INTERACTION OF TyO-OIMENSIowI\L TRANSVERSE 

JET WITH A SUPERSOWIC UAINSTREM 

BY 

6.6. Kra-r 

and 

S. N. Tiwari 

Research kport 

For the period ending August 1983 

Prepare4 for the 

National Aeronautics and Space Wministration 

Langley &search Center 

Hampton, Virginia 

Under 

Robert H. Tolson, Technical Monitor 

Office of the Chief Scientist 

Want N6R 47-003-052 

December 1983 
DEPARTMENT OF MECHANICAL ENGINEERING AND MECHANICS 

SCHOOL OF ENGINEERING 

OLD DOMINION UNIVERSITY 

NORFOLK, VIRGINIA 

INTERACTION OF TWO-DIMENSIONAL TRANSVERSE 

JET WITH A SUPERSONIC MAINSTREAM 

BY 

G. 0. Kraemer 

an d 

S. N. Tiwari 

Research Report 

For the perirJ ending August 1983 

Prepared for the 

National Aeronautics and Space Wministration 

Langley Research Center 

Hampton, Vi yinia 

Under 

Gr ant NGP 47-003-052 

Robert H. To1 son, Technical Monitor 

Office of the Chief Scientist 

Submitted by the 

Old Domin’on University Research Foundation 

P. 0. Box 6369 

Norfolk, Virginia 23508 

December 1983 
FOREUORD 

The work presented in this report was conducted as a part of the "Graduate Engineering Research Participation in Aeronautics" progran during the 

period 1980-82. 

1982, but certain modifications were made in 1983. 

by the NASAILangley Research Center through Grant NGR-47-003-052. 

cipal investigator of the Grant was Dr. A. Sidney Roberts, Professor of 

Mechanical Engineering and Mechanics at Old Dominion University. The Grant 

was monitored by Hr. Robert H. Tolson, Chief Scientist, NASWLangley 

Research Center. 

Langley Research Center for providing extensive guidance and help during the 

entire course of this study. 

The work was essentially completed by the end of August 

The work was supported 

The prinThe authors are grateful to Dr. R. Clayton Rogers of NASA 

ii 
iii 

TABLE OF CONTENTS 

Page 

LIST OF TABLES ................................................... v 

LIST OF FIGURE .................................................. vi 

LIST OF SYMBOLS .................................................. x 

1 . INTRODUCTION.,,, ............................................. 1 

2 . APPARATUS AED PROCEDURE ...................................... 5 

2.1 Model Apparatus ......................................... 5 

2.2 Instrumentation ........................................ 13 

2.3 Survey Procedure ....................................... 17 

3 . DATA REDUCTION .............................................. 18 

4 . RESULTS AND DISCUSSION ...................................... 21 

4.1 Visual Data ............................................ 25 

4.2 Surface Pressure Oistribution .......................... 28 

4.3 Surface Mole Fraction Oistribution ..................... 41 

4.4 Static and Pitot Pressure Profile ...................... 48 

4.5 Mole Fraction Profile .................................. 62 

4.6 Mass Flux Profile ...................................... 69 

5 . COMPARISON OF THEORY WITH DATA .............................. 74 

5.1 Model for Theoretical Investigation .................... 74 

5.2 Comparison of Results for Surface 

Oisttibutions .......................................... 76 

5.3 Comparison of Results for Downstream Profile ........... 82 

6 . CONCLUDING REMARKS .......................................... 97 
iv 

REFERENCES.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99 

APPENDIX A. ERROR ANALYSIS.. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .lo2 
V 

LIST OF TABLES 

Tab1 e Page 

1. Surface tap location........ ................................. 9 

2. Test conditions for surface pressure distributions ............................................. ..22 

3. Mean test conditions for the downstream surveys ............. 23 
vi 

LIST OF FIGURES 

Figures Page 

1. Sketch of the aerodynamic features .......................... 6 

(a) Sketch of model.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 

(b) Photograph of model.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 

2. Schematic of the jet supply ..............,................ 12 

3. Survey probe design and position in probe r Ae ..... . . .. . .14 

4. 

5. 

Schematic of sample collection system ...................... lb 

Schlieren photographs for helium injection, 

b = 0.043 cm ...............................................26 

6. Schlieren photographs for nitrogen injection, 

b = 0.043 cm... ............................................27 

7. Surface pressure di stri buti on correi ati on 

(a) PR = 10, helium injectant ...... . .. . ... ...... ..... ..... 30 

(b) PR = 10, tiitrogen injectant ........................... 31 

(c) b x PR = 1.1, nitrogen injectant ...................... 32 

8. Effect of jet pressure on the surface pressure 

distribution, b = 0.056 cm: 

(a) Helium injectant ....... .............................. 34 

(b) Nitrogen injectant .................................... 35 

9. Dependence of x1 on the jet parameters for 

he1 ium and ni troien: 

(a) For jet strength ........................................ 38 

(b) For jet mnmentum factor, y x b x PR ................. 38 j 
Figure 

10. Correlation of surface pressure distributions 

by ~1.5, b = 0.056 cm 

vii 

Page 

(a) Upstream surface distributions offset by x1 5. . . .39 

(b) Downstream surface distributions scaled 

Injectant mole fraction surface distribution 

correl a ti on 

by ~1.5......*..e.......*.....o..*.o.........o.......39 

11. 

(a) PR = 10, helium injectant. .......................... ..42 

(b) PR = 10, nitrogen injectant ........................... 43' 

(c) b x PR = 1.1, nitrogen injectant. ..................... 45 

12. Effect of jet pressure on the surface mole fraction 

distribution, b = 0.056 cm: 

(a) Helium injectant ...................................... 46 

(b) Nitrogen injectant .................................... 47 

13. Nondimensional static pressure profile 

correlations 

(a) PR = 10, x/b = 58. .................................. 51 

(b) b x PR = 1.1 .......................................... 52 

14. Effects of downstream location of the static 

pressure profiles, PR = 10, b = 0.056 cm.. ................ .54 

15. Effect of jet pressure on the static pressure 

profiles, x/b = 68, b = 0.056 cm ........................... 55 

16. Noadimensional pitot pressure profile 

correl ati on 

(a) PR = 10, x/b = 68. ................................... .58 

(b) b x PR = 1,1............. ............................. 59 

17. Effect of downstream location on pitot pressure 

profiles, PR = 10, b = 0.056 cm. ........................... 60 

18. Effect of jet pressure on the pitot pressure 

profiles, x/b = 68, b = 0.056 cm ........................... 61 
Figure 

Jiii 

Page 

19 . 

20 

21 

22 . 

23 . 

24 . 

25 . 

26 . 

lrrjectant mole fraction profile correlation 

(a) PR = 10. x/b = 68 ..................................... 64 

(b) b x PR = 1.1 .......................................... 65 

Effect of downstream location on injectant mole 

Effect of jet pressure on injectant concentration 

Injectant mass flux profiles. b = 0.056 cm: 

(a) Helium injectant. PR = 10 ............................. 71 

(b) Helium injectant. PR = 20 ............................. 71 

fraction profiles. PR = 10. b = 0.056 cm ................... 66 

profiles. x/b = 68. b = 0.056 cm ........................... 68 

(c) 

(d) 

Integrated mass flux variation with downstream 

survey location: 

(a) Total mass for PR = 5. 10. and 20 ..................... 73 

(b) Injectant mass ........................................ 73 

Comparison of surface pressure distributions. 

b = 0.056 cm: 

Nitrogen injectant. PR = 10 ........................... 71 

Nitrogen injectant. PR = 20 ........................... 71 

(a) Nitrogen injectant .................................... 76 

(b) 

Comparison of injectant mole fraction surface 

distributions. b = 0.056 cm: 

(a) Nitrogen injectant .................................... 80 

(b) t-!elfum injectant ...................................... 81 

Compari scIn of static pressure profiles. 

b = 0.056 cm: 

He1 ium injectant ...................................... 77 

(a) Nitrogen injectant .................................... 84 

(b) He1 ium injectant ...................................... 85 

(c) He7 ium injectant ...................................... 86 
Figure 

ix 

Page 

27 . Compari son of pi tot pressure prof i 1 es . b = 0.056 cm: 

(a) Nitrogen. injectant .................................... 88 

(b) Helium inject ant...............^.......... ............ 89 

(c) Helium injectant ...................................... 90 

28 . Comparison injectant mole traction profiles. 

b = 0.056 cm: 

(a) Nitrogen injectant .................................... 91 

(b) Helium injectant ...................................... 91 

29 . Comparison of injectant mass flux profile .................. 93 

30 . Comparison of total mass flux profile ...................... 94 

31 . Comparison of Mach number profile .......................... 95 

A.l Relative Mach number error ................................ 106 

A.2 Relative mass flux error .................................. 108 
X 

a 

b 

cP 

CD 

hS 

F 

mj 

3 

~TM 

M 

N/O 

P 

pb 

Ppl ume 

Pt 

PW 

PW ,- 

PR 

R 

- 

T 

Tb 

LIST OF SYMBOLS 

local sound speed 

jet gap width 

specific heat at constant pressure 

discharge coefficient of the jet 

frequency of the turbine meter 

jet shock height (Eq. 4.2) 

jet mass flow rate 

model inlet ide,’ mass flow rate 

turbine meter mass flow rate 

mach number 

nitrogen to oxygen ratio 

static pressure 

tunnel supply pressure 

effective jet back pressure 

pi tot pressure 

jet total pressure 

turbine meter pressure 

surface pressure 

surface pressure from first surface tap 

jet tG mainstream static pressure ratio 

gas constant = universal gas constant/molecular weight of 

gas 

static temperature 

tunnel supply te:.- erature 
't,j 

TTM 

U 

X 

x1 .5 

X 

Y 

2 

a 

Y 

e 

P 

jet total temperature 

turbine meter temperature 

axial velocity 

axial distance (Fig. la) 

location at which pJp- = 1.5 in upstream region 

volume fraction 

vertical distance (Fig. la) 

transverse di stance (Fi g. 1 a) 

mass fraction 

specific heat ratio 

separation shock deflection angle 

density 

Subscripts 

1 air quantity 

j jet quantity 

QD undisturbed mainstream quantity 

xi 
lNTERACTION OF A TWO-DIMENSIONAL TRANSVERSE 

JET WITH A SUPERSONIC MAINSTREAM 

G. 0. Kraemerl and S. N. Tiwari2 

S lMMARY 

An experimental investigation of the interaction of a two-dimensional 

sonic jet injected transversely into a confined main flow has been conducted. The main flow consisted of air at a Mach nunber of 2.9. The effects of 

varying the jet parmeters on the flow field were examined using surface 

pressure and composition data. 

using static pressure, pitot pressure, and composition profile data. The 

jet parmeters varied were gapwidth, jet static presfure, and injectant species of eithw heliun or nitrogen. 

were 0.039, 0.056, anu 0.1[!9 cm for the gapwidth .id 5, 10, and 20 for the 

jet to mainstrean static presbure ratios. 

produced by the mixing and interaction of the jet with the mainstream wer? 

related tr, the jet momentun. The data wer? used to demonstrate the validity 

of an existing two-dimensional elliptic flow code. 

Also, the downstream flow field was examined 

The values of the jet parm-eters used 

The features of the flow field 

'Graduate Research Assistant, Department of Mechanical Engineering and 

Mechanics, Old Doqinion Universitv, Norfolk, Virginr? 23509. Present 

affiliation, AVCO-Lycoming, Strat 'ord, Conn. 06491. 

Eminent Professor, Department of Me,,hanical Engineering and Mechanics, Old 

Dominion University, Norfolk, Virginia 23508. 
1 

1. INTRODUCTION 

A serious effor? is currertly underway to design hydrogen 

fueled, supersonic cornbustion raqjets (scramjets) for hypersonic 

vehicle propulsion. In the present concept, gasem hydrogen fuel 

is injected from transverse and parallel fuel injectors, located on 

instream struts, into the supersonic mainstream air flowing through 

the combustor ‘,1 j*. At high flight speeds, a large portion of the 

fuel is added from transverse fuel injectors due to their rapid 

mixing and heat releasing qualities. At lower flight speeds, an 

increased portion of the fuel might be added from parallel fuel 

injectors to prevent posribl e thermal choking. These fuel injectors 

are generally operated at sufficient jet stagnation pressures so 

that the jet flow is sonic at the jet exit. 

The flow produced by the interaction of a transve7w fuel jet 

with a supersonic mainstream is quite cmplex. 

for example, observed many of the typical flow features. The jet 

gas expands into the primary flow forming a plume shaped body, which 

eventually termina?es at a strong normal shock wave. Formation of a 

curved bow shock and the separation of the turbulent boundary layer 

results from the obstruction produced by the jet body. An up‘;tream 

separation shock is formed above the recirculation region. Down- 

:t.-earn of the jet, the flow turns downward to the injection surface 

Sterrett et al. [2], 

* The number in brackets denote references. 
2 

producing a recompression shock near the location of boundary layer 

reattachment. A low pressure downstream recirculation region is 

formed due to the rapid expansion of the mainstream flow behind the 

jet. Both of these recirculation regions contain embedded regions 

of subsonic and supersonic flow. 

regions, an elliptic flow theory is needed to analytically describe 

the transverse jet interaction (TJI) flors field. Because of the 

complexity and the large computer storage required to solve the 

el liptic ccwnputational flow theory, only the two-dimensional flow 

case has been examined at present [31. 

Due to these enbedded subsonic 

Historically, interest in Ltis type of TJI flow field was for 

applications to rocket thrust vector control, hypersonic vehicle 

guidance control, and scramjet fuel injectors. These areas have 

been examined for the three-dimensional case, as discussed in a 

recent review by Rogers [4]. A critical review by Werle [51 

examined the two-dimensional TJI literature until 1968. In this 

review and other i 1 terature after 1968 i2-161, the two-dimensional 

investigations were for application to thrust vector control and 

vehicle guidance control. Thrust vector control investigations 

[17,183 sought to predict the shape and location of the bow shock by 

assuming that there was no upstream boundary layer or separated 

region. Vehicle guidance control investigations were conducted to 

predict tbe increased side force due to the altered pressure field 

in the upstream separated region. These investigations provided 

useful information about the jet penetration and sur.-3ce pressure 

distributions .and led to an increased understanding of the TJI 

phenomenon. 
Since 1968, two-dimensional TJI investigations have been, 

general, directed towards developing scaling relationships for 

3 

in 

Characterizing the flow for vehicle guidance control applications. 

A comon Sal ing parameter was the effective obstruction height 

which was predicted from either a method using a force balance or a 

physical analogy. In the first method [71 the jet was 

mathematically substituted by a hemicylinder control volume of jet 

gas facing the primary flow. The cylinder's radius was calculated 

from a balance of the jet momenturn flux out of the downstream face 

with the drag force on the upstream face (usually by a Newtonian 

drag model). Another popular method [6, 13, 15, 163 used a physical 

analogy between a jet exhausting into a quiescent atmosphere with 

one exhausting into a supersonic flow. 

pressure, the jet shock height was calculated. Once the jet 

penetration was determined from the calculated cy1 inder radius or 

jet shock height, correlations were developed to predict the 

upstream separation distance. All previous two-dimensional 

investigations were for unconfined flows, and thse investigations 

were limited to the collection of surface pressure and composition 

distributions and visual data. In a confined flow, however, Wu et 

al. [9] predicted that the "squeezing" of the flow would cause a 

significant decrease in the jet penetration at the same 

conditions. This would result in a smaller flow field disturbance. 

For an assumed jet back 

Past applications of two-dimensional TJI data required only 

1 irni ted experimental investigations for unconfined flows. The current development of flow theories useful for scramjet kesign 

requires data for the flow field near the jet in a confined super- 
. 4 

sonic flow. Acquisition of these data are the primary consideration 

of the present experimental investigation. Another objc stive of 

this study is to increase the understanding of the flow field and 

deternine various scaling factors, correlations, and empirical 

relationships. To meet these objectives experimental datz. for a 

cold flow are obtained at the various jet parameters of jet 

strength, jet gap v’dth, and injectant species. 

The apparatus and procedures used to conduct the experimental 

Investigation are presented in Chap. 2. A discussion of the assumptions and equations used to reduce the data is given in Chap. 3. 

Experimental results are discussed in Chap. 4. Theory and data are 

compared in Chap. 5. Conclusions drawn from this investigation are 

presented in Chap. 6. The appendix presents the error analysis of 

the method used to detennine local Mach -number and mass flux. 
5 

2. APPARATUS AND PROCEDURE 

As mentioned in the introduction, the flow produced by the 

interaction of a transverse fuel jet with a supersonic flow is quite 

complex as shown in Fig. 1. The apparatus and procedures used in 

the experiment31 investigation of this flow are presented in this 

chapter. The model configuration, model supply, and jet supply are 

discussed in Sec. 2.1. The instrumentation and survey procedures 

are discussed in Secs. 2.2 and 2.3 respectively. 

2.1 Model Apparatus 

A sketch of half of the uniform rectangular duct model is shown 

in Fig. 2a. One of the two identical stainless steel injector 

plates is shown in the sketch. 

apart. A-iither identical stainless steel side wall is separated 

from the one shown by 3.81 cm. When assembled the model is 30.5 cm 

long. The side wall is seen to have a 20.3 cm long glass window. 

Before oolting the model together a thin film of room-temperature 

vLlcaniziig rubber is applied to seal the model and prevent leaks. 

Tc.s* figure shows the initial sharp leading edge of 5' and the 

The injector plates are 7.62 cm 

slnt injector spans the injector plate at a distance of 17.8 cm 

aownstream of the leading edge. 

s de walls src spaced to fit flush and parallel with the nozzle side 

walls. Along the injector plate's centerline and in four lateral 

r,us are flush surface taps containing 0.152 cm tubing (Fig. 2b). 

These surface tap locations are given in Table 1. 

The inside surfaces of the model 
6 

SEPARATI 

hi I X i FIG SOUiiDAi? Y 

RECOHPRESS I or4 

P,E!'iTTACHPlENT 

JET 

M=l 

SHOCK 

Fig. 1 Sketch of the aerodynamic features. 
7 

c9 

I 

Q, 

ro 

a! 

w 

0 

v) 

- 

u, 

u, 

J 

c3 

a 

X 

XI 1 z 

0 

s 

0 

m 

c 

qr 

E 

0 

-0 

0 

E 

rc 

-0 

r 

V 

w 

Q, 

Y 

m 

.. 

E 

0 

u 

.r 

m 

L 

3 

cn 

L‘ 

C 

0 

U 

UJ 

U 

0 

E 

9 

* ORICYNAL FAGE 18 

Table 1. Surface tap location OF POOR Qg;/;ifT~' 

For b = 0.039 cm 

upstream Downstream Upstream Downstream 

- 

X 

-0.25 

-0.50 

-0.79 

-1.06 

-1.28 

-1.53 

-1.79 

-2.04 

-2.29 

-2.29 

-2.29 

-2.29 

-2.29 

-2.29 

-2.29 

-2.29 

-2.54 

-3.05 

-3.56 

-4.07 

-4.58 

z 

0 

0 

0 

0 

0 

0 

0 

0 

1.77 

1.26 

0.75 

0.24 

0 

-0.52 

-1.02 

-1.53 

0 

0 

0 

0 

0 

X 

0.23 

0.53 

0.74 

1 .oo 

1.27 

1.52 

1.80 

2.06 

2.30 

2.30 

2.30 

2.30 

2.30 

2.30 

2.30 

2.30 

2.56 

3.07 

3.59 

4.09 

4.58 

2 

0 

0 

0 

0 

0 

0 

0 

0 

1.31 

1.01 

0 -50 

0 

-0.26 

-0.77 

-1.27 

-1.78 

0 

0 

0 

0 

0 

x 

-0.25 

-0.50 

-0.78 

01.03 

01.28 

-1.54 

-1.79 

-2.04 

-2.29 

-2.29 

-2.29 

-2.29 

-2.29 

-2.29 

-2.29 

-2.29 

-2.57 

-3.07 

-3.58 

-4.09 

-4.59 

z 

0 

0 

0 

0 

0 

0 

C 

c 

1. 77 

1.26 

0.75 

0.24 

0 

-0.52 

-1.02 

-1.53 

0 

0 

0 

0 

0 

x 

0.25 

0.47 

0.73 

1.03 

1.24 

1.51 

1.77 

2 -02 

2.28 

2.28 

2.28 

2.213 

2.28 

2.28 

2.28 

2.28 

2.53 

3.04 

3.55 

3.05 

4.56 

Z 

0 

0 

0 

0 

0 

0 

0 

0 

1 .31 

1.01 

0.50 

0 

-0.26 

-0.77 

-1.27 

-1.78 

0. 

0 

0 

0 

0 

* 

Zero z location is on centerline of model, dimensions in cm 
10 

ORlGlNAL !g 

OF POOR QUALlfl Table 1. Concluded. 

For b = 0.109 arid 0.056 cm 

upstream Downstream 

For b = 0.039 cm 

Upstream Downstream 

X 

-5.08 

-5.59 

-5.59 

-5.59 

-6.10 

-t .60 

-7.10 

-7.63 

-7.63 

-7.63 

-8.64 

-9.66 

-10.46 

-1 1.68 

-12.69 

-13.67 

-15.26 

z 

0 

0.75 

0 

-1.54 

0 

0 

0 

1.51 

0 

-0.77 

0 

0 

0 

0 

0 

0 

0 

X z X 

5.11 0 -5.1 1 

6.13 0 -5.61 

7.15 0 -5 .G1 

-5.61 

-6.10 

-6.63 

-7.13 

-7.64 

-7.64 

-7.64 

-8.56 

-9.68 

-10.70 

-11.71 

-12.73 

-14.00 

-15.27 

2 X 2 

0 5.07 0 

0.75 6.09 0 

0 7.10 0 

-1.54 

0 

0 

0 

1.51 

0 

-0.77 

0 

0 

0 

0 

0 

0 

0 

I 
11 

The steel side walls of the model were modified to aid in 

spilling the ndzzle side wall boundary layer and to permit surveys 

closer to the jet. Two solid stainless steel side walls were 

constructed with a 10' sharp leading edge and to overlap the 

injector plate by 0.32 m. The model length was reduced by removing 

the last 5.08 cm of the model. The gap widths of the slot injector 

used were 0.039, 0.056, and 0.109 cm with a respective slot height 

to gap width aspect ratio of 16.3, 11.3, and 5.8. 

The model was bolted flush atop an aluminum nozzle, with the 

model centered and square with the nozzle exit. The twodimensional, Mach number 2.9 nozzle supplied the model with a constant air flow at a nominal total pressure of 2.07 MPa and an 

ambient total temperature of 300 K. 

supply section near the nozzle. An expected unit Reynolds number at 

these nominal conditions was 1.5 x 10 per meter in this blow down 

tunnel operation. The expected unit Reynolds number for the jet 

7 8 increased from 7.6 x 10 to 6.4 x 10 per meter with the jet 

pressure. 

Both were measured in a large 

8 

A schematic of the system for delivering the jet gas supply of 

either helium or nftrogen gas is shown in Fig. 3. The jet gas was 

delivered by a 1.27 cm stainless steel tubing from 0.054 m3 standard 

cylinders at an initial pressure of about 14 MPa. After an initial 

pressure regul ati ng value, an ai r operated presstire regulating Val ve 

was used to set the desired jet total pressure. Downstream, a standard turbine meter with a 19.1 cm long and 1.57 cm diameter flow 

straightening tube was used to determine the jet gas volumetric flow 

rate. Measured pressure and temperature at the turbine meter and 
12 

I 4 I 

* TTll 

PTM 

L J 

%a 

t 

Pressure Regulated 

Val ve 

1 

I 

U 

F1 ow Control 

Val ve 

Relief Valve 

Jet Gas Supply Cylinders 

Fig. 3. Schematic of the jet supply. 
13 

flow straightening tube assenbly were used to compute the jet mass 

flow rate. At1 identical system delivers the jet gas to the other 

jet plenum. 

2.2 Instrumentation 

2.2.1 Visual Method 

Schlieren photographs were taken to examine the shock structdre 

for the various jet strengths and injectant species.. This jqlepass schlieren system consisted of a mercury vapor lamp, L 

spherical mirrors, and a vertical knife edge. Reference wires were 

placed exterior to the flow for the photographs. 

2.2.2 Probes 

Instream surveys were made with either a six probe pitot rake 

or a six probe static rake. Details of the probe tips and installation into the probe rake can be seen in Fig. 4. More information 

about the short static probe can be found in a report by Pinckney 

[19]. The pitot probes (0.32 cm O.D.) were welded flush together to 

allfw collection of gas samples near the injection surface. The 

static probes were spacea 1.02 cm tip to tip so that they would not 

interfere with one another. A support of adjustable height in back 

of each injector plate maintained the prQbes parallel to the undisturbed mainstream flow as they traversr:a UI~ ,xdel vertically. A 

1 inear sl i de potentiometer-vol tmeter system was used to monitor the 

first probe position from the injector plate. This system bad an 

estimated accuracy of about 0.005 cm. 

2,2.3 Gas Sampling and Analysis System 

A schematic of the sampling system for one of the six possible 
0.32 O.D. 

k--- 7.62 :i 

4 

1.27 Square Drill Rod 

0.0343 I.D., 4 Holes Equally Spaced 

\ 

Detail of static probe 

0.32 G.D. 0.06 Diameter Opening 

J. 0.25 O.D. 

t 

Detail of pitot probe 

Fig. 4. Survey probe design and position in probe rake, ail 

dimensions in CA. 
SOUrces is shown in Fig. 5. The system allowed individual collection and storage of six samples at one time #n one of four sets of 

six sample collection bottles. 

For Sample collection, the system was first preevacuated. When 

sampling was desired, the probe side vacuum system was closed. 

Then, the appropriate valves were opened to allow the sample to 

establish flaw through the collection bottles for about ten 

seconds. Next, a valve on the vacuum side of the sample bottle was 

close '. After a few seconds, a valve on the probe side of the 

sample bottle was clased to isolate the sample. This procedure was 

repeated for all focr sets of sample bottles. 

The samples were analyzed individually by a quadrapole mass 

spectrometer. To maintain a uniform analysis procedure an automatic 

sequencer was used to control sample delivery. After an evacuation, 

the sample collection bottle was briefly opened to fill the sample 

coil. Then by use of a downstream venf, the sample was delivered to 

the mass spectrometer system dt room pressure. By using a controlled vacuum system the pressure at the mass spectrometer's porous 

plug entrance was kept at approximately 3.4 KPa. After establishing 

this condition, the analysis data were recorded for ten seconds. 

The mass spectrometw was calibrated with air, he1 ium, and hydrogen 

individually prior to analyzing the collected samples. 

2.2.4 Other Instrumentation 

Wall static pressures were measured by usirlg an Electronic 

Scanning Pressure system siv'-ir to that described by Trexler 

1201. 

pressure transducers. 

The measurements were made by IF' "9 Ki i absglute range 

The p; . I sa .+ rz were accurate within 
16 

1 

1 

7 

1 

rc Check 

Val ve 

Hechani sm 

Sanple Line From Probe Rake 

fl 

6 b 

T 

Sample Collection 

Bottles, 6 in Each Set 

Vacuum t 

4 Meter Sample Coil 

Vacwn 

llass Spect rone ter 

Sys ten 

or 

Vacuun 

Vent 

Sclenoid Valve 

r>a Air Operated Valve 

Fig. 5. khematic of sample collection syste811. 
17 

0.25 percent of full scale. The tunnel and jet total pressures were 

wasured by 3.45 hPa gauge range pressure transducers. All six 

Pitot probe pressures were measured by 1.38 Wa gauge range pressure 

transducers. 'The static pressure rrreasureslents were de by 0.345 

MPa or less absolute range pressure transducers. Standard copper 

constantan themcouples were used to make the temperature measurements, and they were specified to be accurate within 1" C by the 

manufacturers. A two point calibration of the individual thermocouple was determined by use of a reference thennocouple and a known 

po tenti a1 source . 

2.3 Survey Procedure 

Vertical surveys were made at the injector plate centerline at 

downstream locations of 34, 64, 68, 71, 114 jet gap widths for jet 

to mainstream static pressure ratios of 5 to 20. Pitot and static 

pressure surveys were made by recording the pressure from the 

appropriate probe rake at 4 to 5 locations across the duct. When 

the probe rake was moved to the desired location, a signal could be 

sent to a remote computer *o record the data. The data were 

averaged over one second before being printed and stored. Analysis 

of several one second data records, spaced three seconds apart at 

the same test conditions, showed the one second average was 

sufficient to provide precise values. 

the jnjection wall, both pitot pressure and gas samples were 

collected for certain test conditions. Gas samples were collected 

from selected surface taps during static surveys. In general, gas 

samples were collected for a jet mainstream static pressure ratios 

of 10 to 20. 

At selected locations near 
18 

3. DATA REDUCTION 

Data froa separate pitot and static pressure surveys and the 

gas saqle analysis (if collected) were combined to determine the 

local flow properties at each of the pitot probe locations for 

similar test conditions (i-e-, same jet conditions and downstream 

location). The local flow properties were calculated at the pitot 

probe locations, since the pitot probes were used to collect 

instream gas samples. Since pitot and static data were recorded at 

different locations, the static pressures were calculated by a cubic 

spline interpolation at the pitot probe locations. Where gas 

samples we& not collected, the local mixture composition was 

assumed to be that of air. 

! 

A mass spectrometer was used to determine the gas sample compostti% based on analysis of the major peak of nitrogen, helium, 

oxygen, and argon. During a ten second data co1;ection period the 

peak height and the porous plug pressure were averaged after an 

equal and separate analysis interval for each constituent. These 

data and a calibration constant were used to determine the mole 

fraction of each constituent by an existing program c21]. 

The calibration constant for each constftuent was calculated by 

subtracting the background peak height in a vacuua from the peak 

height observed for a known concentration of constituent and 

dividing by the product of toe porous plug pressure and known 

concentration of constituent. In this and subsequent data reduction 
19 

the mode1 fraction of the consTituents of air were assumed to be 

0.7803 nitrogen, 0.2099 oxygen, and 0.0098 argon. A linear Lever 

rule relationship was used to calculate the mole fraction of eat'. 

constituent by again subtracting the background fm the sample peak 

height and dividing by the product of the porous plug pressure and 

the calibration constant. Although a simple oroportionality between 

the poraus plug pressure and the peak height was assumed in the 

program, a nonlinear relationship rttlly ex) stea. This asslrotption 

caused a maximum error in the mole fraction of 0.004 for air. The 

mole fractions of N2, 02, and He were finally norma1i:ed by their 

sum to correct for drift in the analizer. 

In order to determine the mole fraction of air in each sample, 

the sample was considered to be a binary mixture of air and 

injectant. For helium injection, the calculation of the Zir- mole 

fraction was made directly. For nitrogen injection, the mole fraction of air was determined from the increase in the nitrogen to 

oxygei. ratio (N/O) above that of air 

N/O = (X /Xr, )/(0.7803/0.2099) 

N2 2 

where X.. and X, are observed mole fractions of N2 and O2 

N2 "2 

respectively. The mole fraction of air is then found by 

1))/(1 + 0.7803(N/0 - 1)) 
20 

Then, the mass fractions for air and injectant were determined using 

the molecular weight of dry air as 28.97, nitrogen as 28.00, and 

helium as 4.00. 

From the mixture specific heat ratio, pitot pressure, static 

pressure, air mass fraction, and tunnel total pressure and temperature, the local mixture Mach number and the total (and injectant) 

mass flux were computed by using the equations for the onedimensional isentropic flow of an ideal gas [22]. The’mixture 

specific heat ratio was calculated by mass averaging the specific 

heats and gas constants for air and injectant 3as. The value of the 

universal gas constant was taken as 28980 for air, 20787 for helium, 

and 29103 J/kg-mole K for nitrogen. The total and injectant mass 

fluxes were integrated by a trapezoidal rule method to examine the 

overall data quality. The discharge coefficient of the jet was 

determined from the turbine meter mass flow rate divided by the 

ideal jet mass flow rate. The turbine meter volumetric flow rate 

was found from a linear least squares curve fit to calibration data 

relating it to the turbine meter frequency. 

various segments of the fairly linear curve so that no significant 

error occurred in the calculation of the turbine mass flow rate. An 

errcr analysis of the Mach number and mass flux equations is given 

in Appeidix A. 

This was done over 
21 

4. RESULTS AND DISCUSSION 

Results Of an experimental investigation of the interaction and 

mixing of a two-dimensional sonic jet, injected transversely into a 

Mach number 2.9 air mainstream, are discussed in this chapter. Test 

conditions included variation of the jet gap width (b), the jet-tomainstream static pressure ratio (PR), and tbe injectant species of 

either helium or nitrogen. Tests were conduc.ted for nominal values 

of PR of 5, 10, and 20 at gap widths of 0.039, 0.056, and 0.109 cm. 

Typical features of the flow were visualized qualitatively in 

schlieren photographs. Distributions of pressure and injectant mole 

fraction were obtained along the centerline of the injection wall. 

Profiles of static pressures, pitot pressures, and injectant mole 

fraction were obtained along the injection wall centerline at locations 1.9, 2.8, 3.8, 6.4, and 7.0 cm downstream of the jet. Scaling 

parameters, correl ati ons , and empi ri cal re1 ati ons are presented for 

the surface distributions and vertical profiles. An examination of 

the nature of the jet parameters governing the flow was made from 

the data trends and empirical relationships. 

The test conditions, jet mass flow rate (inj), and discharge coefficient of the jet (C,) are givep in Table 2 for runs in which the 

surface pressure distributions were measured, and Table 3 for runs 

in which surveys of the downstream flow were made. Gas samples were 

collected from surface taps during static pressure surveys. 

test conditions were found to vary less than 0.5 p?rcent from the 

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25 

mean survey value given in Table 3. 

were close to the desired nominal values (PR = 5, 10, and 20). 

general , the discharge coefficient of the jet {varies between 0.84 

and 0.95. 

The actual jet pressure ratios 

In 

4.1 Visual Data 

The basic flow features are visualized by schlieren photographs, and typical results are shown in Figs. 6 and 7. 

shows the flow features produced by helium injection at several jet 

pressures. A separation shock, bow shock, and recompression shock 

are typical features produced by the jet disturbance. A small jet 

plume is observea near the injector surface for the larger jet 

pressure ratios. Weak shocks of about 1" turning angle originate at 

the leading edge of the injection wall. A fixed set of externalFigure 6 

reference lines aid in observing the effects of increasing the jet 

pressure. As the jet pressure increases, the origin of the separation shock moves upstream while maintaining a nearly constant angle 

of 32". Also, the bow shock increases in initial curvature and 

location in the upstream region. 

notable effects on the downstream flow features. The b3w shock is 

displaced further away from the injector surface and the angle of 

the linear portion of the bow shock increases slightly (from 29" to 

about 32'). The recompression shock angle (about 21") appears to be 

almost a Mach line; however, the location of the shock does not seem 

to be influenced by the change in PR. As a result of the larger bow 

shock angle, the two shocks diverge further downstream. At the same 

downstream location, the separation distance between the shocks 

increases as PR increases. This result is due to the bowshock's 

Increasing the PR produces several 


28 

increased initial curvature and shock angle in the 

Similar resd ts re observed fdr nitrogen injection 

near regi on. 

n Fig. 7, 

although the flow fie1 1 disturbance produced is smaller for nitrogen 

injection at the same PR. 

Similar flow features were observed for air :njection into an 

unconfined flow by Sterret and Barber C21. For air injection, Werle 

et al. [lo, 111 calculated a nearly constard seporation shock 

turning angle (13.4') at various jet strengths using an oblique 

shock wave theory. 

duced a larger disturbance than nitrogen injection at the same PE. 

These past investigations showed results similar to tha< noted in 

this study, alt$ough they were conducted for unconfined flo! at 

Thayer [lP1 observed that helium injection prohigher values or" PR. 

4.2 Surface Pressure Distributions 

The surface pressure distribution data is preser.tea !I Figs. 8 

and 9. 

by the surface pressure from the first surface tap (the value of 

which is given in Table 21, so as to account for possible changes in 

the tunnel supply conditions. As shown in Fig. 2, the right hand 

coordinate system is centered at the jet in such a way that the distance increases positively moving downstream from tt.2 jet. The surface location is nondimensionalited by the jet gap width. 

In each figure, the surface prr;sure is nondimens omlized 

Typical features for the surface pressure distributions are 

shown for a weak helium jet in Fig. 8a. Upstream the surface pressure increases from unity between about x/b = -45 to the first 

pressure plateau at x/b = -28. Closer to the jet, the surface 

pressure rises to a second plateau at x/b = -5. 

#u 

- A lo: pressure 
29 

region extends from inmediately downstream of the jet to a region of 

rapid pressure rise at x/b = 12. The surface pressure reaches a 

peak pressure at x/b = 25 and then slow11 decreases approaching 

unity. These features are the result of the blockage and deflection 

of the supersonic mainstream by the jet expansion plume. The 

blockage of the flow is large enough to cause an adverse pressure 

gradient to separate the upstream boundary layer. The separation 

the boundary layer results in the fomation of a separation shock, a 

recirculation region, and a bow shock. The upstream surface pressure features are a consequence of the separation shock. 

of the jet, the rapid expansion of the flow over the jet plume . 

causes a low pressure downstredm recirculation region. Near the 

location of the reattachment of the boundary layer, the surface 

pressure rises to a peak pressure. Then, it slowly returns to a 

value near unity sinCe the recompression shock lies upstream of 

where the boundary layer reattaches. Similar trends (and features) 

a- noted for nitrogen injection in Fig. 8b, although the helium 

injection case produces a larger flow field disturbance. 

- 

Downstream 

Analogous resu?ts in surface pressure data were noted for 

helium and nitrogen injection for strong jet strengths in an unconfined flow [12]. These much stronger jets produced a larger more 

distinctive upstream second pvessure platsau region, which was 

associated with separation of an upstream turbulent boundary layer 

[2], and is noted in results of this study because of the large 

mainstream Reynolds number (5.6 x 10 per meter) of the present 

investigation. Since analogous flow features were noted between the 

unconfined and confined flow data the empirical relations developed 

7 
30 

n 

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32 

09!GiNAt PAGE 55 

OF POOR QUALITY 

m P 0 

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33 

for unconfined flows should be useful in examining also the results 

of this study. 

Correlations of the surface pressure data are presented for a 

particular injectant species in Figs. 8. The effects of varying 

only the gap width on the surface pressure distributions are indicated for a helium j e t i n Fig. 8a. A good correlation of the data 

is found by scaling the surface locations by b. Therefore, a change 

in the size of b directly affects the size of the surface pressure 

distribution. For the largest b (b = 0.109 an), the reduced locations of the upstream separation and downstream reattachment of the 

boudary layer may be due to three-dimensional effects. This effect 

is not so pronounced for the nitrogen injection case presented in 

Fig. 8b, for which the upstream separation distance is smaller. In 

spite of the early initiation of the upstream pressure rise for b = 

0.109 an, a good agreement is observed in the plateau region. 

Another good correlation is observed by comparing data at similar 

values of (b PR) in Fig. 8c for nitrogen injection. Notice, the 

surface locations are not scaled for this comparison. Similar 

trends were noted also in other results obtained in this study, 

since the sonic injectant flow out of the jet is for an adiabatic 

condition and ideal gas. Both methods for correlating the data are 

representative of the change in the jet momentum. 

The effects of increasing the jet pressure on the surface 

pressure distribution are presented for a helium jet in Fig. 9a. 

The surface pressure disturbance increases with increasing PR. 

surface pressure distribution features are not altered in general . 

except for the presence of a second pressure plateau at about x/b = 

The 
34 

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Po a 

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36 

-10 for PR = 20. Figure 9b presents analogous data trends for 

nitrogen injection. As noted earlier, the disturbance is smaller 

for nitrogen injection. 

It has been noted in previous investigations [12, 231 that the 

upstream pressure riss occurs before the actual separation of the 

turbulent boundary layer. Thayer [12] defined the separation distance as the location (xlO5) at which p /p 

approach has been taken in this investigation due to the lack of a 

simple and accurate method of determining the actual point of separation. 

= 1.5. The same w w,- 

In the past investigations for unconfined flows, ~1.5 was 

related to the jet parameters by a power law relationship and by a 

linear relationship. Thayer [12] correlated the dependence of x1 5 

on b and the jet strength. This is expressed by a power law relationship as 

where the quantity B is dependent on the injectant and free stream 

densities and free stream Reynolds number. The value of C was found 

to be 0.77 for helium, hydrogen, and nitrogen. A simple linear 

relationship was developed by Werle et al. [lo] to express the jet 

shock height (hS) in terms of the jet parameters and pressure acting 

about the jet plume (pplume) as 

(4.2) . 
37 

where Pplume /p is defined to be 2.8 (the second surface plateau 

pressure). This relationship can be expressed in terms of ~1.5 for 

this investigation as 

= 1.4 y. b PR x1 .5 J (4.3) 

Both correlations were applied to the available data for ~1.5. 

Correlations for ~1.5 with the jet parameters are presented in 

Fig 10. A separate least squares curve fit is shown for data from 

the largest gap width (b = 0.109 cm) due to the previously noted 

early separation. A good correlation is provided by the power law 

relationship as shown in Fig. loa. The exponent for the data (0.67 

for b = 0.039 and 0.056 cm, and P.80 for b = 0.109 cm) is near the 

value determined by Thayer for Eq. (4.1). A better correlation is 

shown in Fig. 10b and is given by the linear relationship 

/b = B yj PR + C '1.5 (4.4) 

The slope for the least squares fit of the data (1.5 for b = 0.039 

and 0.056 cm, and 1.8 for b = 0.109 cm) is almost the value determined from Werle's relationship. 

Eq. (4.4) relates ~1.5 to the relative change i n j e t momentum(y. b PR). 

For a constant width sonic jet, 

\ 

3 

Correlations of the surface pressure (pw) distributions by ~1.5 

are presented in Fig. 11 for b = 0.056 cm. Figure lla presents the 

results of offsetting the surface locations by X1.5 and shows that 

the surface pressure distributions are well correlated into a single 
38 

100 

- 9 .5 

b 

10 

ORIGINAL PAGE 19 

OF POOR QUALITY 

- - 

- 

P 

b (cn) B C 

- A’ A 0.039,0.056 5.4 0.67 

- 0 0.109 2.9 0.80 /2 

- 

- A’ 

- /$/ 4b 

/ 

I I I I I I Ill I I I 1 IIIII 

(d) For Jet Strength 

loo r 

60 

1.5 

b 

X 

- 

40 

20 

0 ~ __~ 

10 20 30 40 

(d) For Jet llomentum Factor, y. b PI? 

J 

Fig. 10. Dependence of x,,~ on the jet parameters for helium 

and qi trogen. 
35 

3. 

2’ 

A 

0 

ORIGINAL PAGE fS 

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he1 i um 

nitrogen 

C] 

A A 

AA 

i n jec tant 

.+GC] 1 nitrogen 

I A 

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I 1 I I 

- 20 G 20 40 60 

(a) Upstream Surface Pressure Distribution Offset by x1 

1 .o 

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- A 

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injectant 

01 I I I I I 

0.2 0.4 0.6 0.8 1 .ii 

x’xl .5 

(b) Downstream Surface Pressure Distribution Scaled by x, 

Fig. 11. Correlation of surface pressrrre distributions by x1 .59 b = 0.056 cm. 
40 

distribution by this method. A reasonable mean value for the first 

plateau pressure is observed to be p /p ‘c 

= 2.4 at (x - xle5)/bZ 30. w w,- 5 The second plateau pressure (about p,/p,,, = 2.8) is located 

at (X - ~1.5 )/b 2 55. No dependence on the injectant species is 

noted in the figure. The downstream surface distributions rise from 

a region of fairly constant low pressure at x/xle5 = 0.37 to a peak 

pressure at x/xla5 = 0.65 (Fig. llb). 

pressure is slightly higher for helium injection. Also, the 

- .1) 

In general, the downstream 

downstream scatter is not related to the jet pressure used. Somewhat analogous results were found by Wer:e et al. [ll] using the jet 

shock height; this air injection investigation exhibited a similar ’ 

scatter in the downstream region. Thus, a good sing?e distribution 

is obtained for either the upstream or downstream surface pressures 

based on ~1.5, which is related to the jet parameters (and jet 

momentum) by Eq. (4.3). This correlation may not be applicable to 

the case of large values of the gap width because of the early 

upstream separation . The surface pressure features have been described and related 

to the jet parameters. The surface pressure disturbance is controlled by the relative jet momentum (yj b PR). 

or downstream distribution is obtained by using ~1.5 to correlate 

the data. This quantity is found to be linearly dependent on the 

A single upstream 

relative jet momentum. For a particular injectant soecies, the 

surface pressure data for various gap widths arc related by scaling 

the surface location by b. 

(b PR) are correlated well for unscaled locations. In general, the 

surface pressure disturbance increases with the re1 ati ve jet 

Also, data compared at the same ;slue of 
41 

momen turn. 

4.3 Surface Mole Fraction Distributions 

Surface injectant mole fraction (Xj) distributions are presented in Figs. 12 ;Ind 13. Samples of the gas mixture near the 

surface are collected tnrough surface taps almg the injection wall 

center1 ine. Typical features of the surface Xj distributions are 

shown for helium injection in Fig. 12a. The upstream injectant 

species sprei.d extends ahead of the location of x1.5 (Le., x/b = 

-60). The value of Xj rises to a plateau at x/b = -40. Closer to 

the jet (at x/b = -25), X- increases almost linearly. Downstream of 

tho jet, a region of low concentration (and highly scattered data) 

extended to about x/xl 

tion where the law downstream pressure region terminates. Then Xj 

increases rapidly to a peak value near the location associated with 

boundary layer reattachment at x/xIm5 = 0.65 (i.e., x/b = 27). A 

gradual decrease in concentration occurs further downstream. Analogous trends are noted for nitrogen injection in Fig. 12b; however, 

the Yacal concentration is much smaller than for helium injection. 

For this two-dimensional flow, it would be expected that a high 

J 

= 0.35 (i.e., x/b = 18). This is the iocaconcentration of injectant species would occur in the recirculation 

region downstream of the jet. However, this trend is not exhibited 

in the results presented in Figs. 12a and b. 

three-dimensional effects may account for tile low concentration of 

injectant species in the recirculation region downstream of the 

jet. In this region, a large scatter in data is noted for different 

Entrained air or 

gap widths. 

favorably. Therefore, entrained air is probably the cause for the 

Further downstream, however , the resul ts compare 
42 

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44 

data scatter. 

The results presented in Fig. 12 also provided a method for 

correlating the data for various values of b and PR. The effects of 

varying only the gap width on the surface distribution of Xj are 

presented for a helium jet in Fig. 12a and for a nitrogen jet in 

Fig. 12b. Both figures indicate good correlations of the data by 

sca’ling the surface locations by b. A good correlation is observed 

by comparing data at similar values of b PR in Fig. 12c for nitrogen 

injection. Note that the surface locations are not scaled for this 

comparison. Both methods of correlating the data demonstrate the 

direct dependence of the Xj distributions on the relative jet 

momentum. Unlike the surface pressure distributions, Figs. 12a and 

b show large differences in local values of Xj between the helium 

and nitrogen injection cases. P.s such, this would not allow a 

simple correlation af the composition data for different injectant 

species by the jet parameters. 

The effects of doubling the jet pressure on the surface di 

butions of Xj are shown for a helium j e t i n Fig. 13a. The jet 

strength has only slight effects on the Xj distributions except 

extending the regions of influence. The increased upstream rec 

tri - 

for 

rculation region results in an increase in the upstream penetration of 

injectant. Boundary 1 ayer reattachment occm further downstream of 

the jet as does the location of the maximum concentration. 

13b presents similar treods in the data for nitrogen injection. 

these results a slightly larger value of Xj is seen throughout the 

upstream region for PR = 20. Again the helium concentrations at . 

same x locations and jet conditions are much larger than the 

Figure 

In 
45 

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48 

nitrogen distributions. 

The only other upstream surface Xj data reported in the published literature were for helium and nitrogen jets in unconfined 

flows for high jet strengths [12]. These results are significantly 

different from the findings of this investigation. These results 

indicate an upstream plateau region in which the concentratioa is 

nearly constant. Also, the plateau Xj values were over 40 percent 

larger in the previous investigation. The reason for the differences in the distribution data is assumed due to the much larger 

jet strengths and the different mainstream flow conditions used in 

the previous study. 

. 

The surface injectant mole fraction distributions have been 

described and related to the jet parameters. The surface distribution of Xj is shown to be controlled by the relative jet momentum 

for a particular injectant species. Therefore, the relative magnitude of b and PR determine the distribution of Xj along the surface. 

Surface X. distributions could not be correlated reasonab;y by xlm5. 

Doubling the jet strength produced only slSght differences in the 

distributions except for extending the regions of influence. 

J 

4.4 Static and Pitot Pressure Profiles 

Profiles of static pressure profile data from surveys of 

downstream flows are presented in Figs. 14-16; pitot pressures are 

nondimensional ited by the tunnel supply pressure (pb), whose mean 

values are given in Table 3 for each test condition survey location. 

The individual values of the supply pressure never varied from the 

mean value by more than 0.5 percent. 

downstream locations of x = 1.9, 3.8, and 6.4 cm for b = 0.056 cm. 

- 

Surveys were made at the 
49 

Also, surveys were made at x = 2.8 cm for b = 0.039 cm and at x = 

7.0 cm for b = 0.109 cm. All of these surveys are made along the 

center line of the injection surface (i.e., t = 0). 

Many features of the pressure profiles can be related to the 

vi sua1 observations of section 4.1 and downstream surface pressure 

distributions presented ill section 4.2. As discussed in section 

4.1, there is a strong downstream bow shock above a weak recompression shock. As such, the pressure would increase to a maximum at 

the bow shock and increase upon crossing the recompression shock. 

Recovery of the flow behind the recompression shock was indicated by 

the downstream surface pressures in section 4.2. The vertical distance between the two shocks increases for locations further downstream or for the same location with larger values of PR. The 

recompression shock location is not influenced by varying PR. 

Firrally, the schlieren photographs and surface pressure data indicate that a larger disturbance is pro;,.d by helium injection than 

nitrogen injection. 

\ 

Typical static pressure profile trends are presented in Fig. 14 

for PR = 10 at x/b 2 70. It is noted that for helium injection, the 

recompressicn shock occurs at about y/b = 20. Between the injection 

surface and the recompression shock, the static pressure recovers to 

the undisturbed mainstream value of p/pb = 0.032 (for tbe Mach 

number flow of 2.9). Upon crossing the recompression shock, the 

static pressure decreases to a minimum value. Then it increases in 

a linear fashion to a maximum pressure at y/b = 70 (the location of 

the bow shock). Thus, the fairly linear pressure rise between the. 

shocks indicates a region of large expansion fan. The relatively 

- 
50 

broad region of maximum pressure is representative of the bow shock 

location. This effect is produced by the interaction of the bow 

shock with static pressure probe geometry (i.e., the 0.77 an between 

the probe tip and pressure port). Above the bow shock the static 

pressure returns to the expected undisturbed value at y/b = 81. 

From oblique shock theory, the bow shock angle was calculated by 

using the static pressure values and was found to be 20'. 

trends in results are noted for nitrogen injection. However, the 

locations of both the recompression shock and the bow shock are 

higher by y/b = 7 for helium injection. Their effects are relatively small. As such, the injectant species has a snail effect on 

the static pressure variation. 

CI 

Similar 

5 

For a particular injectant species, Figs. 14a and b present a 

method for correlating the data for various values of b and PR for 

either helium or nitrogen injection. A direct dependence is 

observed for the static pressure profile on the gap width in Fig. 

14a for either injectant. A very good agreement is observed for 

data at similar values of b x PR and x-location in Fig. 14b for 

helium injection. Note that the vel-tical locations are unscaled in 

the figure. 

cm due to the different downstream profile locations (i.e., x = 6.4 

cm for b = 0.056 cm and x = 7.0 cm for b = 0.109 cm). Analogous 

results are observed for nitrogen injection. 

lating the data demonstrate the direct dependence of the downstream 

static pressure disturbance on b and PR (i.e., the relative jet 

momentum). 

The shock locations are slightly elevated for b = 0.109 

Both methods of correTypical downstream development of the static pressure profiles 
51 

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53 

are shown in Fig. 15 for PR = 10. For helium injection, the changes 

in pressure across the recompression shock and bow shock are reasonably independent of the downstream profile location. 

almost constant shock turning angles would be obtained by oblique 

shock theory. The bow shock turning angle was found to be approximately 11", and the recompression shock turning angle was between 

-6' and -8'. As a result, the Go shocks diverge from one another 

further downstream. Also, the slope of the linear pressure rlse 

increases from approximately 600 (at x/b = 34) to 900 (at x/b = 

114). Analogous results are observed for the nitrogen injection 

Therefore, 

case. 

Typical effects of increasing PR are shown by the static pressure profiles at x/b = 68 in Fig. 16. The nominal values of PR used 

are 5, 10, and 20. For helium injection, the recompression shock is 

at a constant vertical location of y/b = 30. At this location, the 

pressure approaches a minimum value of p/pb = 0.018 for PR = 20. 

the region between the shocks, the slopes of the pressure rise are 

almost identical. The bow shock location and shock strength increases with PR. 

angles were found to be 9', ll', and 13'. 

pressure data from different profiles agree very well after the bow 

shock locations. Therefore, the flow beyond the shock is not 

affected significantly by the flow field disturbance produced by the 

jet. Analogous resul ts are observed for nitrogen injection. The 

slope of the linear pressure rise between the shocks had a mean 

value of 820 with a variance of less than 12 percent. 

is independent of the injectant species. 

In 

For increasing values of PR, the bow shock turning 

Note that the static 

This variance 
54 

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56 

- 

In general , the static pressure profiles are almost independent 

of the injectant species. The two notable exceptiops, ,lowever, are 

the higher recompression shock and bow shock locations and the lower 

minimum pressure associated with the recompression shock for he1 ium 

injection. Below 3he recompression shock and above the bow shock, 

the static pressure is approximatelj the value expected in t4e 

undisturbed mainstream. However, a nearly linear rise in static 

pressure occurs from the mfninum value at the recompression shock tc\ 

a maximum value at the bow shock locatfop. This phenomenon is probably the result of a re?+on with a large downstream expansion fan. 

The distance between the two snocks increases with the value of b 

and PR and with downstream locatim, althocgh the shock angles are 

apparently independent of ?e downstream after x/b = 34. 

particular injectant species, the downstream static pressure disturbance is directly related to the change in b and PR (i.e., the 

relative jet momentum). lhe data exhibit only a slight dependence 

on the injectant species; therefore, a simple correlation of the 

data for either injectant species could not be formulated based on 

the jet momentum. 

For a 

The pitot pressure profiles are presented in Figs. 17-19. 

These data are for jet conditions and downstream locaticns analogous 

to those presented in the static vessure profiles. Therefore, analogous results would be expected for the same downstream locations 

except in the boundary layer region. 

The typical trends in the pitot pressure profiles are shown in 

Fig. 17a for helium and nitrogen injection. These trends are very 

similar to those discussed previously for the static pressure 
57 

profiles including the linear pressure rise %tween the shocks. 

notable exception is in the boundary layer regions. The solid symbols indicate the surface pressure. On the wall opposite the jet 

the boundary layer has a thickness of less than 0.03 cm. Similar 

values of the boundary layer thickness were calculated using the 

one-seventh power velocity distribution law C241. The injection 

wall boundary layer is indicated by the rapid pressure rise from the 

surface to a constant value of approximately pt/pb = 0.36, which 

corresponds to the pitot pressure in the undisturbed mainstream. 

The boundary layer extends to about ylb = 20 for heliun injection 

and t o y l b = 13 for nitrogen injection. Thus, the boundary layer 

thickness is increased for helium injection by y/b = 7 (a similar 

increase was noted for the shock locations). For helium injection, 

the minimum and maxiwn pitot pressures are increased by Pt/Pb = 

0.03. 

pressur- profiles; this effect may be attributed to the bow shock 

interaction with the probe geometry. 

A 

Note that the bow shock region is not broadened in the pitot 

As previously discussed, the direct dependence of the downstream rressure fiela on the changes in b and PR is shown by the 

pitot pressure profile comparisons in Fig. 17a for various values of 

b and in Fig. 17b or various values of b PR. 

injectant species, the good corrslation of the data represents its 

direct dependence on the change in the relative jet momentum. 

For a particular 

Typical downstream development of the pi ,,Tt pressure profiles 

-. is presented for PI? = 1. 'I Fig. 18. For helium injection, the 

boundary layer thickness does not increase significantly further 

downstream. The change in pressure upon crossing either shock is 
58 

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62 

independent of the downstream location. 

for the nitrogen injection data. 

Similar results are noted 

Typical effects of increasing PR on the pitot pressure profiles 

are shown at one downstream location (x/b = 68) in Fig. 19. From 

the helium injection profiles, the boundary layer thickness 

increases with PR. The other effects on the data trends were discussed earlier for the static pressure data. Analogous results are 

observed in the pitot pressure data for nitrogen injection. 

Results presented in this section show an analogous trend in 

static and pitot pressure data. However, there is one exception, 

the boundary-layer region indicated in the pitot pressure data. 

boundary layers thickness increases with PR, but not signficantly 

The 

with the downstream location along the injection surface. From both 

the static and pitot pressure data correlations, it is noted that 

the downstream pressure field disturbance is directly related to the 

changes in relative jet momentum for a particular injectant species. 

Also, the disturbance is slightly increased for helium injection. 

4.5 Mole Fraction Profiles 

The trend in injectant mole fraction (Xj) profiles is shown in 

Figs. 20-22 for different downstream locations and jet conditions. 

The Xj data was determined from gas samples collected by the pitot 

probes. 

since the analyzer error was about two percent. 

The Xj values less than 0.02 should be considered pure air, 

To aid in examining 

the data trends, the vertical axis (i.e., the y-location) is 

expanded three-fol d larger than used for pressure profiles. 

However, the distance between Xj values is less than 0.3 cm 

(diameter of pitot probe body). The X. data presented are for the J 
63 

same downstream locations (and jet conditions) are used in the pressure profile figures. 

Typical trends in the X - profiles are presented in Fig. 20a. J 

For heliun injection, the injectant mole fraction decreases from a 

maximum at the surface. The Xj profile resembles one side of a 

Gaussian distribution curve. A reasonable exponential least squares 

fit was found for this data, as discussed later in this section. 

The injectant is seen to penetrate the flow to about y/b = 18. For 

nitrogen injection, the values of Xj are smaller and penetration 

distance extends to y/b = 15. 

For a particular injectant species, Figs. 20a and b present a 

method for correlating the data for various values of b and PR. As 

with pressure profile data, the Xj profile data are directly 

affected by the changes in b (Fig. 20a) and b PR (Fig. 20b). 

these methods of correlating the data are applicable equally to 

either the helium or nitrcrgen injection case. 

Also, 

The typical effects of the downstream location on the Xj profiles are shown in Fig. 21. For helium injection, the profiles are 

unaffected by the increase in the downstream location. However, a 

slight decrease in Xj values is noted near the surface at x/b = 114. 

Analogous results are seen for the nitrogen injection case. 

the results presented in these figures (and results obtained for PR 

= 20 at X/D = 341, the downstream mixing profiles are observed to be 

fu? ly devel oped by the 1 ocati on of the boundary-1 ayer reattachment. 

From 

The effects of increasing PR on the downstream mixing are shown 

in Fig. 22 for x/b = 68. 

height (defined as iocation where Xj = 0.02) increase with PR for 

The values of Xj and the penetration 
64 

30 

20 

b (cc) 

0 

0.2 0.6 1 .o 

'j 

30 

20 

'Y/ .b 

10 

0 

NITROGEY 1FiJECTA:dT k 

0.2 0.6 1 .o 

*j 

Fig. 20a. Injectant mole fractior, profile correlatioc: 

PR = 10, x/b = 68. 
65 

N I TROG EN I !I JE CTANT 1.5 

1 .o 

I 1 

0.2 1 .o 

Fig. 20b. Injectant mole fraction profile correlation: 

b PR.= 1.1 cn. 
66 

30 r HELIUM INJECTANT 

0 

0.2 G .6 1 .o 

'j 

NITROGEN INJECTANT 

r 0 114 

0 

Q 

0 

0.2 0.6 1 .o 

'j 

fig. 21. Effect of downstream location on injectant mole 

fraction profiles, PR = 10, b = 0.056 cm. 
67 

helium injection. Also, the general shape of the profile is 

affected by increasing PRY especially further away from the injection surface. 

Analogous effects are noted for the nitrogen injection 

profiles. For the three-dimensional case, Rogers [4] fitted similar 

concentration profiles with a Gaussian-type exponential curve fit. 

For the two-dimensional case, the equation is of the form 

(4.5) 

For both injectants, the penetration height can be approximated by 

where ~1.5 can be found from the relative jet momentum (Y. b PR) 

using Eq. (4.3). The separation shock deflection angle (8) is found 

to be 12.8’ from the first surface plateau pressure. A good correlation is shown in Fig. 22 for a particular injectant species and 

jet pressure, and the least squares fit is given by the exponential 

relationship of Eq. (4.5). The exponent, (8) is seen to increase 

with the jet pressure; however, no general relationship was found 

between the jet parameters and the coefficients A or B. Although 

the Xj profiles are very much dependent on the injectant species and 

jet pressure, the penetration height is directly related to the 

changes in relative jet momentum. 

J 

The downstream profiles of Xj have been examined for the typical effects of downstream locations and variation of the jet para- 
68 

20 2.65 

10 4.36 

20 

y/b 

10 

0 

1.93 

2.9E 

- 

n 

0 

0 

PR A - B 

1.83 

3.52 

PJITROGZN INJECTANT 30k PR A B I I I 

20 

Ylb 

10 

I .v 

Fig. 22. Effect of jet pressure on injectant concentration 

profiles, x/b = 68, b = 0.056 m. 
69 

meters. In general , the concentration decreases further awcv from 

the injection surface. The profiles are fully developed before the 

location of boundary layer reattachment (x/x1,5'= 3-65]. Also, 

there is only a slight amount of mixing further downstream. 

Increasing PR causes an increase in the size and shape of the profiles. Although the helium injection profiles are larger than 

nitrogen injection profiles at analogous jet conditions due to the 

smaller molecular weight, the downstream penetration height can be 

determined from the same linear relationship for either injectant. 

The penetration height is directly related to the relative jet 

momentum and upstream separaticn distance. For a particular injectant species, the downstream mixing is directly effected by changes 

in b or the relative momentum. 

I 

4.6 Mass Flux Profiles 

The downstream mass flux profiles were examined to provide 

additional insight into the overall data quality. The injectant 

mass flux profiles are shown for FR = 10 and 20 in Figs. 23., The 

results of trapezoidal rule integration of the mass flux profiles 

are shown in Fig. 24a for the total mass flow rate and in Fig. 24b 

for the jet mass flow rate. The mass flux was determined from the 

mean tunnel conditions, the pitot pressure, the air mass fraction, 

and the interpolated static pressure. The small values of mass flux 

at the surface ()I = 0) values result from the variation in the surface pressures between the pitot and static surveys. The effect of 

these nonzero values is to increase the integrated mass flux by less 

than one percent. The integration of the mass flux profiles was 

performed by a trapezoidal rule method. 
70 

The typical trends of the injectant mass flux profiles are 

shown in Figure 23a for helium injection. Note that the solid 

symbols represent the surface values. The mass flux increases to a 

maximum value at about ylb = 7 and then decreases to zero at about 

y/b = 23. In general, the profile is fully developed by the first 

dcmstredm location. The effects of doubling the jet pressure are 

shown in Fig. 23b. D Sling the jet pressure increases the maximum 

mass flux location to -I/b = 30 while decreasing the value of the 

maximum mass flux. For nitrogen injection in Figs. 23b and 23c, 

similar trends of the data can be seen. The maximum mass flux 

appears to be larger and occurs clczer to tne surface (y/b = 5) than 

for the helium injection case. 

pressure produces similar trends as noted for the helium injectiorl 

case. Also, the penetration height is about y/b = 30 for the nitrogen injection case. 

In Fig. 23d, doubling the jet 

The injection mass flux profiles are fully developed by xjb = 

34. The broadened profiles are a result of seemingly random data 

scatter and not due to increased downs-ream mixing. 

value of PR, both injectants have the same upper limit of injectant 

mass transport. Also, over half of the injected mass is transported 

below y/b = 10. 

At ne sme 

An analysis of the measurement errors effecting the mass flow 

rate calculations is giver, in Appendix A. The indicated errors 

influence local values only by a few percent at most. However ent: 

integrated injectant mass flow rate could have a 20 percent er'-or 

due to turbulence efforts [253. 

A measure of the overall data quality is shown ai the actual 
71 

D 

0 

HEL I U1 IfJJECTANT 

PR = 10 

1 

X/ b 

68 

114 

I 

30 ..:: NITROGEM 

PI? I10 

INJECTANT 

0 

@ 0 

HELIUI: I:JJECTA',IT 

-A PR = 20 

a 

0 

1 

i 0 

0 A 

I3 

A 0 

!liT!?OGE!I IN JECTA:IT 

PR = 20 r 

f§P 

U* 

i 

Fi3. 23. 1,ijectant ass flux pr f.l;.s, b = 0.056 cm. 
72 

downstream locations in Fig. 24a, where the integrated mass flux is 

determined by integrating vertically at the tunnel centerline, nondimensionalized by the tunnel and turbine meter mss flow rates is 

shown. The tunnel mass flow rate is found frm the mean tunnel 

conditions given in Table 3. Therefore, the ideal nondimensionalized value will be ucity for a two-dimensional flow with no 

measur~~nent errors. The nondimensional ized mass flow rate decreases 

almost uniformly from 1.1 at x = 1.9 an to a value of almost 1.0 at 

x = 6.4 cm. The larger error values closer to the jet are probably 

due to the larger pressure gradients, since the slope of the 

pressure-rise between the shocks was observed to be influenced 

mostly by the downstream location -'n bec. 4.4. The mass flow rates 

are found not to be significantly affected by the jet pressure or 

injectant species. 

these results. 

The good quality of the data is demonstrated by 

The -njectant mass flow rate variation with downstream location 

and jet parameters is shown in Fig. 24b. In general, the indicated 

data quality is better for the larger values of PR for either injectant species. 

att ''uted to turbulence effects. Therefore, the data quality is 

considered good except for the helium injection case at x = 2.8 cm 

Generally, the error is less than 20 percent arld is 

and for PR = 19. 

The injeccarit mass flux profiles have been characterized and 

examined. Despite the apparent data scatter in these profiles, the 

integrated*resul ts demonstrpte the good overall data quality in this 

region. The integrated total mass flow rates indicate the good 

overall data quality and two-dimensionality for this investigation. 
wfp ucrs; 

0 

i + 4M 1.0 -- 

1.1- 

1.0, 

0.9, 

0.8- 

0.7- 

0.6- 

0.5, 

A &! 

8 

ea, 

A - €I- -- 

nitrogen 

0 

ai- 

- 

0.9 1-1 

0 2 4 6 8 

X (cm) 

(a) Total Mass For PR = 5, 10, and 20. 

A 

0 

0 

0 

a 

0 

A 

0 

U 

0 

0 

0 

PR injectant 

A 

0 

Fig. 2;. Integrated inass flux variztion with downctream 

survey 1 oca ti on. 
74 

5. COMPARISON OF THEORY WITH DATA 

As discussed in Chap. 4, the transverse jet interaction with a 

confined supersonic flow produces a complex mixing and interaction 

phenomena. The comp!exity of the flow field would make an analytical mdel very useful for parametric studies for SCRAMJET engine 

design. A three-dirnensional code is not available at presenc:; 

however, a two-dimensional code exists to examine this type of flow. 

The data presented in Chap. 4 are useful in establishing the 

validity of the existing analysis. In this chapter, a comparison 

will be made between the data and code developed for similar flows. 

5.1 Model for Theoretical Investigation 

Drummond has developed a two-dimensional elliptic flow theory 

to describe this complex flow field [3]. 

discretionary form of the full Navier-Stokes equations using a timesplit McCormack scheme C261. A ccqvdinate transformation by Smith 

and Weigel is used to concer'-?ate the grid near the injector in both 

the horizontal and vertical axes [27]. Complete descriptim of this 

computational model is available in the cited references. This 

computational model was used to obtain theoretical results by using 

the appropriate conditions for the present experimental model. 

The code solves the 

Theoretical results were obtained Cor three separate cases to 

examine the effects of varying the injectant species and ;':t 

pressure. 

helium injection with PR = 10 or 20. 7ne other jet conditions used 

These were for nitrogen injection with PR = IC) and for 
75 

were a total temperature of 300 K, b = 0.056 Cm, and a Mach number 

of 1.00. The inlet conditions used were a total temperature 300 K, 

a total pressure of 2.07 MPa, and a Mach number of 2.90 for air 

flow. The results for all three cases were allowed to advance in 

time to a steady state solution. However, mal1 oscillations were 

noted in the results. These are similar to the small oscillations 

at frequencies less than 50 Hr noted in the previous experimcntal 

studies for analogous flaws 128-301. 

5.2 Comparisons of Results for Surface Distributions 

Cmpari sons of the surface pressure data with the theoretical 

Tesults are shown in Figs. 25. The coordinate system and nondimensional parameters used for the comparisons are the same as given in 

Chap. 4 

25a for PR = 10. 

separat on occurs earlier in the data (x/b = -35) than the theoretical results (x/b = -30) The data and theoretical results 

compare well after x/b = -23, the location near the initiation of 

the first plateau pressur-e region. A small drop in the surface 

pressure is observed for the theoretical results very near the jet 

(x/b = -3). A similar decrease in the surface pressure (very near 

.the jet) was noted in the air injection investigation by Sterrett 

and Barber [2]. Downstream of the jet, the agreement is good aside 

from the following two exceptims. The theoretical results show the 

initiation of the downstream pressure rise at an earlier location 

(x/b = 8) than the data (x/b = 13). Also, the theory does not 

predict the downstream peak pressure observed in the data at x/b = 

27. Therefore, the turning of the flow associated with boui.dary 

For nitrogen injection, the results are compared in Fig. 

The results show that the initiation of upstream 
76 

ORIGINAL PAGE 1S 

OF POOR QUALITY 

0 

03 

c 

CJ 

ez, 

0 

L OC, U 

.C 

c 

.. 

0 

v) 

0 

I LL 

*r 0 

c3 

m 
77 

=IN a00 P 

.P 

c 

01 

I 

.. 

E 

V 

W 

L 

c L 

0 

ul 
78 

layer reattachment is not properly predicted by the code. For 

heliua injection, a similar comparison with data is seen in Fig. 25b 

for PR = 10. 

produces a larger pressure on the surface. Therefore, the . 

comparison appears to be of poor quality, although the trend is 

analogous to that noted for PR = 10 cases. 

theoretical results compxed well with the data. However, the code 

underpredicts the location of the boundary layer separation and the 

beginning of the downstream pressure rise and does not show the 

existence of the downstream peak pressure. 

In the same figure, doubling the helium ‘et pressure 

In general, the 

Comparisons between data and theoretical results for the surface injectant mole fraction (X-) are shown in Figs. 26. For 

nitrogen injection, Fig. 26a shows a poor comparison with data. 

theoretical results agree well with the location of the upstream 

injectant spread (x/b = -31). Thereafter (in the upstream region), 

the code predicts trends similar to the data, but it indicates much 

larger concentrations. 

ends at about x/b = -8 for both theory and data, also the value of 

X is seen to increase closer to the jet. In the plateau region, 

the theory predtcfs a value of Xj approximately 2.5 times larger 

than the data (Xj = 0.08). 

and theoretical results is poor. 

data in the downstre. 

J 

The 

The first Xj plateau occurs at x/b = -20 and 

j 

Downstream, the agreement between data 

The lad values of Xj i,ndicated by 

,-ecirculation region are probably due to 

entrained air or three-dimensional effects. As wch, one wou d not 

expect a gocld agreement between the data and theory in this 

region. 

values downstream of the recirculation region (x/b = 28). In 

Note that both theory and data show a similar trend n Xj 
79 

general, the code 

that found in the 

- 

predicts a surface distribution of Xj similar to 

data, but the theory overpredicts tht zsncc?!t-rb - 

tion. This difference could be due to the sample collectic,i system, 

collecting samples a significant distance above the injectant 

surface. This off-surface sample collection would lower the value 

of Xj in the data. To determine this, theoretical results for a 

small-constant height above the injection surface (y = 0.13 and 0.?7 

cm) were also compared with data in Fig. 26a. 

the upstream region, the penetration is greatly undcrpredicted by 

the theory fsr y = 0.13 cm at x/b = -22 and for y = 0.27 an at x/b = 

-14. For either distribution, the concentration increases over the 

data's plateau region. The results, therefore, indicate that the 

off-surface sample collection would cause the concentration to 

increase without a plateau region. However, a plateau region does 

exist for the data. Thus, only theoretical results for the surface 

are considered for comparisons with the data. 

It is rioted that in 

Compari-on between data and theory are shown in Fig. 26b for 

helium injection. For PR = 10, the upstream plateau region extends 

from about x/b = -38 to -25 for the data and from x/b = -21 to -10 

for the theoretical results. For PR = 20, the upstream lead 

occurs at about the same location (x/b = -60) for the data and 

results. 

-36 to -14 for the data and from x/b = -35 to -13 for the results. 

After the plateau region, the values of Xj increase closer to the 

jet. 

at x/b = -4 for PR = 20. The trends in the data are represented 

well by the code for the PR = 20. The trends in the data sre 

Also, the upstream plateau region extends from aBout x/b = 

A sample collection prcblem most likely caused the low value 
80 

i 

I 

!D i 

cz 

4 

Iu 

LLI 

7 

z U 

N 

u 

0 

Q3 

0 

rc 

0 * 

0 

N 

n 

OX 

x 

0 

cu I 

0 

e 

I 

o 

a 

I 

0 

03 

I 
81 

I 

I 

I 

I 

I 

I 

I 

I 

II 

I 

I 

I 

QO 

0 Q 

0 

0 

a 

Q 

0 

- 

a: 

0 

CD F 

0 0 a- 

% 

cv 

0 

0 

00 

0 

W 

0 

a 

0 

cu 

n 

O\ X 

3 

cv 1 

0 

c+ 

I 

0 

a 

I 

0 

43 

I 

0 

.. 

E 

c, 

0 

II 

A 

m 

e*?- 

€- 

OQ, 

us 

c 

Ln 

cv 
represented well by the Code for the PR 

agreement for the PR = 10 case; A valid downstream comparisor! 

cannot be made for reasons previously discussed for the 

r e c i r c u l a t l o n region. Further downstream, the code correctly 

predicts the trend of decreasing concentration but overpredicts the 

val ues. 

20 case and in fair 

In general, the code correctly predicts the trends of the 

injectant mole fraction distributions. However, the values of the 

injectant mole fraction are greatly overpredicted by the theti?y. 

This lack of agreement for the value of the injectant mole fraction 

is not believed to be due to errors in the method of surface sample 

collection. 

5.3 Cornparisor. of Results for Downstrean Profiles 

Comparisons of the static pressure profiles data with theory 

are presented in Fig. 27 for the survey, locations of x/b = 34 and 

680 For nit-dgen injection, the results are compared with data in 

Fig. 27a for PR = 10. Both the data and theory show thst the recompresston shock is about y/b = 13 for x/b = 34 and at about y/b = 22 

for x/b = 68. A linear pressure rise is observed between the 

shocks; however, a smaller slope is noted for the theoretical 

results because the bow shock is located closer to the ,rface. At 

x/b = 34, the bow shock location is seen to be lower for the theory 

(y/b = 34) than the data (y/b = 46). 

681, the b.4 shock location in the theoretical results (y/b = 54) 

has increased in distance away from the location in the data (y/b -: 

75!. By oblique shock theory, the bow shock angle is found to be 

29" for the data. However, in the theoretical results, tne bow 

Fu, ther downstream (at x/y = 
83 

shock angle decreases from 31" to 29' further downstream. 

accounts for the increasing distance between the bow shock locations 

for data and theory further downstream. In the theoretical results, 

the blunt bow shock indicates the distance between computational 

grid points. Fim this indication of the grid spacing at the bow 

shock location, the bow shock is seen to be smeared over only about 

three grid points (i.e., from y/b = 54 to 75 at x/b = 68). After 

the bow shock region, the statSc pressure is a; ah st the undisturbed 

value (p/pb = 0.032) for 50th data and theory. 

theoretical results agree very well with the data trends. However, 

the shock structure is incorrectly predicted with regards to the 

recompression shock strengt!! and the bow shock location and 

strength. 

This 

In general, the 

A similar comparison with the data is shovrn in Figs. 27b and 

27c for helium injection. For PR = 10, the bw shock angle is fwnd 

to be approximately 29" from the data (Fig. 27bj. The theoreticol 

results, however, show that the bow shock angle decreases from 37" 

at x/b = 34 to 29" at x/b = 68. 

iltLble decreases from 37" to 33" over the same region. 

pression shock is located at y/b = 12 for x/b = 34 and at y/b = 26 

for x/b = 68. Thnse locations are the same for both the data and 

For the theory. however, the shock 

The recomresults and for both jet pressures. 

In general, the theory predicts the trends in data very well 

with the exception of the shock strength and bow shock location. 

the same PR, the theoretical results predict the downstrzam static 

pressure field equally well for either injectant species. For the 

same injectant species, doubling the jet pressure mainly affects the 

At 
84 

ORIGINAL PAGE 19 

OF POOR QUP.LlTY 

7 50 

120 

90 

Ylb 

60 

30 

0 

THEORY DATA 

A 

0 

--- 

- 

A p PR = 70 

NITROGEN INJECTAU 

- 

- M 

- x/b 

34 

68 

/ 

------- 

0.08 0.13 

Fig. 27a. Comparison of static pressure profiles, b = 0.CSO CR: 

nitrogen injectant. 
a5 

ORIGINAL PAGE IS 

OF POOR QUALln 

TiiEORY DATA 

A 

0 

--- .L 

- 

HEL I Ut? I tl JECTANT 

PR = 10 

- x/b 

34 

68 

J 

0.10 

Fig. 27b. Comparison of static pressure profiles, b = 0.056 cn: 

he1 i ur injectant. 
86 

15 

12 

y/ b 

60 

30 

0 

> 

/ 

_----- /- 

- e-------- 

HEL I U!! i 1: JECTArIT 

PR = 20 

1 I 0.E 0.04 0.06 0.08 . 0.1C 0.12 

Fig. 27c. Comparison of static pressure profiles, b = 0.056 cm: 

helium injectant. 
a7 

prediction of the bow shock strength. The theory does predict 

correctly the independence of the recompression shock location with 

varying values of PR. 

The pitot pressure profiles are compared in Figs. 28 for the 

downstream locations of x/b = 34 and 60. For nitrogen injection, 

Fig. 28a shows a good agreement between the theory and data up to 

the theoretical bow shock location. The shock locations, of course, 

are the same as in the static pressure profiles. Both the recompression and bow shock strengths are underpredicted by the theory. 

After the bow shock, the data and theoretical results approach the 

undisturbed Vahe of Pt/Pb = 0.36. For helium injection, a similar 

comparison is shown in Fig. 28b for PR = 10 and in Fig. 28c for PR = 

20. Note that the agreement with data is not affected by the injectant species or jet pressure except for the bow shock location. In 

general, the theory predicts the trends in data very well. 

the shock strengths are underpredicted in the pitot pressure 

rasul ts. 

However, 

The injectant mole fraction profiles are compared in Figs. 29 

at x/b = 34 and 68. Note that the vertical axis is expanded three 

times larger than previously used for the pressure profiles. 

nitrogen injection, Fig. 29a shows a good agreement between the 

theory and data. 

from the wrface to the first instream data point (y/b = 5). 4t the 

surface, the mean value of Xj from the surface to the first instream 

data point (y/b = 5). At the surface, the mean value of Xj is 0.56 

for the data and 0.94 for the theory. 

observed after the first instream data point. 

For 

However, the theory overpredicts the value of Xj 

Good agreement wSth data is . 

For helium injection, 
58 

1% 

121 

9( 

Y/b 

61 

3 

THEORY DATA x/b 

NITROGEN I NjEiTAflT 

PR = 10 

0 

A 

I J 

0.2 0.4 0.6 0.8 

Pt/Pb 

Fig. 28a. Comparison of pitot pressure profiles, b = 0.~56 CR: 

ni trogen injectant. 
ORIGINAL PAGE 13 

OF PiOR QUALrrYl 

150 r THEORY DnTA xlb 

A '7 I-= IEL IUY Ill JECTANT 

120 

0.2 0.4 0.6 0 

Pt'Pb 

90 

Ylb 

60 

30 

.8 

Fig. 28b. Comparison of pitot pressure profiles, b = 0.056 cm: 

ne1 i urn injectant. 
90 

150 

120 

90 

Y/b 

60 

30 

0 

II 

THEORY DATA x/b 'X 

I I I I 

0.2 0.4 0.6 0.8 

Fig. 28c. Comparison of pitot pressure profiles, b = 0.056 cm: 

he1 i urn injectant . 
91 

ORIGINAL PAGE fq 

OF POOR QUALITY, 

N I TROGEti INJECTANT 

PR = 10 

20! 

(a) tii trogen Injectant 

H E L I Uti I N J EC TAN T 

PR = 10 

THEORY DATA 

(b) He1 i urn Injectant 

Fig. 29. Comparison of injectant mole fraction profiles, b = 0.056 cn. 
92 

a similar comparison is shown in Fig. 29b for PR = 10. A better 

agreement is evident from the mean surface X. values of 0.83 for the 

data and 0.9: for the theory. The results for PR = 20 are also compared in Fig. 29b. 

decreases the agreement near the surface (y/b > 10). Good agreement 

in theoretical results is observed after y/b = 10. However, the 

theory predicts a slightly lower concentration. 

good agrement between the data and theory is observed except very 

near the surface. 

J 

It is seen that doubling the jet pressure 

In general, a very 

The above comparisons reveal that, in general, the theory predicts the trends in data very well. However, in certain regions the 

theory does not correctly predict the locations and values of the 

profile quantities. The bow shock location is underpredicted by the 

theory; the bow shock strength is overpredicted in the static 

pressure profiles and underpredic”3d in the pitot pressure profiles. 

In both profi les, the recompression shock strength is underpredicted. The injectant concentration is overpredicted very near the 

surface. The extent of these disagreements is further examined by 

comparing the injectant mass flux, total mass flux, and Mach number 

profiles in Figs. 30 to 32, respectively. 

cal case examfned is for helium injection w th PR = 10 at x/b = 68. 

As discussed in Sec. 3, the Mach number and mass flux are determined 

primarily by interpolating the value of the static pressure at pitot 

pressure locations and by using the Rayleigh pitot formula. 

Downstream profiles of injectant mass flux (a.pU) are shown in 

Fig. 30. The injectant mass flux increases to an off-surface maximum before decreasing to zero at about y/b = 21. The maximum value 

n each figure, the typiJ 
93 

for the theoretical results is located at y/b = 3, whereas the 

maximum value for the data is at about y/b = 7 (Fig. 23a). This 

value appears to be less than one. However, the maximum value for 

theory is 1.24. The theory correctly predicts the profile trends 

but not the location or values of the injectant mass flux near the 

surface (y/b < 11) due mainly to the overprediction of Xj near the 

surf ace. 

Downstream profiles of the total mass flux (pu) are compared in 

Fig. 31. Very good agreement is observed except near the location 

of the recompression shock (y/b = 20) and the bow shock (y/b = 60 

for theory). The theory overpredicts the mass flux near the recompression shock and underpredicts the mass flux near the bow shock by 

p(puIT = 0.12. The theory accurately predicts the boundary layer 

region at the opposite wall. 

well with the data. 

In general, the theory agrees very 

The Mach number (MI profiles are shown in Fig. 32. At the 

locations previously noted, the Mach number is underpredicted by 0.4 

at the shock locations. However, the theory predicts the general 

trends of the data very well. 

In the downstream mixing regfon, the overprediction of the concentration near surface by the theory has a signlficant effect on 

the injectant mass flux profile. Therefore, the theory predicts 

that most of the injectant mass transport occurs closer to the 

surface. Weaker recompression and bow shock strengths are predicted 

by the theory, even though the bow-shock strength is overpredicted 

in the static pressure results. 

7.e essential features of the coflplex flow field have been 
94 

30 

20 

Y /b 

10 

0 

HELIUM INJECTANT 

PR = 10 

x/b = 68 

J b = 0.056 cm 

0 DATA 

- THEORY 

I 

0.14 

Fig. 30. Comparison of injectant nass flux profile. 
95 

ORIGINAL PAGE 19 

OF POOR QUALITY 

1 .o 

PU/ ( PU 

Fig. 31. Comparison of total mass flux profile. 

2 .o 
96 

0: 

- 

150 

120 

90 

Ylb 

60 

30 

0 

DATA 

THEORY 

% a 

I I I + 

0.8 1.6 2.4 3.2 3.8 

M 

Fig. 32. Comparison of Mach number profile. 
97 

described by this computational analysis. Aside from a few noted 

exceptions, the theoretical results cMpare very well with the data. 

?he locations of upstream boundary layer separation and downstream 

bow shock are underpredicted. Also, the recompression and bow shock 

are underpredicted by the theory. The concentration of injectant is 

overpredicted in the nea:’ surface region. The grid site and turbulence model used in the theory my .lave caused these differences. 

Since the computer code was not optimized for the particular experimental conditions, it should be considered valid due to the 

generally good agreement with data for this complex flow field. 
98 

6. CONCLUDIN6 Ru4ARKS 

The flaw field near a two-dimensional jet has been investigated. From a perpendicular slot nozzle, an underexpanded helium or 

nitrogen jet has been injected into a confined Ma..> nurnber 2.9 flow. 

The flow field produced by the jet mixing and interaction has been 

investigated over a range of jet parameters. Ths jet parameters 

considered were the injectant species, jet static pressure, and gap 

width. -Surface distribution and downstream profile data were used 

to develop enpitical correlations and as a data base for an existing 

flaw theory. 

The flow field disturbance is Increased by increasing the gapwidth, increasing the jet static pressure, or injecting helium 

instead of nitrogen. 

mined by the product of the gap width, jet static pressure, and 

injectant's specific heat ratio. This product was directly related 

to the relative size of the flow field disturbance, and was related 

linearly to the upstream separation distance. Using the upstream 

separation distance, a correlation has been developed to relate the 

upstream (or downstream) surface pressures into a single distribution fr>r the jet conditions examined. The downstream injectant 

pene'ration height is directly proportional to the upstream separation di stircce. Thus, the surface disturbance and downstreammixing limit are dependent on the relative change ir! the jet 

momen Turn. 

The relative change in jet momentlrm was deter- 
For a particular injectant species, methods have been devel cped 

to correlate the data based on the relative change in the jet monenturn (i.e., the product of the gap width and jet static pressure). 

The extent of mixing and interaction of tk jet with the mainstream 

is related directly to the change in either the gap width or 

relative change in jet momentum. The flow-field disturbance is only 

slightly affected by the injectant used; however, the mixing in the 

flow field is affected greatly. The change in the flow field 

features can be related to changes in the jet parameters examfned. 

Results frm an elliptic flow theory were compared witb the 

data. 

described by this computational analysis. Aside from the few noted 

exceptions, the theoretical results compare very well with the data. 

The theory underpredicts locations of upstream boundary layer 

separation and downstream bow shock, and the recompression and bow 

shock strengths. .The concentration of injectant is overpredicted in 

regions closer to the surface. The computational grid size and 

turbulence model used in the theory may have caused these diffirences. Since the analysis was not optimized for the particular 

expsrimental conditions, and because of the uncertainty of the 

accuracy of the mole fraction downstream of the injector in the 

recdrculation region, the code should be considered valid because of 

the reasonably good agreement with data for this complex flow field. 

The essential features of the complex flow field have been 
100 

REFERENCES 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

a. 

9. 

10. 

Jones, R. A. and Huber, P. W., "Airframe-Integrated Propulsion 

System for Hypersonic Cruise Vehicles," Presented at the 11th 

Congress of the Aeronautical Sciences, Lisbon, Portugal, 

September 1978. 

Sterrett, 3. R., Barber, J. B., Alston, 0. W., and Romeo, 0. 

J ., "Experimental Investigations of Secondary Jets from TwoDimensional Nozzles with Various Exit Mach Numbers for 

Hypersonic Control Application, " NASA TND-3795, January 1967 . 

Drumond, J. P. and Weidner, E. H., "A Parametric Study of 

Staged Fuel Injector Configurations for Scramjet Applications," 

AIM Paper No. 81 - 1468, July 1981. 

Rogers, R. Clayton, "A Two-Dimensional Model of the Interaction 

of a Transverse Jet in a Supersonic Stream with Application to 

Supersonic Stream," Ph.0. Thesis, 1979, North Carolina State 

University at Raleigh. 

Werle, M. J., "A Critical Review of Analytical Methods For 

Lstimating Control Forces Produced by Secondary Injection; The 

Two-Dimensional Problem, " NOLTR-68-5, Naval Ordnance Laboratory, White Oak, Maryland, January 1968. 

Spaid, F. W. and Zukoski, E. E., "A Study of the Injection of 

Gaseous Jets from Transverse Slots with Supersonic External 

Flows," AIAA Journal, Vo!. 6, No. 2, February 1968, pp. 205- 

21 2. 

Neilson, J. ti., Gilchrist, A., and Lee, C. K., "A Theory for 

the Side Force Produced in Two-Dimensional Nozzles by Secondary 

Gas Injection," Aeronautical Journal, Vol. 72, pp. 267-274, 

March 1978. 

- 

Kaufman, L. G. and Koch, F., "High Speed Flows Past Transverse 

Jets," RE - 348, Grumnan Aircraft Engineering Corp., Bethpage, 

New York , October 1968 . Mu, 3. M. and Aoyama, K., "Analysis of Transverse Secondary 

Injection Penetration into Confined Supersonic Flow," AIM 7th 

Aerospace Sciences Meeting, AIM Paper No. 69-2, January 1969. 

Werle, M. J., Driftmeyer, R. T., and Shafter, D. G., "Jet 

Interaction-Induced Separation of Supersonic Turbulent Boundary 

Layers - The Two-Dimensional Problem," AIM 3rd Fluid and 

Plasma Dynamic Conference, Los Angeles, California, Paper No. 

70-765, June 1970. 
101 

11. 

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13. 

14. 

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23. 

Werle, M. J., Driftmeyer, R. T., and Shafter, D. G., "Downstream Pressure Distributions for Two-Dimensi onal Jet 

Interaction," AIM Journal, Vol. 8,' No. 6, June 1970, pp. 1165- 

1167. 

Thayer, W. J., "The Two-Dimensional Separated Flow Regf on 

Upstream of Inert and Chemically Reactive Transverse Jets," 

Ph.D. Thesis, Department of Mechanical Engineering, University 

of Washf ngton, March 1971. 

Young, C. T. K. and Barfield, B. F., "V?SCOUS Interaction of 

Sonic Transverse Jets with Supersonic External Flows," AIAA 

Journal, Vol. 10. do. 7, July 1972, pp. 853-855. 

Spaid, F. W., "Two-Dimensional Jet Interaction Studies at Large 

Values of Reynolds and Mach Numbers," AIAA Journal, Vol . 13, 

No. 11, November 1974, pp. 1430-1434. 

- 

Andreev, A. E. and Shmanenkov, V. N., ?ieparation-Zone 

Parameters Ahead of a Jet Obstacle," Transactions of Izvestiya 

Akademii Navk SSSR-Mikharika ZhikdosSi i Gata, Vel. 10, No. 2, 

- June 19/6 9 PP* 281 297- 

Krishtal , V. I., "Application Factor of Two-Dimensional 

Transverse Sonic Jet Interacting with Supersonic Stream," 

Izvestiya VVA, Aviatsionnayu Tekhnika, Vol 22, No. 1, January 

1919 s PP- 102 - 105- 

Broadwell, J. E., "Analysis of the Fluid Mechanics of Secondary 

Injection for Thrust Vector Control ," AIM Journal Vol. 1, No. 

5, May 1963, pp. 1067-1075. 

Hsia, H. T.! Karamcheti, K., and Seifert, H. S., "Perturbation 

of Supersonic Flow by Secondayt Injection (VI," Journal of 

Spacecraft, Vol. 2, No. 1, 1965, pp. 67-72. 

Pinckney, S. Z., "A Short Static-Pressure Probe Design For 

Supersonic Flow," NASA TN 0 - 7978, July 1975. 

Trexler, C. A., "Instant-Reply Data System For Combustion 

Tests," Presented at the 17th JANNAF Combr!stion Meeting, 

Hampton, Virginia, September 1980. 

McClinton, C. R., NASA Langley Research Center, Hampton, 

Virginia, Personal comnunication. 

Anon., "Equations, Tables, and Charts for Compressible Flow," 

NASA TR 1135, 1953. 

Zukoski, E. E., "Turbulence Boundary Lcyer Separation in Front 

of a Forward Facing Step," AIAA Journal, Vol. 5, No. 10, 

October 1967, pp. 1746-1753. 
102 

24. Schlichting, H., Boundary Layer Theory, McGraw Hill, New York, 

Vo:. 7, 1979. 

25. Torrence, M. G., "Concentration Measurements of an Injected Gas 

in a Supersonic Stream," NASA TN D - 3860, January 1967. 

26. McCormack, R. W. and Baldwin, E. S., 'A Numerical Method for 

Solving the Navier-Stokes Equations with Application to ShockBoundary Layer Interactions," AIAA Paper No. 75 - 1, January 

1975. 

27. Smith, R. E. and Weigel, B. L., "Analytic and Approximate 

Boundary Fitted Coordinate Systems for Fluid Flow Simulation," 

AIM Paper No. 80 - 0192, January 1980. 

28. Bogdonoff, S. M., 'Some Experimental Studies of the Separation 

of Supersonic Turbulent Boundary Layers," Princeton University 

Report 336, June 1955. 

29. Kistler. A. L., "Fluctuating Wall Pressure Under a Separated 

Flow," Journal -Acoustical Society of America, Val . 36, March 

1964, pp. 543 -5. 5 0 

30. Speaker, W. V. and Ailman, C. M., "Spectra and Space Time 

Correlation of the Fluctuating Pressures at a Wall Beneath a 

Supersonic Turbulent Boundary Layer Perturbed by Steps and 

Shock Waves," NASA CR - 486, May 1966. 
APPENDIX A 

ERROR ANALYSIS 
104 

APPENOIX A 

ERROR ANALYSIS 

An error analysis was performed to examine the possible contribution of measurement errors in determination of the Mach number (M) 

and total mass flux (pu). The measurement errors were considered 

from the supply temperature thermocouple (To), pitot pressure Ipt) 

transducer, static pressure (p) transducer, and composition 

analysis. 

compared of a binary mixture of ideal gases (i .e., air and 

injectant). These equations were differentiated by a chain rule 

expansion for the measured flow parameters. In the final step, the 

derivatives were replaced by a finite difference representation. 

The equations used assumed the flow was adiabatic and 

The equations for the local Mach number error (AM) were determined for both the subsonic and supersonic cases. For this 

evaluation, the error in the mass averaged specific heat ratio (y) 

was 

A.1 . 

where the mass fraction measurement error of air (a,) was determined 
from the 

pressure 

(R) are 

subsonic 

mole fraction error. 

(C,) and universal gas constant per gram molecular weight 

constants for the particular gas. The error for the 

range of Mach numbers is given by 

The specific heat at constant r 

A. 2 

The error for the supersonic Mach number range can be found using 

the Rayleigh supersonic pitot formula, as 

A. 3 

The relative error of the Mach number (WM) is used in the mass 

flux error determination. 

The error in the mass flux was determined by assuming the flow 
106 

contains only the u velocity componenf. The mass flux error can be 

expressed in terms of the density (PI, M, and the sound speed (a) by 

Therefore, the error in the static temperature (TI and sound speed 

is needed in addition to Eqs. A.1, 4.2, and A.3. By assuming that 

the local total temperature is the same as the supply temperature, 

the static temperature error is 

12 y-1 2 -1 AT/T = AT~/T~ - [MAM(y-l) + M AyIC1 + 7 M I A.5 

The local sound speed error ten can be determined by 

By combining Eqs. A.4 to A.6, the mass flux error term can be 

expressed as 

A.7 

Relative error in the Mach number and mass flux was examined 

over a range of Mach numbers from one to three, since the flow was 
107 

supersonic over most of the flow field. Also, the relative error 

terms were evaluated for helium or nitrogen injection over a range 

of mab, fractions from zero to one. The tunnel supply conditions 

and assumed measurement error must be defined to obtain the relative 

error terms. The static and pitot pressure were determined by the 

Rayleigh supersonic pitot formula for a given value of M, injectant 

mass fraction (a.), and for the nominal supply pressure of 2.07 MPa. 

Static temperature was determined for a particular value of M, a 

and a nominal total temperature of 300 K. From Sec. 2.3, the values 

J 

j' 

of the assumed measurement error were taken as 1. K for Tt, 862 Pa 

for P, 3.70 KPa for Pt, and 0.02 for the mole fraction. Results 

from three typical cases of M, a and species are presented for 

discussion in Figs. A.l and A.2. 

j' 

Typical trends in the percent error in the calculated Mach 

number are shtwn in Fig. A.1. For nitrogen injection with 

= 0.10, the results are seen to have a smal 1 maximum percent 'j 

error of 0.6 for M = 1.75. This trend with M for nitrogen injection 

was essentially the same for other values of a For helium 

injection, the Mach number error is observed to have a large 

3' 

dependence on M and a 

in M is less than 2.2 percent. 

increased dramatically over the entire M range examined. 

in Mach number increases to a maximum of 9.2 percent for M = 1.75 

and then decreases to about 4.5 percent by M = 2.3. 

For values of ai c 0.50, the maximum error 3' c 

As a. decreases to 0.10, the error 

J 

The error 

The M error is 

essentially insignificant for nitrogen injection. However, the M 

error may be large in the mixing region for helium injection; 

essentially in regions of low helium concemtration, where the M 
108 

3 

2 

t.1 

1 

ORIQlNAL PAGE 19 

OF ?OOR QUALITY 

e, a; = 0.10 

0 2 4 6 8 10 

Figure A.l. Relative Mach Number Error. 
109 

error increases dramatically. 

Typical trends for the mass flux error are shown in Fig. A.2, 

For nitrogen injection with uj = 0.10, the error increases from 

almost zero for M = 1 to 2.2 percent for M = 3. For helium 

injection with aj = 0.10, the trend and values are observed to be 

very similar to the nitrogen case except near a small peak at M = 

1.5. A similar trend occurs for helium injection with a = 0.50. 

For this case, the mass flux error rises to peak value (3.1 percent) 

at M = 1.6; then decreases to a local minimum of about 1.7% (for M = 

2.2) before increasing to a value of 3.3 percent for M = 3. 

Therefore, thece results show that the mass flux error as a result 

of measurement errors should be small for either helium or nitrogen 

injection. 

j 

The contribution of the measurement errors hcs been examined 

for both injectants. The measurement errors contribute less than a 

few percent error to the calculated local Mach number (for nitrogen 

injection) and mass flux. However, the possible measurement error 

contribution to the calculated Mach number may be large for helium 

injection in the mixing region, since the error increases dramatically with the decrease in helium concentration. 
110 

3 

2 

M 

1 

ORIGJNAL PAGE iS 

OF POOR QUALiTY 

*- I I 

0 2 4 6 8 

Figure A.2. Relative Class Flux Error.