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9

INVESTIGATION OF THREE PARALLEL

JETS IMPINGING ON A VERTICAL PLATE

Nawaf Mohammed Al-Fadul

FACULTY OF ENGINEERING

KING ABDULAZIZ UNIVERSITY, JEDDAH

SAFAR 1424H - APRIL 2003G

10

11

INVESTIGATION OF THREE PARALLEL

JETS IMPINGING ON A VERTICAL PLATE

By

Nawaf Mohammed Al-Fadul

A thesis submitted in partial fulfillment of the requirements for the degree of

Master of Science in Mechanical Engineering / Mechanical Power.

FACULTY OF ENGINEERING

KING ABDULAZIZ UNIVERSITY

JEDDAH, SAUDI ARABIA

SAFAR 1424H –APRIL 2003G

12

INVESTIGATION OF THREE PARALLEL

JETS IMPINGING ON A VERTICAL PLATE

By

Nawaf Mohammed Al-Fadul

We certify that We have read this thesis and that in our opinion is fully adequate

in scope and quality as a thesis for the degree of Master of Science.

Thesis Supervisors:

-------------------------------------------------

Dr. Mohammed Hussain Albeirutty

-------------------------------------- Prof. Jafer Abdulrahman Sabbagh

13

INVESTIGATION OF THREE PARALLEL

JETS IMPINGING ON A VERTICAL PLATE

By

Nawaf Mohammed Al-fadul

This thesis has been approved and accepted in partial fulfillment of the

requirements for the degree of Master of Science

Examiners:

-------------------------------------------- Dr. Mohammed H. Albeirutty , Examiner / Supervisor

-------------------------------------------- Prof. Jafer A. Sabbagh , Examiner /Co-supervisor

----------------------------------------------------------

Dr. Ibrahim E. Megahed , Examiner

----------------------------------------------------------

Dr. Abdulhaiy M. Radhwan , Examiner

14

ACKNOWLEDGEMENT

First I would like to express my gratitude to King Abdulaziz City of Sciences and

Technology (KACST) for their support and funding of this research work.

Also I would like to express my thanks to both of my advisors Professor. Jafer Sabbagh

and Dr. Mohammed Al-Beirutty for their great and continuous overall supervision in

this research until it reached the final required form.

My thanks also is extended to the technical and workshop staff members of thermal

engineering department for their great help and assistance during the manufacturing of

the experimental setup parts.

15

INVESTIGATION OF THREE PARALLEL

JETS IMPINGING ON A VERTICAL PLATE

Nawaf Mohammed Al-Fadul

ABSTRACT

This thesis depicts an experimental study of the flow field characteristics

of three parallel two-dimensional jets impinging on a normal plate as the

case of VTOL aircraft operating near the ground.

Throughout the course of this work, the flow field characteristics of two

free jets are studied. The results are compared to previous similar studies

in the literature .The results are also compared to that of three free jets

arrangement. The flow field of three impinging parallel jets colliding on a

vertical plate is also investigated. In addition the effect of changing some

parameters such as the jets velocity strength and the distance between the

jets exit plane and the vertical impinging plate is studied.

The measurements of the resultant flow field for free and impinging jets

were conducted using hot-wire probes technique, this included extensive

measurements of the turbulent structure of flow field. Flow visualizations

results which reveal the flow field shape were also obtained using oil chalk

mixture method .All pressure readings on the ground and the vertical

impinging plate were measured using pressure taps connected to an

electronic transducer.

The overall impinging measurements show that in the case of equal

strength impinging jets, the middle jet interact with the interior wall jets

formed by the two outside jet after impinging and lose its strength. In

unequal jets case, the strong middle jet attracts the two weaker side jets

and act as a single jet after impingement. The result shows also that if two

adjacent strong jets interact with one weaker side jet the weaker side jet is

attracted to the middle strong jet and lose its strength, the final velocity

profile becomes similar to two impinging jets.

16

TABLE OF CONTENTS

ACKNOWLEDGEMENT……….……………………….……….…….…..……......v

ABSTRACT...……………………………..………………..……………..…………vi

TABLE OF CONTENTS...…………………..………………..…………..……..…..viii

LIST OF TABLES …………………………………………………………………. .x

LIST OF FIGURES...……………………………………..…………………....….....xii

LIST OF SYMBOLS ….…………….…………………..……………..…..….……..xv

CHAPTER I INTRODUCTION AND LITERATURE REVIEW ……………… 1

1.1 Introduction ……………………………………………………………..

1

1.2 literature review …………………………………………………………

2

1.3 Research objectives …………………………………………………......

7

CHAPTER II EXPERIMENTAL SETUP ……………………………………… 9 2.1 Setup and alignment …………………………………………………….. 9

2.2 Instrumentations ………………………………………………………..

15

2.2.1 Single normal wire probe …………………………………..

16

2.2.2 Triple-sensor gold-plated wire probe ……………………….

17

2.2.3 Data Acquisition …………………………………………….

18 2.3 Calibration of hot-wires ………………………………………………..

19

CHAPTER III MEASUREMENTS AND FLOW VISUALIZATION ……......30 3.1 Symmetry Check ………………………………………………………. 30

vii

17

3.2 Comparison of Single and Triple wire measurements ………………… 32

3.3 Two parallel free jets measurements ………………………………….. 34

3.4 Three parallel free jets measurements ………………………………… 36

3.5 Three parallel impinging jets measurements ………………………….. 37

3.6 Flow Visualization Technique ……………………………………….. .

39

CHAPTER IV DISCUSSION OF RESULTS ………………………………….. 40

4.1 Free jet measurements ………………………………………………….

40

4.1.1 Interaction of two free parallel jets …………………………

40

4.1.2 Interaction of three free parallel jets ………………………..

41

4.1.3 Variations of momentum in three parallel jets ……………..

45

4.1.4 Comparison between free jets arrangement results ……......

47 4.2 Impinging jets results …………………………………………………. 50

4.2.1 Single impinging jet ………………………………………..

51

4.2.2 Three parallel impinging jets ………………………………..

51

CHAPTER V CONCLUSIONS AND RECOMMENDATIONS ……………… 77

5.1 Conclusion ……………………………………………………………...

77

5.2 Recommendations ………………………………………………………

78

REFERENCES …………………………………………………………………….80

APPENDIX – I TABULATED RESULTS ……………………………………...83

APPENDIX – II COMPUTER PROGRAM. …………………………………… 105

18

LIST OF TABLES

TABLE PAGE

I.1 summery of all vertical plate positions, measurement wire distances and the type of wire used in the measurements…………………………….. 85

I.2 Mean velocity components and fluctuations results of three parallel

free jets at x/tp=30……………………………..………………………..….. 86

I.3 Mean velocity components and fluctuations results of three parallel

free jets at x/tp=50……………………………………………………….… 87

I.4 Mean velocity components and fluctuations results of three parallel

free jets at x/tp=80………………………………………………………… 88

I.5 Mean velocity components and fluctuations results of three parallel

free jets at x/tp=140…………………………………………………..……. 89

I.6 Mean velocity components and fluctuations results of three parallel

impinging jets at H=10cm , x=5cm (x/tp=10)…..………………………... 90

I.7 Mean velocity components and fluctuations results of three parallel

impinging jets at H=20cm , x=5cm (x/tp=10)……………………………. 91

I.8 Mean velocity components and fluctuations results of three parallel

impinging jets at H=20cm , x=10cm (x/tp=20)…………………………… 92

I.9 Mean velocity components and fluctuations results of three paralle

impinging jets at H=30cm , x=10cm (x/tp=20). …..……………………… 93 I.10 Mean velocity components and fluctuations results of three parallel

impinging jets at H=30cm , x=20cm x/tp=40) 94

I.11 Mean velocity components and fluctuations results of three

parallel impinging jets at H=45cm , x=23cm (x/tp=46)………………..… 95

I.12 Mean velocity components and fluctuations results of three

parallel impinging jets at H=45cm , x=24cm (x/tp=48)………………… 96

I.13 Mean velocity components and fluctuations results of three

parallel impinging jets at H=45cm , x=28cm (x/tp=56)…………………… 97

I.14 Mean velocity components and fluctuations results of three

parallel impinging jets at H=45cm , x=34cm (x/tp=68)…………………… 98

I.15 Mean velocity components and fluctuations results of three

parallel impinging jets at H=45cm , x=40cm (x/tp=80)……………………. 99

I.16 Axial mean velocity and fluctuation results o f three unequal (Uo1=Uo2=2Uo3) parallel impinging jets at H=45cm, x=40cm 100

I.17 Axial mean velocity and fluctuation results o f three unequal

(Uo1=Uo3=.5Uo2) parallel impinging jets at H=45cm, x=40cm 101

I.18 Upstream flow pressure distributions results for three parallel

Impinging jets at different impinging plate distances . 102

I.19 Upstream flow pressure distributions results for three parallel unequal

impinging jets at H=45 cm. 103

I.20 Ground plane static pressure distributions results for three parallel

equal and unequal impinging jets at H=45 cm and x=4, 28 cm. 104

x

19

LIST OF FIGURES

Figure Page

2.1 Test rig schematic diagram 9

2.2 Tope views of the old and the modified jet nozzles........................................... 10

2.3 Side view of jets blocks and vertical impinging plate ……………………... ... 11 2.4 Traverse mechanism side view 11

2.5 Air blowers feeding the three jets . 12

2.6 Side view of jets blocks 12

2.7 Dynamic flow board for data acquisition system 13

2.8 Traverse mechanism components 14

2.9 Pressure electronic manometer. 15

2.10 Single wire probe (Miniature wire type provided by Dantec Dynamic

site www.dantecdynamics.com) 16

2.11 Triple wire probe (provided by Dantec Dynamic

site www.dantecdynamics.com). ..17

2.12 Constant Temperature Anemometer layout diagram (by Dantec Dynamic

site www.dantecdynamics.com......................................................... 19

2.13 Velocity components vectors in the laboratory coordinates........................... .. 20

2.14 Velocity components vectors in the wire coordinates ....................................... 21

2.15 Single sensor robe .............................................................................................. 23

2.16 Triple sensor probe ............................................................................................ 24

2.17 Side view and front view photos of the round jet…........................................ .. 28 2.18 Calibration curves for (a) single and (b) triple wire probes 29

3.1 Velocity profiles to check jet (1) symmetry 31

3.2 Velocity profiles to check jet (2) symmetry . 31

3.3 Velocity profiles to check jet (3) symmetry . 31

3.4 Comparison of jets symmetry check between current and pervious

studies 32

3.5 Velocity profiles using single and triple wire measurements for a single

free jet at L=50 cm… 33

3.6 Comparison of Axial velocity profile at x/tp=20 between current and

pervious studies 34

3.7 Axial mean velocity profiles of upstream merging region of the two

free parallel jets. 35

3.8 Axial turbulence intensity profiles for double jets arrangement 35

3.9 Axial mean velocity profiles of three free parallel jets. 36

3.10 Schematic diagram of the flow field of three impinging jets 37

4.1 Variations of maximum velocity along the centerline of each

jet with axial distance 43

4.2 Trajectory of the central streamline of each of the three jets. 44

4.3 Axial turbulence intensity profiles in the merging region of three free

parallel jets 44

4.4 lateral turbulence profiles of upstream merging region of three free

parallel jets 45

4.5 Shear stress profiles in the merging region of the three free parallel jets 45

4.6 Variations of momentum of upstream merging region of three free

parallel jets. 47

4.7 Variations of flow momentum along the centerline of each jet with

axial distance. 48

xii

20

4.8 Velocity profiles at x/tp=20 for double and triple jets arrangements 49

4.9 Velocity profiles at x/tp=50 for double and triple jets arrangements . 49

4.10 Axial turbulence intensity profiles at x/tp=50 for double and triple

jets arrangements . 50

4.11 Growth of jet width with downstream distance for single , double

and triple jets arrangements . 51

4.12 Flow visualization of single impinging jet at H=45 cm 52

4.13 Flow visualizations pattern for three equal impinging jets at different

plate distances. 53

4.14 Flow visualizations pattern for two equal impinging jets at different

plate distances [7]. 54

4.15 Pressure distribution across the impinging vertical plate at different

distances from the jets exit 55

4.16 Flow visualization of three impinging jets at H=10 cm.. 56

4.17a Axial and lateral velocity profiles for three equal impinging jets at

x/tp =10 and H=10 cm 56

4.16b Axial and lateral velocity profiles for three equal impinging jets at

x/tp =10 and H=10 cm (corrected on the basis of Fig.4.16) 57

4.18 Axial turbulence intensity profile for three equal impinging jets at

x/tp =10 and H=10 cm 57

4.19 Flow visualization of three impinging jets at H=20 cm 58

4.20a Axial velocity profiles for three equal impinging jets at x/tp =10

and H=20 cm 59

4.20b Axial velocity profiles for three equal impinging jets at x/tp =10

and H=20 cm (corrected on the basis of Fig.(4.19)…... .................................... 59 4.21a Lateral velocity profiles for three equal impinging jets at x/tp=20, 40

and H=20 cm 60

4.21b Lateral velocity profiles for three equal impinging jets at x/tp=20, 40

and H=20 cm (corrected on the basis of Fig.4.19) 60

4.22 Axial intensity profiles for three equal impinging jets at x/tp =10,20

and H=20 cm 61

4.23 Flow visualization of three impinging jets at H=30 cm 61

4.24a Axial velocity profiles for three equal impinging jets at x/tp=20, 40

and H=30 cm 62

4.24b Axial velocity profiles for three equal impinging jets at x/tp=20, 40

and H=30 cm (corrected on the basis of Fig.4.23) 62

4.25a Lateral velocity profiles for three equal impinging jets at x/tp =20, 40

and H=30 cm. 63

4.25b Lateral velocity profiles for three equal impinging jets at x/tp =20, 40

and H=30 cm (corrected on the basis of Fig.4.23) 63

4.26 Axial turbulence intensity profiles for three equal impinging jets at

x/tp =20, 40 and H=30 cm 64

4.27 Flow visualization of three impinging jets at H=45 cm 65

4.28 Static pressure distribution across the ground horizontal plate for

three equal strength jets at H=45 cm……………………………………….... 66

4.29a Flow map for the right side of the visualization pattern of three

impinging jets at H=45 cm……..……………….....................…………… .... 66

4.29b Velocity vectors at the measuriments locations of three impinging

jets at H=45 …….………………………………………………………….… . 67 4.30a Axial velocity profiles for three equal impinging jets at x/tp =46

48, 56, 68, 80 and H=45 cm…………………………………………….….… 68

4.30b Axial velocity profiles for three equal impinging jets at x/tp =46

48, 56, 68, 80 and H=45 cm (corrected on the basis of Fig.4.27)………..…... 68

4.31 Lateral velocity profiles for three equal impinging jets

at H=45 cm………………………….……………….………………..…..…… 69

4.32 Axial turbulence intensity profiles for three equal impinging jets

at x/tp =46, 48, 56, 68, 80 and H=45cm ……………………..………....……...69

4.33 Pressure distribution across the impinging vertical plate for

three equal and unequal jets at H=45 cm…………………...…..………… ..... 70

xiii

21

4.34 Static pressure distribution across the ground horizontal plate three

unequal strength jets (Uo1=Uo3=50%Uo2) at H=45 cm……………..……71

4.35 Static pressure distribution across the ground horizontal plate for three

unequal strength jets (Uo1=Uo2=2Uo3) at H=45 cm…………………… 72

4.36 Flow visualization of three un equal impinging jets (Uo1=Uo3=0.5 Uo2)

at H=45 cm…………………………………………………………………… 73

4.37 Flow visualization of three un equal impinging jets (Uo1=Uo2=2 Uo3)

at H=45 cm………………………………………………………………… 73

4.38 Axial mean velocity profiles for three equal and unequal impinging

jets at H=45 cm……………………………………………………………… 74

4.39 Axial turbulence intensity profiles for three equal and unequal impinging jets at H=45 cm ………………………………………………….. 75

4.40 Flow visualization of three impinging jets at H=70 cm……………………. 76

4.41 Axial mean velocity profiles for three equal and unequal

impinging jets at H=70 cm…………………………………………………. 77

4.42 Axial turbulence profiles for three equal impinging jets at

x/tp =46, 48, 56, 68, 80 and H=70cm 77

22

LIST OF SYMBOLS

H : distance between vertical impinging plate and jets exit

plane [ cm]

J : velocity momentum [m2/s2].

Jp : pressure momentum [m2/s2].

Jt : total momentum [m2/s2].

Jo : jet exit momentum [m2/s2].

L : axial measuring distance from the jet exit [cm]

l : jet nozzle length (49 cm)

S : the distance between the centerline of the jets [ 17 cm].

tp : jet nozzle thickness [ 0.5 cm].

U, V, W : air velocity components in lab coordinate [m/s].

x , y , z : axial , lateral and vertical directions in the lab coordinates [cm]

Uo1 ,Uo2 ,Uo3 : jets exit velocity [ 45 m/s].

Ueff : effective velocity [m/s].

u', v', w' : velocity fluctuations components along x , y and z

respectively [m/s].

u'v', u'w', v'w : shear stress components [m2/s2].

Greek letters:

: air density [kg/m3].

321 ,, : air velocity components in wire coordinates [m/s].

23

CHAPTER - I

INTRODUCTION AND LITERATURE REVIEW

1.1 Introduction

The impingement of jets in fluid mechanics has many extensive engineering

applications. Results of researches in this field are being utilized in several functions

and purposes, this includes cooling and drying operations, cleaning electronic

components, annealing of metal and glass, tempering operations, cooling turbine blades

and combustion walls, materials processing and manufacturing, and also in the design

of efficient (V/STOL) aircraft jets.

The investigation of the flow fields of impinging jets has been the subject of

considerable researches over the past 25 years, and still the focus of many significant

authors in the literature today. Researches topics under studies have been arranged and

classified on the basis of jets shape and configuration, this including confined or free

jet, single or multiple jets, turbulent or laminar flow jet, simple or complex jets, etc. It

is also classified on the basis of impingement surface where moving or stationary

surface is considered, with or without cross flow.

One of the important reasons behind investigating such flow fields is to furnish a

better understanding of complex flow fields produced by the impinging of multi-jets on

normal or inclined surfaces. The nearest application example of such area of research

can be seen from the jets produced by aircraft, rockets and missiles engines, in these

cases the optimization between near field engine flow configuration and far field

configuration is significant, it can only be achieved by a good engineering knowledge

1

24

and understanding of the resultant flow field produced by the impinging of the

interacted engine jets with the ground. On this study, the project is mainly concerned

with the investigation of the flow field formed by the impingement of three two

dimensional parallel air jets on a vertical plate using hot-wire anemometer technique

and flow visualizations.

1.2 literature review

So far, many investigators have performed experimental and numerical studies to

predict the flow field structure and heat transfer of a single impinging jet with different

configurations, many have also presented empirical corrections based on their data,

however the new studies of the flow field of multiple jets are still few comparing to

single jet configuration, this is in spite of currently developed researches which are

being carried out on this field.

Now referring to literature and considering the most relevant papers to this project

concerning the impingement of jets on surfaces, we could find that, Elbanna et al [1],

studied the flow field structure generated by the impingement of two free parallel air

jets normally on a flat plate, the experimental results with flow visualization have

shown good measurements of mean velocities, pressure, and turbulent intensities and

revealed the influence of both geometric parameters and the relative strength of both

jets on the fountain and other flow properties.

Barata [2], also studied the characteristics of three-dimensional fountain flows

produced by the impingement of three-axisymmetric jets on a ground plane with cross

flow. The experimental results showed the presence of a complex vortex formed around

each impinging jet and fountain upwash flow , the results were then confirmed

numerically using k-ε model , Barata et al [3],[4] also found experimentally the mean

25

and turbulent velocity characteristics of single and multiple jets impingement through a

low velocity cross flow , they studied the shear layer surrounding the jets , the

impingement regions , and fountain upwash flow zone and measured the turbulent

structure parameters , their comparison of predicted and measured results shows that

the k-ε model is useful for the prediction of the mean flow field but fails to predict the

turbulent structure due to near- wall viscous effects.

On the other hand a research on an axisymmetric jet impinging on concave surfaces

has been studied by Hibara and Sudou [5] ,their resulting figures showed the

distribution of mean velocity ,turbulence energy , Reynolds stress components and the

static pressure.

Flow visualization technique is an interesting tool that provides valuable insight into

complex flow fields. This important tool is used regularly in air flow experiments. It

shows the behavior of the jet flow stream lines and verifies the shape of flow direction.

It is also essential for estimating a velocity profile and confirming the graphical

measurements data, moreover flow visualization is significant tool to insure the jets

symmetry shape, shows any jets deflection and describe any vortices that may occur in

the flow field. Several flow visualization techniques are used by different investigators

in the literature. Some methods are based on using a simple technique of spreading a

mixture of Kerosene and chalk on plane sheet .Elbanna and Sabbagh [6 ] conducted

experiments on flow visualization for two free jets impinging on vertical plate .The

results showed good velocity profiles , visualization and stress distributions. Other

investigators used smoke generators or Lazer Induced Fluorescence (LIF) techniques

[8]. Also Bernard [7] has employed different visualization techniques in order to

describe the flow pattern due to 15 jets impinging on a plane wall. The spreading over

method revealed the jet influence on the impinged surface and Lazer visualizations

26

sheet emphasized complex vortical structures. Velocity measurements were realized to

confirm this observation and to specify flow pattern. In addition, Bernard [9] has also

studied the wall flow generated by these jets. A comparison between two cases of flow

visualization techniques of two impinging axisymmetric circular jets have been carried

experimentally by Shoe-B et al [8], in one case they used Lazer induced fluorescence

(LIF) to visualize the flow structure, while they utilized smoke in the second.

Quantitative information has been obtained from these visualized flow regimes using

two different digital imaging systems. Results were presented for both the jet profile

shapes and the rate at which the jet expands in the downstream direction. These results

compare favorably with data obtained using established anemometry techniques.

On the other hand Behrouzi [10], presented predictions of the flow of a twin-jet

impingement on ground plane using the standard two-equation k-ε turbulence model,

the predictions were compared with Lazer Doppler Velocimetry experimental results.

The fountain formation region was qualitatively predicted .The quantitative under-

prediction of fountain development characteristics was observed to be around 50%, this

is probably due to fountain unsteadiness, which is not included in the steady state

Computational Fluid Dynamics predictions. Lazer Doppler Velocimetry measurements

were also used by Behrouzi and McGuirk [11] in order to study a closely spaced pair

of jets with same or different jet velocities. The jets interact with each other, with a

cross-flow and with an opposite solid wall .Emphasis was placed on the presentation of

the mean velocity and r.m.s contours in the fountain formation region between the jets.

The effect of jet imbalance and velocity ratio was studied, and then preliminary

Computational Fluid Dynamics predictions of the flow using a k-ε turbulence model

were presented.

27

Many researchers have carried out several numerical and computational studies on jet

impingement in the literature [12-17], most computational results in these researches

were compared and confirmed experimentally using either Lazer Doppler Velocimetry

or hot wires techniques .In addition , Dianat [18] has modified a k-ε turbulence model

to use it as the basis of predictions of the flow results from the orthogonal impingement

of circular 2-dimensional jets on a flat surface. Results in general confirmed the

superiority of the Reynolds stress transport equation model for predicting mean and

fluctuating velocities within the region of such flow.

The vertical take-off and landing military airplane (VTOL) working on the rough

ground was studied by each of Chuang and Cheng in [19]. They have employed the

SIMPLE-C algorithm, power-law scheme, two equation k-ε turbulent models, and

alternating direction implicit method in numerical simulation. The properties of the

flow field structure of the impinging twin-jet such as pressure, velocity, turbulent

kinetic energy and lift force under the effects of different width and height were solved

and shown. They have concluded that the lift force is strongly affected by the squeezed

and shortened effects of recirculation zones induced beside the twin-jet inlet. Similarly

Behrouzi and McGuirk [20],also have reported an experimental study of a closely-

spaced pair of interacting jets in the presence of both cross-flow and an opposing solid

wall , This experiment was used to gather validation data suitable for testing

Computational Fluid Dynamics model predictions of multi-jet ground impingement

flows.

Moreover, experimental and numerical studies of round high speed impinging jets with

varying nozzle height and pressure ratio were studied and presented by Knowles and

Myszko [21]. Wall jet growth was seen to be approximately linear with radius but

depend on nozzle height and pressure ratio.

28

On the other hand, Disimile and Savory [22] have investigated a mixing region of

two identical incompressible air jets at two different angles (45º,35º) . Their work has

confirmed that the growth of the 45-deg jet after impingement in the plane normal to

the nozzle plane was greater than that in the 35-deg case, but in the nozzle plane the

growth rate for both cases was identical and similar to that of a single jet. Similar to

this approach , a mixing mechanisms in a pair of liquid jets have been carried out by

Ashgriz, Brocklehurst and Talley [23].

Furthermore, an experimental research has been carried out by Knowles and Bray

[24] to study the flow fields associated with single and twin jets impinging in cross-

flows, using ground plane pressure profiles and flow visualization. Parameters such as

cross-flow-to-jet, velocity ratio, cross-flow boundary-layer thickness, nozzle height and

their effect on the position of the ground vortex have been investigated. Results showed

that the ground vortex moves away from the nozzle centerline as cross-flow-to-jet

velocity ratio is decreased, also the rate of change of position, however, depends on

other parameters. In addition to this work they have used the PHOENICS code [15] to

model the flow field surrounding subsonic and under-expanded jets impinging on a

ground plane in the presence of a cross-flow, for cases with both a fixed ground plane

and a 'rolling road'. The ground vortex formed in cross-flow is shown to move with

varying effective velocity ratio and with rolling road operation in the same manner as

experimentally observed.

Prasad, Mehta, and Sreekanth [25], also conducted an experimental and numerical

studies to investigate the impingement flow field produced on a typical axisymmetric

jet deflector. They concluded that these experiments will be useful for the design of a

typical axisymmetric jet deflector during the liftoff phase of a rocket.

29

An under-expanded sonic jet impinges on a perpendicular flat plate, a shock wave

forms just in front of the plate and some interesting phenomena can occur in the flow

field between the shock and the plate. This phenomenon was indicated by Iwamoto

[26] who presented experimental and numerical results on the flow pattern of this

under-expanded impinging jet. In the numerical calculations the two-step Lax-

Wendroff scheme was applied, assuming inviscid, axially symmetric flow. Some of the

pressure distributions on the plate showed that the maximum pressure did not occur at

the center of the plate and that a region of reversed flow exists near the center of the

plate. Nakabe and et al [27] have presented a study to examine the interaction between

two inclined impinging jets in in-line and staggered arrangements with cross-flow. It

was observed that the geometrical arrangement of the inclined jets had an influence on

the interaction between the two jet flows, on the vortical structures generated in the

downstream of the jets, and eventually on the enhanced regions of jet impingement heat

transfer. They had cooperated before this experiment also in a similar project approach

by studying the generation of longitudinal vortices in internal flows with an inclined

impinging jet for enhancing the target plate heat transfer [28]

Jet array configurations also have been subjected recently to some studies by

researchers, Arjocu and Liburdy [29] have studied the large scale structure formation

of a three-by-three jet array at low Reynolds number (466 and 1474) , this is as in the

case of cooling electronic components. The effects of the impingement distance were

studied over a range of impingement distance for jet diameters of two to seven. They

concluded that distinct changes were noted in the resulting vortex structure when the

impinging distance increases from 2 to 6 jet diameters. They also conducted an

experiment to investigate the near surface turbulence characteristics of an impinging

elliptic jet array at low Reynolds number [30]. In this experiment the dynamics of a

30

three-by-three elliptic jet array were analyzed relative to the flow structures within the

array. Two jet aspect ratios were used .The effects of impinging distance were studied

in the range of one to six jet hydraulic diameters. Also flow visualizations were used

for the identification of structures and quantitative analysis. The results have shown

that the integrated surface layer vorticity depends on the jet aspect ratio and

impingement distance.

1.3 Research objectives

In this thesis we extend the study on jet impinging by investigating the flow field of

three free parallel two-dimensional jets impinging on a flat plate normal to their axes.

The main objectives of this study could be summarized in the following points :

1. To predict the flow field of three interacting free parallel two-dimensional jets

impinging on a plate normal to their axis using hot wire technique. The study

includes the influence of changing some parameters on the resultant flow field

such as the location of the vertical plate and / or jets velocities.

2. To investigate the turbulence structure in the interacting jets upstream, wall jets

and fountains.

3. To study the resulting flow field by flow visualization technique.

4. To study the jets pressure distribution along the vertical impinging plate and the

lower wall of the test rig.

In addition the results of this investigations will help in understanding the flow

structure of two types of different wall jets interactions, specially between the middle

jet and the two outer jets after impingement .The application of the results is important

in vertical take off and landing aircrafts jets and in the application of multi jets for

cooling purposes such as cooling turbine blades.

31

CHAPTER – II

EXPERIMENTAL SETUP

This chapter demonstrates the experimental setup and instrumentations used for the

measurements of this work. Some detail description about the experiment test rig is

presented in section 2.1. The measuring instruments and tools are covered in section

2.2. Finally section 2.3 discusses the wire calibration in some details.

2.1 Setup and alignment

An existing test rig for jet studies [6] has been modified to suit the present research

requirements. The test rig consists of two supported parallel walls confining three

identical jets blocks as shown in Fig. 2.1 below.

Figure 2.1 Test rig schematic diagram

air

flo

w

air flow

scr

ee

ns

Dimensions in mm

9

32

(b) Modified nozzle top

view

The width of each wall is 2 m in the lateral direction and the length is 3 m in the axial

direction. The jet blocks are separated by equal distances and connected to three air

blowers to supply air. Before air converges to the nozzle exit, it passes through three

settling chambers for producing uniform velocities along the length of the slots .Each

jet block contains three grids to reduce the size of turbulence. The contraction ratio of

the nozzles in the horizontal direction is 13:1, each nozzle slot has a width tp=5 mm and

a length l=490 mm in the vertical direction. The exit frame of each jet nozzle outlet in

this experiment was modified to a new design as shown in Fig.2.2, in order to correct

an observed jet deflection in the old nozzle. Each nozzle slot, spans all of the distance

between the two confining walls to prevent air leak into the low-pressure regions

between the jets.

Figure 2.2 Tope views of the old and the modified jet nozzles.

The vertical impinging plate is set on moving part between the two horizontal confining

walls normal to the nozzles axes as shown in Fig.2.3. The confining walls extend 1 m

to either side of the midline between the three jets; traverse is carried out spanwise of the

(a) Old nozzle top

view

33

nozzle slot and in the lateral direction to determine the degree of uniformity of the flow

emanating from the nozzle.

Figure 2.3 Side view of jets blocks and vertical impinging plate .

The nozzles are designed with a contraction ratio of 13 :1 as mentioned before and

aspect ratio of 89:1, this to insure the two-dimensionality of the flow field. Overall

experiment test rig photos are shown in Figs. 2.4-2.8.

Figure 2.4 Traverse mechanism side view

34

Figure 2.5 Air blowers feeding the three jets .

Figure 2.6 Side view of jets blocks

35

Figure 2.7 Dynamic flow board for data acquisition system

The mean velocities of the flow and the turbulent intensities are measured using DISA

5600 hot-wire anemometers connected to a data acquisition system (as will be shown

later). The hot-wire anemometer is fixed on a locally modified traverse mechanism .

This mechanism is used for axial and lateral flow measurements, as shown in Fig. 2.8.

In this experimental research work , flow visualizations of the impinging jets are

carried out in order to show the behavior of the jet flow stream lines and verify the

shape of flow direction. This is done by spreading a mixture of kerosene and chalk

powder on a black Perspex sheet placed horizontally on the test rig lower wall between

the jets exit plane and the vertical impinging plate.

36

Figure 2.8 Traverse mechanism components

Finally the average flow field pressures and surface pressure along the lower plate

and the plate normal to the flow is measured using pressure taps of 0.5 cm diameter

evenly distributed in the middle part of the lower wall and vertical plates and

connected to a pressure transducer or electronic manometer as shown in Fig. 2.9.

37

Figure 2.9 Pressure electronic manometers.

2.2 Instrumentations

Constant Temperature Anemometry (CTA) or Hot Wire Anemometry - is a widely

accepted tool for fluid dynamic investigations in gases and liquids and has been used as

such for more than 50 years. It is a well-established technique that provides information

about flow velocity. There are several types of hot wires probes currently being used ,

the very famous types used in the measurements are single normal wire ,single slanted

wire , X-wire and triple wire . All velocities and velocity fluctuations across the jets

flow field in the experiment were measured using two types of constant temperature hot

wires probes manufactured by Dantec Company, namely, the single normal wire and

the triple wire. The following sections describe briefly these probes.

2.2.1 Single normal wire probe

The wire configuration used in the experiment is known as normal or straight wire

probe, it is called Miniature Wire Probe Platinum-plated tungsten (55P01). The wire as

38

shown in Fig. 2.10 has 5 m diameter and 1.2 mm length, it has straight prongs and

sensor perpendicular to probe axis. The wire is welded directly to the prongs and the

entire wire length acts as a sensor. The probe body is a 1.9 mm diameter ceramic tube,

equipped with gold-plated connector pins that connect to the probe supports by means

of plug-and-socket arrangements. It is a general purpose probe recommended for most

measurements in one-dimensional flows of low turbulence intensity. The accuracy of

turbulence measurements may be reduced because of interference from the prongs. On

the other hand, the more rigid construction makes it more suitable for high speed

applications without the risk of self-oscillation. It can be used when measuring mean

and fluctuating velocities in free-stream one-dimensional flows and it mounts with the

probe axis parallel to the direction of the flow. The single-sensor wire probes are

available in five different configurations.

Figure 2.10 Single wire probe (Miniature wire type by Dantec Dynamic

site www.dantecdynamics.com).

2.2.2 Triple-sensor gold-plated wire probe

The Triple-sensor gold-plated wires probe as shown in Fig. 2.11 is available in one

straight configuration for gas applications only, it is referred to as, Gold-plated tri-axial

39

probe (55P91). It has three mutually perpendicular sensors, consisting of gold-plated

wires. The gold-plated probes have 5 µm diameters, 3 mm long platinum-plated

tungsten wire sensors. The wire ends are copper and gold-plated to a thickness of 15 to

20 µm, leaving an active sensor, 1.25 mm, on the middle of the wire. They are designed

for measurements in high-turbulence flows of three-dimensions. The sensors form an

orthogonal system with an acceptance cone of 70.4°. The prong ends are all

perpendicular to the sensors. This gives minimum prong interference and increases the

accuracy, when the three probe signals are decomposed into velocity components. It is

used for measurement of the U, V and W velocity components in an instationary three-

dimensional flow field and provides information for calculation of the full Reynolds

shear stress tensor. It also mounts with the probe axis in the main flow direction. The

resulting velocity vector must be within the acceptance cone.

Figure 2.11 Triple wire probe provided by Dantec Dynamic site

www.dantecdynamics.com

Sensor identification

3 sensors perpendicular to each

other inside a sphere of 3 mm

40

2.2.3 Data Acquisition

The data acquisition system used to collect and analyze the turbulent flow data is called

" AcqWire " devolped by Dantec company . "AcqWire " is an application software for

Constant Temperature Anemometer (CTA) system intended for experimental

measurements and analysis of fluid flow. The program performs data acquisition, data

processing and file manipulation. It can be used with any thermal sensor anemometer

systems which output an analogue signal in the range 0-10 v. This signal is a

continuous analogue voltage .In order to process the signal digitally it has to be

sampled as a time series consisting of discrete values digitized by an analogue-to-

digital converter (A/D board), see Fig.2.7.The parameters defining the data acquisition

are the sampling rate (SR) and the number of samples, (N). They together determine the

sampling time as T=N/SR. The values for SR and N depend primarily on the specific

experiment. The main characteristics of the data acquisition system are summarized in

the following points :

Resolution: min. 12 bit (~1-2 mV depending on range).

Sampling rate: min. 100 kHz (allows 3D probes to be sampled with approx. 30

kHz per sensor).

Simultaneous sampling: (if not sampled simultaneously there will be phase lag

between sensors of 2- and 3D probes)

External triggering: (allows sampling to be started by external event)

Signal Conditioning of anemometer output , see Fig. 2.12.

Increases the AC part of the anemometer output and improves resolution.

Allows filtering of anemometer

- Low pass filtering is recommended

41

- High pass filtering may cause phase distortion of the signal

Sample rate and number of samples: Time domain statistics (spectra) require

sampling rate 2 times the highest frequency in the flow.Amplitude domain statistics

(moments) require uncorrelated samples. Sampling interval min. 2 times integral time

scale.Number of samples is sufficient to provide stable statistics (often several

thousand samples are required).Proper choice requires some knowledge about the flow

aforehand, [32].

Figure 2.12 Constant Temperature Anemometer layout diagram (by Dantec

Dynamic site www.dantecdynamics.com)

2.3 Calibration of hot-wires

Calibration establishes a relation between the CTA output and the flow velocity. It is

performed by exposing the probe to a set of known velocities, U, and then record the

voltages, E. A curve fit through the points (E,U) represents the transfer function to be

used when converting data records from voltages into velocities. A continous

relationship is provided by calibraion polynomial which is computed by curve fitting

the calibration points.The output of the calibration polynomial is the effective cooling

velocity which the probe senses. It should be equal to the reference velocity component

when the sensor is normal to the fluid velocity at the time of calibration , ie Ueff =U.

42

W

U

V

yi

xi

zi

U

The anemometer output for the "jth

" sensor, Ej is related to the corresponding effective

velocity, Ueffi , by the calibration polynomial.

21 2

neff O j j n jU C C E C E ......C E (2.1)

where CO , C1 .....Cn, are called the calibration coefficients. The effective cooling

velocity, Ueff , is equivalent to the linearized anemometer output.

The laboratory coordinate system usually defined relative to the experimental facility

by the orthogonal unit vectors (x y zi ,i ,i ). The fluid velocity vector U can be written

according to the laboratory coordinates as:

x y zU U i V i W i (2.2)

where, U, V, W, are the components of U in the directions of x, y, z,

respectively as shown in Fig .2.13 below .

Figure 2.13 Velocity components vectors in the laboratory coordinates.

43

3i

1i

2i

1

2

3

U

The wire coordinate system is a right-hand ruled Cartesian coordinate system defined

relative to the axis of the sensors. A sensor aligned with wire coordinate axis 1 is

called sensor 1, a sensor aligned with axis 2 is sensor 2 and a sensor aligned with axis 3

is sensor 3. The wire coordinate is also defined by the orthogonal unit vectors 1 2 3i , i , i .

A fluid velocity vector, U decomposed into wire coordinates is described by:

1 1 2 2 3 3U i i i (2.3)

where 1 2 3, , , are components of U in the direction of 1 2 3i , i , i , respectively as

shown Fig.2.14below.

Figure 2.14 Velocity components vectors in the wire coordinates.

The thermal sensor is cooled by velocity components in all directions. In this respect

the theory of angular response of thermal sensors began with the concept of "Cosine

Law". This law is a model for the angular response of thermal sensors which assumes

44

the sensor to be insensitive to the component of velocity parallel to the sensor.

Therefore the Cosine Law can be defined using wire coordinates directions as:

2

3

2

2

2

1 0 effU

2

3

2

1

2

2 0 effU (2.4)

02

2

2

1

2

3 effU

The position of the zero term in the above three equations reveals the major assumption

involved in the Cosine Law: there is no contribution to the effective cooling of the

sensor in the direction of the wire.

However an improved model was developed by Finn Jorgensen of Dantec Electronic,

Denmark [31], to account for the distinct contributions to the effective cooling velocity

of the three velocity components in the wire coordinates system.

So, by interfering the effect of Jorgensen's principle on the Cosine Law of the previous

3 wire equations they were modified to:

2 2 2 2 2 21 1 2 3 eff y pU k k

2 2 2 2 2 22 1 2 3 eff p yU k k (2.5)

2 2 2 2 2 23 1 2 3eff p yU k k

The yaw factor, ky provides a contribution to the effective cooling velocity due to the

velocity component tangential to the wire. The pitch factor, kp , provides a contribution

to the effective cooling velocity due to the velocity component normal to the wire and

perpendicular to the plane of the supports. Typically, ky =0.15- 0.2, and kp=0.9-1.02.

45

Jorgensen's equations are especially used for triple sensor probes, since at any given

point in the fluid the three unknown velocity components can be solved for using the

set of three equations.

The application of Cosine Law and Jorgensen's equations on the two probes types used

is given in the following, sections.

Single Sensor Probe:

Figure 2.15 Single Sensor Probe:

With a single sensor probe as shown in Fig. 2.15 above , it is usually straightforward to

align the wire coordinate system with the laboratory coordinate system. For this

orientation, zyx ii,ii,ii 321 , and W,V,U 321 .

Now from the Cosine Law and for one dimensional flow where V=0 and W=0, we

obtain:

2 2effU U or U=Ueff2 (2.6)

Probe stem

Z

x

46

The result shows that the linearized anemometer output, Ueff of a single sensor probe is

a direct indication of the instantaneous component of fluid velocity in the x direction of

the laboratory coordinate system. It has to be noted that the effective velocity

measurements are collected after all wires have been calibrated.

Triple Sensor Probe:

Figure 2.16 Triple sensor probe.

The triple sensor probe as shown in Fig. 2.16 above has three sensors mounted

orthogonally. The three sensors define the 3 directions of the wire coordinate system.

Using Jorgensen's equations with the planes of supports defined previously we can

write:

2 22 2

1 1

2 2 2 2

2 2

22 2 233

1

1

1

y peff

eff p y

eff p y

k kU

U k k

U k k

(2.9)

Probe stem

45°

55°

35°

3

1

z

x

35°

2

y

47

Solving for the components of U in wire coordinates, yields:

12 2 22

11

2 2 2 2

2 2

2 22 23 3

1

1

1

y p eff

p y eff

effp y

k k U

k k U

Uk k

(2.10)

To transpose the velocity vector from wire to laboratory coordinates, the components of

the vector in wire coordinate should be multiplied by the direction cosines of the solid

angle subtending the unit vectors of the two coordinate systems. This can be expressed

mathematically as:

1

2

3

ij

U

V cos y

W

(2.11)

where yij is the solid angle subtended by the unit vectors i j( i ,i ) , i=1,2,3 ,j=x,y,z.

Assume the probe stem is horizontal and defines the x direction, the vertical direction

defines the z direction, wire 3 is in the vertical plane as shown in the previous figure .

The direction cosine matrix for Dantec triple sensor probes [31] is given by:

45 35 3 45 35 3 54 7

45 45 0

45 35 3 45 35 3 35 3

o o o o o

o o

ij

o o o o o

cos cos . cos cos . cos .

cos y cos cos

cos sin . cos sin . cos .

(2.12)

This is the default transformation used to obtain the velocity components U, V, W in

laboratory coordinates defined above.

48

Now if the instantaneous velocity components of the jets flow are determined then the

velocity fluctuations components also can be determined as:

__'

__'

__'

u U ( t ) U

v V ( t ) V

w W ( t ) W

(2.13)

where the mean velocity components are determined from :

1

1N__

i

i

U UN

,

1

1N__

i

i

V VN

,

1

1N__

i

i

W WN

(2.14)

Now the mean square value of the velocity fluctuations components are defined as

2 2

1

1N

'i

i

u (U U )N

, 2 2

1

1N

'i

i

v (V V )N

, 2 2

1

1N

'i

i

w (W W )N

(2.15)

Consequently the root mean square value of the velocity fluctuation components can be

determined as:

2 '

rmsu u ,

2'rmsv v

, 2'

rmsw w

(2.16)

The level of turbulence or the turbulence intensity components then can be calculated

as :

rms

ti

uu

U ,

rmsti

vv

V ,

rmsti

ww

W

(2.17)

49

On the other hand the Reynolds shear stress components can be calculated by the

relations:

1

1N

' 'i i

i

u v (U U )(V V )N

1

1N

' 'i i

i

u w (U U )(W W )N

(2.18)

1

1N

' 'i i

i

v w (V V )(W W )N

All above equations are computationally determined using Quick Basic program for

faster calculations of results (see Appendix-III).

Calibration of Hot wire experimentally:

For better and accurate results both triple and normal single wires probes are calibrated

before each measurement set. A single probe calibration was carried out in the

laboratory using a round jet as shown in Fig.2.17. The wire is set very near to the jet

exit opening with the probe aligned parallel to the flow direction .The air blower is

then started at the highest jet exit velocity (Uo=45 m/s), while the probe is adjusted

back and forth near the jet exit ,the minimum possible turbulence intensity level should

be achieved by adjustment . The jet exit velocity could be found from the dynamic

pressure at the jet exit using electronic manometer. At the highest jet velocity the

corresponding wire voltage is measured also using Dantec Acqwire software . The

blower speed is then reduced gradually until the lowest blower velocity value is

reached. At each blower speed the jet velocity and the corresponding wire voltage are

50

measured. The velocity values should cover all the jets velocity range in the flow field

span .The resultant calibration (velocity-voltage) curve is then fitted with minimum

possible standard deviation points using the Acqwire software.

The calibration of the triple wire is also required before use and could be achieved by

the same procedure of the single wire calibration process, however there are additional

steps that should be accounted for this calibration. The triple wire probe is set near the

jet exit plane first and then tilted by 35o from the axis of the jet centerline , after that

each wire is set normal to the jet centerline and calibrated individually while following

a similar procedure to that applied to the single wire as stated above. Different velocity

values and corresponding wire voltages are applied and measured at each wire. Fig.

2.18 shows a sample set of calibration curves of the single and triple wire probes.

(a) round jet side view

(b) round jet front view

Figure 2.17 Side view and front view photos of the round jet.

51

(a) Single wire

1.6

1.8

2

2.2

2.4

2.6

2.8

5 10 15 20 25 30 35 40 45 50

Effective velocity (m/s)

E ,

volt

1.6

1.8

2

2.2

2.4

2.6

2.8

5 10 15 20 25 30 35 40 45 50

Effective velocity (m/s)

E ,

vo

lt

wire 1

wire 2

wire 3

(b) Triple wire

Figure 2.18 Calibration curves for (a) single and (b) triple wire probes

52

CHAPTER – III

MEASUREMENTS AND FLOW VISUALIZATION

This chapter explains the method and the steps of taking measurements and readings

in this project. Jets symmetry check is important in the measurements and this is

discussed in section 3.1. The measurement techniques results using single and triple

wire probes are then presented in section 3.2. Sections 3.3-3.5 introduce the method of

taking measurements of two and three planar free and impinging jets. Finally the flow

visualization technique of the impinging jets is discussed in section 3.6 .

3.1 Symmetry Check

Before taking any measurements the jet symmetry is checked. To confirm jet

symmetry, the measurements of mean velocity at different locations across the jet flow

field should be identical. This was done in the lab for the three jets using single normal

hot-wire probe. The test of symmetry for jets was conducted by taking measurements at

three axial locations across the flow field of each jet. Data were collected at 20 points

in the lateral direction for each jet. On this basis jets symmetry was checked and the

results were symmetric for all locations. Figs.3.1-3.3 show the velocity profiles for

symmetry check for the three jets. Obviously seen in these figures that the three

velocity profiles of jet 1and jet 3 are approximately overlap but for jet 2 there is little

deviation. This deviation is appeared while many trials were applied to the jet nozzle

outlet in order to correct this deviation during design process.

30

53

0.6

0.7

0.8

0.9

1

1.1

-0.14 -0.1 -0.06 -0.02 0.02 0.06 0.1 0.14

y/L

for x/tp=60

for x/tp=100

for x/tp=140

m

U

U

0.6

0.7

0.8

0.9

1

1.1

-0.14 -0.1 -0.06 -0.02 0.02 0.06 0.1 0.14

y/L

for x/tp=60

for x/tp=100

for x/tp=140

m

U

U

0.6

0.7

0.8

0.9

1

1.1

-0.14 -0.1 -0.06 -0.02 0.02 0.06 0.1 0.14

y/L

for x/tp=60

for x/tp=100

for x/tp=140

m

U

U

Figure 3.1 Velocity profiles to check Figure 3.2 Velocity profiles to check

jet (1) symmetry . jet (2) symmetry .

Figure 3.3 Velocity profiles to check

jet (3) symmetry .

54

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

y/L

Current Result

Elbanna and Sabbagh result [6]

m

U

U

The jets symmetry results were compared also with similar previous studies conducted by

Elbanna and Sabbagh [6] , as shown in Fig. 3.4 .The observed deviation in the figure

between the two resultant velocity profiles also came from the difference in the jet nozzle

outlet design in the two studies as shown early in Fig.2.2 .

Figure 3.4 Comparison of jets symmetry check between

current and perivous studies.

3.2 Comparison of Single and Triple wire measurements

In this project, single wire probe was used to measure the air flow velocity and

fluctuation in one direction, triple wire probe was used to measure mean velocity and

velocity fluctuations in three directions along the flow field. The concept of constant

temperature anemometer reading is that, the velocity is measured by its cooling effect on a

heated single sensor. A feed-back loop in the electronics keeps the sensor temperature

constant under all flow conditions. The voltage drop across the sensor thus becomes a

direct measure of the power dissipated by the sensor. The anemometer output based on

the calibration file therefore represents the instantaneous velocity in the flow. All

55

0.6

0.7

0.8

0.9

1

1.1

-0.14 -0.1 -0.06 -0.02 0.02 0.06 0.1 0.14

y/L

Single wire

Triple wire

m

U

U

experimental measurements were taken manually across the jet at specified locations.

To compare the velocity readings using single and triple wires probes, the velocity

measurements were conducted for a single jet at 45 cm distance from jets exit plane

using both wire techniques. Results are graphically shown in Fig. 3.5. It was concluded

that the two results are identical and approximately overlap.

Actually, it was more suitable to use triple wire for flow measurements if all velocity

components in all direction were required. In this project single wire probe was easier

and more convenient to use in conducting impinging region measurements or where the

flow contains vortices of known direction.

Figure 3.5 Velocity profiles using single and triple wire

measurements for single free jet at L=50 cm.

3.3 Two parallel free jets measurements

Single wire was used for measurements of axial average velocity at different locations

for the two free jets arrangement, this was done to compare and check the velocity

56

distributions crosswise the two jets with similar studies in the literature [6] as shown in

Fig.3.6.

Figure 3.6 Comparison of Axial velocity profile at x/tp=20

between current and perivous studies.

Measurements were taken at four axial distances from jets exit plane, namely 10, 25, 30

and 35 cm. At each location 20 points on each side of the centerline of the two parallel

jets were measured. The measurements start after aligning wire probe properly with the

jets centerline. Wire probe is set exactly normal to the flow using right angle ruler .The

probe is transferred automatically any / where in the lateral or axial direction using the

traverse mechanism. The starting measuring point is the jets centerline .At this point the

probe is held to acqwire data using a sampling rate of 2048 , then the collected data is

saved as an ASCII file mode for later processing of data using code in QuickBasic.

The probe is moved then to next point and the same procedure is followed to save and

collect data. The same steps are repeated at all points along the traverse direction of the

flow field. The traverse mechanism should be moved carefully to the new distance, this

was carried out manually in the lab using screwed steel bar connected to the traverse

mechanism.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

y/s

Current result

Elbana & Sabbagh result [6]

1o

U

U

57

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

y/s

x/tp=20 x/tp=50

x/tp=60 x/tp=70

1o

U

U

0

0.1

0.2

0.3

0.4

0.5

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

y/s

u'/U

o1

x/t=20x/t=50x/t=60x/t=70

2'u

U

Figure 3.7 shows the graphical presentation of mean velocity ratio at those locations for

two parallel free jets, while Fig. 3.8 shows the axial turbulence intensity profiles for

two equal free jets.

Figure 3.7 Axial mean velocity profiles of downstream merging

region of two free parallel jets.

Figure 3.8 Axial turbulence intensity profiles for double jet arrangement .

58

0.12

0.16

0.2

0.24

0.28

0.32

0.36

0.4

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

y/s

x/t=30x/t=50x/t=80x/t=140

1o

U

U

3.4 Three parallel free jets measurements

The experimental study of three parallel free and impinging jets measurements is the

main goal in this project. In free jets study triple wire technique is used in all

output measurements including average velocity components ratios

(U/Uo1,V/Uo1,W/Uo1), Reynolds normal stress components (u'2/ Uo1

2, v'

2/ Uo1

2, w'

2/Uo1

2)

and Reynolds sheer stress components (u'v'/Uo12 , u'w'/Uo1

2 , v'w'/Uo1

2). The

replacement between single and triple wire probe was required some care in the

experiment, this was necessary to avoid wires breakage due to surface contact. Also

when the probes are replaced, each jet was adjusted and aligned properly with the new

wire probe stem to insure good and accurate measurements.

In this experiment four axial distances 15, 25, 40 and 70 cm were selected along the

flow direction of the interacted jets for the measurement of the velocity components as

shown in Fig.3.9.

Figure 3.9 Axial mean velocity profiles of three free parallel jets

During the calibration process the triple wire was oriented in such a way that wire 3 of

the probe must point up [32]. The wire probe should be aligned properly with the jet

59

nozzle centerline to avoid any asymmetry that may take place in the flow field later.

The movement of triple wire was controlled manually using remote control device

connected to the probe holding arm , this device is able to move the arm in lateral and

axial directions for measurements. Data was collected at each position using Acquire

data acquisition software at a sampling rate of 2048. The collected data is saved as

mentioned previously in ASCII files for later analysis by a computer program written in

QBasic language.

3.5 Three parallel impinging jets measurements

In these measurements, three parallel jets with equal velocities are impinged on a

vertical plate, this plate was placed normal to the jets air flow at different distances

from the jets exit 10, 20, 30, 45 and 70cm. At plate distance 70 cm from the jet exit

plane, the triple wire was used for the measurements of the impinging jets flow field, in

this confined flow two traverse distances were selected, one at 30 and the other at 60

cm from jets exit .The measuring points along these traverse locations were started

from the centerline of the middle jet which is also the center of the interacted jets

region see Fig.3.10.The measurements were taken at equally spaced points on the right

and the left side of the centerline.

S

Upwash Stagnation

points

Negative pressure

region

Impinging plate

Velocity profile

Figure 3.10 Schematic diagram of the flow field of three impinging jets

60

Data collection process is the same that described earlier in section 3.3. Measurements

were conducted after aligning the wire with the direction of the flow as mentioned

earlier. At 60 cm measuring distance wall jets exist after impinging, the wire probe was

rotated approximately 90o from it's centerline , this is to make the probe normal to the

expected flow of the jets and consequently measure the flow velocity of the wall jet.

At the other selected plate distances (45,30,20 and 10 cm from the jets exit) , it was

detected that some rotating vortices and reverse flow may occurred at the locations of

measurements in the flow field as revealed by the visualization pattern In this case

triple wire was not used for the flow measurements in these regions .This was due to

the inflexible moving of the wire probe in these narrow regions and also to avoid any

wrong data which may caused by the random flow stream directions produced by

vortices . However a single wire was used for the measurements in these flow regions

.It was required a method to know the flow directions and to collect the correct flow

measurements. One trial was accomplished by setting the wire probe normal to the jets

exit air stream in the vortex region and then velocity components (U,V) are found by

rotating the wire two times toward the lab coordinates (x,y) based on the

corresponding reading values of Ueff1,Ueff2 . At each measuring point there are two data

that should be collected and saved , one is Ueff1 where the wire is parallel to the lateral

direction and the other is Ueff2 where the wire is parallel to the axial direction .Each of

these two velocities has two components (U,V) in wire or lab coordinates . Now

solving equation (2.5) for two dimensional case then U, V could be determined.

Consequently the corresponding velocity fluctuations and stresses could also be found.

This method was used in all other flow measurements at the above mentioned plate

61

distances. Table I.1 summarizes all distances of the impinging plate and the type of hot

wire used in the measurements.

On the other hand the surface pressure of the incident flow along the vertical

impinging plate and also the static pressure at all previous distances were measured,

these measurement were carried out using pressure taps of 0.5 cm diameter evenly

distributed on the middle part of the vertical plate , the taps are connected to a

pressure transducer and /or electronic manometer which gives the pressure reading .

3.6 Flow Visualization Technique

Due to the limited budget available to this research work , flow visualization is

obtained using the simple technique of spreading a mixture of kerosene and chalk on a

Perspex sheet placed horizontally between the jets exit plane and the vertical plate.

Four Perspex black sheets with different widths of 10, 20, 30 and 50 cm were used for

this purpose.

Good flow visualization was achieved after some experimental trials. The technique

is based on uniformly spreading a layer of light oil such as kerosene on black Perspex

sheet, fine chalk powder is then sprinkled uniformly on the oil layer across and along

the flow area using a piece of cloth. The sheet is set in front of the jets nozzle on the

lower wall of the test rig and parallel to the flow .Jets are then run and passed over the

chalk-oil mixture, the stream lines formed by the mixture reveal the shape of the

resultant flow field .The jets are stopped and the Perspex plate is left to dry for one or

two days and then photographed .This process was repeated many times in order to

obtain satisfactory flow visualization image of the resultant flow field.

62

Before conducting visualization experiments the jets are also adjusted so that they

have equal velocity strengths and flow symmetry, this was done each time the vertical

impinging plate is moved to a different position along the flow direction.

63

CHAPTER - IV

DISCUSSION OF RESULTS

In this chapter all results of free and impinging jets measurements are discussed.

Section 4.1 discuss the results of two and three free jets arrangements. The study of

three equal and unequal impinging jets results at different impinging plate locations is

presented in section 4.2. The results of the flow pressure distributions on the impinging

plate for equal and unequal impinging jets are discussed in section 4.3 and 4.4. The

static ground plane pressure results are also covered by these two sections.

4.1 Free jet measurements

This section shows the study of two and three free parallel jets results. In each

jetsarrangement, different measuring locations across the flow field were selected ,the

resultant shape of the interacted free jets is then studied . All calculations results of this

section are tabulated in Appendiix-1.

4.1.1 Interaction of two free parallel jets

Referring to the graphical presentation of two parallel equal free jets in Fig. 3.7, it can

be seen that at distance x/tp=20 , the mean velocity profiles of the two jets are identical

and the resultant bell shape of the two velocities looks very steep. The two jets did not

merge into each other yet at this distance. Figure 3.6 has shown a comparison of the

mean velocity profile obtained at x/tp=20 with that obtained by Elbanna and Sabbagh

41

64

[6] .The figure shows that the velocity profiles of the two studies have nearly similar

shape . However the shift in the two velocity readings is due to the difference in the

nozzles outlet design between the two cases, this gives a difference flow divergence at

the jet exit.

At x/tp=50 the velocity profiles of the jets indicate that the two jets start approaching

each other ,the flow velocities become weaker and the velocity profiles shape turn out

to be more flatter. Further increase in the distance from the jets exit plane (x/tp=60)

makes the two jets start to merge into each other and the velocity profiles become more

flatter. At x/tp= 70 the two jets almost have reached a complete merging, the resultant

velocity shape of the two jets become slightly similar to that produced by the single jet.

The turbulent intensity distribution at different measuring distances (x/tp=

20,50,60,70) of the two free jets is shown previously in Fig.3.8, at each distance the

figure shows high intensity near the edge of each jet with minimum intensity value at

the centerline of the jet., this is due to the nozzle edge effect and the air entrainment, it

disappears later as the two jets merge and become weaker.

4.1.2 Interaction of three free parallel jets

Figure 3.9 has shown graphically the interaction of three parallel free jets at different

locations .It can be seen from the figure that at distance of x/tp=30 the mean velocity

profiles of the three jets are approximately similar and the velocity bell shape of the

three jets looks steep and sharp. It clearly obvious at this distance that the merging of

the three jets did not occur yet and each jet is independent. At x/tp=50 the velocity

profiles of the jets indicate that the two side jets are starting to approach the middle jet.

The velocities strength get weaker and the velocity profiles shape become less

65

m

o

U

U1

x/tp

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

Jet 1Jet 2Jet 3

sharpness. Further increase in the distance from the jets exit plane (x/tp=80) bring the

three jets to merge more into each other, the velocity shape become more flatter. At x/

tp=140 the three jets approximately reach a complete merging, the resultant velocity

shape of the three jets become similar to that produced by a single jet.

Figure 4.1 shows the variations of maximum velocity at the centerline of each jet with

axial distance. As shown from the figure that Um is decreasing with the increase in x/tp

until x/tp=80 then it becomes constant and equal for all jets.

Figure 4.1 Variations of maximum velocity along the centerline

of each jet with axial distance.

Figure 4.2 also shows the approach of the outside jets centerline to the middle jet. As

can be seen by the figure when the axial distance increases, the two outside jets are

attracted gradually to the middle jet until they merge.

66

-1.5

-1

-0.5

0

0.5

1

1.5

20 30 40 50 60 70 80 90 100 110 120 130 140

x/tp

y/s

Jet 1Jet 2Jet 3

Figure 4.2 Trajectory of the central streamline of each of the three jets.

The variations of turbulent intensity components with lateral and axial distance for the

three jets are shown in Figs. 4.3 and 4.4 respectively.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

y/s

u'/U

o1

x/t=30

x/t=50x/t=80

x/t=140

2'u

U

Figure Figure 4.3 Axial turbulence intensity profiles in the merging region of

three free parallel jets

67

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

y/s

x/t=30x/t=50x/t=80x/t=140

2

1o

v '

U

Figure 4.4 Lateral turbulence profiles in the merging region of three free

parallel jets.

It can be noted from these figures that the intensities profiles are shrinking and

reducing with the increasing in the distance from the jets exit plane. Turbulent

intensities in the axial direction look sharp near the jets nozzle comparing to that in the

lateral direction, this is due to the effect of nozzle edges and the entrainment of air.

Also the shear stress profile is presented in Fig. 4.5.

0

0.0003

0.0006

0.0009

0.0012

0.0015

0.0018

0.0021

0.0024

0.0027

0.003

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

y/s

u'w

'/U

o1

x/t=30x/t=50x/t=80x/t=140

2

1

''

OU

vu

Figure 4.5 Shear stress profiles in the merging region of three free

parallel jets.

68

As shown by the figure, the level of shear stress decreases with the axial distance from

the jets exit, it has very low overall values and could be neglected.

4.1.3 Variations of momentum in three parallel jets

The total conservation of momentum equation [32] state that

Time rate of change of the time rate of change of net rate of flow of linear

linear momentum of the = the linear momentum + momentum through

system of the contents of the control surface

the control volume

or

sys contents of c .v

sys cv cs

F F

DU dV U dV U U dA

Dt t

The first term on the left is the total rate of momentum which is donated as Jt , the first

term on the right side could be neglected for steady flow and the second term in the

right is the rate of momentum leaving the control surface which is the jets velocity

momentum J and the jets pressure momentum Jp in this experiment . So the above

equation could be written as:

Jt= J + Jp

(4.1)

(4.2)

69

0

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

0.36

0.4

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

y/s

x/t=30

x/t=50x/t=80

x/t=140

o

J

J

where Jt= 2 2'

cs(U u ) dy (4.3)

Jp =2

c.s csp dy (U ) (4.4)

The integration in the pervious equation is an indication for total fluid particles

momentum in the entire system. It can be observed that the velocity fluctuation term is

introduced in the equation to consider the turbulence effect.

The distributions of velocity momentum J with axial distance for the three jets are

shown in Fig. 4.6, it can be seen that the velocity momentum profiles behave the same

trend as the velocity profiles shown previously in Fig. 3.9. The distributions of pressure

momentum Jp can be seen from the pressure distributions on the vertical plate which

will be shown later.

Figure 4.6 Variations of momentum in the merging region of three free

parallel jets

70

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120 140

x/tp

Jet 1Jet 2Jet 3

The variation of centerline momentum with axial distances for each jet is shown in

Fig.4.7. As shown by the figure , when the measuring distance from the jet exit

increases the kinetic energy decreases gradually, thus the maximum momentum also

decreases , this decrease is contributed to the entrainment of air with the jets stream. , at

x/tp=80, the maximum momentum does not change much with any further increase

beyond this distance.

Figure 4.7 Variations of flow momentum along the centerlin

each jet with axial distance.

4.1.4 Comparison between free jets arrangement results

The flow behavior of the dual jets and triple jets is similar. Figs.4.8-4.10 show the

velocity and turbulent intensity profiles of two and three jets .It can be seen from the

figures that in the two jets arrangement the jets start to approach each other earlier than

the three jets case, but as the axial distance from the jets exit increase the three jets

merge earlier than that of the two jet and the profiles look more steeper.

71

0.1

0.2

0.3

0.4

0.5

0.6

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

y/s

Three free jetsTwo free jets

1o

U

U

0.16

0.2

0.24

0.28

0.32

0.36

0.4

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

y/s

Dual jets

1oU

U

0.12

0.16

0.2

0.24

0.28

0.32

0.36

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

y/s

Triple jets

1oU

U

Figure 4.8 Velocity profiles at x/tp=20 for two and three jets arrangements.

Figure 4.9 Velocity profiles at x/tp=50 for double and triple jets arrangements .

72

0

0.1

0.2

0.3

0.4

0.5

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

y/s

Three jets

2'u

U

0

0.1

0.2

0.3

0.4

0.5

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

y/s

Dual jets

2'u

U

Figure 4.10 Axial turbulence intensity profiles at x/tp=50 for double and

triple jets arrangements .

Figure 4.11 shows the growth profiles in the half jet width against the axial distance for

single and dual jets results which are obtained from ref.[6] .The figure includes also the

growth profile for triple jets result of the current study .It is clear that the half jet width

in single and dual jets increase more rapidly with distance than that for triple jet , this is

because the triple jets velocity profile become steeper with the increase in the distance

comparing to the single and dual jets case .

73

x/tp

0

2

4

6

8

10

12

0 20 40 60 80 100

Triple jetsDual jets from ref.[6] Single jet from ref.[6]

Poly. (Triple jets)

y0.5/tp

Figure 4.11 Growth of jet width with downstream distance for

single , double and triple jets arrangements.

4.2 Impinging jets results

This section discuss the comments on the results of the jets impinging on the vertical

plate as well as the results of single, double and triple impinging jets .All calculations

results of this section are tabulated in Appendix-I. The comments of results are

demonstrated on the basis of flow visualization and the graphical presentation of the

data collected of each jet arrangement, this is explained in the following paragraphs.

4.2.1 Single impinging jet

Referring to Fig. 4.12 below, it shows the visualization of single impinging jet at 45

m/ s exit flow velocity and impinging on a vertical plate placed at 45 cm from the jet

74

exit .It can be seen from the figure the formation of the upwash in the downstream flow

region .The figure shows also that the jet flow is broken down into two parts after

striking the impingement plate, one part forms the outside wall jet as moving flow

fountain and the other part is reflected back and interacted with downstream flow .The

jet is spreading more with the axial distance while the jet velocity strength gradually

decreasing .

Figure 4.12 Flow visualization of single impinging jet at H=45 cm

4.2.2 Three parallel impinging jets

Setting the vertical plate across the free jets path at different distances from the jet exit

plane cause changes in the resultant flow field shape. Figure 4.13 shows the changes of

the flow field shape for three impinging parallel jets of equal strength with changes in

the distances between the jets exit plane and the vertical plate.

Vertical

plate

Jet exit

75

Figure 4.13 Flow visualizations pattern for three equal impinging jets at

different plate distances.

The figure shows that each jet collides with the plate and produces two wall jets .These

two wall jets move away from the two outside jets (jet 1 & jet 3) after impinging. The

two other wall jets which are produced by the middle jet collide with the opposing two

(4.13e) H=70 cm

(4.13d) H=45

cm

(4.13c) H=30 cm

(4.13b) H=20 cm

(4.13a) H=10

cm

76

wall jets which formed by the impinging of the two outer jets on the plate and form

vortices. Figure 4.14 shows a similar earlier study on the visualization of two

impinging jets of equal strength at different plate locations [7]. It describes how the

nature of the flow field is influenced by changing the distance H between the nozzle exit

plane and the vertical plate.

Figure 4.14 Flow visualizations pattern for two equal impinging jets at different

plate distances [7].

(4.14a) H=15 cm

(4.14b) H=20 cm

(4.14d) H=50

cm

(4.14c) H=25 cm

77

0.12

0.18

0.24

0.3

0.36

0.42

0.48

0.54

0.6

-2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2

y/s

H=10

H=20

H=30H=45

H=70

2

1

1

2O

P

U

The figure shows also the existence of vortices, stagnations points and wall jets in some

flow field regions. The resulting flow field in this study seems less complex than the

three impinging jets case, this is because less jets interactions and impact flow take

place. In the following paragraphs the results of the flow field resulting from three

parallel jets impinge on a vertical plate are presented and discussed in more details.

1. Impinging plate distance H/tp =20 (H=10 cm):

At this distance the pressure profile as shown in Fig. 4.15 below shows high pressure

values on the vertical plate due to the high kinetic energy of the flow.

Figure 4.15 Pressure distribution across the impinging vertical plate at different

distances from the jets exit.

On the other hand Fig. 4.16 shows two vortices existing in the midway between the jets

exit plane and the vertical plate. These vortices are formed by the air entrainment

between the downstream moving jets and the upstream moving fountain.

78

Figure 4.16 Flow visualization of three impinging jets at H=10 cm

The figure shows also the outside wall jets which are produced by the two outer jets. In

this region the flow is very complex due to the small distance between the jet exit plane

and the vertical plate. The two opposing wall jets of the outer jets interact with the

middle impact jet and form a complex flow field, this result in a very weak middle jet,

see Fig.4.17a. In this figure it can be seen that the axial velocity profile has two high

values at the outer jets and low value at the middle jet , the lateral velocity profile

shows nearly equal maximum velocity value at the centerline of each jet but with lower

level comparing to the axial velocity . Fig.4.17b is corrected form of Fig.4.17a which

considers the flow direction and the negative values of the velocity components. This

figure was plotted with the aid of Fig 4.16 by following the flow direction using stream

lines in the visualization pattern at this plate distance.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

y/s

Mea

n V

elo

city

Ra

tio

U/Uo1V/Uo1

H=10

cm

Figure 4.17a Axial and lateral velocity profiles for three equal impinging

jets

at x/tp =10 and H=10 cm

Vertical plate

79

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

y/s

Mea

n V

elo

cit

y R

ati

oU/Uo1V/Uo1

Figure 4.17b axial and lateral velocity profiles for three equal impinging jets at

x/tp =10 and h=10 cm (corrected on the basis of fig. 4.16 )

Figure 4.18 shows the graphical presentation of turbulent intensity of this flow field.

The turbulent intensity profile as shown fluctuates with the lateral distance and has

random shape. The hot wire in this case can only gives an indication for the intensity

measurements less than or equal to 30% of the mean velocity.

H =10 cm

x/tp =10

0

1

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

y/s

2'u

U

Figure 4.18 Axial turbulence intensity profile for three equal impinging

jets at x/tp =10 and H=10 cm.

80

2. Impinging plate distance H/tp =40 (H=20 cm):

At this plate distance , the impinging pressure downstream become weaker due to the

less velocity strength as shown in Fig 4.15. The total pressure starts to decrease with

an increase in lateral distance until y/s =0.6 then the pressure returns to grow up

laterally until y/s=1.1. As y/s just exceeds 1.1 sudden drops takes place to the flow

pressure and continue decreasing until reaches atmospheric. The jets spread further

before striking the plate at this distance , as a result, the shape of resultant flow field in

this region has more changes as shown in Fig. 4.19.

Figure 4.19 Flow visualization of three impinging jets at H=20 cm.

The distance between the jet exit plane and the plate is still small and the jets do not

merge with each other yet. It is clearly seen from the figure the formation of wall jets

which are moving away from the outside jets and produced by the impingement of the

two outside jets with the plate. Also it shows the formation of the upwash moving

upstream by the impact of the opposing wall jets from the outside jets (jet1 & jet 3) and

the middle jet, furthermore it shows the formation of four vortices produced by the

interaction of the upwash flow with the uptream flow. The middle jet flow is affected

more by the influence of other jets and become weaker as shown in Fig. 4.20a and Fig.

4.21a. It is clear that the middle jet velocity level at x/tp = 10 is higher than that at x/tp =20

Vertical plate

81

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

y/s

x/t=10x/t=20

1oU

U

H=20 cm

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

y/s

x/t=10x/t=20

1oU

U

and this may due to more entertained flow, back wash and vortices. These two figures

are modified in direction with the aid of Fig 4.19 and replotted in Fig.4.20b and

Fig.4.21b respectively to show the velocity direction in the resulting flow field as

mentioned earlier.

Figure 4.20a Axial velocity profiles for three equal impinging jets

at x/tp =10,20 and H=20 cm

Figure 4.20b Axial velocity profiles for three equal impinging jets at x/tp

=10,20 and H=20 cm (corrected on the basis of Fig. 4.19 )

82

0.1

0.2

0.3

0.4

0.5

-1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

y/s

x/t=10x/t=20

1o

V

U

H=20

cm

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

y/s

x/t=10x/t=20

1o

V

U

Figure 4.21a Lateral velocity profiles for three equal impinging jets at

x/tp=10, 20 and H=20 cm.

Figure 4.21b Lateral velocity profiles for three equal impinging jets at x/tp=10,

20 and H=20 cm (corrected on the basis of Fig. 4.19 )

On other hand, Fig. 4.22 shows that the axial turbulent intensity in this region increases

with the axial distance but fluctuate with the increase in the lateral distance.

83

0

1

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

y/s

x/t=10x/t=20 H=20 cm

2'u

U

Figure 4.22 Axial intensity profiles for three equal impinging jets at x/tp =10,20

and H=20 cm.

3. Impinging plate distance H/tp =60 (H=30 cm):

The flow visualization pattern at this plate distance in Fig.4.23 shows two vortices exist

outside the two outer main jets close to the midway between the plate and the exit

plane. Two other vortices can also be seen near the jets exit plane. In the figure there is

a stagnation region also observed in the downstream region.

Figure 4.23 Flow visualization of three impinging jets at H=30 cm.

Vertical plate

84

0.1

0.2

0.3

0.4

0.5

-2.4 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2 2.4

y/s

x/t=20x/t=40

1oU

U

-0.5

-0.3

-0.1

0.1

0.3

0.5

-2.4 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2 2.4

y/s

U/U

o1

x/t=20x/t=40

1oU

U

Figure 4.24a and Fig.4.25a show the variation of the absolute mean velocity

components against the lateral distance for this flow field. It can be noticed that the

increase in the axial distance makes the jets merge more with each other and the

velocity profiles get shrink and become random. Figure 4.24b and Fig.4.25b show the

velocity corrected profiles based on the direction of the flow in this region.

Figure 4.24a Axial velocity profiles for three equal impinging jets

at x/tp=20, 40 and H=30 cm

Figure 4.24b Axial velocity profiles for three equal impinging jets at x/tp=20, 40

and H=30 cm (corrected on the basis of Fig. 4.23 ).

85

0.1

0.2

0.3

0.4

0.5

-2.4 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2 2.4

y/s

x/t=20x/t=40

1o

V

U

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-2.4 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2 2.4

y/s

x/t=20x/t=40

1o

V

U

Figure 4.25a Lateral velocity profiles for three equal impinging jets at x/tp =20,

40 and H=30 cm.

Figure 4.25b Lateral velocity profiles for three equal impinging jets at x/tp =20,

40 and H=30 cm (corrected on the basis of Fig. 4.23 ).

86

0

1

-2.4 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2 2.4

y/s

x/t=20x/t=40

H/tp=60

2'u

U

The total pressure distribution on the vertical plate as shown in Fig.4.15 shows a high

pressure between the two outer jets and high pressure drop outside the two jets. The

pressure is high and almost constant until y/s =1, then it starts to decrease gradually

until it reaches atmospheric This explains the shape of the two wall jets and the upwash

outside the two outer main jets. Fig.4.26 shows the axial turbulence intensity profiles at

two traverse distances (x/tp=20,40). The profile is fluctuating with axial and lateral

distances as shown by the figure, the reason behind unstable velocity fluctuations

profiles is due to the fact that these measurements were taken near a high turbulence

regions which contain vortices.

Figure 4.26 Axial turbulence intensity profiles for three equal impinging jets

at x/tp =20, 40 and H=30 cm.

4. Impinging plate distance H/tp =90 (45 cm):

Figure 4.27 describes the nature of the resultant flow field behind the vertical plate at

this distance. The figure mainly shows a formation of two wall jets and two rotating

vortices in the middle plane of the resulting flow field. The two vortices are formed by

87

the interaction between the two impact wall jets which bend toward the downstream

and the two main outer jets. It is obvious from the figure that the impinging region

diverges more on the vertical plate with the increase in the plate distance. The jets

become weak and almost merge as it reaches the plate. The figure also shows large

stagnation region exist between the jets exits.

Figure 4.27 Flow visualization of three impinging jets at H=45 cm.

The total pressure distribution shown in Fig. 4.15 shows very low pressure level in this

region and the pressure profile looks almost straight. Also Fig.4.28 shows the static

pressure distribution of the three equal impinging jets at H=45 cm. As shown by the

figure that at the lower axial distance x=4cm the static pressure values are almost

constant, but when the axial distance increases the pressure profile changes. The

maximum value of pressure ratio is 0.2 at y/s=0.35, this value decreases with any

increase or decrease in the lateral distance along the flow field .The static pressure

profile at x/tp=56 is approximately symmetric around the center line of the middle jet.

Vertical plate

88

0.02

0.12

0.22

0.32

0.42

0.52

-2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2

y/s

x/tp=8

x/tp=56

2

1

1

2O

P

U

H=45 cm

Jet 1 Jet 2

Figure 4.28 Static pressure distribution across the ground three equal

strenghth jetsat H=45 cm.

In this region also velocity vectors are drawn as shown in Fig.4.29a on the basis of the

magnified picture of the flow visualization sheet of Fig.4.27. Figure 4.29b shows the

measured velocity vectors distribution at the axial locations of measurements on the

right side of this flow field region. The directions of the velocity vectors in this region

were determined with the help of Fig.4.29a.

Figure 4.29a Flow map for the right side of the visualization

pattern of three impinging jets at H=45 cm.

89

X=40 cm

X=34 cm

X= 28 cm

X=24 cm X=23 cm

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4.0

y/s

Figure 4.29b Velocity vectors at the measuriments locations of three impinging

jets at H=45 cm.

The graphical presentation of velocity profiles of this flow field is illustrated in

Figs.4.30a-4.32 As can be seen from the figures that the mean axial velocity profile

has two symmetrical bell shapes around the two outside jets region. As the axial

distance increases the velocity ratio decreases accordingly and the bell shape of the

velocity becomes flatter due to impingement The axial turbulence intensity as shown

in Fig. 4.32 has uniform profiles for the shorter axial (distances x/tp =46,48) and

random profiles for further distances (x/tp=56,68,80) , the fluctuations are high in the

outside region compared to the inside region , it can be noted also that as the axial

distance increases the turbulent intensity decrease in the middle flow field region. On

the other hand the lateral mean velocity shown in Fig. 4.32 decreases with the increase

in lateral distance in y/s for axial locations x/tp>45 and increase with the increase in

y/s for axial locations x/tp <54.

90

0.12

0.16

0.2

0.24

0.28

0.32

-2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2

y/s

x/tb=46x/tb=48x/tb=56x/tb=68x/tb=80

1o

U

U

H=45 cm

-0.4

-0.32

-0.24

-0.16

-0.08

0

0.08

0.16

0.24

0.32

0.4

-2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2

y/s

x/tb=46x/tb=48x/tb=56x/tb=68x/tb=80

1o

U

U

H=45 cm

Figure 4.30a Axial velocity profiles for three equal impinging jets

at x/tp =46, 48, 56, 68, 80 and H=45 cm.

Figure 4.30b Axial velocity profiles for three equal impinging jets at x/tp =46, 48,

56, 68, 80 and H=30 cm (corrected on the basis of Fig. 4.27).

91

0.12

0.16

0.2

0.24

0.28

40 45 50 55 60 65 70 75 80 85 90

x/tp

Y/S=1.0588

1.1765

1.2941

1.4118

1.6471

1.8824

1oU

V

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

y/s

u'/U

o1

x/tb=46

x/tb=48

x/tb=56

x/tb=68

x/tb=80

2'u

U

Figure 4.31 Lateral velocity velocity profiles for three equal impinging jets

at H=45 cm.

Figure 4.32 Axial turbulence intensity profiles for three equal impinging jets

at x/tp =46, 48, 56, 68, 80 and H=45cm.

92

0.02

0.12

0.22

0.32

0.42

0.52

-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

y/s

Uo1=Uo2=Uo3

Uo1=Uo3=0.5Uo2

Uo1=Uo2=2Uo3

2

1

1

2O

P

U

H=45 cm

5. Unequal impinging jets at plate distance (H=45cm):

Figure 4.33 shows the pressure distribution on the vertical impinging plate at H=45 for

unequal strength three jets. For the first form of unequal jets where Uo1=Uo3=0.5Uo2,

the pressure values are high and concentrated in the middle region of the flow field

toward the strong jet. These pressure values decrease more rapidly toward the two

outside weak jets until it reaches the atmospheric pressure. The pressure distribution on

the same figure for the second form of the unequal jets where Uo1=Uo2=2Uo3,

indicate that the higher pressure values on the plate accumulate at the strong two jets

region, it decrease gradually toward the weak jet until it reach around atmospheric

value .The pressure distribution curve for equal jets under the same conditions shows

symmetrical pressure values on each side of the resultant flow field. The pressure

values are considerably low comparing to the strong jets region in the unequal jets case

.This indicate that the equal strength jets could affect each other and reduce their

momentum during interaction, consequently the pressure of the impact jets on the

impinging plate become lower.

Figure 4.33 Pressure distribution across the impinging vertical plate for

three equal and unequal jets at H=45 cm.

93

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

-2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2

y/s

x/tp=8

x/tp=56

2

1

1

2O

P

U

H=45 cm

For the unequal impinging jets case where the two outside jets velocity strengths are

half of the middle jet Fig.4.34 shows that the static pressure distribution profiles look

approximately uniform at the two axial measuring distances. However there are two

lower pressure values at y/s =0.35 ,-0.35 around the center line of the middle jet for

x/tp=8 , these two values are corresponding to the higher two values in the static

pressure profile at x/tp=56 , the two profiles have a symmetric pressure distribution

around the centerline of the jets as shown in the figure .

Figure 4.34 Static pressure distribution across the ground horizontal plate

three unequal strenghth jets (Uo1=Uo3=50%Uo2) at H=45 cm.

Figure 4.35 shows also the static pressure distribution of the second form of the

unequal jets where the two jets have equal velocity strength (jet1 & jet2) and the third

jet has 50% strength. It can be noticed that the pressure profile at x/tp=8 looks little

straight but not symmetric due to the difference in the jets strength, the pressure values

are slightly low across the flow field and the lower static pressure value at y/s=0.35.

94

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

-2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2

y/s

x/tp=8

x/tp=56

2

1

1

2O

P

U

H=45 cm

The figure also shows the static pressure profile of the unequal jets at axial distance

x/tp=56. It is obvious from the figure that when the lateral distance from the centerline

of the jets increases the static pressure also increases until y/s=0.5 in the strong jets

region and y/s=0.35 in the weak jets region , where it starts to decrease later with

further increase in the lateral distance until it reaches near atmospheric pressure. The

pressure distribution profile is clearly seen asymmetric around the centerline as a result

of the difference in the jets strength.

Figure 4.35 Static pressure distribution across the ground horizontal plate for

three unequal strenghth jets(Uo1=Uo2=2Uo3) at H=45 cm.

At this plate distance also of H=45 cm, the measurements of mean velocity and axial

velocity fluctuation of three unequal jets were taken, for two different exit velocity

ratios, namely Uo1=Uo3=0.5Uo2 and Uo1=Uo2=2Uo3. The resulting flow fields are

shown in Fig. 4.36 and Fig. 4.37 respectively.

95

Jet 1

Jet 3

Vertical plate

Jet 2 Jet 3

Figure 4.36 Flow visualization of three un equal impinging jets (Uo1=Uo3=.5 Uo2)

at H=45 cm.

Figure 4.37 Flow visualization of three un equal impinging jets (Uo1=Uo2=2 Uo3)

at H=45 cm.

Figure 4.38 shows the mean velocity profile of the unequal jets at the axial distance

x/tp=80. The figure also includes the velocity profiles of equal jets at the same axial

measuring distance. As can be seen from the figure that the velocity profile shape of

the unequal jets where (Uo1=Uo3=0.5Uo2) behaves as if it were a single jet , the two

weak jets do not have any effect on the strong jet , they only merge with the strong jet

and then combined together to produce a nearly single jet. The velocity profile of the

other three unequal jets where (Uo1=Uo2=2Uo3) has two bell shapes, this indicates

that the middle strong jet attract the weak jet and combined together to form a single

Vertical plate

Jet 3 Jet 2 Jet 1

96

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

y/s

U/U

o1

Uo1=Uo2=Uo3

Uo1=Uo2=2Uo3

Uo1=Uo3=.5Uo2

1oU

U

H=45 cm

x/tp =80

jet. The outside strong jet and the combined middle strong jet then conserve their

strength and produce two velocity bell shapes.

Figure 4.38 Axial mean velocity profiles for three equal and unequal impinging

jets at H=45 cm

By comparing the two velocity shapes of unequal jets to the equal three jets in the

same figure, one can conclude that the three equal jets velocity profile shows two bell

shapes after impinging; the two outside jets interact with the middle jet and reduce its

strength, the three jets eventually decompose to two jets. This is a similar case as in the

velocity profile for the unequal jets (Uo1=Uo2=2Uo3) where two strong side and

middle one weak side jet are interacted. However the velocity profile looks flatter in the

unequal jets case. On the other hand the axial turbulence intensity profiles for equal and

unequal jets , as shown in Fig.4.39 show that the intensity profile of the unequal jets

looks smooth comparing to that of the equal jets, this may be contributed to the higher

turbulence level resulting from the impact flow in the equal jets after impingement.

97

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

y/s

u'/U

o1

Uo1=Uo2=Uo3

Uo1=Uo2=2Uo3

Uo1=Uo3=.5Uo2

H=45 cm

X/tp =80

2'u

U

The figure shows high intensity value at the centerline of the jets , this value and

similar previous values have came from some error in the measurements.

Figure 4.39 Axial turbulence intensity profiles for three equal and unequal

impinging jets at H=45 cm.

6. Impinging plate distance H/tp =140 (H=70 cm):

The flow field produced at this distance in Figure 4.40 shows that the jets have a long

flow stream path before striking the plate, this makes the jets merge completely as they

reach the plate. The resulting fountain flow at this plate distance is weak due to the low

pressure on the plate. The wall jets result from the impingement of the jets with the

plate are moving horizontally toward the lateral direction and nearly parallel to the

vertical plate. In this region fewer vortexes are formed due to less interaction between

the upwash fountain and the downstream moving jets, also stagnation points are shown

near the plate and near the jets nozzle.

98

Jet 3 Jet2 Jet 1

Vertical plate

Figure 4.40 Flow visualization of three impinging jets at H=70 cm .

Figure 4.41 and Fig.4.42 show the profiles of axial velocity and velocity fluctuation

ratios at two measuring distances (x/tp=60,120). In this region data was collected using

triple wire probe. At x/ tp=60 the mean velocity and axial velocity fluctuation profiles

show symmetric steeper bell velocity shape. At x/tp= 120 the wire probe was rotated

about 90o parallel to the direction of flow in the wall jets resulted by the impinging, this

approach was tried in order to make the flow normal to the wires and give a reasonable

flow measurements. As shown in Fig.4.40, the velocity profile look smooth and has

symmetrical shape around the jets centerline, the profiles also indicate that the middle

jets merge completely with the two outer jets and form nearly flat shape profile. The

99

0.15

0.18

0.21

0.24

0.27

0.3

-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

y/s

U/U

o1

x/tb=60x/tb=120

1oU

U

H=70 cm

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

y/s

u'/U

x/t=60

x/t=120

2

1o

u'

U

H=70

cm

pressure profile at this distance where H=70 cm shows very low values as shown in Fig

4.15, it becomes just above the atmospheric and almost constant.

Figure 4.41 Axial mean velocity profiles for three equal impinging jets

at x/tp =60, 120 H=70 cm.

Figure 4.42 Axial turbulence profiles for three equal impinging jets at

x/tp =60, 120 and H=70cm.

100

CHAPTER - V

CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusion

The overall study of this project come up with the following conclusions

1. In the free parallel jets case when the three jets reach a complete merging as

shown by Fig.3.9 at x/tp=140, the velocity profile turn to have single bell shape

and behave as if it were single jet.

2. The velocity profiles of the three free jets look similar to that of the two free

jets, but the velocity bell shape in the three jets looks sharper, where the jets in

the two free jets merge earlier, see Fig.4.8.

3. The visualization patterns and the velocity profiles for the three impinging jets

show that the two outer impinging jets interact with the middle jet and greatly

reduce it's strength, the resultant velocity profile then behaves as if it were two

impinging jets.

4. In the unequal impinging jets case where the two outer jets strength is half that

of the middle jet , then the resultant total pressure and mean velocity are nearly

identical as shown in Figs.4.33 and Fig. 4.38 respectively, the three profiles

behave as if they were a single jet, the middle strong jet attract the weak jets

and combined together to form one strong jet.

5. In the unequal impinging jets case where one outer jet strength is half of the two

equal strong jets, then the weak jets is attracted to the middle strong jet and lose

78

101

it‟s strength, the final velocity and intensity profiles show two peak values

around the two strong jets as shown in Fig.4.38 and Fig.4.39 respectively.

6. The axial turbulence intensity profiles in unequal impinging jets case looks

more uniform comparing to that in the equal impinging jets as shown in Fig. 4.

39.

7. As the vertical plate distance (H) increase the rotating vortices formed in the

flow field move gradually toward the lateral direction.

8. The hot wire technique used in this experiment is insensitive to flow direction

especially in the regions contain vortices, and not suitable to measure high

turbulence intensity values.

5.2 Recommendations

This project has been conducted under available measuring and visualization lab tools

which still used in some fluid researches .For better experimental results, the recent

flow measuring techniques are recommended to replace the existing techniques for

both measuring and visualization purposes . The hot wire system could be replaced by

another more sensitive technique such as Lazer Doppler Anemometer LDA) or Partial

Imaging Velocimetry (PIV) which are currently being used in variety fields of fluid

measurements researches. Visualization methods are also being modified for better

imaging of fluid particles and streamlines. Lazer sheet visualization is one example of

recent techniques used for visualization, it is recommended to replace the oil

visualization pattern which was used in this experiment.

This project could be extended in the future to hold the confirmation of the results

theoretically and computationally. In other word the experimental results of this

102

research are suggested to be confirmed computationally using solution of the time-

averaged Navier-Stokes equations.

103

REFERENCE

1. Elbanna, H., Gahin., S., and Rashed, M. 1.1., "Investigation of Two Plane Parallel

Jets," AIAA Journal, Vol.21, pp. 986-991, July 1983.

2. Barata. Jorg. M. M. "Fountain Flows produced by Multiple Impinging Jets in A

cross-flow", AIAA Journal, Vol.34, pp. 2523-2530, Dec 1996.

3. Barata-J-M-M ;Durao-D ;Heitor-M-V. "Velocity characteristics of multiple

impinging jets through a cross-flow", Journal of Fluids Engineering,-Transactions of

the ASME, v 114 n2, p 231-239 , Jun 1992.

4. Barata-J-M-M ;Durao-D ;Heitor-M-V; McGuirk-J-J."Impingement of single and twin

turbulent jets through a cross-flow", AIAA Journal, v 29 n4, p 595-602 , Apr 1991.

5. Hibara, H., Sudou, K., "Axisymmetric jet impinging on concave surface ", JASME,

vol. 62 n 597, pp 1819-1826 , May 1996.

6. Elbanna, H. and Sabbagh, J. A., “Investigation of two impinging jets as Applied to

VTOL Aircraft”, Final Report ,Research Grant 05-413, College of Engineering ,King

Abdul Aziz Univ. , Jeddah , Saudi Arabia, 1987.

7. Elbanna, H. and Sabbagh, J. A., "Flow visualization and Measurements in a Two-

Dimensional Two-impinging-Jet Flow", AIAA Journal, Vol.27, pp.20-425,

April.1989.

8. Bernard-A; Bousgarbies-J-L; Brizzi-L-E. " Study of several jets impinging on a plane

wall: Visualizations and Lazer velocimetry investigations", Experimental and

Numerical Flow Visualization-and Lazer Anemometry American Society of

Mechanical Engineers,-Fluids-Eng , v 13, ASME, New York, NY, USA. 5p,1997.

9. Shoe-B; Disimile-P-J; Savory-E; Toy-N; Tahouri-B." Image analysis of two

impinging jets using Lazer induced fluorescence and smoke flow visualization",

International Society for Optical Engineering. v 1521, WA, USA. p 34-45.

10. Bernard-A; Brizzi-L-E; Bousgarbies-J-L." Wall flow generated by a group of jets

impinging on a plane surface",Comptes-Rendus-de-l'Academie-de-Sciences-Serie-

IIb:-Mecanique,-Physique,-Chimie,-Astronomie.; 326(6): 373-378, 1998.

11. Behrouzi-P. "Numerical studies of twin-jet impingement for STOVL flow

application", journal of the Chinese Institute of Engineers,-Transactions of the

Chinese Institute of Engineers, Series-A-Chung-kuo-Kung-Ch'eng-Hsuch-K'an. v 23

n 6, p 669-676, Nov 2000.

104

12. Behrouzi-P; McGuirk-JJ. "Lazer Doppler velocimetry measurements of twin-jet

impingement flow for validation of computational models", Optics and Lazers in

Engineering. v 30 n 3-4, p 265-277 , Sep-Oct 1998.

13. Jun-Liu; Zhang-Taifeng; Hong-Chen. "Numerical simulation of impinging jet

produced by missile", Journal of Propulsion and Technology. v 21 n 1, p 30-32,

2000.

14. Chuang-S-H; Chen-M-H; Lii-S-W; Tai-F-M." Numerical simulation of twin-jet

impingement on a flat plate coupled with cross-flow", International Journal for

Numerical Methods in Fluids. v 14 n 4 , p 459-475 , Feb 28 1992.

15. Pegues-W-J; Vanka-S-P." Numerical study of twin-jet impingement upwash flow",

ASME and FED (Fluids Engineering Division) Publication. v 94., p 97-103,1990

Spring.

16. Knowles-K; Bray-D."Computation of normal impinging jets in cross-flow and

comparison with experiment", International Journal for Numerical Methods in

Fluids. v 13 n 10, p 1225-1233 , Dec 1991.

17. Chuang,-S-H; Nieh,-T-J." Numerical simulation and analysis of three-dimensional

turbulent impinging square twin-jet flow fieldwith no-cross-flow", International

Journal for Numerical Methods in Fluids. vol. 33, no. 4, pp. 475-498, 2000.

18. Ince,-N.Z.; Leschziner,-M.A." Computation of three-dimensional jets in cross-flow

with and without impingement using second-moment closure ", engineering

turbulence modeling and experiments. Rodi,-W.; Ganic,-E.N. (eds.) ,24-28. pp. 143-

153,Sep 1990.

19. Dianat,-M.; Fairweather,-M.; Jones,-W.P." Predictions of axisymmetric and two-

dimensional impinging turbulent jets", International Journal of heat and fluid flow .

vol. 17, no. 6, pp. 530-538,1996.

20. Chuang-Shu-Hao; Cheng-Po-Jen." Block effects of an impinging twin-jet on a flat

plate Transactions of the Aeronautical and Astronautical Society of the-Republic of

China. v31 n2, p 151-162 , Jun 1999

21. Behrouzi-P; McGuirk-JJ 'Twijet impingement flow survey data for CFD validation of

STOVL flows" , Canadian Aeronautics and Space Journal. v 45 n 4, p 350-357, Dec

1999.

22. Knowles-K; Myszko-M." Radial wall jets formed by high speed impinging jets",

High Speed Jet Flows, American Society of Mechanical Engineers, Fluids

Engineering Division (Publication)-FED. v 214, ASME, New York, NY, USA. p 53-

58,1995.

23. Disimile-P-J; Savory-E; Toy-N." Mixing characteristics of twin impinging circular

jets", Journal of Propulsion and Power. v 11 n 6, p 1118-1124 , Nov-Dec 1995.

105

24. Ashgriz-N; Brocklehurst-W; Talley-D." Mixing mechanisms in a pair of impinging

jets", Journal of Propulsion and Power. v 17 n 3, p 736-749 , May/June 2001.

25. Knowles-K; Bray-D. "Ground vortex formed by impinging jets in cross-flow"

,Journal of Aircraft. v 30 n 6, p 872-878, Nov-Dec 1993.

26. Prasad-J; Mehta-R; Sreekanth-A." Impingement of supersonic jets on an

axisymmetric deflector" AIAA-Journal. v 32 n 7, p 1535-1538, Jul 1 994.

27. Iwamoto-J. "Impingement of under-expanded jets on a flat plate", Journal of Fluids

Engineering,-Transactions of the ASME, v 112 n 2, p 179-184 , Jun 1990.

28. Nakabe-K; Fornalik-E; Eschenbacher-JF; Yamamoto-Y; Ohta-T; Suzuki-K.

"Interactions of longitudinal vortices generated by twin inclined jets and

enhancement of impingement heat transfer", International Journal of heat and fluid

flow, v 22 n 3 , p 287-292 , June 2001.

29. Nakabi-K; Suzuki-K; Inaoka-K; Higashio-A; Acton-JS; Chen-W. " Generation of

longitudinal vortices in internal flows with an inclined impinging jet and

enhancement of target plate heat transfer", International Journal of heat and fluid

flow,v19 n 5, p 573-581 , Oct 1998.

30. Arjocu-S; Liburdy-J. " Large scale structures in a multi-jet impinging array",

Individual Papers in Fluids Engineering American Society of Mechanical Engineers,

Fluids Engineering Division (Publication)-FED. v 207, ASME, New York, NY,

USA. p 17-24,1995.

31. Arjocu-Simona; Liburdy-James-A." Near surface characterization of an impinging

elliptic jet array", Journal of Fluids Engineering-Transactions of the ASME , v 121 n

2, p 384-390,1999.

32. Dantec Elektronik . "acqwire", Technical Referance Manual , Developed by Dantec

Electronics , Inc.Allendale , NJ, USA , 1989.

33. Munson ; Young; Okishi." Fundamentals of fluid mechanics", Text book by John

Wiley & Sons,Inc.3rd ed . update , p 228,1998.

106

APPENDIX – I

TABULATED RESULTS

107

TABLE I .1 Summary of all vertical plate positions, measurement wire

distances and the type of wire used in the measurements.

Location

of measurements

from the jet exit plane

10

cm

20

cm

30

cm

45

cm

50

cm

70

cm

5 cm

Single

wire

10 cm

Single

wire

Single

wire

15 cm

Single

wire

Triple

wire

20 cm

Single

wire

23 cm Single

wire

24 cm Single

wire

28 cm

Single

wire

30 cm Triple

wire

Triple

wire

34 cm

Single

wire

40 cm Single

wire

60 cm Triple

wire

y

s

1O

U

U

1O

V

U

1O

W

U

2

21O

u

U

'

2

21O

v

U

'

2

21O

w

U

'

21O

u v

U

' '

21O

u w

U

' '

21O

v w

U

' '

u

U

'

v

U

'

w

U

'

O

J

J

Impinging plate

distances from

jet nozzle

exit

i

108

TABLE I .2 Mean velocity components and fluctuations results of three parallel

free jets at x/tp=30.

TABLE I .3 Mean velocity components and fluctuations results of three parallel

free jets at x/tp=50.

0.0589 0.2904 0.0161 0.0613 0.0049 0.0063 0.0078 0.0010 0.0014 0.0004 0.2410 0.2733 0.3041 0.1143

0.1176 0.2036 0.0068 0.0402 0.0033 0.0029 0.0038 0.0010 0.0005 0.0003 0.2821 0.2645 0.3028 0.0892

0.1765 0.1570 0.0048 0.0274 0.0005 0.0007 0.0009 0.0001 0.0001 0.0001 0.1424 0.1685 0.1911 0.0448

0.2353 0.1505 0.0082 0.0241 0.0001 0.0003 0.0004 0.0000 0.0001 0.0001 0.0664 0.1151 0.1329 0.0251

0.4118 0.1479 0.0119 0.0209 0.0000 0.0002 0.0001 0.0000 0.0000 0.0001 0.0000 0.0956 0.0676 0.0228

0.5883 0.1496 0.0102 0.0245 0.0000 0.0002 0.0003 0.0000 0.0000 0.0001 0.0000 0.0945 0.1158 0.0219

0.7059 0.1642 0.0036 0.0389 0.0004 0.0008 0.0013 0.0000 0.0002 0.0001 0.1218 0.1723 0.2196 0.0224

0.7647 0.2182 0.0148 0.0625 0.0021 0.0032 0.0040 0.0009 0.0009 0.0003 0.2100 0.2593 0.2899 0.0274

0.8235 0.3247 0.0461 0.1014 0.0027 0.0054 0.0071 0.0008 0.0011 0.0001 0.1600 0.2263 0.2595 0.0497

0.8824 0.3632 0.0446 0.0983 0.0024 0.0064 0.0085 0.0002 0.0003 0.0001 0.1349 0.2203 0.2538 0.1081

0.9412 0.3101 0.0162 0.0676 0.0035 0.0062 0.0078 0.0004 0.0004 0.0004 0.1908 0.2539 0.2848 0.1343

1.0000 0.2068 0.0076 0.0428 0.0017 0.0030 0.0036 0.0003 0.0002 0.0000 0.1994 0.2649 0.2901 0.0997

1.0588 0.1538 0.0073 0.0264 0.0002 0.0006 0.0008 0.0001 0.0001 0.0000 0.0920 0.1593 0.1839 0.0445

1.1762 0.1486 0.0128 0.0161 0.0000 0.0002 0.0002 0.0000 0.0000 0.0001 0.0000 0.0952 0.0952 0.0239

1.2941 0.1510 0.0193 0.0076 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0662 0.0000 0.0221

0.0000 0.3441 0.0067 0.0770 0.0041 0.0067 0.0087 0.0002 0.0003 0.0005 0.1861 0.2379 0.2711 0.0228

-0.0589 0.2680 0.0006 0.0722 0.0050 0.0055 0.0068 0.0007 0.0017 0.0004 0.2638 0.2767 0.3077 0.1143

-0.1176 0.1782 0.0041 0.0450 0.0012 0.0019 0.0021 0.0000 0.0005 0.0001 0.1944 0.2446 0.2572 0.0768

-0.1765 0.1553 0.0028 0.0301 0.0001 0.0005 0.0008 0.0000 0.0001 0.0000 0.0644 0.1440 0.1821 0.0330

-0.2353 0.1512 0.0064 0.0227 0.0001 0.0003 0.0003 0.0000 0.0000 0.0000 0.0661 0.1146 0.1146 0.0242

-0.4118 0.1490 0.0102 0.0193 0.0000 0.0002 0.0002 0.0000 0.0000 0.0001 0.0000 0.0949 0.0949 0.0230

-0.5883 0.1499 0.0068 0.0222 0.0000 0.0002 0.0002 0.0000 0.0000 0.0000 0.0000 0.0943 0.0943 0.0222

-0.7059 0.1603 0.0018 0.0334 0.0002 0.0008 0.0012 0.0001 0.0001 0.0001 0.0882 0.1764 0.2161 0.0225

-0.7647 0.2145 0.0125 0.0424 0.0021 0.0032 0.0035 0.0002 0.0000 0.0003 0.2136 0.2637 0.2758 0.0259

-0.8235 0.3192 0.0199 0.0467 0.0032 0.0065 0.0077 0.0005 0.0001 0.0005 0.1772 0.2526 0.2749 0.0481

-0.8824 0.3695 0.0326 0.0573 0.0028 0.0072 0.0097 0.0002 0.0004 0.0011 0.1432 0.2296 0.2665 0.1051

-0.9412 0.2952 0.0200 0.0611 0.0035 0.0055 0.0083 0.0001 0.0013 0.0007 0.2004 0.2512 0.3086 0.1393

-1.0000 0.1958 0.0112 0.0388 0.0013 0.0023 0.0030 0.0001 0.0005 0.0001 0.1841 0.2449 0.2797 0.0906

-1.0588 0.1521 0.0051 0.0265 0.0001 0.0005 0.0007 0.0000 0.0000 0.0000 0.0657 0.1470 0.1739 0.0396

-1.1764 0.1499 0.0081 0.0137 0.0000 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0667 0.0667 0.0232

-1.2941 0.1508 0.0037 0.0125 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0225

109

TABLE I .4 Mean velocity components and fluctuations results of three parallel

free jets at x/tp=80

y

s

1O

U

U

1O

V

U

1O

W

U

2

2

1

'

O

u

U

2

2

1

'

O

v

U

2

2

1

'

O

w

U 2

1

' '

O

u v

U

2

1

' '

O

u w

U

2

1

' '

O

v w

U

'u

U

'v

U

'w

U

O

J

J

0.0353 0.2400 0.0024 0.0512 0.0020 0.0037 0.0044 0.0001 0.0004 0.0000 0.1863 0.2534 0.2764 0.0661

0.0706 0.2126 0.0028 0.0426 0.0020 0.0028 0.0037 0.0003 0.0003 0.0001 0.2104 0.2489 0.2861 0.0596

0.1059 0.1853 0.0048 0.0357 0.0014 0.0021 0.0025 0.0004 0.0003 0.0001 0.2019 0.2473 0.2698 0.0472

0.1412 0.1673 0.0017 0.0277 0.0008 0.0013 0.0016 0.0003 0.0002 0.0001 0.1691 0.2155 0.2391 0.0357

0.2118 0.1539 0.0068 0.0256 0.0002 0.0005 0.0007 0.0001 0.0001 0.0001 0.0919 0.1453 0.1719 0.0288

0.3176 0.1754 0.0147 0.0453 0.0008 0.0014 0.0021 0.0003 0.0005 0.0001 0.1613 0.2133 0.2613 0.0239

0.3529 0.2052 0.0269 0.0577 0.0016 0.0025 0.0034 0.0008 0.0008 0.0003 0.1949 0.2437 0.2842 0.0316

0.3882 0.2472 0.0439 0.0799 0.0017 0.0034 0.0041 0.0007 0.0007 0.0002 0.1668 0.2359 0.2590 0.0437

0.4235 0.2777 0.0526 0.0881 0.0014 0.0034 0.0049 0.0004 0.0005 0.0003 0.1347 0.2100 0.2521 0.0628

0.4941 0.2601 0.0258 0.0625 0.0019 0.0039 0.0047 0.0000 0.0001 0.0004 0.1676 0.2401 0.2636 0.0785

0.5294 0.2166 0.0154 0.0469 0.0016 0.0031 0.0035 0.0000 0.0002 0.0001 0.1847 0.2571 0.2731 0.0696

0.5647 0.1711 0.0080 0.0344 0.0006 0.0014 0.0016 0.0001 0.0001 0.0001 0.1432 0.2187 0.2338 0.0485

0.6353 0.1496 0.0110 0.0188 0.0000 0.0003 0.0003 0.0000 0.0000 0.0001 0.0000 0.1158 0.1158 0.0299

0.7059 0.1523 0.0204 0.0074 0.0000 0.0003 0.0001 0.0000 0.0000 0.0001 0.0000 0.1137 0.0657 0.0224

0.0000 0.2536 0.0048 0.0595 0.0018 0.0040 0.0048 0.0000 0.0005 0.0001 0.1673 0.2494 0.2732 0.0232

-0.0353 0.2333 0.0074 0.0564 0.0020 0.0032 0.0044 0.0003 0.0006 0.0002 0.1917 0.2425 0.2843 0.0661

-0.0706 0.2010 0.0074 0.0492 0.0015 0.0024 0.0033 0.0002 0.0006 0.0001 0.1927 0.2437 0.2858 0.0564

-0.1059 0.1774 0.0060 0.0432 0.0009 0.0014 0.0022 0.0001 0.0004 0.0001 0.1691 0.2109 0.2644 0.0419

-0.1412 0.1636 0.0072 0.0337 0.0003 0.0010 0.0015 0.0000 0.0002 0.0000 0.1059 0.1933 0.2367 0.0324

-0.2471 0.1645 0.0001 0.0257 0.0004 0.0011 0.0015 0.0001 0.0000 0.0001 0.1216 0.2016 0.2354 0.0271

-0.2824 0.1770 0.0008 0.0263 0.0007 0.0015 0.0021 0.0001 0.0000 0.0000 0.1495 0.2188 0.2589 0.0275

-0.3176 0.2097 0.0068 0.0336 0.0015 0.0027 0.0036 0.0002 0.0001 0.0000 0.1847 0.2478 0.2861 0.0320

-0.3529 0.2464 0.0121 0.0354 0.0018 0.0036 0.0046 0.0003 0.0000 0.0001 0.1722 0.2435 0.2753 0.0455

-0.3882 0.2740 0.0176 0.0370 0.0017 0.0041 0.0053 0.0002 0.0003 0.0001 0.1505 0.2337 0.2657 0.0625

-0.4235 0.2741 0.0166 0.0444 0.0017 0.0040 0.0057 0.0002 0.0004 0.0000 0.1504 0.2307 0.2754 0.0768

-0.4588 0.2538 0.0145 0.0441 0.0019 0.0036 0.0055 0.0000 0.0007 0.0002 0.1717 0.2364 0.2922 0.0768

-0.4941 0.2197 0.0149 0.0431 0.0016 0.0030 0.0041 0.0002 0.0007 0.0001 0.1821 0.2493 0.2914 0.0663

-0.5294 0.1855 0.0125 0.0381 0.0009 0.0018 0.0028 0.0002 0.0004 0.0001 0.1617 0.2287 0.2853 0.0499

-0.5647 0.1609 0.0017 0.0283 0.0003 0.0009 0.0013 0.0001 0.0001 0.0001 0.1076 0.1865 0.2241 0.0353

-0.6353 0.1490 0.0128 0.0168 0.0000 0.0002 0.0002 0.0000 0.0000 0.0001 0.0000 0.0949 0.0949 0.0262

-0.7059 0.1529 0.0107 0.0105 0.0000 0.0002 0.0001 0.0000 0.0000 0.0001 0.0000 0.0925 0.0654 0.0222

110

y

s

1O

U

U

1O

V

U

1O

W

U

2

2

1

'

O

u

U

2

2

1

'

O

v

U

2

2

1

'

O

w

U

2

1

' '

O

u v

U

2

1

' '

O

u w

U

2

1

' '

O

v w

U

'u

U

'v

U

'w

U

O

J

J

0.0000 0.2173 .0055 0.0395 0.0007 0.0020 .0028 0.0001 0.0001 0.0000 0.1218 0.2058 0.2435 0.0479

0.0221 0.2164 0.0035 0.0407 0.0007 0.0022 0.0026 0.0001 0.0001 0.0000 0.1223 0.2167 0.2356 0.0475

0.0441 0.2143 0.0024 0.0436 0.0007 0.0023 0.0028 0.0000 0.0001 0.0001 0.1235 0.2238 0.2469 0.0466

0.0662 0.2089 0.0012 0.0409 0.0007 0.0019 0.0026 0.0001 0.0002 0.0001 0.1267 0.2087 0.2441 0.0443

0.0882 0.2052 0.0036 0.0403 0.0007 0.0019 0.0024 0.0001 0.0001 0.0000 0.1289 0.2124 0.2387 0.0428

0.1324 0.2109 0.0099 0.0464 0.0008 0.0019 0.0027 0.0001 0.0002 0.0001 0.1341 0.2067 0.2464 0.0453

0.2206 0.2307 0.0125 0.0516 0.0009 0.0024 0.0030 0.0000 0.0002 0.0002 0.1300 0.2124 0.2374 0.0541

0.2426 0.2230 0.0123 0.0473 0.0008 0.0022 0.0028 0.0001 0.0001 0.0001 0.1268 0.2103 0.2373 0.0505

0.2647 0.2105 0.0068 0.0400 0.0009 0.0022 0.0024 0.0001 0.0002 0.0001 0.1425 0.2228 0.2327 0.0452

0.3088 0.1705 0.0041 0.0340 0.0004 0.0011 0.0014 0.0001 0.0001 0.0000 0.1173 0.1945 0.2195 0.0295

0.3529 0.1527 0.0019 0.0279 0.0001 0.0005 0.0004 0.0000 0.0000 0.0000 0.0655 0.1464 0.1310 0.0234

0.3971 0.1519 0.0002 0.0289 0.0001 0.0002 0.0002 0.0000 0.0000 0.0000 0.0658 0.0931 0.0931 0.0232

0.4412 0.1565 0.0004 0.0285 0.0001 0.0002 0.0002 0.0000 0.0000 0.0001 0.0639 0.0904 0.0904 0.0246

0.0000 0.2173 0.0055 0.0395 0.0007 0.0020 0.0028 0.0001 0.0001 0.0000 0.1218 0.2058 0.2435 0.0479

-0.0221 0.2166 0.0026 0.0408 0.0007 0.0022 0.0028 0.0001 0.0001 0.0001 0.1221 0.2165 0.2443 0.0476

-0.0441 0.2172 0.0054 0.0410 0.0007 0.0021 0.0026 0.0000 0.0002 0.0001 0.1218 0.2110 0.2348 0.0479

-0.0662 0.2178 0.0034 0.0383 0.0007 0.0021 0.0028 0.0000 0.0001 0.0000 0.1215 0.2104 0.2430 0.0481

-0.0882 0.2179 0.0039 0.0369 0.0008 0.0023 0.0028 0.0002 0.0001 0.0002 0.1298 0.2201 0.2428 0.0483

-0.1765 0.2253 0.0014 0.0385 0.0009 0.0026 0.0035 0.0001 0.0002 0.0000 0.1332 0.2263 0.2626 0.0517

-0.2206 0.2134 0.0057 0.0375 0.0009 0.0023 0.0027 0.0000 0.0003 0.0000 0.1406 0.2247 0.2435 0.0464

-0.2426 0.1979 0.0081 0.0395 0.0008 0.0021 0.0026 0.0000 0.0003 0.0001 0.1429 0.2316 0.2577 0.0400

-0.2647 0.1790 0.0048 0.0337 0.0005 0.0015 0.0019 0.0000 0.0001 0.0001 0.1249 0.2164 0.2435 0.0325

-0.2868 0.1635 0.0028 0.0330 0.0003 0.0010 0.0013 0.0000 0.0001 0.0000 0.1059 0.1934 0.2205 0.0270

-0.3088 0.1564 0.0001 0.0315 0.0002 0.0006 0.0008 0.0000 0.0001 0.0001 0.0904 0.1566 0.1808 0.0247

-0.3529 0.1502 0.0022 0.0317 0.0000 0.0002 0.0003 0.0000 0.0000 0.0000 0.0000 0.0942 0.1153 0.0226

-0.3971 0.1538 0.0008 0.0321 0.0001 0.0002 0.0002 0.0000 0.0000 0.0000 0.0650 0.0920 0.0920 0.0238

-0.4412 0.1581 0.0034 0.0311 0.0001 0.0002 0.0002 0.0000 0.0000 0.0000 0.0633 0.0895 0.0895 0.0251

111

TABLE I .5 Mean velocity components and fluctuations results of three parallel

free jets at x/tp=140

y

s

1O

U

U

1O

V

U

1O

W

U

2

2

1

'

O

u

U

2

2

1

'

O

v

U

2

2

1

'

O

w

U 2

1

' '

O

u v

U

2

1

' '

O

u w

U

2

1

' '

O

v w

U

'u

U

'v

U

'w

U

O

J

J

0.0252 0.2249 0.0068 0.0443 0.0003 0.0013 0.0015 0.0000 0.0000 0.0002 0.0770 0.1603 0.1722 0.0514

0.0504 0.2254 0.0061 0.0436 0.0003 0.0013 0.0015 0.0000 0.0001 0.0002 0.0768 0.1600 0.1718 0.0509

0.0756 0.2245 0.0058 0.0392 0.0004 0.0014 0.0017 0.0000 0.0001 0.0002 0.0891 0.1667 0.1837 0.0511

0.1009 0.2182 0.0003 0.0358 0.0004 0.0015 0.0016 0.0001 0.0000 0.0001 0.0917 0.1775 0.1833 0.0508

0.1261 0.2069 0.0003 0.0353 0.0005 0.0017 0.0017 0.0001 0.0000 0.0000 0.1081 0.1993 0.1993 0.0480

0.1512 0.1896 0.0016 0.0322 0.0005 0.0016 0.0014 0.0001 0.0001 0.0001 0.1179 0.2110 0.1973 0.0433

0.1765 0.1715 0.0002 0.0305 0.0003 0.0012 0.0011 0.0001 0.0000 0.0001 0.1010 0.2020 0.1934 0.0365

0.2017 0.1597 0.0018 0.0286 0.0002 0.0008 0.0006 0.0001 0.0000 0.0000 0.0886 0.1771 0.1534 0.0297

0.2269 0.1526 0.0002 0.0283 0.0001 0.0004 0.0003 0.0000 0.0000 0.0000 0.0655 0.1311 0.1135 0.0257

0.2521 0.1504 0.0004 0.0282 0.0000 0.0002 0.0002 0.0000 0.0000 0.0000 0.0000 0.0940 0.0940 0.0234

0.2773 0.1521 0.0005 0.0297 0.0000 0.0002 0.0002 0.0000 0.0000 0.0000 0.0000 0.0930 0.0930 0.0226

0.3026 0.1576 0.0007 0.0336 0.0001 0.0002 0.0003 0.0000 0.0000 0.0001 0.0635 0.0897 0.1099 0.0231

0.0000 0.2260 0.0051 0.0423 0.0003 0.0014 0.0015 0.0000 0.0000 0.0001 0.0766 0.1656 0.1714 0.0249

-0.0252 0.2230 0.0056 0.0431 0.0003 0.0013 0.0016 0.0000 0.0000 0.0000 0.0777 0.1617 0.1794 0.0000

-0.0504 0.2216 0.0073 0.0397 0.0004 0.0015 0.0018 0.0000 0.0000 0.0001 0.0903 0.1748 0.1915 0.0514

-0.0756 0.2171 0.0066 0.0414 0.0004 0.0014 0.0020 0.0000 0.0001 0.0001 0.0921 0.1723 0.2060 0.0500

-0.1009 0.2049 0.0062 0.0391 0.0004 0.0014 0.0020 0.0001 0.0002 0.0002 0.0976 0.1826 0.2183 0.0495

-0.1261 0.1877 0.0039 0.0374 0.0004 0.0011 0.0019 0.0001 0.0002 0.0003 0.1066 0.1767 0.2322 0.0475

-0.1512 0.1712 0.0033 0.0358 0.0003 0.0008 0.0014 0.0000 0.0001 0.0002 0.1012 0.1652 0.2186 0.0424

-0.1765 0.1588 0.0043 0.0323 0.0001 0.0006 0.0009 0.0000 0.0001 0.0002 0.0630 0.1542 0.1889 0.0356

-0.2017 0.1528 0.0037 0.0325 0.0001 0.0003 0.0005 0.0000 0.0000 0.0001 0.0654 0.1134 0.1463 0.0296

-0.2269 0.1502 0.0033 0.0323 0.0000 0.0002 0.0002 0.0000 0.0000 0.0000 0.0000 0.0942 0.0942 0.0253

-0.2521 0.1514 0.0029 0.0328 0.0000 0.0001 0.0002 0.0000 0.0000 0.0000 0.0000 0.0661 0.0934 0.0235

-0.2773 0.1547 0.0017 0.0333 0.0001 0.0002 0.0002 0.0000 0.0000 0.0001 0.0646 0.0914 0.0914 0.0226

-0.3026 0.1576 0.0007 0.0336 0.0001 0.0002 0.0003 0.0000 0.0000 0.0001 0.0635 0.0897 0.1099 0.0229

112

TABLE I .6 Mean velocity components and fluctuations results of three parallel

impinging jets at H=10cm , x=5cm (x/tp=10).

y

s

1O

U

U

1O

V

U

'u

U

'v

U

1o

u

U

'

1o

v

U

'

2

1

' '

O

u v

U

0.05882 0.26909 0.22242 0.20944 0.46443 0.05636 0.10330 0.00337

0.11765 0.28719 0.20700 0.00020 0.50961 0.00006 0.10549 0.00000

0.17647 0.25865 0.18079 0.05723 0.63912 0.01480 0.11555 0.00070

0.23529 0.20546 0.17275 0.29087 0.67595 0.05976 0.11677 0.00101

0.29412 0.16986 0.16312 0.06256 0.71890 0.01063 0.11726 0.00011

0.35294 0.14772 0.15386 0.11927 0.76480 0.01762 0.11767 0.00017

0.52941 0.13976 0.14424 0.00580 0.82067 0.00081 0.11838 0.00001

0.70588 0.13950 0.13567 0.01482 0.87365 0.00207 0.11853 0.00001

0.88235 0.18639 0.15231 0.11392 0.78040 0.02123 0.11886 0.00019

0.94118 0.53026 0.21277 0.01273 0.77895 0.00675 0.16574 0.00078

1.00000 0.50382 0.23003 0.04490 0.92655 0.02262 0.21313 0.00303

1.05882 0.16693 0.14722 0.22257 1.44768 0.03715 0.21313 0.00002

1.17647 0.13071 0.13090 0.01268 1.62909 0.00166 0.21325 0.00001

1.29412 0.13201 0.13181 0.02031 1.61787 0.00268 0.21325 0.00000

1.41176 0.13381 0.13298 0.01978 1.60363 0.00265 0.21325 0.00000

0.00000 0.30293 0.26873 0.39954 0.34553 0.11527 0.08843 0.00971

-0.05882 0.28254 0.23354 0.21991 0.48765 0.05918 0.10847 0.00354

-0.11765 0.30155 0.21735 0.00021 0.53509 0.00006 0.11076 0.00000

-0.17647 0.27158 0.18983 0.06009 0.67108 0.01554 0.12133 0.00074

-0.23529 0.21573 0.18139 0.30541 0.70975 0.06275 0.12261 0.00106

-0.29412 0.17835 0.17128 0.06569 0.75485 0.01116 0.12312 0.00012

-0.35294 0.15511 0.16155 0.12523 0.80304 0.01850 0.12355 0.00018

-0.52941 0.14675 0.15145 0.00609 0.86170 0.00085 0.12430 0.00001

-0.70588 0.14648 0.14245 0.01556 0.91733 0.00217 0.12446 0.00001

-0.88235 0.19571 0.15993 0.11962 0.81942 0.02229 0.12480 0.00020

-0.94118 0.55677 0.22341 0.01337 0.81790 0.00709 0.17403 0.00082

-1.00000 0.52901 0.24153 0.04715 0.97288 0.02375 0.22379 0.00318

-1.05882 0.17528 0.15458 0.23370 1.52006 0.03901 0.22379 0.00002

-1.17647 0.13725 0.13745 0.01331 1.71054 0.00174 0.22391 0.00001

-1.29412 0.13861 0.13840 0.02133 1.69876 0.00281 0.22391 0.00000

-1.41176 0.14050 0.13963 0.02077 1.68381 0.00278 0.22391 0.00000

113

TABLE I .7 Mean velocity components and fluctuations results of three

parallel impinging jets at H=20cm , x=5cm (x/tp=10).

y

s

1O

U

U

1O

V

U

'u

U

'v

U

1o

u

U

'

1o

v

U

'

2

1

' '

O

u v

U

0.0588 0.1897 0.1695 0.2302 0.1324 0.0437 0.0225 0.0009

0.1177 0.1894 0.1747 0.2926 0.2530 0.0554 0.0442 0.0021

0.1765 0.1894 0.1747 0.2926 0.3339 0.0554 0.0583 0.0021

0.2353 0.2124 0.1894 0.3672 0.3483 0.0780 0.0660 0.0024

0.2941 0.2141 0.1830 0.4132 0.3812 0.0885 0.0698 0.0020

0.3529 0.2123 0.1786 0.0942 0.6870 0.0200 0.1227 0.0020

0.4118 0.2021 0.1758 0.2103 0.7347 0.0425 0.1292 0.0017

0.4706 0.1910 0.1666 0.2920 0.8123 0.0558 0.1353 0.0023

0.5294 0.1801 0.1641 0.0176 0.8525 0.0032 0.1399 0.0001

0.6471 0.1667 0.1593 0.1348 0.8860 0.0225 0.1412 0.0004

0.7647 0.1614 0.1577 0.0536 0.8995 0.0087 0.1419 0.0001

0.8824 0.1620 0.1607 0.1424 0.8977 0.0231 0.1442 0.0006

0.9412 0.2845 0.2364 0.3912 0.6127 0.1113 0.1449 0.0015

1.0000 0.5798 0.3746 0.0786 0.4663 0.0456 0.1747 0.0045

1.0588 0.1872 0.1591 0.2974 1.1139 0.0557 0.1772 0.0017

1.1177 0.1318 0.1313 0.0158 1.3502 0.0021 0.1772 0.0000

1.2353 0.1314 0.1329 0.0160 1.3343 0.0021 0.1773 0.0000

0.0000 0.2985 0.2126 0.6406 0.0375 0.1857 0.0078 0.0014

-0.0588 0.1954 0.1746 0.2371 0.1364 0.0450 0.0231 0.0010

-0.1177 0.1950 0.1799 0.3014 0.2606 0.0571 0.0455 0.0022

-0.1765 0.1950 0.1799 0.3014 0.3439 0.0571 0.0601 0.0022

-0.2353 0.2187 0.1951 0.3782 0.3588 0.0803 0.0680 0.0025

-0.2941 0.2205 0.1885 0.4256 0.3927 0.0911 0.0718 0.0021

-0.3529 0.2187 0.1839 0.0970 0.7076 0.0206 0.1264 0.0021

-0.4118 0.2081 0.1811 0.2167 0.7568 0.0438 0.1330 0.0018

-0.4706 0.1968 0.1716 0.3007 0.8366 0.0574 0.1394 0.0023

-0.5294 0.1855 0.1690 0.0181 0.8781 0.0033 0.1441 0.0001

-0.6471 0.1717 0.1641 0.1388 0.9126 0.0231 0.1454 0.0004

-0.7647 0.1663 0.1624 0.0552 0.9265 0.0089 0.1461 0.0001

-0.8824 0.1668 0.1655 0.1467 0.9246 0.0238 0.1485 0.0006

-0.9412 0.2931 0.2435 0.4029 0.6311 0.1146 0.1492 0.0016

-1.0000 0.5972 0.3858 0.0809 0.4803 0.0469 0.1799 0.0046

-1.0588 0.1928 0.1639 0.3063 1.1473 0.0573 0.1826 0.0017

-1.1177 0.1358 0.1352 0.0163 1.3907 0.0021 0.1826 0.0000

114

TABLE I .8 Mean velocity components and fluctuations results of three

parallel impinging jets at H=20cm , x=10cm (x/tp=20).

y

s

1O

U

U

1O

V

U

'u

U

'v

U

1o

u

U

'

1o

v

U

'

2

1

' '

O

u v

U

0.11765 0.35132 0.21922 0.73426 0.98532 0.25796 0.21600 0.03687

0.17647 0.29121 0.22495 0.29232 0.96595 0.08513 0.21729 0.00201

0.29412 0.22879 0.19951 0.36774 1.11708 0.08414 0.22287 0.00417

0.41176 0.26775 0.19046 0.37984 1.18113 0.10170 0.22495 0.00311

0.52941 0.28050 0.18510 0.43372 1.26281 0.12166 0.23374 0.00772

0.58824 0.28103 0.18243 0.09857 1.28938 0.02770 0.23522 0.00073

0.64706 0.26126 0.18173 0.11743 1.31912 0.03068 0.23972 0.00142

0.70588 0.24449 0.17930 0.33891 1.41376 0.08286 0.25349 0.00683

0.76471 0.24147 0.17745 0.16127 1.44100 0.03894 0.25570 0.00131

0.82353 0.22274 0.17914 0.11910 1.43596 0.02653 0.25724 0.00074

0.88235 0.20192 0.18754 0.17874 1.40828 0.03609 0.26410 0.00216

0.94118 0.21714 0.19225 0.36091 1.37479 0.07837 0.26431 0.00082

1.00000 0.27703 0.18724 0.15532 1.41584 0.04303 0.26510 0.00088

1.05882 0.36283 0.18711 0.21188 1.41701 0.07687 0.26514 0.00036

1.11765 0.42274 0.19275 0.58148 1.40764 0.24581 0.27132 0.01416

1.17647 0.42274 0.19275 0.58148 1.43901 0.24581 0.27737 0.01416

1.23529 0.27865 0.17289 0.44869 1.60431 0.12503 0.27737 0.00023

1.35294 0.15389 0.14541 0.10456 1.90756 0.01609 0.27737 0.00001

1.47059 0.13403 0.13399 0.01254 2.07011 0.00168 0.27737 0.00000

0.00000 0.32536 0.20015 0.00132 0.85848 0.00041 0.16682 0.00007

-0.11765 0.36186 0.22580 0.75629 1.01488 0.26570 0.22248 0.03798

-0.17647 0.29995 0.23170 0.30109 0.99493 0.08768 0.22381 0.00207

-0.29412 0.23565 0.20550 0.37877 1.15059 0.08666 0.22956 0.00430

-0.41176 0.27578 0.19617 0.39124 1.21656 0.10475 0.23170 0.00320

-0.52941 0.28892 0.19065 0.44673 1.30069 0.12531 0.24075 0.00795

-0.58824 0.28946 0.18790 0.10153 1.32806 0.02853 0.24228 0.00075

-0.64706 0.26910 0.18718 0.12095 1.35869 0.03160 0.24691 0.00146

-0.70588 0.25182 0.18468 0.34908 1.45617 0.08535 0.26109 0.00703

-0.76471 0.24871 0.18277 0.16611 1.48423 0.04011 0.26337 0.00135

-0.82353 0.22942 0.18451 0.12267 1.47904 0.02733 0.26496 0.00076

-0.88235 0.20798 0.19317 0.18410 1.45053 0.03717 0.27202 0.00222

-0.94118 0.22365 0.19802 0.37174 1.41603 0.08072 0.27224 0.00084

-1.00000 0.28534 0.19286 0.15998 1.45832 0.04432 0.27305 0.00091

-1.05882 0.37371 0.19272 0.21824 1.45952 0.07918 0.27309 0.00037

-1.11765 0.43542 0.19853 0.59892 1.44987 0.25318 0.27946 0.01458

-1.17647 0.43542 0.19853 0.59892 1.48218 0.25318 0.28569 0.01458

-1.23529 0.28701 0.17808 0.46215 1.65244 0.12878 0.28569 0.00024

-1.35294 0.15851 0.14977 0.10770 1.96479 0.01657 0.28569 0.00001

-1.47059 0.13805 0.13801 0.01292 2.13221 0.00173 0.28569 0.00000

115

TABLE I .9 Mean velocity components and fluctuations results of three

parallel impinging jets at H=30cm , x=10cm (x/tp=20).

y

s

1O

U

U

1O

V

U

'u

U

'v

U

1o

u

U

'

1o

v

U

'

2

1

' '

O

u v

U

0.0588 0.3059 0.2419 0.4840 0.9596 0.1481 0.2321 0.0247

0.1177 0.2744 0.2187 0.1641 1.6180 0.0450 0.3539 0.0120

0.1765 0.2335 0.1926 0.3362 1.9707 0.0785 0.3795 0.0108

0.2941 0.2040 0.1741 0.1290 2.3374 0.0263 0.4068 0.0039

0.4118 0.1993 0.1685 0.3275 2.4195 0.0653 0.4076 0.0017

0.5294 0.1917 0.1569 0.3449 2.6034 0.0661 0.4084 0.0016

0.5882 0.1763 0.1590 0.2570 2.5835 0.0453 0.4107 0.0020

0.7059 0.1763 0.1590 0.2570 2.5982 0.0453 0.4131 0.0020

0.7647 0.1815 0.1662 0.2206 2.4884 0.0400 0.4136 0.0008

0.8235 0.2227 0.1686 0.2257 2.4532 0.0503 0.4136 0.0001

0.8824 0.3015 0.1818 0.0906 2.2759 0.0273 0.4137 0.0002

0.9412 0.3898 0.2003 0.1989 2.0836 0.0775 0.4173 0.0043

1.0000 0.3835 0.2151 0.2083 2.0067 0.0799 0.4316 0.0088

1.0588 0.2798 0.1858 0.0417 2.3367 0.0117 0.4340 0.0005

1.1177 0.1916 0.1549 0.3274 2.8018 0.0627 0.4341 0.0004

1.1765 0.1379 0.1361 1.4763 3.1890 0.2036 0.4341 0.0010

1.2941 0.1320 0.1322 0.0080 3.2834 0.0011 0.4341 0.0000

1.4118 0.1319 0.1332 0.0225 3.2589 0.0030 0.4341 0.0000

0.0000 0.3042 0.2230 0.4390 0.7672 0.1297 0.1661 0.0209

-0.0588 0.3151 0.2491 0.4985 0.9884 0.1525 0.2391 0.0255

-0.1177 0.2826 0.2253 0.1690 1.6666 0.0464 0.3645 0.0124

-0.1765 0.2405 0.1983 0.3463 2.0298 0.0809 0.3909 0.0111

-0.2941 0.2101 0.1793 0.1329 2.4076 0.0271 0.4190 0.0040

-0.4118 0.2053 0.1735 0.3373 2.4920 0.0672 0.4199 0.0017

-0.5294 0.1974 0.1616 0.3553 2.6815 0.0681 0.4206 0.0017

-0.5882 0.1816 0.1637 0.2647 2.6610 0.0467 0.4231 0.0020

-0.7059 0.1816 0.1637 0.2647 2.6761 0.0466 0.4255 0.0020

-0.7647 0.1869 0.1712 0.2272 2.5631 0.0412 0.4260 0.0009

-0.8235 0.2294 0.1736 0.2325 2.5268 0.0518 0.4260 0.0001

-0.8824 0.3106 0.1872 0.0933 2.3441 0.0281 0.4261 0.0002

-0.9412 0.4015 0.2063 0.2049 2.1461 0.0799 0.4299 0.0044

-1.0000 0.3950 0.2215 0.2145 2.0669 0.0823 0.4445 0.0090

-1.0588 0.2882 0.1913 0.0430 2.4068 0.0120 0.4471 0.0006

-1.1177 0.1974 0.1596 0.3373 2.8859 0.0646 0.4471 0.0004

-1.1765 0.1421 0.1402 1.5206 3.2847 0.2097 0.4471 0.0011

-1.2941 0.1360 0.1362 0.0082 3.3819 0.0011 0.4471 0.0000

-1.4118 0.1359 0.1372 0.0232 3.3566 0.0031 0.4472 0.0000

116

TABLE I .10 Mean velocity components and fluctuations results of three

parallel impinging jets at H=30cm , x=20cm (x/tp=40).

y

s

1O

U

U

1O

V

U

'u

U

'v

U

1o

u

U

'

1o

v

U

'

2

1

' '

O

u v

U

0.05882 0.23297 0.19125 0.22298 0.21973 0.05195 0.04202 0.00192

0.11765 0.25082 0.19488 0.06493 0.21668 0.01629 0.04223 0.00007

0.17647 0.26292 0.19976 0.81151 0.55679 0.21336 0.11122 0.02195

0.29412 0.26249 0.20114 0.44087 0.68296 0.11572 0.13737 0.00933

0.41176 0.22538 0.19199 0.14459 0.71620 0.03259 0.13750 0.00020

0.47059 0.21954 0.18300 0.38967 0.77689 0.08555 0.14217 0.00309

0.52941 0.20289 0.17905 0.21474 0.80748 0.04357 0.14458 0.00115

0.58824 0.20440 0.16999 0.20929 0.86678 0.04278 0.14735 0.00122

0.70588 0.21191 0.16520 0.01461 1.19076 0.00310 0.19671 0.00040

0.76471 0.24147 0.16379 0.06431 1.20378 0.01553 0.19717 0.00021

0.82353 0.25112 0.16993 0.14699 1.16133 0.03691 0.19735 0.00031

0.88235 0.26269 0.17115 0.21916 1.15425 0.05757 0.19755 0.00052

0.94118 0.25614 0.17872 0.40883 1.10729 0.10471 0.19789 0.00122

1.00000 0.24655 0.17776 0.47498 1.41228 0.11710 0.25104 0.01809

1.05882 0.23913 0.17336 0.13484 1.67036 0.03224 0.28958 0.00465

1.11765 0.21114 0.17004 0.29684 1.70883 0.06267 0.29058 0.00151

1.17647 0.19240 0.15689 0.32092 1.85318 0.06175 0.29075 0.00061

1.29412 0.15183 0.14269 0.09983 2.03867 0.01516 0.29090 0.00014

1.41176 0.13766 0.13996 0.00716 2.07959 0.00099 0.29105 0.00001

1.64706 0.13655 0.13567 0.13125 2.14535 0.01792 0.29107 0.00005

1.88235 0.13538 0.13499 0.01891 2.16257 0.00256 0.29191 0.00006

0.00000 0.23234 0.19654 0.39738 0.10653 0.09052 0.02052 0.00183

-0.05882 0.23763 0.19508 0.22744 0.22413 0.05299 0.04286 0.00196

-0.11765 0.25584 0.19878 0.06623 0.22101 0.01662 0.04308 0.00007

-0.17647 0.26818 0.20376 0.82774 0.56793 0.21763 0.11344 0.02239

-0.29412 0.26774 0.20516 0.44969 0.69662 0.11803 0.14012 0.00952

-0.41176 0.22989 0.19583 0.14748 0.73052 0.03324 0.14025 0.00020

-0.47059 0.22393 0.18666 0.39746 0.79243 0.08726 0.14501 0.00315

-0.52941 0.20695 0.18263 0.21904 0.82363 0.04444 0.14747 0.00117

-0.58824 0.20849 0.17339 0.21348 0.88412 0.04364 0.15030 0.00124

-0.70588 0.21615 0.16850 0.01490 1.21458 0.00316 0.20064 0.00041

-0.76471 0.24630 0.16707 0.06560 1.22786 0.01584 0.20111 0.00021

-0.82353 0.25614 0.17333 0.14993 1.18456 0.03765 0.20130 0.00032

-0.88235 0.26794 0.17457 0.22354 1.17734 0.05872 0.20150 0.00053

-0.94118 0.26126 0.18229 0.41701 1.12944 0.10680 0.20185 0.00124

-1.00000 0.25148 0.18132 0.48448 1.44053 0.11944 0.25606 0.01845

-1.05882 0.24391 0.17683 0.13754 1.70377 0.03289 0.29537 0.00474

-1.11765 0.21536 0.17344 0.30278 1.74301 0.06392 0.29639 0.00154

-1.17647 0.19625 0.16003 0.32734 1.89024 0.06299 0.29657 0.00062

-1.29412 0.15487 0.14554 0.10183 2.07944 0.01546 0.29672 0.00014

-1.41176 0.14041 0.14276 0.00730 2.12118 0.00101 0.29687 0.00001

-1.64706 0.13928 0.13838 0.13388 2.18826 0.01828 0.29689 0.00005

-1.88235 0.13809 0.13769 0.01929 2.20582 0.00261 0.29775 0.00006

117

TABLE I .11 Mean velocity components and fluctuations results of three

parallel impinging jets at H=45cm , x=23cm (x/tp=46).

y

s

1O

U

U

1O

V

U

'u

U

'v

U

1o

u

U

'

1o

v

U

'

2

1

' '

O

u v

U

0.1176 0.2275 0.2104 0.2146 0.1140 0.0488 0.0240 0.0001

0.2353 0.2246 0.2134 0.2046 0.1244 0.0460 0.0265 0.0001

0.3529 0.2202 0.2095 0.1715 0.1357 0.0378 0.0284 0.0001

0.4706 0.2095 0.2026 0.1211 0.1509 0.0254 0.0306 0.0001

0.5882 0.2133 0.2010 0.1489 0.2410 0.0318 0.0484 0.0003

0.7059 0.2239 0.2030 0.1791 0.2473 0.0401 0.0502 0.0001

0.8235 0.2563 0.2004 0.2246 0.2568 0.0576 0.0515 0.0001

0.9412 0.2703 0.1936 0.2334 0.2661 0.0631 0.0515 0.0000

1.0000 0.2611 0.1943 0.2286 0.2683 0.0597 0.0521 0.0001

1.0588 0.2568 0.2038 0.2364 0.2644 0.0607 0.0539 0.0001

1.1176 0.2378 0.2075 0.2295 0.2674 0.0546 0.0555 0.0001

1.1765 0.2297 0.2068 0.2027 0.2880 0.0466 0.0596 0.0002

1.2353 0.2205 0.2128 0.1847 0.2992 0.0407 0.0637 0.0002

1.2941 0.2132 0.2197 0.1257 0.3046 0.0268 0.0669 0.0002

1.4118 0.2102 0.2257 0.0898 0.3023 0.0189 0.0682 0.0001

1.5294 0.2097 0.2318 0.0802 0.3017 0.0168 0.0700 0.0001

1.6471 0.2116 0.2320 0.0866 0.3086 0.0183 0.0716 0.0001

1.7647 0.2117 0.2309 0.0836 0.3103 0.0177 0.0717 0.0000

1.8824 0.2110 0.2113 0.0808 0.3499 0.0170 0.0739 0.0002

2.3529 0.2095 0.2281 0.0848 0.3252 0.0178 0.0742 0.0001

0.0000 0.2388 0.2087 0.2280 0.0877 0.0533 0.0180 0.0001

-0.1176 0.2321 0.2146 0.2189 0.1163 0.0498 0.0245 0.0001

-0.2353 0.2291 0.2177 0.2087 0.1269 0.0469 0.0270 0.0001

-0.3529 0.2246 0.2137 0.1749 0.1384 0.0386 0.0290 0.0001

-0.4706 0.2137 0.2067 0.1235 0.1539 0.0259 0.0312 0.0001

-0.5882 0.2176 0.2050 0.1519 0.2458 0.0324 0.0494 0.0003

-0.7059 0.2284 0.2071 0.1827 0.2522 0.0409 0.0512 0.0001

-0.8235 0.2614 0.2044 0.2291 0.2619 0.0588 0.0525 0.0001

-0.9412 0.2757 0.1975 0.2381 0.2714 0.0644 0.0525 0.0000

-1.0000 0.2663 0.1982 0.2332 0.2737 0.0609 0.0531 0.0001

-1.0588 0.2619 0.2079 0.2411 0.2697 0.0619 0.0550 0.0001

-1.1176 0.2426 0.2117 0.2341 0.2727 0.0557 0.0566 0.0001

-1.1765 0.2343 0.2109 0.2068 0.2938 0.0475 0.0608 0.0002

-1.2353 0.2249 0.2171 0.1884 0.3052 0.0415 0.0650 0.0002

-1.2941 0.2175 0.2241 0.1282 0.3107 0.0273 0.0682 0.0002

-1.4118 0.2144 0.2302 0.0916 0.3083 0.0193 0.0696 0.0001

-1.5294 0.2139 0.2364 0.0818 0.3077 0.0171 0.0714 0.0001

-1.6471 0.2158 0.2366 0.0883 0.3148 0.0187 0.0730 0.0001

-1.7647 0.2159 0.2355 0.0853 0.3165 0.0181 0.0731 0.0000

-1.8824 0.2152 0.2155 0.0824 0.3569 0.0173 0.0754 0.0002

-2.3529 0.2137 0.2327 0.0865 0.3317 0.0182 0.0757 0.0001

118

TABLE I .12 Mean velocity components and fluctuations results of three

parallel impinging jets at H=45cm , x=24cm (x/tp=48).

y

s

1O

U

U

1O

V

U

'u

U

'v

U

1o

u

U

'

1o

v

U

'

2

1

' '

O

u v

U

0.00000 0.24080 0.20030 0.24360 0.04840 0.05870 0.00970 0.00010

0.11760 0.23890 0.20220 0.23430 0.06160 0.05600 0.01240 0.00010

0.23530 0.22070 0.20830 0.18300 0.44250 0.04040 0.09220 0.00080

0.35290 0.21310 0.20500 0.13340 0.45500 0.02840 0.09330 0.00010

0.47060 0.21150 0.20170 0.13550 0.46550 0.02870 0.09390 0.00010

0.58820 0.21550 0.20250 0.15740 0.46640 0.03390 0.09440 0.00010

0.70590 0.23300 0.19830 0.21320 0.47700 0.04970 0.09460 0.00000

0.82350 0.26530 0.19470 0.22500 0.48620 0.05970 0.09460 0.00000

0.88240 0.27880 0.19430 0.22170 0.48750 0.06180 0.09470 0.00000

1.00000 0.27690 0.19370 0.23230 0.48950 0.06430 0.09480 0.00000

1.05880 0.25860 0.19790 0.23090 0.48140 0.05970 0.09530 0.00010

1.11760 0.23610 0.20240 0.22610 0.47150 0.05340 0.09540 0.00000

1.17650 0.22100 0.20750 0.17640 0.46390 0.03900 0.09630 0.00010

1.23530 0.21160 0.21430 0.13000 0.45780 0.02750 0.09810 0.00020

1.29410 0.20740 0.22060 0.09250 0.44520 0.01920 0.09820 0.00000

1.41180 0.20910 0.22940 0.08480 0.43990 0.01770 0.10090 0.00020

1.64710 0.20910 0.23000 0.08400 0.44030 0.01760 0.10130 0.00010

1.88240 0.20630 0.23040 0.07490 0.46470 0.01550 0.10710 0.00030

2.11760 0.20710 0.22350 0.07490 0.49230 0.01550 0.11000 0.00020

0.00000 0.24802 0.20631 0.25091 0.04985 0.06046 0.00999 0.00010

-0.11760 0.24607 0.20827 0.24133 0.06345 0.05768 0.01277 0.00010

-0.23530 0.22732 0.21455 0.18849 0.45578 0.04161 0.09497 0.00082

-0.35290 0.21949 0.21115 0.13740 0.46865 0.02925 0.09610 0.00010

-0.47060 0.21785 0.20775 0.13957 0.47947 0.02956 0.09672 0.00010

-0.58820 0.22197 0.20858 0.16212 0.48039 0.03492 0.09723 0.00010

-0.70590 0.23999 0.20425 0.21960 0.49131 0.05119 0.09744 0.00000

-0.82350 0.27326 0.20054 0.23175 0.50079 0.06149 0.09744 0.00000

-0.88240 0.28716 0.20013 0.22835 0.50213 0.06365 0.09754 0.00000

-1.00000 0.28521 0.19951 0.23927 0.50419 0.06623 0.09764 0.00000

-1.05880 0.26636 0.20384 0.23783 0.49584 0.06149 0.09816 0.00010

-1.11760 0.24318 0.20847 0.23288 0.48565 0.05500 0.09826 0.00000

-1.17650 0.22763 0.21373 0.18169 0.47782 0.04017 0.09919 0.00010

-1.23530 0.21795 0.22073 0.13390 0.47153 0.02833 0.10104 0.00021

-1.29410 0.21362 0.22722 0.09528 0.45856 0.01978 0.10115 0.00000

-1.41180 0.21537 0.23628 0.08734 0.45310 0.01823 0.10393 0.00021

-1.64710 0.21537 0.23690 0.08652 0.45351 0.01813 0.10434 0.00010

-1.88240 0.21249 0.23731 0.07715 0.47864 0.01597 0.11031 0.00031

-2.11760 0.21331 0.23021 0.07715 0.50707 0.01597 0.11330 0.00021

119

TABLE I .13 Mean velocity components and fluctuations results of three

parallel impinging jets at H=45cm , x=28cm (x/tp=56).

y

s

1O

U

U

1O

V

U

'u

U

'v

U

1o

u

U

'

1o

v

U

'

2

1

' '

O

u v

U

0.00000 0.21440 0.16680 0.01540 0.22490 0.00330 0.03750 0.00010

0.11760 0.21700 0.17380 0.19840 0.32990 0.04300 0.05730 0.01900

0.23530 0.21890 0.16970 0.12230 0.37610 0.02680 0.06380 0.00080

0.35290 0.21720 0.16800 0.17680 0.61930 0.03840 0.10400 0.00320

0.47060 0.21040 0.16780 0.20240 0.62850 0.04260 0.10550 0.00070

0.58820 0.22270 0.16050 0.45790 0.68140 0.10200 0.10940 0.00290

0.70590 0.23910 0.15950 0.11580 0.72170 0.02770 0.11510 0.00100

0.82350 0.26490 0.15270 0.42610 0.77310 0.11290 0.11800 0.00300

0.94120 0.25340 0.14780 0.48760 0.89400 0.12350 0.13210 0.00730

1.05880 0.22330 0.14680 0.95950 0.95470 0.21420 0.14020 0.01000

1.11760 0.20110 0.14190 0.04800 0.99420 0.00970 0.14100 0.00020

1.17650 0.18550 0.14180 0.29780 0.99890 0.05520 0.14160 0.00070

1.23530 0.17000 0.13870 1.31450 1.02230 0.22350 0.14180 0.00180

1.29410 0.15650 0.13850 0.19490 1.43470 0.03050 0.19870 0.00420

1.41180 0.14080 0.13650 0.04920 1.45560 0.00690 0.19870 0.00000

1.64710 0.13340 0.13500 0.02340 1.47230 0.00310 0.19880 0.00000

1.88240 0.13300 0.13460 0.02360 1.47940 0.00310 0.19910 0.00000

2.11760 0.13400 0.13420 0.02590 1.48410 0.00350 0.19910 0.00000

2.35290 0.13320 0.13420 0.02370 1.48350 0.00320 0.19910 0.00000

0.00000 0.21869 0.17014 0.01571 0.22940 0.00337 0.03825 0.00010

-0.11760 0.22134 0.17728 0.20237 0.33650 0.04386 0.05845 0.00190

-0.23530 0.22328 0.17309 0.12475 0.38362 0.02734 0.06508 0.00080

-0.35290 0.22154 0.17136 0.18034 0.63169 0.03917 0.10608 0.00330

-0.47060 0.21461 0.17116 0.20645 0.64107 0.04345 0.10761 0.00070

-0.58820 0.22715 0.16371 0.46706 0.69503 0.10404 0.11159 0.00300

-0.70590 0.24388 0.16269 0.11812 0.73613 0.02825 0.11740 0.00100

-0.82350 0.27020 0.15575 0.43462 0.78856 0.11516 0.12036 0.00310

-0.94120 0.25847 0.15076 0.49735 0.91188 0.12597 0.13474 0.00740

-1.05880 0.22777 0.14974 0.97869 0.97379 0.21848 0.14300 0.01020

-1.11760 0.20512 0.14474 0.04896 1.01408 0.00989 0.14382 0.00020

-1.17650 0.18921 0.14464 0.30376 1.01888 0.05630 0.14443 0.00070

-1.23530 0.17340 0.14147 1.34079 1.04275 0.22797 0.14464 0.00180

-1.29410 0.15963 0.14127 0.19880 1.46339 0.03111 0.20267 0.00430

-1.41180 0.14362 0.13923 0.05018 1.48471 0.00704 0.20267 0.00000

-1.64710 0.13607 0.13770 0.02387 1.50175 0.00316 0.20278 0.00000

-1.88240 0.13566 0.13729 0.02407 1.50899 0.00316 0.20308 0.00000

-1.23772 0.17829 0.14410 0.32042 1.24743 0.06300 0.17399 0.00090

-1.31134 0.17721 0.14366 0.32216 1.26472 0.06316 0.17611 0.00090

120

TABLE I .14 Mean velocity components and fluctuations results of three

parallel impinging jets at H=45cm , x=34cm (x/tp=68).

y

s

1O

U

U

1O

V

U

'u

U

'v

U

1o

u

U

'

1o

v

U

'

2

1

' '

O

u v

U

0.00000 0.18570 0.16020 0.21310 0.22500 0.03960 0.03600 0.00140

0.11760 0.18630 0.16090 0.10140 0.23800 0.01890 0.03830 0.00020

0.23530 0.19500 0.16000 0.29940 0.25200 0.05840 0.04030 0.00070

0.35290 0.19450 0.15830 0.18990 0.45240 0.03690 0.07160 0.00220

0.47060 0.20480 0.15870 0.34580 0.49850 0.07080 0.07910 0.00240

0.58820 0.22440 0.16080 0.41470 0.50810 0.09310 0.08170 0.00190

0.70590 0.23360 0.16210 0.20460 0.54150 0.04780 0.08780 0.00150

0.82350 0.24960 0.15740 0.05140 0.59410 0.01280 0.09350 0.00040

0.94120 0.23610 0.15400 0.14070 0.62680 0.03320 0.09650 0.00080

1.05880 0.21260 0.15900 0.25320 1.22080 0.05380 0.19410 0.00910

1.11760 0.20230 0.15750 0.02940 1.24880 0.00590 0.19670 0.00020

1.17650 0.18560 0.14890 0.27920 1.32700 0.05180 0.19760 0.00100

1.23530 0.17850 0.14940 0.13370 1.32230 0.02390 0.19760 0.00010

1.29410 0.17160 0.15320 0.19880 1.30210 0.03410 0.19950 0.00090

1.41180 0.15440 0.14530 0.05390 1.37740 0.00830 0.20010 0.00010

1.64710 0.13850 0.14190 0.01670 1.41300 0.00230 0.20040 0.00000

1.88240 0.13640 0.13750 0.04700 1.45810 0.00640 0.20040 0.00000

2.35290 0.13520 0.13950 0.04800 1.43700 0.00650 0.20040 0.00000

0.00000 0.19130 0.16500 0.21950 0.23180 0.04080 0.03710 0.00140

-0.11760 0.19190 0.16570 0.10440 0.24510 0.01950 0.03940 0.00020

-0.23530 0.20090 0.16480 0.30840 0.25960 0.06020 0.04150 0.00070

-0.35290 0.20030 0.16300 0.19560 0.46600 0.03800 0.07370 0.00230

-0.47060 0.21090 0.16350 0.35620 0.51350 0.07290 0.08150 0.00250

-0.58820 0.23110 0.16560 0.42710 0.52330 0.09590 0.08420 0.00200

-0.70590 0.24060 0.16700 0.21070 0.55770 0.04920 0.09040 0.00150

-0.82350 0.25710 0.16210 0.05290 0.61190 0.01320 0.09630 0.00040

-0.94120 0.24320 0.15860 0.14490 0.64560 0.03420 0.09940 0.00080

-1.05880 0.21900 0.16380 0.26080 1.25740 0.05540 0.19990 0.00940

-1.11760 0.20840 0.16220 0.03030 1.28630 0.00610 0.20260 0.00020

-1.17650 0.19120 0.15340 0.28760 1.36680 0.05340 0.20350 0.00100

-1.23530 0.18390 0.15390 0.13770 1.36200 0.02460 0.20350 0.00010

-1.29410 0.17670 0.15780 0.20480 1.34120 0.03510 0.20550 0.00090

-1.41180 0.15900 0.14970 0.05550 1.41870 0.00850 0.20610 0.00010

-1.64710 0.14270 0.14620 0.01720 1.45540 0.00240 0.20640 0.00000

-1.88240 0.14050 0.14160 0.04840 1.50180 0.00660 0.20640 0.00000

-2.35290 0.13930 0.14370 0.04940 1.48010 0.00670 0.20640 0.00000

121

TABLE I .15 Mean velocity components and fluctuations results of three

parallel impinging jets at H=45cm , x=40cm (x/tp=80).

y

s

1O

U

U

1O

V

U

'u

U

'v

U

1o

u

U

'

1o

v

U

'

2

1

' '

O

u v

U

0.11760 0.16330 0.15790 0.02220 0.31950 0.00360 0.05040 0.00010

0.23530 0.16630 0.15730 0.08120 0.58000 0.01350 0.09120 0.00100

0.35290 0.17300 0.15590 0.10750 0.62330 0.01860 0.09710 0.00060

0.47060 0.17650 0.15930 0.03470 0.85480 0.00610 0.13620 0.00060

0.58820 0.18430 0.16340 0.26920 0.85730 0.04960 0.14010 0.00160

0.70590 0.19510 0.17350 0.00780 0.80830 0.00150 0.14030 0.00000

0.82350 0.20040 0.18130 0.01520 0.86600 0.00300 0.15700 0.00020

0.94120 0.20460 0.19440 0.34600 0.80780 0.07080 0.15700 0.00020

1.05880 0.19840 0.21250 0.35940 0.75200 0.07130 0.15980 0.00210

1.17650 0.19220 0.22180 0.32370 0.81850 0.06220 0.18150 0.00540

1.29410 0.17860 0.21580 0.03280 0.84320 0.00590 0.18200 0.00010

1.41180 0.16580 0.21320 0.13150 0.95800 0.02180 0.20420 0.00200

1.64710 0.14860 0.20720 0.04060 0.98560 0.00600 0.20420 0.00000

1.88240 0.14810 0.19570 0.00780 1.05830 0.00120 0.20710 0.00000

2.11760 0.14230 0.19770 0.03660 1.07940 0.00520 0.21340 0.00030

2.35290 0.13870 0.19150 0.07360 1.14110 0.01020 0.21850 0.00050

2.58820 0.13700 0.19270 0.16130 1.14920 0.02210 0.22140 0.00080

2.82350 0.13760 0.18810 0.17440 1.42470 0.02400 0.26800 0.00360

0.00000 0.16960 0.16790 0.74820 0.25560 0.12330 0.04170 0.00490

-0.11760 0.16820 0.16260 0.02290 0.32910 0.00370 0.05190 0.00010

-0.23530 0.17130 0.16200 0.08360 0.59740 0.01390 0.09390 0.00100

-0.35290 0.17820 0.16060 0.11070 0.64200 0.01920 0.10000 0.00060

-0.47060 0.18180 0.16410 0.03570 0.88040 0.00630 0.14030 0.00060

-0.58820 0.18980 0.16830 0.27730 0.88300 0.05110 0.14430 0.00160

-0.70590 0.20100 0.17870 0.00800 0.83250 0.00150 0.14450 0.00000

-0.82350 0.20640 0.18670 0.01570 0.89200 0.00310 0.16170 0.00020

-0.94120 0.21070 0.20020 0.35640 0.83200 0.07290 0.16170 0.00020

-1.05880 0.20440 0.21890 0.37020 0.77460 0.07340 0.16460 0.00220

-1.17650 0.19800 0.22850 0.33340 0.84310 0.06410 0.18690 0.00560

-1.29410 0.18400 0.22230 0.03380 0.86850 0.00610 0.18750 0.00010

-1.41180 0.17080 0.21960 0.13540 0.98670 0.02250 0.21030 0.00210

-1.64710 0.15310 0.21340 0.04180 1.01520 0.00620 0.21030 0.00000

-1.88240 0.15250 0.20160 0.00800 1.09000 0.00120 0.21330 0.00000

-2.11760 0.14660 0.20360 0.03770 1.11180 0.00540 0.21980 0.00030

-2.35290 0.14290 0.19720 0.07580 1.17530 0.01050 0.22510 0.00050

-2.58820 0.14110 0.19850 0.16610 1.18370 0.02280 0.22800 0.00080

-2.82350 0.14170 0.19370 0.17960 1.46740 0.02470 0.27600 0.00370

122

TABLE I .16 Axial mean velocity and fluctuation results o f three unequal

(Uo1=Uo2=2Uo3) parallel impinging jets at H=45cm, x=40cm

y

s

y

x

1O

U

U

'u

U

1o

u

U

'

-1.5882 -0.6750 0.1378 0.0645 0.0089

-1.5294 -0.6500 0.1380 0.0653 0.0090

-1.4118 -0.6000 0.1383 0.0673 0.0093

-1.2941 -0.5500 0.1383 0.0663 0.0092

-1.1765 -0.5000 0.1384 0.0680 0.0094

-1.0588 -0.4500 0.1392 0.0705 0.0098

-0.9412 -0.4000 0.1403 0.0740 0.0104

-0.8235 -0.3500 0.1416 0.0839 0.0119

-0.7059 -0.3000 0.1443 0.0956 0.0138

-0.5882 -0.2500 0.1487 0.1183 0.0176

-0.4706 -0.2000 0.1539 0.1392 0.0214

-0.3529 -0.1500 0.1633 0.1613 0.0263

-0.2353 -0.1000 0.1726 0.1875 0.0324

-0.1176 -0.0500 0.1762 0.1958 0.0345

0.0000 0.0000 0.1735 0.1902 0.0330

0.1176 0.0500 0.1683 0.1861 0.0313

0.2353 0.1000 0.1589 0.1744 0.0277

0.3529 0.1500 0.1537 0.1699 0.0261

0.4706 0.2000 0.1559 0.1867 0.0291

0.5882 0.2500 0.1580 0.2015 0.0318

0.7059 0.3000 0.1667 0.2246 0.0374

0.8235 0.3500 0.1738 0.2325 0.0404

0.9412 0.4000 0.1715 0.2084 0.0357

1.0588 0.4500 0.1631 0.1819 0.0297

1.1765 0.5000 0.1507 0.1475 0.0222

1.2941 0.5500 0.1427 0.1017 0.0145

1.4118 0.6000 0.1403 0.0907 0.0127

1.5294 0.6500 0.1400 0.0878 0.0123

123

TABLE I .17 Axial mean velocity and fluctuation results o f three unequal

(Uo1=Uo3=.5Uo2) parallel impinging jets at H=45cm, x=40cm

y

s

y

x

1O

U

U

'u

U

1o

u

U

'

-1.5882 -0.6750 0.1378 0.0645 0.0089

-1.5294 -0.6500 0.1380 0.0653 0.0090

-1.4118 -0.6000 0.1383 0.0673 0.0093

-1.2941 -0.5500 0.1383 0.0663 0.0092

-1.1765 -0.5000 0.1384 0.0680 0.0094

-1.0588 -0.4500 0.1392 0.0705 0.0098

-0.9412 -0.4000 0.1403 0.0740 0.0104

-0.8235 -0.3500 0.1416 0.0839 0.0119

-0.7059 -0.3000 0.1443 0.0956 0.0138

-0.5882 -0.2500 0.1487 0.1183 0.0176

-0.4706 -0.2000 0.1539 0.1392 0.0214

-0.3529 -0.1500 0.1633 0.1613 0.0263

-0.2353 -0.1000 0.1726 0.1875 0.0324

-0.1176 -0.0500 0.1762 0.1958 0.0345

0.0000 0.0000 0.1735 0.1902 0.0330

0.1176 0.0500 0.1683 0.1861 0.0313

0.2353 0.1000 0.1589 0.1744 0.0277

0.3529 0.1500 0.1537 0.1699 0.0261

0.4706 0.2000 0.1559 0.1867 0.0291

0.5882 0.2500 0.1580 0.2015 0.0318

0.7059 0.3000 0.1667 0.2246 0.0374

0.8235 0.3500 0.1738 0.2325 0.0404

0.9412 0.4000 0.1715 0.2084 0.0357

1.0588 0.4500 0.1631 0.1819 0.0297

1.1765 0.5000 0.1507 0.1475 0.0222

1.2941 0.5500 0.1427 0.1017 0.0145

1.4118 0.6000 0.1403 0.0907 0.0127

1.5294 0.6500 0.1400 0.0878 0.0123

124

TABLE I .18 Upstream flow pressure distributions results for three parallel

impinging jets at different impinging plate distances .

y/s

H=10 cm H=20 cm H=30 cm H=45 cm H=70 cm

P

( mH2O) 21o

P

U

P

( mH2O) 21o

P

U

P

( mH2O) 21o

P

U

P

( mH2O) 21o

P

U

P

( mH2O) 21o

P

U

0 0.11 0.4441 0.1 0.4037 0.0888 0.3585 0.0095 0.0384 0.0078 0.0315

0.1765 0.1 0.4037 0.098 0.3956 0.087 0.3512 0.009 0.0363 0.007 0.0283

0.3529 0.07 0.2826 0.085 0.3431 0.089 0.3593 0.0085 0.0343 0.0065 0.0262

0.5294 0.06 0.2422 0.075 0.3028 0.085 0.3431 0.0085 0.0343 0.0065 0.0262

0.7059 0.058 0.2341 0.08 0.323 0.083 0.3351 0.0088 0.0355 0.0068 0.0275

0.8824 0.04 0.1615 0.09 0.3633 0.09 0.3633 0.0095 0.0384 0.0075 0.0303

1.0588 0.11 0.4441 0.1 0.4037 0.068 0.2745 0.0096 0.0388 0.0076 0.0307

1.2353 0.0998 0.4029 0.065 0.2624 0.05 0.2019 0.0075 0.0303 0.0075 0.0303

1.4118 0.013 0.0525 0.015 0.0606 0.03 0.1211 0.008 0.0323 0.006 0.0242

1.5882 0.004 0.0161 0.01 0.0404 0.01 0.0404 0.0065 0.0262 0.0045 0.0182

1.7647 0.003 0.0121 0.005 0.0202 0.005 0.0202 0.0055 0.0222 0.0035 0.0141

1.9412 0.0001 0.0004 0.001 0.004 0.003 0.0121 0.0045 0.0182 0.0025 0.0101

2.1176 0.0001 0.0004 0.001 0.004 0.001 0.004 0.0025 0.0101 0.0015 0.0061

2.2941 0.0001 0.0004 0.001 0.004 0.001 0.004 0.0015 0.0061 0.0015 0.0061

2.4706 0.0001 0.0004 0.001 0.004 0.001 0.004 0.0015 0.0061 0.001 0.004

0 0.11 0.4441 0.1 0.4037 0.0888 0.3585 0.0095 0.0384 0.0078 0.0315

-0.176 0.11 0.4441 0.098 0.3956 0.0875 0.3532 0.009 0.0363 0.007 0.0283

-0.353 0.08 0.323 0.0925 0.3734 0.088 0.3553 0.0088 0.0355 0.0068 0.0275

-0.529 0.065 0.2624 0.082 0.331 0.09 0.3633 0.0087 0.0351 0.0067 0.027

-0.706 0.062 0.2503 0.088 0.3553 0.085 0.3431 0.009 0.0363 0.007 0.0283

-0.882 0.03 0.1211 0.095 0.3835 0.089 0.3593 0.0095 0.0384 0.0075 0.0303

-1.059 0.1175 0.4744 0.11 0.4441 0.065 0.2624 0.0097 0.0392 0.0077 0.0311

-1.235 0.1075 0.434 0.06 0.2422 0.045 0.1817 0.0096 0.0388 0.0076 0.0307

-1.412 0.01 0.0404 0.02 0.0807 0.025 0.1009 0.0085 0.0343 0.0065 0.0262

-1.588 0.005 0.0202 0.015 0.0606 0.01 0.0404 0.007 0.0283 0.005 0.0202

-1.765 0.003 0.0121 0.0055 0.0222 0.005 0.0202 0.006 0.0242 0.004 0.0161

-1.941 0.0001 0.0004 0.001 0.004 0.003 0.0121 0.005 0.0202 0.003 0.0121

-2.118 0.0001 0.0004 0.001 0.004 0.001 0.004 0.0025 0.0101 0.0015 0.0061

-2.294 0.0001 0.0004 0.001 0.004 0.001 0.004 0.0015 0.0061 0.0015 0.0061

-2.471 0.0001 0.0004 0.001 0.004 0.001 0.004 0.0015 0.0061 0.001 0.004

125

TABLE I .19 Upstream flow pressure distributions results for three parallel

unequal impinging jets at H=45 cm.

Y y/s

Uo1=Uo2=2Uo3 Uo1=Uo3=.5Uo2

P

( mH2O) 21o

P

U

P

( mH2O) 21o

P

U

0 0 0.08 0.322963 0.128 0.516741

3 0.176471 0.095 0.383519 0.099 0.399667

6 0.352941 0.095 0.383519 0.0437 0.176419

9 0.529412 0.092 0.371407 0.0399 0.161078

12 0.705882 0.098 0.39563 0.0309 0.124744

15 0.882353 0.095 0.383519 0.0224 0.09043

18 1.058824 0.092 0.371407 0.022 0.088815

21 1.235294 0.075 0.302778 0.0219 0.088411

24 1.411765 0.055 0.222037 0.0195 0.078722

27 1.588235 0.05 0.201852 0.0225 0.090833

30 1.764706 0.023 0.092852 0.02 0.080741

33 1.941176 0.021 0.084778 0.0205 0.082759

36 2.117647 0.019 0.076704 0.0187 0.075493

39 2.294118 0.018 0.072667 0.0185 0.074685

42 2.470588 0.019 0.076704 0.018 0.072667

45 2.647059 0.017 0.06863 0.0195 0.078722

48 2.823529 0.018 0.072667 0.019 0.076704

51 3 0.016 0.064593 0.018 0.072667

54 3.176471 0.017 0.06863 0.01 0.04037

0 0 0.08 0.322963 0.126592 0.511057

-3 -0.17647 0.07 0.282593 0.097911 0.39527

-6 -0.35294 0.065 0.262407 0.043219 0.174478

-9 -0.52941 0.045 0.181667 0.039461 0.159306

-12 -0.70588 0.035 0.141296 0.03056 0.123372

-15 -0.88235 0.025 0.100926 0.022154 0.089435

-18 -1.05882 0.025 0.100926 0.021758 0.087838

-21 -1.23529 0.019 0.076704 0.021659 0.087439

-24 -1.41176 0.02 0.080741 0.019286 0.077856

-27 -1.58824 0.019 0.076704 0.022253 0.089834

-30 -1.76471 0.019 0.076704 0.01978 0.079853

-33 -1.94118 0.018 0.072667 0.020275 0.081849

-36 -2.11765 0.016 0.064593 0.018494 0.074662

-39 -2.29412 0.021 0.084778 0.018297 0.073864

-42 -2.47059 0.022 0.088815 0.017802 0.071867

-45 -2.64706 0.018 0.072667 0.019286 0.077856

-48 -2.82353 0.02 0.080741 0.018791 0.07586

-51 -3 0.018 0.072667 0.017802 0.071867

-54 -3.17647 0.02 0.080741 0.00989 0.039926

126

TABLE I .20 Ground plane static pressure distributions results for three parallel equal and unequal impinging jets at

H=45 cm and x=4, 28 cm.

y y/s

x=4cm x=28 cm

Uo1=Uo2=Uo3 Uo1=Uo2=2Uo3 Uo1=Uo3=.5Uo2 Uo1=Uo2=Uo3 Uo1=Uo2=2Uo3 Uo1=Uo3=.5Uo2

P

(m H2O) 21o

P

U

P

( mH2O) 21o

P

U

P

( mH2O) 21o

P

U

P

(mH2O) 21o

P

U

P

( mH2O) 21o

P

U

P

( mH2O) 21o

P

U

0 0 0.0225 0.09083 0.0224 0.09043 0.0241 0.09729 0.0241 0.09729 0.0228 0.09204 0.025 0.10093

6 0.35294 0.0198 0.07993 0.021 0.08478 0.018 0.07267 0.0515 0.20791 0.0245 0.09891 0.042 0.16956

12 0.70588 0.025 0.10093 0.023 0.09285 0.0225 0.09083 0.0413 0.16673 0.0223 0.09003 0.041 0.16552

18 1.05882 0.0249 0.10052 0.0227 0.09164 0.0223 0.09003 0.0281 0.11344 0.022 0.08881 0.0272 0.10981

24 1.41176 0.02 0.08074 0.0222 0.08962 0.0215 0.0868 0.022 0.08881 0.0218 0.08801 0.024 0.09689

30 1.76471 0.018 0.07267 0.02 0.08074 0.02 0.08074 0.02 0.08074 0.02 0.08074 0.02 0.08074

0 0 0.0225 0.09083 0.0224 0.09043 0.0241 0.09729 0.0241 0.09729 0.0228 0.09204 0.025 0.10093

-6 -0.3529 0.0223 0.09003 0.0218 0.08801 0.0233 0.09406 0.0498 0.20104 0.0254 0.10254 0.0452 0.18247

-12 -0.7059 0.0228 0.09204 0.023 0.09285 0.0228 0.09204 0.0412 0.16633 0.0238 0.09608 0.0238 0.09608

-18 -1.0588 0.0224 0.09043 0.0228 0.09204 0.019 0.0767 0.0253 0.10214 0.0227 0.09164 0.0243 0.0981

-24 -1.4118 0.0188 0.0759 0.0219 0.08841 0.0189 0.0763 0.022 0.08881 0.0223 0.09003 0.0235 0.09487

-30 -1.7647 0.018 0.07267 0.02 0.08074 0.018 0.07267 0.02 0.08074 0.022 0.08881 0.022 0.08881

104

127

APPENDIX – II

COMPUTER PROGRAMES

128

„Calculating the velocity components and flactuations in Lab coordinates

'from the measured effective velocities using triple wire

OPEN "f1.txt" FOR OUTPUT AS #1

INPUT "x="; x

INPUT "uo="; uo

'GOTO 5

PRINT #1, " nx k1 eta U V W u' v' w' u'v' u'w'

v'w' ur vr wr vu wu "

FOR k = 0 TO 30

IF k = 0 THEN OPEN "3jp7300.asc" FOR INPUT AS #2

IF k=1 Then k=k+1

IF k = 2 THEN OPEN "3jp7302.asc" FOR INPUT AS #2

IF k=3 Then k=k+1

IF k = 4 THEN OPEN "3jp7304.asc" FOR INPUT AS #2

IF k=5 Then k=k+1

IF k = 6 THEN OPEN "3jp7306.asc" FOR INPUT AS #2

IF k=7 Then k=k+1

IF k = 8 THEN OPEN "3jp7308.asc" FOR INPUT AS #2

IF k=9 Then k=k+1

IF k = 10 THEN OPEN "3jp73010.asc" FOR INPUT AS #2

IF k = 11 THEN OPEN "3jp73011.asc" FOR INPUT AS #2

IF k = 12 THEN OPEN "3jp73012.asc" FOR INPUT AS #2

IF k = 13 THEN OPEN "3jp73013.asc" FOR INPUT AS #2

IF k = 14 THEN OPEN "3jp73014.asc" FOR INPUT AS #2

IF k = 15 THEN OPEN "3jp73015.asc" FOR INPUT AS #2

IF k = 16 THEN OPEN "3jp73016.asc" FOR INPUT AS #2

IF k = 17 THEN OPEN "3jp73017.asc" FOR INPUT AS #2

IF k = 18 THEN OPEN "3jp73018.asc" FOR INPUT AS #2

IF k=19 Then k=k+1

IF k = 20 THEN OPEN "3jp73020.asc" FOR INPUT AS #2

IF k=21 Then k=k+1

IF k = 22 THEN OPEN "3jp73022.asc" FOR INPUT AS #2

IF k = 23 THEN k=k+1

IF k = 24 THEN OPEN "3jp73-24.asc" FOR INPUT AS #2

IF k=25 Then k=k+1

IF k = 26 THEN OPEN "3jp73-26.asc" FOR INPUT AS #2

IF k=27 Then k=k+1

IF k = 28 THEN OPEN "3jp73-28.asc" FOR INPUT AS #2

IF k=29 Then k=k+1

IF k = 30 THEN OPEN "3jp73-30.asc" FOR INPUT AS #2

USUM = 0: VSUM = 0: WSUM = 0: UV1 = 0: UW1 = 0: VW1 = 0

UDASH1 = 0: VDASH1 = 0: WDASH1 = 0: i = 0: n = 1024: ind = 0

FOR i = 1 TO n

INPUT #2, uef1, uef2, uef3

E1 = -.519042 * uef1 ^ 2 + .520857 * uef2 ^ 2 + .478862 * uef3 ^ 2

IF E1 < 0 THEN ind = ind + 1

IF E1 < 0 THEN GOTO 6

EPSI1 = E1 ^ .5

129

E2 = .478862 * uef1 ^ 2 - .519042 * uef2 ^ 2 + .520857 * uef3 ^ 2

IF E2 < 0 THEN ind = ind + 1

IF E2 < 0 THEN GOTO 6

EPSI2 = E2 ^ .5

E3 = .520857 * uef1 ^ 2 + .478862 * uef2 ^ 2 - .519042 * uef3 ^ 2

IF E3 < 0 THEN ind = ind + 1

IF E3 < 0 THEN GOTO 6

EPSI3 = E3 ^ .5

U = .577 * EPSI1 + .577 * EPSI2 + .57786 * EPSI3

V = -.7071 * EPSI1 + .7071 * EPSI2

W = -.577 * EPSI1 - .577 * EPSI2 + .81614 * EPSI3

USUM = USUM + U

VSUM = VSUM + V

WSUM = WSUM + W

IF EOF(2) THEN 10

6 NEXT i

10 CLOSE #2

nx = n - ind

uav =abs(USUM / nx): vav =abs(VSUM / nx): wav =abs(WSUM / nx)

'GOTO 15

IF k = 0 THEN OPEN "3jp7300.asc" FOR INPUT AS #2

IF k=1 Then k=k+1

IF k = 2 THEN OPEN "3jp7302.asc" FOR INPUT AS #2

IF k=3 Then k=k+1

IF k = 4 THEN OPEN "3jp7304.asc" FOR INPUT AS #2

IF k=5 Then k=k+1

IF k = 6 THEN OPEN "3jp7306.asc" FOR INPUT AS #2

IF k=7 Then k=k+1

IF k = 8 THEN OPEN "3jp7308.asc" FOR INPUT AS #2

IF k=9 Then k=k+1

IF k = 10 THEN OPEN "3jp73010.asc" FOR INPUT AS #2

IF k = 11 THEN OPEN "3jp73011.asc" FOR INPUT AS #2

IF k = 12 THEN OPEN "3jp73012.asc" FOR INPUT AS #2

IF k = 13 THEN OPEN "3jp73013.asc" FOR INPUT AS #2

IF k = 14 THEN OPEN "3jp73014.asc" FOR INPUT AS #2

IF k = 15 THEN OPEN "3jp73015.asc" FOR INPUT AS #2

IF k = 16 THEN OPEN "3jp73016.asc" FOR INPUT AS #2

IF k = 17 THEN OPEN "3jp73017.asc" FOR INPUT AS #2

IF k = 18 THEN OPEN "3jp73018.asc" FOR INPUT AS #2

IF k=19 Then k=k+1

IF k = 20 THEN OPEN "3jp73020.asc" FOR INPUT AS #2

IF k=21 Then k=k+1

IF k = 22 THEN OPEN "3jp73022.asc" FOR INPUT AS #2

IF k = 23 THEN k=k+1

IF k = 24 THEN OPEN "3jp73-24.asc" FOR INPUT AS #2

IF k= 25 Then k=k+1

IF k = 26 THEN OPEN "3jp73-26.asc" FOR INPUT AS #2

IF k= 27 Then k=k+1

IF k = 28 THEN OPEN "3jp73-28.asc" FOR INPUT AS #2

IF k=29 Then k=k+1

IF k = 30 THEN OPEN "3jp73-30.asc" FOR INPUT AS #2

130

FOR i = 1 TO n

INPUT #2, uef1, uef2, uef3

E1 = -.519042 * uef1 ^ 2 + .520857 * uef2 ^ 2 + .478862 * uef3 ^ 2

'IF E1<0 THEN IND=IND+I

IF E1 < 0 THEN GOTO 18

EPSI1 = E1 ^ .5

E2 = .478862 * uef1 ^ 2 - .519042 * uef2 ^ 2 + .520857 * uef3 ^ 2

'IF E2<0 THEN IND=IND+I

IF E2 < 0 THEN GOTO 18

EPSI2 = E2 ^ .5

E3 = .520857 * uef1 ^ 2 + .478862 * uef2 ^ 2 - .519042 * uef3 ^ 2

'IF E3<0 THEN IND=IND+I

IF E3 < 0 THEN GOTO 18

EPSI3 = E3 ^ .5

U = .577 * EPSI1 + .577 * EPSI2 + .57786 * EPSI3

V = -.7071 * EPSI1 + .7071 * EPSI2

W = -.577 * EPSI1 - .577 * EPSI2 + .81614 * EPSI3

UDASH = (U - uav) ^ 2: VDASH = (V - vav) ^ 2: WDASH = (W - wav) ^ 2

UDASH1 = UDASH1 + UDASH: VDASH1 = VDASH1 + VDASH: WDASH1 =

WDASH1 + WDASH

UV = (U - uav) * (V - vav): UW = (U - uav) * (W - wav): VW = (V - vav) * (W - wav)

UV1 = UV1 + UV: UW1 = UW1 + UW: VW1 = VW1 + VW

IF EOF(2) THEN 20

18 NEXT i

20 CLOSE #2

vu=Vav/Uav:wu=wav/Uav:N1 = (uo^2)* nx

udsa =abs(UDASH1 / N1): vdsa =abs(VDASH1 / N1): wdsa =abs(WDASH1 / N1)

uvda =abs(UV1 / N1): uwda = abs(UW1 / N1): vwda =abs(VW1 / N1)

ur=sqr(abs(udash1))/(nx*uav):vr=sqr(abs(vdash1))/(nx*uav):wr=sqr(abs(wdash1))/(nx*uav

)

uavr=uav / uo: vavr=vav / uo: wavr =wav / uo: k1 = k / x:eta=k/17

PRINT #1, USING "####.####";nx;k1;eta;uavr;vavr; wavr; udsa; vdsa;

wdsa;uvda;uwda;vwda;ur;vr;wr;vu;wu

'PRINT TAB(10); "VAV="; VAV

'PRINT TAB(10); "WAV="; WAV

'PRINT #1, "UDSA=";

'PRINT TAB(10); "VDSA="; VDSA

'PRINT TAB(10); "WDSA="; WDSA

'PRINT TAB(10); "UV="; UVDA

'PRINT TAB(10); "UW="; UWDA

'PRINT TAB(10); "VW="; VWDA

NEXT k

CLOSE #1

END