AD-A258 161

International Workshop

on

MATHEMATICAL METHODS IN COMBUSTION

Villa Olmo, Como, Italy18-22 May 1992DTIC

OU 2, 199a.1N

Final Technical Report

written by

Luigi De LucaDipartimento di Energetica

Politecnico di Milano32 Piazza Leonardo da Vinci

20133 Milano, ItalyPh.: (0039-2) 2399-3912, Fax: (0039-2) 2399-3940

Elaine S. OranLaboratory for Computational Physics

Naval Research LaboratoryWashington, DC 20375, USA

Ph.: (001-202) 767-2960, Fax: (001-202) 767-4798

M. Quinn Brewster1)epartment of Mechanical and Industrial Engineering

University of Illinois at Urbana-Champaign1,14 Mechanical Engineering Building

Urbana, IL 61801, USAPh.: (001-217) 244-1628, Fax: (001-217) 244-6534

Mikhail Kh. StreletsState institute of Applied Chemistry

14 Dobrolyubov Avenue19178 Saint Petersburg, Russia

Ph.: (007-812) 238-5353, Fax: (007-812) 232-5844

and Boris V. NovozhilovInstitute of Chemical Physicsltussian Academy of Sciences

4 Kosygin Street117977 Moscow, Russia

Ph. (007-95) 938-2156, Fax: (007-95) 939-7127

"92-30612 Diqt L.uz_= ,)

I Nfl lra re

T3 / ITR VILLA OLMIO 92/ PAG;E )

NOMENCLATURE

A = nondim. function used in frequency response function theory13 = nondim. fuction used in frequency response function theoryc = specific heat, cal/g KE() activation energy, cal/moleE() = E( )/R/T() , nondimensional activation energyk = thermal conductivity, cal/cm s K; also: ZN parameter (see section 9)m = mass burning rate, g/cm 2 sn = ballistic or pressure exponent in the steady-state burning rate lawns pressure exponent in the surface pyrolysis lawp pressure, atmq energy flux intensity, cal/cm2 SQ heat release, cal/g (positive exothermic)r ZN parameter (see section 9)ri) burning rate, cm/sR universal gas constant; 1.987 cal/mol K or 82.i atm cm 3 /mol KRp = propellant response to pressure fluctuations, nondimensionalRq = propellant response to external radiation fluctuations, nondimensionalt -time coordinate, sT temperature, KT 0 = initial sample temperature, Kx space coordinate, cm

Greek symb,.Isthermal diffusivity, cm 2/sZN parameter (see section 9)

A = wavelength, gmpl ZN parameter (see section 9)I'/ =frequency, Hz; also: ZN parameter (see section 9)p density, g/cm3

Up =burning rate temperature sensitivity, 1/K27ri/, circular frequency, rad/s

0=./rb2 , nondimensional circular frequency

Subscripts and sperscritsc condensed-phaseg gas-phasep) pressureq radiations burning surface- =steady-state value

AtbbreviationsAIP = Ammonium Perchlorate (NI1 4CI0 4)131)1' = teckstead-Derr-Pricel)l = Double-BaseFM Flame Modeling methodKTSS Krier-T'ien-Sirignano-Summerfield transient flame modelPI)L Pressure Deflagration LimitPU PolyUrethanesQSHOI) = Quasi-Steady Homogeneous One-DimensionalT F Transfer FunctionZN Zeldovich-Novozhilov method

T3/ FTR VILLA OLMO 92/ PACiE I

1. TECHNICAL PROGRAM

The final program of the Workshop and list of participants is attached.Xerox copies of most presentations are available and were distributed toregistered participants, In this final report, summarizing statements andbasic discussions on specific topics are treated. References are mainly madeto papers presented at this Workshop, but other papers from the openliterature are mentioned when necessary.

2. BACKGROUND OF WORKSHOP

Combustion problems offer exce:jent opportunities to develop bothanalytic tools and numerical methods. But too often the two worlds interactonly superficially. Mathematicians do not regard working on the needs fromreal world as professionally rewarding, while computer practitioners andengineers consider possible contributions from mathematicians too abstract,if not just useless. Both judgments are biased and this does not lead toproductive interactions.

3. OBJECTIVES OF WORKS HOP

The overall objective of the Workshop was to try to improvecommunications and promote cross-fertilizations between appliedmathematicians and computational scientists, by pointing out promisingdirections as well as effective means of interaction. Specific objectives of theWorkshop were to critically compare analytic to numerical approaches,assess potentials and limitations of both, and hopefully foster newdevelopments in combustion. To this end, a proper mix of formal lectures,specialized presentations, informal discussions, and constructivecross-criticism was implemented.

-, FOJ a

!ra.' ?i&i r-

4. TOPICS SELECTED FOR DISCUSSIONS - ASI .

The specific topics considered for discussions in this Final TechnicalReport on the Workshop nre: ,

L. Synergism between analytic and numerical methods; Y.. ,2. Numerical simulations and limitations;3. Solid propellant combustion (as an example of problem). , -

T3 / FTR VILLA OLM0 92/ PAGE 2

5. DISCUSSION PANEL

This Final Technical Report has been edited by the main investigatorbased on written inputs received by all co-authors and on discussions, heldafter the Workshop, mainly with Dr. E.S. Oran (Naval Research Laboratory,Washington, USA), Prof. M.Q. Brewster (Illinois University atUrbana-Champaign, USA), Prof. Novozhilov (Russian Academy of Sciences,Moscow, Russia), Prof. M.Kh. Strelets (State Institute of AppliedChemistry, Saint Petersburg, Russia), and Prof. V.E. Zarko (RussianAcademy of Sciences, Novosibirsk, Russia).

6. SYNERGISM BETWEEN ANALYTIC AND NUMERICAL METHODS

In principle, analytic methods are applied at the initial stages ofinvestigations of combustion problems. Further investigations to determinedetails of solutions are often performed by numerical methods. Thus,synergism between analytic and numerical methods plays an important rolein combustion and sciences in general. However, problems ofcommunications and mental attitude exist between the combustiontheoreticians using analytic and numerical approaches. From the point ofview of numerical scientists, a notable resistance was felt from traditionalscientists to accept computer simulation as a tool for studying combustion.Historically, this is understandable since combustion is a relatively olddiscipline, in contrast for example with plasma physics which grew up withcomputers. While in the US this resistance has been slowly disappearingduring last few years, in other countries traditional approaches still prevail.

Ir any event, real problems are too difficult for all combustion scientistsand thus they should be strongly encouraged to use all weapons availablefrom their arsenal to attack a given problem. Computational tools should bewell integrated with analytic tools. Both methods seek approximations tothe full solution, since explicit and exact solutions are only rarely available.Both methods provide different yet useful sorts of information toformulations of the problem less complex than the full problem. Numericalmethods require a computational grid but provide complete knowledge abouta discrete set of points, while analytic methods involve limiting cases orcritical values of a parameter but provide parameter dependence. Synergismbetween the two approaches allows scientists to get more than just the sumof the two individual parts, and this is felt to be a key factor for futureperspectives in sciences and engineering.

Papers properly exploiting the potential of this synergism were presentedat the Workshop by Matkowsky on gasless combustion, Merzhanov on avariety of combustion problems ranging from thermal explosions to burningof heterogeneous systems, De Luca on solid propellant combustion, Oran onseveral reactive fluid dynamics problems, and others.

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Oran specifically emphasized the need and advantages of synergism.These are probably better appreciated with reference to the following generaldiagram recalled by Novozhilov:

* data a model eqns a data analysis* implementation * interpretation* computer

where the * indicates the only point where there is no strong interactionbetween analytic and numerical approaches. But, in fact, the separationbetween the two approaches is not always so clear; most theoretical solutionsend up with equations that cannot be solved in closed form and thus someform of numerical solution is required.

As an example, consider the case of the imploding detonation describedby Oran at the meeting. The simulation solved the time--dependent,compressible equations for density, momentum, and energy coupled to somerepresentation of chemical reactions and heat release. The result was acomplete description of these quantities as a function of position and time.The analytic approach reduced the equation set to a one-dimensionalequation for Mach number or perturbation amplitude as a function of radius.The solutions are first- or second-order ordinary differential equations.Unless fairly drastic approximations are made, these equations must besolved numerically (and solutions are not straightforward to obtain becauseof singularities in the solutions). Both approaches require numericalmethods, but differ in the level of approximation of the model equations andthe methods of solution of the resulting model.

There are a number of obvious and not so obvious ways that the analyticand simulation methods can be used together to attack a problem. The firstarea is in the field of numerical analysis, which can be be used to eitherderive a numerical algorithm or to explain when and why a technique works.Although this was not a topic of the present Workshop, it is a major area ofresearch throughout the world. More and more journals and books exist forthis sort of exposition (e.g., Journal of Computational Physics). This area iswithin the province of the computational scientist.

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Another area of interaction is that of using analytic methods to improvenurnerical methods. This was mentioned by several speakers, butparticularly emphasized by Matkowsky and Oran. Some examples ofsynergism include: how to optimize computational points, how to optimizenumerical time steps, or even how to incorporate a Riemann solution into asolution of the coupled compressible continuity equation. This area is withinthe province of the computational scientist.

A third area of interaction concerns the use of an analytic solution as abenchmark, validation or a starting point for a simulation. This is perhapsthe starting place for synergism between the computational scientist andtraditional analyst. Such an interaction usually teaches everyone something:the computational scientist learns to use the computer program and theanalyst learns more about the limits of validity of the theory.

Probably a less common idea, although one that is growing inrecognition of what it can do, is to use a result from a simulation as astarting point for analysis of a system. In this sense, the simulation eitherproauces a new phenomenon which may be further explained or whoseexistence can be justified by analysis or produces a data set that can beanalyzed, much :ike an experiment. An example of the former is theunreacted pockets of material cut off by the interaction of transverse wavesbehind propagating detonations (see presentation by Oran). An example ofthe latter would be to use a computationally generated data set from acalculation of a mixing layer to look for attractors, chaos, or long-termmixing trends. An advantage here is that the computational data isrelatively clean with conditions that are more controlled than what anexperiment can produce.

With specific respect to this classical issue of analysis vs computation,Matkowsky remarked in the closure session of the Workshop that the enemyof computation is not analysis, and the enemy of analysis is not computation,but rather the enemy of Loth is the problem. Oran proposed to modifysomewhat this statement: the problem is the challenge of both camps, andthe enemy is our own limitation and mental rigidity. With these thoughts inmind, cooperation is worthwhile and stimulating for practitioners of bothmathematical approaches; in combustion often synergism is already anaccepted reality (see next sectioli).

7. NUMERICAL SIMULATIONS IN COMBUSTION

Nine lectures were devoted to both the development of new numericalapproaches and their application to combustion processes simulation. Whenanalyzing the topics and contents of these lectures, two distinct featuresemerge, as revelead by the plenary lecture on "Limitations and Potentials ofNumerical Methods for Simulating Combustion" given by Oran.

T3 / FTR VILLA OLM0) 92/ PAGE 5

The first striking feature concerns the synergism, very promising andalready progressing in combustion, between analytic and numericalapproaches. This was the unifying theme of the Workshop and is discussedin Section 6.

The second striking feature concerns the fast increase of both computercapabilities and efficiency of numerical methods, an observation made inseveral presentations. This provides new qualitative possibilities to scientificand industrial users, permitting then to solve complicated, "real life"combustion problems involving multistage chemical kinetics, multi-dimensional fluid dynamics, and their interaction. Examples of suchcomputations were given by Oran; Shur; De Michele, Pasini, and Tozzi; andHeiser.

New efficient numerical algorithms for simulation of combustion anddetonation processes were presented by Di Blasi; Nekhamkina and Strelets,and Valorani and Di Giacinto. An original idea to describe chemical sourceterms in finite-difference schemes was presented by Continillo and Baruffo.

8. NUMERICAL LIMITATIONS

Consider the question of limitations of computational methods. Thecurrent limits are dictated by the: 1) computer speed and available memory,2) algorithm efficiency, and 3) input data. In everything we do there aretradeoffs and balances. Concerning numerical limitations, the particulartradeoffs and balances depend very much on the problem being addressed.

Consider first the issue of computer speed and memory. The limits noware gigaflops and gigabytes, respectively, and this is increasing dramaticallyto the point where teraflops computers are expected in the next few years.Important conceptual breakthroughs that will allow this are parallelprocessing with distributed memories. Such computers make possible thedirect numerical simulation of turbulent reacting flows, albeit in rathersimplified geometries, or transient flows over complete airplanes. Eventhough not everyone has such computers available, the raw computationalpower generally attainable on a desktop is also exponentially increasing.

.Algorithmic efficiency involves tradeoffs between such qualities asaccuracy, speed, and robustness. This is very problem dependent and thebalances can change quickly. What is optional for today's computers is notnecessarily optimal for tomorrow.

Input data can always be a problem. Often it is not available in theform we need in a computation or we do not know the values in the rightparameter regime. In such cases, we can use theoretical values, extrapolateexperimental values, or simply guess and use the computation to determinereasonable ranges of values. This area requires constant interaction withexperiments or more fundamental theories.

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Finally, Oran draws the attention on a forefront area in numericalsimulation, and that is the problem of treating complex geometries withmoving bodies. The dream is to have simple, rectilinear structural grids withsimple, vectorizable and parallelizable algorithms, that can accurately treat aproblem as difficult as a manta ray moving through water (flexible body).

Unstructured, triangular or tetrahedral grids perhaps have optimalflexibility but are not easy to use or well suited to parallel computing.Hexahedral block-structured grids allow only moderately complexgeometries but intrinsically have problems at corners and with distortions.Ne v developments in globally structured rectilinear grids have the promise ofbeing the most accurate and most suitable to parallel computations.However, they represent a back-step to less complexity that is often hard toaccept, and they require some further development.

In summary and with respect to the limits of computation, these varyfrom problem type to problem type. However, over the last five years, theincrease in scientific abilities to simulate flames, detonations, and reactingturbulent flows is enormous and has every promise of continuing to increasein such a dramatic fashion. This growth is accomplished by combiningadvances from many fields, ranging from experimental determination ofinput data (e.g., chemical rates) to advances in numerical algorithms, toadvances in computers, and to advances in diagnostics (e.g., visualization).

9. SOLID PROPELLANT COMBUSTION

The following is an extract of the Final Technical Report (De Luca etal., 1990) on a previous Workshop held in Milan, Italy, 12-14 Nov 90, whichwas a convenient starting point for this specific theme at this Workshop.

"The most fully developed and utilized mathematical models employ aone-dimensional approximation that is rigorously applicable only topropellants that are homogeneous and burn with geometrically stable planarsurfaces. It is also widely assumed that the dynamic response of the gasphase is quasi--steady. Within these assumptions, there are two independentapproaches to analysis referred to here as the Zeldovich-Novozhilov (ZN)and the Flame Modeling (FM) approaches.

For quasi-steady gas phase, the basic assumptions and results of theapproaches are the same. In principle, ZN is quicker while FM, being morecomplex, is also more informative. However, for fully transient burning, thegas phase has to be explicitly taken into account and, therefore, only FM canbe implemented ...

The specific set of assumptions mentioned above is collectively referredto as the QSHOD assumptions. See Novozhilov, 1992 and Price, 1992 for acomplete discussion on respectively ZN approach and QSHOD assumptions.

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9.1 Nonlinear Modeling as an Example of SynergismSeveral research groups developed nonlinear models (along numerical and

sometimes analytic guidelines) of unsteady solid propellant combustion undera variety of assumptions, but primarily the QSHOD assumptions. TheItalian group has focussed on the FM approach and its connections with ZN,while the US and Russian groups have thus far used the ZN approach. Someextension to consider in-depth (distributed) condensed phase reactions hasalso been reported.

Within the QSHOD framework, the Italian group performed a completeanalysis of transient burning and combustion stability by properly combininganalytic and numerical methods. The stability analysis requires thesteady-state temperature profile corresponding to a given set of operatingconditions to be explicitly known (static or uncoupled stability); in the caseof a forced transition between two different sets of operating conditions, boththe initial and final steady-state temperature profiles need to be explicitlyknown (dynamic or transitional or coupled stability). A first application ofsynergism lies right here: analytic methods conveniently provide steadythermal profiles only for the simplest configurations (for example,temperature - independent thermophysical properties), while numericalmethods in principle can furnish any kind of thermal profile. It can be notedin this respect that the wanted steady thermal profile can also be obtained byexperimental means and then mathematically described by any convenientapproach. This stresses the possibility, and convenience, of a "full"synergism among analytic, numerical, and experimental techniques at leastat this point of the whole procedure.

An integral analytic technique is then applied to the steady thermalprofiles obtained either analytically or numerically. This technique impliesthe etvdidation of a disturbancc tLhc:mal layer thickness propagating in timeand of the temperature just at the edge of this layer. Another form ofsynergism can be seen here: either analytic or numerical methods are appliedaccording to the kind of steady thermal profile. An analytically definedfunction, called static restoring function, is then evaluated mainly bynumerical means but resorting to analytic means when singularities are met.From this function, bifurcation diagiains are ub.aincd fL: a w. •e range ofoperating conditions and for real world solid propellants. By cross-plottingbifurcation diagrams, stability diagrams are found for the wanted propellantand set of operating conditions.

The final results of this nonlinear transient burning and stability analysiscan be checked by analytic techniques (mainly for uncoupled stabilityproblems), numerical techniques (mainly for coupled stability problems),experimental techniques, or any combination of them. The point here is thata synergistic approach yields richer results and allows information to flowfrom one domain to another, thus permitting a constructive interaction andcontinuous improvement. Likewise, validation of a synergistic approachallows different techniques to be implemented, compared, and improved. Itis underlined that the above analysis could not be carried out for any realisticapplication without a numerical support, and viceversa the numerical sidewould only be simulative without the analytic support.

Fi / [IH VILLA OLM o 92/ PAGF V

Representative results reported at the Workshop (see the presentation byPagani, Verri, and Salsa and that by De Luca) include "isolas" of stability,several bifurcation phenomena, existence and multiplicity of steady-statesolutions, frequency of self-sustained oscillatory solutions, and so on. Inparticular, the complex interplay of diabaticity (positive or negative) of theburning sample with pressure (or any other operating condition) would bevery cumbersome to understand by either numerical or experimental means.The variety of situations possibly arising from nonadiabatic and nonlinearburning is just too wide and too sensitive to initial conditions to be fullyunderstood without a unifying interpretation. This can solely be providedthrough an analytic viewpoint.

An example is the behavior of a solid propellant burning, with differentlevels of diabaticity, near its pressure deflagration limit (PDL). This is aproblem of static or uncoupled stability. The sheer existence of a PDL isexperimentally known since 40 years; a computer simulation can detect butnot explain the occurrence of a PDL; several analytic approaches attemptedin the past could not justify the presence of a PDL. The combined analysisof PDL by analytic, numerical, and experimental means prompted the ideathat PDL is reached when the self-sustained oscillatory solution, in turntriggered for decreasing pressure as an Hopf bifurcation, looses its stability.The frequency of the self-sustained oscillatory burning can be evaluatedanalytically, while its amplitude can be measured by numerical tests; byexperimental means one can easily verify only frequencies. For diabaticitydifferent from zero, the above picture is further complicated by: 1) thepresence of a second, unstable steady-state solution for heat loss less than acritical value; 2) no steady- state solution for heat loss larger than thiscritical value; 3) one steady-state solution for heat input (of different naturefor different values of heat input); 4) stable steady-state self-sustainedoscillatory burning for heat input and pressure below some critical value; 5)stable steady-state time-invariant burning for heat input and pressureabove this critical value. Details about this complex behavior were reporteda• the Workshop. The point here is simply that it would be very difficult todiscriminate all of these overlapping trends without a well coordinatedanalytic and numerical efforts (synergism).

Another example is the dynamic extinction limit found when fasttransients are imposed between two otherwise stable, time-invariant steady-state burning solutions. This is a problem of dynamic or transitional orcoupled stability. The above non!inear stability analysis is able to detect acritical value of burning rate under which extinction neces.arily follows formonotonically decreasing pressure (for example), whereas numericalcomputations or experimental tests can only indirectly perceive the existenceof this limiting value. This critical value corresponds to an unstable root ofthe perturbed energy equation. On the other hand, numerical computationscan only prove the unstable or "repulsive" nature of this critical value ofburning rate; even experimental methods are of marginal help in thisinstance, since unstable configurations cannot be directly observed. Again,the combined use of analytic, numerical, and experimental techniques allowsa full understanding of phenomena otherwise intractable or at least puzzlingby separate implementation of standard investigation techniques.

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Other specific advances and developments in mathematical modeling ofsolid propellant combustion, which were reported at this Workshop, aresummarized briefly. Although not discussed for a matter of space, differentforms of synergism can be exploited for the following problems as well.

9.2 Equivalence of Linearized, Pressure-Driven ZN and FM Descriptions

Under the QSHOD assumptions, the ZN and FM descriptions oflinearized, pressure-driven unsteady propellant combustion have previouslybeen described as being equivalent within a somewhat limited scope of thedescriptions (King, 1980; T'ien, 1984; De Luca et al., 1990; Beckstoad, 1991).A more complete equivalence was shown (Son and Brewster, 1992) by formalextension to the 4th and last parameter in the descriptions (the Jacobianparameter in ZN) as follows:

A [FM nomenclature] = [ZN nom-enclature]r

13 [F'M nonienclature] = [ZN nornenclaturel

1 [I"NI no enclclatrlle - 1! [ZNI !h in cirlaturel

TI, [I"MI nOlIWCnclatIrMj'] J7N' Ir INl1mreC

whet, :T -

11 Tp

'I ,-T, d In p

k ( 'I T ; ' V ) I f'I . 0rI-

r ....

It was noted by l)e Luca that there are computational difficulties, however,with using a value of n, (or ý) other than zero for transient buiiiing.Moreover, at present, there does not appear to be sufficiently accuratesteady-state experimental data to warrant the use of non-zero n, values.

T3i F':H VII.LA 01,MW 2/ PAGE II)

9.3 Extension of Linearized, ZN and FM Descriptions to Radiation-Driven

The extension of the linearized ZN and FM theory to the radiationdriven case was reported by Italian, Russian and US researchers at theWorkshop. Similar results were reported by all groups, but minor differencescould also be detected in the approaches. The US group presented results forboth FM and ZN formulations; the Italian group also implemented bothformulations but preferably uses FM, employing ZN mainly for comparison,the Russian group adopted the ZN formulation only.

In addition, the US group emphasized that, like in the pressure-drivencase, the two FM and ZN approaches are equivalent if consistent parameterdefinitions are made. Between the US and Russian formulations of the ZNapproach, there was also a difference in the way that the ZN parameters aredefined. The US group considered the net radiant flux to the propellantsurface, q, to be a third indcpcndent variable, in such a way that

rb = rt(pTc,q)

"T,= T,(p,Tc,q)

The ZN parameters are thus defined as:

= ~nr)> O1nrj,

nrp 1(Anq

1 (JFŽ [ I 1 Yl

T,-'I0: l rp T,-Tc, DI nq

i~n r )k- (T, "I r-

r- -

with - -'- q -- qr -- k

The Russian group invoked the equivalence principle, by which

rl,(p,To,q) rb(p,'F o)

where

'1% += + -pe-r b~c

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This approach leads to ZN parameters defined as follows:

k*-(T,-To) ( 9lnrbo8T0 To*

If the equivalence principle holds, then the Russian formulation seemspreferable since it is simpler. However, Zarko expressed doubts about thevalidity of the equivalence principle; for details see Zarko, 1992. Brewsteremphasized that the equivalence principle may still hold if consideration istaken of the fraction of radiation absorbed below the rate-controlling layer(cf Konev and Klevnoi, 1966; Ibiricu and Williams, 1975).

9.4 Transfer Function Between Linearized Radiation- and Pressure-DrivenResponse Functions

It has been widely recognized that it would be very advantageous if thegeneral complex-valued, frequency-dependent transfer function

R)TF_--•L

for converting the easily measured linearized radiation-driven responseunction Rq to the linearized pressure-driven response function Rp) could be

reduced to a simple constant, namely the ratio of the steady-state burningrate sensitivities:

TF = -v [ZN nomenclature] = n [FM nomenclature]14 q

In a previous study limited to negligibly small q values (De Luca, 1976) ithad been reported that the only condition, besides the inherent QSHODassumptions, necessary for this simple relation to hold was the limit ofsurface absorption (opaque propellant). However, it has been recently found(Son and Brewster, 1992), and reported at this Workshop, that there is an

effect of the mean radiant flux, q, on the ZN or FM parameters (r,k,v,, or

A,B,n,n,) that adds an extra restriction. Namely, for sufficiently large qvalues there is a change in the steady-state parameters such that in general

r* r , i* #I

k* k , #

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where * indicates q > 0 and no * indicates q = 0. In order for TF = V/Vq tohold, in addition to surface absorption, it is necessary for the mean radiantflux to be small enough that

r* r , /.*. V//

k*- k , A*- A .

Since it is impossible to have an oscillating component of q with q - 0 , andsince surface absorption may be a difficult condition to achieve (even forwhat are ordinarily thought of as opaque material - wavelengthcombinations, e.g. AP - 10.6 ptm), it remains to be seen whether or not theseconditions can be achieved experimentally.

Nevertheless, it was emphasized at the Workshop that converting Rqdata to Rp data is only a part of the potential benefit of the unsteadyradiation - driven combustion technique. The ability to investigate thefundamental combustion mechanisms and test various combustion theories,which is afforded by the simplicity and versatility of this technique, is abenefit which perhaps surpasses that of direct Rp -. Rq conversion.

9.5 Linear Stability Analysis of Radiation Augmented Combustion atConstant Pressure

Advances were also reported in linear stability analysis of radiation -augmented propellant combustion by several research groups. In general, it

has been reported that external radiation (q > 0) tends to stabilizecombustion (or increase the region of stable combustion) over the case

without external radiation (q = 0). However, for a given level of externalradiation, distributing the absorption of the radiant energy deeper in thepropellant (reducing the propellant opacity) apparently decreases the domainof stability. The underlying physical reasons for these trends could not bediscussed at the Workshop. It was also noted that stability is very sensitiveto condensed phase heat release and activation energy parameters. Theseissues need to be further explored.

9.6 Steady State Combustion Modeling: Negative Exponent Effect

The issue of negative exponent (mesa burning) was also discussed brieflyat the Workshop. A presentation by Yin ascribed negative exponent inAP/PU propellants to melting and covering of AP particles by the binder onthe propellant surface. A detailed model of the process based on the BDPmodel was presented.

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In relation to negative exponent behavior in homogeneous propellants,Novozhilov speculated on a unique possible mechanism for the behavior. Hesuggested that the combustion may actually be microscopically oscillatory inthe negative exponent region (with a reduced mean component of burningrate) due to the steady-state parameters (r,k) crossing into the intrinsicallyunstable domain for this pressure range.

10. CONCLUSIONS

From this Workshop it appears as though a fruitful synergism betweenanalytic and numerical methods already exists in several areas ofcombustion. This synergism looks capable of furthering our understanding offundamental issues and providing reasonable guidelines for practicalapplications. A careful comparison of analytic to numerical developments,possibly together with experimental information for a conclusive validation,is an approach that stresses cooperative interaction (synergism).

Lack of communications between analysis and computation is a real factdue to different languages, backgrounds, professional interests, mentalattitude, and finally just historical developments in sciences. But it shouldbe overcome. Both analysis and computation benefit from each other. Inprinciple, analytic methods are predictive but can only be applied tosimplified problems, while numerical methods can afford very complexproblems but are only simulative. Synergism will be more fruitful than justthe sum of the two parts and is expected to trigger substantial progress inthe current understanding of combustion and sciences in general.

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11. REFERENCES

Beckstead M.W., (1991), "A Review of Soviet Combustion and CombustionInstability Work on Solid Propellants", 28th JANNAF Combustion Meeting,San Antonio, TX, 1991.

De Luca L., (1976), "Solid Propellant Ignition and Other UnsteadyCombustion Phenomena Induced by Radiation", Ph. D. Thesis, Aerospaceand Mechanical Sciences Department, Princeton University, NJ, AMSReport No. 1192-T.

De Luca L., Price E.W., Beckstead M.W., Novozhilov B.V., and Zenin A.A.,(1990), International Workshop on "Transient Combustion and Stability ofSolid Propellants", Final Technical Report, Milano, Italy, 12-14 Nov 90.

Ibiricu M.M. and Williams F.A., (1975), Influence of Externally AppliedThermal Radiation on the Burning Rate of Homogeneous Solid Propellants",Combustion and Flame, Vol. 24, pp. 185-188.

King M.K., (1980), "Composite Propellants Combustion Modeling: Pressure -

Coupled Response Functions", AIAA Paper 80-1124.

Konev E.V. and Klevnoi S.S., (1966), "Burning of a Powder in the Presenceof Luminous Radiation", Combustion Explosion and Shock Waves, Vol. 2,No. 4, pp. 33-41.

Novozhilov B.V., (1992), "Theory of Nonsteady Burning and CombustionStability of Solid Propellants by the Zeldovich-Novozhilov Method",Chapter 15 in Nonsteady Burning and Combustion Stability of SolidPropellants, L. De Luca, E.W. Price, and M. Summerfield Volume Editors,AIAA Progress in Astronautics and Aeronautics, Vol. 143, pp. 601-641.

Price E.W., (1992), "L* Instability", Chapter 9 in Nonsteady Burning andCombustion Stability of Solid Propellants, L. De Luca, E.W. Price, and M.Summerfield Volume Editors, AIAA Progress in Astronautics andAeronautics, Vol. 143, pp. 325-361.

Son S.F. and Brewster M.Q., (1992), "Linear Burning Rate Dynamics ofSolids Subjected to Pressure or External Radiant Flux Oscillations", Journalof Propulsion and Power, under Press.

T'ien J.S., (1984), "Transient Burning of Solid Propellants", Chapter 14 inFundamentals of Solid Propellant Combustion, K.K. Kuo and M.Summerfield Volume Editors, AIAA Progress in Astronautics andAeronautics, Vol. 90, pp. 791-832.

Zarko V.E., Simonenko V.N., and Kiskin A.B., (1992), "Radiation-DrivenTransient Burning; Experimental Results", Chapter 10 in NonsteadyBurning and Combustion Stability of Solid Propellants, L. De Luca, E.W.Price, and M. Summerfield Volume Editors, AIAA Progress in Astronauticsand Aeronautics, Vol. 143, pp. 363-398.

International Workshop

on

MATHEMATICAL METHODS IN COMBUSTION

Final Program

Centro di Cultura Sclentifica "A. Volta"Villa Olmo, Como, Italy

18-22 May 1992

International Workshop

on

MATHEMATICAL METHODS IN COMBUSTION

Centro di Cultura Scientifica "A. Volta"

Villa Olmo, Como, Italy

18-22 May 1992

sponsored by

Dipartimento di Energetica, Politecnico di Milano, Milano, Italy

Dipartimento di Matematica, Politecnico di Milano, U.O. del

Progetto Equazioni Differenziali MURST 40%, Milano, Italy

IAC/CNR, Roma, Italy

CNPM/CNR, Peschiera Borromeo, Milano, Italy

Convex Computer Italia, Agrate Brianza, Milano, Italy

Centro Ricerche FIAT, Orbassano, Torino, Italy

European Research Office, USARDSG, London, UK

European Office of Aerospace Research and Development, EOARD, London, UK

and under the auspices of

The Italian Section of The Combustion Institute, Napoli, Italy

TECHNICAL COMMIrTEE

Prof. L DE LUCA. Prof. C.D. PAGANI Prof. A. TESEI

Dipartimento di Energetica Dipartimento di Matematica lAO

Politecnico di Milano Politecrico di Milano CNR

Milano, ITALY Milano. ITALY Roma, ITALY

Dr. E.S. ORAN Pro. B.V. NOVOZHILOV rrof. M.Kh. STRELETSLab. for Computational Physics Institute of Chemical Physics State Institute of Applied Chemistry

Naval Research Laboratory Russian Academy of Sciences Saint PetersburgWashington, DC, USA Moscow. USSR Saint Petersburg, Russia

ORGANIZING COMMIITEE

Prof Luigi De Luca Ms. Marisa CascardiDr. Luciano Galtenti Mr. Fabio CozziMs Anna Maria Pulle Ms. Letizia RattiMr Giovanni Colombo Mr. Ugo Scaglione

Mathematical Methods in Combustion

Monday, 18 May 1992 Villa Olmo, Room 'Olimpo"

08.30 Registration

09.15 L De Luca, R. Reichenbach, V. CalareseIntroductory Remarks

ANALYTICAL FUNDAMENTALS B.V. Novozhilov chairman

09.30 B.J. MatkowskySynergism of Analytical and Numerical Approaches in Combustion

10.30 R. Natalini and A. TeseiBlow-Up of Phenomena for Some Parabolic and Hyperbolic Models in Combustion Theory

11.00 coffee break

11.30 A.G. MerzhanovOn the Role of Computer-Aided Calculations in Combustion Theory

12.00 C.D. Pagani, M. Verri, and S. SalsaNonlinear Burning Stability of Solid Propellants: an Analytical Approach

12.30 B.V. NovozhilovOn the Theory of Surface Spin Burning

13.00 R. Dal PassoOn a Moving Boundary Problem Arising in Fluidized Bed Combustion

1330 lunch

MATHEMATICAL APPLICATIONS B.J. Matkowsky chairman

14.30 L De LucaNonlinear Transient Burning of Solid Propellants: a Simple Example of Synergism between Analytical andNumerical Methods

15.00 D. Grune and D. HenselBurning Behaviour of Solid Propellants at High Pressure and High Loading Density

15.30 coffee break

16.00 N. KidinAcoustics and Control of Combustion Instabilities

16.30 D.A. Goussis and S.H. LamDerivation of Simplified Models in Chemical Kinetics

17.00 Round Table Discussion

17.30 End of Session

Tuesday, 19 May 1992 Villa Olmo, Room "Olimpo"

8.50 L. De LucaIntroductory Remarks

NUMERICAL FUNDAMENTALS M.K. Strelets chairman

09.00 E.S. OranLimitations and Potentials of Numerical Methods for Simulating Combustion

10.00 C. Di BlasiNumerical Simulation of the Dynamics of Flame Spreading over Liquid Fuels

10.30 M.Kh. SchurNavier-Stokes Simulation of Supersonic Combustion in Continuous Wave HF-Chemical Lasers Based onCompressibility _C.;aling Method

11.00 coffee break

11.30 G. Continillo and S. BaruffoOn the Approximation of Chemical Reaction Terms in Finite-Difference Calculations

12.00 G. De Michele, S. Pasini, and A. TozziCombustion Optimation in Power Station Boilers by Advanced Modeling Technology

12.30 R. HeiserA Navier-Stokes Solution of the Heat Transfer to Gun Barrels

13.00 F. MaguglianiComputers in Science and Engineering Practical Applications

1330 lunch

DETONATION PROCESSES E.S. Oran chairman

14.30 0. Nekhamkina and M.Kh. SureletsApplication of Efficient Riemann Solver and TDV Scheme for Numerical Simulation of Detonation Waves inHydrogen-Oxygen Mixtures

15.00 M. Valorani and M. Di GiacintoNumerical Analysis of Detonative Processes

15.30 coffee break

16.00 H E. Longting and P. ClavinCritical Conditions for Detonation Initiation by Non Uniform Hot Pockets of Reactive Gases

16.30 A. LunardiStability of Travelling Waves in Deflagration to Detonation Transition Models

17.00 Round Table Discussion: Assessment of Numerical Methods

17.30 End of Session

Wednesday, 20 May 1992 Villa Olmo, Room "Olimpo"

08.50 L. De LucaIntroductory Remarks

LINEAR COMBUSTION STABILITY A.G. Merzhanov chairman

09.00 B.V. NovozhilovCombustion Stability of Solid Propellants ZN- and FM- Approaches

09.30 P. ClavinAcoustic Instabilities of Flames

10.00 V.E. Zarko and A.B. KiskinStability and Transient Radiation-Driven Solid Propellant Combustion

10.30 J.YinStudies on Mathematical Models of Solid Propellant Combustion at Northwestern Polytechnical Institute, Xi'an,China

11.00 coffee break

11.30 M.Q. Brewster and S. SonMathematical Modeling of Unsteady Combustion of Energetic Solids Subject to External Radiation

12.00 F. Cozzi and L De LucaRadiation-Driven Frequency Response Function by Flame Models

12.30 Round Table Discussion: Linear Combustion Stability

13.30 lunch

CLOSURE SESSION L. De Luca chairman

14.30 R. Reichenbach and V. CalareseUS Guidelines for Research Proposals

15.00 B.J. Matkowsky, B.V. Novozhilov, and A. LunardiFuture Perspectives in Analytical Methods

15.30 coffee break

16.00 E.S. Oran, M.Kh. Strelets, and C. Di BlasiFuture Perspectives in Numerical Methods

16.30 General Discussion

17.15 L De LucaSummary and Conclusions

17.30 Closure of Workshop

International Workshop

on

MATHEMATICAL METHODS IN COMBUSTION

List of participants

Centro di Cultura Scientifica "A. Volta"

Villa Olmo, Como, Italy

18-22 May 1992

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Prof Vaknria BACCHELLIDipartimento di MaternaticaPolitecnico di Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex 333467 POLIMI IPhone (0039-2) 2399-4529Fax (0039-2) 2399 45683

Mr Salvatore BARUFFOI RC /CN B328 Via Diocleziano80124 Naipoli. ItalyTelexPhone (0039 81) 570-b8G-1Fax (0039-81) 762-2915

Prof M Quinn BREWSTERDepartment of Mechanical and Industrial EngmneoringUniversity of Illinois at Urbana-Champaign144 Mochanircal Fngineerinq Buildinq1206 West Green StreetUrbana, IL 61081, USA

Phont, 1001 21i7) 244 160ý1Fio (001 21 7) 244435243-

Dr Vlaiirnhlu CALARESEECARD, US)AF

01,1Ol M,ir~leb m 8.Len N ~ i L 1IF-K

Pherie ýOl)'i 71) 40,j44;I-ax1 X (1)-044 i' ) 7 14- 14,3

Prof Gwawajrlo CHIAT I IDiparlinrento di Meccanica ted Af' *rerlak itiUnt-wrs,taizl J RoIini 'Ia Sapwn.',i'18 va~ Lud(O"l:anal0018. 4 Ri ma Italy'

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URA[', i 1I1i CNHS, Univen,jlte doi Frivenci,Centre Saint Jeromv13397 Mae..ille Cfeilex). I raro sTelex 405iF ACSTJJ[Phone (00113i 9) 128 81211F a~x (0033; J) 1(2A 5261

Mr. Giovanni COLOMBODipartimento di EnergeticaPolitecnico di Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex: 333467 POUMI IPhone: (0039-2) 2399-3871Fax : (0039-2) 2399-3940

Doti. Tarcisio COLOMBOAlta RomeoRAT Auto20020 Arese, MI, ItalyTelex :Phone : (0039-2) 9339-2972Fax : (0039-2) 938-0769

Dr- Gaetano CONTINILLOIRC/CNR328 Via Diodeziano80124 Napoli, ItalyTelex- 722392 INGENA IPhone: (0039-81) 570-5864Fax : (0039-81) 762-2915

Mr. Fabio COZZIDipartimento di EnergeticaPolitecnico di Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex: 333467 POUMI IPhone: (0039-2) 2399-3872Fax : (0039-2) 2399-3940

Dr, Giuliano D'ANDREAScience AdviserUSASETAF36100 Vicenza, ItalyTelexPhone (0039-444) 505-409Fax : (0030-444) 505-409

Prof. Luigi DE LUCADipartimento di EnergeticaPolitecnico di Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex: 333467 POUMI IPhone: (0039-2) 2399-3912Fax : (0039-2) 2399-3940

Prof Colomba DI BLASIDiparlimento di Ingegneria ChimicaUniversitA di Napoli80 Piazzale V. Tecchio80125 NapoliTelex:Phone (0039 81) 768 2264Fax : (0030-81) 593-6936

Prof. Luciano GALFETTIDipartimento di EnergeticaPolitecnico ci Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex: 333467 POLIMI IPhone: (0039-2) 2399-3926Fax : (0039-2) 2399-3940

Dr. D.A. GOUSSISMechanical Engineering DepartmentSchool of EngineeringUniversity of Patras26000 Patras, GreeceTelex:Phone: (0030-61) 997-242Fax : (0030-61) 997-271

Mr. Dietrich GRUNEISL (Institut Franco-Allemand de Recherches de Saint Louis)Group B6/PCH, Dept. B12 rue de I'lndustrie, Boite postale No. 34F-68301 Saint Louis, FranceTelex: 8811386Phone: (0033) 8969-5000 ext. 5073Fax : (0033) 8969-5002

Ing. Plinio GUERRERIConvex Computer S.p.ACentro Direzionale ColleoniPalazzo Onone, 317 Viale Colleoni20041 Agrate Brianza, MI, ItalyTelex: 326423 SIAVBC IPhone: (0039-39) 605-8024Fax : (0039-39) 609-1079

Dr. Rudi HEISERFraunhofer-Institut fur KurzzeitdynamikErnt-Mach-lnstitut Abteilung fur F311istik18 HauptstrasseD-7858 Weil am Rhein, GermanyTelex:Phone: (0049-7621) 7-1067Fax : (0049-7621) 7-6925

Prof. Nick(lai KIDINInstitute Cthemical Kinetics and CombustionUSSR Academy of SciencesSiberian Branch630090 Novosibirsk, RussiaTelex. 133148 KING SUPhone: (007-3832) 35-7030Fax : (007-3832) 35-2350

Prof. Alessandra LUNARDIDipartimento di MatematicaFacoltA di ScienzeUniversita di CagliariVia deUl'OspedaleCagliari, Italyc/o: Scuola Normale Superiore

Pisa, ItalyTelex:Phone: (0039-50) 597-290Fax : (0039-50)

Ing. Fabrizio MAGUGLIANIConvex Computer S.p.A.Centro Direzionale ColleoniPalazzo Orione, 317 Viale Colleoni20041 Agrate Brianza, MI, ItalyTelex: 326423 SIAVBC IPhone: (0039-39) 605-8024Fax : (0039-39) 609-1079

Prof. Bernard J. MATKOWSKYDepartment of Engineering Sciences and Applied MathematicsMcCormick School of Engineering and Applied ScienceNorthwestern UniversityEvanston, Illinois 60208, USATelex:Phone: (001-708) 491-5396Fax : (001-708) 491-2178

Prof. A. G. MERZHANOVInstitute of Structural MacrokineticsRussian Academy of Sciences142432 Chernogoloka, Moscow Region, RussiaTelex: 411701 SFERA SUPhone: (007-95)Fax - (007-95)

Dr. Roberto NATALINIIAC/CNRIstituto Applicazioni Calcolo 'Mauro Picone"Consiglio Nazionale delle Ricerche137 Viale del Policlinico00161 RomaTelex:Phone: (003943) 8847-01Fax - (0039-6) 440-4306

Dr. Rafiaele NICOLAZZOUniversitO di Napoli80, Piazzale Tecchio80125 Napoli

Prof. Boris V. NOVOZHILOVInstitute of Chemical PhysicsRussian Academy of Sciences4 Kosygin Street117977 Moscow V-334, RussiaTelex: 411701 SFERA SUPhone: (007-95) 939-7127Fax • (007-95) 938-2156

Dr. Elaine S. ORANLaboratory for Computational PhysicsCode 4044/4004Naval Research LaboratoryWashington, DC 20375, USATelex:Phone: (001-202) 767-2960Fax : (001-202) 767-4798

Ing. Sauro PASINIENEL-CRTNVia A. Pisano, 12056100 Pisa, ItalyTelex:Phone: (0039-50) 53-5630Fax : (0039-50) 53-5651

Dott. Francesca PISTELLAIAC/CNRIstituto Applicazioni Calcolo "Mauro Picone"Consiglio Nazionale delle Ricerche137 Viale del Policlinico00161 RomaTelex:Phone: (0039-6) 8847-01Fax : (0039-6) 440-4306

Ms.Anna Maria PULLE'Dipartimento di EnergeticaPolitecnico di Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex: 333467 POUMI IPhone: (0039-2) 2399-3801Fax : (0039-2) 2399-3940

Ing. Alberto QUARANTADirettoreCNPM/CNRIstituto Propulsione ed EnergeticaConsiglio Nazionale delle Ricerche69 Viale Francesco Baracca20068 Peschiera Borromeo, MI, ItalyTelexPhone. (0039-2) 715015Fax : (0039-2) 714063

Ms. Letizia RATTIDiparlimenlo di EnergeticaPolitecnico di Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex: 333467 POLIMI IPhone: (0039-2) 2399-3872Fax : (0039-2) 2399-3940

Dr. Roy E. REICHENBACHAeronautics and Mechanics Branch, ChiefEuropean Research OfficeUSARDSG (UK)223 Old Marylebone RoadLondon NW1 5TH, UKTelex:Phone: (0044-71) 409-4423Fax : (0044-71) 724-1433

Prof. Sandro SALSADipartimento di MatematicaPolitecnico di Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex: 333467 POUMI IPhone: (0039-2) 2399-4553Fax : (0039-2) 2399-4568

Mr. Ugo SCAGUONEDipartimento di EnergeticaPolitecnico di Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex: 333467 POUMI IPhone: (0039-2) 2399-3872Fax : (0039-2) 2399-3940

Prof. Michael L SCHURDepartment of Physics and MechanicsState Technical University197198 Saint Petersburg, RussiaTelex: 121345 PTB SUPhone: (007-812) 238-5353Fax : (007-812) 232-2027

Dott. Mauro SGHERRIDirettore GeneraleConvex Computer S.p.ACentro Direzionale ColleoniPalazzo Orione, 317 Viale Colleoni20041 Agrate Brianza, M1, ItalyTelex: 326423 SIAVBC IPhone: (0039-39) 605-8024Fax : (0039-39) 609-1079

Prof. Michael Kh. STRELETSState Institute of Applied Chemistry14 Dobrolyubov Av.197198 Saint Petersburg, RussiaTelex, 121345 PTB SUPhone: (007-812) 238-5353Fax : (007-812) 232-5844

Ing. MWuro VALORANIDiparlimento di Meccanica e AeronauticaUniversitA di Roma "La Sapienza"18 Via Eudossiana00184 Roma, Roma, ITALYTelex:Phone (0039-6) 4458-5281Fax (003943) 488-1759

Prof. Maurizio VERRIDipartimento di MatematicaPolitecnico di Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex: 333467 POUMI IPhone: (0039-2) 2399-4526Fax : (0039-2) 2399-4568

Ing. Luigi VIGEVANODipartimento di Ingegneria AerospazialePolitecnico di Milano40 Via Golgi20133 Milano, ItalyTelex: 333467 POUMI IPhone: (0039-2) 2399-4057Fax : (0030-2) 2399-4034

Prof. Jinqi YINDepartment of Astronautical EngineeringNorthwestern Polytechnical University (NPU)P.O. Box 164Xi'an, Shaanxi Province 710072, ChinaTelex: 70185 NWTRUY CNPhone: (0086-29) 53351Fax : (0086-29) 751-959

Ing. Claudio ZANOTiICNPM/CNRIstituto Propulsione ed EnergeticaConsiglio Nazionale delle Ricerche69 Viale Francesco Baracca20068 Peschiera Borromeo, MI, ItalyTelex:Phone: (00c,9-2) 715015Fax • (0039-2) 714063

Prof. Anna ZARETTIDipartimento di MatematicaPolitecnico di Milano32 Piazza Leonardo da Vinci20133 Milano, ItalyTelex: 333467 POUMI IPhone: (0039-2) 2399-4512Fax : (0039-2) 2399-4568

Prof. V.E. ZARKOInstitute of Chemical Kinetics and CombustionUSSR Academy of SciencesSiberian Branch630090 Novosibirsk, USSRTelex: 133148 KING SUPhone: (007-3832) 35-7030Fax - (007-3832) 35-2350