NASA Contractor Report 4129 

Part II 

NASA-CR-4129-PT -2 

19880014368 

Acoustically Excited Heated Jets 

II-In Search of a Better Understanding 

J. Lepicovsky, K. K. Ahuja, W. H. Brown, 

M. Salikuddin, and P. J. Morris 

CONTRACT NAS3-23708 

JUNE 1988 

UlNGLEY RESCARCI-l C'-NTEC? 

NI\S/\ 

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https://ntrs.nasa.gov/search.jsp?R=19880014368 2019-03-14T19:40:22+00:00Z
NASA Contractor Report 4129 

Part II 

Acoustically Excited Heated Jets 

II-In Search of a Better Understanding 

J. Lepicovsky, K. K. Ahuja, 

w. H. Brown, and M. Salikuddin 

Lockheed Aeronautical Systems Company-Georgia 

Marietta, Georgia 

P. J. Morris 

Pennsylvania State University 

University Park, Pennsylvania 

Prepared for 

Lewis Research Center 

under Contract NAS3-23708 

NI\SI\ 

National Aeronautics 

and Space Administration 

Scientific and Technical 

Information Division 

1988 
FOREYORD 

This report was prepared by Lockheed Aeronautical Systems CompanyGeorgia Division, Marietta, Georgia for NASA-Lewis Research Center, 

Cleveland, Ohio under contract NAS3-23708, entitled "Experimental 

Investigation of the Effects of Acoustic Excitation on Hot Jet Mixing." 

The work was performed under a two phase effort. 

Mr. James R. Stone was the Project Manager for NASA-Lewis Research Center 

for the Phase I effort. Lockheed's Program Manager was Dr. H. K. Tanna. 

Dr. Ed Rice was the Project Manager for NASA-Lewis Research Center for the 

Phase II effort. Lockheed's Program Manager was Dr. K. K. Ahuja. 

The program was conducted over a period of five years. During this 

period, however, the originally proposed goals for this study were 

substantially modified by the NASA project manager and emphasis was put on 

the ivnestigation of excitability of high speed, highly heated jets. 

Because of this, the final report presents a chronological rather than a 

thematic development of the subject. 

Technical help from Messrs. R. H. Burrin, C. R. Huie, and J. F. Songer is 

particularly acknowledged. 

The authors are particularly grateful to Mr. Uwe von Glahn of NASA-Lewis 

for his continuous support, various lively discussions and useful 

suggestions during the course of this work. 

iii 
This Page Intentionally left Blank 
CONTENTS 

SUMMARY 

Page 

1 

1.0 INTRODUCTION . . . . . 2 

2.0 A CLOSER LOOK AT THE DISCREPANCIES BETWEEN MEASUREMENTS AND 

3.0 

4.0 

THEORETICAL PREDICTIONS . . . . . . . . . . . . 4 

2.1 INTRODUCTORY REMARKS. . . . . . . . . . . 4 

2.2 CALCULATIONS. . .. ............. 4 

2.2.1 The Effect of Jet Exit Mach Number. . . • . • . 4 

2.2.2 The Effect of Jet Temperature. . . . 9 

2.2.3 The Effect of Initial Boundary Layer Thickness. 14 

2.2.4 The Development of the Unexcited Jet. • 18 

2.3 DISCUSSION OF THE THEORETICAL PREDICTIONS 18 

SELF EXCITATION TESTS . . . . • 

3.1 MEASUREMENT PHILOSOPHY .. 3.2 TEST RESULTS ........ . 3.2.1 Unbaffled Jet Data .. 3.2.2 Baffled Jet Data .• 

3.2.3 Conclusions for the Self-Excitation Tests. 

EXTERNAL EXCITATION OF HEATED JETS . . . . . . . . . 4.1 GENERAL REMARKS ............... . 4.2 TEST FACILITY AND THE EXTERNAL EXCITATION SOURCE. 

4.3 PROCEDURE TO MEASURE EXCITATION LEVELS. 

4.4 RESULTS . . . . . . . . . . . . 4.4.1 Unheated High Speed Jet ......... . 4.4.2 Heated High Speed Jet ........•.. 

22 

22 

25 

25 

25 

29 

30 

30 

30 

34 

43 

45 

45 

5.0 EFFECTS OF NOZZLE-EXIT BOUNDARY LAYER CONDITIONS ON JET 

EXCITABILITY . . . . . . . . . . . . . . . . • • . . . . 48 

5.1 INTRODUCTORY REMARKS . . . . . . . . . . . . . . • . 48 

5.2 NOZZLE-EXIT BOUNDARY LAYER CHARACTERISTICS. . . . . 48 

5.2.1 Boundary Layer Total-Head Velocity Profiles. . 48 

5.2.2 Integral Characteristics. . . . . . . • . . • •. 49 

5.2.3 Shape Factors. . . . . . . . . . . • . . . 53 

5.3 BOUNDARY LAYER MODIFICATION. . . . . . . . . . 57 

5.4 EXCITATION TESTS WITH MODIFIED BOUNDARY LAYERS. . . . .. 63 

5.4.1 Unexcited Jets . . . . • .. 63 

5.4.2 Excited Jets . . . . . .. 68 

5.5 CONCLUSIONS.. . . . . 74 

LIST OF SYMBOLS 

REFERENCES . . . . 

v 

84 

85 
SUMMARY 

This is Part 2 of a three-part report on the excitability of heated jets 

under the influence of acoustic excitation. Our efforts to understand the 

lack of excitability of high speed heated jets by internal excitation are 

described here. The theoretical predictions discussed in Part I are 

examined in detail to find explanations for the observed discrepancies 

between the measured and the predicted results. Additional testing was 

performed by studying the self excitation of the shock containing hot jets 

and also by exciting the jet by sound radiated through source tubes 

located externally around the periphery of the jet. The effects of 

nozzle-exit boundary layer conditions on jet excitability was also 

investigated. It is concluded that high speed, heated jet mixing rates 

and consequently also the jet excitability strongly depends on nozzle exit 

boundary layer conditions. Considerable further work is still needed to 

understand the excitability of the heated jets before they can be 

controlled effectively by artificial excitation. 
1.0 INTRODUCTION 

This report is Part 2 of a three-part report on the excitability of heated 

jets under the influence of acoustic excitation. The effects of internal 

excitation on jet mixing were described in detail in Part 1. The 

excitation sound in this case emitted from eight acoustic drivers located 

some distance upstream of the nozzle exit. Effects of boundary layer 

thickness, jet Mach number, excitation level, and excitation frequency were 

measured for both heated and unheated jets. Detailed flow visualization 

was also made to substantiate most of the observed effects. The most 

important conclusion of these results was that we were able to excite 

unheated jets at all jet Mach numbers examined, but the highly heated jets 

were found to be excitable only at the low jet Mach numbers. For example, 

at a jet Mach number (M·) of 0.3, the heated jet was even more excitable 

than the unheated jet, but at an Mj = 0.8, the heated jet did not appear to 

be excitable. 

This lack of excitability for the high Mach number jets was not only 

disappointing, but was contradictory to the theoretical predictions 

according to which heated jets should in fact be somewhat more excitable at 

a given jet Mach number and excitation level and excitation Strouhal 

number. 

In this Part 2 of the report are described our efforts to understand the 

above anomalous behavior of hot jets. After having discovered the above 

results, we repeated our experiments and indeed the same results were 

obtained. The first step, therefore, was to reexamine the theoretical 

predictions and look for some obvious explanation. An assessment of the 

predictions versus measurements was, therefore, made first and is described 

in the next section. As a result of this assessment, it was concluded that 

a new and more powerful acoustic source was required. In addition, a new 

method of directly measuring the acoustic excitation levels was needed. It 

was decided that the use of an external excitation source will fulfill 

these requirements. But before designing and fabricating this source, some 

unique experiments were performed that indicated what kind of excitation 

levels will be needed if the experiments with the external source were to 

be successful. These experiments are described in Section 3.0. The 

results from these experiments, which incorporated studying the effects of 

naturally occurring screech in supersonic jets on jet flow behavior, helped 

us reach some very important conclusions about the excitability of the 

heated jets. The adopted method of excitation level measurement is also 

presented in the same section. 

The results for the external excitation are presented in Section 4.0. The 

jet in this case was excited by sound impinging right at the nozzle lip. 

2 
The sound was directed at the 

eight electroacoustic drivers. 

outside the flow, true levels of 

nozzle lip. 

lip by eight equispaced tubes connected to 

Since the tube openings were located 

excitation were measured just outside the 

Finally, the last section, Section 5.0, describes experiments on the 

effects of nozzle-exit boundary layer conditions on jet excitability. This 

task was added to the original program in an effort to understand limited 

excitability of highly heated jets at certain jet operating conditions. 

The results, acquired under this task, indicate that nozzle-exit boundary 

layer conditions play an important role as far as jet excitability is 

concerned. 

However, this conclusion is based on a narrow range of jet operating 

conditions. Further work is still needed to generalize the derived 

conclusions for a broader range of jet operating conditions. 

3 
2.0 A CLOSER LOOK AT THE DISCREPANCIES BETWEEN 

MEASUREMENTS AND THEORETICAL PREDICTIONS 

2.1 INTRODUCTARY REMARKS 

The purpose of this section is to examine the response of a high Mach 

number heated jet to upstream acoustic excitation. The predictions are 

based on an analysis which has been reported in References [2.1], [2.2], 

and [2.3]. The details of the analysis will not be repeated here. 

However, it is useful to review the elements of the model. For a given 

excitation level and frequency and given jet operating conditions, the 

coupling between the acoustic excitation and the jet instability waves is 

calculated. The degree of coupling is a function of the local width of the 

jet. Once the instability wave, which has zero amplitude at the jet exit, 

is excited, its growth is calculated on the basis of inviscid instability 

theory. The development of the jet flow itself, which may be characterized 

by a few scaling parameters, such as the jet mixing layer thickness, the 

jet centerline velocity and the maximum turbulent kinetic energy, is 

determined from an integral energy analysis. Simple models, based on the 

eddy viscosity concept, have been used to describe the production of 

turbulent kinetic energy and the interaction between the excited 

instability wave and the small-scale turbulence. It should be emphasized 

that the model is based on a compressible flow analysis. An analytic 

solution to the thermal energy equation, Crocco's relationship, is used to 

relate the local static temperature to the local jet velocity. 

This section first considers the predicted and measured response of an 

unheated jet at both low and high Mach numbers. The effects of jet heating 

are then examined. The influence of the jet exit boundary layer thickness 

on the jet response is also considered. Finally, a discussion of the 

discrepancies between prediction and experiment, and suggestions for key 

experiments to either confirm or invalidate the prediction model for high 

temperatures, is given. 

2.2 CALCULATIONS 

2.2.1 The Effect of Jet Exit Mach Number 

For unheated jets some comparisons between prediction and experiment were 

given in References [2.1] and [2.3]. Those experiments were conducted at 

Mach numbers of 0.58 and 0.78. Further comparisons are made here with the 

4 
data given by Chan [2.4] for a Mach number of 0.2 and further data given in 

Reference [2.1] at a Mach number of 0.78. These comparisons provide 

further confirmation that the model predicts successfully the properties of 

cold, excited jets for a wide range of Mach numbers. 

A critical test of the prediction scheme is its ability to predict the 

pressure level of the excited instability wave on the jet centerline. This 

level provides an indication of the presence of an instability wave which 

influences the development of the jet. It should be noted that the model 

predicts the absolute level of the excited instability wave for a given 

excitation level. 

Figure 2.1 shows a comparison between the predicted centerline pressure 

level and the measurements by Chan [2.4]. Taking the pressure level at the 

jet exit to be 125 dB, the predicted maximum wave amplitude on the jet 

centerline is 2.5 dB below the measured value. Taking an excitation level 

of 130 dB gives only a 1 dB difference. For these levels of excitation, 

which are well above the 'threshold' level for this jet Mach number, the 

non-linear response of the jet can be seen. The peak moves closer to the 

jet exit. This corresponds to an increase in the spreading rate of the jet 

and decrease in the potential core length. The more rapid drop in the 

instability wave amplitude with axial distance compared to the measured 

values is probably due to the influence of small-scale pressure 

fluctuations towards the end of the potential core. 

A similar eomparison between prediction and experiment is shown in Figure 

2.2. Several excitation levels are considered for this jet exit Mach 

number, however, this time for high jet exit Mach number of 0.8. The 

predicted 'threshold' level for this Mach number is much higher, at about 

Le = 122 dB, so the instability wave response is nearly linear. This can 

be seen by comparing the relative amplitude between the instability wave 

peak and the excitation level. In all cases, this ratio is approximately 

21 dB. This is confirmed by the measurements and the agreement, bearing in 

mind the absolute nature of the predictions, is excellent. 

Figure 2.3 shows the effect of excitation level on the relative Mach number 

on the jet centerline at X/D 9. This ratio was used extensively in 

Reference [2.2] and is the ratio of the centerline Mach number for the 

excited case to its value in the unexcited case. The predictions indicate 

that there is no change for excitation levels less than 120 dB. This is 

confirmed by the measurements. This excitation level corresponds to the 

'threshold' level reported by Moore [2.5] of 0.08 percent of the jet exit 

dynamic head. The measurements indicate that at the highest excitation 

levels, the relative Mach number is as low as 0.83. This value is not 

predicted by the present model. This is probably related to the simplicity 

of the turbulence models for production and dissipation. For the sake of 

simplicity, it has been assumed that these models have the same empirical 

coefficients in all regions of the jet. This assumption could be relaxed 

5 
A Experiment: Chan [5 ] 

Prediction: S 0.375, M. 0.197 

Le 125 dB J 

e --..... ---- L 130 dB 

e 

20 

r--

~ 

""d 

Lf) 

N 

r-l 

r-l 

p.. 

'-' 

0 

r--

r-l 

p.. 

'-.. 

p.. -10 '-' 

M 

0 

rl 

0 

N 

0 1 2 3 4 5 6 

X/D. 

J 

Figure 2.1 Centerline pressure level in a low Mach number~ unheated jet 

6 
Prediction Experiment L (dB) e Pred ic tion: M. = 0.806, T /T 1.0 

6. J r a 

124 S 0.39 

e -----..- 0 130 Experiment: M. 0.78, T /T = 1.0 

J r a ------ 0 138 S 0.4 

e 

160 

0 

150 

"'""' Ctl 

P-I 

If) 

I 

0 

r-l 

~ 140 N 

r-l 

CJ 

H 

.. ~ 130 '"Cl 

'-' 

P 

CJ 

() 

P4 

110~----~------~--=-----L------~-------d------~ 

o 2 4 6 8 10 

X/R. 

J 

Figure 2.2 Centerline pressure level in a high Mach number, unheated jet 

7 
.-.. 

0'\ 

Or""") 

0 

"-:x: 

'-' 

8 

• Experiment) Relative Mach Number 

o Prediction 

6 Predicted relative half width 

1.0 

0.9 

0.8 

100 110 

0.08% 

120 130 140 

Test Point 1 

Mj 0.806, Tr/Ta 

S 0.39 

e 

\\\ 

150 

1.0 

0.9 

0.8 

160 

Excitation Level, Le (dB) 

1.0 

-II) 

Or""") 

0 

"-:x: 

'-' 

Figure 2.3 Effect of excitation level on centerline Mach number 

and jet width 
and somewhat better agreement obtained, but this would violate the basic 

intent of the model, which attempts to model the basic physical processes 

with the minimum of empIrICIsm. The overall good agreement between the 

predictions and experiments provides justification for this approach. 

Also shown in Figure 2.3 is the predicted relative half-width of the jet at 

X/O = 5. These predictions indicate that there is a larger relative change 

in this parameter with excitation than in the centerline Mach number 

further downstream. Thus this ratio would be used as a measure of the 

response of the jet. 

These calculations, and those previously reported, indicate that the 

prediction model is based on the correct physical processes. In the next 

subsection, the effects of jet temperature on the response of the jet to 

excitation is examined. 

2.2.2 The Effect of Jet Temperature 

Figure 2.4 shows the predicted response of a jet to excitation for the same 

Mach number as in Figure 2.3. However, the jet is heated in this case to a 

stagnation temperature ratio of 2.29. The threshold level is seen to have 

been reduced slightly by the increase in the jet temperature. The relative 

changes in the centerline Mach number and the jet thickness are somewhat 

lower than the predicted changes for the unheated case as can be seen by 

comparison with Figure 2.3. However, the measured values indicate that 

there is no change in the jet centerline Mach number for the range of 

excitation levels considered and the excitation Strouhal number of 0.39. 

From the viewpoint of the predictions, the decrease in the jet's response 

with higher temperature is r~adily understood. The details of the 

prediction model and definition of the coupling coefficients used in this 

model are given in Reference 2.3. Here, Figure 2.5 shows a comparison of 

the calculated coupling coefficients for the heated and unheated cases. 

The real and imaginary parts are shown since the relative phase of the 

acoustic excitation wave and the excited instability wave is important. 

However, the magnitude of the coupling coefficient gives a gross indication 

of the receptivity of the jet. Since the magnitude is relatively 

independent of the jet temperature, it can be inferred that the initial 

growth in amplitude of the instability wave or the receptivity of the jet 

will be similar in both cases. Figure 2.6 shows the calculated growth rate 

of the instability wave as a function of the local jet width for the two 

cases. Though the maximum growth rate for the heated case is higher, the 

unheated case shows growth for a wider range of jet thicknesses. This 

results in the centerline pressure levels shown in Figure 2.7. The excited 

instability wave grows to a high amplitude close to the jet exit and then 

decays rapidly. The instability wave in the unheated case has a large 

9 
10 

o Predicted relative Mach number Test 

6 Predicted relative half width M. 

J 

S 

e 

1.0 

0.9 

Point 

0.806, 

0.39 

'0 , 

4 

" 

T IT 

r a 

2.29 

1.0 

,-... 

If') 

0.9 

0.8L-------~------~------~------~------~-------J 0.8 

100 110 160 120 130 140 

Excitation Level, L (dB) e 

150 

Figure 2.4 Effect of excitation level on centerline Mach number 

and jet width 
'" 

U 

H 

p... 

0.5 

Figure 2.5 

C • pl 

0.04 

Hot: M. 

J 

Cold: M. 

J 

0.08 

b/R. 

J 

0.806, T IT = 2.29 

r a 

0.806, T IT = 1.0 

r a 

0.12 0.16 

Variation of coupling coefficients with jet width for heated 

and unheated jets 

11 
1 ? 

Or-) 

p::; 

H ~ 

I 

2 

1 

~ 

\ 

\ 

" , 

, 

, 

Hot : M. 

J 

Cold: M. 

J 

0.806, T IT 

r a 

0.806, T IT r a 

2.29 

1.0 

o ~------~-------i~------~~~~=--__ ~------~--------, 

------- " 

------ -.... ....... 

-1 ~------~ ______ ~ ______ _d ________ ~ ______ ~ ______ _ 

o 0.2 0.4 0.6 0.8 1.0 1.2 

b/R. 

J 

Figure 2.6 Variation of axial growth rate with jet width for heated 

and unheated jets 
M. == 0.806, S = 0.39, L 140 dB 

J e e 

Hot T IT 2.29 

r a 

Cold: T IT = 1.0 

r a 

17o.------~------_T-------_r------,_------~----_, 

120L-----~2------~4~----~6-------8~----~1~0------

Figure 2.7 

X/R. 

J 

Comparison of the predicted centerline pressure levels for 

heated and unheated jets 

13 
amplitude over a larger axial extent. Since the finite amplitude wave only 

influences the jet development when it is above a particular high level, 

approximately a local value of 150 dB in this case*, the instability wave 

for the unheated jet interacts significantly over a wider range. This 

results in a greater change in the jet properties in the unheated case. 

Figures 2.8 and 2.9 show the predicted effect of excitation level on the 

relative Mach number and the jet thickness for a Mach number of 0.305 with 

no heating and a stagnation temperature ratio of 2.74 respectively. It can 

be seen that the 'threshold' level is reasonably predicted. As in the high 

Mach number case, the relative changes are greater in the unheated case for 

values of excitation well above the 'threshold' level. However in this 

case, though measurements of the effect of excitation level were not made, 

the measurements reported in Reference [2.2] and in Part I show that the 

heated jet is more responsive to excitation than the unheated jet. 

Thus it is clear that the prediction scheme is unable to match the measured 

data for the case of heated jets. In order to find the reason for this 

discrepancy, the influence of the initial boundary layer thickness and the 

effects of jet heating on the development of the unexcited jet have been 

examined. 

2.2.3 The Effect of Initial Boundary Layer Thickness 

Careful measurements of the initial boundary layer thickness as a function 

of jet temperature have been made [2.2]. These indicate that at a fixed 

exit Mach number, the boundary layer thickness decreases as the stagnation 

temperature increases. 

In the prediction model the mean velocity is assumed to have a Gaussian 

shape at all points downstream of the jet exit. In fact, there is a 

transition from a boundary layer profile to this Gaussian form. Thus the 

choice of an initial thickness of b/RJ 0.02 was based on matching the 

momentum thicknesses of the boundary layer and by a comparison between the 

predicted jet development and measurements in the unexcited case [2.1]. 

Figure 2.10 shows the effect of the initial jet thickness on the peak level 

of the instability wave on the jet centerline. The location of this peak 

may vary along the jet centerline. For a range of initial thicknesses up 

to twice the value used in the present calculations, there is little change 

in the peak value. There is also very little change in all the other 

predicted properties of the developing jet. It is only for very thick 

initial boundary layers that the jet's response to acoustic excitation is 

reduced. 

*This level is an estimate based on calculations for a wide range of jet 

conditions [2.1]. 

14 
,-.. 

0\ 

.f""') 

0 

........ 

:x: 

'-' 

o Predicted relative Mach number M = 0.305, T IT 1.0 

j r a 

6 Predicted relative half width S 0.46 

1.0 

0.9 

0.8 

80 90 

e 

0.08% 

--"--0........ ....... ....... 0. 

"" " '" ~ , 

"" 

,. 

100 110 120 

Excitation Level, L (dB) e 

1.0 

""-

CV1 

"I""") 

0 

'-:x: 

""~ '-' 

'> "-

0.9 

0.8 

130 140 

Figure 2.8 Effect of excitation level on the jet centerline Mach 

number and jet width 

15 
16 

0 Predicted relative Mach 

6, Predicted relative half 

2p Ip.v. 2 

e J J , 

number 

width 

(%) 

M. 

J 

S e 

0.014 0.046 0.144 

1.011"""""' ..... R 

0.9 

0.8 

80 90 

0.08% 

100 110 120 

Excitation Level, L (dB) e 

0.305, T IT 

r a 

0.46 

1.0 

0.8 

130 140 

2.74 

M "'" 

II 

Figure 2.9 Effect of excitation level on the jet centerline Mach 

number and jet width 
160 

150 

140 

o 

Figure 2.10 

M. 

J 

S 

e 

0.806, T IT = 2.29 

r a 

O 39 L = 140 dB . , e 

0.04 0.08 0.12 

Initial Thickness, b IR. 

o J 

0.16 

Predicted effect of initial thickness of jet mixing layer on 

peak centerline pressure level 

17 
2.2.4 The Development of the Unexcited Jet 

It is important to assure that the unexcited jet development is being well 

predicted, since the spreading rate of the jet, for example, has a 

significant effect on the development of the instability wave. It is known 

that both the jet Mach number and the jet temperature alter the rate at 

which a jet develops. Figures 2.11 and 2.12 show a comparison between the 

measured and predicted centerline Mach numbers for the unheated and heated 

jets respectively. The simple nature of the integral scheme is the cause 

of the discontinuity in the derivative of the centerline Mach number at the 

end of the potential core. Though the agreement is not perfect, it is 

clear that the model is able to predict the different rates of development 

of both heated and unheated jets. 

2.3 DISCUSSION OF THE THEORETICAL PREDICTIONS 

The reason for the discrepancies between the predicted response of the 

heated jet and its measured response remains unclear. In view of the 

success of the model for the unheated case it would seem that the essential 

physical processes have been correctly modeled. In order to either confirm 

or invalidate the theory further measurements are required. These are 

discussed below. 

It is essential that the excitation level at the jet exit be known. This 

is particularly important at the high Mach number condition since the 

'threshold' level is so high. The measurement of the excitation level 

should be as direct as possible. It should be noted that the best 

agreement between prediction and experiment occurs when the pressure level 

at the jet exit, and along the jet centerline, has been measured directly. 

It is probable that the transmission coefficient of the nozzle is 

influenced by the flow velocity and temperature. This influence should be 

determined. Without a confident measurement of the excitation level the 

experimental data may be misleading. 

The prediction scheme is based on velocity as a dependent variable and the 

Mach numbers have been computed using Crocco's relationship. In case this 

relationship does not hold, particularly in the developed jet and for high 

temperatures, the experimental data should be converted to velocity data 

using the corrected total temperature measurements. 

The single point 

centerline at 9 

18 

measurement of the 

diameters provides a 

relative Mach 

useful means 

number on the jet 

for measuring the 
0.6 

0.5 

o 

Figure 2.11 

0 

5 

Unexcited Unheated 

Test Point 1 

Prediction: 

Experiment: 

X/D. 

] 

M. 

] 

M. 

] 

Jet 

0.806, T /T 1.0 

r a 

0.798, T /T 1.0 

r a 

10 

Variation of the centerline Mach number with axial distance 

19 
20 

0 

1.0~--------------------~ 

0.9 

'r) 0.8 ;:;:-; 

"'-

~ 

0.7 

0.6 

0.5 

o 

o 5 

Unexcited Heated Jet 

Test Point 4 

Prediction: M. 0.806, T /T 2.29 

J r a 

Experiment: M. 0.806, T /T 2.28 

J r a 

o 

10 

X/D. 

J 

Figure 2.12 Variation of the centerline Mach number with axial distance 
response of the jet to excitation. However, it is to be expected that the 

greatest influence of the jet excitation will be observed closer to the jet 

exit. Thus it is proposed that radial traverses in the annular mixing 

region of the jet be performed. These can be used to calculate the 

relative jet half-width as predicted in subsection 2.2. It is expected 

that these relative changes will be greater than those for the Mach number 

further downstream and will provide a more sensitive measure of the jet's 

receptivity. 

Once the excitation level has been accurately determined, the laser 

velocimeter can be used, in the heated jet, to detect the presence and 

properties of the excited instability wave. This is most easily 

accomplished using the phase averaging technique along the jet centerline. 

A detailed survey of the mean velocity and turbulence levels will provide 

data to further confirm that the properties of the unexcited jet are being 

correctly modeled. They will also enable the predicted changes in the 

turbulent kinetic energy to be verified. The use of the laser velocimeter 

will enable a direct measurement to be made of velocity and will verify the 

previous measurements based on total pressure and temperature probes. 

The availability of this data, particularly the careful verification of the 

actual excitation level, will provide essential data to either confirm or 

suggest improvements in the present prediction procedure. 

It should be noted that at the time these recommendations were made, it was 

expressed by the NASA technical monitor that it was important to 

demonstrate that high Mach number heated jets can be controlled by 

excitation. As discussed in Section 1.0 and in the subsequent section, not 

all the recommendations given above could be followed through. Instead, 

attempts were made to increase the excitation levels at the exit by 

installing an external excitation source, the levels of which could be 

measured directly around the jet periphery. 

21 
3.0 SELF-EXCITATION TESTS 

As explained in the previous section, it was conceivable that for the test 

conditions at which little change was observed in the jet structure as a 

result of acoustic excitation, the true excitation levels were not high 

enough. It was, therefore, decided to install a new source of sound so 

that the opening of the source tubes were located just outside the heated 

jet. It was expected that by so doing, the effects of flow on sound 

propagation to the nozzle lip will be minimized, and also it will be 

possible to measure the true levels of excitation sound by placing a 

microphone right at or near the jet lip outside the jet flow. 

Before embarking upon a detailed design of an external sound source, 

however, it was important to have some guidelines as to the possible 

magnitude of excitation that might be adequate. 

In this section some unique tests are described that enabled us to design 

the external excitation source and which also let us derive some 

categorical conclusions about the excitability of supersonic hot jets. 

3.1 MEASUREMENT PHILOSOPHY 

It is a well known fact that screech from supersonic shock-containing jets 

is, in essence, a result of some form of self excitation of the jet by the 

sound emitted from some distance downstream of the jet [Ref. 3.1 - 3.3]. 

In fact, if the jet cannot be excited, the screech will not be present. It 

was decided, therefore, to first determine if the heated jet used in our 

study showed the evidence of the presence of screech. If present, a 

measurement of its amplitude near the nozzle lip will indicate an order of 

magnitude that is needed to excite the hot, high speed jet used here. 

While we were acquiring these data, it was thought that some extremely 

useful results would be obtained if we could come up with a method to 

modify the level of screech at the nozzle lip with simultaneous measurement 

of the flow behavior. Based upon some earlier experience at Lockheed 

[3.4], it was decided to mount a large baffle just upstream of the nozzle 

lip as shown in Figure 3.1. In a similar study by Ahuja [3.4, 3.5], it was 

found that by moving the baffle axially, the screech could be modified, and 

in some cases suppressed completely. It was confirmed by Ahuja that the 

presence of screech excited a well defined large-scale structure or 

instability wave in the jet, which completely disappeared on suppressing 

the screech. A typical result from this study is shown in Figure 3.2 for 

an unheated jet. 

22 
N 

W 

Figure 3.1 Baffle arrangement for the "Self Excitation" tests 
Figure 3.2 

24 

Changes produced in the jet flow structure by traversing the 

baffle by less than 0.16 cm (1/16 in). (PR = 2.197) 
In the present tests, the jet was heated to reservoir temperature of 670 K 

and it was exhausted at a Mach number of 1.12. These are the same 

conditions at which internal excitation was found to have little effect on 

the jet flow structure. 

3.2 TEST RESULTS 

3.2.1. Unbaffled Jet Data 

The noise spectra from the heated supersonic jet were monitored at 2.54 cm 

(1 inch) from the nozzle lip in the plane of the jet exit. As shown in 

Figure 3.3, a well defined tone was observed, which became noticeable only 

when the jet became supersonic. This is the tone associated with the 

screech. The level associated with this screech tone was found to be 137 

dB. In our internal excitation studies, this high level could not be 

achieved at this jet operating condition and could be part of the 

explanation as to why we were unable to excite the heated supersonic jet. 

The mere presence of a screech in the heated jet indicated that the heated 

jet is excitable and negated the earlier tendencies of concluding, based 

upon the results obtained from internal excitation, that heated jets may 

not be excitable. 

3.2.2 Baffled Jet Data 

Having established the evidence of the presence of screech and its 

magnitude near the lip, the baffle shown in Figure 3.1 was mounted, and the 

corresponding noise spectra measured by the microphone mounted near the 

nozzle lip. This time, the baffle was also traversed by small distances 

upstream of the nozzle lip. The corresponding spectra are shown in Figure 

3.4. Clearly the screech magnitudes changed drastically, as a function of 

the baffle location. (This is because of the change in the feedback path 

length [see Reference 3.4]). 

For those baffle locations for which the screech noise levels were 

different, the jet total pressure distribution along the centerline was 

measured with a pitot probe. It was indeed found, that the higher the 

screech level, the larger was the jet Mach-number decay rate. Typical 

results are shown in Figure 3.5. Although no measurements were made to 

establish the effects of the presence of the baffle on entrainment, it is 

expected, based upon available evidence [3.6], that the baffle will have 

little effect on the velocity profiles. 

25 
tv 

'" 

CD 

\) 

I 

& 

140 

120 

100 

~ Screech 

fD/Vj - 0.56 

80 L--1-~~~~~ .... , a 2. 4. 6. 8. Hl. 12. 14. 16. 18. 

F re9uenoy - KHz 

Figure 3.3 Near field jet noise sepectrumof the bare jet 

(Mj = 1.12 1 Tt = 670 K1 R = 2.54cm, e*= 90°) 
"" '-J 

140 

CD 

-0 120 

I 

fu 

100 

80 

x L"'( in) 

____ 1.5 --- ---

~._____ 2.0 IrO.5 

fiaf f1 f' 

--- D 

__ -,-='f-~ rt-----Pitot Prohe 

Fr~uenoy - KHz 

Figure 3.4 Near field jet noise spectra with the baffle located at 

different position. 

(Mj = 1.12, Tt = 670K, R = 2.54cm, e*= 90°) 
28 

1600~~--~---r--'-~T---r--'---T--~--'---~~~~--__ ............. "~ 

Pressure ratio 

1500 

M· J 1.12 

Tt 670 K 

1400 

1300 

1200 

1100 

1000 

900 Bn f f 1 (' 

1 3 

= 

5 

, . 

"- ~ , . 2.196 , 

x 

\ 

, 

~ 

\ 

\ 

'8 

\ 

\ \y 

\ . 

\ 

~ 

\ 

--- \ -- - -- -

--"-------- R ---

Pitot Prohe 

7 9 

Axial Location, X/O 

\ 

\ 

~ 

\ 

11 

No Baffle 

(Screech Level 

140 dB) 

With Baffle 

at L*'= 1.5 in 

(Screech Level 

127 dB) 

\ 

\ 

"-

, 

\. 

13 

Figure 3.5 Effect of suppressing screech noise on centerline mean velocity 

decay 

(0 = 5.08 cm,O BAFF = 8.7 cm) 
3.2.3 Conclusions for the Self-Excitation Tests 

The results presented here are rather important in that they point out that 

a heated supersonic jet is excitable so long as the excitation levels are 

high enough. They also provided us an impetus to go ahead and design and 

fabricate the external excitation source. 

29 
4.0 EXTERNAL EXCITATION OF HEATED JETS 

4.1 GENERAL REMARKS 

It was shown in Part 1 of this report that high-speed, highly heated jets 

do not appear to respond to internal upstream acoustic excitation as 

strongly as the low speed heated and unheated jets. One of the possible 

reasons for this behavior was attributed to the fact that the actual 

excitation levels at the nozzle exit plane might not have been sufficiently 

high to produce the desired response in the high-speed, high temperature 

jets. In addition, the excitation levels at the nozzle exit plane were not 

measured directly for the heated jets, but were deduced from the cold jet 

measurements assuming no effect of the flow temperature on the efficiency 

of the acoustic excitation source section and the supply duct. 

To improve the efficiency of the excitation source and overcome the above 

mentioned uncertainty, it was decided to design and fabricate a new source 

section which would excite the flow externally. The new external 

excitation source is described in the next subsection. The adopted method 

of excitation level measurement is presented in Subsection 4.3. 

4.2 TEST FACILITY AND THE EXTERNAL EXCITATION SOURCE 

A detailed description of the Lockheed's jet flow facility and associated 

instrumentation is given in Part 1 of this report. Here, a description of 

the external excitation source only is presented. 

Before the new external excitation source section was designed, three 

separate source configurations, shown in Figure 4.1, were checked out for 

their acoustic performance. Configuration #1 consisted of a 3.5 cm 

diameter tube connected directly to the 3.5 cm opening of an Altec driver 

body, whereas in configuration #2 a converging duct with an inlet of 10 cm 

diameter and a source opening of 3.15 cm diameter was used. Thus in 

configuration #2, the sound from the Altec driver opening (dia = 3.5 cm) 

escaped into a larger space before converging back into a smaller opening. 

As shown below, this arrangement radiated up to 20 dB less noise through 

the final source opening. 

To determine if noise amplitude could be increased considerably by 

decreasing the size of the source opening, configuration #3 was tested. In 

this configuration, an inverse conical horn was used such that the duct 

30 
.-I 

'**" ~ 

o 

-,-\ 

~ 

cO 

\..l 

:::l 

bl) 

-,-\ 

4-1 

t:: 

o 

() 

Q) 

() 

\..l 

:::l 

o 

(/l 

31 
32 

C'J 

:f:I::: 

s:: 

o 

oM 

.J-I 

en 

Io-! 

;:; 

00 OM 

4-l 

s:: 

o 

C) 

(/) 

C) 

Io-! 

;:; 

o 

t/) 
(j) 

() 

l-I 

::; 

o 

rJ) 

33 
carrying the sound decreased in size from 3.5 cm to approximately 0.64cm. 

As shown in Figure 4.2, the performance of configuration #3 was comparable 

to that of configuration #2, but configuration #1 was far superior. (These 

measurements were made at about 1.2 cm from the exit along its centerline.) 

It was decided therefore to use configuration #1 for the designed external 

excitation source section. 

A sketch of the new external excitation source section for Jet Flow 

Facility is shown in Figure 4.3. It consists of a steel sleeve clamp 1 

which slips over the 10 cm air supply duct just upstream of the nozzle. Two 

sets of 8 tubes, 2 and 4, are welded on this tube in the fashion of the 

spokes of a wheel at 450 intervals. These form the supports and guides for 

the driver assemblies 3, 5, and 6 which are connected by lugs, 9 and 10, to 

the fork end of rods 8 and 11, which can move in the tubes 2 and 11 and be 

secured with set screws. In this way the source tubes which are fitted 

inside the source tube sleeves 3 and secured with set screws, may be moved 

relative to the jet. In the sketch, the driver assembly is shown at an 

angle of 300 to the jet axis with the 1.38 diameter source tube at its 

closest proximity to the jet shear layer (it could be placed closer if the 

exit of the source tube were smaller or made elliptical). The driver 

assemblies may be moved vertically to change the distance of the source 

tube exit from the jet and, in addition, may be pivoted about the bolt in 

the left hand lug 8 to change the angle. The slots in the lug 10 allow 

this rotation. Finally, the driver tube 5 may be moved in the sleeve 3 to 

allow tuning of resonant frequencies of the driver tube. Photographs of 

partially assembled source section are shown in Figure 4.4. 

The assembled external excitation source section, mounted on the supply 

duct of the jet facility, is shown in photographs in Figure 4.5. 

4.3 PROCEDURE TO MEASURE EXCITATION LEVELS 

A constant, sufficiently high level of excitation was desired throughout 

the required Strouhal number range. Driver limitations however, forced the 

compromise on a nominal level of 147 dB, measured at the center of the 

nozzle exit, which was attainable over all but the upper end of the 

frequency range. The natural frequencies of the system, i.e., where local 

peaks in level occur, were chosen for the test points. At each of these 

frequencies, the voltage input to the power amplifiers was adjusted to 

produce a jet-exit centerline excitation level of 147 dB in the absence of 

flow. The corresponding input level was recorded and subsequently used to 

reproduce that condition with flow. Table 4.1 shows the test point 

frequencies and levels for the heated jet runs. Some details of the 

adjustments made to obtain the same level and phase output from each of the 

34 
160.0 ---..-------------------. 

150.0 

~ 

m 

"C 140.0 

Z 

~ 

Z 

....... 

~ 130.0 

...-

~ -J 

C. 120.0 

(/) 

110.0 

Figure 4.2 

Configuration #1 

/- 0 --/ ~-.......... 

c/D D- O 

Configuration #2 

/0 

I \ / "- -6. 

-------6. -<-6. \ / 

0 "-

" o~ _ 0"" 

Configuration #3 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 

FREQUENCY (KHZ) 

Sound pressure levels measured at 1/2 inch from the exits of 

the three, source openings 

35 
W 

0'\ 

" DRIVER MOVES 

IN & OUT FOR 

TUNING 

CHANGE t 

DISTANCE 

FROM JET 

100 W AL TEC 

DRIVER 

~ 

SCREWS 

Figute 4.3 

®LUG:jLUG DETAIL -

PROVIDES PIVOT 

TO CHANGE ANGLE CD ROD OF SOURCE TUBE 

TUBE 

2. a NOZZLE 

LUG 

External source section 

TUBE 

" 

EIGHT IDENTICAL 

ASSEMBLIES AT 

45° INTERVALS 
W 

'-.J Figure 4.4a Front view of partially assembled source section 
w 

co 

Figure 4.4b 

Rear view of partially assembled source section 
39 
40 

~ .r! 

? 

(l) 

"0 

.r! 

[J) 

I 

c: 

o 

.r! 

-I-' 

() 

(l) 

[J) 

(l) 

() 

~ 

;::i 

o 

tf) 
PEAK EXCITATION EXCITATION 

FREQUENCY VOLTAGE LEVEL 

Hertz Vrms dB 

150L~ 1.14 146.8 

1894 1.065 146.8 

2310 0.092 146.8 

2502 1.18 146.8 

2817 1.125 146.8 

3009 0.94 146.8 

3015 0.98 146.8 

3200 1.18 146.8 

3499 1.18 146.8 

3702 0.99 146.8 

3880 1.16 146.8 

4136 1.245 143.9 

4412 1.24 144.6 

4700 1.29 139.6 

4999 1.25 137.9 

5415 1.33 141.0 

5606 1.30 140.0 

5994 1.33 135.1 

Table 4.1 Typical excitation frequencies and levels. 

41 
acoustic drivers are discussed below. 

Driver Tube Adjustment 

The driver tubes shown in Figure 4.3 have a sliding section that can be 

used to tune the system and to compensate for differences in driver 

diaphragm position, cut length of the tube, or tube end position. Initial 

adjustment was made to peak the output of each tube, one at a time, as 

measured at the centerline of the jet nozzle and at a single representative 

frequency and driver input level. This provided the maximum output that 

could be achieved by length adjustment. Care was taken to assure that each 

path was the same in terms of effective wavelengths. That was necessary so 

that at other frequencies the same relative phase would exist among all the 

tubes. 

The tubes were adjusted by watching the waveform from the jet-axis 

microphone as the tube lengths were varied about the minimum common length 

that produced a peak level. The peak was identified visually, and the tube 

was locked into place at that length. 

Level Setting 

After the initial length setting, the power amplifiers, which share a 

common input signal, were adjusted one at a time to obtain a common signal 

level at the centerline microphone. At this point, the drivers should all 

be producing essentially the same signal so that optimum power is delivered 

to the jet region. 

Phase Adjustment 

A final phase adjustment was made by examInIng the phase between the input 

signal to the amplifiers and the signal at the centerline microphone, again 

taken one driver at a time. Slight adjustments in tube length brought the 

phases to within a few degrees of each other at a frequency of about 4 kHz. 

This was considered adequate since the maximum frequency, hence the 

shortest wavelength and greatest phase deviation possibility, would be 

about 6 kHz. 

Excitation Levels 

The excitation levels quoted throughout this report are those measured at 

the nozzle axis at X/D = 0.125 at the focus of the driver tubes with no 

nozzle flow. The measurements were made directly in the no-flow case. The 

centerline level was measured using a microphone on the nozzle axis, and 

the amplifier setting was recorded for that level. This amplifier setting 

was then used to produce that same excitation level for both no-flow and 

flow cases. 

42 
Circumferential Measurements 

After all the adjustments were made, one final check was made to verify the 

uniformity of the excitation level around the jet. For this check, all the 

drivers were operated simultaneously and at the same input level. 

Measurements were made along the lip line and in line with each driver tube 

exit. The uniformity of the excitation levels outside the nozzle lipline 

for the frequency that most excited the jet is shown in Figure 4.6. The 

measurements here correspond closely to the center of the driver tubes and 

to the spaces between adjacent tubes. The uniformity is seen to be quite 

good; the spread in level is + 2 dB, and the maximum phase difference is 

13.5 degrees. The average of the circumferential levels is 148.7 dB, while 

the centerline level is 149.9 + 0.5 dB. 

Measurements made outside the shear layer show higher levels with flow than 

without. The level with unheated flow was 2 dB + 1 dB higher, and the 

level with heated flow was 1.5 dB + 1 dB higher. 

4.4 RESULTS 

The major objective of this part of the study was to verify the 

excitability of highly heated, high speed jets using the external 

excitation source section. Thus, the experimental effort was focused on 

the following two jet operating conditions. 

Test 

Condition 

1 

2 

Mach 

Number 

0.8 

0.8 

Total 

Temperature 

290 K 

670 K 

At these jet operating conditions, experiments were carried out to 

determine the excitation Strouhal number that produces the strongest 

effects on the jet plume. As for the internal excitation, presented in 

Part 1, the Strouhal number optimization was based on changes of local Mach 

number on the jet centerline at nine nozzle exit diameters downstream of 

the nozzle exit plane. 

Acoustic excitation conditions were restricted to a relatively narrow range 

because of the low response of acoustic drivers for frequencies above 6 

kHz. This limits the excitation Strouhal number to the range of Stj ~ 0.7 

at the extreme jet operating condition (Test Condition 2). The excItation 

level at the nozzle exit plane on the jet centerline was kept at 147 + 2dB 

43 
44 

2.0 mm 

TOP 

LOOKING 

INTO THE 

NOZZLE 

f :=; 1504 Hz 

V. := 1.0 Volts 

1 

i := 149.9 dB 

Figure 4.6 Excitation source circumferential directivity. 
during the course of the experiments. 

4.4.1 Unheated High Speed Jet 

A distribution of relative Mach number as a function of excitation Strouhal 

number for the unheated jet of Mj 0.8 is plotted in Figure 4.7. The 

centerline excitation level is 147 dB up to the Strouhal number 0.75. 

Then, the level decreases to 135 dB at the maximum plotted Strouhal number. 

As seen in this figure, the response of the unheated jet is very 

pronounced. The jet is affected at practically all examined Strouhal 

numbers. The most effective Strouhal number range is from 0.25 to 0.6 

when the jet centerline local' Mach number at X/O 9 decreases to an 

average to 75% of its value for the unexcited jet. At the Strouhal number 

of 0.3, the jet exhibits a sharp local mlnlmum with the relative Mach 

number dropping to as low as 62%. It has to be pointed out, however, that 

the jet shows tremendous scatter in this response in the range of Strouhal 

numbers from 0.23 to 0.36. Obviously, in this region, the jet is very 

sensitive to small changes in the excitation Strouhal number. 

4.4.2 Heated High Speed Jet 

The effect of excitation Strouhal number on high speed, highly heated jet 

(Mj = 0.8, Tt = 670 K) is shown in Figure 4.8. The centerline excitation 

level was kept constant at 147 dB up to the Strouhal number of 0.50. After 

that, the excitation level drops to 135 dB at the maximum Strouhal number. 

As seen in Figure 4.8, the response of this jet to the acoustic external 

excitation is significantly weaker than is the response of the unheated 

jet. Nevertheless, the relative Mach number distribution indicates that 

this highly heated, high speed jet is excitable at certain Strouhal 

numbers. Two local minima in the relative Mach number distribution can be 

observed. The first minimum is at the excitation Strouhal number 0.19, 

where the relative Mach number drops to 90% of the unexcited value. The 

second minimum, at the Strouhal number 0.5, is a little shallower at about 

94% of the unexcited value. Thus, it appears that the heated jet of Mj = 

0.8 and Tt = 670 K is excitable in two relatively narrow regions centered 

around Strouhal numbers 0.19 and 0.5. Outside of these two regions, no 

effects of excitation on heated jets were observed. The validity of this 

finding, of course, is restricted to the range of applied excitation 

levels. 

In conclusion, it was a worthwhile exercise to conduct these tests with the 

external excitation in that they showed that if high enough excitation 

levels are used, the heated jet, even at high speeds can be modified by 

artificial excitation. The precise mode in which coupling takes place in 

this case can, however, be determined only by further work. 

45 
46 

c -:l 1.1 

"'" x 

(l.) 

2 1 

cr: 

w 

CD 0.9 

2 

:::> 

Z 

I 0.8 

u 

« 

2 

W 0.7 

> 

~ 

« 

--1 

w 0.6 

0::: o 0.5 1 

STROUHAL NUMBER, 

1.5 

St . 

J 

Figure 4.7 Excitation Strouhal number effects on 

relative Mach number on jet centerline at 

X/D = 9. M. = 0.8; T = 290 K (unheated) J t 
~ 

w 

1.1 

1 

CD 0.9 ~ 

:::> 

z 

I 0.8 

u 

<t: 

:2 

W 0.7 

> 

r-

<t: 

---I 

w 0.6 ~ o 0.5 1 

STROUHAL NUMBE'R I 

1.5 

St . 

J 

Figure 4.8 Excitation Strouhal number effects on 

relative Mach number on jet centerline at 

X/D = 9. M, = 0.8, T = 670 K (heated) J t 

47 
5.0 EFFECTS OF NOZZLE-EXIT BOUNDARY LAYER 

CONDITIONS ON JET EXCITABILITY 

5.1 INTRODUCTORY REMARKS 

An experimental program carried out under this contract took various turns 

during the course of its conduct. Tasks were modified or added to the 

original program in accordance with the updated NASA-Lewis requirements in 

an effort to demonstrate that fluid mIxIng in high-speed highly heated jets 

can be enhanced by artificial excitation. This resulted in a requirement 

to thoroughly investigate the effects of nozzle-exit boundary layer 

conditions on excitability of heated free jets. Similar experiments were 

already initiated under the Phase I effort in 1983. However, they were not 

completed as intended because of funding limitations. Due to these 

limitations, the accomplished results of these experiments in 1983, 

reported in Part I, Section 5, did not satisfactorily answer the question 

of the role of nozzle exit boundary layer conditions on jet excitability. 

The current set of experiments on the effects of nozzle-exit boundary-layer 

conditions on jet excitability was carried out in three stages. The first 

stage consisted of a thorough investigation of nozzle-exit boundary-layer 

behavior under various jet operating conditions. The second stage was 

devoted to boundary layer modification to eliminate the dependence of the 

exit boundary layer on jet operating conditions. Finally, in the third 

stage, after eliminating the nozzle exit boundary layer dependence on jet 

operating conditions, the external excitation experiments were carried out 

for selected jet operating conditions. 

5.2 NOZZLE-EXIT BOUNDARY LAYER CHARACTERISTICS 

5.2.1 Boundary Layer Total-Head Velocity Profiles 

Boundary-layer velocity profiles were calculated from total-head velocity 

distributions measured across the nozzle-exit boundary layers. All the 

velocity profiles were calculated assuming a flow with constant static 

temperature equal to the core flow temperature. The reason for this simple 

approach was that the temperature distribution across the investigated 

heated-flow boundary layers was unknown. 

For a given profile survey, all the calculated velocity values at discrete 

points across the boundary layer were fitted with an analytical curve based 

48 
on the parametric cubic spline fitting subroutine ICFSKU from the IMSL 

library [5.1]. As examples, four velocity profiles containing the 

experimental points as well as their fitted curves are shown in Figure 5.1. 

Boundary-layer thicknesses Ao.995 and A were calculated from the fitted 

analytical curve as distances from the nozzle inner wall where the local 

velocity reaches 99.5% and 100% of the velocity value in the jet core. A 

distribution of the boundary-layer thickness Ao.995 as a function of the 

nozzle operating conditions, expressed in terms of the jet exit Reynolds 

numbers, is shown in Figure 5.2. As seen in this figure, the boundarylayer thickness rapidly decreases from an initial value with an increasing 

jet Reynolds number and reaches- its minimum for a critical Reynolds number 

of ReJ = 0.3*106. After that, the boundary-layer thickness rapidly 

increases, reaches a local maximum and then decreases again. In spite of a 

noticeable scatter of the boundary-layer thickness values, it is clear from 

Figure 5.2 that the flow temperature does not play any significant role for 

nozzle operating conditions below the critical Reynolds number. Above the 

critical Reynolds number (ReJ 0.3*106), however, the effects of the 

elevated flow temperatures are clearly traceable. Three separated branches 

appear to emerge for the nozzle operating conditions above the critical 

Reynolds number, each associated with a certain jet total temperature (285 

K, 500 K, and 700 K). Thus, in this region, the flow temperature must be 

considered as an additional parameter to the jet-exit Reynolds number, 

influencing the nozzle-exit boundary-layer development. 

5.2.2 Integral Characteristics 

Boundary-layer integral characteristics provide a basic description of the 

velocity distribution behavior in a particular boundary layer. The three 

commonly used integral characteristics are displacement, momentum, and 

energy thicknesses (&, e, E). These characteristics are defined as follows 

[5.2]: 

" 

<5 == J ( 1 - f2 ~ ) dy 

o p},U~ 

where A is the boundary layer entire 

local velocity reaches the core-flow 

thickness (a radial distance where a 

velocity) and subscript A denotes 

49 
..., 

L 1.0 

"'" 0... 

2 

0.8 

~ 

w 

m 0.6 

:2 

=:) 

z 0.4 

::r::: 

u 

« 

:2 0.2 

~ 

w 

~ 0.0 

0.0 

..., L 1.0 ~ 

0... 

2 0.8 

~ 

w 

m 0.6 

2 

=:) 

z 0.4 

::r::: 

u 

« 

2 0.2 

~ 

w 

~ 0.0 

0.0 

Figure S.la,b 

50 

0.5 1.0 1.5 

DISTANCE, 'j (mm) 

0.5 1.0 1.5 

DISTANCE, 'j (mm) 

2.0 

2.0 

UNTRIPPED JET 

MJ = 0,106 ± 0,004 

T TJ = 703.4 ± 2,7 K 

TTJ / TA = 2.39 

UJ = 55.6 ± 2,1 m,s-1 

ReJ == 41,230 

PA = 98.181 kPa 

TA = 294.9 K 

DJ == 50.8 mm 

UNTRIPPED JET 

MJ = 0.338 ± 0.000 

TTJ = 277.5 ± 0.5 K 

T TJ / T A == 1.00 

UJ = 111,7 ± 0,3 m.s-1 

ReJ = 419,370 

P A = 98.250 kPa 

T A == 276.8 K 

DJ == 50,8 mm 

Nozzle exit boundary layer head-velocity profiles. 

a. 

b. 
...., 

2 1.0 

'--. 0... 

2 

0.8 

0:.:: 

w 

CD 0.6 

2 

::::::) 

z 0.4 

I 

U 

« 

2 0.2 

.-J 

w 

0:.:: 0.0 

0.0 

...., 

2 1.0 

'--. 0... 

2 

0.8 

cr::: 

w 

CD 0.6 

2 

:::J 

z 0.4 

I 

U 

« 

:2 0.2 

.-J 

w 

0:.:: 0.0 

0.0 

Figure 5.1c,d 

0.5 1.0 1.5 

DISTANCE, Y (mm) 

0.5 1.0 1.5 

DISTANCE. Y (mm) 

2.0 

2.0 

UNTRIPPED JET 

MJ = 0.860 ± 0.002 

TTJ:::: 499,7 ± 1.8 K 

T TJ / T A = 1.75 

UJ = 359.4 ± 1.4 m.s--' 

Re J = 585,560 

PA = 97.630 kPa 

T A = 284.8 K 

DJ = ,50.8 mm 

UNTRIPPED JET 

MJ == 0.956 ± 0,001 

T TJ:::: 280.4 ± 0,3 K 

T TJ / T A == 1.00 

UJ := 295.4 ± 0.3 m.s-1 

Re J = 1,412,630 

PA = 97.837 kPa 

T A == 281.1 K 

DJ "" 50.8 mrn 

Nozzle exit boundary layer head-velocity profiles. 

c. 

d. 

51 
Ln 

/',) 

TOTAL TEMPERATURE: o 285 K , !J. 500 K, 0 700 K I <> 800 K • 'i1 900 K 

.......--... 2.0 

E 

E '--.-/ 

If) 

m 

m 

0 1.5 r~ ,< cP 00 00 0 

o fl 0 

'Yo o !J. 0 0 

(J) flo I.::. 0 

0 0 (J) fl fl 0 0 

w 0 0 

!J. !J. 

z o 0 1.0 ~o 9 8 0 ~ 'ilv fl 

u 8 ~~o 0 I 

f- §t<> 

-l 

m 0.5 

a 0.2 0.4 0.6 0.8 1.2 1.4 1.6 

REYNOLDS NUMBER, ReJ ( * 10

6 

) 

Figure 5.2 Nozzle exit boundary layer thickness distribution. 
values at the outer edge of the boundary layer. As mentioned above, the 

velocity calculation is based on an assumption of a constant flow 

temperature. The calculation of the integral characteristics is based on 

the assumption of a constant property fluid (TT = const, p = const). The 

integral characteristics were calculated from fitted analytical curve using 

numerical integration utilizing the IMSL subroutine DCADRE [5.1]. 

A dependance of the integral characteristics on jet operating conditions is 

shown in Figure 5.3. As seen in this figure, the jet exit Reynolds number 

has a dramatic effect on these characteristics, resembling behavior of the 

boundary-layer thickness distribution shown in Figure 5.2. The data 

scatter in these plots appears to be smaller than that for the boundarylayer thickness distribution. 

Consider displacement thickness in Figure 5.3a. It decreases rapidly with 

an increasing jet Reynolds number and reaches its minimum for a critical 

Reynolds number of ReJ = 0.3*106. Beyond the critical Reynolds number, the 

displacement thickness suddenly increases and then remains more or less 

constant until the nozzle exit velocity approaches the transonic region 

where the displacement thickness starts slowly to drop off (ReJ = 1.2*106, TT = 285 K). A closer inspection of this plot reveals that above the 

critical Reynolds number the displacement thickness always drops off when 

the jet exit velocity reaches the transonic region which, for the elevated 

jet total temperatures, occurs at lower jet-exit Reynolds numbers (ReJ = 

0.6*106 , TT = 500 K and ReJ = 0.4*106 , TT = 700 K). Again, the effect of 

the jet temperature on the nozzle-exit boundary layer-development is 

independent from the effect of the jet-exit Reynolds number alone. 

A similar trend exists in the remaInIng plots in Figure 5.3 for the 

momentum and energy thickness development. The three branches for the flow 

temperatures of 285 K, 500 K, and 700 K are even more distinguishable in 

the region above the critical Reynolds number. After reaching their maxima 

beyond the critical Reynolds number, both the momentum and energy 

thicknesses gradually decrease with an increasing jet-exit Reynolds number 

without a noticeable drop off in the vicinity of the transonic region. 

5.2.3 Shape Factors 

Shape factors describe the 

The displacement-momentum 

as [5.2]: 

shape 

and 

of the boundary-layer velocity profile. 

energy-momentum shape factors are defined 

53 
Hoe 0 / e 

and 

H8e = 8 / e. 

The significance of the boundary-layer shape factors lies in detection of 

boundary layer transition from laminar to turbulent. For example, it is 

well established that for a flat-plate boundary layer, the displacementmomentum shape factor exhibits a sudden drop from a value of 2.6 for the 

laminar layer to a value of about 1.4 for the turbulent boundary layer 

[5.2]. 

As seen in Figure 5.4, at the jet Reynolds number of ReJ = 0.3*106, the 

displacement-momentum shape factor Hoe drops from 2.5 to 1.9 for the 

unheated flow (TT = 285 K), to 2.1 for the flow heated to 500 K, and onl~ 

to 2.3 for the flow heated to 700 K. Thus, the jet Reynolds number 0.3*10 

marks the end of the laminar regime of the nozzle exit boundary layer. In 

the transitional and turbulent regions, the value of the displacementmomentum shape factor strongly depends on the flow total temperature, as 

was already noticed in the case of the integral characteristics. It is 

higher for higher flow temperatures. After the boundary layer transition, 

the value of the displacement-momentum shape factor increases with an 

increasing jet Reynolds number. 

Analogous behavior can also be observed for the energy-momentum shape 

factor H8 e. In this case, however, the value of the shape factor increases 

for the laminar/turbulent transition. The increasing flow total 

temperature diminishes the rise of this factor during transition in 

comparison with the laminar boundary-layer value. 

As the nozzle exit velocity approaches the 

factors exhibit a reversal in their trends. 

the unheated flow (ReJ = 1.2*106 , TT = 285 K). 

0.6*106 , TT = 500 K and Re~ = 0.4*106 , TT 

scatter prevents drawing a SImilar conclusion 

The reason for this trend reversal is not quite 

transonic region, both shape 

This is obvious at least for 

For the heated flows (ReJ = 

= 700 K), the experimental 

with sufficient confidence. 

apparent. 

The findings from this part of the study can be summarized as follows: 

54 

For the laminar nozzle-exit boundary layer, the boundary layer 

thickness and integral characteristics are functions of the jet 

Reynolds number only. Shape factors, for the laminar exit 

boundary layer, are constant. No difference between heated and 

unheated jets was observed. 
"E TOTAL TEMPERATURE! 0 285 K. A 500 K • 0 700 K. <> 800 K . V 900 K 

g 0.4 v I I I I I I I 

(j) 

(j) 

W 

Z 

~ 

u 

I 

lIZ 

w 

2 

w 

U 

<t: 

-l 

Cl. 

(j) 

o 

[J 

0.3 

0.2 Io 

~ 0 0 0 0 0",0Ll. 0 0 

L.> t:. Ot:. t:. 

Va 

a 0 V 0 D "IDA 0 V IJ 

D D o '" 

00 o 

o 

00 

o o o o 

o 

-

-

0.1 ~ ____ L-I _____ L-I ____ ~I ____ ~I ____ ~I ____ ~I ____ ~I ____ ~ 

o 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 

REYNOLDS NUMBER. Re J ( * 106

) 

TOTAL TEMPERATURE: 0 285 K • A 500 K • 0 700 K , <> 800 K , V 900 K 

'E 0.3 .----r------"r----....,----,.I---rl---.,--'---r-I----, 

$ 

(j) 

(j) 

w 

Z 

~ 

u 

I 

t-

:2 

::::> 

Iz 

w 

:2: 

o 

:2 

0.2 I0.0 

o 

I 

0.2 

I I 

0.4 0.6 

o o 

I 

0.8 

00 

REYNOLDS NUMBER. 

00 00 

o 0 00 

1.6 

TOTAL TEMPERATURE: 0 285 K • A 500 K. 0 700 K . <> 800 K , v 900 K 

'E 0.3 

g 

(j) 

(j) 

w 

z 

~ 

u 

I 

I-

>--

C) 

0.2 

0.1 II 

o 0 o 00 

o 

en o '" 

Ll. DO 

o 0 voc:;rl AJ [J o 

"fS/ <> 

D 

, 

o 

o 00 o o 00 

o o 00 

Q 

c:r:: 

w 

Z 

w 0.0 L-____ L-__ ~ ____ ~ ____ ~I ____ ~ _____ ~I ____ ~I __ ~ 

o 0.2 0.4 0.6 0.8 1.2 1.4 1.6 

REYNOLDS NUMBER. ( * 106 ) 

Figure 5.3 Boundary layer integral characteristics. 

55 
TOTAL TEMPERATURE: o 285 K, t!. 500 K , 0 700 K , 0 800 K , 'il 900 K 

2.8 I I I I I 

~ 

'0 

:r: ° 0 " [¥@- ° ~ 2.4 ~91t:l"£ - cr:: o 00 0 0 

f- ~A 0 o 08 u A At!. 0 

Ii o l;, 00 

w 2.0 I- 00 - 0- Cb 0 0 ° 0 

« 0 

::r: 0 

VJ 

1.6 I I I I I I 

0 0,2 0.4 0.6 0.8 1 1.2 1.4 l.B 

REYNOLDS NUMBER, ReJ ( * 106 

) 

TOTAL TEMPERATURE: o 285 K, t!. 500 K, 0 700 K , 0 800 K , 'V 900 K 

1.8 I I I I I 

~ 

<v 

I 

1.7 - Cb 00 00 - cr:: 0 0 

0 o t!. A 00 

f- A t!.I:A A 0 0 o 00 U 0 

Ii 'V 0 00 o 0 

w 1.6 1-'i3~ "ovi S. 0 - 0-

« 

:r: 

VJ 

1.5 I I I I I I I 

0 0,2 0.4 0.6 0.8 1 1.2 1.4 1.B 

REYNOLDS NUMBER, Re J ( * 106 

) 

Figure 5.4 Shape factor distributions. 

56 
For the turbulent nozzle-exit boundary layer, the boundary 

layer thickness, integral characteristics, and shape factors 

are functions of the jet exit Reynolds number and flow 

temperature. The results show that the flow temperature, for 

the turbulent exit boundary layer, must be considered as an 

independent parameter. 

5.3 BOUNDARY LAYER MODIFICATION 

Boundary layer modification was aimed at elimination of the nozzle-exit 

boundary layer dependence on jet operating conditions. A number of 

parameters may characterize the nozzle-exit boundary layer conditions. 

The important parameters, from our point of view, are boundary layer 

displacement-momentum shape factor HS9 and boundary layer momentum 

thickness 9. Thus, the main objective of the boundary layer modification 

was to keep these two parameters constant, therefore, independent of the 

jet operating conditions. 

To achieve the above stated goal, it was decided to trip the boundary 

layer inside the test nozzle, similarly as it was done under the Phase I 

effort. This time, however, the tripping rings were placed relatively far 

upstream of the test-nozzle exit plane. (The test facility has been 

redesigned, after the Phase I experiments, to enable an easier access 

inside the test nozzle.) 

The main effort was devoted to 

a high speed, highly heated 

temperature of 670 K. Several 

diameters were employed. The 

a ring placed 67 mm upstream 

diameter was 1.63 mm. 

nozzle-exit boundary layer modification of 

jet of Mach number 0.8 and jet total 

tripping rings of different ring and wire 

most satisfactory results were achieved for 

of the nozzle exit plane. The ring wire 

The effect of jet operating conditions on untripped nozzle exit boundary 

layers is shown in Figure 5.5. This figure shows nozzle-exit boundary 

layer profiles for unheated and heated jets at Mach number 0.8. As seen 

in this figure, there is a significant difference between the nozzle-exit 

boundary layer profiles for an unheated jet and jet heated to 700 K. The 

unheated jet has a displacement-momentum shape factor (Hse) of 2.084 and 

momentum thickness (9) of 0.13 mm. The shape factor value indicates that 

the nozzle-exit boundary layer is in the transition between laminar and 

turbulent states. The jet heated to 700 K (Figure 5.5b), however, has a 

laminar nozzle-exit boundary layer profile with the following 

characteristics: Hse = 2.517, 9 = 0.10 mm. 

57 
..., 

::2 1.0 

"-lL 

:2: 

0.8 

cc 

w 

co 0.6 

:2: 

:::) 

z 0.4 

I 

U 

« 

2: 0.2 

--i 

w 

cc 0.0 

..., 

::2 1.0 

"-lL 

:2: 

0.8 

cc 

w 

co 0.6 

:2: 

:::) 

z 0.4 

I 

U 

« 

2: 0.2 

--i 

w 

cc 0.0 

Figure 5.5 

58 

0.0 0.5 1.0 1.5 

DISTANCE, Y (mm) 

0.0 0.5 1.0 1.5 

DISTANCE, Y (mm) 

2.0 

2.0 

UNTRIPPED JET 

MJ = 0.799 ± 0002 

TTJ = 289.1 ± 0.1 K 

TTJ / TA = 0.98 

UJ = 256.8 ± 0.7 m.s-1 

Re J = 1,060,300 

PA = 97.422 kPa 

T A = 293.7 K 

DJ = 50.8 mm 

UNTRIPPED JET 

MJ = 0.797 ± 0.002 

TTJ = 700.1 ± 1.1 K 

T TJ / T A = 2.54 

UJ = 395.8 ± 1.1 m.s- 1 

ReJ = .354,190 

PA = 98.181 kPa 

T A = 276.1 K 

DJ = 50.8 mm 

Nozzle exit boundary layer profiles of unheated and 

heated, untripped, Mach number 0.8 jets. 
The tripped boundary layer profiles for similar jet operating conditions 

are shown in Figure 5.6. As seen in this figure and in the previous one, 

there is no significant difference between untripped and tripped nozzle 

exit boundary layer profiles for unheated jets. The unheated tripped jet 

nozzle-exit boundary layer characteristics (Hoe = 1.901, e = 0.13 mm) are 

close to those of the unheated untripped jet. However, the heated-tripped 

jet boundary-layer profile noticeably differs from that for the untripped 

jet and it is similar, as planned, to the unheated jet nozzle-exit 

boundary layer profile. The boundary layer profile of the heated tripped 

jet has the following characteristics: Hoe = 1.911 and e = 0.15 mm. 

As seen from the above discussed results, the nozzle-exit trippedboundary-layer characteristics at a Mach number of 0.8 are not 

significantly altered with a change in jet total temperature. Thus, the 

selected way of boundary layer modification satisfied the requirement of 

elimination of the nozzle-exit boundary layer dependence on jet operating 

conditions. A summary of all nozzle-exit boundary layer characteristics 

for a jet Mach number of 0.8 is given in Table 5.1. . 

Similar experiments were conducted also for a jet exit Mach number of 0.3. 

A summary of boundary layer characteristics for untripped and tripped 

conditions for this jet exit Mach number is given in Table 5.2. As seen 

in this table, the same tripping ring generated a thicker, more turbulent 

nozzle-exit boundary layer at the jet Mach number of 0.3 than it did for 

the higher jet exit Mach number of 0.8. 

It should be noted here, that the tripped boundary layer momentum 

thicknesses of the Mach number 0.8 jet for unheated and heated conditions 

stay within the range of momentum thickness values generated naturally in 

the untripped jet (Figure 5.3). In the case of Mach number 0.3 jets, 

however, the tripped boundary layer momentum thicknesses are twice or 

three times the corresponding values for untripped jets. 

None of the tripping rings used generated identical nozzle-exit boundary 

layers for both, low and high jet exit Mach numbers. To exchange the 

tripping rings during excitation experiments, however, the external 

excitation section must be dismounted (Figure 4.5.). Because the 

excitation source tuning and calibration are laborious and time consuming 

procedures, it was decided to conduct excitation experiments only with the 

tripping ring which satisfied the main condition: that the nozzle-exit 

boundary layers for unheated and heated high speed jets be similar. 

59 
...., 

~ 1.0 

"-. 0... 

:2 

0.8 

0::: 

w 

co 0.6 

:2 

::::) 

z 0.4 

I 

U 

« 

2 0.2 

-.i 

w 

0::: 0.0 

0.0 

...., 

2 1.0 

"-. 0... 

:2 

0.8 

0::: 

w 

co 0.6 

2: 

::) 

z 0.4 

I 

U 

« 

2 0.2 

-.i 

w 

0::: 0.0 

0.0 

Figure 5.6 

60 

0.5 1.0 1.5 

DISTANCE, Y (mm) 

0.5 1.0 1.5 

DISTANCE, Y (mm) 

2.0 

2.0 

TRIPPED JET 

MJ = 0.790 ± 0.001 

T TJ = 284.1 ± 0.1 K 

TTJ I TA == 0,98 

UJ = 252.0 ± 0.4 m.s- 1 

ReJ == 1,074,390 

PA = 97,962 kPa 

TA = 290.4 K 

DJ "" 50.8 mm 

TRIPPED JET 

MJ == 0.787 ± 0.002 

T TJ = 651.6 ± 1.6 K 

T TJ ITA = 2,27 

UJ == 377.9 ± 1.5 m.s-' 

Re J = 378,670 

PA = 97.837 kPa 

TA = 287.3 K 

DJ = 50.8 mm 

Nozzle exit boundary layer profiles of unheated and 

heated, tripped, Mach number 0.8 jets. 
0\ 

,...... 

MJ TT HOa H08 0 

(K) (mm) 

a 8 

(mm) 

Rea ReJ 

0.80 289 2.084 1.658 0.26 0.13 0.21 2633 1,060,300 

Untripped 

0.80 700 2.517 1.603 0.25 0.10 0.16 694 354,190 

I 

I 

--t I 

0.79 284 1.901 1.700 0.25 0.13 0.22 2747 1,074,090 \ Tripped I 

0.79 652 1. 911 1. 717 0.29 0.15 0.26 1115 378,670 

I 

Table 5.1 Nozzle exit boundary-layer characteristics of Mach number 0.8 jet 
0'1 

I'V 

MJ TT Hoe H08 0 e 8 Ree ReJ 

(K) (mm) (mm) (mm) 

0.30 284 2.328 1.626 0.29 0.13 0.20 887 359,420 

Untripped 

0.30 700 2.522 1.598 0.27 0.11 0.17 246 118,690 

-----

0.30 279 1.590 1. 775 0.33 0.21 0.36 1470 364,170 

CPed 

0.30 653 1.516 1. 790 0.43 0.29 0.51 732 129,800 

Table 5.2 Nozzle exit boundary layer characteristics of Mach number 0.3 jet 
5.4 EXCITATION TESTS WITH MODIFIED BOUNDARY LAYERS 

After having finished the nozzle-exit boundary layer modification 

experiments, external excitation tests commenced. The excitation tests 

were conducted in the same manner as described earlier in Section 4.0. 

The jet response to the excitation Strouhal number was determined by 

measurement of flow Mach numbers at the jet centerline at nine nozzle exit 

diameters downstream of the nozzle exit plane. Accurate probe positioning 

at the jet centerline required repeated measurements of both vertical and 

horizontal jet-velocity profiles. This procedure was necessary because 

the nozzle geometric axis moved due to thermal expansions when the flow 

was heated. 

5.4.1 Unexcited Jets 

Radial profiles of unheated and heated unexcited jets of Mach number 0.8 

are shown in Figure 5.7. As seen in this figure, at this jet exit Mach 

number the effect of heating the flow was to provide noticeable decrease 

of the centerline local Mach number at X/D 9, thus indicating 

considerable broadening of the jet plume. 

Low speed unheated and heated jets of Mach number 0.3, however, behaved 

differently. As seen in Figure 5.8, where radial profiles for Mach number 

0.3 jets are depicted, no significant decrease of the centerline local 

Mach number at X/D 9 was observed due to the flow heating. These 

findings are summarized in Figure 5.9. In this figure, only the peak 

values of jet radial profiles are shown. The figure clearly points out 

the differences between the effects of flow heating at low and high jet 

exit Mach numbers. 

Radial profiles at X/D = 9 for Mach number 0.8 jets with tripped nozzle 

boundary layers are plotted in Figure 5.10. A comparison of Figures 5.7 

and 5.10 shows that a change in nozzle-exit boundary layer conditions 

itself caused changes in the flowfield of a heated Mach number 0.8 jet. 

For the heated jets, the flow Mach number at the jet centerline at X/D = 9 

increased from 75% of the jet exit Mach number for the untripped jet to 

82% of the tripped jet. For the unheated jets, however, the change is 

hardly noticeable. 

These results show the significance of the nozzle-exit boundary layer 

parameters on high Mach number free jet development. As described in the 

previous subsection, the applied boundary layer modification did not alter 

the nozzle-exit boundary layer parameters for the unheated jets of Mach 

number 0.8. In accordance with that, no significant changes in the jet 

flow Mach number at X/D = 9 were observed. 

63 
1.0 I I I UNTRIPPED JET -, 

:2 

"-.... 

Od ~f> 0.815 ± CL M = 0.001 .:d: 0.8 - J c- o T TJ = 287.8 ± 0.4 K 

a::: 0 6 W TTJ/TA= 1.00 0 /j, 

m 0.6 r 0 - U = 260.5 ± 0.5 m.s-' :2 0 ~ J 

=> 0 ~ ReJ Z =:: 1,101,090 

0 

I ~ 0.4 r - () 0 6'6 PA =:: 98.112 kPa « 0 

.:d: 0 '.6. TA = 287.7 K 

~ 0.2 r 0 ~ - a::: D = 50.8 mm 0 J 

Z X/DJ = 9.00 I I I 0.0 

-4 -2 0 2 4 

RADIAL DISTANCE, Y/R J 

1.0 \ -, , , UNTRIPPED JET 

:2 

"-.... 

0.818 ± CL M = 0.002 .:d: 0.8 - J r 

0& ~o T TJ = 671.1 ± 1.4 K 

a::: 

W 0 Q TTJ/TA= 2.30 

m 0.6 - 0 6 - uJ == 396.8 ± 1.1 m.s- 1 

:2 0 Q 

=> 0 Q Re J Z =:: 386,.390 

0 Q 

I 0.4 0 Q - () r 0 Q PA = 98.526 kPa « 0 0 

.:d: 0 °0 TA == 292.4 K 

~ 0.2 c- - a::: DJ == 50.8 mm 0 

Z X/D J =:: 9.00 I I I 0.0 

-4 -2 0 2 4 

RADIAL DISTANCE, Y/R J 

Figure 5.7 Radial profiles at X/D 9 of unheated and heated, 

untripped, Mach number 0.8 jets. 

64 
1.0 UNTRIPPED JET ""') 

:2 

""-

0.315 ± 0.004 a. MJ = ::2 0.8 

T TJ == 280.0 ± 1.0 K 

n::: 

w T T J I T A = 0,99 

IT) 0.6 UJ = 104.8 ± 1.5 m.s- 1 

::2 

~ \ ReJ z ::: 387,110 0 

I \ 0 

0.4 0 \ 0 0 PA = 98.733 kPa « 0 \ :2: 0 T A = 283.5 K 

0 

~ 0.2 0° 

" ex:: 0 DJ ::: 50.8 mm 0 00 

Z ocP X/OJ = 9.00 0.0 

-4 -2 0 2 4 

RADIAL DISTANCE, Y/R J 

1.0 UNTRIPPED JET ""') 

::2 

""-a. MJ ::: 0.321 ± 0.005 ::2 0.8 

T TJ = 795,0 ± 7.9 K 

n::: 0 

W T TJ I T A = 2.73 ° IT) 0.6 ° Q 

UJ = 177.2 ± 3.7 m.s-1 ::2 0 Q 

~ 0 a 

z 0 Q ReJ ::: 111.040 

0 a 

I 0.4 0 0 

0 0 Q PA = 98.664 kPa « 0 a 

2 ° 6

0 TA = 291.1 K 0° ~ 0.2 60. 

0° <)0 ex:: cPo DJ = 50.8 mm 0 ~6. z 0 ~t. X/OJ = 9.00 0.0 

-4 -2 0 2 4 

RADIAL DISTANCE, Y/RJ 

Figure 5.8 Radial profiles at X/O 9 of unheated and heated? 

untripped, Mach number 0.3 jets. 

65 
Figure 5.9 

66 

0.9 

J 

2 

~ 

D-

:2 

~ 0.8 

0 

I-- « 

cr:: 

0:::: 

W 

CD 

2 

:J 

Z 

:::r::: 

u 

<C 

2 

0.7 

0.6 

o 

o 

1 1.5 2 2.5 3 

TEMPERATURE RATIO, T TJ/T A 

Total temperature effects on centerline local Mach number 

at X/D = 9 of unexcited jets. 
1.0 ..., I I I TRIPPED JET 

:2 

"-... OC ~~ a... MJ = 0.801 ± 0.001 2 0.8 f- a -

<t, T T~ = 278.8 ± 0.2 K 

0::: 0 

W TTJ/TA = 1.00 

m 0.6 f- - UJ = 252.6 ± 0.5 m.s- 1 2: 

:J Re z J = 1,124,590 

I 0.4 I- - U 

« PA ::: 98.300 kPa 

L TA ::: 280.0 K 

~ 0.2 f- - 0::: OJ ::: 50.S mm 0 

Z 

X/OJ ::: 9.00 I I I 0.0 

-4 -2 0 2 4 

RADIAL DISTANCE, Y/R J 

1.0 I "'") I I TRIPPED JET 

2: 

"-... a... MJ = 0.802 ± 0.001 2 0.8 - 0 

~~ - 0 T T~ ::: 652.4 ± 0.8 K 

0::: 0 

w T TJ ITA = 2.34 

m 0.6 - - UJ ::: 384.6 ± 0.8 m,s-1 :2 

:) ReJ := 388,950 Z 

I 0.4 f- - U PA := 98.266 kPa « 

L TA := 279.0 K 

~ 0.2 f- -

0::: OJ := 50.B mm 0 

Z X/D J = 9.00 I I I 0.0 

-4 -2 0 2 4 

RADIAL DISTANCE, Y/R J 

Figure 5.10 Radial profiles at X/D 9 of unheated and heated, 

tripped, Mach number 0.8 jets. 

67 
For the Mach number 0.8 heated jets, however, the boundary layer tripping 

changed the nozzle-exit boundary layer characteristics, namely the 

momentum thickness and the displacement~momentum shape factor. 

Correspondingly, the flowfield measurements indicate closing of the jet 

plume and decreased mixing for the tripped; thicker, turbulent boundary 

layer in comparison to the untripped, thinner, laminar nozzle-exit 

boundary layer. This indicates that free jet mixing and development may 

also be controlled by nozzle exit boundary layer modification. 

Radial profiles for tripped unheated and heated Mach number 0.3 jets are 

shown in Figure 5.11. These radial profiles do not noticeably differ from 

the profiles for untripped Mach number 0.3 jets (Figure 5.8). No firm 

conclusions are presently based on this fact because, as mentioned above, 

the tripped nozzle exit boundary layer thickness of Mach number 0.3 jet is 

far beyond the range of naturally developed boundary layer thickness for 

these jet operating conditions. 

5.4.2 Excited Jets 

As mentioned above, the jet response to the acoustic excitation was 

determined by measurement of flow local Mach numbers at the jet centerline 

at X/D = 9. The excitation Strouhal number effects for the untripped jets 

of Mach number 0.8 were already discussed in Section 4.4. For 

convenience, the relevant plots are shown here again in Figures 5.12 and 

5.13 with the corresponding excitation levels added. In these figures, 

the flow Mach number of the excited jet is compared with the Mach number 

at the same point in the jet flowfield, but in the absence of acoustic 

excitation (peak values from Figure 5.7). As seen in Figure 5.12, the 

unheated jet is affected at practically all examined Strouhal numbers. 

The heated jet (Figure 5.13), however, shows significantly weaker response 

to the applied acoustic excitation. Furthermore, the jet response is 

limited to certain frequencies only. 

The excitation Strouhal number effects on unheated and heated tripped jets 

are shown in Figures 5.14 and 5.15. Apart from a small shift in the 

optimum excitation frequency, both jets show the same response to the 

acoustic excitation. For the optimum excitation frequency, the centerline 

flow Mach number at X/D 9 drops to 80% of the unexcited value, 

indicating the jet plume opening and increased mixing due to acoustic 

excitation. The similar response to external acoustic excitation by both, 

unheated and heated tripped jets is a significant result showing the 

nozzle-exit boundary layer conditions play key roles in jet excitability 

and mIxIng. When the nozzle-exit boundary layer conditions were 

identical, there was no difference between heated and unheated jets. 

68 
1.0 ..., 2 

'-....-.. a.. 

2: 0.8 r0::: 

w 

m 0,6 I- :2 

~ 

Z 

I 0.4 I- U 

« 

2: 

~ 0.2 I0.:::: 

0 

Z 

0.0 

-4 

1.0 ..., :2 

'-....-.. a.. 

2: 0.8 

0::: 

w 

m 0.6 2: 

~ 

Z 

I 0.4 u 

« 

2: 

2: 0.2 

0::: 

0 

Z 

0.0 

-4 

Figure 5.11 

I I I 

P'Di - 0 

0 

-

-

-

I I I 

-·2 0 2 4 

RADIAL DISTANCE, Y/R J 

-2 0 

RADIAL DISTANCE, 

TRIPPED JET 

M = J 0.304 ± 0.000 

T TJ = 276.9 ± 0.1 K 

TTJ/TA= 0,99 

UJ ==: 100.7 ± 0,2 m.s- 1 

Re J = 376,640 

PA :=:: 98.266 kPa 

TA ::::: 279.2 K 

oJ ::::: 50.8 mm 

X/OJ = g,OO 

TRIPPED JET 

MJ = 0,303 ± 0.002 

TTJ = 651.1 ± 2.3 K 

T TJ / T A = 2,33 

UJ = 151.9 ± 1.2 m,s-1 

Re J = 131,070 

PA = 98.266 kPa 

TA ::::: 279.9 K 

OJ = 50.8 mm 

X/OJ = g,OO 

Radial profiles at X/D = 9 of unheated and heated? 

tripped, Mach number 0.3 jets. 

69 
....... 

o 

c 

::s 

~ 

""'-x 

Q> 

:2: 

0::: 

w 

CD 

2: 

:::> 

z 

I 

U 

« 

2: 

~ 

W 

0::: 

Figure 5.12 

1.1 

to 

0.9 

0.8 

07r~ \1\1'7 \1 WVWWV 

\1\1 

0.6 \1 \1\1 

\1 

\1 

0 0.5 

STROUHAL NUMBER 1 St J 

-.J 

-1150 W 

> 

W 

-.J eo 

-i140 Z -0 

0 

1130 

1.5 

~ -.JCll 

IU 

X 

W 

UNTRIPPED JET 

MJ = 0_819 ± 0.001 

TTJ = 287.3 ± 1.1 K 

TTJ / TA = 1.01 

UJ = 261.5 ± 0.7 m.s-1 

ReJ = 1,099,070 

PA = 97009 kPa 

T A = 28·5.4 K 

DJ = 50.8mm 

X/OJ = 9.00 

Excitation Strouhal number effects on unheated, untripped, 

Mach number 0.8 jet. 
'-J 

t-' 

1.1 c 

:J 

~ 

'" x 1.0 Q) 

~ 

CL 

w 0.9 

CD 

"2 

::::> 

z 0.8 

I 

u 

<.( 

2 

..J 07[~ 'J'YW\JllWl 

W 

[y: 0.6 ~'Y ~ 'Y 

'J 

0 0.5 

STROUHAL NUMBER, 

-1 

---j150 W 

> 

W 

-1m 

---j140 z -0 

0 

1130 

1.5 

~ ~ f-.-l 

U 

X 

W 

St J 

UNTRIPPED JET 

M~ = 0.824- ± 0.003 

T TJ = 669.3 ± 3.9 K 

T TJ / T A = 2.32 

UJ = 399.2 ± 2.2 m.s- 1 

Re J = 385,560 

PA = 97.009 kPa 

T A = 288.5 K 

DJ = 50.8 mm 

X/OJ = 9.00 

Figure 5.13 Excitation Strouhal number effects on heated, untripped, 

Mach number 0.8 jet. 
" /'.:) 

2 

C 

:::J 

1.1 

~ 1.0 Q.) 

2 

8J 0.9 

ill 

2 

:) 

Z 0.8 

I 

U 

« 

2 0.7 

---l 

W 

cr:: 

Figure 5.14 

0.6 

---I 

150 W 

> 

\l \l \l \lWV \l \l V \l W 

---1m 

Z -0 

140 0 

~ QJ 

~---I 

TRIPPED JET 

MJ = 0801 ± 0.001 

TTJ= 279.1 ± 0.1 K 

TTJ / TA = 1.00 

UJ = 252.7 ± 0.2 m.s-1 

ReJ = 1,122.720 

PA = 98.300 kPa 

TA = 278.8 K 

DJ = 50.8 mm 

X/OJ = 9.00 

L-________ L-__ ~----L-----__ ~I 130 U 

X o 0.5 1.5 w 

STROUHAL NUMBER, StJ 

Excitation Strouhal number effects on unheated, tripped, 

Mach number 0.8 jet. 
...... 

w 

1.1 c 

:s ::;E 

.......... 1.0 x 

<1> 

::2: 

rY 0.9 w 

m 

2: 

:) 

z 0.8 

:r: 

0 

« 

::2: 0.7 I 

.-J 

W 

0::: 0.6 I-

---l 

--1 150 

\l'Il 'V\l'\Jl.J'V 'il'il 'il 'il 

W 

> 

W 

---lm 

-1140 "\l 

Z-o 

Q 

~ ---lCU 

fTRIPPED JET 

MJ = 0.801 ± '0.002 

TTJ = 652.7 ± 3.1 K 

T TJ / T A = 2.34 

UJ = 384.6 ± 1.8 m.s-t 

ReJ = 388,530 

PA = 98.266 kPa 

TA = 278.9 K 

OJ = 50.8 mm 

X/OJ = 9.00 

~--------~--------~------~1130 0 

X o 

Figure 5.15 

0.5 1.5 W 

STROUHAL NUMBER 1 StJ 

Excitation Strouhal number effects on heated, tripped j 

Mach number 0.8 jet . 
To assess the net gain of jet mixing enhancement due to acoustic 

excitation, the results must be compared on a common basis. In Figures 

5.12 through 5.15, the jet excitability was judged based on a relative 

change between excited and unexcited states. In Figures 5.16 through 

5.19, however, the flow Mach number at X/O 9 is normalized by the jet 

exit Mach number. There are no surprises for unheated untripped and 

tripped jets (Figures 5.16 and 5.18). Both jets respond similarly to the 

acoustic excitation. For heated jets, as shown above in Figures 5.13 and 

5.15, the tripped jet seemed to be more excitable than the untripped one. 

However, the heated tripped jet's initial centerline Mach number at X/O = 

9 was substantially higher than the one for the untripped jet. It appears 

that the greater excitability of the heated tripped jet results from the 

decreased jet mixing due to the boundary layer tripping as discussed 

above. A closer inspection of Figures 5.17 and 5.19 reveals that for the 

same excitation level of 147 dB the centerline flow Mach number at X/O = 9 

drops to approximately 65% of the jet exit Mach number regardless of the 

flow temperature or nozzle exit boundary layer conditions. It appears 

free jet mixing and development may be controlled by flow excitation as 

well as nozzle exit boundary layer modifications. 

For completeness, the results of excitation experiments for tripped, 

unheated and heated, Mach number 0.3 jets are shown in Figures 5.20 

through 5.23. No conclusions are derived from these results because of 

the noncompatibility of the nozzle-exit boundary layer conditions between 

untripped and tripped states for this jet exit Mach number. 

5.5 CONCLUSIONS 

Based on the above described experiments for Mach number 0.8, unheated and 

heated jet, the following conclusions were derived: 

1. The free jet mixing rate strongly depends on nozzle exit boundary 

layer conditions. 

2. Relative jet excitability, in terms of a ratio of flow local Mach 

numbers of excited and unexcited states at the optimum excitation 

frequency, is a strong function of nozzle exit conditions but is 

independent of flow temperature. 

3. Absolute jet excitability at the optimum excitation frequency, in 

terms of the ratio of the flow local Mach number to the jet exit 

Mach number for an optimum, appears to be a function of the 

excitation level only. 

74 
"'-.I 

IJ1 

-:I 

~ 

'-..... !l.. 

L 

0:::: 

w 

CD 

~ 

:J 

Z 

I 

(.) 

« 

~ 

~ 

0:::: 

0 

Z 

Figure 5.16 

0.9 

0.8 

0.7 

0.6 

05l~ 'iJ'iJ'l 'iJ W'iJ'ilil'iJ'ilil 

'iJ'iJ 

0.4 'iJ V''iJ 

'iJ 

'iJ 

0 0.5 

STROUHAL NUMBER, St J 

I 

i 

~ 

--1150 

--1140 

1130 

1.5 

...J 

W 

> W ,-., 

...J(l) 

Z -0 

0'--" 

~ ~ I-...J 

U 

X 

W 

UNTRIPPED JET 

MJ = 0.819 ± 0.001 

TTJ = 287.3 ± 1.1 K 

T TJ / T A = 1.01 

UJ = 261.5 ± 0.7 m.s-1 

ReJ = 1,099,070 

PA = 97.009 kPa 

T A = 285.4 K 

DJ = 50.8 mm 

X/DJ = 9.00 

Excitation Strouhal number effects on unheated, untripped, 

Mach number 0.8 jet. 
......, 

0\ 

J 

~ 

.......... 0... 

~ 

0::: 

w 

(I). 

:2 

:::) 

z 

:r: 

u 

« 

2 

~ 

0::: 

0 

z 

Figure 5.17 

0.9 

0.8 

0.7 

0.6 

0.5 l~ -1150 

V\lW\lllWl 

0.4 'iflV "V -1140 

\l 

'V 

~--------~------~~------~I 130 

o 0.5 1.5 

STROUHAL NUMBER, St J 

-1 

W 

> 

W 

-1 en 

Z-o 

o 

~ -1l1J 

I----' 

o 

X 

w 

UNTRIPPED JET 

M" = 0.824- ± 0.003 

TTJ = 669.3 ± 3.9 K 

T TJ / T A = 2.32 

UJ = 399.2 ± 2.2 m.s- 1 

ReJ = 385,560 

PA = 97.009 kPa 

TA = 288.5 K 

DJ = 50.8 mm 

X/OJ = 9.00 

Excitation Strouhal number effects on heated, untripped, 

Mach number 0.8 jet. 
-..J 

-..J 

-:l 

~ 

............ 

a.. 

~ 

0:: 

W 

m 

2: 

::::) 

Z 

I 

o 

« 

.2 

~ 0:: 

o 

Z 

09 h,.---' ~ 

0.8 ~ \ jl /" 

0.71- ~~ 

0.6 

0.5 150 

\l \l \l \l W'V \l \l \l \l 

0.4 140 

~------~--------~------~!130 

o 0.5 1.5 

STROUHAL NUMBER, ~J 

..J 

W 

> 

W 

..Jm 

z -0 

0 

~ ..Jv 

(3 

X 

w 

TR1PPED JET 

MJ = 0.801 ± 0.001 

T TJ = 279.1 ± 0.1 K 

TTJ/T A = too 

UJ = 252.7 ± 0.2 m.s- 1 

ReJ = 1,122,720 

PA = 98.300 kPo 

T A = 278.8 K 

OJ = 50.8 mm 

X/DJ = 9.00 

Figure 5.18 Excitation Strouhal number effects on unheated, tripped, 

Mach number 0.8 jet. 
""'J 

00 

0.9 ~ 

~ 

--........ a.. ~ 0.8 

0:::: 

W 

m 0.7 ~ 

:::::) 

Z 

I 0.6 

0 

« 

2 

::;i 0.5 r 

0:::: W'V'i1v:lJV\l\l\l'V 

0 

Z 

0.4 f-

~ 150 

'V\l 

-1140 

-.J 

W 

> 

W 

-1m 

z -0 

o 

i= Q.l 

<{-I 

j---: 

TRIPPED JET 

MJ = 0.801 ± 0.002 

TTJ= 652.7± 3.1K 

T'TJ / T A = 2.34 

UJ = 384.6 ± 1.8 m.s- 1 

ReJ = 388,530 

PA = 98.266 kPa 

TA = 278.9 K 

OJ = 50.8 mm 

X/OJ = 9.00 

~ ______ ~ ________ -L ________ ~I 130 U 

X o W 

Figure 5.19 

0.5 1.5 

STROUHAL NUMBER, St J 

Excitation Strouhal number effects on heated, tripped, 

Mach number 0.8 jet. 
'-J 

\D 

1.1 c 

j 

~ 

"-.. 

1.0 x 

<I> 

2 

n:::: 0.9 w 

co 

2 

:::) 

z 0.8 

I 

U 

<{ 

2 0.7 

~ 

W 

0::: 0.6 

0 

Figure 5.20 

'iJ -]150 

'iJ 'iJ 'iJ 'iJ 'iJ 'iJ 'iJ 'iJ 

'iJ'iJ l140 

130 

0.5 1.5 

-.l 

w 

> W,....... 

-.lro 

ZV 

0 

~ -.lQ) 

fU 

x 

w 

TRIPPED JET 

MJ = 0.304- ± 0.001 

= 278.0 ± 0.1 K 

T TJ / T A = 1.00 

UJ = 100.9 ± 0.4- m.s-t 

Re J = 374,800 

PA = 98.300 kPa 

T A = 279.3 K 

DJ = 50.8 mm 

X/D J = 9.00 

STROUHAL NUMBER, St J 

Excitation Strouhal number effects on unheated, tripped, 

Mach number 0.3 jet. 
00 

o 

C 

::l 

~ 

"-.... x 

<l> 

L 

ri 

w 

en 

2 

~ 

z 

:r 

o 

« 

:2 

---1 

W 

0::: 

Figure 5.21 

1.1 

1.0 

0.9 

0.8 

0.7 

0.6 

v 150 

\1 v 'iI v \1 'V'V 'l \1 'V 'V 'V 

140 

---1 

W 

> 

W ----- ---1m 

z'U 

0'--' 

5 QJ 

~---1 

TRIPPED JET 

M,; = 0.301 ± 0.002 

TTJ = 650.9 ± 2.3 K 

TTJ / TA = 2.32 

UJ = 151.2 ± 1.5 m.s- 1 

ReJ = 130,540 

PA = 98.266 kPa 

TA = 280.3 K 

OJ = 50.8 mm 

X/OJ = 9.00 

L-------~--------~--------~1130 U 

X o 0.5 1.5 W 

STROUHAl NUMBER, &J 

Excitation Strouhal number effects on heated, tripped, 

Mach number 0.3 jet. 
ex> 

~ 

J 

~ 

.......... 0... 

:::2: 

a: 

w 

ill 

:2 

::::> 

z 

I 

o 

« 

2 

~ 

a: 

o 

z 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

Figure 5.22 

0 

1

150 \/ 

\/ \/ \/ \/ \/ \/ V \/ 

\/'rl l140 

130 

0.5 1.5 

---l 

w 

> 

W 

---lm 

z""O 

0 

~ ---leu 

I0 

x 

w 

TRIPPED JET 

MJ = 0.304- ± 0.001 

TTJ = 278.0 ± 0.1 K 

T TJ / T A = 1.00 

UJ = 100.9 ± 0.4- m.s- 1 

ReJ = 374,800 

PA = 98300 kPa 

T A = 279.3 K 

DJ = 50.8 mm 

X/OJ = 9.00 

STROUHAL NUMBER I StJ 

Excitation Strouhal number effects on unheated, tripped, 

Mach number 0.3 jet. 
00 

N 

J 

~ 

"'" a.. 

0.9 

~ 0.8 

0:::: 

W 

~ 0.7 

=:=) 

z 

::r.:: 0.6 

o 

« 

2: 

:2 

0:::: 

o 

Z 

Figure 5.23 

0.5 

0.4 

'\] 150 

'\] '\] \l \l I'J \l\l \l \l '\] \l \l 

140 

-.-I 

W 

> 

W 

-.-1 m 

z "Q 

0 

~ -.-Iv 

TR1PPED JET 

MJ = 0.301 ± 0.002 

T TJ = 650.9 ± 2.3 K 

T TJ / T A = 2.32 

UJ = 151.2 ± 1.5 m.s-1 

ReJ = 130,540 

PA = 98.266 kPa 

T A = 280.3 K 

DJ = 50.8 mm 

X/DJ = 9.00 

~ ________ ~ ______ ~~ ______ ~J 130 U 

X o 0.5 1.5 W 

STROUHAL NUMBER 1 St J 

Excitation Strouhal number effects on heated, tripped? 

Mach number 0.3 jet. 
4. Jets with a thin laminar nozzle exit boundary layer appear to be 

more selective as far as the optimum excitation frequency is 

concerned than those with a thick turbulent nozzle exit boundary 

layer. 

5. Free jet mIxIng and development may be controlled by flow excitation 

as well as by nozzle exit boundary layer modification. 

These conclusions, as mentioned above, may apply to the Mach number 0.8 

jets, flow excitation conditions investigated, and the nozzle used in 

these tests. Further work is needed to generalize these conclusions for a 

broader range of jet operating conditions. 

83 
b 

BL 

half jet width 

boundary layer 

LIST OF SYMBOLS 

cpi 

cpr 

D 

coupling coefficient (imaginary part) 

coupling coefficient (real part) 

nozzle exit diameter 

f 

H 

k 

L 

L* 

M 

frequency 

shape factor 

wave number 

level 

distance 

Mach number 

p pressure 

PR pressure ratio 

R nozzle exit radius 

Re Reynolds number 

St,S Strouhal number 

T temperature 

U axial velocity 

V,v radial velocity 

Vi driver voltage 

X axial coordinate 

Y,y radial coordinate 

6 displacement thickness 

€ energy thickness 

A boundary layer thickness 

p density 

e momentum thickness 

e* angle 

Subscripts 

84 

a,A ambient 

c centerline 

e,ex excited 

j,J jet, based on nozzle diameter 

P probe 

r 

s 

t, T 

un 

6 

€ 

e 

reservoir 

static 

total 

unexcited 

based on displacement thickness 

based on energy thickness 

based on momentum thickness 
[2.1] 

[2.2] 

[2.3] 

[2.4] 

[2.5] 

[3.1] 

[3.2] 

[3.3] 

[3.4] 

[3.5] 

[3.6] 

[5.1] 

[5.2] 

E-4002 

REFERENCES 

Ahuja, K. K.; Lepicovsky, J.; Tam, C. K. W.; Morris, P. J.; and 

Burrin, R. H.: Tone-Excited Jet -- Theory and Experiments. NASA CR3538, 1982. 

Lepicovsky, J.; Ahuja, K. 

Tone-Excited Heated Jets. 

K.; Salikuddin, M.; and Morris, P. J.: 

Lockheed Report LG84ER0032, 1984. 

Tam, C. K. W.; and Morris, P. J.: Tone-Excited Jet -- Theory and 

Comparison with Measurements. J. Sound Vib., Vol. 102, pp. 119-151, 

1985. 

Chan, Y. Y.: Spatial Waves in Turbulent Jets. Physics Fluids, Vol. 

17, pp. 46-53, 1974. 

Moore, C. J.: The Role of Shear Layer Instability Waves in Jet 

Exhaust Noise. J. Fluid Mechanics, Vol. 80, pp. 321-367, 1977. 

Powell, A.: The Noise 

the Critical Pressure. 

Emanating from a Two-Dimensional Jet Above 

Aero. Quart. Vol. 4, pp 103-122, 1953. 

Powell, A.: On the Mechanism of Choked Jet Noise. Proc. Phys. 

Soc., Vol. 66, Pt. 12, pp. 1039-1056, 1953. 

Yu, J. C. and Seiner, J. M.: Nearfield Observations of Tones 

Generated from Supersonic Jet Flows. AIAA Paper 83-0706, 1983. 

Ahuja, K. K.: Basic Experimental Study of Coupling Between Flow 

Instabilities and Incident Sound. NASA CR-3789, 1984. 

Ahuja, K. K.: Some Unique Experiments on Receptivity. AIAA Paper 

No. 85-0533. 

Masters, G. F· The Effects of Upstream Nozzle 

Incompressible Turbulent Flow from Rectangular 

Transactions of the CSME, Vol. 5, pp. 197-203, 1979. 

Shaping on 

Nozzles, 

IMSL Library, Edition 9, International Mathematical & Statistical 

Libraries, Inc., Houston, 1981. 

Schlichting H.: Boundary-Layer Theory, 7th edition, McGraw-Hill 

Book Company, New York, 1979. 

85 
NI\S/\ 

National.Aeronautlcs and 

Space Admin'lstration 

Report Documentation Page 

1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. 

NASA CR-4129, Part II 

4. Title and Subtitle 5. Report Date 

Acoustically Excited Heated Jets June 1988 

II - In Search of a Better Understanding 6. Performing Organization Code 

7. Author(s) 8. Performing Organization Report No. 

J. Lepicovsky, K.K. Ahuja, W.H. Brown, 

M. Salikuddin, and P.J. Morris 

LG86ER0022 (E-4002) 

9. Performing Organization Name and Address 

Lockheed Aeronautical Systems Company - Georgia 

Dept. 72-74, Zone 403 

10. Work Unit No. 

505-62-91 

11. Contract or Grant No. 

NAS3-23708 

Marietta, Georgia 30063 

13. Type of Report and Period Covered 

~1-2.-s-p-on-so-r'-lng-A-g-en-C-y-Na-m-e-a-nd-A-d-dr-es-s------------------------------~ Contractor Report 

Final National Aeronautics and Space Administration Lewi s Research Center 14. Sponsoring Agency Code 

Cleveland, OH 44135-3191 

15. Supplementary Notes 

Project Manager, Edward J. Rice, Internal Fluid Mechanics Division, NASA Lewis 

Research Center. J. Lepicovsky, K.K. Ahuja, W.H. Brown, and M. Sa1ikuddin, 

Lockheed Aeronautical Systems Company - Georgia. P.J. Morris, Pennsylvania 

State University, University Park, Pennsylvania. 

16. Abstract 

The second part of a three-part report on the effects of acoustic excitation on 

jet mixing includes results of an experimental investigation directed at resolving the question of poor excitability of some of the heated jets. The theoretical predictions discussed in Part I are examined in detail to find explanations 

for the observed discrepancies between the measured and the predicted results. 

Additional testing was performed by studying the self excitation of the shock 

containing hot jets and also by exciting the jet by sound radiated through source 

tubes located externally around the periphery of the jet. The effects of nozzleexit boundary layer conditions on jet excitability was also investigated. It is 

concluded that high speed, heated jet mixing rates and consequently also the jet 

excitability strongly depends on nozzle exit boundary layer conditions. 

17. Key Words (Suggested by Author(s)) 

Sound-flow interaction; Jet mlxlng; Flow 

visualization; Velocity and temperature 

measurement; Large-scale structures 

18. Distribution Statement 

Unclassified - Unlimited 

Subject Category 02 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page) 21. No of pages 

Unclassified 88 

NASA FORM 1626 OCT 86 *For sale by the National Technical Information Service, Springfield, Virginia 22161 NASA-Langley, 1988 
End of Document