Research Collection

Doctoral Thesis

Optical density and velocity measurements in cryogenic-gasflows

Author(s): Jensen, Olaf

Publication Date: 2003

Permanent Link: https://doi.org/10.3929/ethz-a-004621600

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ETH Library

Diss ETH No 15259

Optical Density and Velocity Measurements

in Cryogenic-Gas Flows

A dissertation submitted to the

SWISS FEDERAL INSTITUTE OF TECHNOLOGY

ZURICH

for the degree of

Doctor of Technical Sciences

presented by

Olaf Sven Jensen

Dipl -Phys (Humboldt University of Berlin)born on August 04, 1973

citizen of Germany

accepted on the recommendation of

Prof Dr Thomas Rosgen, examiner

Prof Dr Andreas Dillmann, co-exammer

PD Dr Jean Paul Kunsch, co-examiner

Dr Ing habil Markus Raffel, co-exammer

2003

Acknowledgments

I'm grateful to Prof T Rosgen for supervising my research and

for his tremendous support during my work at the Institute of Fluid

Dynamics (IFD) Especially his unlimited patience in discussing and

solving every technical, theoretical and computational problem I want

to acknowledge Furthermore, I want to thank him for his many creative

ideas and for thoroughly revising my reports and my thesis

I want to thank Prof A Dillmann (TU Berlin) and Dr M Raffel

(DLR Gottingen) for acting as co-exammers for my Ph D thesis and for

their valuable input

I'm indebted to Dr J P Kunsch (ETH) for teaching me a lot of thingsabout fluid dynamics and for many fruitful discussions about theoretical

and experimental problems

Additionally, I want to thank P Weber (ETH) and R Holliger (ETH)for their help with constructing all the electronic modules and mechanical

parts for my experimental setup and for acting as troubleshooters when

problems arose I also want to thank B Maspero (ETH) for taking care

of the administrative tasks with great reliability and H P Caprez for his

aptitude to fix every computer problem Furthermore, thanks go to my

colleagues Dr R Bommels and A Landolt for many useful discussions

about technical and scientific topics

The time spent at the institute was very fruitful and I want to thank

all my colleagues and friends for keeping up my spirits during this project

and for creating such a comfortable environment to work in Especially

my friends and colleagues A Kubik, Dr R Bommels and Dr S Stolz

helped me through the difficult times during my research with many

non-scientific conversations

Zurich, November 2003 Olaf Sven Jensen

Contents

Nomenclature V

Abstract VII

Kurzfassung VIII

1 Introduction 1

1 1 Flow Problem 3

1 2 Experimental Facility 3

1 3 Measurement Problem 5

1 4 Organization of Contents 5

2 Measurement Techniques 7

2 1 Correlation Schemes for Velocity Measurements 7

2 2 PTV, PIV, ICV or LSV? 9

2 3 Background Oriented Schlieren (BOS) 11

2 4 Thermocouples 13

3 Experimental Setup 15

3 1 Heavy-Gas Channel 15

3 11 Continuous Release of Evaporated Cryogenic N2 16

3 12 Sudden Release of Evaporated Cryogenic N2 17

3 2 Ambient-Air Seeding 18

3 2 1 Ultrasonic Fog Generator 19

3 2 2 Helium-Bubble Generator 19

3 2 3 Solid Particle Seeding 21

3 3 Setup for Optical Velocity Measurements 22

3 4 Setup for Background Oriented Schlieren (BOS) 24

3 5 Thermocouples 25

4 Results 27

4 1 Seeding of the Cryogenic Cloud 27

4 2 Evaluation of ICV and LSV 33

4 3 Seeding of the Ambient Air 36

4 4 Optical Velocity Measurements Continuous Release 42

4 4 1 Spreading over a Horizontal Surface 43

IV Contents

4 4 2 Spreading over a Forward Facing Step 50

4 5 Optical Velocity Measurements Sudden Release 60

4 5 1 Spreading over a Horizontal Surface 62

4 5 2 Spreading across a Backward Facing Step 67

4 5 3 Sudden Release with Talcum Powder Seeding 68

4 6 Optical Density Measurements (BOS) 74

4 6 1 Continuous Release over a Horizontal Surface 74

4 6 2 Continuous Release over a Forward Facing Step 77

4 6 3 Setup for Sudden Release 80

5 Summary and Conclusion 85

5 1 Recommendations for Future Work 88

A Measurement Techniques: Basics 91

A 1 Correlation Schemes 91

A 2 Laser Speckle Velocimetry (LSV) 95

A 3 Background Oriented Schlieren (BOS) 96

A 3 1 Poisson Equation 98

A 3 2 Finite Difference Approximation 100

A 3 3 Direct Integration in ID 101

A 4 Least-Squares Collocation 102

A 5 Thermocouples 104

B Results: Experimental Conditions 105

B 1 Setup for Continuous Release 105

B 2 Setup for Sudden Release 105

B 3 Background Oriented Schlieren 106

Bibliography 107

Curriculum vitae 114

Nomenclature

Roman symbols

A aperture size

AF amplification factor

a subwmdow of image 1

b subwmdow of image 2

C correlation map

c cross-correlation coefficient

d displacement function of correlation

dp diameter of particleD distance between two mesh points

EMF thermoelectric voltage

f focal lengthh heightH relative humidityM size of image in pixels in x-direction

m mass flow

N size of image in pixels in y-directionn index of refraction

P pressure

P electrical power

R perfect gas constant

s speckle size

S sensitivityT temperature

u velocity in the x-direction

V velocity in the y-directionw width of the channel

Greek symbols

ö relative error

A wavelength

/x quadratic difference of subwmdows

$ phase factor

p density

VI Nomenclature

standard deviation

Other symbols

3" Fourier transform

* convolution

(0 Fourier transformed variable

(') mean value

Subscripts

a ambient

b bulk

f frontal

T temperature

W wall

u velocity in x-direction

X in x-direction

y in j/-direction

Superscripts

complex conjugate

Abbreviations

BFS

BOS

CCD

DFT

FFT

FFS

ICV

IFD

LIF

LSV

PIV

PTV

SIV

Backward Facing Step

Background Oriented Schlieren

Charge Coupled Device

Discrete Fourier Transform

Fast Fourier Transform

Forward Facing Step

Image Correlation VelocimetryInstitute of Fluid DynamicsLaser Induced Fluorescence

Laser Speckle VelocimetryParticle Image VelocimetryParticle Tracking VelocimetryScalar Imaging Velocimetry

VII

Abstract

The propagation behavior of cryogenic gas clouds in a heavy-gaschannel is studied for different release scenarios with image correlation

velocimetry (ICV) and background oriented Schlieren (BOS) in combi¬

nation with supplemental thermocouple measurements These cryogenic

gas clouds are generated by evaporation of liquid nitrogen Two different

configurations for the generation of the clouds are used One features the

continuous release of cryogenic nitrogen evaporated by electrical heatingover a time interval of up to five minutes The second configuration fea¬

tures the sudden release of a specified amount of evaporated nitrogenBoth release scenarios are investigated in the context of the propaga¬

tion over a horizontal surface Additionally, the flow resulting from the

scenario for continuous release is studied in the presence of a forward

facing step whereas the suddenly released cloud is studied in the vicinity

of a backward facing step With the implemented diagnostics the two

important parameters velocity and temperature are determined for the

different propagation scenarios at several positions in the channel

The velocity measurements are conducted with a planar velocimetry

system It makes the extraction of two-dimensional velocity-vector maps

possible For the flow visualization ice-particles are used that are gener¬

ated during the evaporation process of the liquid nitrogen Additionally,the surrounding flow is seeded with talcum powder The combination of

a background oriented Schlieren (BOS) system and thermocouples allows

the extraction of two-dimensional temperature profiles that are averagedover the width of the heavy-gas channel Both measurement methods

for velocity and temperature are implemented and evaluated for their

performance in the experimental context encountered in the heavy-gaschannel

VIII

Kurzfassung

Das Ausbreitungsverhalten kryogener Schwergaswolken wird unter¬

sucht fur verschiedene Freisetzungsszenarien mit unterschiedlichen optis¬

chen Methoden Dabei werden zweidimensionale Geschwindigkeitsmes¬

sungen mit einem Image Correlation Velocimetry (ICV) System

durchgeführt Zusätzlich werden mit einem Background Oriented

Schlieren (BOS) System Messungen ausgeführt, welche in Kombina¬

tion mit Thermoelementsmessungen in zweidimensionalen Temperatur¬

profilen der kryogenen Schwergaswolken resultieren Die Schwergas¬wolken werden durch die Verdampfung von flussigem Stickstoff erzeugt,wobei generell zwei verschiedene Konfigurationen verwendet werden

Bei der ersten Methode wird der flussige Stickstoff durch elektrische

Heizer verdampft und breitet sich dann kontinuierlich im Kanal aus

Die zweite verwendete Methode beinhaltet die Verdampfung einer spez¬

ifischen Menge Stickstoff, die dann plötzlich frei gesetzt wird und sich

anschliessend ausbreitet Die mit beiden Verfahren erzeugten Schwer¬

gaswolken werden unter horizontaler Ausbreitung untersucht Zusätzlich

werden die kontinuierlich frei gesetzten Wolken bei der Ausbreitung über

ein vorspringende Stufe untersucht wahrend die plötzlich frei gesetzten

Wolken zusätzlich bei der Ausbreitung über eine ruckspringende Stufe

untersucht werden Mit den implementierten Diagnostiken werden fur

alle Ausbreitungsszenarien die wichtigen Parameter Geschwindigkeit und

Temperatur an mehreren Positionen im Kanal bestimmt

Die Messung der Geschwindigkeiten wird mit optischenLichschmttverfahren durchgeführt, womit zweidimensionale

Geschwindigkeitsmessungen möglich sind Die dafür notwendige Sicht¬

barmachung der Strömung erfolgt mit Eispartikeln, die wahrend der

Verdampfung des Stickstoffs automatisch gebildet werden Zusätzlich

wird die Aussenstromung mit Talkpulver markiert Die Kombination

des Background Oriented Schlieren (BOS) Verfahrens mit den Ther¬

moelementsmessungen erlaubt die Extraktion von zweidimensionalen

Temperaturprofilen, die über die Breite des Kanals gemittelt sind Beide

Messverfahren werden im experimentellen Kontext im Schwergaskanalauf ihre Leistungsfähigkeit hm evaluiert

Chapter 1

Introduction

The widespread storage and transport of chemicals and liquefied

gases like propane can result in the accidental release of dense gases

into the environment Examples of such releases include the accidents in

Flixborough in England (1974) and Mexico-City (1984) with thousands

of casualties Therefore, the behavior of these released dense gases is

still of major concern in current safety studies Recent publications in

this area include studies about the release of hazardous materials in ur¬

ban areas (Scaperdas & Hebden, 2003) and in the relatively new area of

homeland security in the United States (Serafin et al, 2003) This studyfrom the National Research Council investigates mainly the deliberate

release of hazardous materials, e g during a terrorist attack

Gases are called heavy or dense gases when their density is higherthan the density of the ambient air They can be generated from several

sources with different properties (Billeter, 1995) and can be grouped into

four different categories

• The first category includes all the gases with a molecular weight

higher than that of the ambient air at room temperature Theyretain their higher density during the propagation until they are

diluted due to air entrainment

• The second category includes cryogenic gases At room tempera¬

ture, they may have no higher density than the ambient air, but

due to their generation process they possess very low temperatures

and therefore high densities During the propagation, the densityis reduced by heat addition (e g conduction, heat transfer etc )and air entrainment

• The third category includes aerosols and particle-laden flows

Aerosols are formed for instance when a pressurized and liquefied

gas escapes through a leak The resulting free jet is mixed with

air and a cloud is generated consisting of gas, small droplets of the

liquefied gas and ambient air In addition the density is increased

due to the temperature drop caused by the expansion The densityof this mixture is higher compared to the ambient air Particle-

laden flows are called heavy gases when the average density of the

2 Introduction

gas and the particles is higher than the density of the ambient air

Avalanches can be compared to this category of heavy gases to

some extent as well

• The fourth category is generated by chemical reactions between a

released gas with low density and the ambient air This can lead

to the formation of heavy-gas clouds

The spreading behavior of gases strongly depends on the density ratio of

the gas to the ambient air With a density close to the one of the ambient

air the behavior is mostly passive, 1 e the gas moves with the prevailingflow conditions of the surrounding air Contrary to this behavior, gases

with a density higher than the ambient air are driven by gravity alongthe ground In this context, it is even possible for the gravity driven flow

to propagate against the wind

Experimental investigations of heavy-gas flows have a long tradition

Because field trials like the Thorney Island experiment (1985) are very

expensive, facilities in size appropriate for laboratories were designedAt the Institute of Fluid Dynamics (IFD) of ETH Zurich, several stud¬

ies have been conducted to investigate the spreading of isothermal dense

clouds in various facilities (Billeter (1995) and Müller (1997)) Another

facility is the heavy-gas channel used throughout this study Several

studies have been carried out in this facility with cryogenic gas clouds

(Zumsteg (1988) and Grobelbauer (1995)) The mam measurement tech¬

nique in those studies were arrays of thermocouples It was possible with

this technique to measure temperatures locally and to deduce indirectlymean velocities from the temperature measurements in case of unsteadyreleases An analysis of these data can be found in Kunsch (1997) Un¬

fortunately, the approach based on thermocouples does not allow the

determination of velocities inside the flow in larger areas Therefore,new measurement techniques are needed for a better understanding of

cryogenic gas flows

The scope of this work lies in the implementation of new diagnosticsin the context of the heavy-gas channel in combination with different

release scenarios of evaporated liquid nitrogen The mam focus is put

onto quantitative flow visualization techniques supplemented with ther¬

mocouple measurements as a reference In the following sections, the

project will be described briefly

1.1 Flow Problem 3

1.1 Flow Problem

In this study, several release and subsequent spreading scenarios are

investigated with optical diagnostics

• The first scenario includes the continuous release and spreading of

a cryogenic nitrogen cloud over a horizontal surface This setup is

appropriate for the evaluation of flow visualization techniques and

for the extraction of global parameters of the flow

• The second scenario is similar to the first one, except that a forward

facing step is placed on the horizontal surface This represents an

application of the diagnostics to more complicated flows Addition¬

ally, this setup presents a commonly investigated flow environment

(Huerzeler & Fannelop, 1990) which should allow the identification

of distinct features in the flow in the vicinity of the step In the

context of neutrally buoyant flows without a free surface, the for¬

ward facing step was investigated numerically by Wilhelm (2001)

• The third scenario includes the propagation over a horizontal sur¬

face of a dense gas cloud that is generated by the sudden release of

a fixed amount of evaporated liquid nitrogen Due to the unsteadynature of this flow type, the extraction of meaningful data is ex¬

pected to be more difficult because of the limited time available

for measurements during a single experiment

• The fourth scenario uses also the setup with the suddenly released

cloud, but the measurements are carried out at a backward facing

step The goal is to visualize the influence of the step on the cloud

including the separation vortex

1.2 Experimental Facility

The experimental facility used throughout this study is depicted in Fig¬ure 1 1(a) and the schematic view in Figure 1 1(b) The source of the

liquid nitrogen is located in the release chamber For the different sce¬

narios, the setup can be changed easily The first and second scenario

allow the continuous propagation of the cloud from the release chamber

along the floor of the channel In the third and fourth scenario, a speci¬

fied amount of liquid nitrogen is evaporated in the release chamber For

this purpose, the shutter is closed to confine the cloud for a specific time

4 Introduction

(a) Picture of the heavy-gas channel. The release chamber is located on the left

hand side.

îlease Cham

with S hutte:

flber ansparen

Walls

!

t

nsula

<

tedf oor

Steps

1280 mm 6190 mm

12070 mm

1150 mm

(b) Schematic view of the heavy-gas channel.

Figure 1.1: Snapshot and schematic view of the heavy-gas channel.

1.3 Measurement Problem 5

interval which is generally needed for the evaporation process After

opening the shutter, the cloud can spread along the floor of the channel

The floor of the channel is made of insulating material to reduce the

heat conduction into the cloud and hence to prevent a loss of negative

buoyancy To allow optical access into the flow, the walls of the channel

are made of a transparent material (plexiglas)

1.3 Measurement Problem

The measurement of detailed velocity vector maps of the propagating

cloud is one of the major goals of this thesis The movement of the am¬

bient air in the vicinity of the cloud is also important to assess the impact

of heavy-gas flows on the surrounding air and vice versa Therefore, a

planar imaging system is build up for velocity measurements based on

image correlation processing This system would allow the application of

techniques like particle image velocimetry (PIV), image correlation ve¬

locimetry (ICV) or laser speckle velocimetry (LSV) All these measure¬

ment techniques allow a "real-time" analysis for slow flows in the form

of 2D velocity vector maps The appropriate measurement techniquehas to be identified during the experiments To put these correlation

techniques to work, seeding particles in the flow are necessary to make it

visible The appropriate seeding particles for the cryogenic flow and the

ambient air have to be identified in the experimental context as well

The second important parameter of cryogenic flows is the temper¬

ature To acquire more detailed temperature profiles of the flow than

with thermocouples, a background oriented Schlieren (BOS) system is

implemented With this system, it should be possible to measure 2D

temperature profiles averaged across the width of the channel for all

release scenarios

1.4 Organization of Contents

In chapter 2 the implemented measurement techniques for velocity and

temperature are described in more detail The experimental setup for

all release scenarios and the measurement methods are given in chapter3 In chapter 4 the performance of the alternatives for the flow visu¬

alization and the measurement techniques are evaluated Additionally,detailed velocity vector maps and temperature profiles are given for the

6 Introduction

different release scenarios A summary of the results and a final assess¬

ment of the implemented techniques are given in chapter 5 as well as

recommendations for future work

In appendix A the mathematical and physical background of the

measurement techniques is explained more thoroughly The detailed

conditions of all the experiments presented in chapter 4 are given in

appendix B

Chapter 2

Measurement Techniques

The mam focus of this thesis lies on the implementation of optical

diagnostics in the context of the heavy-gas channel Emphasis is put

especially on optical velocity measurements with correlation schemes

Furthermore, optical measurements of the index of refraction are carried

out to calculate 2D temperature fields Thermocouple measurements are

complementary to the optical techniques and important as an indepen¬dent reference The aforementioned techniques will be explained brieflyin the next sections For a more detailed explanation appendix A should

be consulted

2.1 Correlation Schemes for Velocity Measurements

The correlation of flow images for the calculation of velocities is a well

established technique In this context, the method of the image acquisi¬

tion is important It is possible to either expose the same active frame

from the digital camera once or several times These are called the

single frame/single exposure or single frame/double (multiple) exposure

techniques The improvement in data acquisition hardware makes the

single frame/single exposure method in many cases available even for

short interframe delays This is preferable, because directional ambigu¬

ity is eliminated with this approach Therefore, the details for single

frame/double exposure measurements are not discussed here For fur¬

ther information see Adrian (1991)The background for the correlation based schemes is the processing

of two sequential digital images into smaller interrogation regions (seeWillert & Ghanb (1991), Gm & Merzkirch (2000)) The concept is

shown in Figure 2 1 Here, the regions a and b are the subimages of

the full frame with a size of M by N pixel The correlation can then

be calculated for each pair of corresponding subwmdows This can be

achieved with either a least-squares difference approach

p = ^2(a - b)2 - mm (2 1)m,n

8 Measurement Techniques

Image 1

Timet

Image 2

Time t+dt

d(mn)

Estimated field of

diplacement function

Figure 2 1 Conceptual arrangement of frame-to-frame subsamphng for two

consecutive images

or the calculation of the cross-correlation coefficient

Cov(a, b)

y/Var(a) Var(b)max (2 2)

The method using the least-squares algorithm is called Minimum

Quadratic Difference (MQD) It can be shown that the MQD method

and the cross correlation are identical except for the normalization Fur¬

ther details are given m appendix A 1

The effective calculation of the cross-correlation is another issue to be

addressed here This topic is discussed extensively m the literature, for

instance see Raffel et al (1998) or Lourenco (2000) In Figure 2 2, the

concept for the digital image processing is shown It is based on the rela¬

tion between the correlation integral and its Fourier transform (Brigham,1974) The correlation integral can be calculated by multiplication of

the corresponding Fourier transforms This is the correlation theorem

The final result is then obtained by an inverse Fourier transform This

method assumes for the calculation of the correlation a periodic repre¬

sentation of the images m the frequency domain To prevent wraparoundeffects due to the periodicity of the data, a window-masking approach is

used (see Raffel et al (1998) and McKenna & McGillis (2002))The subpixel interpolation is another important point m the extrac¬

tion of high resolution data This approach is available as long as the

intensity profile of the correlation peak is spread over several neighbor¬

ing pixel The "real" position of the peak can then be interpolated bydifferent means Standard approaches to this problem use for instance

2.2 PTV, PIV, ICV or LSV? 9

Input jnage samplingat position (m,n)

Output

(mn)

—

Real to complexFFT

Complex

conjugate

multiplication

Correlation

data

Complex to real

inverse FFT

Peak

detection

(mn)

Real to complexFFTImage 2

Figure 2 2 Numerical processing flow-chart of the correlation process

the centroid method, curve fitting with a Gaussian or Whittaker's re¬

construction scheme (see Lourenco (2000)) Among these methods, the

Gaussian fit usually performs best Recently, another method was pro¬

posed by Rosgen (2003) This method takes advantage of the "sine"

function which represents an ideal interpolator (Meijering, 2002) This

interpolation method was used for the extraction of high resolution data

from the experiments A more detailed explanation of the mathematical

background is given in appendix A

2.2 PTV, PIV, ICV or LSV?

In the field of optical velocity measurements, different kinds of images

can be correlated with the schemes discussed in section 2 1 In case

of particle tracking velocimetry (PTV), the behavior of distinguishable

particles in the flow is used to derive velocity data This can be achieved

with the presented correlation scheme (Saga et al, 2001) Particle image

velocimetry (PIV) (Hesselink, 1988) is used for the tracking of ensembles

of particles, as long as single particles can be identified in the images At

even higher particle densities in the flow or very large fields of view, single

particles can no longer be identified In this case it is possible to correlate

observable variations in the particle concentration in the images One

method incorporating this idea was proposed by Dahm et al (1992) and

is called scalar imaging velocimetry (SIV) (see also Su & Dahm (1996a)and Su & Dahm (19966)) It uses an iterative scheme to reconstruct the

flow field from four-dimensional spatiotemporal data with the advective-

diffusive transport equation Image correlation velocimetry (ICV) is

another technique for the correlation of textured images It was proposed

by Tokumaru & Dimotakis (1995) and incorporates an affine coordinate

transform with translation and deformation of the subwmdows to match

10 Measurement Techniques

successive images A similar method of correlating textures in images is

described by Fmcham & Spedding (1997) (see also Fmcham & Delerce

(2000)) The ICV approach was implemented by Merkel et al (1996),Grunefeld et al (2000a), Grunefeld et al (20006), Deusch et al (2000)and Fielding et al (2001), where laser induced fluorescence (LIF) images

are correlated An evaluation of the ICV method (also called CIV for

concentration image velocimetry) can be found in Scarano (2002) If the

seeding density is nearly homogeneous and neither single particles can be

identified nor variations in the concentration of tracers can be observed,the ICV method is no longer feasible One alternative might then be the

correlation of speckle patterns (Fomin, 1998) This approach is called

laser speckle velocimetry (LSV) The speckle patterns are formed due to

the interference of the coherent light reflected from the light scattering

particles in the flow These patterns have only a very limited lifetime,so the experimental setup requires a special comparatively short timing

for the acquisition of the images In the context of slow flows and largefields of view this can cause problems, because the speckle pattern would

almost remain motionless between the capture of two consecutive images

This would make the calculation of velocities very difficult

The choice of the velocity measurement technique is not always in

the hand of the experimentalist More often, the nature of the flow and

the available seeding determine the availabilty of the methods Due to

the nature of the flow encountered in the heavy-gas channel, the choice

is limited here for example to ice particles for the visualization of the

lower layers of the flow These particles are generated automatically

during the formation of the cloud Therefore, the density of the seedingcan be controlled in a limited range only with the lower limit still too

high for the identification of single particles This limits the choice of

interrogation techniques to ICV or LSV Both methods are implementedwith the correlation scheme This is somewhat different to the approachfrom Tokumaru & Dimotakis (1995), which uses a higher order scheme

that includes deformations of the interrogated area The correlation

algorithm described above covers only the first order of the original ICV

scheme, but due to the nature of the flow it is not necessary here to

go further in most cases The same approach was taken by Fmcham &

Spedding (1997), who also used a simple correlation scheme to extract

velocities from textured images

The mathematical details of the implemented techniques are ex¬

plained in appendix A 1 for the correlation scheme and in appendix A 2

2.3 Background Oriented Schlieren (BOS) 11

for the speckle method

2.3 Background Oriented Schlieren (BOS)

The classical Schlieren technique is very demanding from the experi¬

mental point of view (Settles (2001), Vasil'ev (1971)) Recently, new

approaches were proposed by Dalziel et al (2000) and Meier (2002) that

visualize density fluctuations m variable density flows A successful ap¬

plication for large scale experiments is presented m Richard & Raffel

(2001) The methods contain a much simpler setup than the classical

techniques while taking advantage of the sensitive correlation algorithmsm combination with the advancement m digital image acquisition and

processing power In the present experiment, this provides the oppor¬

tunity to measure the 2D temperature field m a fairly straightforwardmanner Normally this is difficult to accomplish, because a large array

of sensors would be required to achieve the same result The extraction

of 3D data by image reconstruction from projections, l e computerized

tomography (Jam, 1989), is also a possibility This method requires a

large number of projections which makes the use of several cameras nec¬

essary (McMackm et al, 1999), because the resolution of this technique

depends on the used number of different projections These require¬

ments make this method technically demanding and expensive Hence,the mam focus is aimed at 2D data only which can be acquired with a

single camera

Reference

Image

Distorted

Image

mage samplingat position (mn)

Output

(mn) \Gladstone Dale

Correlation

algorithm

Displacementfield

Integration of

gradient field

Field of

index of refraction

I.

2D temperature

field^

f"

(mn)

Calibration

temperatures

Figure 2 3 Flow-chart of the temperature calculation with BOS

The background oriented Schlieren technique (BOS) or "synthetic"Schlieren method is based on the distortion of one image due to density

changes compared to an undistorted reference image This approach can

be best compared with laser speckle density photography described by

Kopf (1972) and Wernekmk & Merzkirch (1987) The processing of the

12 Measurement Techniques

images is shown in Figure 2.3. The first part of the flow-chart is similar to

the velocity measurement techniques with the correlation method. Here,a structured background image is observed with a phase object placedbetween the background image and the camera as depicted in Figure 2.4.

The images are taken in a way that one image is the reference image and

the second one is distorted by the phase object (Merzkirch, 1974). This

object can be a heat source that changes the temperature and therefore

the density. Here, the cold heavy-gas cloud is responsible for the densityvariations. In contrast to velocity measurements, the two images do

not have to be recorded in a rapid succession but can be taken minutes

apart. The only prerequisite is the unchanged alignment of the setup.This is very important, because the image distortions due to the phase

object are usually very small. The correlation of both images results in a

field of displacement vectors in the observed area. From this vector field

Figure 2.4'. Influence of phase object onto optical rays (exaggerated). For the

density gradient applies: dp/dx = 0 and dp/dy > 0.

which represents the gradient of the index of refraction, the refractive

index n(x, y) can be calculated with different techniques. One way is to

solve the Poisson equation An = g in discrete form. Another approachis to directly solve for n(x,y) from the measured field Vn(x,y) by using

a finite-difference approximation scheme, say, of fourth order (Hirsch(1994), Jacobson (2000)). The calculated index of refraction n(x,y) can

be inserted into the Gladstone-Dale equation (A.29) (Vasil'ev (1971),Smits & Lim (2000)) and in combination with the equation for perfect

gases (A.28) we get

Lightsource

ci • n(x,y) + c2(2.3)

2.4 Thermocouples 13

with two unknown constants c\ and c2 They have to be determined byadditional temperature measurements In the present case, thermocou¬

ple measurements (section 2 4) are used They are taken at the same

time as the corresponding images The full mathematical details of the

calculation are described in detail in appendix A 3

The direct integration of the gradient field in ID is another approachIt is feasible for flows with strong gradients in one direction only The

index of refraction can then be calculated directly with

n(y) = /-TT- dy + n0 (2 4)

Jo dv

By combining this equation with the Gladstone-Dale equation, we obtain

T(y) = —, TTr...... i (2 5)

1+ ( f^-1Jo" ff dy

/o°° f? dy

The constant temperatures Tw = T(x, y = 0) and Ta(x, y = oo) are the

wall temperature and the ambient air temperature, respectively This

equation has to be solved for every column in the gradient matrix to

obtain the whole temperature field The advantage of this procedureis the low demand on computer power, but the disadvantage is the ex¬

trapolation of the calibration temperatures Tw and Ta measured at one

location xcai to (x, y = 0) and (x, y = oo) for every x in the field of view

This is possible for flows with weak temperature gradients along x only,but for many flow problems it is not applicable The full derivation of

the integral is explained in appendix A 3

2.4 Thermocouples

Thermocouples are a well established technique for temperature mea¬

surements Their working principle is based on the thermoelectric ef¬

fect, the so-called Seebeck effect (see Weissmantel & Hamann (1995))The principle here is the different response of the two involved materials

to temperature differences between two points Due to the different re¬

sponses of the two materials, a potential builds up in the thermocoupleThis very low voltage can be amplified and then translated to a temper¬

ature The sensitivity of the probes to temperature gradients dependson the materials they are made of and the calibration process The ther¬

mocouples used throughout the experiments were especially designed as

14 Measurement Techniques

fast responce probes in the context of the heavy-gas channel by Zumsteg

(1988) They consist of Chromel / Alumel components This combina¬

tion is widely used, because it provides a good sensitivity over a large

temperature range from as low as 73 K up to 1530 K For more details

on the used probes and the calibration see appendix A 5

The temperatures measured with this technique are used as the

boundary conditions for the background oriented Schlieren method (seesection 2 3) Therefore, a high accuracy is necessary because of the sen¬

sitivity of the Schlieren method to the calibration temperatures

Chapter 3

Experimental Setup

The experiments conducted for this project incorporate two different

release conditions of the evaporated cryogenic nitrogen in the heavy-gaschannel. Both setups are investigated mainly with the optical velocitymeasurement technique and the BOS method. In the following sections,the different setups of the channel and the configuration of the applied

diagnostics are described in more detail.

3.1 Heavy-Gas Channel

The main experimental facility for this project is the heavy-gas channel.

It is designed to investigate the propagation of high-density clouds. In

this context, "high density" means densities larger than the ambient air.

The density of the released clouds can vary from twice that of the am¬

bient air to densities higher by a small fraction only. Due to this higher

density the clouds propagate along the floor of the channel. A snapshotof a continuously released heavy-gas cloud is shown in Figure 3.1. The

Figure 3.1: Snapshot of a heavy-gas cloud in the channel taken during a

continuous-release experiment.

current setup is chosen to create cryogenic gas clouds generated by the

evaporation of liquid nitrogen under different conditions. The schematic

16 Experimental Setup

view of the channel is shown in Figure (3 2) It has a length of twelve

meters, is 1 2 meters wide and has a height of one meter It consists

of three distinctive sections The first section is the release chamber

Release Chamber Transparent

1 1<>

Steps

1280 mm 6190 mm

12070 mm

1150 mm

Figure 3 2 Schematic view of the heavy-gas channel

Here, the liquid nitrogen is evaporated under controlled conditions to

produce clouds with varying properties The second part consists of a

horizontal surface This section can be used to investigate the "undis¬

turbed" propagation of the heavy-gas cloud and for the installation of

obstacles like fences or step like features The third section is composedof consecutive steps that can be varied in height and length This sec¬

tion is meant to represent idealized topographic features and providesadditional acceleration of the flow

During the project, two different evaporation methods were used to

generate cryogenic heavy-gas clouds with variable properties The first

method incorporates the sudden release of the evaporated liquid nitrogen

from the release chamber With the second method it is possible to

continuously release a cryogenic gas cloud from a heated Dewar container

filled with liquid nitrogen Both methods will be explained in more detail

in the next sections

3.1.1 Continuous Release of Evaporated Cryogenic N2

The continuous-release setup is designed to generate a heavy gas cloud

in a generic configuration for the extraction of global parameters of the

flow Therefore, a steady source is needed to produce a continuous dense-

3.1 Heavy-Gas Channel 17

gas flow with a variable mass-flow rate in the heavy-gas channel The

previously established method (Zumsteg (1988), Grobelbauer (1995))to pour the liquid nitrogen onto a free water surface is not sufficient,because the water surface freezes over after a short time interval This

effect limits the heat transfer necessary for the evaporation of the liquid

nitrogen As a consequence, only a limited amount of the liquid nitrogen

can be evaporated in a given time interval Another problem with a free

water surface is the high number density of the ice-particles in the cloud

generated during the evaporation process due to the direct contact with

the water For optical access into the cloud, the ice-particle densitymust not be too high Therefore, an evaporation setup is needed which

permits the reproducible variation of the particle density at least to some

extent

One possible solution is the use of electrical heating to evaporate the

liquid nitrogen in the dewar container The reservoir of liquid nitrogen

has to be large enough to produce a heavy-gas flow for a duration suf¬

ficient for the experiments The advantage of the electrical heating lies

in the possibility of controlling the power used to evaporate the nitro¬

gen while providing a good reproducibility of the evaporation conditions

The applied heating system consists of several immersion heaters of dif¬

ferent power levels that are placed inside the Dewar container The

applied power can be varied by using any combination of heaters of 300

W and 1000 W With this setup, the amount of evaporated nitrogen can

be varied in small steps A reasonable range lies in a mass-flow rate

between 7 gram per second and 15 gram per second In this range, it is

possible to extract information from the cloud with the available opticalmethods Additionally, this mass-flow rate allows for a suitable dura¬

tion of four to five minutes of experimentation with the available Dewar

container

3.1.2 Sudden Release of Evaporated Cryogenic N2

The second setup is used to generate suddenly released heavy-gas clouds

in the channel This setup was extensively studied for instance by Zum¬

steg (1988) and Grobelbauer (1995) With this configuration, a specifiedamount of liquid nitrogen is evaporated in the closed release chamber

After a selected time interval, the cloud is released and starts to propa¬

gate along the channel The first version of the release chamber included

a water basin to provide a sufficient heat reservoir for evaporation of the

18 Experimental Setup

liquid nitrogen During the evaporation, ice-particles are formed due

to nucleation (Jacobson, 2000) creating a largely opaque cryogenic gas

cloud This is to be avoided when performing optical measurements in

the cloud Therefore, the amount of water in the cloud has to be reduced

This can be done by covering the water surface during the evaporation

process, but one has to assure sufficient heat conduction to evaporate the

nitrogen completely in an acceptable time interval To fulfill all these

requirements, a copper tub is placed in the release chamber on top of

the water basin This prevents the generation of too many ice-particlesin the cloud while providing ample heat conduction to evaporate the liq¬uid nitrogen One drawback of this method compared to the free water

surface setup is the thermal stress generated in the copper tub by the

cryogenic liquid To reduce this problem, the copper must have direct

contact to the water basin Without the water, the copper tub would be

destroyed after only a few experiments due to thermal stress

The time needed for complete evaporation depends on the used

amount of nitrogen and the required opacity of the resulting heavy-gascloud When using an amount of 1 kg of liquid nitrogen, it is necessary

to wait up to 45 s for complete evaporation while achieving a sufficientlylow opacity suitable for optical measurement techniques The shutter

which is held shut by switchable magnets is automatically opened after

the chosen time interval needed for the evaporation and the heavy-gascloud starts to propagate along the channel

3.2 Ambient-Air Seeding

The ice-particle seeding used to visualize the cryogenic gas flow does not

cover the intermediate layer between the ambient air and the heavy-gascloud For the acquisition of the full velocity profile of the heavy-gas

flow, especially in the continuous-release case, the part of the mixing

layer between the visible layer of the cloud and the ambient air needs

to be visualized Therefore, additional seeding is needed for this region

This can be provided by different means (Melling (1997), Jermy (2002))In the present context, three techniques were studied that are thought to

be suitable for the cryogenic gas flow The first technique uses an ultra¬

sonic fog generator and the second a helium-bubble generator (Machacek(2003)) The last method includes very small solid particles (powder)like T1O2 (Melling, 1997) or talcum powder (Lengweiler et al, 1997) for

flow visualization

3.2 Ambient-Air Seeding 19

3.2.1 Ultrasonic Fog Generator

The first technique takes advantage of ultrasonic fog generators. They

generate small droplets of water in the range of lpm to 10 pia that can

be used as seeding. The generator used has five membranes as shown

in Figure 3.3 that produce the fog by inducing cavitation in the water

above the membranes. To separate the varying sizes of droplets to some

Figure 3.3: Ultrasonic fog generator with five membranes.

extent, the height of the container the generators are placed in is chosen

in a way that only the smaller particles can escape. This is necessary,

because the larger droplets would not follow the heavy-gas cloud as goodas the small particles while disturbing the flow significantly and changingits humidity.

An array of such generators can be placed anywhere along the chan¬

nel. Their position should be as far as possible away from the measure¬

ment position. In this way, the seeding is more likely to move passivelywith the surrounding flow.

3.2.2 Helium-Bubble Generator

The second choice for the additional seeding is a helium-bubble gener¬

ator. A schematic view is shown in Figure 3.4. It was developed byMachacek (2003) for wind tunnel experiments. Helium-bubble seedingis a long established technique for the visualization of flow phenomena

(Müller, 1996). The principle here is that the light helium gas inside

20 Experimental Setup

the bubble compensates the additional weight of the soap membrane of

the sphere. By varying the amount of soap and helium, the weight of

the bubble can be "tuned" to be of neutral density compared to the

surrounding environment. Their normal disadvantage of poor visibility

Soap pressure tank

Safety valve

Shut offvalve

with venting

Pressurized helium

Pressurized air

Shut off valve

Fine regulationvalves

Figure 3.4: Schematic view of the helium-bubble generator.

Figure 3.5: Picture of the orifice type nozzle with removed cap.

is not of concern here, because the laser light sheet used for visualiza¬

tion provides sufficient illumination. Furthermore, the poor visibility is

normally only a problem with high speed flows that are not present in

the heavy-gas channel. A real problem in our experimental context is

the contamination of the channel with the soap. This is especially im-

3.2 Ambient-Air Seeding 21

portant for the sensitive thermocouples that could be damaged by the

soap Additionally, it is difficult to clean the thermocouples The advan¬

tage of the helium-bubble generator is the variability of the generatedbubbles by choosing different nozzles for the generation of the bubbles

During the experiments, an orifice type nozzle with a diameter of 2 mm

is used as shown in Figure 3 5 (Machacek, 2003) The bubbles have

then approximately the same diameter With this setup, the amount

of generated helium-bubbles is sufficient to visualize the flow above the

heavy-gas cloud in the field of view

3.2.3 Solid Particle Seeding

The use of small solid particles like T1O2 or talcum powder as additional

seeding is another possibility for flow visualization The advantage of

this approach is the availability of particles with a controlled size dis¬

tribution The disadvantage is the contamination of the facility with

the dust particles This can be dangerous again for the thermocouples

(see section 3 5), because the powder can stick to the sensitive wires and

therefore change their response time to temperature variations Due to

this contamination, the thermocouples have to be cleaned with com¬

pressed air after each experiment

The size distribution of the used particles lies in the range of 1 pm

for T1O2 (Melling, 1997) The talcum powder was bought at a local

pharmacy Therefore, the exact particle size distribution is not known,but tests showed a good response to local velocity variations in the am¬

bient air The residence time of the particles is about one minute in a

quiescent environment It is possible to calculate the size of the particleswith Stokes drag law (Gerthsen & Vogel, 1993) and the assumption of

spherical particles in a viscous fluid with a very low Reynolds number

This yields (Raffel et al, 1998)

y (Pp - Pairjg

with the diameter of the particle dp, the dynamic viscosity »7=18 10~5

Ns/m2, the density of the particle pp, the density of air patr, the velocityinduced by gravitation v and the gravitational acceleration g = 9 81

m/s2 The observed falling velocities of the particles undisturbed byexternal influences is approximately v « 0 01 m/s and the density of

22 Experimental Setup

the talcum powder is pp = 2700 kg/m3 (Lengweiler et al, 1997) The

density of air can be neglected because it is much smaller than the densityof the talcum powder This yields a particle diameter of dp « 11pmThis seems to be quite large compared to the particle size dp = 1 2pm

presented by Lengweiler et al (1997), but the calculation here is only an

approximation of the real diameter, because the "true" velocity induced

by gravitation alone is not known due to external influences

3.3 Setup for Optical Velocity Measurements

As was stated before, the mam focus of this thesis lies on the establish¬

ment of optical velocity measurements in the heavy-gas channel There¬

fore, a 2D PIV system was build up It consists of the light-sheet optics

with three cylindrical lenses, a double cavity Nd YAG laser1 (170 mJ

output per pulse, pair repetition rate of 15 Hz) and a 10 bit digital cam¬

era2 with a 984 by 1008 pixel resolution The camera has a matched

acquisition rate of 30 frames per second The setup is shown in Figure

(3 6) The whole system is placed on a movable breadboard as shown

in Figure 3 7 In this way the system can be positioned anywhere alongthe channel without changing the relative positions of the optical com¬

ponents Hence, the complexity of the optical alignment procedure is

minimized while allowing several measurements at different positions

during the same day This is important, because the number density of

the ice-particles depends on the changing humidity

With this equipment, it is then possible to generate a light-sheet with

a thickness of 2 mm and a width of 60 cm at its base while maintaining

a high intensity inside This allows for a good contrast in the pictures

captured with the CCD camera The field of view observed normallywith the camera is about 40 cm high and 40 cm wide The reason for

this large window is the correlation of structures due to density varia¬

tions in the ice-particle distribution By decreasing the field of view the

structures become larger, hence the resolution is not increased and the

correlation between two images becomes worse This will be discussed

in more detail in chapter 4

1 Continuum Surelite 1-15

2Pulmx TM-1040

3.3 Setup for Optical Velocity Measurements 23

Open TransparentChannel Walls

Light-Sheet

Flow

Laser Timing

Figure 3.6: Setup for velocity measurements. Only a part of the channel is

shown.

Light-Sheet Optics /

Turning Mirror

Figure 3.7: Picture of the optical setup for the velocity measurements.

24 Experimental Setup

3.4 Setup for Background Oriented Schlieren (BOS)

The setup for computerized background oriented Schlieren (BOS) or syn¬

thetic Schlieren is rather simple as shown in Figure 3 8 For this tech¬

nique, only few hardware components are necessary The setup consists

mainly of a structured background image placed behind the Schlieren

object, e g the heavy-gas channel, and a camera placed on the oppo¬

site side The cameras used here are 1008 by 1018 pixel CCD cameras3

with a frame rate of 15 Hz and a dynamic range of 10 bit In addition,the background image has to be illuminated with an appropriate lightsource

The dot pattern used as the background image is generated with a

Sobol sequence algorithm according to Press et al (1997) It generates a

quasi-random sequence avoiding the chance clustering that occurs with

uniformly random points Furthermore, the autocorrelation of the Sobol

pattern approximates a delta function This pattern is then printed on

to a large transparency that is observed across the heavy-gas channel

An electroluminescent foil4 is used as the light source This has the

benefit of a uniform illumination of the background image that is simplyfixed on top of the foil The intensity of the light source can be changed

by applying variable voltages and frequencies to the foil Because of

the high sensitivity of the BOS method, changes in the position of the

structured background image due to thermal effects in the light source

have to be avoided Therefore, it is necessary to fix the transparency

and the electroluminescent foil between two glass plates Otherwise, the

movement of the image could lead to a gradient in the measured data

not representing the real flow

Another important point is the choice of the distance of the CCD

camera from the channel To eliminate effects due to perspective dis¬

tortions, the camera has to be placed as far away from the channel as

possible This requires a lens with a large focal length to project onlythe background image onto the CCD chip of the camera and to providea sufficient resolution For this purpose, a zoom lens with a focal length

range between 80 mm and 200 mm was used This allows for a high

flexibility in the optical arrangement

The two reference temperatures needed for the calculation of the

temperature field from the index of refraction in the whole field of view

3Pulmx TM-1010

4Lumitec ELF 1652

3.5 Thermocouples 25

Open TransparentChannel Walls

Random Pattern with

Background Illumination

Flow

fDataCCD-Camera

Figure 3 8 Schematic view of the setup for BOS

are determined by thermocouple measurements (see section 3 5) Probe

rakes with nine thermocouples each are placed at the left and right edgeof the field of view of the camera This provides the necessary temper¬

ature measurements as close as possible to the observed area without

disturbing it Additionally, the redundant thermocouples can be used

for verification purposes

3.5 Thermocouples

The recording of the temperature distribution is important in the context

of cryogenic gas clouds Therefore, fast response thermocouples were

used throughout all experiments The thermocouples were designed by

Zumsteg (1988) with a response time of less than 0 1s To achieve

a good estimate of the temperature distribution along the channel, 45

probes are mounted onto five rakes and then placed at different positions

Each rake contains nine probes, which can be varied in height to capturethe full vertical temperature profile Additionally, 16 probes are flush

mounted along the floor of the channel

Chapter 4

Results

The choice of the applied seeding for flow visualization experiments

is a crucial part and therefore investigated first Thereafter, the whole

setup is evaluated for its performance and then the results of the velocitymeasurements are presented for the different release types At the end of

the chapter, temperature measurements analyzed with the backgroundoriented Schlieren technique are presented

Before we start with the investigation of the seeding, the positions

of the field of view of the camera in the channel will be shown These

positions are specified in Figure 4 1, a reduced sketch of Figure 3 2

All future references regarding measurement positions in the channel

are made to this figure The coordinate axes are defined so that the

x-direction is parallel to the floor of the channel and the y-direction

perpendicular (see Figure 4 1) to it Due to the geometry of the facilitythere are good reasons to assume that 2D structures in the flow dominate

The five measurement positions are located at x\ = 2 95 m, X2 = 4 25

Measurement Positions

XFlow

1 2 3 4

1280 mm 6190 mm 1150 mm

Figure 4 1 Specification of the measurement positions All experiments are

conducted at the five depicted positions

m, 13 = 5 2 m, 14 = 6 65 m and x$ = 7 2 m from the center of the

release chamber

4.1 Seeding of the Cryogenic Cloud

A picture taken from a suddenly released cloud is shown in Figure 4 4(a)Because the visible seeding is formed automatically, additional seeding

28 Results

is not needed inside the cloud It would even be difficult to bring in

additional seeding that can be visualized among the already existing

particles The source of these particles is the evaporation process Dur¬

ing the evaporation, ice particles are formed due to either homogeneousor heterogeneous nucleation (Jacobson, 2000) of water Homogeneousnucleation takes place when a critical supersaturation dependent on tem¬

perature is reached whereas heterogenous nucleation takes place in the

presence of external nucleating agents like dust particles (Gierens (2002),Wood et al (2002)) On one hand, the low temperatures present duringthe evaporation process could make it possible that supersaturation oc¬

curs On the other hand, nucleating agents are ubiquitous in the labora¬

tory due to the use of the talcum-powder seeding Hence, both nucleation

processes can be present during the evaporation phase dependent on the

actual humidity and number of dust particles The dominating nucle¬

ation process is still unclear, although heterogeneous nucleation will most

likely provide a major contribution to the number of ice-particles Due

to this uncertainty only the general term nucleation is used when needed

in the following paragraphs The mean diameter of the ice-particles is

dp « 2pm according to Ruff et al (1988) Ninety percent of the particlesare less than 4pm in diameter Therefore, they should be suitable as pas¬

sive tracers for flow visualization The tracer particles are automatically

generated during the evaporation phase, which is a major advantage

Unfortunately, they have also drawbacks One problem is the high den¬

sity in many investigated configurations that can even prevent certain

measurements Therefore, the control of the seeding density is crucial

and will be investigated in the next paragraph Another problem en¬

countered here is the continuous melting of the ice-particles during the

propagation of the cloud This has an especially large impact when the

temperature in the cloud rises over 0°C, but even at lower temperatures

some seeding is lost at least in the mixing layer between the ambient air

and the propagating cloud This can be seen in Figure 4 2 for a steadycloud propagating along the heavy-gas channel, where a reduced visible

height becomes apparent These visible heights are calculated accordingto Figure 4 3 for each experiment The shown average temperatures rep¬

resent the visible layers of the flow This process of melting ice-particlesis accelerated at temperatures around T = 273 K where the visible heightof the cloud decreases dramatically The result is an incomplete natu¬

ral seeding that is present in the whole propagation process Therefore,additional tracers are needed for the unseeded parts This problem is

4.1 Seeding of the Cryogenic Cloud 29

12

11 5

11

105

10

a 95

75

7

* T in [K] |

*

274

273

272

271

270 —

1-

269

268

267

266

4 5

x[m]

Figure 4-2: Influence of temperature on the ice-particles and the visibility in

the case of a continuously released cloud propagating along the channel.

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Intensity [a u ]

(a) Average image of a continuous-

release experiment

(b) Average intensity profile over

height of Figure 4.3(a)

Figure 4-3: 4-3(a): Average image of a continuous release experiment gener¬

ated by averaging of 150 frames; 4-3(b): Intensity profile over height of Figure

4.3(a) generated by averaging in the x-direction.

30 Results

treated in section 4.3.

(a) Heavy-gas cloud suddenly released from an open water surface.

(b) Heavy-gas cloud suddenly released from a dry solid surface.

Figure 4-4'- Examples of heavy-gas clouds with high and low number of ice-

particles generated with the sudden-release setup. A rod with thermocouples

can be seen on the right side.

Two main sources contribute to the number of ice-particles in the

heavy-gas cloud. One source is the presence of an open water surface

during the evaporation process and the second one is the humidity that

is always present in the ambient air. The effect of both sources on the

visibility will be explained in the next two paragraphs.

The effect of the presence of an open water surface during the evapo-

4.1 Seeding of the Cryogenic Cloud 31

ration is important for both the continuous and sudden-release setup In

case of a sudden release, the difference between evaporation on open and

covered water surfaces can be seen in the Figures 4 4(a) and 4 4(b) Both

clouds were generated using the same amount of LN2 and they were re¬

leased after an identical evaporation time The cover of the water surface

is the copper tub described in section 3 12 Optical measurements in

the cloud are possible only in the setup with the covered water surface

Therefore, all the experiments dealing with a sudden release are carried

out with the cover only In case of a continuous release, the cover is also

important The reason is the very low temperature of the evaporated

nitrogen when it leaves the Dewar container If it is placed in the water

basin with a free surface, ice-particles are formed which results in a high

opacity of the cloud Therefore, the Dewar container is always placedon top of the copper tub to minimize the amount of ice-particles in the

flow

After removing the first source of ice-particles in the heavy-gas cloud,

only the ambient humidity remains The humidity is not easily controlled

in laboratories, unless they are sealed from the environment Therefore,the influence of varying humidity on the visibility of the cloud is investi¬

gated first In Figure 4 5, snapshots of a part of two different clouds are

shown They were both taken under the same continuous-release condi¬

tions, but on two consecutive days with strongly varying humidity which

differed by about 50% In contrast to the influence of this phenomenonon the visibility, the bulk velocity of the cloud remains unchanged with

m « 0 25m/s at the chosen measurement position The temperature

distribution over the height of the cloud is unchanged as well, as shown

in Figure 4 5(c) Therefore, measurements conducted under the same

experimental conditions, except for the humidity, are comparable quan¬

titatively Furthermore, the number density of the ice-particles does not

appear to have a significant impact on the overall cloud dynamics Un¬

fortunately, not every combination of humidity and mass-flow rate of

liquid nitrogen is possible, because the number of ice-particles dependson the amount of evaporated LN2 as well This results in the uncomfort¬

able situation of nearly uncontrollable humidity in the laboratory and

the need for a more or less defined range of seeding densities One way

to control the seeding is to change the amount of evaporated nitrogen

to allow optical accessibility to the flow A second way is to wait longerwith the data acquisition after the immersion heaters are switched on

The reason is the limited supply of humidity in the release chamber

32 Results

(a) Relative humidity fa 19% (b) Relative humidity fa 27%

290

Humidity 19%

Humidity 27%

285

280

Ê 275-

270-

265 !—

20 40 60 80 100 120 140 160

Height [mm]

(c) Temperature profile over height for different humidities

Figure 4-5: Influence of humidity on the visibility and temperature distribution

of a cloud generated under otherwise identical conditions.

4.2 Evaluation of ICV and LSV 33

which results in lower seeding densities at the later stages of the exper¬

iments Another problem encountered in this context is the constant

loss of seeding due to melting of the ice-particles (see first paragraph in

this section) The further away from the release chamber (see Figure3 2) the measurements take place, the less seeding is available For mea¬

surements at varying distances from the release chamber but under the

same evaporation conditions, the seeding density has to be as high as

possible closest to the release chamber while still allowing optical access

into the cloud This assures in most cases a sufficient seeding density at

the farthest measurement position

When summarizing the performance of the ice-particle seeding, this

method presents advantages and disadvantages The positive part is the

natural occurrence of this passively behaving seeding as an inherent part

of the cloud The negative part is the difficulty to control the seeding

density, the constant loss of seeding particles during the propagationof the cloud and an incomplete seeding of the flow, especially at the

interface between the mam part of the cloud and the ambient air The

last problem is discussed in more detail in section 4 3

4.2 Evaluation of ICV and LSV

As explained in section 4 1, the ice-particles are used as tracers In

Figure 4 6, a representative snapshot of a continuous-release experimentilluminated with a light sheet is shown The very high density of the

seeding makes it impossible to identify single particles or groups of par¬

ticles But the large scale structures in the flow are easy to identify and

can therefore be used as "tracers" in the context of ICV These patterns

move with the flow and retain their shape for a duration sufficient for the

application of correlation techniques The quality of the correlation de¬

pends then on the size, shape and visibility of the textures To compute

correlations that represent the flow, a large part of the structure should

fit inside the interrogation window to avoid exclusively linear features

This is mandatory, because the correlation of straight lines only in the

interrogation window may lead to incorrect results To assure this con¬

dition with the captured images, either the interrogation window or the

field of view should be chosen large enough The effect of different sizes

of the field of view can be seen in Figure 4 6, Figure 4 7 and Figure 4 8

The smaller field of view in Figure 4 6 resolves large structures which

make large interrogation windows necessary Hence, the effective résolu-

34 Results

tion in "real-world" coordinates is the same Therefore, the larger field

of view (Figure 4 8) is chosen for all conducted measurements to increase

the global field of view Here, the interrogation window can always be

chosen to have only 32 by 32 pixel without the negative influence of the

shape of the structures

0 0 05 0 1 0 15

Width [m]

Figure 4 6 Size of the original field of view width =18 5 cm, height =19 cm

The images presented in Figures 4 6 to 4 8 contain some high fre¬

quency noise that reduces the quality of the correlation By applyinga Gauss filter to the image with a size of 5 by 5 pixel, the quality of

the correlation can be improved This can be seen in the histograms of

the quality of the cross correlation coefficients shown in Figure 4 9 The

peak in the distribution of the cross correlation coefficients in the unfil-

tered case is « 0 6 and for the filtered case at « 0 7 With this filter, the

quality of the cross correlation can therefore be increased significantlyIn contrast to ICV, the LSV technique does not perform well in this

experimental context According to equation (A 17), the size of the

subjective speckle depends on the aperture A of the lens To generate

sufficiently large speckle patterns for correlation purposes, the aperture

has to be very small This reduces the amount of light able to enter

the camera so far that not much information can be gained from the

images Another problem is the decorrelation of the speckle patterns

in the related image pairs The decorrelation occurs due to the limited

lifetime of the speckle patterns and the use of two independent lasers

4.2 Evaluation of ICV and LSV 35

0.15

0.05

0.05 0 1 0 15 0.2

Width [m]

Figure 4-7: Size of the original field of view: width =24 cm, height =25 cm.

0 25

1" 015

0.05

0 0.05 0 1 0 15 0.2 0 25 0.3 0.35

Width [m]

Figure 4-8: Size of the original field of view: width =39 cm, height =40 cm.

36 Results

Cross correlation coefficient Cross correlation coefficient

(a) Unfiltered (b) Filtered with Gauss

Figure 4 9 Histograms of correlation coefficients for an image pair Figure

4 9(a) was computed with unfiltered images and Figure 4 9(b) with filtered im¬

ages

This decorrelation becomes significant here at approximately 100 ps In

the context of the encountered slow flow, the fluid is almost motionless

during this time interval This makes the computation of the velocities

very difficult, because the images of the corresponding pair are nearlyidentical The second problem is the use of two independent lasers

Because the speckles are generated by self interference of the scattered

light, different speckle patterns from the two independent laser beams

can result Therefore, the use of one laser with a high repetition rate

would be necessary to assure similar properties of the two light sheets

and to provide the required resolution in time of the flow

4.3 Seeding of the Ambient Air

The lack of information about the velocity profile in the intermediate

mixing layer between the seeded flow and the quiescent air requires ad¬

ditional seeding Several techniques are evaluated to provide the missing

visualization They are explained in the next paragraphs The working

principles of those techniques are described in section 3 2

The first method uses an ultrasonic fog generator With this device

it was possible to generate particles (water droplets) that had a long

4.3 Seeding of the Ambient Air 37

residence time in a sealed tank used for preliminary tests These par¬

ticles would be suitable for flow visualization experiments However,in the actual experiments with the heavy-gas channel a long residence

time of the particles could not be achieved and it was not possible to

effectively separate the larger from the smaller particles This resulted

in a strong disturbance of the cloud when placing the generator close

to the light sheet, thus rendering the measurement useless When plac¬

ing the generator far away from the measurement position close to the

release chamber, the cloud and the additional seeding mixed and be¬

came indistinguishable No additional information about the flow could

be obtained in this way Additionally, the correlation between two cor¬

responding images decreased, because the seeding in the cloud became

more dense and the features which are normally correlated vanished

The second method incorporates a helium bubble generator It uses

an orifice type nozzle that produces bubbles of about 2 mm in diameter

The bubbles are generated slightly upstream of the light sheet This

limits the contamination of the facility to the few measurement posi¬

tions while providing a sufficient seeding density The bubbles disappear

immediately at contact with the seeded part of the cloud due to their

fragility This can be seen in Figure 4 12(c) The bubbles move down¬

ward with constant velocity and vanish as soon as they hit the cryogenic

cloud, which is the reason for the missing velocity vectors in the lower

part of the plot One problem in the context of seeding with helium bub¬

bles is the difficult handling of the generator as mentioned by Machacek

(2003) The bubbles have not a uniform weight on a day to day basis

and even during one experiment the size and weight can differ to some

extent This results in different responses to the surrounding flow field

This phenomenon is not a problem in wind tunnel experiments with

high velocities, but with velocities in the range of 0 2 m/s, the varying

response can lead to unreliable results

The last method investigated uses simply small solid particles that

should follow the flow passively In this case, two different powderswere investigated, î e T1O2 and talcum powder The first choice, 1 e

T1O2, proved not to be suitable here, although having the proper size

and weight for passive behavior in the flow Unfortunately, the seedingsticks to all surfaces rather strongly thereby contaminating the chan¬

nel Additionally, the T1O2 is difficult to clean up after the experiments

which causes reduced optical accessibility in the long run after many

experiments Therefore, talcum powder is used which can be removed

38 Results

easily from the facility after the experiments Several tests showed a

passive behavior of the particles in the slow moving flow To visualize

the unseeded parts of the flow, the powder is carefully introduced into

the flow slightly upstream of the light sheet with the smallest velocity

possible

The performance of the different seeding techniques under similar ex¬

perimental conditions is shown in Figure 4 11 for the velocity component

parallel to the floor and in Figure 4 12 for the component perpendicularto the floor of the channel

In Figure 4 11(a) and 4 12(a), a representative case without ad¬

ditional seeding is shown A top-hat profile for the velocity in the

x-direction can clearly be seen in combination with a vanishing y-

component

The results with the ultrasonic fog generator are shown in Figure4 11(b) and 4 12(b) The generator was placed upstream in the release

chamber, because a smaller distance to the measurement position dis¬

turbed the flow strongly It is obvious, that with this setup no additional

information about the flow can be gained Additionally, the quality of

the correlation is decreased compared to the setup without additional

seeding

The result from the helium-bubble tests are shown in Figure 4 11(c)and 4 12(c) With this technique, the velocity distribution in the inter¬

mediate layer can be made accessible It is important to note that the

velocity of the bubbles is always negative (pointing downward) in the

field of view and vanishes nowhere The reason is most likely the way

the bubbles are introduced into the channel, because a finite velocity is

required for the bubbles to arrive at the measurement position Several

problems are encountered with the helium bubble seeding The first one

can be deduced from Figure 4 12(c), l e the high falling speed of the

same magnitude as the velocity of the cryogenic flow This makes the

qualitative identification of the unseeded velocity profile possible, but

it is still difficult to deduce the surrounding flow conditions from the

trajectories of the helium bubbles Additionally, the results presentedhere for the helium-bubble seeding are difficult to acquire, because of

the laborious handling of the helium-bubble generator as already men¬

tioned (see section 3 2 and Machacek (2003)) This became apparent

during some experiments with the falling velocity being in the range of

v « 0 15m/s 0 35m/ s This is not acceptable for a quantitative anal¬

ysis Another drawback is the low seeding density available This makes

4.3 Seeding of the Ambient Air 39

02

Width [m]

(a) No additional seeding. (b) Ultrasonic fog generator.

(c) Helium bubbles. (d) Talcum powder.

Figure 4-10: Snapshots of experiments conducted with different additional

seeding techniques; Figure 4- 10(a): Experiment without additional seed¬

ing; 4- 10(b): Additional seeding generated with the ultrasonic fog genera¬

tor; 4- 10(c): Additional seeding generated with the helium bubble generator;

4.10(d): Additional seeding generated with the talcum powder.

40 Results

Velocity in x-direction

0 35

03

0 25

E,

ci°2

I

0 15

01

0 05

-0 1 -0 05 0 0 05 0 1 0 15 0 2 0 25 0 30

Velocity [m/s]

- Velocity in x-direction

-0 1 -0 05 0 0 05 0 1 0 15 0 2 0 25 0 3

Velocity [m/s]

(a) No additional seeding. (b) Ultrasonic fog generator.

-01 -0 05 0 0 05 0 1 0 15 0 2 0 25 0 3

Velocity [m/s]

03 -

_0 25 -

5)°2 "

"

0 15 -

01 -

0 05 -

0 —

-0 1 -0 05 0 0 05 0 1 0 15 0 2 0 25 0 3

Velocity [m/s]

(c) Helium bubbles. (d) Talcum powder.

Figure Jhll: Velocities parallel to the floor of experiments for continuous re¬

lease; Figure Jhll(a): Experiment without additional seeding; Jh 11(b): Addi¬

tional seeding generated with the ultrasonic fog generator; Jh 11(c): Additional

seeding generated with the helium bubble generator; Jh 11(d): Additional seeding

generated with the talcum powder.

4.3 Seeding of the Ambient Air 41

Volocity iny-diroction |

-025 -02 -015 -0 1 -005 0 0 05 01 0 15

Volocity [m/s]

| Volocity iny-diroction |

i °2"

"

0 15-

01 -

0 05-

0--0 25 -0 2 -0 15 -0 1-0 05 0 0 05 0 1 0 15

Volocity [m/s]

(a) No additional seeding. (b) Ultrasonic fog generator.

-025-02-015-01-005 0 005 01 0

Volocity [m/s]

0 25-02-015-01-005 0 005 01 01

Volocity [m/s]

(c) Helium bubbles. (d) Talcum powder.

Figure Jh12: Velocities perpendicular to the floor of experiments for continu¬

ous release; Figure Jh 12(a): Experiment without additional seeding; Jh 12(b):Additional seeding generated with the ultrasonic fog generator; Jh 12(c): Addi¬

tional seeding generated with the helium bubble generator; Jh 12(d): Additional

seeding generated with the talcum powder.

42 Results

it necessary to widen the light sheet from about 2 mm to 2 cm to illu¬

minate a sufficient amount of bubbles to obtain enough information for

a complete flow representation The approach even works for the lower

layers of the flow, because the structures correlated with ICV extend

into the z-direction and remain therefore clearly visible The wideningof the light sheet can cause problems with the reflection of light from the

floor of the channel into the field of view In this context, the thinner

light sheet causes fewer problems than the widened one with the chosen

optical arrangement

The results of the experiments performed with the talcum powder

seeding of the flow are shown in Figure 4 11(d) and 4 12(d) Comparingthe result for the velocity in x-direction for the seeding with helium-

bubbles and talcum powder, it appears that the helium-bubble seeding

performs as good as the talcum powder seeding From Figure 4 12(c) and

4 12(d) it becomes apparent that the solid particles from the powder fall

more slowly than the bubbles In fact, they are more passive than the

bubbles in the surrounding flow and their higher «-velocity in the upper

part is most likely caused by the initial momentum with which they are

introduced into the flow The relatively high v-velocity in the upper partof Figure 4 12(d) has its origin also in the spraying process of the powderinto the channel Under special circumstances it is possible to achieve

a constant v-velocity throughout the field of view of about 0 015m/s,but due to the manual dispersion of the powder this result is not alwaysensured Apart from this, the measurements with the talcum powderare relatively easy to reproduce, because the particle size distribution

remains constant and is only based on the manufacturing process

To summarize this overview of the different techniques investigated,the talcum powder presented the easiest and most reliable way to visu¬

alize the ambient air flow It can be applied without too much effort,reacts passively to the flow (see also Lengweiler et al (1997)) and does

not contaminate the facility too much It is therefore used as additional

seeding wherever it is needed in the following experiments

4.4 Optical Velocity Measurements: Continuous Re¬

lease

The setup with the continuous-release conditions represents a rather

generic case Similar experiments with Argon were performed byHuerzeler & Fannelop (1990) (see also Fannelop (1994)) This arrange-

4.4 Optical Velocity Measurements: Continuous Release 43

ment permits the acquisition of large amounts of data that can be aver¬

aged for the extraction of global parameters This can be used to test

the general applicability of the implemented optical diagnostics In the

following two subsections, the performance will be investigated first in

the case of unobstructed spreading over a horizontal surface and second

over a forward facing step

The velocities presented in this section are deduced from the images

with a size of the interrogation window of 64 by 32 pixel In combina¬

tion with an overlap of 75% of the adjacent interrogation windows, each

correlation map contains up to 58 data points in the x-direction and up

to 123 data points in the «-direction The resolution in the «-direction

was chosen to be higher than in the x-direction, because the variation of

the velocity over the height is more important for the continuous-release

configuration These 2D correlation maps are then averaged over the

measurement interval of 10 s, l e 150 correlation maps The presentedID velocity profiles are calculated by averaging the already averaged2D correlation map along the x-direction The average profiles are cal¬

culated by averaging of the correlation maps According to Meinhart

et al (2000) this approach performs better than the averaging of the

velocity-vector maps

4.4.1 Spreading over a Horizontal Surface

The reproducibility of the measurements is investigated first Results

are shown for velocity and temperature measurements from six consec¬

utive releases in Figure 4 14 The velocities are calculated by averaging

of 150 2D correlation maps This means an average of a measurement

over the duration of ten seconds From the averaged map, the median

is taken to calculate the average velocity of the part of the cloud which

is naturally visible The experimental evidence indicates that the «-

velocity profiles are fairly uniform inside the lower layers of the cloud

so that the median-analysis of the distribution appears justified The

temperatures were taken with thermocouples during the same time in¬

terval with a sampling frequency of 100 Hz Therefore, each data point

should be quite reliable due to the large amount of data available for the

statistics A sample of these velocity and temperature measurements is

shown in Figure 4 13 Calculating the uncertainty of the velocity and

temperature measurements from the values in Figure 4 14, we have the

standard deviation for the velocity au « 0 005 m/s and for the tempera-

44 Results

- Velocity In x direction

01 0 05 0 0 05 01 0 15 02 0 25 03

Velocity [m s]

270 275

Temperature [K]

(a) Velocity (b) Temperature

Figure 4 13 Samples of velocity and temperature measurements used for the

investigation of the reproducibility

ture (Jt ~ 0 4 K Requiring the "true" value to be within the confidence

interval of the measured value with 95 % probability, the absolute error

becomes (Gerthsen h Vogel, 1993) au 95%= 1 96<yu for the velocity and

aT 95%= 1 96cry for the temperature This results in a relative error of

5«=^% =4 3%«

°T,95%.

5T =T

-=0 3%(4 1)

with the median velocity « = 0 23 m/s and the average temperature

T = 268 3 K The presented temperatures are the average temperaturesof the layers of the flow seeded with ice-particles and are calculated from

the same part of the flow as the median velocities

A measurement error can also be determined from a singlecontinuous-release experiment The bulk velocity calculated from the

150 2D velocity vector maps as a function of time is shown in Fig¬ure 4 15(a) These data correspond to experiment number 2 in Figure4 13(a) The relative error can be calculated with equation (4 1) for the

velocity With the standard deviation au « 0 0054 m/s and the me¬

dian velocity « « 0 237, the relative error is Su = <tu 95%/w = 4 5%

A similar analysis for the error of the temperature measurements can

be carried out with the time resolved temperature data shown in Fig-

4.4 Optical Velocity Measurements: Continuous Release 45

ure 4 15(b) This yields the standard deviation <jt « 0 5 K and the

mean temperature T = 268 3 K The resulting relative error is then

ST = o-Tg5%/T = 0 4% These errors are nearly identical to the er¬

rors determined from the investigation of the reproducibility (equation(4 1)) Therefore, these relative errors will be assumed for all subsequent

velocity and temperature measurements During this investigation, no

additional seeding was employed for the measurements

i

12 3 4 5 6 7

Exp nr

(a) Velocity (b) Temperature

Figure 4 14 Reproducibility of velocity and temperature measurements of six

consecutive releases at position 2 (see Fig 4 I) The error bars are deduced

from the relative errors in equation (4 1)

The influence of varying electrical power used for the evaporation of

the liquid nitrogen in the Dewar container is another issue to be looked

at Therefore, a series of measurements is carried out with varying elec¬

trical heating in the dewar The result is shown in Figure 4 16 for both

the velocity « and the temperature T Again, the presented velocities

and temperatures are valid for the lower layers of the flow only A clear

dependence on the increased heating can be observed for both the veloc¬

ity and the temperature This happens due to the larger mass-flow rate

from the Dewar that increases the driving potential and therefore the ve¬

locity of the cloud while decreasing the temperature The trend is clear

for the temperature, but one data point from the velocity measurements

appears too low This can be explained by the larger relative error of

the velocity measurements compared to the measured temperatures

The behavior of velocity and temperature at different distances from

280 r-

278-

276-

274-

272-

=-270-

268-

266-

264-

262-

260-

46 Results

0 26

0 25

0 24

j;0 23f

I 0 22

0 21

02

i*f*L.

274

273

272

271

^270

« 269

I 268

267

266

265

264,0

(a) Bulk velocity dependent on time (b) Temperature dependent on time

Figure Jh15: Bulk velocity and temperature as a function of time for a singlecontinuous-release experiment. The data represent the velocity and tempera¬

ture of experiment 2 in Figure 4.14.

0 28

0 27

0 26

0 25

0 24

0 23

0 22

°2lk)0 2000 2500

P[W]3000

(a) Velocity

78

76

74

72

70

68

66

64

62

1500 2000 2500

P[W]

(b) Temperature

Figure 4-16: Velocity and temperature at position 2 (see Fig. 4-1) as a function

of the applied electrical heating in the dewar.

4.4 Optical Velocity Measurements: Continuous Release 47

the source is shown in Figure 4 17 Each data point represents one ex¬

periment conducted under the same release conditions While moving

along the channel, the temperature of the cloud increases linearly This

can be understood easily, because heat transfer from the floor and the

ambient air into the cloud are responsible for this increase (Kunsch &

Fannelop (1995), Kunsch (1997)) The behavior of the velocity is not

as clear as the behavior of the temperature, although a small increase is

indicated by the data The reason for the increase of the velocity cannot

be found in the melting of the ice-particles at the interface between the

lower layers of the cloud and the ambient air (see Figure 4 2), althoughthe velocity is normally slightly smaller than the average velocity of the

top-hat profile at the interface (Figure 4 13(a) If this part is not vi¬

sualized anymore due to the lack of seeding, the averaging would yield

slightly larger velocities This effect is already taken into account by

assuming the average velocity being the median value of the profile, be¬

cause the interface only influences the few uppermost velocity vectors of

the profile (Figure 4 11(a)) Furthermore, measurements with additional

talcum seeding show the same increase in the velocity Another cause

can be the slight inclination of the channel This is very small comparedto the length of the channel, but an influence on the velocity of the cloud

cannot be ruled out

-i , , , 1 2801 . . . .

1

278-

276-

274-4

-

272- *

2270- »

"268*

266 -

264-

262-

_j i i i 1260 ' ' ' '

34567234567

x[m] X [m]

(a) Velocity (b) Temperature

Figure 4 17 Velocity and temperature as a function of the distance from the

release chamber The distances correspond to the positions 1, 2, 3 and 4 (seeFig 4 1)

0 27-

0 26-

0 25-

^0 24-

=0 23-

0 22-

021 -

02L

48 Results

The measurements presented so far did not show the full picture of

the velocity profile, because the additional seeding was not employedFor the following measurements, talcum powder is introduced into the

channel upstream of the laser-light sheet to visualize the normally un¬

seeded parts of the flow In Figure 4 18, velocity profiles within the

complete field of view are shown for position 1 and 3 in the channel

The profiles are generated by averaging three consecutive experiments

containing 150 2D velocity vector maps each Therefore, each vector

contains up to 26100 correlation maps, in the best case where dropoutsare absent and no data points are rejected due to low correlation val¬

ues The actual number depends on the experimental conditions that

are mostly affected by the opacity of the flow The «-velocity in Fig¬ure 4 18(a) and 4 18(c) has a nearly constant value above the height of

0 2m The height of the boundary between the cryogenic flow and the

ambient air can be identified by temperature measurements Accordingto Figure 4 19, this boundary lies approximately at 0 2 m, l e where

room temperature prevails The most likely explanation for the non-

vamshmg «-velocity is the movement of the seeding itself Because the

seeding is introduced into the flow upstream of the light-sheet, its veloc¬

ity has to be nonzero and a non-vanishing horizontal momentum cannot

be ruled out This velocity not only depends on the flow conditions of

the ambient air but also on the dispersion method Variations between

measurements conducted under similar experimental conditions validate

this assumption The velocity outside the cryogenic flow is therefore the

result of the combined influence of the existing ambient air flow and the

dispersion process of the talcum powder The same explanation holds

true for the «-component of the velocity (see Figure 4 18(b) and 4 18(d))The dispersion process is clearly the dominant factor in this case, be¬

cause a global «-velocity should be very small in the density-driven flow

Additionally, the talcum powder is dispersed one meter above the flow

Hence, it should have a negative (pointing downward) velocity in the

«-direction because of the chosen frame of reference (Figure 4 1)The mass-flow rate m at the two different positions in the field of

view can be calculated by

m = w p(y) «(«) dy (4 2)Jo

with the density p, the height h, the width of the channel w and the

velocity « in x-direction The density can be obtained from the temper-

4.4 Optical Velocity Measurements: Continuous Release 49

- Volocity iny-diroction |

-01 -0 05 0 0 05 0 1 0 15 0 2 0 25 0 3

Velocity [m/s]

-0 25 -0 2-0 15-0 1-0 05 0 0 05 0 1 0 1

VQlocity [m/s]

(a) Position 1; u-velocity (b) Position 1; v-velocity

04n=

0 35-

03-

^0 25-

5)°2"

"

0 15-

01 -

- Volocity iny-diroction

-01 -0 05 0 0 05 0 1 0 15 0 2 0 25 0 3

Velocity [m/s]

-0 25 -0 2 -0 15 -0 1-0 05 0 0 05 0 1 0 15

Volocity [m/s]

(c) Position 3; u-velocity (d) Position 3; v-velocity

Figure Jh18: Global velocity profile for the x- and y-direction taken at two

positions (see Fig. Jhl) in the channel. Each profile is averaged over three

consecutive experiments.

50 Results

300

295

290

^ 285

280

275

"'"0 50 100 150 200 250

Height [mm]

Figure 4 19 Temperature distribution at four positions taken at the same time

as the velocities in Figure 4 18 The points at zero height are acquired with

probes flush mounted on the floor along the channel

ature profiles in Figure 4 19 and the perfect gas equation (A 28) This

yields for position 1 a mass-flow rate of m\ « 45 g/s and for position 3

of rri2 ~ 51 g/s The increase in the mass flow between the two positions

can most likely be explained by air entrainment

4.4.2 Spreading over a Forward Facing Step

The second configuration for the continuous-release setup incorporates

a forward facing step (FFS) This serves to illustrate the applicabilityof the implemented measurement techniques in a more complicated flow

configuration

A typical picture of a flow over a forward facing step is depictedin Figure 4 20(a) This image is generated by averaging the individual

frames acquired for the velocity measurements It represents the aver¬

age of 300 images which corresponds to a ten second interval The im¬

ages were taken during an experiment without additional seeding The

separation bubble can be seen clearly at the leading edge of the step

Due to the increased temperature, no seeding is present inside this bub-

Position 1

Position 1 Floor Probe

Position 2

Position 2 Floor Probe

Position 3

Position 3 Floor Probe

Position 4

Position 4 Floor Probe

4.4 Optical Velocity Measurements: Continuous Release 51

ble and velocity measurements are not possible there with the available

techniques A surface plot of the absolute velocity corresponding to Fig¬ure 4 20(a) is shown in Figure 4 20(b) Comparing Figure 4 20(a) and

4 20(b) shows several interesting features The lack of data inside the

separation bubble is clearly visible The expected very small velocity in

the recirculation region in front of the step is also observable Relatively

high velocities are encountered at the leading edge of the step, where the

«-velocity is larger than in most other parts of the flow Above the step,

the flow contracts and accelerates for reasons of continuity The behav¬

ior of the two components of the velocity can be observed in detail in

Figure 4 21 for the x-component (Figure 4 21(a)) and the «-component

(Figure 4 21(b)) Here, the recirculation region, the acceleration and the

contraction of the flow can be identified from the «-velocity vector maps

The change in direction of the «-velocity at the leading edge of the step

is also clearly visible

To determine the influence of the forward facing step on the flow,measurements are carried out closer to the release chamber, l e up¬

stream and directly at the step Because the information about the full

velocity profile in the field of view is important, three positions are inves¬

tigated with the additional talcum seeding The first two positions are

located upstream of the FFS and the last one is located exactly at the

step The results for the upstream positions (position 1 and 2) are shown

in Figure 4 22 and for the position at the step (position 3) in Figure 4 23

The velocity profiles presented for position 3 consist of averages of two

separate experiments, l e two different releases carried out under the

same conditions

The most striking feature visible in Figure 4 22 is the velocity defect

(called "dip" in what follows) between the height of 15 cm and 25 cm for

both positions It is noteworthy here that the velocity above this "dip"in the profiles is higher than the velocity in the case of unobstructed

spreading (see Figure 4 18) This shape can be observed reproducibly at

positions 1 and 2 and is visible until close to the step At position 3 the

"dip" weakens due to the influence of the step on the velocity profileAbove the step, the expected behavior of contraction and acceleration

can be observed This can clearly be deduced from the «-velocity profileand to a lesser extent from the profile of the «-velocity To get a better

overview of what happens, the x-component and the «-component of the

velocities at all three positions are shown in a combined plot in Figures4 24 and 4 25 respectively For heights above 25 cm an acceleration

52 Results

Q.25

's 0.15

i 0,1

0.05

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Width [m]

(a) Average image of a continuous-release experiment over

the FFS.

Absolute velocity [m/s]

0.05 0 1 0.15 0.2 0.25 0 3 0 35

Width [m]

(b) Surface plot of the absolute velocity over the FFS. This

plot corresponds to the image in Figure 4.20(a).

Figure 4-20: Average image and absolute velocities of the flow.

4.4 Optical Velocity Measurements: Continuous Release 53

04

0 35

03

0 25

: 02

0 15

0 1

0 05

0-0 05 0 0 05 0 1 0 15 0 2 0 25 0 3 0 35

Width [m]

(a) Position 3; «-velocity

04

0 35

03

0 25

b,02

0 15

0 1

0 05

-0 05 0 0 05 0 1 0 15 0 2 0 25 0 3 0 35

Width [m]

(b) Position 3; a-velocity

Figure 4-21: Velocity profiles for the x- and y-direction at position 3 (see Fig.

4-1) taken without additional talcum seeding. Reference velocities with \u\ =

0.3 m/s and \v\ =0.1 m/s respectively are depicted on top of each figure.

54 Results

Velocity in x-direction |"

Volocity I "i y-diroction

0 35

03

0 25

02

015

01

0 05

-01 -0 05 0 0 05 0 1 0 15 0 2 0 25 0 3

Velocity [m/s]

-025 -02 -015 -01 -005 0 0 05 01 015

Volocity [m/s]

(a) Position 1; u-velocity (b) Position 1; v-velocity

Velocity in x-direction | - Volocity in y-diroction |

-01 -0 05 0 0 05 0 1 0 15 0 2 0 25 0 3

Velocity [m/s]

-025 -02 -015 -01 -005 0 0 05 01 015

Volocity [m/s]

(c) Position 2; ^-velocity (d) Position 2; v-velocity

Figure Jh22: Velocity profiles in the x- and y-direction taken at position 1 and

position 2 (see Fig. 4.1). The forward, facing step is located downstream at

position 3.

4.4 Optical Velocity Measurements: Continuous Release 55

(a) Position 3; «-velocity

0 4r

0 BO¬

OS¬

TS-

,02-

0 15-

0 1 -

0 05^ i

0

= 1 il

-9*—>.—> —>,—>,—>

01 02 03 04 05 06 07

Width [ml

(b) Position 3; a-velocity

Figure 4-23: Velocity profiles for the x- and y-direction at position 3 (see Fig.

4-1) taken with additional talcum seeding. Reference velocities with \u\ = 0.3

m/s and \v\ =0.1 m/s respectively are depicted on top of each figure.

56 Results

between position 1 (x = 2 5) m and position 2 (x = 4 7 m) can be

observed for the x-component of the velocities At heights below 15 cm,

the «-velocities are nearly constant until close to the recirculation region

at the forward facing step The velocities below 15 cm are obtained

from the lower layers of the cloud seeded with ice-particles For the

«-component, no such clear trend is observable

The presentation of the velocity maps m Figures 4 24 and 4 25 can

be improved by interpolating the data with a least-squares collocation

scheme (Montz (1989), Niemeier (2002)) The result of such a calcula¬

tion is shown m Figure 4 26 with a chosen signal-to-noise ration of 0 5

and a spatial correlation length of 3 m referred to the x-axis The ve¬

locity defect at midheight upstream of the forward facing step becomes

more clear m this presentation Additionally, the disappearance of this

"dip" at the step becomes more distinct For a detailed description of

the least-squares collocation scheme refer to appendix A 4

The temperature profiles for the three positions measured with ther¬

mocouples are shown m Figure 4 27 The probes at position 3 are located

on top of the step, so they are effectively 10 cm higher than the probesat position 1 and 2 When comparing the temperature profiles with the

profiles taken during unobstructed spreading, the general shape of the

profiles does not change The temperatures are slightly lower upstreamof the forward facing step and room temperature is reached at larger

heights compared to the spreading without obstructions

At the present time, no theoretical explanation exists for the behavior

of the flow upstream of the step The shape of the velocity profile cannot

be the result of unsteady effects, because measurements conducted at

different times showed the same qualitative results Furthermore, all the

results are obtained by averaging the data over a time-interval of ten

seconds The mass-flow rate at the different positions can be calculated

with equation (4 2) This yields for position 1 a mass-flow rate of mi «

30 g/s, for position 2 of m,2 « 42 g/s and for position 3 on top of the step

a mass flow of m% « 60 g/s The ratio of the mass-flow rates between

two neighboring positions is approximately

Wl^

W2^ q 7

with a nearly constant distance between the adjacent positions of about

one meter This constant ratio of the mass-flow rates of two neighboring

positions could be caused by large scale flow phenomena An indication

4.4 Optical Velocity Measurements: Continuous Release 57

[lu] H|ß!8H

Figure 4 24 Overview over flow velocities in the x-direction along the channel

for the setup incorporating the forward facing step Reference velocities with

«|=03 m/s are depicted on top of the figure

58 Results

[LU] 1U.6J8H

Figure 4 25 Overview over flow velocities in the y-direction along the channel

for the setup incorporating the forward facing step Reference velocities with

\v\ = 0 05 m/s are depicted on top of the figure

4.4 Optical Velocity Measurements: Continuous Release 59

iiiitiuiDnnillff/ffml.

nmmmmmmmm)

mniimiiiiirtmmrrmtmmiiiifi

mmtiHimmmmtmrmmrmr.

nm\niimffimmmrrnmnnur.

\mummmmimmmtm

öCO

öc\j

ö

»iiinitiiimririmmiiuinr

mntimmmmimm

mniHimmmiHi

«miiiiimtttmirimiin

nttiuiiiiitmmmmim

mtmmmmmmn

ntiimiitiimmimm

tnnimiitimmnmmi

mtnmiiimuummwi

LO

CD

LO

c6

CO

LO

c\i

[lu] 1U.6J8H

Figure J^.26: Interpolated velocity vector map with the velocities taken from

Figures 4-24 and 4-25. The interpolated data are calculated with a least-squarescollocation scheme. The signal-to-noise ration is 0.5 and the correlation length

is 3 to.

60 Results

300

295

290

_285

280

275

270

0 50 100 150 200 250

Height [mm]

Figure 4 %7 Temperature distribution corresponding to the measurements

shown in Figure 4 %% and 4 %3 Position 3 (see Fig 4 1) ls located on top

of the step

for this phenomenon can be deduced from the structures in the velocity

profiles in Figure 4 24 Unfortunately, the available «-velocities are not

reliable enough to serve as an indicator for this entrainment process

This uncertainty in the «-velocity is caused by the way the additional

seeding is introduced into the flow and cannot easily be eliminated

4.5 Optical Velocity Measurements: Sudden Release

The data from the sudden-release setup are more difficult to analyze than

those from the setup for continuous release, because it is not possible to

average to such a large extent The reason is the unsteady nature of the

flow Therefore, the data presented are more noisy than in the previous

section Up to three consecutive velocity vector maps are averaged to

obtain results with reasonable quality Hence, the presented velocities

are averaged over a time interval of 0 2 seconds

In Figure 4 28, the temperature measured with thermocouples is

shown as a function of time for the five measurement positions in the

channel The cloud is released from the evaporation chamber at t = 0

4.5 Optical Velocity Measurements: Sudden Release 61

Figure 4-28: Temperature as a function of time for five positions (see Fig. 4-1)in the channel. The thermocouples are positioned two centimeters above the

floor of the channel.

s and then propagates along the channel. The presented temperatures

are acquired with five probes mounted two centimeters above the floor

of the channel. With these temperatures, it is possible to deduce the

frontal speed of the cloud via the arrival time at each known position.This results in a frontal speed of Uf = 0.5 m/s for the chosen setup. The

velocities acquired with ICV are then compared to this result.

In Figure 4.29, a snapshot of a suddenly released heavy-gas cloud

is shown. The amount of liquid nitrogen and the evaporation time are

chosen to allow the formation of distinct structures in the cloud for im¬

age correlation purposes. This is even more important here than in the

continuous-release case, because it is not possible to average many con¬

secutive correlation maps as already mentioned. The results presentedare derived from similar pictures, although the shape of the frontal struc¬

ture can vary for different experiments. The most prominent feature

always observed in the images is the foremost point or "nose" which is

somewhat higher than the floor of the channel (Simpson, 1997). In con¬

trast to the change of the general shape, the velocity and the temperatureof the cloud are well reproducible.

The velocity profile in the frontal region is measured at three posi¬tions. The first two are located on the horizontal part of the channel

62 Results

(position 1 and 3) and the third position is located at the backward

facing step (position 5) (see Fig. 4.1).The velocities presented in this section are deduced from the images

with a size of the interrogation window of 32 by 32 pixel. In combination

with an overlap of 75% of the adjacent interrogation windows, each cor¬

relation map contains up to 120 data points in the x-direction and up to

123 data points in the «-direction. The correlations maps are averaged

according to Meinhart et al. (2000) where necessary.

Figure 4-29: Snapshot of the frontal structure of a suddenly released cloud.

4.5.1 Spreading over a Horizontal Surface

The velocity profile for position 1 is shown in Figure 4.30. This 2D pro¬

file is the averaged result of three consecutive velocity maps. It is clearlyvisible that the quality of the data in Figure 4.30 is inferior comparedto the data from the continuous-release experiments. More detailed in¬

formation can be gained from the scatter plot in Figure 4.31(a) and the

histograms of the velocities in Figure 4.31(b) and 4.31(c). The bulk ve¬

locity in x-direction of the cloud can be obtained from Figure 4.31(b).A detailed analysis of the histogram with a cluster-analysis algorithm1

1Matlab fuzzy "c-means" algorithm

4.5 Optical Velocity Measurements: Sudden Release 63

(Bezdek, 1981) results in a bulk-velocity of ut, « 0 51 m/s This is in

good agreement with the frontal velocity of «y = 0 5 m/s deduced from

the thermocouple measurements (Figure 4 28) The «-component of the

velocity (Figure 4 31(c)) is biased slightly to positive velocities, l e up¬

ward movement in the chosen frame of reference (Figure 4 1) These

velocity vectors are located mostly at the upper left region in the inter¬

face to the ambient air (Figure 4 30) In the same area of the plot, the

«-velocity has partly a negative component Those velocities could be

an indication for the presence of the strong frontal vortex that is formed

due to the slumping motion of the heavy-gas cloud during the instan¬

taneous release (Britter, 1989) Unfortunately, this vorticity cannot be

analyzed due to the insufficient quality of the data

04

0 35

03

,0 25

.°2

015

01

0 05

00 0 05 0 1 0 15 0 2 0 25 0 3 0 35

Width [m]

Figure 4 30 Velocity vector map taken at position 1 (see Fig 4 1)

In Figure 4 32, the velocity data for position 3 are shown The ve¬

locities are obtained again by the averaging of three consecutive maps

At this position, the quality of the data in the vector map and the his¬

tograms is higher compared to position 1 The reason lies in better

visible textures in the correlated images From Figure 4 33(b), the bulk

velocity of the cloud can be determined to be ut, « 0 49 m/s which

agrees well with the frontal velocity The «-component is slightly biased

to positive velocities as observed at position 1 The x-component of the

64 Results

05-

~:ßiWr:

-0 5-

-1 5L-1 5 -0 5 0 0 5

u-Velocity [m/s]1 5

(a) Scatter plot of v- against u-velocity

(b) u-Velocity (c) v-Velocity

Figure 4 31 Scatter plot of the velocity (Figure 4 31(a)) and corresponding

histograms of the x- and y-components of the velocities (Figure 4 31(b) and

4 31 (c)) at position 1 (see Fig 4 1)

4.5 Optical Velocity Measurements: Sudden Release 65

velocity has also negative values in the same region as the «-velocityThis could again be caused by the vortex in the frontal region The

existence of the vortex in the frontal region is supported by the scatter

plot of the velocities in Figure 4 33(a) This velocity distribution shows

a pattern that is most likely generated by a vortex in the field of view,

l e a frontal vortex

04

0 35

03

„0 25

E,

| 02

CD

015

01

0 05

"0 0 05 0 1 0 15 0 2 0 25 0 3 0 35

Width [m]

Figure 4 32 Velocity vector map taken at position 3 (see Fig 4 1)

With the available velocity vector maps it is possible to calculate the

time dependence of the bulk-velocity in the field of view This can be

done most effectively with the already mentioned cluster analysis of the

histograms of the velocity maps In Figure 4 34, the histograms of the

velocities as a function of time are shown for position 1 and 3 These

data are then analyzed which results in several clusters with the largest

being the bulk velocity The result of this analysis is shown in Figure4 35 for positions 1 and 3 At position 1 the velocity is slightly higher

compared to position 3 and shows a small increase over time The veloc¬

ity at position 3 shows a decreasing behavior Because it is not possibleto measure the velocity maps simultaneously at two positions duringone experiment, these different magnitudes in the velocities are maybecaused by slight differences between the evaporation processes of the liq¬uid nitrogen The errorbars in Figure 4 35 are computed with equation

66 Results

05-

-0 5-

-1 5L-1 5 -0 5 0 0 5

u-Velocity [m/s]1 5

(a) Scatter plot of v- against u-velocity

15 -1 -0 5 0 0 5 1 15

u-Velocity [m/s]-1 -0 5 0 0 5 1

v-Velocity [m/s]

(b) u-Velocity (c) v-Velocity

Figure 4 33 Scatter plot of the velocity (Figure 4 33(a)) and corresponding

histograms of the x- and y-components of the velocities (Figure 4 33(b) and

4 33(c)) at position 3 (see Fig 4 1)

4.5 Optical Velocity Measurements: Sudden Release 67

(4.1) on page 44. Here, the standard deviation is simply calculated from

the variance of the bulk velocities. Although unusual, this approach is

somewhat justified by the large scatter of up to 10% of otherwise stronglycorrelated consecutive bulk velocities (Figure 4.35). The relative error

resulting from this approach is öu « 8.6%, approximately twice as largeas the relative error for the setup for continuous release.

15 105005115 15105005115

u Velocity [m/s] u Velocity [m/s]

(a) Position 1 (b) Position 3

Figure 4-34'- Histograms of the velocity as a function of time at position 1 and

3 taken from velocity maps like the ones depicted in Figures 4-30 and 4-32.

4.5.2 Spreading across a Backward Facing Step

A picture of the suddenly released cloud at the backward facing step

(position 5) is shown in Figure 4.36. The detachment of the cloud from

the floor of the channel can be clearly seen. A separation vortex is then

formed which rotates in the clockwise direction. This is the oppositedirection of the vortex formed due to the slumping motion during the

instantaneous release phase. Unfortunately, the evolution of the vortic¬

ity along the channel can not be visualized, because the initial vorticitycould not be analyzed as explained in the previous paragraph. The re¬

sulting velocity vector map at position 5 is shown in Figure 4.37 with

the corresponding scatter plot (Figure 4.38(a)) and the histograms (Fig¬ure 4.38(b) and 4.38(c)). The step in Figure 4.37 has a height of 20

centimeters. This is the real height of the step which is not fully visible

68 Results

Wmm0 05 1 15 2 25 3

Time [s]

(a) Position 1 (b) Position 3

Figure 4 35 Bulk velocity as a function of time for positions 1 and 3 (see Fig

4 1) computed from the histograms in Figure 4 34

in Figure 4 36 Figure 4 37 provides indication for a stagnation point at

approximately x « 0 16 m The vortex visible in Figure 4 36 cannot be

reproduced completely in the velocity field because of weaker textures

in the image and due to the used correlation algorithm The influence

of the backward facing step on the velocity distribution in the cloud can

also be analyzed with the histograms in Figure 4 38(b) and 4 38(c)In the histogram for the «-velocity, two peaks are observed The largerone represents the bulk-velocity with ut, « 0 5 m/s This is in good

agreement with the frontal speed deduced from the thermocouple mea¬

surements The peak at zero velocity represents the flow field in the

recirculation region where the bulk-velocity and the local velocity of the

vortex cancel out each other In the histogram of the «-velocity (Figure4 38(c)), a similar pattern with two peaks can be observed The larger

peak at zero velocity represents again the region where the velocity of

the flow upstream of the step prevails The second peak at « « —0 5

m/s represents the downward movement in the recirculation region

4.5.3 Sudden Release with Talcum Powder Seeding

Until now, only the region of the flow field seeded naturally with îce-

particles were analyzed Therefore, measurements are conducted with

additional talcum seeding to visualize the ambient air flow This is more

4.5 Optical Velocity Measurements: Sudden Release 69

0.2

Width [m]

Figure 4-36: Snapshot of a suddenly released cloud taken at the backward facing

step (position 5 (see Fig. 4-1))-

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Width [m]

Figure 4-37: Velocity vector map taken at the backward facing step (position 5

(see Fig. 4.1)).

70 Results

05

-0 5

-1 5L-1 5 -0 5 0 0 5

u-Velocity [m/s]1 5

(a) Scatter plot of v- against u-velocity

(b) u-Velocity (c) v-Velocity

Figure 4 38 Scatter plot of the velocity (Figure 4 38(a)) and corresponding

histograms of the x- and y-components of the velocities (Figure 4 38(b) and

4 38(c)) at position 5 (see Fig 4 1)

4.5 Optical Velocity Measurements: Sudden Release 71

difficult here than in the continuous-release case because of the short time

it takes the heavy-gas cloud to cross the field of view of the camera. The

measurements are carried out only at position 3. In Figure 4.39, the

complete velocity vector map in the field of view is shown. The regionof the image covered by the visible heavy-gas cloud is represented by the

large velocities in x-direction. In the part seeded with talcum powder,

0 4 1 1 1 1 1 1 1 1

0 35-,

03-,

;

„

0 25 -

£ 02-

'

CD . _ . .

015: : : : : : : :—

:

01 -

0 051

0 0 05 0 1 0 15 0 2 0 25 0 3 0 35

Width [m]

Figure 4-39: Velocity vector map taken at position 3 (see Fig. 4-1) with addi¬

tional talcum seeding.

the particles move only upward. The most likely explanation is that the

ambient air is pushed upward by the approaching front. The different

regions in the velocity vector map shown in Figure 4.39 can be analyzedin more detail in Figure 4.40. The scatter plot of the «- against the

«-velocity in Figure 4.40(a) shows two separate distributions. A cluster

analysis shows that one distribution is located around « « 0.46 m/s and

« « 0.04 m/s and represents the propagating cryogenic cloud with a

bulk-velocity of ut, « 0.5 m/s. The other one is located around « « 0.02

m/s and « « 0.2 m/s and represents the ambient air flow visualized

by the talcum-powder seeding. Both regions are also distinguishable in

Figure 4.40(b). The additional seeding has a «-velocity of less than 0.05

m/s and a «-velocity that points upward. This upward movement is

caused by the approaching cloud as is further supported by Figure 4.41.

72 Results

04

02

£. 0

^ -0 2

-0 4

-0 6

05 1

u-Velocity [m/s]

1 5

(a) Scatter plot of v- against u-velocity

-0 6 -0 4 -0 2

v-Velocity [m/s]

(b) u-Velocity (c) v-Velocity

Figure 4 40 Scatter plot of the velocity (Figure 4 40(a)) and corresponding

histograms of the x- and y-components of the velocities (Figure 4 40(b) and

4 40(c)) at position 3 (see Fig 4 1)

4.5 Optical Velocity Measurements: Sudden Release 73

110-

100-

90-

« 80-

I 70-

8 60-

05 0 05 1 15 -08-06-04-02 0 02 04 06

u Velocity [m s] V-Veloclty [m s]

(a) u-Velocity (b) v-Velocity

Figure 4 41 Histograms of the velocity distribution in the field of view beforethe cloud arrives at position 3 (see Fig 4 1)

Here, the data represent the flow m the field of view approximately one

second before the cryogenic cloud reaches the measurement position

The movement of the ambient air is nearly zero except for a very small

velocity m the positive x- and «-directions These velocities are most

likely caused by the way the particles are introduced into the channel

When comparing the bulk-velocities measured under similar experi¬

mental conditions during the setup for sudden release with and without

additional talcum seeding, the agreement is quite good In case with¬

out the additional seeding, the bulk-velocity is u\, « 0 49 (Figure 4 33

and m case with additional seeding it is u\, « 0 46 (Figure 4 40 This

difference is small enough to be explained by the measurement error of

approximately 9%

Peak-Locking

Several scatter plots of the velocities show some form of regular cluster¬

ing This can be observed m Figure 4 31(a) and 4 38(a) The reason

is presumably not a consequence of peak-locking (Raffel et al, 1998),because the regular patterns do not appear all the time or at the char¬

acteristic spacing ±n/2 pixel For example m Figure 4 40(a), the visible

clusters represent two separate regions with different velocities Addi¬

tionally, the velocities measured during the continuous release do not

45-

40-

Ï30-

l 25-

L

74 Results

show any traits associated with peak-locking

4.6 Optical Density Measurements (BOS)

In this section, the 2D temperature distribution will be investigated for

three different experimental setups The first setup deals with the con¬

tinuous release of the cloud and subsequent spreading over the horizontal

surface The second setup uses the forward facing step in combination

with the continuous-release case The last configuration investigated is

the sudden-release setup All the measurements are conducted at posi¬

tion 4 (see Figure 4 1) This position was chosen because the best optical

accessibility exists here for the background oriented Schlieren measure¬

ments During the experiments, the density of the ice-particles in the

cloud is an important parameter, because the structured background im¬

age is visualized across the width of the channel (see Figure 3 8 on page

25) Therefore, the density of the ice-particles should be reduced as far

as possible with the measures described in section 4 1

4.6.1 Continuous Release over a Horizontal Surface

The first setup investigated is the generic case with the continuous

spreading of the cryogenic gas cloud on the horizontal surface in the

channel In Figure 4 42, a typical image pair for a background oriented

Schlieren (BOS) measurement is shown These images are not averagedas are all the data presented in this section, because there is nearly no

difference in the quality of the data between averaged and nonaveragedmeasurements The calibration image is depicted in Figure 4 42(a) and

the image distorted by the cloud can be seen in Figure 4 42(b) The

structured background visible in both images is a point mask generatedwith a Sobol algorithm (Press et al, 1997) The two temperatures needed

for the calibration are acquired with thermocouples They are located on

the left edge (ordinate axis) of the images in Figure 4 42 On each side of

the field of view, nine thermocouples are placed at varying heights Onlytwo of the eighteen thermocouples are used for the calibration, the other

temperatures are used to verify the calculated temperatures locally It

should be noted that two calibration images taken before and after the

experiment are necessary, because changes of the optical alignment can

be detected in this way This is required because the measured shifts

in the dot pattern are very small and even weak vibrations caused by

4.6 Optical Density Measurements (BOS) 75

^S®SÄ^pÄ^^c^f#Ä#iS

^r^^;^^^^^^"âTîi:^t^^ïpfr^^«v/.j-v^"^srw;'.^*v^

aK^;.>"ô^:^Ü.1b

WiiM^$S&Êl0^fiK^¥SÊ00.1 ^^^Î^^^B^Sft

0.05 ^^lÉ$l^ife^^ï^^^^S^lî^|^^A|

i^^^^É^S^^^^^^^^S^^^^^^^

0.25

(a) Without cloud (b) With cloud

Figure 4-4%'- Typical images of a BOS measurement. The left picture is the

calibration image.

the laboratory's' air conditioning apparatus or other sources can create

displacement vectors in the same order of magnitude as the phase objectin the subsequent evaluation.

In Figure 4.43, the result of the correlation of the images in Figure4.42 is shown. The background image is shifted due to the influence of

the phase object. Particularly large gradients can be observed in the

mixing region between the lower layers of the cryogenic flow and the

ambient air. The corresponding displacement vector data (Figure 4.43)are then integrated with the finite difference approximation scheme to

derive the index of refraction n(x,y) in the field of view (see appendix

A.3.2). The temperature field can finally be calculated with equation

(A.31)

T(x,y)ci -n(x,y) + c2

with the constants defined by

ci =

1

Tw

nw

and C2 =

Tuc\nw

The subscript a stands for ambient air conditions and W for the condi¬

tions close to the wall. In Figure 4.44(a), the resulting temperatures cal¬

ibrated with the data from the thermocouple measurements are shown.

76 Results

0.25-

0.2-

E""0.15-^z

CT

0

0.05 -

0L _J , 1_ U ,

0 0.05 0.1 0.15 0.2 0.25

Width [m]

Figure 4-43: Displacement of the structured background image due to the phase

object.

The expected increase of the temperature along the x- and «-directions is

clearly visible in Figure 4.44(a) and even more clearly in Figure 4.44(b).Here, the temperature is shown at the left and right edges of Figure

4.44(a) together with the thermocouple measurements. The agreement

between both methods is very good. This is more important for the right

edge of the image, because both thermocouples used for the calibration

are located on the left, upstream edge of the image. Therefore, a good

agreement between both methods can be expected on the left hand side.

The errors shown in Figure 4.44(b) represent the errors calculated in sec¬

tion 4.4.1. They are valid for all measurements presented in this section

(section 4.6).

In Figure 4.45, the temperatures are calculated for the same experi¬ment (see Figure 4.42) with the Poisson solver (see appendix A.3.1). The

results look very similar to Figure 4.44, although the temperatures at

the top agree slightly better for the calculation with the Poisson solver.

The reason for this difference is most likely the different implementationof the boundary conditions. The Poisson solver uses only the normal

components of the measured data for the boundary conditions whereas

the finite difference scheme uses the full information. Until now, it is

not possible to decide which algorithm performs better. In order to

4.6 Optical Density Measurements (BOS) 77

better identify the relative advantages and disadvantages of the two al¬

gorithms, the more complicated geometry with the forward facing step

is investigated with BOS

4.6.2 Continuous Release over a Forward Facing Step

First, the field of view is positioned on top of the step In Figure 4 46,

one image taken during the experiment is shown The expected separa¬

tion bubble can be identified as in Figure 4 20(a) The results for the

temperature field calculated with the finite difference approximation and

the Poisson solver are shown in Figure 4 47 and Figure 4 48 respectively

Here, the separation bubble can also be identified although not as clearlyas expected Both the finite difference method and the Poisson solver

produce similar results, but the agreement between the calculated tem¬

peratures and the thermocouple measurements is not as good as in the

previous setup The Poisson solver performs again slightly better than

the finite difference method when comparing the BOS result with the

thermocouple measurements

A more challenging geometry in the field of view incorporates the full

forward facing step with the recirculation region The analysis of this

setup turned out to be more problematic One such example is shown in

Figure 4 49 Here, no quantitative global agreement could be achieved

between the thermocouple measurements and the computed tempera¬

tures (Figure 4 49(b)) on the right hand side Only the left hand side

agrees reasonably well which is also the side where the reference temper¬

atures were inserted Possibly, the large temperature gradients in the

streamwise direction are responsible for the increasing deviations Due

to perspective distortions, different parts in the streamwise direction are

averaged which can be problematic with large gradients By subtractingthe mean gradient in the streamwise direction from the measured data,the results can be improved but inconsistencies remain Furthermore,the subtraction is not physically justifiable and therefore not shown

The only reliable approach for the acquisition of correct results thus ap¬

pears to be the careful selection of the field of view in order to obtain

simple geometries as shown in Figure 4 47 and 4 48

78 Results

10 15 20 25

Width [cm]

(a) 2D temperature profile in the field of view

over a horizontal surface

S5285-

- - Left Edge—— Right Edge-+- Right Thermocouples-^ Left Thermocouples

10 15 20

Height [cm]

(b) Temperature distribution over the heightat the left and right edge of Figure 4.44(a)together with thermocouple measurements

Figure 4-44: Temperature in the field of view at position 4 (see Fig. 4-1) ln

comparison with thermocouple measurements. The temperatures are calculated

with the finite difference approximation method and the probe data are averagedover 10s.

4.6 Optical Density Measurements (BOS) 79

10 15 20 25

Width [cm]

(a) 2D temperature profile in the field of view

over a horizontal surface

- - Left Edge— Right Edge-^- Right Thermocouples-^ Left Thermocouples

Heigfif[ci 20 25

(b) Temperature distribution over the heightat the left and right edge of Figure 4.45(a) to¬

gether with thermocouple measurements

Figure 4-45: Temperature in the field of view at position 4 (see Fig. 4-1) ln

comparison with thermocouple measurements. The temperatures are calculated

with the Poisson solver and the probe data are averaged over 10s.

80 Results

0 25

02

oj

0 0 05 0 1 015 0 2 0 25

Width [m]

Figure 4-46: Snapshot of the cryogenic cloud at the forward facing step.

4.6.3 Setup for Sudden Release

The last setup investigated is the sudden-release case. Here, the timingis critical, because the image acquisition and the thermocouple measure¬

ments are carried out with independent systems. Therefore, the mea¬

surements have to be synchronized afterwards. An example of a suddenlyreleased cloud is shown in Figure 4.29 on page 62. The experiment an¬

alyzed here was carried out under the same conditions as the velocitymeasurements with the sudden-release setup. In Figure 4.50, the results

are shown for one such measurement at position 4 (Figure 4.1). The

surface plot in Figure 4.50(a) shows a continuous increase in tempera¬

ture from inside the cloud to the ambient air. Nearly no temperature

fluctuations can be observed in the cloud that are normally seen in the

time-dependent thermocouple measurements (see Figure 4.50(b)). These

time-dependent fluctuations should be translated into spatial fluctua¬

tions in the 2D measurements, but due to the averaging over the depthof the channel with the BOS technique, none can be observed. This is

confirmed Figure 4.50(b), where the thermocouple measurements show

larger fluctuations than the calculated temperatures. The reason for

these fluctuations is the lack of averaging in time. In the former experi¬ments with the continuous release setup, the temperatures were averagedover ten seconds which is not possible in the sudden-release case. Apartfrom this problem, the agreement between both measurement techniquesis very good as shown in Figure 4.50(b).

4.6 Optical Density Measurements (BOS) 81

(a) 2D temperature profile in the field of view

on top of the FFS.

Edge

ThermocouplesThermocouples

10 15 20

Height [cm]

(b) Temperature at the left and right edge of

Figure 4.47(a)

Figure 4-4^: Temperature in the field of view at position 4 (see Fig. 4-1) ln

comparison with thermocouple measurements. The temperatures are calculated

with the finite difference approximation method and the probe data are averagedover 10s.

82 Results

5 10 15 20 25

Width [cm]

(a) 2D temperature profile in the field of view

on top of the FFS.

300

295

„290

2 285

275

0 5 10 15 20 25 30

Height [cm]

(b) Temperature at the left and right edge of

Figure 4.48(a)

/ /

/ /

/ i-

I

I

ft

/ / '

11.

- - Left Edge/ / — Right Edge

*^£^JJ—h^- Right Thermocouples

"~'~. -* Left Thermocouples

Figure 4-48: Temperature in the field of view at position 4 (see Fig. 4-1) ln

comparison with thermocouple measurements. The temperatures are calculated

with the Poisson solver and the probe data are averaged over 10s.

4.6 Optical Density Measurements (BOS) 83

10 15 20

Width [cm]

(a) 2D temperature profile in the field of view at

the FFS.

310

305

„300

0

S 295

ns

1.290E0

*"285

280

275

- - Left EdgeRight Edge

-^- Right Thermocouples-* Left Thermocouples

fi't't'-TJ10 15 20 25

Height [cm]

(b) Temperature at the left and right edge of

Figure 4.49(a)

Figure 4-49: Temperature in the field of view at position 4 (see Fig. 4-1) ln

comparison with thermocouple measurements. The temperatures are calculated

with the finite difference approximation method and the probe data are averaged

over 10s.

84 Results

10 15

Width [cm]

(a) 2D temperature profile in the field of view

for a sudden release experiment

295 ' 1

v290

0)

2 2850)Q.

£

""280

/

1P

V

275

T

Left EdgeRight EdgeRight ThermocouplesLeft Thermocouples

10 15 20

Height [cm]

(b) Temperature at the left and right edge of

Figure 4.50(a)

Figure 4-50: Temperature in the field of view at position 4 (see Fig. 4-1) m

comparison with thermocouple measurements. The temperatures are calculated

with the finite difference approximation method and the probe data are averaged

over 10s.

Chapter 5

Summary and Conclusion

The results presented in this study show the general possibility to in¬

vestigate the spreading of cryogenic dense-gas clouds with optical meth¬

ods With the applied techniques, the two important parameters velocityand temperature of the propagating clouds could be measured A planar

image velocimetry system and a background oriented Schlieren system

were built up for the determination of the velocities and temperatures

respectively This was accomplished for several release scenarios in the

heavy-gas channel In the context of optical velocity measurements,the flow-visualization of the cryogenic gas flow and of the ambient air

in the interrogation region were realized successfully The velocimetry

system and the Schlieren system allow both to derive instantaneous two-

dimensional data Presently, small scale fluctuations in both velocity and

temperature were not accessible with the optical methods in combina¬

tion with the employed experimental setup For the velocimetry, this

was due to the spatial averaging implied by the ICV algorithm The

synthetic Schlieren method eliminated small scale fluctuations due to its

inherent line-of-sight integration

The seeding needed for the optical velocity measurements was pro¬

duced in a two-step process for first the lower cryogenic gas layer and

second the ambient air The dense-gas flow generated by evaporation of

LN2 is seeded naturally with ice-particles that are formed by nucleation

due to the present humidity of the ambient air This ice-particle seed¬

ing has the advantage of being ubiquitous in the cryogenic flow under

all examined evaporation conditions The disadvantage of this approachis the varying seeding density depending on the presence of open wa¬

ter surfaces in direct contact with the evaporating LN2, the humidityof the air and the used amount of nitrogen For optical access into the

flow, the ice-particle density must not be too high Because the presence

of open water surfaces prohibits optical measurements, uncovered water

surfaces were avoided during the experiments The humidity is very diffi¬

cult to control for large scale laboratory experiments (Figure 3 2 on page

16) Hence, it was only possible to change the seeding density by either

changing the amount of evaporated LN2 or by changing the evaporation

time of the LN2 for both the continuous-release and the sudden-release

86 Summary and Conclusion

setups The visualization of the behavior of the ambient air in the inter¬

rogation region was realized with talcum powder that moves passivelywith the surrounding flow The talcum powder performed better in com¬

parison with neutrally buoyant helium-bubbles and a fog of small water

droplets (Figure 4 11 and 4 12) No problem existed with the control of

the seeding density of the talcum powder during the experiments

The velocities presented are computed from the flow images with

image correlation velocimetry (ICV) Due to the nature of the utilized

seeding, only the textures in the images can be correlated because no

individual particles can be identified It is therefore necessary to utilize

large fields of view and velocity fluctuations at very small scales could

not be identified with this approach

Velocity measurements were conducted for three different setups to

validate the applicability of the implemented diagnostics The first setup

investigated the unobstructed spreading of a continuously released cloud

over a horizontal surface Here, the performance of the applied seedingcould be extensively tested As a result, averaged 2D velocity profiles in

the field of view with a size of 40 cm by 40 cm could be determined for dif¬

ferent positions in the facility (Figure 4 18) This allows, in combination

with thermocouple measurements, the identification of the mass-flow

rate in each interrogation region along the channel The second setup

incorporated a forward facing step that was added to the first setup

At several positions upstream of and directly at the step, the velocity

profiles could be determined The influence of the step on the flow could

be identified in the velocity data at the various measurement positions

(Figure 4 24 and 4 25) An unexpected feature in the velocity profiles

upstream of the step shows a global recirculation caused by the step

This became manifest in a reproducible "dip" in the velocity profile and

an unusual large velocity above it (Figure 4 22) These features are onlyvisible when the additional talcum seeding is employed No explanationcould be found yet in the literature for this phenomenon The last setup

investigated in this context is the sudden release of the heavy-gas cloud

At different distances from the release chamber, the 2D velocity vector

maps were measured (Figure 4 31 and 4 33) Bulk-velocities of the clouds

computed from the velocity maps could be compared successfully to the

velocities derived from the thermocouple measurements In addition,the maps partly show the strong frontal vortex formed by the slumpingmotion of the heavy-gas cloud during the instantaneous release Further¬

more, measurements with the sudden release setup were conducted at a

87

backward facing step Here, the development of the separation vortex

in the recirculation region can be clearly visualized Unfortunately, the

velocity map does not reproduce the vortex completely and the qualityis low This may be improved by applying more sophisticated algorithmswith warping of the interrogation windows for the correlation of the im¬

ages Finally, the influence of the propagating cloud onto the ambient air

could be visualized by employing the additional talcum seeding (Figure4 39)

The temperatures presented in 2D are determined with the back¬

ground oriented Schlieren system, that relies on the measured distor¬

tion of an image by a phase object With a correlation algorithm, the

displacement of the image due the phase object can be calculated and

translated into temperatures Because the image is observed across the

width of the channel, only averaged temperature profiles are obtained

Therefore, no temperature fluctuations can be made accessible with this

method

The background oriented Schlieren system was applied to the three

setups already described in the context of the velocity measurements

In case of the unobstructed spreading of a continuously released cloud,the 2D temperature distribution could be determined with good accu¬

racy This was compared locally with several thermocouples (Figure4 44) When using the system in the more complicated geometry of the

backward facing step, the agreement between BOS and the thermocou¬

ple measurements decreased This decrease depends on the complexityof the geometry in the field of view The investigations with the field

of view positioned on top of the step still produced good results (Figure4 48) When the full step was in the field of view of the camera the

results were poor The reason is most likely the perspective distortion

in the imaging system in combination with the more difficult implemen¬tation of the boundary conditions in this case (Figure 4 49) For the

sudden release setup, the agreement was again very good between the

BOS results and the thermocouple measurements (Figure 4 50) Here

the evaluation algorithm worked reliably due to the simple geometry in

the field of view

88 Summary and Conclusion

5.1 Recommendations for Future Work

In this study, the presented data show mostly velocities and tempera¬

tures averaged over time or space Especially with the optical methods,no small scale fluctuations were accessible in a reasonable setup The

measurement of the concentration of the heavy-gas cloud was also out

of reach with the present diagnostics For a complete description of the

cloud and for later comparison with numerical results, the facility should

be modified In particular, the evaporation process of the liquid nitrogenand the visualization of the flow have to be redesigned Additionally, di¬

agnostics are required to measure the concentration distribution in the

cloud and to obtain better temperature measurements Suggestions will

be made in the following paragraphs

The heavy-gas channel was designed for investigations at a relatively

large scale with thermocouples To make the measurements less cum¬

bersome and more accurate with the optical diagnostics, first the optical

accessibility into the channel should be improved This could be achieved

for instance by installing new transparent side walls in the channel that

allow optical access down to the boundary layer at every measurement

position Currently, this is only possible at few locations in the chan¬

nel Second, the channel should be resized to smaller dimensions This

would even allow measurements with different, more expensive gases like

Argon, because only smaller amounts would be needed In combination

with those gases, the talcum powder could be used as the seeding for

flow visualization

Another issue is the evaporation of the liquid nitrogen To reduce the

ice-particle density or to even remove them completely from the flow, the

evaporation could take place in a closed pipe system This approach was

chosen for the evaporation of liquid hydrogen by Statharas et al (2000)The seeding could then be mixed into the unseeded cloud as needed

An alternative seeding technique could be the use of fluorescent par¬

ticle tracers These tracers would be independently visible from the

ice-particles due to the different spectral response This approach makes

the study of mixing / entrainment processes possible Furthermore, the

diagnostics are technically not too demanding because already standard

or Peltier-cooled cameras are sufficiently sensitive Possible problemswould arise from the contamination of the test section Preliminarymeasurements in this direction with a fluorescent aerosol composed of

fine water droplets mixed with blancophore have been carried out sue-

5.1 Recommendations for Future Work 89

cessfully.

Another, more advanced approach could be the use of fluorescent

gases for the cloud or the ambient gas. Several possibilities for the choice

of the gases exist like NO, acetone or biacetyl. This approach would allow

the application of diagnostics like molecular tagging velocimetry (MTV)(Koochesfahani et al. (2000), Smits & Lim (2000)) for velocimetry and

laser induced fluorescence (LIF) (Miles & Lempert (1997), Miles et al.

(2000)) for concentration measurements. The combined measurement of

fluorescence / phosphorescence effects could be used to study interfacial

phenomena (Hu & Koochesfahani, 2002). Unfortunately, this approachis technically fairly involved due to UV imaging / laser requirements and

the need for intensified cameras to detect the weak optical signals.

6600 6700 6800 6900 7000 7100

Temperature [a u ]

(a) Temperature profile of the floor

of the channel in 2D

(b) Temperature profile from Figure

5.1(a) averaged along the aï-direction

Figure 5.1: Temperature profile of the floor of the channel at the forward facing

step in the continuous release case taken with a infrared camera.

Another interesting technology for temperature measurements are

infrared sensors. With this technology it is possible for instance to mea¬

sure the temperature of the floor of the channel in a two-dimensional

geometry. This could be a complementary method to the BOS tech¬

nique which provides profiles in the x-j/-plane whereas with an infrared

camera profiles in the x-z-plane (see Figure 3.2) can be obtained. This

technique would be mainly useful in steady flows encountered e.g. dur¬

ing the continuously released flows. Preliminary measurements with a

90 Summary and Conclusion

infrared camera in the vicinity of a forward facing step are shown in Fig¬ure 5 1 The camera is placed downstream of the backward facing step

and looks upstream It is possible to identify flow features like the sepa¬

ration bubble with this technique Because the measured temperatures

are dependent on the emissivity of the material, the jump in temperaturebetween the region in front of the step and behind the separation bubble

on top of the step is exaggerated The reason is the different thickness

of the floor of the channel and the additional step placed in the channel

The changes to the setup (especially the evaporation conditions) in

combination with the additional diagnostics would allow for a more de¬

tailed investigation of the influence of the forward facing step on the

global flow features upstream of the step It would especially be im¬

portant to reproduce the velocity vector maps measured with the ICV

method and to investigate the influence of different heights of the step

on the flow upstream

1MID IR, Sensitivity 20 inK, Resolution 320 by 240 pixel

Appendix A

Measurement Techniques: Basics

A.l Correlation Schemes

The principal mathematical idea of correlation schemes is either to max¬

imize or minimize a function that represents the similarity/discrepancybetween two subwmdows a%3 and bk>i In case of cross-correlation

schemes we have to maximize the cross-correlation coefficient (Bronstem& Semendjajew, 1991)

.,:-/

C^KjA+^+O(A1)

^Var(ah0) Var{bl+k>3+i)

with the covanance

1

Cov(ahJ,bk,i)(M -1)(N-1)

M-l N-l (A 2)

/ _, / _,(«î+m,j+n — ßj,j)(0fc+TO,i+n — "fc,i)i

ra=0 n=0

the variance

Var(a%j) = Cov(al^,al^) (A 3)

and the mean value of the interrogation region

M N

H'3

~

W^N&1.-I — .

r_ N 2-^ 2-^ at+m>J+n (A 4)

ra=ln=l

The same equation applies for the calculation of bk,i The subtraction

of the mean value makes the calculation independent to linear transfor¬

mations of the form a' = a a + ß In case of the Minimum QuadraticDifference (MQD) method (Gm & Merzkirch, 2000) we have to minimize

92 Measurement Techniques: Basics

the equation

MM

M N

ra=l n=l

M N

l) — (bk+m,l+n — bk,l)]

—

2_^i £,((a, — «) + (bk+m,l+n — bk,l)ra=l n=l

— 2(aTO)„ — a)(bk+m,i+n — bk,i))M N

=

2_^ _^,((am,n — a) + (bk+m,l+n ~ bk,l) )m=ln=l

12(«m,ra — «)(^fc+m,i+ra ~ bk,l)

(am,n ~ a)2 + (bk+m,l+n ~ bk,i)2

Combining equation (A 2), (A 3) and equation (A 5) yields

2 Cov(a,bk,i)f>k,i = Var(a) +Var(bk,i) 1

Var(a) + Var(bkyi)

(A 5)

(A 6)

For the last term in equation (A 6) can be shown that — 1 < 2

Cov(a, b)/[Var(a) + Var(b)] < 1 is valid (Bronstem & Semendjajew,

1991) This term is apart from the normalization identical to the defini¬

tion of the cross-correlation and the only variable term in equation (A 6)Therefore, the cross-correlation method is except for the normalization

identical to the MQD method

The effective calculation of the correlation is another issue, because

it is very expensive to directly solve equations (A 1) and (A 6) due to

the computational effort needed With todays computers, the computa¬

tion of the correlation with fast Fourier transforms (FFT) (Russ (1999),Bngham (1974)) is mandatory while correlating large amounts of data

The Fourier transform in discrete form (DFT) for a 2D image i{k,l) is

defined as (Jam, 1989)

M-1N-1

DFT[,(fc,0] = / £,£ = E £ «(M)*-'2**-^M' N,

7 fc=0 1=0

(m,n) = (0,0) (M-1,AT-1)

(A 7)

A.l Correlation Schemes 93

and the inverse transform

DFT".m n

M'N

M-\ N-l

- l(k n=J_ V V l(

— - 1 e^T+#)[,)MN ^ ^ \M'Nj

m=0 n=0 v '

(k,l) = (0,0) (M-1,N-1)

(A 8)

The correlation of two images can then be written with the correlation

theorem (Brigham, 1974) as

M-l N-l

C(s,t)= £ £\i(fc,Z)*2(s + M + Z)fc=0 1=0

1-1DFT"

m n \ I m n

ll m'n2{m'n

(A 9)

with II the complex conjugate of image i\(k,l) transformed with equa¬

tion (A 7) The part of equation (A 9) with the DFT looks more difficult

to compute, but with todays FFT algorithms for the calculation of the

DFT, the complexity of the computation is in the order of 0(N2log2N)for a NxN image The direct computation of the sum in equation (A 9)is in case ofJV = Mm the order of 0(N4) (Raffel et al, 1998)

Unfortunately, there are also drawbacks in form of the assumed pe¬

riodicity of the data One effect of this approach is "aliasing" (Raffelet al, 1998), ie the images are wrapped around That leads to dis¬

tortions of the correlation estimate close to the image edges This can

be reduced in several ways One approach uses "zero-padding", where

the image is surrounded by zeros to prevent the overlap of real data in

the image centers Another way is the application of a gradual window

function that removes the image information at the edges while slightly

blurring the correlation result The approach with a window function

is only feasible for small offsets of the correlation peak because of "bias

errors" (Raffel et al, 1998) To keep the offset small, a priori knowledgeabout the flow can be used to shift the second subwmdow by a fixed

amount (determined by the mean flow) The search is then carried out

around this shift with minimized effect of the wrapped edges This ap¬

proach with the discrete offset is only necessary for large offsets of the

correlation peak compared to the size of the subwmdow

Another issue in this context is the finding of the "true" position of

the correlation peak The algorithm implemented here (Rosgen, 2003)

94 Measurement Techniques: Basics

begins with the fact that a function sampled with a rate A can be recon¬

structed by its samples via (see Oppenheim & Schafer (1975), Bngham

(1974))

oo oo

C(x,y) = y, /, C(mA, nA)smc(i — mA)smc(y — nA) (A 10)ra= — oo n= —oo

with the smc function (cardinal sine)

smc(i — rnA)

smc(y — nA) =

sm(i — rnA)x — mA

sm(y — nA)

y— nA

(All)

The problematic part here is the infinite sum m equation (A 10) m com¬

bination with the finite nature of the correlation map C(mA, nA) The

simple implementation with

M-l N-l

C(x,y) = 2_\ /_, C(mA,nA)smc(x— mA)smc(y — nA) (A 12)

ra=0 n=0

would not work properly, because a function can only be reconstructed

from its samples by equation (A 10) with infinite spatial support Ap¬

plying equation (A 12), l e interpolation of a finite data set, leads onlyto errors due to spectral leakage (Rosgen, 2003) A solution could be

the periodic continuation of the data set, but this increases the com¬

putational complexity By working in the Fourier domain, this problemcan be circumvented, because periodicity of the data is automatically as¬

sumed with this approach Applying the convolution theorem (Bngham,1974) to equation (A 10) we get

C * smc & 9(C) S'(sinc) (A 13)

with the Fourier transform 9~ while the symbol * means the convolution

between the two terms The Fourier transform of the smc function is

a "top hat" with the cutoff at half the sampling frequency at 1/(2A)This represents an ideal band-pass in the frequency domain that leaves

from equation (A 13) only the calculation of the Fourier transform of the

A.2 Laser Speckle Velocimetry (LSV) 95

correlation map

C(k,l) = 9(C(mA,nA))M-1N-1 (A i4\

m=0 n=0

This transformed correlation map is already known from the cross-

correlation computation (see equation (A 9)) For the true position of

the correlation peak one can then write

1M-l N-l

C(x°>y°} = JFWÄ1 £ £ C^Oe'2^^ (A 15)fc=0 1=0

Because we are not interested in the full correlation map but only in the

precise position of the peak, equation (A 15) does not have to be solved

directly Instead we can search for some phase factors

$ki(xo,yo) =expkx0

j2ir[jyo_\

MA NA)_

(k,l) = (0 M-1,0 N-l)

(A 16)

that maximize equation (A 15) This nonlinear equation for (xo,yo) can

be solved with Newton's method in an iterative way For further details

see Rosgen (2003)The code used here is implemented with the correlation scheme de¬

scribed so far in MQD mode and cross-correlation mode with a masking

function, optional discrete window offset and the peak finding algorithm

utilizing the smc interpolation

A.2 Laser Speckle Velocimetry (LSV)

Speckle patterns are always present when coherent light is scattered at

rough surfaces They are then formed due to 3D multiple beam interfer¬

ence of the scattered light If the speckle patterns are formed on a screen

by collecting and focusing the light, one speaks of "subjective" speckle

patterns The size of the speckles are related to the optical properties of

the lens system and the wavelength of the light It can be described as

(Fomin, 1998)f

s = 122\(l + M)±- (A 17)

96 Measurement Techniques: Basics

with the speckle size s, wavelength A, focal length /, aperture size A

and the magnification M The size of the speckle can then be varied to

appear large enough on the CCD camera for later correlation by changingthe optical setup With the wavelength A = 532 nm, the magnification

M<1, the focal length / = 50 mm and the aperture size A « 1 mm, the

size of the subjective speckle on the CCD chip should be approximatelys « 30 /*m This is larger than the size of the pixel on the chip of 9 by 9

/*m Hence, the speckle should be detectable with this setup as long as

a sufficient amount of light reaches the CCD chip with this very small

aperture

The velocity vector maps can be determined by correlating (see sec¬

tion A 1) the speckle patterns in the two corresponding images the same

way as with ICV Due to the short lifetime of the speckle pattern caused

by the change in the spatial distribution of the particles scattering the

light, the time interval between the two pulses must be in the range of

10 100 /xs in our experimental context

A.3 Background Oriented Schlieren (BOS)

Fermât 's variational principle for the behavior of light in an mhomoge-neous medium states that electromagnetic waves traveling between two

points always take the route having the smallest optical path length In

mathematical form it is defined as (Merzkirch, 1974)

ö / n(x,y, z) ds = 0 (A 18)

with n(x,y,z) the refractive index field and s oriented along the light

ray For a beam parallel to the z-axis, it is possible to simplify equation

(A 18) (see Merzkirch (1974) and Dalziel et al (2000)) to the following

pair of differential equations

d2x

dz2

à2 y

dz2

1 dn dx 1 dn

ndx dz n dz

1 dn dy 1 dn

n dy dz n dz

(A 19)

This set of equations describes the path of the light inside an lnhomo-

geneous object (phase object) as shown in Figure A 1 In most cases,

these coupled partial differential equations can not be solved for the

A.3 Background Oriented Schlieren (BOS) 97

Lightsource

Structured

backgroundPhase object Camera

Figure A.l: Sketch of influence of the phase object on rays of light for the

y-direction. The dashed line stands for the case without the phase object.

unknown index of refraction that we usually want to determine. By as¬

suming only infinitesimal deviations for the rays inside the phase object,i.e. dxjdz <C 1 and dyjdz <C 1 while having a non-negligible curvature,

equation (A.19) is reduced to

(A.20)

Integrating this set of equations gives the tangent of the angle of deflec¬

tion a of the ray of light for the x- and j/-direction. We obtain

d2x

dz2

1 dn

n dx

à2 yc

dz2

1 dn

n dy

dxtan ax = —— =

dz

dytan av = — =

ydz

1 dn-—oten dx

nl_d_

n dy

(A.21)dz.

Backtracking now the ray of light from the image plane to the structured

background object yields between position 1 and 2 (Figure A.l) offsets

of Axi2 = Aj/i2 = 0. The reason for these vanishing offsets is that only

light parallel to the z-axis is captured by the camera due to the optical

setup while assuming a constant index of refraction between position 1

and 2. Inside the phase object (between position 2 and 3), the deviation

98 Measurement Techniques: Basics

of the light can be obtained by integrating equation (A 21) This results

with the assumption of a 2D index of refraction field with variations onlyin x- and y-direction in

(A 22)

The term no is the nominal index of refraction that can be used here,because the difference between the index of refraction n and no are as¬

sumed to be small

The offset between position 3 and 4 depends only on the angle of

the light leaving the phase object at position 3 and is determined byB tan a With equation (A 21) we get

Al2,3 = s:'

f3 1 dn'

J2 nlTxdZ_ dz =Aw2-—2 no dx

Aj/2,3 = r;'

f3 1 dn'

dz =,lW2-—2 n0 dy

f3 1 dn 1 dnAx3 4

= B tan ax = B I ——— dz = B W——

J2 no dx no dx

Ji no dyAj/:'3,4 B tan a

yB W±^

n0 dy

(A 23)

The full offset of the light between the screen and the background image

is then

(A 24)

Ax --= Al2,3 + Ax3)4 == \W(W + 22?)-!^2 no dx

Ay == Aj/2,3 + Aj/3)4 =AW(W + 2B)-p2 n0 dy

This offset can then be numerically processed to obtain the 2D field of

the index of refraction and the temperature field T(x, y) as shown below

A.3.1 Poisson Equation

The solution of equation (A 24) can be found with a Poisson solver This

can be shown by rearranging equation (A 24) to the following form

dn—- = const Aifx.i/)

dxv ,y'

(jfl— = const Ay(x,y),

(A 25)

A.3 Background Oriented Schlieren (BOS) 99

with the definition of const = 2no/[W(W + 2B)] Taking the derivative

of equation (A 24) results in the Poisson equation

d2n d2nAn =

Tr^T + Tr^T= const

dxA dyA^-Ax(x,y) + ^-Ay(x,y) g(x,y) (A 26)

The Poisson equation can be solved e g by discretizing equation (A 26)with a second order, five-point finite difference scheme (Hirsch, 1994)with v Neumann boundary conditions that are directly taken from the

measurements Equation (A 26) takes then the form A n(x, y) = g(x, y)with the matrix A The form of A can be taken directly from Press et al

(1997) Because the system is overdetermmed, the matrix equation is

solved m a linear least-squares sense (Press et al, 1997) by the following

equation

(AT A) n = AT g=>n = (AT A)'1 (AT g) (A 27)

with AT being the transpose of A Unfortunately, the solution n(x, y) is

not unique because of the used v Neumann boundary conditions With

the solution n(x,y), n(x,y) + const is also a possible solution The

constant has to be determined by other means Here, two temperatures

measured with thermocouples (see section 2 4) are used for calibration

Under the assumption of the validity of the perfect gas equation

(Wilcox, 1998)

p = pRT (A 28)

with pressure p, the perfect gas constant R and together with the

Gladstone-Dale equation (Vasil'ev, 1971)

Tl — 1= const (A 29)

we getconst

m

constn = 1 + —— => T = A 30

1 n — 1

Because the solution for n is determined up to another unknown (cali¬bration) constant, equation (A 30) has to be modified to

T(x,y) =l

(A 31)ci n(x,y)+c2

100 Measurement Techniques: Basics

with the constants determined by

Ta Twcl

na - nw

C2 =

1

Tw— c\nw

(A 32)

The subscript a stands for ambient air conditions and W for the condi¬

tions close to the wall The refractive indexes ntt and nw are taken as

the values of the solution n(x, y) at the locations where Ta and Tw are

known

A.3.2 Finite Difference Approximation

Instead of solving equation (A 25) with a Poisson solver, it is possibleto solve this equation for the x- and y-directions with a finite difference

approximation scheme For the points of the experimentally obtained

gradient matrix, a fourth order scheme was used across the nodes shown

m Figure A 2 for the corresponding meshpomts Before the calculation

i-2 l-l l l+l i+2 i-3 i-2 l-l l l+l l-l l l+l i+2 i+3

(a) 4th order central (b) 4th order back- (c) 4th order for¬

ward^) ward(I)

i-4 i-3 i-2 l-l i i l+l i+2 i+3 i+4

(d) 4th order back- (e) 4th order for¬

warder) ward(I)

Figure A 2 Nodes used in the finite difference approximation scheme for the

different meshpomts of the gradient matrix

of the index of refraction, a 3 by 3 Gauss filter is applied to the measured

data for noise removal

According to Jacobson (2000) we get for the different meshpomts m

A.3 Background Oriented Schlieren (BOS) 101

the gradient matrix (Figure A 2)

A2(a

A2(bux r^J-^œ

, „, s

dn%-3nj_i-10n%+18nî+i-6nî+2+nî+3

A 2(c) ITT«

7777; (A 33)

A2(d

A2(e

with the spacing Dx between two meshpomts for the computation of

the index of refraction n(x,y) The spacing between the meshpomts is

defined by the original data acquired from the correlation process The

same set of equations hold true for the j/-direction The index of refrac¬

tion can then be obtained in the same way as described in section A 3 1

with equation (A 27) with a different coefficient matrix A The tem¬

perature field can be calculated by equation (A 31) with the necessary

calibration temperatures

dntj

nt-2 ~ 8n»_i + 8nî+i -

nî+2

dx 12DX

dnt -nt-3 + 6n»_2 - 18n»_i + 10n% + 3nî+idx 12DX

dnt-3n»_i-10n»+18nî+i-6nî+2+nî+3

dx 12DX

dnt 3nj_4 — 16nj_3 + 36nj_2 — 48nj_i + 25n%

dx 12DX

dnt -25nt + 48nî+i - 36nî+2 + 16nî+3 - 3nî+4

dx 12DX

A.3.3 Direct Integration m ID

In cases with simple geometry and negligible temperature gradients in

the streamwise direction, it is possible to handle a 2D problem with a

ID approach (Jemelka et al, 2003) The index of refraction can then be

obtained from the measured gradient field Vn with

n(y) = -rdy

Jo dyn0

Inserting this equation into equation (A 30) gives

const

T(y) = -fV dn

JO dydy + n0 - 1

For i/^Owe get

2Ïconst

w

n0 1

(A 34)

(A 35)

(A 36)

102 Measurement Techniques: Basics

This results with equation (A 35) in

T(y) = — -^ (A 37)^llo^dy + l

For y —> oo we obtain

£_,) 1 /-fU, (A 38,Ta J m - 1 Jo ay

As the final result, equation (A 35) is converted to a form with measured

quantities only

T(y) = t "w„,„. i

(A 39)Tw

1+< TW

KTa -0'

IS «î dv

'

In the experimental context, y —> oo means quantities are obtained in

regions where ambient air conditions prevail

A.4 Least-Squares Collocation

The least-squares collocation method (Moritz (1989), Niemeier (2002)) is

based on the assumption that the measured data 0(xl,yl) (i = 1 M)can be modeled as a sum

0(x, y) = t(x, y) + S(x, y) + N(x, y) (A 40)

with the deterministic "trend" t(x,y) (with varying mean), residual sig¬

nal S(x,y) (with zero-mean) and noise N(x,y) (with zero-mean) The

signal S(x,y) and the noise N(x,y) are assumed to be uncorrelated, l e

E{S N} = 0 with E{ } being the expectation value A bias-free signalis obtained by subtracting the trend from the observation

Ô(x, y) = 0(x, y) - t(x, y) = S(x, y) + N(x, y) (A 41)

The trend t(x, y) is determined by linear regression that incorporates a

stochastic model assuming a correlation of the observed data with some

correlation length The expectation value of the above equation is

E{Ô(x, y)} = E{S(x, y) + N(x, y)} = E{S(x, y)} + E{N(x, y)} = 0,

(A 42)

A.4 Least-Squares Collocation 103

because signal and noise were assumed to have zero-mean

One is looking for an estimate S of the signal at an arbitrary position

(C, n) as a weighted superposition of the known data observations

M

S(Ç,n) =YJaÖ(xa,ya) (A 43)a=l

with the unknown parameters wa The condition is a minimization of

the variance between the unknown true signal and its estimate at that

point,

E{[S(Ç,ri)-S(Ç,ri)}2} -+ mm (A 44)

Substitution of equation (A 43) into equation (A 44) and expanding it

gives

M

E{S2(C,n)}-2Y,^aE{S(C,n)Ö(xa,ya)}+a=1

(A 45)MM

y '

+ ^^WaW0E{Ô(xa,ya)Ô(x0,yb)} —> mm

6=1 a=l

Zeroing the partial derivatives with respect to the unknown parameters

wa results in the basic set of equations

M

Y^wbE{Ô(xa,ya)Ô(xb,yb)} = E{S(C,v)Ô(xa,ya)} (« = 1 M)6=1

(A 46)The expectation values can be further split up to

E{0(xa,ya)0(xb,yb)} =

= E{S(xb,yb)S(xa,ya)} + E{N(xb,yb)N(xa,ya)} (A 47)

E{S(C,v)Ô(xa,ya)} = E{S(C,v)S(xa,ya)}

This yields with the definition of the covariance distance matrix

(Niemeier, 2002) and the zero-mean of S and N

M

}jwb[CSs(xb -

xa,yb- ya)+

6=1

+CNN6(xb-xa,yb-ya)}=Css(C - xa,'n-ya) (a = 1 M)

(A 48)

104 Measurement Techniques: Basics

Here, it was furthermore assumed that the covanances are shift-invariant

and that the noise covariance is a delta function, 1 e no finite spatialcorrelation exists

A.5 Thermocouples

The thermocouples used here are made of the two components Chromel

/ Alumel The design of the probes including the amplifier were done by

Zumsteg (1988) For the calibration procedure, a reference thermometer

with high precision had to be used This requirement was fulfilled bya F250 thermometer with a T100-650 sensor from Automatic SystemLaboratories The absolute error of the measured temperatures with this

combination was ±35 mK This is better than the required precision for

the calibration of the thermocouplesThe output voltage of the amplifier that is translated to temperatures

depends on several parameters and is defined by

Uout = EMF(T) S AF + Offset (A 49)

EMF(T) is the thermoelectric voltage, S the sensitivity, AF the am¬

plification factor and the Offset is the output at T = 273 14 K For

calibration purposes, the output voltage Uout is measured at four differ¬

ent temperatures These points are then fitted with a linear function in a

least squares sense to obtain the amplification factor AF and the Offset

The thermoelectric voltage can be described by a polynomial of fourth

order of the temperature T and the sensitivity of the chosen Chromel /Alumel combination is S = 1/40 5K//j,V (Grobelbauer, 1992) The tem¬

peratures can then be calculated by inserting the polynomial for EMF(T)into equation (A 49) that can be solved with an iterative scheme like the

Newton method

Appendix B

Results: Experimental Conditions

For easier access to the original data, more detailed information are

given for the results presented in chapter 4 The additional information

are sorted in the order they appear in the figures in the results chapter

B.l Setup for Continuous Release

In this section, all the experiments with the continuous-release setup are

shown The data acquisition is always started 90 s after the immersion

heaters in the dewar reservoir are switched on If more than one exper¬

iment is conducted on a single day, the lower and upper limits for the

temperature T, humidity H and electrical heating P are shown

Figure Date T [°C] H [%rh] P [W]

4 2, 4 3 19 12 02 22 23 32 35 2300

45 13/14 01 03 23/23 19/27 3000

4 11(a), 4 12(a) 01 04 03 24 37 2000

4 11(b) ,4 12(b) 01 04 03 24 37 2000

4 11(c),4 12(c) 22 04 03 24 35 2000

4 ll(d),4 12(d) 21 05 03 24 34 2000

4 13, 4 14,4 15 10 01 03 22 21 2300

4 16 07 01 03 24 23 1000 3000

4 17 19 12 02 22 23 32 35 2300

4 18,4 19 31 05 03 23 25 36 43 1600

4 20, 4 21 21 02 03 23 24 2000

4 22(a) ,4 22(b) 01 06 03 23 25 34 35 1600

4 22(c) ,4 22(d) 03 06 03 23 42 1600

4 23 07 06 03 22 25 38 42 1600

4 24, 4 25, 4 26 1/3/7 06 03 22 25 34 42 1600

4 27 01 06 03 23 25 34 35 1600

B.2 Setup for Sudden Release

In this section, all the experiments with the sudden-release setup are

shown The liquid nitrogen is released after 45 s of evaporation for all

106 Results: Experimental Conditions

measurements Like in the previous section, the given range for temper¬

ature and humidity applies to all experiments conducted during a single

day

Figure Date T [°C] H [%rh] m [kg]

4 28 15 06 03 22 23 37 40 1

4 30 4 41 17 06 03 22 24 34 41 1

B.3 Background Oriented Schlieren

The details of the background oriented Schlieren (BOS) measurements

are shown here The first three experiments are conducted with the

continuous-release setup and the fourth experiment is conducted with

the sudden-release setup

• Figure 4 43, 4 44 and 4 45 29 04 2003, T = 23°C, H = 32 %rh,P = 2000 W (continuous release)

• Figure 4 47 and 4 48 10 04 2003, T = 22°C, H = 19 %rh, P =

2000 W (continuous release)

• Figure 4 49 22 04 2003, T = 24°C, H = 35 %rh, P = 2000 W

(continuous release)

• Figure 4 50 11 04 2003, T = 24°C, H = 35 %rh, m=l kg (suddenrelease)

The BOS measurements of the continuous-release setup are conducted

under the same evaporation conditions as explained in section B 1 In

the sudden-release case, the evaporation conditions of section B 2 apply

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Curriculum vitae

Name

Date of Birth

Place of Birth

Nationality

Mai 1999 to

September 2003

December 1998

October 1993 to

December 1998

May 1993

Olaf Jensen

04 08 1973

Berlin, Germany

German

Research assistant and Ph D student at the

Institute of Fluid Dynamics, ETH Zurich

under supervision of Prof T Rosgen

Diploma (equivalent to Masters degree)in physics, Humboldt-Umversify Berlin

(Germany)

Studies in physics, Humboldt-UmversityBerlin

Majors experimental plasma physics and

theoretical solid state physics

"Abitur" (graduation from high school)at the Lise Meitner Gymnasium Berlin

(Germany)