoil variations. In the semiprobablisticmodel of the structure - subsoil interaction, which is under preparation in this project,the effect, of the soils structural strength will be taken into account, following the Czechstandard.

3000

2500

2000

1500

1000

500

8.5 kN ED

11,58 kN

17.78kN

26,24 kN

0,2 0.1 0 -0.1-0,2 0,2 0.1 0 -0,1-0,2

Fig. 3: The deformation of the subsoil under the foundation; experiment in situ

References:

[1]

[2]

[3]

[4]

[5]

[6]

JUCHELKA, M.: Soil Influence on Frame Behaviour, University of Liege, Internalpaper, Liege 1993.WALD. F. - SE1FERT, J.: The Column Base Stiffness Classification, in Nordic SteelColloquium, 9-13 September, Odense 1991, pp. 413-421.MELCHERS, R. E.: Steel Baseplate-Footing-Soil Behaviour, in Colloquium on Struc-tural Connections, ed. Bjorhovde R., Pittsburgh, April, 1991.PENSER1NI, P.: Characterisation e.t moddisation du component des liaisons structuremetalique-fondation, These du doctoral de L'Universite Paris, Paris 1991.WALD, F.: Column-Base Connections, A Comprehensive Stale-of-ihe-Art Review,COST Cl, CVUT, Praha, 1993, s. 54.JIANGUO, X. - WEIJIAN, G. - ZHENPENG, G. - ZHAOHU1, D.: Overturning Re-sistanct. and Rotation of Foundation in Soil under Lateral Loading, Computers andGeotechnics, No. 8, 1989, pp. 157-174.

This research has been conducted at the Faculty of Civil Engineering and the Czech A-cademy in thr Science Department of Applied Mechanics as a part of the research project "AProbabilistic Rigidity and Strength Model of the Steel Frame, Foundation, and Soil Interac-tion" and has been supported by the Czech Grant Agency Grant 103/93/2007. The authorswould like to express thanks to Dr.J.P.Jaspart of Liege University for his help.

208


SIZE EFFECTIN PUNCHING SHEAR FAILURE

OF CONCRETE SLABSP. Bouska, J. Margoldova*, O. Sutner**

CTU, Klokner Institute, Dept. of StructuresSoli'nova 7, 166 08 Praha 6

*CTU, Klokner Institute, Dept. of Structural ReliabilitySoli'nova 7, 166 OS Praha 6

**CTU, Klokner Institute, Laboratory of Mechanical TestingSoh'nova 7, 166 08 Praha 6

Key words: cracking failure, punching shear, size effect, testing

The size effect on fracture behavior of engineering structures, i.e. dependence of loadcarrying capacity of geometrically similar objects on their characteristical dimension, is stilla subject of theoretical and experimental research. It expresses a decrease of the nominalstress on failure with increasing size of a specimen. Due to non-linearity of this effect theproblem can be described with sufficient accuracy neither by common numerical compu-tations nor by analytical methods. Behavior of brittle materials is still analysed mostlyexperimentally or on the basis of empirical relations. Till now size effect was experimentallyproved on:

-diagonal shear failure of concrete beams without stirrups,-torsional failure of concrete beams without stirrups,-punching shear failure of slabs with one-sided reinforcement,-pull-out failure of reinforcing bars,-pull-out failure of headed anchors,-double punch compression failure of concrete cylinders,-compression failure of concrete columns,-split-cylinder concrete failure.

The size effect law is explained by gradual release of the potential energy accumulatedin the structure during propagation of a crack. The law expressing a dependence of nominalstress occuring in fracture area on a characteristic size of the specimen was created forgeometrically similar elements made under the identical conditions.

The major intensions of the research project are:-acquisitions of knowledge in the process of concrete failure during experimental loa-ding, description of crack propagation in concrete,

-experimental determination of parameters of the "size effect" law,-numerical simulation of the experiment including descending branch after reachingthe peak of ultimate stress.

Experimental programme is based on the detailed technical project. According tothe project three series of the testing specimens will be casted from the identical concretemixture, each series contains six specimens, made in geometrically similar shape in scale1 : \/l0 : 10; three specimens of small size, two specimens of medium size and one of large

209

V7in ^ ; : « .


size. All specimens are of octagonal shape in plan view. During the test the specimen willbe supported on a circle and will be punched by a circular steel disc in the centre. Thespecimens for accompanying material tests will be casted together with testing specimens.

Till now four pilot tests on medium and small specimens were finished in the KloknerInstitute. Two diagrams of these tests are shown in Fig. 1 and Fig. 2. Tests and numericalanalysis will be completed in the next year.

F ( kN) t (S)

2 0 0

1 0 0

Fig. 1 Load deflection diagramof medium specimen

20

a (no)

9 0 0

3 0 0

Fig. 2 Loading rate of mediumspecimen

References:

[1] BAZANT, Z. P. - CAO, Z.: Size Effect in Punching Shear Failure of Slabs. ACIStructural Journal, Vol. 84, Jan.-Feb. 1987

[2] BAZANT, Z. P. - OZBOLT, J. - ELIGEHAUSEN, R.: Fracture Size Effect. I.Reviewof Evidence for Concrete Structures, 2, 1992

[3] Punching Shear in Reinforced Concrete. Bulletin d'Information, No. 168, CEB, January1985

[4] BOUSKA, P. - MARG0LD0VA, J.: Dependence of Punching Shear Load Capacity onthe Thickness of the Slab. Grant No. 8145, Preliminary rep., Klokner Institute CTU,Prague, 1993

This research has been conducted at the Klokner Institute of CTU as a part of theresearch project "Size effect in punching shear failure of slabs" and has been supported byCTU grant No. 8145.

210


THE COLUMN-BASE COMPONENTTESTS

F. Wald, J. Seifert, I. Simek,Z. Sokol, J. Pertold

CTU, Fac. of Civil Eng., Dept. of Steel Structures,Thakurova 7, 166 29 Praha 6

Key words: steel structures, semi-rigid connection, column base, tests, component method

For a steel frame analysis, the column-base bending stiffness is as important as thebeam, the column and the beam- to-columii connections stiffness [5]. A few existing experi-mental data concerning column bases from full scale frame tests [1], show that a significantcolumn-base bending stiffness exists for most of the different cases, even for a simple columnbase. The base plate is used as a simple and economical detail, to transfer the load fromthe steel column into the concrete foundation. The base plates should be fixed with twoor four bolts. Both of these details transfer a significant moment into the foundation. Thefirst detail closely resembles the behaviour of a pinned connection while the second detailbehaves more like a fixed joint. The behaviour of the column- base detail depends on thejoint parameters but is best represented as a semi-rigid connection. The rigidity of column-base connections is primarily dependent on the moment-to-normal force interaction. Thepresented review is focused on the column-base component test results [2, 3]. The three testtypes were used to check the stiffness and resistance of the tension side component Fig.l [2,3], of the compression side component Fig. 2 [2, 3] and of the component interaction in thefull scale tests [3]. The main observed problems on the tension side were the prying action[6] and bolt elongation. Fig. 1 shows the deformation of a very thin base plate loaded intension.

r±i12108642

Deformation,nun

40 60 80 100 160

- — 350.0kN•—742.4kN•— 1134.1kNo— 1520.5kN. — 2041.7kN

Fig. 1: The mean values of the deformation of the base plate of test #BT 10

The compression side is more important from the ultimate resistance modelling pointof view. The Eurocode 3 advanced design model is based on resistance of the concreteconcentrated strength and on the flexible plate behaviour. The new proposed model forEurocode 3 (updating in 1995) is more oriented to the separate component description withmore complexity and could bring the necessary accuracy for a moment- rotation description.Fig. 2 shows the deformation on the base plate loaded in compression. Fig. 3 shows the

211


complex 3D problem of the behaviour of the base plate under the H cross section loadedwith eccentricity.

11 Plate 10

0,10,0-0,1-0,2-0 ,3 J

L

Plate 8

Deformationmm

Plate Width, mm

Fig. 2: The mean values of the deformation of the base plate of test #BC 8

All the results of the performed tests have been adopted into the data base [1]. Thedata bank is situated on the computer net and allows co-ordination of the data output of allthe tests carried out on the topic. The data base is expected to lead to the establishmentan acceptable component model of column base behaviour.

PlateS

220

Plate Width, mm

mmDeformation

240 kN

300 kN

420 kN

540 kN

600 kN

Fig. 3: The deformation ol the base plate on the neutral axes, the test #BS 10

References:[1] WALD, F. - SIMEK, I. - BEZDEK, P.: Column-Base Connections, Data base, COBA-

DAT, COST Cl, No. C2-WD/93-03, Liege, 1993.[2] SEIFERT, J. - WALD, F. - BAZANTOVA, Z.: Experimentdlni stanoveni unosnosti a

tuhosti patek sloupu, Experiments with column bases, CVUT, Praha 1993, s. 24.

SIMEK, I. - WALD, F. - BAZANTOVA, Z.: Experimentdlni stanoveni tuhosti cash'patek sloupu, Column-Base Component Experiments, CVUT, Praha, 1993, s. 28.WALD, F. - OBATA, M. - MATSUURA, S. - GOTO, Y.: Flexible Base Plates Be-haviour Using FE Strip Analysis, Acta Polytechnica 1, Vol. 33, No. 1, Prague, 1993,pp. 83-100.WALD, F.: Column-Bast Connections, A Comprehensive State-of-tht-Art Review, TUBudapest, Technical Report No. 12., Budapest, 1993.WALD, F. - OBATA, M. - MATSUURA, S. - GOTO, Y.: Prying Effect of AnchorBolts, JSPS, Nagoya, 1993.

[3]

[4]

[5]

[6]

This research has been conducted at the Faculty of Civil Engineering as a part of theresearch project "Flexibility of Column Bases" which has been supported by Czech Techni-cal University Grant 8118/93. The sponsorship of Czech Convention for ConstructionalSteelwork is gratefully acknowledged.

212

(TU SEMINAR <M THEORY OF CONSTRUCTIONS

STEEL-CONCRETE COMPOSITEELEMENTS AND/OR STRUCTURES

J. Pechar, J. Prochazka*, V. Weiss

CTli, Fac. of Civil Eng., Dept. of Steel StructuresThakurova 7, 166 29 Praha 6

*CTU, Far. of Civil Eng., Dept. of Concrete Structures & BridgesThakurova 7, 166 29 Praha 6

**CT()\ Fac. of Civil Eng., Dept. of Concrete Structures k BridgesThakurova 7, 166 29 Praha 6

Key words: structures, composite structures, composite elements

The following research was carried out on three basic types of composite structures:1. Steel-concrete composite elements and/or structuresThe authors have derived new, more precise and less laborious methods of analysis,

elaborated in the form of computer programs and confirmed by experiments, for the followingsubthemes:

a/ Composite columns (steel tubes filled with concrete) - the COMCO computer pro-gram allows the influence of confinement to be respected.

b/ Partial interaction and semi-rigid connection in steel-concrete composite beams - adesign model based on FEM for both single-span and continuous beams. For the deflection icalculation, it is necessary to introduce a bolt stiffness higher than 2 nominal values given |by a push-out test. The formula contained in EC-4 seems to produce values that are too ismall. |

c/ Transverse stiffness of steel-concrete composite steel bridges - it was proved that jsteel cross beams are unnecessary in most cases. The linear analysis is completed by the Jsolutions in d and e below. i

d/ Comparison of both linear and geometric non-linear analysis of a composite deckroadway bridge - the differences in deformations are less than 5% (the linear analysis beingsufficient).

e/ Plastic model for composite bridge analysis - BS 4500 and EC 3,4 consider the fullplastification in the cross section in determining the ultimate bending moments. Before sucha design approach is accepted in the Czech Republic, it is necessary to analyze all possibleconsequences of low- and high-cycle fatigue, dynamic loading, brittle cracking both in steeland concrete, load and resistance factors, etc. A revision of the Czech National Standardsis unavoidable.

f/ Space structure design in bridges - accurate FEM analysis was developed and verifiedby full-scale tests.

g/ Preflex bridges - this idea was developed both theoretically and for practical designprocedure.

2. Concrete-concrete elements and/or structuresThe actual behaviour of the composite elements of a reinforced concrete beam connected

with a concrete slab caast in situ was studied. The laboratory composite elements weredesigned on the assumption of partial connection by ductile connectors. The ultimate shear

213


resistance in the joint is reached when the st ress in the reinforcement attains the yield value.The ultimate resistance of the composite element need not correspond to the plastificationof the joint, but. some slip can occur in the joint. The authors have derived a new methodof analysis so that the slip in the joint will be incorporated into the design of the structure.The ultimate resistance must be reached after slip in the joint has occured. For a partialconnection, aside from a minimum shear reinforcement in the joint, the roughness of theconcrete surface in the joint is significant. To avoid buckling in the compressed parts of theelement, the shear reinforcement must be placed over the whole length of the joint. Thedesign of the partial connection allowing some slip in the joint is economical.

3. Concrete-plastics composite elementsStresses and strains in a tough but compliant coating, e.g. of glass-reinforced plastics

(GRP) or of polymer concrete, spanned over structure cracks (rnicrocracks) in a core ofcement concrete or of other quasi-brittle but sliffer materials subjected to bending or tensileloads are, naturally, rather low until the start of the first running crack, as previouslyconfirmed with the aid of reflexive photoelasticity. Furthermore, when compared with thefracture energy of the more brittle core, the crack resistance of this core is considerablygreater due to the relatively high energy absorption in strained segments of the coatingover structure cracks during their limited propagation. Such an improvement in the energybalance of qua.si-brit.tle materials is possible because of the limited crack velocity whichenables the transfer of the released strain energy from the region adjacent to a criticalstructure crack into the coating.

A modified approach was subsequently proposed by other authors, namely that themain contribution consists of energy absorption from the debonding of the coating nearthe critical structure crack. Hence, under long-term or cyclic loads, this debonding wouldgradually proceed just before the start of the running crack, and, therefore, the beneficialeffect of a tougher coating should be negligible. But in serial tests, we obtained contraryresults. To verify our original theory, new fatigue tests were performed on cement, concretebeams connected with a GRP coating on the tension face. Double holointerferograms undernormal atmospheric pressure and under vacuum were made both initially and after thestiffness of the beams seemed to decrease slightly during the cyclic loading. The resultsobtained demonstrate that distinct progress in debonding between the coating and the corewas observed only in the vicinity of running cracks. Hence, the small shear forces inducedby the gradual unloading of small regions of the core at. structure cracks during their limitedpropagation are not high enough to considerably enlarge the very narrow debonded segmentsof the coating over these cracks. Thus, our approach based on the energy produced by thestraining of the coating is valid. The formulae involved can be extended to account for thenon-linear fracture behaviour of concrete and of similar materials; then the improvement ofenergy balance ancl of crack resistance is roughly independent of the size of critical structurecracks.

This research has bet n conducted at. the Departments of Slid Structures and of ConcreteStructures and Bridges as a part of the. research project ''Composite load-bearing buildingstructures" and has ban supported by CTU grant No. #014".

214


CO-OPERATION OF CORRUGATEDSHEETING & NON-BEARING BOARDS

T. Vrany, J. Studnicka

CTU, Fac. of Civil Eng., Dept. of Steel Structures,Thakurova 7, 166 29 Praha 6

Key words: sheeting, board, co-operation, connection, screwing, bonding

The behaviour of the composite slabs composed of corrugated sheeting and cementboards is the subject of this paper. Tile research dealing with this problem had two parts:a theoretical investigation and an experimental one. Corrugated sheeting is frequently"sed for the ceilings or roofs of different kinds of buildings. Different types of boards,ordinarily assumed as non-bearing, are often part of such structures. By their connectingwith the sheeting the load-bearing capacity of the slab could be considerably increased.Both materials are connected together either by bonding or by screwing. The compositeslab has a bigger load-bearing capacity than the corrugated sheeting itself thanks to thefollowing effects:

• The composite beam action leads to the redistribution of the stresses from the steelsheeting to the board (especially when the board is placed on the compressed sideof the slab), and to substantial increasing of the slab stiffness. The composition isflexible when the materials are screwed together, or rigid when they are bonded.

• If the board is placed on the compressed side of the slab and the compressed flangeof the sheeting is liable to local buckling due to its extreme slenderness then theconnection reduces the influence of local buckling.

• If the board is placed between the sheeting and the support then no web crippling ofthe sheeting occurs.

For the experimental analysis of the slab the corrugated sheeting VSU 120 02 producedin Koice and the cement board Cetris produced by Severomoravske cihelny Hranice werechosen. The experimental research was comprised of the following parts:

1. determining basic mechanical properties, i.e. modulus of elasticity and compressionstrength of the board Cetris;

2. determining the screw connection stiffness, i.e. the force/movement relation character-istics; It was found that the relation between force and movement can be approximatedby a bi-linear curve.

3. the analysis of the behaviour of the slab in the internal support area;4. the analysis of the behaviour of a simply supported, uniformly loaded composite slab.

For a theoretical analysis of the composite slab it was necessary to define the possiblemodes of failure:

1. Corrugated sheetinga) local buckling in the compression flange occurs when the stresses are close to the

yield strengthb) yield strength is reached in the tension flange of the sheetingc) excessive local deformations arise in the support area

2. Board - compressive (tensile) strength is exceeded3. Fastener - shear failure

215


Fig. 1 Cross-section model for folded plate calculation

Generally, other failure modescan occur, but they were notrelevant in this analysed case[1]. The method of folded plates[2] was found as very suitablefor analysing the composite s-lab. This method is intendedfor analysis of prismatic mem-bers of cross-sections made upof thin parts. Bearing in mind

the assumptions of the theory of elasticity, the method is an exact one because both thebeam and the skin behaviour of all parts of the cross-section is modelled.

For analysing the composite slab, it was necessary to model the connection of thesheeting and the board suitably. It was made by defining dummy members between bothmaterials in such a way so that the characteristic properties of these members approximatethe behaviour of a real connection well. The same approach has already been used for theanalysis of composite steel-concrete beams [3]. Fig. 1 shows the appearance of the modelof the cross-section.

Table 1 shows the results of an example solved in compliance with the assumptionsgiven above. A simply supported uniformly loaded beam was solved in two cases - as thesheeting VSU 120 02 itself and as the composite beam. It is seen from the table that thestiffness was increased by 100 in the second stage. For strength, usually the combinationof failure modes l.a) and 2. is the decisive one (see above). It. means that the strength isincreased by more than 28,5 according to the Tab. 1.

Stress [MPa]

Board Cetris

Steel upper fibres

bottom fibres

Max. deflection [mm]

SheetingVSZ120 02

223.1

164.0

14.4

Composite beam

4.3

64.9

127.6

7.2

Increasing ofcapacity(%]

243.8

28.5

100.0

Tab. 1 Stresses and deflections of simply supported beam, I = 1900 mm, q = 10kN/m2

References:

[1] VRANY, T.: Spolnpnsobeni trapeyovych plechu s nenosnymi deskami Prace k odbornezkousce, CVUT, 1993

[2] KRISTEK, V.: Trovie vijpoctu komiirkovych nosniki SNTL, 1974

[3] KRISTEK, V. STUDNICKA, J.: Analysis of Composite Girders with DeformableConnectors Proc. Inst. Civil Engrs, Part 2, J982

This research has been conducted at the Department of Steel Structures as a part of theresearch project of the research project "The Analysis of Thin-Walled Steel Structures" andhas been supported by the Civil Engineering Faculty grant No. 1122.

216


THE BEAM-TO-BEAM BOLTEDCONNECTION EXPERIMENTS

I. Simek, F. Wald

CTU, Fac. of Civil Eng., Dept. of Steel StructuresThakurova 7, 166 29 Praha 6

Key words: steel structures, semi-rigid connection, beam-to-beam connection, experi-ments, initial stiffness, strength design

One of the most significant innovations in the new European structural design codes isthe inclusion of semi- rigidity. This type of framing provides a greater freedom in design,leading to worthwhile reduction in cost. The basic problem however is obtaining the rea-sonable knowledge of connection behaviour. The new version of Annex J called Annex JJ,which is under preparation for the final version of code (from ENV to EN scheduled in 1995),shows good connections prediction possibilities for connections due to the introduction of acomponent model.

Fig. 1: The tests setup of test #C10/93 and test #C12/93

We have prepared two full scale tests (Fig. 1) to check the validity of using componentmodels for the modelling of beam-to-beam connections. These tests were designed withthin end plates to observe the sensitivity of the design model to the prying forces of thestiffened end plates and to study the influence of a bolt length. The moment rotationaldiagram was recalculated from the deflection as well as directly measured as a rotation ofthe beam's webs on neutral axis. The bolt internal forces were measured by straingaugeelongation in drilled hole in the centre of each bolt. The position of the connection's neutralaxes were estimated from the relative deformations of the end plate. The results of theexperiments are shown on the moment rotation diagram, Fig. 1 and Fig. 2 for tests C10/93and C12/93 (the plate thickness was a main parameter and is expressed in the numbering)[4]. The numerical analytical prediction is represented by an analytical model according toEurocode 3 [1] ("Analytical EC3 model"), by the component model "Model W- S-" [6] andby the model of the new version of "Eurocode 3, Annex JJ" [2].

For the beam-to-beam connections we discovered the importance of the bolts preloadingand the possibility of improving the stiffened end plate model. The improvement for thestrength design has already been implemented into the new Annex JJ design procedureas an alternative method in Annex D [2]. This improvement is significant for the designresistance (see the curves "Alternative method" in Fig. 1 and Fig. 2.) This is possible for

217


the component model itself to be renewed or revised in the of such better knowledge of eachcomponent behaviour. The tests carried out made a first step towards better modelling ofstiffened end plates rigidity.

Moment (kNm)250

Analytical EC3 model Êxperiment200

/ Analytical EC3 model, Annex JJ, Alternative method/ , Analytical EC3 model. Annex JJ

0,005 0,015 0,02 0,025 0,03

Rotation (red)Fig. 2: The moment-rotation diagram of the test #ClO/93

Moment (kNm)300 Experiment

. Analytical EC3 model, Annex JJ, Alternative methodAnalytical EC3 model, Annex J J

B

Model W-S-S

0,005 0,01 0,015Rotation (rad)

Fig. 3: The moment-rotation diagram of the test #C12/93References:

ENV 1993-1-1, Eurocode 3: "Design of steel structures", Part 1.1: general rules andrules for buildings. European Committee for Standardisation (CEN), Brussels, 1992.Technical Working Group 10.4-: "Annex JJ to Eurocode 3", European Convention forConstructional Steelwork (ECCS), Publication No. TC10.2-37, Istanbul, 1993.ANDERSON, D. - COLSON, A. - JASPART, J. P. - WALD, F.: Ekonomicke stycnikypro ocelove rdmy, Connections and Frame Design for Economy, Stavebni obzor, c. 10,Praha 1993.SIMEK, I. - WALD, F.: Experimentdlni vyzkum pftpoje nosniku na nosntk, Experi-ments with Beam-to-Beam Bolted Connections, Research Report, CVUT, Praha 1993.WALD, F. - SOKOL, Z.: Pfesnost metody ndhradnich tuhosti pfi navrhovdni rdmv spoddajnymi stycniky, The Error in the Modified StifFnes Method for Semi-Rigid FrameDesign, Acta Polytechnica, c.l, Praha 1991, s.19-30.WALD, F. - STEENHUIS, M.: The Bcam-to-Column Bolted Joint Stiffnes accordingto Eurocode 3, Workshop COST Cl, Strasbourg, 1993.

[1]

[2]

[3]

W

[5]

[6]

This research has been conducted at the Department of Steel Structures as a part of theresearch project "Semi-Rigid Design" and has been supported by CTU grant No. 1121. Thesponsorship of Czech Convention for Constructional Steelwork is gratefully acknowledged.

218

^


NON-DESTRUCTIVE DEFLECTIONTESTING OF PAVEMENTS

B. Novotny

CTU, Klokner Institute, Dept. of Composite Materials and ConstructionsSoli'nova 7, 166 08 Praha 6

Key words: deflection testing, inverse problem, deflection compliances, far-field behaviour

Non-destructive deflection testing (NDT) is one element of the current monitoring efiFortby the US Strategic Highway Research Program (SHRP). To close the existing gap betweenanalysis and application in practice, SHRP Expert Task Groups advocate in [1] that theforward calculation, which will be discussed in this paper, be addressed.

A mathematical model of pavement is composed of n elastic, isotropic layers, supportedby an elastic, isotropic halfspace, the pavement subgrade. Known are layer thicknesses hiand Poisson's ratios e,; to be determined are layer moduli E,. The load generated by anNDT device is regarded as quasistatic and is represented by a uniform loading of intensityq over a circular area of radius a. Pavement surface deflection response u>,- is measured inm points r = r; and the analytical part of the NDT is formulated as an inverse problem: todetermine moduli £, in such a way that the deflection based error functional

attains its minimum. Here, (,\. are weighting coefficients and w(r; E) denotes the surfacedeflections of the pavement model

ti»(r; E) = / w{t; E) /,(£) J0(r£) rf£ , (2)Jo

where Jm(£) is the Bessel function, /,,(£) is the loading function

and io(^; E) represents the "structural" deflection function reflecting structural and materialproperties of the pavement. Using the transfer matrix approach, we have determined thefirst three Taylor's series coefficients of tt>(£; E) at £ = 0 :

= 2(1-!/„+,)/£!,,

(4)

219

^ 4-v-iw.


where Hn is the overall pavement thickness, fik is the shear modulus and the quantities ctkand [Ik are geometrical and material characteristics of the pavement layers

ck = -jr, fa = • (5)ti t*

"Deflection compliance" Cm comprises material properties of the subgrade only, whilecompliances Ci. and Ci, reflect the geometrical and material properties of the complexpavement/subgrade structure. They have been derived independently of the pavement loa-ding type and should possess substantially greater revelatory value on the behaviour of thepavement/subgrade structure than artificially created characteristics based on the theory ofcomposite plates and shells.

After rewriting (2) in the form

w(r; E) = whom{r; £n+1,i/n+1)+ r"] f W - ' f c E)-w(0; E)] MrÔ MO d£ , (6)Jo

where Whom denotes the surface deflection of the homogeneous halfspace having the subgradematerial properties J?n+1 and j/n+i

; E) f.(0 Mrt) dt, , (7)

it can be shown that expression (6) may be used :

(a) to effectively calculate deflections in far-away points (r >• a), after making use of

[Mr-1*; E) - MO; E)] ~ r'*t C™ + \ r"2f2 C<f>, (8)

a procedure, which may be efficiently applied when numerical solution of a contactproblem is considered;

(b) to reconstruct the "seed moduli" at the beginning of the inverse problem iterativesolving procedure; the subgrade modulus approximation fiJJJJ, is derived from

Whom(r3; £?£+,, JVH) ~ w, , r, ~ 10a . (9)

The higher-order compliances Ci1' and Ci2) may be used to control the direction-searchstage of the solving procedure and prevent possible pathological "zig-zag" behaviour.

In the same way, the horizontal displacement compliances Ci have been derived andwill be used to control the solving process in cases when the "testing" load also has a hori-zontal component.

References:[1] Nondestructive Deflection Testing and Backcalculation for Pavements- TRR No. 1377

(Proc. Symp., Nashville, 1991), TRB NRC, Nat. Acad. Press Washington D.C., 1992

This research has been conducted at the Department of Composite Materials and Con-structions as a part of the research project "Micro- and Macromechanics of Composite Struc-tures" and has been supported by GA CR grant No. 103/93/1046.

220


PEDESTRIAN DYNAMIC LOADINGAND RESPONSE OF FOOTBIDGES

M. Studnickova

CTU, Klokner Institute, Department of MechanicsSoli'nova 7, 166 08 Praha 6

Key words: vibration, dynamic response, absorbers, response of pedestrians, naturalmodes and frequencies

Rhytmical human body motion e.g. walking, running, jumping can cause heavy vibra-tions of structures. There were several accidents of footbridges caused by marching peopleand in recent years there have been examples of footbridges that have proved to be unac-ceptably lively to pedestrians. The latter is namely the case of steel or composite footbridgesthat possess very low damping.

The only rule in the Czech Standard CSN 73 6203 [1] considering the dynamic effectsof pedestrian says, it is necessary to be careful when the footbridge lowest frequency invertical f0 is in the range 1,4 to 3,3 Hz, or to carry out the dynamic calculation in case ofsuspension or cable - stayed footbridges. No other detailed instructions are given.

The aim of this work is to produce a simple method for the reliable assessment of thefootbridge response to dynamic excitation caused by pedestrians, to specify various typesof human activity, to define the dynamic loading, to assess criteria of dynamic responseacceptable to users.

Number of tests show that the dynamic loading caused by pedestrian can be representedby the formula

F(t) = G + Gi.sin(2irfKt) + G2.sin(4xfKt - y>2) + G3.sin(6TrfKt - v?3) (1)

where G = static weight of person, Gi = Fourier coefficients, /*• = footstep rate, ipi =relative phase angle.

Presenting formula (1) in the other way, defining J- = at\, the terms a< are calleddynamic factors of i-th harmonic.

Factors Oj obtained by tests for heavy traffic are summarised in Table 1. For one personwalking QJ = 0,4, a2 = 0,1 and 03 = 0,1.

Tab. 1

The dynamic response depends especially on the lowest bending frequency of the foot-bridge in vertical /0. If the frequency /„ is higher than 4,5 Hz, the dynamic response causedby pedestrian walking or running is negligible.

If the frequency f0 is in the range 1,6 - 2,4 Hz or 3,2 - 4,5 Hz, the dynamic response fromthe moving people can be significant. In that case it is necessary to calculate the vibrationsconsidering both serviceability and ultimate limit states. It is almost sure, that in this

221

Activitywalking, joggingrhytmic exercises

« i

1,11,6

o2

0,20,6

0,10,2


case the vibrations will be unacceptable. The possible measures are either to avoid thesefrequency ranges by changing material, stiifness and span of the structure, or to enlarge thedamping using dampers and absorbers.

A suitable absorber of minimum mass is to be used when dynamic response is excessive.It is necessary to calculate the absorber and to tune it after the footbridge was built. Theabsorbers were successfully used e.g. in the U. K.

Design of a footbridge to static loading doesn't usually cause any problems. Moreproblematic is sometimes to comply with vibration serviceability criteria.

These criteria in vertical and horizontal directions are proposed in the form given byFig. 1 and Fig. 2. According to these criteria the vertical acceleration of the footbridgeto the action of one person walking along the footbridge should be less than that given bythe curve of Fig. 1. The pace rate of the person is to be equivalent to the lowest verticalfrequency of the footbridge (or the half of it). The horizontal acceleration caused by wind(for mean wind speed vm = 15ms"1) shouldn't exceed values given by the curve of Fig. 2.

1 . 0 T

- —'- T n5

— - unacceptable -

O.I

3 I. S 6 7 a ,0

frequency [Hz]

i.o 3 ( S E 7 S 1 0

frequency [Hz)

Fig. 1 Fig. 2

The results of the calculations and measurements of footbridges can be summarisedas follows. For the footbridge of an unusual shape or static system the dynamic analysisshould be carried out in any case. This analysis contains the calculation of natural modesand frequencies up to 4,5 Hz, the response of the footbridge to pedestrian loading and towind loading.

For other footbridges greater than 20 m, the dynamic analysis should be done, if anyof the following criteria are meta) the lowest vertical frequency of the footbridge is less than 4,5 Hzb) the lowest frequency in horizontal (perpendicular to the bridge axis) is less than 1 Hz.

References:

[1] CSN 13 6203: 1986 Loading of bridges

This research has been conducted at the Department of Mechanics as a part of theresearch project "Modelling of Structural Systems and Dynamics Loads" and has been sup-ported by CTU grant No. Sl/,7.

222


MATHEMATICAL MODEL OF RAILVEHICLE GUIDING QUALITIES

J. Siba, T. Heptner, J. Kolaf, R. Musil

CTU, Fac. of Mechanical Eng., Dept. of Automobiles, ICE & Rail VehiclesTechnicka 4, 166 07 Praha 6

Key words: rail vehicle, mathematical model, bogie, wheelset, guiding, creep characteris-tics

In 1991 - 92 partial theoretical studies were made within the framework of researchsupported by IG. The aim was to create definitional relations describing phenomena thatare not considered in known mathematical models of vehicle-track system interactive effects.

The influence of wheel tread profile, gauge, rail head profile and rail cant were studied ingreater detail. Four types of wheel tread profiles (UIC-ORE /S 1002/, taper 1/20, KKVMZand BP 8), rails S49, R65, UIC60 and 1/20 or 1/40 cant were considered. The characteristicsare evaluated from two viewpoints:

1) The ability to run stably in the straight track. The effective conicity value plays animportant role.

2) The ability to curve negotiation without longitudinal creep.The stand for 1/3 scale wheel-rail tests has been completed in the experimental part of

the research.Further problems have been studied:- the complete definition of wheel-rail lateral and longitudinal creep characteristics- the connection of curve wheel tread profiles with wheelset longitudinal dynamics and

specific characteristics of driving wheelsets- the kinematic and force relations of radial steered wheelsets- the basic idea and the simulational model of dynamically and quasi-statically acting

active elements in the bogie-carbody connection- the consideration of geometrical errors and of elasticity of running gear and rail main

parts.The mathematical model of the two bogie four axle car (Fig. 1) was completed in 1993

by using these partial studies. The model has 14 degrees of freedom in the described con-ception ( for the present without the last mentioned influences of elasticity). It is linearisedto make the analyses easy in the first stage.

It is possible to evaluate the guiding characteristics of four-wheelset rail vehicles bothin curve and straight parts of track. The conditions of stable vehicle running by highervelocity with consideration of track irregularities and of ambiguous influence of radial steeredwheelsets are determined in the first case. The model makes possible the evaluation oflateral vehicle-track force effects during the curve negotiation and then the evaluation ofthe derailment safety, track position stability and vehicle kinematic gauge keeping.

The answer to these questions is the pre-condition for design and operation of higherspeed rail vehicles. The reconstruction of existing vehicles for higher speed operation on thepresent rail network is necessary to consider as the first step. The studies [1-4] were donewith this aim. The evaluation of the locomotive quasi-static characteristics (Fig. 2) by the

223


higher speed curve negotiation by the Iiigher values of unbalanced centrifugal forces was apart of these studies.

References:

[1] SIBA, J.: Modtrnizact kokjovych vozidel, Uspory v zeleznicni doprave (2.cast), V$DSZilina 1993, Pg. 39-47

[2] HEPTNER, T.: Pojezdy soucasnych osobnich vozu . Uspory v zeleznicnf doprave(2.cast), VSDS Zilina 1993, Pg. 171-176

[3] KOLAR, J.: Modtlovani vodicich vlastnosti ndkladnich vozu , Uspory v zeleznicni do-prave (2.cast), VSDS Zilina 1993, Pg. 183-190

[4] VLASAK, J. - MUSIL, R.: Vlastnosti oplimalizovaneho profilu tramvajovych kol, Us-pory v zeleznicni' doprave (2.cast), VSDS Zilina 1993, Pg. 177-181

This research has been conducted at the. Department of Automobiles, ICE and RailVehicles as a part of the research, project "Rail Vehicle Guiding Characteristics" and hasbeen supported by CTU grant No. 8028.

Ft9. Linn.nc :sar model

Fig. Z

-afcer*! suspensi

224


ASSESSMENT OF DIFFERENTMETHODS FOR MEASURINGTHE EFFECT ON A TRACK

STRUCTURE UNDER LOADINGH. Krejcinkova, B. Kubat

CTU, Fac. of Civil Eng., Dept. of Railway ConstructionThakurova 7, 166 29 Praha 6

Key words: rail, superstructure, track under loading, strain gauge

Determining the strain on a superstructure at a given instant during the crossing ofa railway vehicle requires a complex approach to the analysis of a vehicle - track system.Vehicle motion on the track structure initiates dynamic loading, the character of whichdepends, among other factors, on the structure and quality of the railway track and vehicleand on the stage of their wear. The method of experimental measurements is the mostaccurate method for determining instantaneous track dynamic strain .

In carrying out grant N. IM6, the Department of Railway Construction analyzed variousmethods, using direct, measurements of the forces on a track superstructure, whereby therail is a dynamotnetric element.

Tensometric resistive elements are used for short-time controlling of the effect of railwayvehicles on the track. At the location at which they have been placed, they scan deforma-tions in the loadod structure. Measured parameters depend on the configuration of thetensometric elements on the structure being investigated. Measuring relative deformationswith the help of tensometric elements is based on the knowledge that the force on a solidbody deforms this body in the affecting force direction as in the perpendicular direction tothe affecting force direction. The deformation in the affecting force direction is defined byHooke's law in the elastic deformation zone, and the deformation in the perpendicular di-rection to the affecting force direction is dependent on Poisson's ratio. Between the relativevariation in resistance and the relative deformation of an element, a linear dependence isvalid.

Measuring under such extreme conditions in traffic is limited timewise by the durabilityof the tensometric resistive elements. The advantages of these methods are that the tenso-metric resistive elements can be rapidly and easily installed, that the the track geometry isundisturbed, and that the elastoplastic properties of the superstructure remain undisturbed.It is necessary to calibrate known forces for the particular superstructure and the particularkind of rail seating before each measurement is taken.

Altogether, four basic alternatives for ascertaining components of the forces generallyacting on a structure were proposed - measuring relative deformations in the rail head, thefoot and the web, and the hole in the rail web. The individual methods were analyzedunder equivalent conditions of loading and seating in the central laboratories of the Facultyof Civil Engineering , Czech Technical University, Prague. Each method can only determinesome components of force.

225

:^ =-v'


In Fig. 1, it is shown that the method of measuring rail head deformations is the mostsensitive method for measuring changes in the horizontal transversal component Y of ageneral force acting with the varying vertical force Q and the null longitudinal force N. Themeasured signal is linear for the working range.

I-1000 -

-1500-

-2000 -

-85006020 40

Fbiw YQcN)

Fig. 1

The following conclusions can be made on the basis of the measurements taken and theresults processed :

- the type of measurements depends on the location of tensometric elements on theconstruction,

- the accuracy of a chosen method depends on the accuracy of the placement of tenso-metric elements on the construction,

- the measuring method chosen definitely depends on the output quantity required.

The aim of this research was to assess the suitability of each method for measurementson working track. The utilization of these methods makes it possible to classify railway linesin preparation for the introduction of new structural elements and materials.

References:

[1] TARRAN, F. C : Direktmessung von Schwellenbelastungen Schienen der Welt, Jan.1987

[2] FUEHRER, G.: Oberbauberechnung, Verlag fuer Verkehrwesen 108 Berlin, 1978

[3] WEBER, H. H.: Zur direkten Messungen der Kraefte zwischtn Rad und Schienc GlasersAnnalen, 7/1961

This research has been conducted at the Department of Railway Construction as a partof the research project "Ndvrh a ovefeni metodiky mefeni siloveho pusobeni v konstrukcikoleje pod zatizenim" and has been supported by FCE CTU grant No. 1146.

226


FATIGUE CRACK GROWTHPREDICTION

UNDER RANDOM LOADINGM. Ruzicka

CTU, Fac. of Mechanical Eng., Dept. of Elasticity fc Strength of MaterialsTechnicka 4, 166 07 Praha 6

Key words: fatigue, crack growth, life prediction

The significance of fatigue crack growth prediction is obvious in aircraft structures, sincethe fail-safe design philosophy is applied to these structures. The fail-safe design philosophyimplies that cracks are allowed in certain structures. The fatigue crack growth predictionshave to be made during aircraft design to satisfy damage tolerance requirements and tosettle inspection periods.

The use of fracture mechanics is expressed by the relation between the crack propagationrate da/dn and the stress intensity factor Ka. Two significant milestones for fatigue crackgrowth under constant amplitude loading in relation with the stress intensity factor havebeen developed. The first one was proposed by Paris:

J = ^./C (i)and the second by Forman

da A2.I<"'2

dn (1-R).KC-Ka ^For aircraft loading histories such as variable amplitude loading and flight simulation

loading, the relation between the crack growth rate and the stress intensity factor becomesmore complex. Some crack growth prediction models have been compared and discussed.Two well-known crack growth models account for interaction effects based on plastic zonesizes: Wheeler's model and Willenborg's model. The next Elber's and Schijve's modelsare based on residual stresses in the crack tip zone. It was decided to adopt the ONERAmodel for the life prediction [1]. This model is based on the crack closure mechanism and itrequires a cycle by cycle crack opening stress level calculation. The computer program of themodified ONERA model and the comparison of the prediction results and the test resultswere done, using the data from VZLU Praha [2]. A comparison between the test resultsand the predictions showed that the ONERA model qualitatively predicted the effects ofthe load spectrum variations applied in the present test (spectrum with and without signcycles). This confirms that crack closure concepts are still important in predicting crackgrowth under flight simulation loading of Czech aircrafts.

References:[1] SCHIJVE, O.: Fatigue Crack Growth Predictions for Spectrum Loading Delft University

Report 526, 1987 Replace this line by more information (journal, pages, publisher, yearetc.).

227


[2] RUZICKA, M. - FIALA, J.: Fatigue Test of the Aircrafts Undercarriages Report VZLUPraha, 1994 (in print)

This research has been conducted at the Department of Strength of Materials, FMECTU and the VZLU Praha as a common research project

228


VISCOELASTIC INSTABILITYIN THEORY OF STRUCTURES

V. Kovarik

CTU, Klokner Institute, Dept. of Composite Materials and ConstructionsSoli'nova 7, 166 08 Praha 6

Key words: critical loading, distributional correspondence principle, eigen-value, elasticrange, life-time, stability problem, utilizability time, viscoelastic range

From the mathematical point of view, any stability problem is an eigen-value problem.In this respect the transition from the elastic to the viscoelastic range does not bring anychange. A somewhat different situation occurs when accepting the technical point of view.The main differences observed in this respect are described in the following. For moredetails concerning the problem itself, the distributional concept of this problem, as well asthe mathematical tools employed see [l]-[3] and [4], respectively.

Elastic solutions to stability problems of beams, rods, columns, plates and shells ofrevolution can often be expressed in the following general form :

Vcr = f{geom) y{E) , (1)

where Vcr denotes the critical value of such quantities as axial compression, shear loading,radial loading, inner pressure etc., J(geom) stands for a function involving geometricalparameters only of the structure considered and ^>(E) represents the function of materialcharacteristics such as the Young (E) and shear (G) moduli, Poisson's ratio (;<), etc.

Solutions for corresponding (conjugate) viscoelastic problems are easily found by meansof the distributional correspondence principle. First, the conjugate elastic solution (1) islocated above the positive time semi-axis :

Vcr = f(georn) <p(E) h(t), (2)

where h(t) is the Heaviside (unit step) function. Next, the elastic constants are replaced in<r>(E) by their viscoelastic equivalents

s-M11, <z~agi, !-/>«, ito receive

<P(E) ~ $ f1)(/e). (4)The symbols R\, Rs and Di, Ds represent relaxation (R) and creep (D) functions, lowerindices j , s denote uniaxial compression and shear, respectively. The material characteristicsmentioned are expressed as right-sided distributions

R(t) = r{t) k(t), D{t) = d{t) h(t), (5)

where r(t), d(t) are smooth functions of time. The upper index f'l in (3) and (4) means thedistributional (generalized) time derivative defined by the relations similar to

= r(0+) 6(t) + r<l\t). (6)

229


The upper index ' ' ' in this equation denotes the classical time (dot) derivative, the symbol6(t) stands for the Dirac measure which is the distributional derivative of the Heavisidefunction k(t) and, also, the unit element of the convolution algebra. It should be noted,that the symbol of the first distributional derivative with $ in (1) has been introduced forformal purposes.

Finally, the dot product in (2) is replaced by the distributional convolution and theviscoelastic solution is arrived at

Vcr[t) = f(gcom) * [ I J * h = f(geom) $ * /i'1 ' = f(geom) Q*6 = f(geom) Q(R) . (7)

It can be shown, that (7) is a monotonir decreasing function of time, while the conjugateelastic solution (1) represents a constant.

Now, let N be the given loading of the proper kind and let. .s0 denote the desired safetycoefficient. Then, the stability condition reads

Vcr < So N . (8)

Independently of time, in an elastic case this condition either is satisfied, or it is not. In theviscoelastic case, it may happen, that the condition (8) is met for t —> 0+ while for sometime t > 0 this inequality is no longer valid. If so, the concept of the utilizability time t.ucan be introduced as the solution of the transcendental equation

VcrW - .s0 ;V = 0 . (9)

Often, the term the critical time tcr is employed instead of <„ defined by (9) for so = 1.The necessary and sufficient condition for the existence of tcr is lvr(oo) < N, provided thatVCT(0+) > N. Evidently, the existence of tCT is the necessary (but not sufficient) conditionfor the existence of t.u.

As soon as it. is observed that the condition (8) is satisfied for t — > 0+, while for / —» ooit does not hold, the utilizability time <„ has to be found and compared with the desiredlife-time tj of the construction. If tu > ti, the construction can be accepted. In the oppositecase, if tu < <;, the construction considered cant be utilized for times longer than tu.

References:

[1] K0VAR1K, V'.: Stresses in layered shells of revolution. Academia, Praha; Elsevier,Amsterdam 1989

[2] K0VAR1K, V.: Theory of viscoelasticity (in Czech). Graduate Level Textbooks, Vol. 3,Klokner Institute, 1992

[3] K0VAR1K, V.: Solution of viscoelastic structures (in Czech). Graduate Level Text-books, Vol. 4, Klokner Institute, 1993

[4] ZEMANIAN, A. H.: Distribution theory and transformation analysis. McGraw-Hill,New York J 965

This research has been conducted at the Department of Composite Material* and Con-structions as a part of the research project "Mechanics of Composite Materials1' and hasbeen supported by CTU grant No. 8009.

230


OBSERVATION METHODOF TUNNELING

J. Bartak

CTU, Fac. of Civil Eng., Dept. of GeotechnicsThakurova 7, 166 29 Praha 6

Key words: tunneling method, observation, NATM, NMT, measuring, bolting

Two major tunneling nations, Norway and Austria, have long traditions in using shot-crete and rock bolts for tunnel support, yet there are significant differences in philosophyand the areas of application between NATM (New Austrian Tunneling Method) and NTM( Norwegian Method of Tunneling).

NATM appears most suitable for soft ground which can be excavated by machine orhand, where jointing and overbreak are not dominant, where a smooth profile can oftenbe formed and where a complete load bearing ring can be established. Monitoring appearsto play a significant part in deciding on the timing and extent of primary and secondarysupport.

NTM appears most suitable for harder ground, where jointing and overbreak are dom-inant and where drill and blasting or hard rock TBM's (Tunnel Bohring Machine's) arethe most usual methods of excavation. Bolting is the dominant form of rock support sinceit mobilises the strength of the surrounding rock mass in the best way. Rigid steel setsor lattice girders are inappropriate in harder rock due to potential overbreak. Potentiallyunstable rock masses, with discontinuities and clay-fill joints, increasingly need shotcreteand fibre reinforced shotcrete to supplement the systematic bolting. A thick load bearingring (a reinforced ring of shotcrete) can be formed as required, and can match an unevenprofile better than lattice girders or steel sets.

It can be stated with some certainty that shotcrete (better fibre reinforced shotcrete)and bolting area the two most versatile tunnel support methods yet devised, as they canbe applied to any profile as temporary or as permanent support, just by changing thicknessand bolting spacing.

In NATM and NMT great emphasis is placed on thorough descriptions of geologicaland geotechnical aspects of the project.

All these cases were carried out and verified under our conditions:

• Tunnel driving of service tunnel under low roof conditions (soft rock with hand exca-vation).

• Driving of underground sewer in harder rock (drill and blasting).

Results of own large geotechnical investigations, statical solutions and field measuring-ments are contained in the grant annual report G 8115 (Tecnical University of Prague)

This research has been conducted at the Department of Geotechnics as a part of theresearch project "Using Observation Method of Tunneling" and has been supported by CTUgrant No. 8115.

231


A METHOD FOR ASSESSING OPTIMALHEAT POWER

D. Vytlacil

CTU, Fac. of Civil Eng., Dept. of Applied InformaticsThakurova 7, 166 29 Praha 6

Key words: computer simulation, unsteady process, thermal network

When designing buildings, computer simulation using thermal node models is used inorder to optimalize the energy and environmental performance of buildings. Using thesemodels, it is possible to solve problems of unsteady processes, which are typical in buildingsbecouse of influences of the external environment as well as influences of the internal heatsources and internal gains.

The design of model elements was described in [1] and [2], but sometimes we need toknow the forcing quantity which evokes changes of temperature in certain model nodes.Equation (1) can be used to identify it:

TK =It can be specified as:

(1)

(2)

TR, 7] and H are the results of the Fourier transform of temperatures in input andoutput nodes, and the thermal transfer function.

INII-RNA1. A IKTI:HI>i;RATURt°

Fig. 1:

233


In formula (2) Hi and s j are assessed. From these values, the time series of the forcingquantity in the input node can be determined. The described process is shown in Fig.l.

Often, the proposed procedure is used to find a thermal flow which will produce adesired internal air temperature, e.g., when supply of heating energy is discontinue. Thiskind of heating is better from the point of view of energy savings, but it needs a highermaximum heating power.

The method was tested using the lumped component Resistive - Capacitative networkmodel to describe one room in a brick building. The model has different elements forexternal and internal walls and also includes the ventilation heal transfer path. Externaltemperature was considered constant.

Results of simulation using a program developed to solve unsteady process problemsare shown in Fig.2. A drop of the internal temperature was 2"C and the heat flow wasassessed for four different time series of internal air temperature. The maximum heat powerwas caculated 7159 W for line 1 (a solid line) and 3361 W for line 4 (a dotted line). Thisinvestigation was done for four different internal air temperature drop (t). The maximumheat power for line 1 was from 3108 W (t=0.5°C) to 8511 W (t=2.5°C), and for line 4 from2159 W (t=0.5"C) to 3762 W (t=2.5°C). The program also caculates middle heat power,assessing energy consumption during the day. Results show lower energy consumption forhigher drop of internal air temperature, but, simultaneously, maximum heat power is higher,which means higher investment costs. The goal could be minimizing running and investmentcosts during the life of the building or the heat source.

INTIiKNAL 21

TliMl'lEHAlURI:

UltAT 7(M'O

IV]

_\v:<•

,S.!.-:^v:"

• i i i i

0 2 4 6 £ 10 ] : 14TIJMi (hours]

Fig. 2:

References:[1] VYTLACIL, D. - MOOS, P.: The sensitivity analysis of building thermal network

elements. Building and Environment, 1, 1993

[2] VYTLACIL, D.: Synthesis of elements in the thermal model. Proceedings of Work-shop'93, CVUT, 1993

This research has been conducted at the Department of Applied Informatics and has notbeen supported by any grant.

234

Documents

CTU SEMINAR 94 - IAEA · P. Zamarovsky NONLINEAR MODELS IN QUANTUM PHYSICS 81 G. Chadzitaskos, A. Kostdi SOUND PROPAGATION IN KLADNO SANDSTONES 83 A". Malinsky DYNAMIC MODEL OF THE