NASA Contractor Report 4129 

Part I I\iASA-CR-4129-PT -I 

19880014367 

Acoustically Excited Heated Jets 

I-Internal Excitation 

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

M. Salikuddin, and P. J. Morris 

CONTRACT NAS3-23708 

JUNE 1988 

U.r~GI ['( Rc.SEAPCH CENTER 

1~o3 REFERENCE 

HOT TO rJ: rA.C:!~ FTIO!I r.ro ::00:; 

NI\S/\ 11111111111111111111111111111111 1111111111111 

NF01835 

https://ntrs.nasa.gov/search.jsp?R=19880014367 2019-03-14T19:42:09+00:00Z
NASA Contracto.r Report 4129 

Part I 

Acoustically Excited Heated Jets 

I-Internal Excitation 

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 
FOREVORD 

This report was prepared by Lockheed Aeronautical Systems Company - Georgia 

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. 

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 

investigation 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. 

Mr. James R. Stone was the Project Manager for NASA-Lewis 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 Center for the Phase II effort. 

Lockheed's Program Manager was Dr. K. K. Ahuja. 

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 . . . . . . . . . . . . . . • . 1.0 INTRODUCTION .......... . 

2.0 LITERATURE SURVEY ...............•• . 2. 1 INTRODUCTORY REMARKS. . . . . . . . . 2.2 THEMATIC CATEGORIZATION. . ....• 

2.2.1 Acoustic/Flow Interaction in Flames and Combustion •. 

2.2.2 Coherent Structures and Jet Mixing. . . ... . 2.2.3 Nonacoustic Excitation of Jets ........... . 2.2.4 Acoustic Excitation of Unheated Jets •.....••. 

2.2.5 Acoustic Excitation of Heated Jets ....•• 

2.2.6 Theoretical Models for Excited Jets 

2.3 CONCLUDING REMARKS ..... . 

3.0 TECHNICAL APPROACH . . . . • . ........ . 3.1 RELEVANT TEST PARAMETERS ....••.. 

3. 2 TEST PLAN . . . . . .. . • . . . . • . 3.2.1 Jet Operating Conditions .....•..••.. 

3.2.2 Acoustic Excitation Conditions 

3.3 PILOT STUDY ..... . 3.4 FLOWFIELD EXPERIMENTS ... . 3.5 THEORETICAL ANALYSIS .... . 

FACILITIES AND DATA ACQUISITION . 4.1 TEST FACILITY .......• 

4.1.1 Jet-Flow Facility .. ~ ..•...••...... 

4.1.2 Upstream Acoustic Excitation Source .........• 

4.1.3 Flow Visualization Setup. . • . . . . ... 4.2 DATA ACQUISITION AND INSTRUMENTATION ..... 4.2.1 Excitation Level Measurement ...• 

4.2.2 Flow Data Acquisition and Reduction ...... . 4.2.3 Instrumentation ....... . 

5.0 NOZZLE EXIT BOUNDARY LAYER EXPERIMENTS ...... . 5.1 UNTRIPPED BOUNDARY LAYER ..... . 5.1.1 Mach Number Effects ... . 5.1.2 Total Temperature Effects. 

5.2 TRIPPED BOUNDARY LAYER .... 5.2.1 Tripping Devices. . . . ....••. 

5.2.2 Velocity Profiles .......... . 

v 

Page 

1 

3 

4 

4 

4 

5 

10 

12 

14 

19 

23 

24 

27 

27 

28 

28 

31 

31 

32 

32 

33 

33 

33 

33 

36 

39 

39 

39 

42 

44 

. 45 

45 

45 

51 

51 

57 
6.0 EXCITATION PARAMETER OPTIMIZATION EXPERIMENTS . . .•. 

6.1 EXCITATION STROUHAL NUMBER EFFECTS. . ......... . 61 

61 

61 

64 

77 

77 

6.1.1 Unheated Subsonic Jets •••. • ..• 

6.1.2 Heated Subsonic Jets •...••• 

6.1.3 Supersonic Jets 

6.2 EXCITATION LEVEL EFFECTS .. 

7.0 FLOW VISULAIZATION 

7.1 UNHEATED JETS ..•...•. 

7.2 HEATED JETS ....... . 

88 

88 

93 

8.0 THEORY AND COMPARISON WITH EXPERIMENT . . . .. ...•. 99 

8.1 STABILITY OF THE JET IN THE D~VELOPED JET REGION. . . . . •. 99 

8.2 COMPARISON WITH THEORETICAL PREDICTIONS. . . . .. . .. 103 

8.2.1 Typical Predictions. . . . . ••...••. 103 

8.2.2 Typical Comparisons. . . . . . . • • • ••••• 104 

9.0 CONCLUSIONS FOR INTERNAL EXCITATION .. 110 

LIST OF SYMBOLS . 114 

REFERENCES . 116 

vi 
SUMMARY 

The major goal of this investigation was to obtain detailed experimental 

data on the effects of acoustic excitation on the mixing of heated jets 

with the surrounding air. To determine the extent of the available 

information on experiments and theories dealing with the effects of 

acoustic excitation on hot jet mixing, an extensive literature survey was 

conducted at the outset of this program. Based on the information gathered 

in the literature survey, a technical approach was developed to carry out a 

systematic set of flowfield measurements and flow visualization for a broad 

range of jet operating and flow excitation conditions. The highest flow 

total temperature used was BOO K and the highest Mach number 1.16. The 

maximum achievable sound levels, as measured at the nozzle exit, were 150 

dB. The exit diameter of the test nozzle was 50.B mm. 

Before acquiring the mean flow data, it was found necessary to first 

determine the effects of jet operating conditions on the nature of the 

boundary layer at the nozzle exit. Detailed optimization experiments were 

then carried out to determine the excitation Strouhal number that produced 

the strongest effects in the centerline mean velocity. Radial profiles 

and centerline distributions of the mean velocity and jet temperature were 

acquired for a range of jet--operating and acoustic excitation conditions. 

Phase-locked flow visualization experiments were also performed at some of 

the test conditions. 

A theoretical analysis of excited 

downstream of the potential core, was 

results of theoretical predictions 

acquired data. 

jets, 

also 

were 

which includes the region 

developed in this study. The 

compared with experimentally 

The main conclusions drawn from Part 1 of this study are as follows: 

1. The sensitivity of heated jets to upstream acoustic excitation 

strongly varies with the jet operating conditions. 

2. The threshold excitation 

temperature. 

level increases with increasing jet 

3. Preferential excitation Strouhal number does not change significantly 

with a change of the jet operating conditions. 

4. The effects of the nozzle exit boundary layer thickness are similar 

for both heated and unheated jets at low Mach number. 
5. A coherent periodic structure in a form of ring vortices is formed in 

the near flowfield of an acoustically exited free jet. The structure 

is very stable with well defined ring vortices at low Mach numbers. 

Certain distortion of this structure was observed for high Mach 

number, unheated jets. 

6. Vortex pairing has been observed on schlieren pictures at some of the 

excitation conditions at low Mach numbers. At high Mach numbers no 

mutual vortex interaction was traceable. 

7. The mean flow measurements are qualitatively supported by the results 

of the flow visualizations. 

8. The predictions from the upgraded theory, compare extremely well with 

the measurements at moderate jet Mach numbers and total temperatures. 

These comparisons are, however, made only for the mean flow data. 

Therefore, further work is needed by way of comparing the measured and 

the predicted unsteady flow quantities. 

It was found that unlike the unheated jets, the high-speed, highly heated 

jets did not respond to internal upstream acoustic excitation. To improve 

our understanding of the excitability of highly heated high speed jets, the 

experiments using external acoustic excitation were also performed. 

Results for the external acoustic excitation are presented separately in 

Part 2 of this report. 

Finally, the plotted results of detailed measurements of Mach number and 

temperature in the jet flowfield, including tabulated experimental data, 

are presented in Part 3. 

2 
1.0 INTRODUCTION 

The main objective of the program described here was to obtain detailed 

experimental data on the effects of relatively strong upstream acoustic 

excitation on the mixing of heated jets with the surrounding air. The 

emphasis was on the assessment of the possibility of obtaining beneficial 

effects from acoustic excitation of heated jets and on the development of a 

better fundamental understanding of the phenomena involved. 

This report describes the results of Part 1 of a two phase study. An 

extensive literature survey was conducted at the outset of this program, 

and is described in Section 2.0 along with a detailed list of relevant 

papers on the subject of jet excitation presented in the section, 

References. The main purpose of this literature survey, was to determine 

the extent of the available information on experiments and theories dealing 

with the effects of acoustic excitation on hot jet mixing. The information 

gathered from this literature survey was then used to plan a technical 

approach to accomplish the study objectives. The technical approach is 

presented in Section 3.0, followed by a description of the facility and 

test procedures used for the experiments. The test facility, and data 

acquisition and reduction procedures are described in Section 4.0. 

For reasons given later, it was decided that an effective approach to 

obtain meaningful results would be to first determine the effects of jet 

operating conditions on the nature of the nozzle exit boundary layer. These 

results are described in Section 5.0. This is followed by a description of 

the detailed optimization experiments in Section 6.0. These optimization 

experiments served to determine the Strouhal number that produces the 

strongest effects in the centerline mean velocity. Results of phase-locked 

flow visualization of heated and unheated, excited and unexcited jets 

operated at the conditions determined by the optimization experiments are 

presented in Section 7.0. The theoretical analysis of excited jets, which 

includes the region downstream of the jet potential core, is presented in 

Section 8.0. A comparison of the calculated velocities with the 

experimental data is also presented in this section. Finally, the general 

discussion and conclusions are presented in Section 9.0. 

Detailed quantitative results for the mean Mach number and temperature 

measurements, consisting of radial profiles and centerline distributions 

measured at selected jet operating conditions, are presented in Part 3 of 

this report, which also contains temperature probe calibration curves. 

3 
2.0 LITERATURE SURVEY 

2.1 INTRODUCTORY REMARKS 

The main objective of this literature survey was to determine the extent of 

the available information on experiments and theories dealing with the 

effects of acoustic excitation on hot jet mixing. After an extensive and 

detailed literature search, it was concluded that the available literature 

dealing with experiments on acoustically excited heated jets is limited to 

a few papers only. 

After having completed the review of the literature on heated excited jets, 

attention was focused on surveying unheated jets, which were excited in 

either acoustical or nonacoustical ways. It was expected that lessons 

learned from the unheated excited jets may have considerable direct bearing 

on the global performance of the heated jets. 

Because of the important role of the organized coherent structures in jet 

mixing, papers on this subject were also reviewed. Since there is a myriad 

of papers dealing with the large-scale or organized turbulent structures, 

most of which were published during the last 10 years, only the papers that 

may have a direct bearing on the subject of excited hot jet mixing were 

encompassed in the present literature survey. 

Attention was paid also to the acoustic/flow interaction in flames and 

combustion. It should be borne in mind that it was the change in the flame 

shape due to the sound effect, observed by Leconte [A.9] in the middle of 

the last century, that led to the discovery of the jet sensitivity to sound 

excitation. 

In summary, altogether approximately 300 papers were reviewed, from which 

about 50 percent have been incorporated in the literature survey described 

below, because of their relevance to the subject of acoustically excited 

hot jet mixing. 

2.2 THEMATIC CATEGORIZATION 

In order to make the reading of the reviewed literature easier and keep 

things in their proper perspective, the papers reviewed in the literature 

survey have been divided into the following six groups. 

4 

Group A: Acoustic/flow interaction in flames and combustion 

Group B: Coherent structures and jet mixing 
Group C: Nonacoustic excitation of jets 

Group D: Acoustic excitation of unheated jets 

Group E: Acoustic excitation of heated jets 

Group F: Theoretical models for excited jets 

Reviewed papers, listed in the section, References, are arranged in an 

alphabetical order within each group. Some of the papers may cover more 

than one category and may, thus, appear in more than one group. 

In the course of the literature search, the results of previous literature 

surveys on the subject of acoustically excited jets made by Brown [A.2] in 

1932, Chanaud and Powell [A.3] in 1962, and Chambers and Goldschmidt [D.I0] 

in 1977 were also used. Previous results presented in a tabular form by 

Chambers and Goldschmidt [D.I0] have been included in Tables 2.1 and 2.2 to 

summarize the important parameters of the previous experiments on excited 

jets (Groups D and E). 

A short description of the work done under each group of papers is now 

presented. The emphasis is, of course, placed on the last three groups. 

2.2.1 Acoustic/Flow Interaction in Flames and Combustion 

The influence of sound upon jets has been observed since at least 1858, 

when Leconte [A.9] noticed gas lamp flames pulsating in synchronization to 

music. In 1867 Tyndall [A.18] found that the flame was unnecessary, the 

fluid of the jet itself was sensitive to sound (Figure 2.1 [A.3]). Tyndall 

explained the effect as early transition of the jet to turbulence, Lord 

Rayleigh [A.1S] followed Tyndall's studies with his own studies of flames, 

smoke jets, and liquid jets disturbed by acoustic standing waves. Brown 

[A.2], in 1932, reviewed the early research on the phenomenon, and 

continued the study of acoustically produced transition in flames and 

smoke jets. Hahnemann and Ehret [A.8], in 1943, were first to use the 

upstream internal excitation by a vibrating diaphragm. Similarly, the 

internal excitation was used by Loshaek et al [A.ll] in 1949. Since then, 

many more papers have been published on this subject. In the early stages 

of the research, the flame served merely to visualize the changes in the 

jet. The later works [A.l, A.4 A.7, A.I0, A.12 - A.14, A. 16, A.17, 

A.19, A.20], however, pay considerable attention to the improvement of the 

mixing and consequently the combustion efficiency and heat transfer by the 

acoustic excitation of flows. 

Thus, what started out as 

subject of many modern 

considerations. 

purely a 

studies 

curiosity 

primarily 

for Leconte has become a 

motivated by practical 

5 
0\ 

AUTHOR EXIT 

[REFERENCEl NOZZLE HACH REYNOLDS STROlJHAL REHARKS 

YEAR SIZE NUMBER NTJHBER NuHBER 

Ahuja et al Round 0.34 - 360,000 - 0.1 - Flowfie1d and 

[D.3J 51 mm 0.96 970,000 1.0 acoustic 

1982 measurements 

Bechert and Round 0.6 500,000 0.48 Acoustic 

Pfizenmaier 40 mm measurements 

[D.5] 

1975 

Berman Round 0.36 660,000 0.8 Bypass jet 

fD.7J Coaxial excitation 

1981 88 mm 

(125 mm) 

Chanaud and Plane 0.003 68 0.45 Experimental 

Powell 1 x 75 mm study of 

[D .12J laminar jets 

Crow and Round 0.07 - 77,500 - 0.15 Flowfield 

Champagne 50 mm 0.12 130,000 0.6 measurements 

[D .13J 

1970 

Heavens Plane 0.6 146,000 1.25 Flow 

[D .17] 4 x 30 mm visualization 

1979 

Table 2.1 Important test parameters of reviewed experiments on acoustic 

excitation of unheated jets. 
"-.J 

AUTHOR EXIT 

[REFERENCE] NOZZLE MACH REYNOLDS STROUHAL REMARKS 

YEAR SIZE NUMBER NUMBER NUMBER 

Hussain and Plane 0.004 - 8,000 - 0.15 - Experimenal 

Thompson 31 x 1400 rnm 0.015 31,000 0.6 study in the jet 

[D.22] initial region 

1980 

Jubelin Round 0.47 785,000 0.3 - Acoustic 

[E.3] 80 ro..m 0.8 measurements 

1980 

Kibens Round 0.1 - 50,000 3.7 - Acoustic 

[D. 24] 25 rnm 0.2 104,000 5.50 measurements 

1979 

Lu Round 1 1,295,000 0.2 - Acoustic 

[D.27] coaxial 5.0 measurements 

1981 62 rnm 

(151 rnm) 

Moore Round 0.3 - 275,000 - 0.3 - Shear layer 

[D. 29] 39 rnm 0.49 400,000 1.27 instability 

1976 measurements 

Morris and Round 0.24 375,000 0.3 Comparison 

Baltas 76 rom between theory 

[F.7] and experiment 

1981 

Table 2.1 (continued) Important test parameters of reviewed experiments 

on acoustic excitation of unheated jets. 

I 

i 

1 

! 
00 

AUTHOR EXIT 

[REFERENCE] NOZZLE MACH REYNOLDS STROUHAL REMARKS 

YEAR SIZE NUMBER NUMBER NUMBER 

Morrison and Round 1.4 - 3,700 - 0.14 - Low Reynolds 

McLaughlin 7mm 2.5 8,700 0.18 number 

[B .43] 10 mm supersonic jet 

1980 

Sarohia and Round 0.1 - 100,000 - 0.14 Flow 

Massier 42 mm 0.9 860,000 visualization 

[D.37] 

1977 

Schmidt Round 0.4 - 710,000 - 0.53 - Flowfield 

[D. 39] 85 nun 0.6 1,065,000 0.62 measurements 

1978 

Vlasov and Round 0.04 - 30,000 - 0.26 - Flowfield 

Ginevskii 10 mm 0.35 260,000 3.89 measurement 

[D. 44] 30 mm 

1967 

Zaman and Round 0.08 - 12,000 - 0.3 - Vortex 

Hussain 25 rom 0.15 120,000 1.6 pairing 

[D.48] 53 mm experiment 

1980 76 mm 

Zhangwei Round 0.15 35,000 1.0 Acoustic and 

[D.50] 12.5 m flowfield 

1982 measurements 

Table 2.1 {concluded} Important test parameters of reviewed experiments on 

acoustic excitation of unheated jets. 
\0 

Author Exit 

TReference] Nozzle Mach Total Reynolds 

Year Size Number Temperature Number 

Ahuja et al Round 0.78 800 K 285,000 

[E. 1] 51 mm 

1982 

, 

Ivanov Round 0.25 400 K 52,000 

[E .2] 12 mm 

1969 

Jubelin Round 0.47 600 K - 250,000 -

[E .3] 80 mm 900 K 390,000 

1980 

Lu Round 1 , 810 K 500,000 

[E.4] Coaxial 

1981 62 mm 

(152 mm) ~-- - -----

Table 2.2 Important test parameters of reviewed experiments on 

acoustic excitation of heated jets. 

Strouhal Remarks 

Number 

0.5 Converging nozzle 

flow and acoustic 

measurements 

0.031 - Diverging diffuser 

0.054 flow and acoustic 

measurements 

0.3 - Acoustic 

0.8 measurements 

0.2 - Acoustic 

5.0 measurements 
In conclusion, the important results derived from the survey of papers in 

the first group can be summarized as follows: 

o jet excitation may improve the combustion process and consequently 

the combustion efficiency 

o acoustic excitation may be used to control the temperature 

distribution at the combustion-chamber exit. 

2.2.2 Coherent Structures and Jet Mixing 

One of the most important discoveries in the field of fluid dynamics in the 

last 15 years is the fact that turbulence is characterized by a remarkable 

degree of order [B.15]. However, the progress in incorporating this 

structure into practical engineering methods has been very slow, mainly 

because the prediction of the large scale turbulent structure behavior, 

under given conditions, is still very uncertain. A simplified view of a 

free jet developing from a thin laminar nozzle boundary layer, showing the 

growth of the coherent structure, is shown in Figure 2.2 [B.58]. 

The intense current interest in large-scale coherent structures stems from 

the expectation that th~se structures play a key role in the transports of 

heat, mass, and momentum and noise production in turbulent shear flows 

[B.25]. The large-scale processes and the resulting mean flow seem to be 

little affected by viscosity [B.48]. The effects of viscosity appear 

indirectly through the initial shear layer conditions and not through 

direct action of viscosity on the developing turbulent structure. The 

evolution of the mixing layer depends significantly on the initial state: 

laminar or turbulent [B.24]. Under certain conditions, the mixing layer 

would spread first, stop spreading for a short distance, and then begin 

spreading again [B.12]. There is little doubt that by choosing the proper 

parameters and conditions, it will be possible to affect the process of jet 

mixing in a desired way. 

The available literature about coherent structures and jet mIXIng is rather 

vast. It was not our intention to make a complete literature survey on 

this subject. Extensive literature surveys on this subject have been 

published by others from time to time, notably by Laufer [B.38] in 1975, 

Roshko [B.48] in 1976, Yule [B.58] in 1978, Hussain [B.25] in 1980, and 

Cantwell [B.12] in 1981. Our literature survey of the papers on coherent 

structures [B.1 - B.58J is restricted to the papers that are most relevant 

to the present program. 

The most important results of this part of the literature search relevant 

to the present program are: 

10 
:. ~~ :~.". I ' I t 1':)1 

(a) (b) 

Figure 2.1 (a) Unexcited smoke jet and 

(b) exc ited smoke jet [A.3 ] . 

PotentIal L'on: 

x 

Transitional floy. outer interfaet: 

Figure 2.2 Turbulent coherent structure development in a 

free jet [B.S8]. 

11 
o jet mixing is controlled by the large-scale structure in the flow 

o more efficient mixing can be achieved by a more rapid growth of 

the large-scale structure in the jet shear layer 

o the evolution of the large-scale structure depends significantly 

on the type of the nozzle exit boundary layer (i.e., whether it is 

laminar or turbulent) 

The key role, which the type of the nozzle exit boundary layer may play in 

the coherent structure growth, requires that any experimental investigation 

of the coherent structure behavior must pay proper attention to possible 

changes of the nozzle exit boundary layer as a function of the experimental 

conditions. 

2.2.3 Nonacoustic Excitation of Jets 

Many efforts have recently been directed towards improving the mixing based 

on the recognized role of the developed large-scale structures in the 

mlxlng process. The growth of the large-scale structure can be stimulated 

when the jet is excited by rotating flow [C.4 - C.7, C.9, C.18], by forced 

pulsation [C.I, C.3 , C.IO, C.13, C.IS C.19], by oscillating vanes or 

plates [C.2, C.II, C.12, C.14, C.18), and, of course, by acoustic 

excitation, which is described in the next subsection. 

The regimes of a planar jet mechanically excited by an oscillating plate 

are shown in Figure 2.3 [C.ll]. 

Upper Zone Regime. For excitation frequencies 

three to four times the natural breakdown 

essentially unaffected by the excitation. 

higher than the order of 

frequency, the jet was 

Preservation Regime. The core flow of the jet tended to be preserved if 

the excitation frequency fell within the region designated in Figure 2.3. 

Matched Excitation Regime. When the excitation frequency was matched with 

the natural breakdown frequency, the effect was to hasten the process of 

vortex formation and growth relative to the natural breakdown state. 

Forced Fusion Regime. At applied frequencies on the order of one-third the 

natural breakdown frequency of the jet, the natural breakdown vortices were 

forced to undergo early fusion (or coalescence), which results in 

formation of large major vortices. 

12 
0:: 

W 

m 

::!: 

:::> 

z 

...J 

<{ 

J: 

:::> 10-1 

o 

0:: 

ten 

Matched 

Excitation 

Forced 

Fusion 

Upper 

Zone 

Lower 

Zone 

Id~ 

REYNOLDS NUMBER 

Figure 2.3 Dimensionless plot of Strouhal number versus Reynolds 

number indicating regimes of excited jets [C.ll]. 

13 
Lower Zone Regime. At excitation frequencies approximately one tenth (or 

lower) of the natural breakdown frequency of the jet, vortex growth was 

unaffected in the formation region. 

In summary, it was found that: 

o 

o 

the reaction of a jet to an 

into several regimes 

applied disturbance can be grouped 

an evolution of the large scale structure in the jet shear layer 

is more rapid if the frequency of an applied disturbance is close 

to the jet natural break down frequency (which is a function of 

the jet Reynolds number). 

2.2.4 Acoustic Excitation of Unheated Jets 

Brown's study [D.9] in 1935 may be considered as the first modern study of 

the phenomenon of acoustic excitation of jets. In recent years, many 

studies [D.1 - D.50] have been initiated to examine the sensitivity of the 

planar and circular jets to acoustic excitation. In most cases, upstream 

or internal acoustic excitation has been used, but some experiments have 

also been conducted by using external acoustic excitation. 

Previous literature surveys on the subject of jet acoustic excitation have 

been made or cited by Chanaud and Powell [D.12] in 1962, Hussain and Zaman 

[D.20] in 1975, Chambers and Goldschmidt [D.10] in 1977, Vlasov and 

Ginevskii [D.45] in 1979, and Ahuja, et al [D.3] in 1982. 

The effects of acoustic excitation on jet behavior are summarized in 

Figures 2.4 [D.3], 2.5 [D.45], and 2.6 [D.45]. The effect of a lowfrequency acoustic signal excitation (Stj 0.2 - 0.6) on a turbulent jet 

results in the enhancement of turbulent mixing, the shear layer broadens, 

the length of the potential core decreases, and turbulence intensity level 

increases significantly in the nozzle near region as seen in Figure 2.4 by 

Ahuja et al [D.3J and in Figure 2.5 taken from Reference D.45. Similar 

results were obtained in 1971 by Crow and Champagne [D.13] and later 

confirmed by Sarohia and Massier [D.37], Schmidt [D.39], Vlasovand 

Ginevskii [D.44, D.45], Hussain [D.21J, and Zaman [D.49], amongst others. 

The enhancement of turbulent mixing can be produced by exciting the shear 

layer with a fluctuating pressure at the nozzle of only 0.08% of the jet 

dynamic head but with the correct Strouhal number, as found by Moore 

[D.29J. This was also observed and confirmed by others [D.3, D.45J. 

On the other hand, the effect of a high-frequency acoustic signal (Stj = 2 - 5) on a turbulent jet results in the attenuation of the turbulent mixing, 

14 
t-' 

V1 

~ 

...... 

~ ~ 

~ 

VI 

Z 

UJ 

Iz 

UJ 

U 

Z 

UJ 

...J 

::;) 

CD 

a: 

::;) 

I20 

16 

12 

8 

It 

MEAN VELOCITY 

TURBULENCE INTENSITY 

~ - 811!!!!' ~.::::. :::: ...... __ 

---- '~,~~ L ',' ..... - (dB) e 

1.0 

'-' 

0.8 ::;) 

....... ", ::;) 

.:':~~~, ~ ~ 

"~~'~' 6 3 ........ "'~ o. UJ 

""~ ::::- ....... .::::~~ :z L e (dB) ...... _-_'........ __ ~_ ..... _ c:( ~ 

UNE~;~T~ -~"" O.~ 136 

141 

-"::::::.---

o ' 0.2 

o 2 It 6 8 10 12 tit 16 18 

AXIAL OISTANCE, X/O 

Figure 2.4 Excitation-level effects on centerline distributions. 

M. = 0.78, U. = 255 mis, Unheated, Static, Stj= 0.5, (0,0) Mode [D.3]. 

J J 
16 

1.0 

'" .......... 

" "- . ..., "- ::::> I - '-... . I 

......... 

::::> '-... 

'-... 

0.5 /"-

>- 2 ,/ ""'- ..... ~ ......... 

......... u "- 0 ......... ........ .....J .................. LJ..J 

::::- - --

0 

0 5 10 15 20 

AXIAL DISTANCE, X/D 

Figure 2.5 Effect of acoustic excitation on centerline distribution 

of mean velocity of a transonic jet. 

M1j = 0.93, Rej =1,260,000 

) unexcited jet 

2) tone excited jet, SS = 0.25, Le 170 dB [D.45] 

Figure 2.6 See next page 

Centerline distribution of turbulence intensity and 

mean velocity at various excitation Strouhal numbers. 

Mj - 0.2, Rej'" 15,000 

a) axial turbulence intensity 

b) radial turbulence intensity 

c) axial mean velocity 

1) StJ= 0.25,2) Stj= 0.3,3) Stj= 2.75 [D.45] 
,-. 

o~ 

. ...., ::::J 

" IN 

11-> 

'S. 

. ...., ::::J 

r' .04 11-

l~ 

>-

lV') 

:z 

UJ 

I-

:z 

UJ 

u 

:z 

UJ 

-J 

::::J 

co 

ex: 

::::J 

I-

>-

tU 

o 

-J 

UJ 

> 

12 

8 

4 

12 

8 

4 

---.. r/ I" 

, (a) 

'-....... -, I , /- '-..... "''/ '-./ '-, 

"I ..... 

/ ',1- ..... , 

/1 ---- -...... 

/' / 

if 

~-==--- tl 

/' --- '-~, /' "-

I ' -:...'----- I 

'-. I 

-, II.. 2 

--.' . 

~ ./: .::.-. 'I,' '- -=:~---

/1 

/ 

1/ / 

-f/ /' // 

/' '--

AXIAL DISTANCE, X/D 

Figure 2.6 For caption see previous page. 

17 
the periodic vortices break up into smaller elements, the shear layer 

becomes thinner, and the length of the potential core increases. A 

comparison of the low and high frequency acoustic excitation effects upon 

jet behavior is shown in Figure 2.6 [D.45]. Similar results were obtained 

also by Zaman and Hussain [D.48, D.49], who found that a noticeable 

suppression occurs over the Strouhal number range 0.008 S Ste S 0.024, and 

the minimum point falls roughly in the Ste range of 0.016 - 0.019. The 

Strouhal number (Ste) in this case was based on the initial shear layer 

momentum thickness rather than on the jet diameter. 

The important parameters of reviewed experimental investigations are 

summarized in Table 2.1. 

It seems reasonable to expect that the jet sensitivity to the acoustic 

upstream excitation is affected by the nozzle exit boundary layer 

conditions. The strong dependance of the large-scale structure growth on 

the jet initial condition (i.e., laminar or turbulent nozzle exit boundary 

layer [B.24]) has already been discussed. Zaman and Hussain found [D.48] 

that, for laminar exit boundary layer, the vortex pairing in the jet shear 

layer occurs regularly in space and time, for Rej < 5 x 104 , but becomes 

intermittent with increasing Rej or fluctuation Intensity in the initial 

boundary layer. 

Finally, some of the listed references deal with the state-of-the-art 

experimental techniques suitable for visualization and measurements in 

unheated and heated jets under acoustic excitation. Stroboscopic 

visualization techniques are presented in References D.17 and D.47, and a 

laser velocimeter capable of conditionally sampled measurements is 

described in References D.6 and D.26. 

The lessons learned from these studies can be summarized as follows: 

o acoustic excitation of unheated 

suppression of the turbulence 

field 

jets can cause either enhancement or 

intensity levels in the nozzle near 

o the jet mIxIng rate, and consequently the jet spreading rate, can also 

be increased or decreased by the upstream acoustic excitation 

o the jet mixing enhancement or suppression, 

jets, depends on the excitation Strouhal 

Reynolds number 

in the case of unheated 

number and on the flow 

o the jet mixing enhancement or suppression depends strongly on the type 

of the nozzle exit boundary layer (laminar or turbulent) and on the 

nozzle exit boundary layer thickness 

18 
These results are consistent with the findings of Subsection 2.2.2, where 

the effects of large-scale structures on jet mixing were discussed. 

The results emphasize the role of the initial condition of the jet shear 

layer (i.e., the type of the nozzle exit boundary layer), and the role of 

the excitation Strouhal number on jet mixing of a tone excited jet. 

2.2.5 Acoustic Excitation of Heated Jets 

As already pointed out, there is a shockingly short list of studies on the 

behavior of tone excited heated jets in comparison with a preponderance of 

papers on the behavior of excited unheated jets. In all, we found only 6 

papers [E.l - E.6] dealing with tone excited heated jets. To some extent, 

it would be possible to consider the early experiments on tone sensitive 

flames as the experiments on heated jets, too. But for all these cases, 

the Reynolds numbers were very small, because of very low operating flow 

velocities to keep the flame stable, and are thus out of the range of flow 

conditions of practical interest to the present program. The important 

parameters of reviewed experimental investigations are summarized in Table 

2.2. 

Jubelin [E.3] investigated the tone excited heated jets of Mach number 

equal to 0.47 at two temperatures equal to 300 K and 600 K and for Strouhal 

number range of 0.4 to 0.7. His investigation was made only from a noise 

generation point of view, and no flow measurements were obtained. He found 

that the noise response of hot jets to acoustic excitation is appreciably 

different from that of unheated jets. By examining the resulting changes 

in the far field jet noise levels, Jubelin concluded that the maximum jet 

sensitivity to excitation decreases slightly when the jet temperature 

increases. On the other hand, by examInIng the acoustic results in a 

different way, it was also concluded by Jubelin that "hot jets appear to be 

more easily 'excitable' than unheated jets." 

A jet of Mach number 0.98 heated up to 800 K was acoustically excited in 

one configuration of Lu's experiments [E.4] on the effects of upstream 

acoustic excitation on coaxial jets. Similar to Jubelin, Lu obtained only 

the acoustic measurements, and no flow measurements were obtained. 

Mickelsen and Baldwin [E.S] investigated the aerodynamic mixing by a 

standing sound wave downstream from a continuous line source of heat. The 

temperature of the flow behind the heat source was very mild, approximately 

10 K higher than the temperature of the surroundings. They found that the 

velocity fluctuations in a periodic sound field contribute to increased 

aerodynamic mixing. 

Ivanov [E.2] measured mean velocity and turbulence intensity behind a 

19 
conical diffuser, which was attached to a convergent nozzle. The length of 

the diffuser was 6.25 nozzle exit diameters. Mach number of the flow at 

the diffuser exit was equal to 0.25 and total temperature was equal to 400 

K. The Strouhal number based on the diffuser exit diameter ranged from 

0.031 to 0.054. He found that the effect of low-frequency acoustic 

excitation was to increase the rate of velocity decay slightly, and 

simultaneously to decrease the turbulence intensity level substantially up 

to 9 diffuser exit diameters. 

All of Ivanov's measurements were made practically beyond the end of the 

jet potential core emanating from the nozzle (the attached diffuser was 

longer than the corresponding length of the jet potential core). Ivanov's 

hot jet results indicate trends similar to those seen in Ahuja et aI's 

unheated jet results for axial distances beyond X/D = 9 shown in Figure 

2.4 [D.2]. 

For the heated jet, however, Ahuja et aI's experiments [E.l] showed an 

opposite trend. As is seen in Figure 2.7, acoustic excitation of the 

heated jet (Mj = 0.78, Tt = 800 K, and Stj = 0.5) increased the length of 

the potential core a little, and decreaseo the turbulence intensity level 

up to X/D = 8. At larger distances increased turbulence intensity levels 

were measured. 

The above mentioned discrepancy complemented by a severe lack of 

experimental data show that further work is definitely needed to assess the 

effects of upstream acoustic excitation on heated jets. No firm conclusion 

can, therefore, be drawn from the results discussed above. 

Despite the lack of sufficient knowledge about excited heated jets, an 

important practical application of this phenomenon was shown by Vermeulen 

et al [E.6]. Acoustic control of mixing process in a small combustor was 

successfully tested. The desired exit plane temperature distribution was 

achieved, while the pressure loss of the combustor and its combustion 

efficiency were insignificantly affected by the acoustic excitation. The 

acoustic modulation can be used to control the exit plane temperature 

distribution. As seen in Figure 2.8 [E.6], it is possible to trim the 

temperature profiles. The temperature profile behavior indicates that 

improved mixing may be due to vortex action. 

The important results learned from this part of the literature survey can 

be summarized as follows: 

20 

o there is a serious lack of experimental data on the subject of 

the effects of acoustic excitation on hot jet mixing 
- - - -- MEAN VELOC I TV 

--_. TURBULENCE I NTENS I TV 

14 

·12 -----'" 1.0 

- , ........ H " "- " ' ....., 

::::I \ '-

Le (dB) 0.9 

~ 10 

\ UNEXCITED \ Le (dB) 

141- \ \ --- ,: \ ~UNEXCITED 0.8 :: 8 VI 

IAJ 

z \ \~'41 ... 

z 

\ \ 0.7 IAJ 6 \ \ (..l 

z 

IAJ \ \ ...I 

::::I 

\ \ CD 

a: 

::::I 

... \ \ 4 0.6 

\ 

\ 

\ 

2 0.5 

o 

o 2 4 6 8 10 12 

AXIAL DISTANCE, X/D 

Figure 2.7 Effects of upstream excitation on the 

centerline distributions of the heated jet. 

Mj = 0.78, Uj = 428 mis, Tt = 800 K, Static, 

Stj = 0.5, (0,0) Mode [E.l]. 

....., 

::::I 

...... 

::::I 

>-

:: 

(..l 

0 

...I 

IAJ 

:-

Z 

<: 

IAJ 

x: 

21 
22 

CENTERLINE 

.j.J 

I-

.......... 

IlLJ O. 1 UNEXCITED 0:: -X--X--I(-

=> I -0-0-0- EXCITED I-

<t 

0:: 

lLJ 

Cl... 0 ~ 

lLJ 

IlLJ 

> 

I- -0. 1 

<t 40 ....J 40 20 0 20 lLJ 

a::: 

RADIUS, r (mm) 

Figure 2.8 Exit plane dimensionless radial temperature 

profiles [E. 6 J. 
o no firm conclusions, as far as the trends in hot jet mixing due 

to acoustic jet excitation are concerned, can be drawn but a 

strong dependence on the excitation Strouhal number, flow 

Reynolds and Mach numbers, and jet temperature may be expected as 

indicated by the discrepancy between known experimental results . 

2.2.6 Theoretical Models for Excited Jets 

The first theoretical model of the stability of tone excited jets was given 

by Rayleigh [F.I0] in 1878. Rayleigh's analysis, based on inviscid models, 

did not agree fully with the experiment. 

Savic [F.ll] developed a theory by applying Tollmien's general criterion of 

instability; he assumed an inflection in the velocity boundary of the jet 

near the nozzle exit [0.14]. Savic's theoretical results appeared to 

explain the results obtained by Brown [0.9]. 

Michelsen and Baldwin [F.4] based their theory on a kinetic analysis of the 

motion of the molecular-diffusion wake and derived equations for the time 

variation of temperature and the time mean temperature at points throughout 

the mixing region. This analysis showed that standing sound waves displace 

the diffusion wake in a manner similar to the displacements of a flag 

waving to a harmonic mode. The wake deformation is greater for higher 

sound intensities. 

McCormack and Cochran [F.3] divided the jet in two separate regions: (a) 

the near field, which contains the potential core; (b) the far field, 

beyond the potential core, which is all mixing region. The near field 

region is considered as a case of the mixing of two uniform streams, one of 

which is at rest. Mathematically, the problem that is dealt with here is 

that of the effect of a periodic source of vorticity on an incompressible 

submerged laminar gas jet. A sort of pressure gradient is set up near 

the jet axis, which results in more rapid transport of momentum in the 

radial direction. Thus, the rate of mixing is accelerated and the 

potential core length shortened. 

Maestrello and Bayliss [F.2] simulated numerically the interaction of an 

acoustic pulse with the experimentally determined mean flowfield of a 

spreading jet. The simulation was obtained by solving the Euler equations 

linearized about the spreading jet. It was shown that some of the observed 

differences in the acoustic spectra of heated and unheated jets can be 

attributed to differences in the stability characteristics of the jets. 

The heating of the jet reduces the amplification of sound due to the flow 

and causes a shift of the farfield spectra toward lower frequencies. 

23 
To date, the most advanced theory of a tone excited jet appears to be that 

of Morris and Tam [F.I, F.5 - F.9, F.12 - F.16]. The theory predicts the 

change in turbulent structure of a round jet in the presence of an 

acoustic excitation. The excitation is assumed to trigger instability 

waves of a known initial amplitude at the jet exit. As these waves 

propagate downstream, they extract energy from the mean flow and transfer 

it to the random turbulence. This results in an increase in the levels of 

the turbulence and a resulting increase in the radiated broadband noise. 

The numerical procedure allows for radial as well as axial variations in 

the averaged properties of the jet. The theory agrees very well with an 

experiment for unheated tone excited jets [F.I, F.6]. A comparison 

between the measured and the predicted rates of spread of unheated 

unexcited and unheated tone excited jets is shown in Figure 2.9. However, 

a discrepancy was found for the case of heated tone excited jet [F.I]. 

In summary, it was found that: 

o only a few attempts have been made at developing theoretical 

models of acoustically excited jets, but the most complete model 

was found to be that of Morris and Tam 

o Morris-Tam model compared well with measurements for unheated 

jets 

o the same model, however, failed to predict the trends for the 

corresponding measurements (to date) for heated jets 

2.3 CONCLUDING REMARKS 

After having reviewed the literature in each of the six groups, it becomes 

quite clear that there exists a shockingly short list of investigations on 

the behavior of acoustically excited heated high speed jets. In fact, in 

addition to the Lockheed work [E.I], only one other experimental study 

[E.2] directly dealing with the subject of the effects of acoustic 

excitation on mlxlng of high speed hot jets was found in the open 

literature. Furthermore, the findings of these two experiments contradict 

each other. 

What is clear, however, is that, for the unheated jets, the acoustic 

excitation can produce either enhancement or suppression of the turbulence 

intensity level in the nozzle near field, and consequently, the jet mixing. 

The severity of this effect depends on the excitation Strouhal number, 

excitation level, and on the flow Reynolds number. The literature survey 

also revealed that, for the unheated jets, the type of the nozzle exit 

boundary layer (laminar or turbulent) may playa key role in the nature of 

24 
tv 

VI 

ct: 

........ 

..0 

::t: 

.-

o 

:3 

u.. 

...J 

c:( 

::t: 

.-

I.J.J 

..., 

1.2 

I 

UNEXC ITED ! 0 MEASURED 

PREDICTED 

1.0t- n ~ 0 EXC ITED MEASURED 

PREDICTED 

2 3 

AXIAL DISTANCE, X/D 

// 

/ 

// 

/ 

,5>/ 

M· = 0.575 (COLD) 

E~C'TAT'ON LEVEL = 141 dB 

EXC !TAT! ON STROUHAL No. =0.5 

AXISYMMETRIC MODE, (O,O) 

4 5 6 

Pigure 2.9 Comparison between measured and predicted rate of spread 

of jet [F.l]. 
the jet response to the upstream acoustic excitation. 

As regards the theoretical models of acoustically excited jets, the model 

developed at Lockheed [F.1] under a previous NASA-Lewis contract (NAS3-

21987) by Morris and Tam still stands out as the most complete model. It 

takes into account the various aspects of flow/acoustic interaction, and 

fully incorporates the role of large-scale turbulent structures on jet 

mIxIng. This theory has been, to a large extent, verified for the unheated 

jets, but a large discrepancy obtained on comparing it with the results for 

the heated jets [E.1], still remain to be resolved. 

The moral to be derived 

excitation as a means of 

potential, but a carefully 

is desperately needed. 

26 

from this literature survey is that acoustic 

increasing mIxIng of heated jets holds great 

planned and well-controlled experimental study 
3.0 TECHNICAL APPROACH 

The objective of this program was to obtain detailed experimental data on 

the effects of relatively strong upstream acoustic excitation on the mixing 

of heated jets with the surrounding air. The major effort was devoted to 

the experimental data acquisition. Some of the experimental results were 

compared with available theory in terms of the relationship between the 

excitation characteristics and changes in the mean velocity distribution of 

the jet for a given jet operating condition. The theory used for this 

comparison was an extension of the theory presented in Reference F.1. 

The major objectives of this work were accomplished by conducting work 

under the following three tasks: 

Task 1: Optimization Study 

Task 2: Flowfield Experiments 

Task 3: Theoretical analysis 

The emphasis 

experimental 

was on Task 2 so as to acquire a sufficient amount of reliable 

data for a future detailed analysis. 

3.1 RELEVANT TEST PARAMETERS 

In an experimental program of the present nature, a large number of 

parameters needs to be considered to determine the effects of acoustic 

excitation on the hot jet mixing. The success of such a program depends 

heavily upon whether the correct excitation parameters and flow conditions 

that show strongest flow changes in response to acoustic excitation can be 

identified. Based upon the literature survey presented in Section 2.0 and 

our experience gained from our earlier work on similar studies, the 

following parameters appear to be the most important for the present 

program. 

Jet operating conditions: 

Nozzle pressure ratio 

Fully expanded jet Mach number 

Jet total temperature 

27 
Upstream acoustic excitation conditions: 

Frequency fe 

Strouhal number Stj 

Level Le 

3.2 TEST PLAN 

In order to determine the effects of the individual parameters on hot jet 

mixing, one significant parameter was varied at a time. The salient 

details of the jet operating and the acoustic excitation conditions at 

which the majority of the experiments were conducted are given below. 

3.2.1 Jet Operating Conditions 

The test plan, as far as jet operating conditions are concerned, is 

summarized in Figure 3.1 and Table 3.1. 

Since the main purpose of this program was to study the mIxIng in heated 

jets, the test matrix had to cover a suitable range of jet temperatures. 

Also, since the Reynolds number of a fixed Mach number gas jet is reduced 

considerably by heating, the question of Reynolds number dependence was 

also addressed. Keeping this in mind, the test matrix, shown in Figure 

3.1, was carefully selected to provide information for: 

(1) varying total temperature at fixed jet Mach number (line A), 

(2) varying jet pressure ratio at fixed jet temperature ratio (lines 

B and C), 

(3) varying jet pressure and temperature ratios at fixed Reynolds 

number (curves D, E, and F), 

(4) varying jet pressure and temperature ratios at fixed jet velocity 

ratio, Uj/ao (curves G and H). 

The solid dots (labeled 1 - 8), shown in Figure 3.1, represent the basic 

jet operating conditions. Additional jet operating conditions were set up, 

to clarify in greater detail the effects of any of the jet parameters on 

hot jet mixing. These additional jet operating conditions are marked by 

empty circles in Figure 3.1. 

28 
:::£: :::£: :::£: :::£: :::£: 

...:::t r---. (j) N (j) --0 00 r---. N (V") ...:::t --0 00 

.j...J .j...J .j...J .j...J .j...J 

2.5 l- I- 71- l- IM· 1.29--?---- -----1--7 J I 

I I '-0 I "-.:.u. I I 

I I ,C) I J~ C • w I ~ ~. I I I + I G I I I I I I .l"..; I E I 0 I I /; I ~ I I 

I- 2.0 I • « 

I ~I I I ~' I 0::: b I : I B w I I I \(J I 8 : 0::: I \>I i-- I I ::> I (f) I F I', I (J.S I I (f) 

w I I I 0::: M. 0.81 itl I "'- I ~e I I 0- J --+--- A-- I 

1.5 ------e---

I 1 I 2 .................. H 14 I 5 

I I ................ I I 

V: ___ I 

u·/ --6 

I I J ao == 0.96 6-.--- D 6 

1.0 

1.0 1.5 2.0 2.5 

TEMPERATURE RATIO, Tt/T b 

const Re = const 

--------- Tt = c.onst 

e Basic test matrix 

o Additional data taken 

Figure 3.1 Jet operating conditions. 

29 
w 

o 

TOTAL PRESSURE JET MACH REYNOLDS 

TEST TEMPERATURE RATIO NUMBER NUMBER 

POINT Tt Rej M· ~ J (MILLION) K ( oF) 

1 294 (70) 1.50 0.78 1.0 

2 367 (200) 1.50 0.78 0.8 

3 489 (420) 1.50 0.78 0.5 

4 672 (750) 1.50 0.78 0.4 

5 811 (1000) 1.50 0.78 0.3 

6 489 (42O) 1.17 0.48 0.3 

7 489 (420) 2.43 1.20 1.0 

8 672 (750) 1.88 0.99 0.5 ~ ~- -- ----------

Table 3.1 Test matrix of jet operating conditions. 

VELOCITY 

RATIO 

Uj/ao 

0.74 

0.83 

0.95 

1. 12 

1.23 

0.60 

1.36 

1.38 

---- -
3.2.2 Acoustic Excitation Conditions 

Acoustic excitation conditions were restricted to a relatively narrow range 

because of the low response of most commercially available acoustic drivers 

at high frequencies. Thus, the maximum achievable excitation frequency, at 

reasonably high excitation level, was fe 4500 Hz, which limited the 

excitation Strouhal number to the range of Stj < 0.6 at the extreme jet 

operating conditions. The maximum achievable excitation levels (Le ), 

measured at the nozzle exit, were Le = 150 ~ 1 dB. 

3.3 PILOT STUDY 

Prior to acquiring comprehensive data, a pilot study was carried out in two 

parts. In part 1, the experiments were carried out to clarify the effects 

of jet Mach number and jet total temperature on the nozzle exit boundary 

layer displacement thickness distribution, and to study the dependence on 

jet Reynolds number. Simultaneously, the type of boundary layer at the 

nozzle exit at various experimental conditions was determined, because it 

was expected that the nature of the boundary layer may play an important 

role in determining the behaviour of acoustically excited jets. These 

experiments are described in Section 5.0. 

In the second part of the pilot study, optimization experiments were 

carried out to determine the excitation Strouhal number that produces the 

strongest effects in terms of the changes in the mean velocities and 

temperatures. As described in Section 6.0, 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. 

For each test condition, the Strouhal number that produced the maximum 

change in the local Mach number on the jet centerline at X/D = 9 was 

selected as the peak Strouhal number for the following flowfield 

experiments. The effects of excitation level on jet behaviour at 

different jet total temperatures were also investigated under the pilot 

study. 

31 
3.4 FLOWFIELD EXPERIMENTS 

The objective of the experiments under this task was to obtain a general 

mean flow survey of the acoustically excited heated jets. These 

experiments were carried out only for those jet operating conditions, where 

the effects of upstream acoustic excitation on jet behaviour were 

determined by the pilot study. The flowfield experiments were performed 

under two tasks consisting of (1) mean flow survey and (2) flow 

visualization. 

The mean flow survey consisted of one centerline distribution and five 

radial profile measurements of Mach number and jet temperature for each of 

the jet operating conditions. The results of flowfield measurements are 

given in Part 3. 

The second task consisted of flow visualization using a unique laser 

schlieren system, developed recently at Lockheed. Phase-locked flow 

pictures were taken for those flow conditions that showed significant 

modification due to upstream tone excitation. The results of flow 

visualization experiments are discussed in detail in Section 7.0. 

3.5 THEORETICAL ANALYSIS 

The formulation of the theoretical analysis, described in Reference F.1 was 

capable of predicting flow behaviour only up to the end of the jet 

potential core. As a part of this program, this analysis of excited jets 

has now been extended to consider the region downstream of the potential 

core. This enables the decay of the centerline velocity to be predicted as 

a function of jet operating and excitation conditions. The analysis in 

this region is more complicated than in the potential core region. This is 

due mainly to the dependence of the mean density on the local centerline 

velocity, which is a dependent variable in the analysis. Two computer 

programs have been written. The first evaluates the coupling between the 

acoustic excitation and the instability wave in the potential core region 

as well as the local growth rates of the instability waves. This 

calculation is performed for given jet operating conditions and a specified 

Strouhal number and azimuthal mode number for the excitation. The second 

program calculates the axial development of the jet and the instability 

wave for specified excitation levels. 

32 
4.0 FACILITIES AND DATA ACQUISITION 

All experiments described in this report were conducted in Lockheed's JetFlow Facility. This facility was also used for all measurements presented 

in Reference D.3. Further details of the test facility and test procedures 

are given below. 

4.1 TEST FACILITY 

4.1.1 Jet-Flow Facility 

The jet-flow facility used in this program is designed to produce parallel, 

low-turbulence, coaxial flows, or single-stream flow with provision for 

simulating flight effects with a large secondary nozzle. Only the primary 

or inner flow was used for the present experiments. A general view of the 

Jet-Flow Facility is shown in Figure 4.1. A cross-sectional view of the 

facility is shown in Figure 4.2. The primary flow enters through a 256-mmdia plenum, followed by an initial contraction to the 102--mm-dia sourcesection duct. The 50.8-mm-dia test nozzle is attached to the sourcesection duct. The plenum to nozzle area contraction ratio is 25. 

Two precisely-machined stainless steel nozzles were used in the present 

program. One of the nozzles is convergent, while the other one is 

convergent-divergent with fully-expanded design Mach number of 1.2. The 

exit diameter of each nozzle is 50.8 mm. 

The jet flow in this facility can be heated to temperature reaching 1000 K 

at pressure ratio exceeding 4. The flow is heated by a through-flow 

propane burner. Both pressure and temperature conditions can be controlled 

either by a computer or manually. 

4.1.2 Upstream Acoustic Excitation Source 

The source section used in this series of experiments is the same source 

section that was used in Lockheed's earlier studies on acoustically excited 

jets [D.2,D.3], but this time it was provided with four additional drivers. 

The source section is depicted in Figure 4.2. It is centered around a 102-

mm-dia air sup ply duct, which is connected to a test nozzle. It utilizes 

eighth 100-W ALTEC model 290E acoustic driver units. Each driver is 

enclosed in a pressure vessel to equalize the pressure across the driver 

33 
34 
w 

V1 

ACOUSTIC 

DRIVER 

(TOTAL OF 8) 

SEALED 

ACOUSTIC 

~ DRIVER 

-----CONTAINER 

DIAPHRAGM 

PRESSURE 

. EQUALIZER t. . .•. I .• 

. . ;:.1...... '" ;.;: '~'. ~:.: . 

MICROPHONE 

I 

RING 

// (TOTAL OF 12) 

~, 

~I 

I 

FLOW ------ ~-~---

PLENUM L~, .... ::1=? 'I 

PRIMARY 

NOZZLE: 

'., 

-:. ,:,' .. :.' .;. ".,",.,... 

~ 

Figure 4.2 Jet flow facility and source section. 

PROBE 

PROBE 

-- POSITIONER 
diaphragm. The tubes connecting 

duct have provision for cooling 

order to protect the diaphragms. 

The sound is funneled to the 

tubes, each tube connected to a 

connector, as seen in Figure 4.3. 

the drivers to the 102-mm-dia air supply 

air for the high-temperature tests, in 

102-mm-dia 

pair of 

duct through four 2S.4-mm-dia 

acoustic drivers through a "Y" 

Since it is important that the 2S.4-mm-dia tubes connecting the driver 

section to the air supply duct do not produce significant flow disturbances 

other than the excitation signal itself, the source-duct-nozzle system has 

been thoroughly calibrated in the past and found to be aerodynamically 

acceptable. 

To ensure that the plane wave (0,0) mode of acoustic excitation was 

generated, both phases and amplitudes of sound at the nozzle exit plane 

were measured by 12 microphones as shown in Figures 4.1 and 4.S. The 

scheme used in this study for excitation mode detection is described in 

detail in Reference D.3. 

4.1.3 Flow Visualization Setup 

The jet-flow facility is equipped with a single-converging-mirror schlieren 

system shown in Figure 4.4. In this system, the light makes a double-pass 

through the test section. The system uses a wedge mirror instead of a 

splitter plate to separate the source and return beams. 

The schlieren system was used for a photographic ensemble averaging of 

periodic structures in a tone excited jet. The method of photographic 

ensemble averaging consists of repeated synchronized triggering of a light 

source and superposition of all the schlieren images on a single 

photographic film to reinforce the image of the coherent periodic structure 

in the flow. The frequency of repeated photographic shots is usually 

limited to low frequencies by shutter mechanical restrictions or lightsource recharging limitations. The schlieren system used here is unique in 

that it enables photographic ensemble averaging of periodic flow structures 

with frequencies up to the order of 100 kHz. 

The system uses monochromatic laser light. The light source consists of a 

continuously operating 18-W Ar-Ion laser, Bragg cell modulator, and a 

spatial filter. In operation, the excited Bragg cell acts as a shutter 

deflecting the laser beam off the spatial filter and thus effectively 

blocking the laser beam from a photographic plate. Because the Bragg cell 

is excited by an electronic signal of a frequency in a MHz range, the 

shutter is no longer limited to low frequencies. A simple electronic 

device controlling the Bragg cell excitation enables the selection of both 

36 
37 
38 
the frequency of photographic shot repetition and the time exposure of each 

of the shots. 

4.2 DATA ACQUISITION AND INSTRUMENTATION 

4.2.1 Excitation Level Measurement 

The excitation levels at the nozzle exit plane, were measured directly only 

for the unheated jets using a 6.4-mm-dia Bruel & Kjaer microphone, fitted 

with a nose cone. For heated jets, however, the excitation level was 

measured indirectly by a microphone ring placed outside the nozzle but in 

the plane of the jet exit. The radial distance between microphone ports 

and the jet axis was 100 mm. The ring consisting of 12 Bruel & Kjaer 

microphones is shown in Figure 4.5. The 12.7-mm-dia Bruel & Kjaer 

microphones were used for this ring. Since the sound pressure levels 

measured by these microphones are not necessarily equal to those present at 

the nozzle exit, the necessary corrections were obtained in advance by 

making simultaneous measurements of the sound levels present at the nozzle 

exit, using a 6.4-mm-dia Bruel & Kjaer microphone, fitted with a nose cone 

and the levels at this microphone ring, for all test conditions and 

excitation frequencies. These calibrations were made for unheated 

conditions, and it was assumed that the corrections from exit plane to the 

ring position were the same for the heated jets. 

4.2.2 Flow Data Acquisition and Reduction 

In view of the large number of data points acquired in this program, it was 

almost imperative that the data acquisition and reduction scheme be as 

automated as possible. A block diagram for acquisition, processing, and 

evaluation of the data is shown in Figure 4.6. The measured pressures are 

converted to analog signals by pressure transducers. These signals, 

together with the signals from temperature probes, are sampled by a DigiLink data acquisition unit. The Digi-Link converts these signals into 

digital values of pressures and temperatures using the probe-staticcalibration curves. The converted values, expressed in engineering units, 

are then supplied to the VAX computer. The flow parameters such as Mach 

and Reynolds numbers, flow velocity and temperature are then computed. All 

the flow characteristics at a given probe location in the jet are 

immediately displayed in a graphical form on the computer terminal. These 

plots are automatically updated with every newly acquired experimental 

point from the jet flowfield. Also a graphical comparison with the data 

already acquired at other experimental conditions can be made during a 

particular test run. The information from the probe positioner is also 

39 
40 
~ 

t-' 

PRESSURE L-..J TEMPERATURE 

PROBES ~ PROBES 

,--- ---------l 

I A/D SAMPLER ~ 

1 I 

I I 

I PRESSURE TEMPERATURE I 

I CALIBRATION CALIBRATION I 

1 I 

I DATA ACQUISITION : 

UNIT DIGI-LINK I ------------ L- __ 

PROBE 

POSITIONER 

,----+-----, r------l 

~ l I .. _=J COMMANDS t . 

I : QUICK I 

f I COpy I 

DATA PRINTING 

DATA PLOTTING I I I 

I I I I COMPARISON WITH 

I PREVIOUSLY I I 

U 

ACQUIRED DATA I 

I I 

I TERMINAL TEKTRONIX 4025 I --------------

I I 

I 

I VIDEO PLOTTER : 

~EKTRONI:" 463~f 

1- - t - - - - - --1-- - - ~ -1-- - - - -, 1--- ~--------I 

I ~-------------~ I 

I I I 

1 MACH AND REYNOLDS NUMBERS, DATA TEMPORARY I 

AND FLOW VELOCITY AND ---- I 

I TEMPERATURE CALCULATIONS STORAGE I I 

I TAPERECORDER 

PRINTER 

PLOTTER I 

II 

I I I 

I : 1 DATA PERMANENT I I I STORAGE 

I 

I 

I 

I 

I I VELOCITY AND TEMPERATURE PROFILES L - - - - - - - - -- I AND CONTOURS CALCULATIONS : 

I FLOW KINETIC ENERGY CALCULATION I 

I COMPUTER 

1 ~ ______________________ VAX 11/780 J I 

Figure 4.6 Data acquisition and reduction scheme. 
stored in the computer memory for subsequent data processing. The data for 

the given experimental condition are kept in the temporary data storage 

until the entire flowfield is mapped. Finally, when the measurement is 

finished the data are transferred in the permanent data storage. 

4.2.3 Instrumentation 

United Sensor probes were used for flow measurements as well as for 

measurements in the nozzle exit boundary layer. The flow survey was made 

with the combined pressure and temperature probe OAT-187-12-CO-C/A-36 , shown in Figure 4.7. The dynamic temperature calibration of this probe is 

discussed in detail in Part 3. The boundary layer probe BR-.020-12-C-11-

.120 was used for boundary layer experiments. The probe is shown in Figure 

4.8. Pressure transducers Validyne P 3050, rated for pressure ranges of 

86 kPa and 350 kPa, were used in connection with the above mentioned 

probes. 

42 
.s::--

w Figure 4.7 Combined pressure and temperature probe. Figure 4.8 Boundary layer probe. 
5.0 NOZZLE EXIT BOUNDARY LAYER EXPERIMENTS 

As pointed out in Section 2.0, considerable discrepancy exists between 

various experimental results on excited hot jets. It was also mentioned 

that one of the possible explanations for this may be attributed to 

differences in the type of the nozzle exit boundary layer that might have 

prevailed in different experiments. Therefore, before proceeding with 

detailed optimization experiments, described in the next section, the 

nature of the nozzle exit boundary layer was investigated. The effects of 

jet Mach number and jet total temperature were investigated for both the 

untripped and tripped nozzle exit boundary layers. The details of these 

experiments and the results therefrom are given below. 

The characteristic thicknesses and shape factors of the boundary layer used 

in the following subsections are defined by the following formulae: 

Displacement Thickness, S : 

Momentum thickness, 9 

Energy thickness, 8 

Shape factor, HS9_: 

44 
Shape factor, H8e~ 

5.1 UNTRIPPED BOUNDARY LAYER 

5.1.1 Mach Number Effects 

The effects of Mach number on the nozzle exit boundary-layer behaviour were 

studied by measuring the boundary layer velocity profiles for various jet 

exit Mach numbers in the range Mj 0.16 through 0.9 (see Figure 5.1). 

Most of these initial measurements were for the unheated jet only. Figures 

5.2 and 5.3 show nozzle exit boundary layer profiles normalized by boundary 

layer momentum thickness as measured for low and high jet exit Mach 

numbers. It was found that for the nozzle arrangement used, the nozzle 

exit boundary layer gradually changed from laminar at low Mach numbers to 

turbulent at high Mach numbers. This becomes clearer on examining the 

variation of the nozzle exit boundary layer displacement thickness, with 

Reynolds number, based on the nozzle exit diameter, as shown in Figure 5.4. 

Variations of the laminar and turbulent boundary layers of the "equivalent 

flat plate" are also shown in this figure. 

The process of boundary layer transition, from laminar to turbulent 

boundary layer profile, involves a large decrease in the shape factor HS9 = 

S/9. In the case of a flat plate, the shape factor decreases from HS9 = 

2.6 in the laminar regime to HS9 1.4 in the turbulent regime. In the 

case of the present nozzle-exit boundary layer this change in the shape 

factor was not so significant, as seen in Figure 5.5. The transition of 

the laminar boundary layer to a turbulent one occurs at a jet Reynolds number Rej = 350,000. 

5.1.2 Total Temperature Effects 

The effects of the jet total temperature on nozzle exit boundary layer 

behaviour were studied at a jet exit Mach number of Mj = O.B. A family of 

nozzle exit boundary layer profiles for different jet total temperatures 

45 
.f:-

0' 

.....-.... 

E 

E 

.............., 

N 

w 

u 

z 

« 

lV) 

o 

2 

1 

o 

o 100 

VELOCITY, 

200 

U 

Tt = 292 K 

300 400 

-1 

(m . s ) 

Figure 5.1 Jet Mach number effects on nozzle exit boundary layer profiles. 
NOZZLE EXIT BOUNDARY LAYER 

VELOCITY PROFILE 

~ N 

w 

u 8 

z 

(j) 

~ 

o 

(/) 

I{l 

--1 5 4 

(j) 

Z 

w 

~ 

o 

o ~~--~~--~--~~--~--~~~ 

o 0.2 0.4 0.6 

DIMENSIONLESS VELOCITY, 

FLOW CONDITIONS: 

Tt = 296.6 K 

UNEXCITED FLOW: 

Mj = 0201 

Re· = 226482 J 

fe = 0 Hz 

Stj = 0.00 

BOUNDARY LAYER PARAMETERS: 

~ = 0.219 mm 8 = 0.091 mm 

HM = 2.407 

0.8 

U/U. J 

Uj = 69.1 m/s 

Ree = 406 

Le = 0 dB 

Ste = 0.0000 

~ = 0.146 mm 

H£8 = 1.604 

Figure 5.2 Low Mach number nozzle exit boundary layer profile. 

47 
48 

NOZZLE EXIT BOUNDARY LAYER 

VELOCITY PROFILEw 

u 8 

Z 

~ (/) 

o 

(f) 

~ .....J 

~ 4 

(f) 

Z 

w 

::?! 

o 

O~~~~--~~~--~-L~~ 

o 0.2 0.4 0.6 

DIMENSIONLESS VELOCiTY, 

FLOW CONDmONS: 

Tt = 292.7 K 

UNEXCITED FLOW: 

Mj = 0.799 

Rej = 1055916 

fe = 0 Hz 

stj = 0.00 

BOUNDARY LAYER PARAMETERS: 

t3 = 0.240 mm 8 = 0.126 mm 

H68 = 1.905 

DB 

U/U. J 

Uj = 258.3 m/s 

Reo = 2619 

Le = 0 dB 

Ste ·= 0.0000 

t = 0.210 mm 

Hell = 1.667 

Figure 5.3 High Mach number nozzle exit boundary layer profile. 
. 

If) 

If) 

w 

z 

::.:: 

w 

-::I: 

ttZ 

w 

::r: 

w 

w 

c:t: 

...J 

a... 

If) 

C; 

O.4r-----~----_r----~------r_----~----_r----_, 

0.3 

0.2 

\ 

\ 

\ 

"EQUIVALENT FLAT PLATE" 

~- LAMINAR BOUNDARY LAYER 

/' r-- TURBULENT BOUNDARY LAYER 

I 

I 

I 

0.600 

Tt = 292 K 

0.1L-____ ____ ____ ______ W_ ____ ____ ____ 

0.2 0.6 1.0 1.4 

REYNOLDS NUMBER, Re. (x 106) 

J 

Figure 5.4 Jet Mach number effects on variation of nozzle exit boundary 

layer displacement thickness. 

49 
2.61 

0 

I 1 ----...2 

i 

00 , I 

I 

\ 

! d I , 

I , 2.2 i -1 i 

I I ! , CD i '0 

::x:: L 9 . 

I 

IX: \ a 

I- \ u _..Q <1: \ LL I ~ 0 -- ----- L.!.J 

1. 8 r 0------0 0 0- 0 <1: 

::r: 

V) I 

I 

I 

i 

f- .... 

I 

J.

4 r 

i 

1 

I 

I 

I 

0.2 0.6 1.0 1.4 

REYNOLDS NUMBER, Re. 

J 

(x 106 ) 

Figure 5.5 Effects of jet Reynolds number on boundary layer shape factor. 

50 
and constant jet Mach number of Mj = 0.8 is shown in Figure 5.6. In order 

to make the profile changes more visible, the curves are plotted in 

physical coordinates. The same figure shows also two additional nozzle 

exit boundary layer profiles for jet exit Mach number of 0.3. As shown in 

the previous subsection, at a jet exit Mach number of 0.8 and unelevated 

flow temperature, the exit boundary layer was found to be turbulent 

(Figures 5.3 and 5.5). A nozzle exit boundary layer profile for Mach 

number 0.8 and heated jet (Tt = 809 K) is shown in Figure 5.7. 

At Mach number 0.8, on raising the plenum total temperature gradually from 

Tt = 290 K (unheated case) to Tt 809 K, the nozzle exit boundary layer 

changed from turbulent to laminar, as seen in Figure 5.8 depicting the 

effects of jet Reynolds number on the boundary layer shape factor. It 

should be noticed that in this process, Reynolds number decreased from Rej 

= 1.06 x 106 to Re· = 0.31 x 106 , as the kinematic viscosity increases with 

increasing temperature. The effect of temperature on the nozzle exit 

boundary layer can best be summarized by plotting the variation of the 

nozzle exit boundary layer displacement thickness, with jet total 

temperature as shown in Figure 5.9. On comparing similar data for the 

unheated jet shown earlier in Figure 5.4, the difference seems to indicate 

that the effects of jet Mach number and jet total temperature do not scale 

universally as a function of nozzle-diameter based Reynolds number. 

5.2 TRIPPED BOUNDARY LAYER 

5.2.1 Tripping Devices 

As a result of the earlier described experiments, it becomes obvious, that 

significant changes take place in the nozzle exit boundary layer as the jet 

total temperature increases. To avoid changes of the nozzle-exit boundary 

layer characteristics due to heating of the flow, a tripping device was 

employed. Two types of tripping devices were used and are designated as 

type A and type B (Figure 5.10). Type A device utilized a 1.6-mm-dia wire 

ring, mounted in the nozzle with a O.l-mm-gap between the ring and the 

nozzle inner wall. Type B device, on the other hand, utilized a 0.4-mm-dia 

wire ring attached firmly to the nozzle inner wall. Both devices consisted 

of a wire ring fitted inside the nozzle and located 6.4 mm upstream of the 

nozzle exit plane. The reasons for this location close to the nozzle exit 

plane were dictated by the nozzle design and by the requirement of simple 

and fast device installation. 

51 
l.n 

~ 

2 

o 0 .6 Mj = 0.80 

• III Mj = 0.30 

,.-.... 

E N E Tt (K) 0> 

N 

'--" 

N 

1 

w 

() 

z 

« l-

(/) 

0 

o 

o 100 200 300 400 500 

-1 

VELOCITY, U (m. s ) 

Figure 5.6 Jet total temperature effects on nozzle exit boundary layer profiles. 
NOZZLE EXIT BOUNDARY LAYER 

VELOCITY PROFILE 

o ~~---~~--~--~~--~~~~~ 

o 0.2 0.4 0.6 0.8 

DIMENSIONLESS VELOCITY/ U/Uj 

FLOW CONDITIONS: Mj = 0.809 

Tt = 809.4 K Rej = 305278 

UNEXCITED FLOW: f e = 0 Hz 

Stj = 0.00 

BOUNDARY LAYER PARAMETERS: 

t) = 0.136 mm () = 0.059 mm 

H68 == 2.305 

Uj = 430.5 m/s 

Reo = 355 

Le = 0 dB 

Ste = 0.0000 

£ = 0.096 mm 

Hee = 1.627 

Figure 5.7 Heated jet nozzle exit boundary layer profile. 

53 
54 

2.6 

• INCREASING 

<b 0 TEMPERATURE 

eo .... I 0 

• 

a:::: 

2.2 

0 0 J- 0 0 0 0 

Lf:. 

w 1.8 0.. 

« 

I 

(J) o M· = J 0.8 

• M· = J 0.3 

1.4 

0 0.5 1 1.5 

REYNOLDS NUMBER, 

Re. 

J ( x 106 

) 

Figure 5.8 Jet total temperature effects on nozzle exit boundarylayer shape factor. 
-

! 

'<J 

~ 

tn 

tn 

UJ 

Z 

:..:: 

u 

-:t: 

IIz 

UJ 

x: 

UJ 

u 

« 

...J 

a.. 

tn 

-

0 

0.4r-----~,--·----~-------~,----~,------~1-------~,----~ 

0.3 I0.2 

I0.1 

M. 0.805 

J 

404 

T t (K) 

/~29J L 290 

491 

/581 

670[::, 

8

1

3L 

809 

1 .1 I 1 I 

0.2 0.6 1.0 

REYNOLDS NUMBER, Re. 

J 

(x 106) 

-

-

-

I 

1.4 

Figure 5.9 Jet total temperature·effects on variation of nozzle 

exit boundary-layer displacement thickness. 

55 
56 

\ 

( 

I 

I 

¢ 1.6 1 0, 

Lf\ 

-& 

6.4 

TRIPPING DEVICE A 

. --- -IlI-----t-

¢ 0.4 00 

. 

o 

Lf\ 

-& 

TRIPPING DEVICE B 

NOZZLE CENTERLINE 

NOZZLE CENTERLINE 

Figure 5.10 Boundary layer tripping devices. 

All dimensions are in mm. 
5.2.2 Velocity Profiles 

The exit boundary layer velocity profile of the tripped, unheated jet at 

constant Mach number of Mj = 0.8, for the A-type tripping device is plotted 

in Figure 5.11 together wlth the shear layer velocity profile measured at 

axial station X/O = 0.098. As seen from this figure, the A-type tripping 

device did not generate a smooth nozzle exit velocity profile. The 

additional humps near the nozzle wall in the Mach number profiles appear to 

be the result of a "jet" through the gap, and a "wake" produced by the 

rather large diameter of the tripping wire. Thus even though the velocity 

profile recovered and smoothed out relatively rapidly, the excessive width 

of the shear layer very close to the nozzle exit was not considered 

adequate to meet the objective of this program. 

The B-type tripping device generated more favorable velocity profiles as 

seen in Figures 5.12 and 5.13. The velocity profiles of tripped, unheated 

and heated jets at constant jet Mach number of M· = 0.8 were measured at 

axial stations X/O = 0.0, 0.125, and 0.25. Momentum/displacement nozzleexit boundary-layer shape factors were calculated for profiles measured at 

X/O = O. The shape factor for the unheated tripped jet was 2.89 and for 

the heated tripped jet it was 2.84. The similarity of the shape factors 

for both tripped jets indicate that the velocity profiles are unaffected by 

heating of the jet, although the tripped nozzle exit boundary layer of the 

unheated jet is thicker than the untripped one at the same jet operating 

conditions. 

The proximity of the tripping device to the nozzle exit plane strongly 

effects the shape of the nozzle exit boundary layer. Thus no conclusion, 

as far as boundary layer character (laminar/turbulent) is concerned, was 

reached from the given set of experimental data. For this reason, the test 

facility was later modified to accommodate a tripping device located 

farther upstream of the nozzle-exit plane. The experiments were rerun with 

this updated tripping device under the Phase II effort and are described in 

Part II of this report. 

57 
VI 

00 

VELOCITY RADIAL PROFILES 

'--" X/D = 0.000 X/D= 0.098 2 

"- 0.] #' 

0 

CL 8 

2 0 0 0 

0 0 

0 

0 0 0 

~ 0.6 c% 0 0 

o~ 0 0 

0::: 0 0 0 

0 

0::: 8 0 

W 0.4 o S 0 

m 0 

0 g L o 0 

==> 0 0 

····7 0.2 0 0 (j 4. __ 

I 0 0 

() 

<C 0' e EE9-9-1. 

~; -1.1 -1 -·1).9 -0.8 -1.1 -1 -0.9 -0.8 

DIMENSIONLESS RADIUS, Z/R 

Mj == 0.800 Uj = 258.9 m/s Rej = 1057251-

T~ = 293,~:-, 1< Tt/Tu = 0.98 

Figure 5.11 Velocity radial profiles of unheated, tripped jet. Tripping device A. 
VI 

\0 

VELOCITY RADIAL PROFILES 

....... 2 . x/o= 0.000 X/O= 0.125 X/O = 0.250 1 

r 0°1 """ a. 0 () 

~ 0 0.8 0 0 () 

~ 0 

0.6 ~ 0 

~ 0 

~ 0 0 0 

0.::: 0 0 

0 0 

0.::: 

0.4 t 0 0 W 0 

rn 0 

L 0 0 0 

~=> 0 0 0 

Z 0.2 0 0 0 0 

O~: 0 0 .I (1 

() 0 0 .... 1' .. 

:.:.: -1.1 -'1 -0.9 -O.B -1.1 -1 -0.9 -0.8 -1.1 -1 -0.9 -0.8 

DIMENSIONLESS RADIUS, Z/R 

Mj :-C' OJ9~~ uj = 25(..3 m/s r~ej = 1055722 

Tl = 2905 1< Tt/To = 0.99 

Figure 5.12 Velocity radial profiles of unheated, tripped jet. Tripping device B. 
0 '" 

VELOCITY RADIAL PROFILES 

.-- X/D= 0.000 X/O = 0.125 X/D = 0.250 2 

O.J oOJO 0 0 

""-. 0 

a. 0 2 0 

0 

0 

0 

0.6 ~ 0 

~ 0 -I t- o -I t- o 

0:::: 0 0 

0:::: 0 1 W -t I- 0 

CD 0 

2 0 0 

:::,) 0 j 0 0 

z 0 0 

I 0 0 

() 0 0 « e 

:2 -1.1 -1 -0.9 -0.8 -1.1 -1 -0.9 -0.8 -1.1 -1 -0.9 -0.8 

DIMENSIONLESS RADIUS, Z/R 

Mj = 0.799 Uj = 389.0 rn/s Rej = ,373517 

1"t = 6722 K Tt/To = 2.29 

Figure 5.13 Velocity radial profiles of heated, tripped jet. Tripping device B. 
6.0 EXCITATION PARAMETER OPTIMIZATION EXPERIMENTS 

The experiments described here were designed to determine the excitation 

parameters that affect the heated jets most strongly. Both, the excitation 

Strouhal numbers and the excitation levels were considered in this 

optimization. In order to truly assess the effects of sound on heated 

jets, complementary measurements for the unheated jets were also made. 

To improve the time efficiency of the entire study, the optimization 

experiments were based on single point flowfield measurements rather than 

on the more time-consuming comparisons of radial profiles and centerline 

distributions. The detailed measurements of the entire flowfield were 

conducted for only those conditions which indicated a significant effect of 

acoustic excitation. 

6.1 EXCITATION STROUHAL NUMBER EFFECTS 

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. The local Mach number at this point was compared with 

the Mach number at the same point but in the absence of upstream acoustic 

excitation. The excitation sound pressure levels were the maximum levels 

of excitation achievable at the particular Strouhal number. 

The optimization exercise for the Strouhal number effects was carried out 

in three parts: (1) unheated subsonic jets, (2) heated subsonic jets, and 

(3) supersonic jets. The results for each of these jets are described 

separately below. 

6.1.1 Unheated Subsonic Jets 

Typical distributions of relative Mach number as a function of excitation 

Strouhal number for a low and a high Mach number are plotted in Figures 6.1 

and 6.2. On the same figures are plotted the excitation levels existent 

at the nozzle exit. As seen in these figures, the most effective Strouhal 

numbers.are Stj = 0.5 and 0.4 for jet Mach numbers Mj = 0.3 and 0.8, 

respectIvely. 

The above described results of Figures 6.1 and 6.2 were for an untripped 

nozzle exit boundary layer. Similar experiments were carried out also for 

61 
62 

c 

:J 

~ X 

::fiG) 

0:: 

W 

m 

::fi 

:::> 

Z 

I 

«, 0 

~ 

w 

> 

~ --I 

w 

0:: 

EXCITATION STROUHAL NUMBER EFFECTS ON RELATIVE MACH 

1.1 

0.9 

0.8 

0.7 

0.6 

NUMBER ON JET AXIS AT X/Oj = 9 

180 

o REL. MACH NUMBER 

11 EXCIT A liON LEVEL 

170 

160 

11 

A 11 

150 

11 A A 

A 

11/l. /l. 

~ 140 

11 

130 

----~----------------~----~--~ ~o o 0.5 1 

STROUHAL NUMBER, St· J 

1.5 

FLOW CONDITIONS: Mj = 0.299 Tt/To = 0.99 

Tt U = 296.0 K j = 102.4 m . S-1 

Rej = 342,670 

Figure 6.1 Low Mach number unheated jet. 

Smooth nozzle. 

"......... 

en 

'"'0 

-..-

Q) 

....J 

....J 

w 

> w 

....J 

Z 

0 

~ t:: 

() 

X 

W 
EXCITATION STROUHAL NUMBER EFFECTS ON RELATIVE MACH 

NUMBER ON JET AXIS AT X/Oj = 9 

1.1 180 

o REL. MACH NUMBER 

bo EXCITATION LEVEL 

c: 170 

::J 

< ~ ill ~ ""0 

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

160 G) 

0::: 0.9 -1 

w 

lD 

~ _.J 

:::> w 

z 150 > 

~ J: 

() Z <t: 0.8 all. All. A 0 ::;; 

W ~ boA 140 I:: > A 0 

~ X 

w ~ A w 

0::: 0.7 

130 

AA 

0.6 i._ ______ ...... _____ --' __ --a... __ ..1 120 

o 0.5 1 1.5 

STROUHAL NUMBER, Stj 

FLOW CONDI1l0NS: Mj = 0.799 Tt/To = 0.99 

Uj = 258.2 m . S-1 Tt = 292.3 K 

Rej = 1,062,804 

Figure 6.2 High Mach -number unheated jet. 

Smooth nozzle, Test Point 1. 

63 
the nozzle equipped with the tripping devices. Figures 6.3 and 6.4 show 

the excitation Strouhal number effects for tripping device A, and Figure 

6.5 shows the similar effects for tripping device B. The effect of the 

increased nozzle exit boundary layer thickness is quite evident in these 

figures. The jet is less prone to excitation, especially for the high jet 

Mach number. The effects of excitation are higher for tripping device B 

than those for tripping device A, because of the thinner nozzle exit 

boundary layer in the case of tripping device B. In all cases, however, 

the most effective Strouhal number still remains in the range of Stj = 0.4 - 0.5. 

6.1.2 Heated Subsonic Jets 

The effects of excitation Strouhal number on heated jets were not 

consistent at different Mach numbers. For example, as may be seen by 

comparison of Figures 6.6 and 6.1, the excitability of the jet at the jet 

Mach number of M· = 0.3, which was heated up to Tt = 811 K has improved 

significantly wi1h respect to the unheated one. However, at high Mach 

number of Mj = 0.8 and total temperature of Tt = 809 K, no effects of 

upstream acoustic excitation on jet mixing were observed at all. This is 

true at least for the achievable excitation levels of Le ~ 148 dB and 

Strouhal numbers of Stj ~ 0.65, as seen in Figure 6.7. This was rather a 

surprising result, and additional experiments were carried out to clarify 

this inconsistency. The conditions for these tests correspond to the line 

A in the chart of jet operating conditions, presented in Section 3.0. The 

results of these experiments are shown in Figures 6.8 through 6.10. The 

results for an intermediate total temperature and Mach number are shown in 

Figure 6.11. The sequence of Figures 6.2, 6.8, 6.9, 6.10, and 6.7 clearly 

shows the effect of increasing jet total temperature on the jet 

excitability at the jet Mach number of M· = 0.8. The higher the jet total 

temperature, the less is the jet affecte~ by upstream acoustic excitation. 

The behavior of tripped, heated jets was consistent with the previously 

acquired results for unheated and heated jets as far as the separate 

effects of tripping and heating are concerned. The tripping device A 

decreased the excitability of the heated jet at low jet Mach number (Figure 

6.12) with respect to the untripped one (Figure 6.6) in a similar way as it 

did for the unheated jets (Figures 6.1 and 6.3). At high jet Mach numbers 

no significant differences were observed between tripped and untripped 

heated jets (Figures 6.13 and 6.7). Similarly, at high jet Mach numbers no 

significant differences were observed when the boundary layer was tripped 

by device B (Figures 6.14 and 6.10). 

Due to a program restriction, the effects of the nozzle exit boundary layer 

64 
c 

;:I 

~ Q) 

::?! 

0::: 

w 

£D 

::! 

:::> 

z 

0 

<t: 

;2 

w 

> 

~ ....J 

w 

a::: 

EXCITATION STROUHAL NUMBER EFFECTS ON RELATIVE MACH 

1.1 

0.9 

0.8 

0.7 

0.6 

NUMBER ON JET AXIS AT X/Oj = 9 

180 

o REL. MACH NUMBER 

11 EXCIT ATION LEVEL 

170 

160 

6. 

6. 6. 6. A A 150 

A 6. 

6. 

6. 140 

A 

6. 

130 

~--~.----~--------------~----~ 120 

o 0.5 1 

STROUHAL NUMBER, St· J 

1.5 

FLOW CONDITIONS: Mj = 0.300 Tt/To = 0.98 

Uj = 102.4 m . s-1 Tt = 294.6 K 

Rej = 345,437 

Figure 6.3 Low Mach number unheated tripped jet. 

Tripping device A. 

,-... 

CD 

'"0 

......, 

Q.) 

....J 

....J 

w 

> W 

....J 

Z 

0 

< I::: 

U 

X 

W 

65 
0.6 ''-----""---'------------------.... 120 

o 0.5 1 1.5 

STROUHAL NUMBER, Stj 

FLOW CONDITIONS: Mj = 0.799 Tt/To = 0.97 

Uj = 259.2 m . s-1 Tt = 295.0 K 

Rej = 1,051,593 

Figure 6.4' High Mach number unheated tripped jet. 

Tripping device A. 

66 
0.6 L.-_ ........ __ --'-__ """-__ ""'-_.....,j ___ ...... 120 

o 0.5 1 1.5 

STROUHAL NUMBER, Stj 

FLOW CONDI110NS: Mj = 0.798 

-1 Uj = 255.4 m . S 

Rej = 1,092,362 

Tt/To = 0.98 

Tt = 286.8 K 

Figure 6.5 High Mach number unheated tripped jet. 

Tripping device B. 

67 
68 

0.6 '---_---' __ --1. ______ -'-__ -'--_---' 120 

o 0.5 1 1.5 

STROUHAL NUMBER, St. J 

FLOW CONDITIONS: Mj = 0.305 

-1 Uj = 170.2 m . S 

Rej = 103,335 

Tt/To = 2.74 

Tt = 811.1 K 

Figure 6.6 Low Mach number heated jet. 

Smooth nozzle. 
c 

:J 

~ Q) 

~ 

0::: 

w 

ill 

::2: 

::) 

z 

I 

0 « 

~ 

w 

> 

.-J 

~ 

W 

0::: 

EXCITATION STROUHAL NUMBER EFFECTS ON RELATIVE MACH 

1.1 

0.9 

0.8 

0.7 

0.6 

NUMBER ON JET AXIS AT X/Dj :::: 9 

180 

o REL MACH NUMBER 

A EXCIT A TION LEVEL 

170 

160 

150 t::t::. I:!. 

f- MI:!. £I" I:!. .ll. 

'1 l'1:!. A 

A 140 

& I:!. 130 

~ __ .~ ____ ~~~~ ____ ~ __ ~ ____ -d 120 

o 0.5 1 

STROUHAL NUMBER, St· J 

1.5 

FLOW CONDIllONS: Mj = 0.809 Tt/T 0 = 2.71 

Figure 6.7 

-1 Uj = 430.5 m . s Tt = 808.9 K 

Rej = 306,720 

High Mach number heated jet. 

Smooth nozzle, Test Point 5. 

,,--.., 

OJ 

""'0 

'--" 

(I) 

.-J 

.-J 

w 

> w 

.-J 

Z 

0 

F- « 

t:: 

0 

X 

uJ 

69 
70 

c 

< Q) 

~ 

0::: 

w 

CO 

~ 

::> 

z 

I 

0 

« 

~ 

~ 

~ .-..J 

w 

0::: 

EXCITATION STROUHAL NUMBER EFFECTS ON RELATIVE MACH 

NUMBER ON JET AXIS AT X/D j = 9 

1.1 180 

o REL. MACH NUMBER 

II EXCITATION LEVEL 

170 

160 

0.9 

II M AA 150 

II A 

0.8 A A 

1:::. 

II II 140 

A llA 

0.7 

AA II 130 

0.6 '___--a. __ ....a... __ """'-__ .a..-______ .....I 

120 

O. 0.5 1 1.5 

STROUHAL NUMBER, St· J 

FLOW CONDITIONS: Mj = O.BOO T tiT 0 = 1.24 

Uj = 289.7 m . S-l Tt = 368.1 K 

Rej = 790,035 

Figure 6.8 High Mach number heated jet. 

Smooth nozzle, Test Point 2. 

,..-.... 

en 

"'0 

"-" 

Q) 

.-..J 

.-..J 

w 

> W 

.-..J 

Z 

0 

!;{ 

t:: 

0 

X 

W 
EXCITATION STROUHAL NUMBER EFFECTS ON RELATIVE MACH 

NUMBER ON JET AXIS AT X/Oj = 9 

1.1 180 

o REL MACH NUMBER 

6. EXCITATION LEVEL 

c 170 

::J 

:::!E 

'x ,....,. <l) a::l 

:::!E "'0 

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

160 d) 

0:::: 0.9 ....J 

w 

a::l 

:.::i! ....J 

:;) W 

z 6.6. 150 > 

6. ~ I 

0 

A A t:..A AAt:.. Z ~ O.B 0 ~ A 

W 6. 140 ~ t::: > 0 

~ x 

W 

...J 

w 0.7 M. 0:::: 

130 

6. 

A 

0.6 120 

0 0.5 1 1.5 

STROUHAL NUMBER, St· J 

FLOW CONDIT10NS: Mj = 0.802 T tiT 0 = 1.65 

Uj = 334.1 m. $-1 Tt = 488.4 K 

Rej = 556,344 

Figure 6.9 High Mach number heated jet. 

Smooth nozzle, Test Point 3. 

71 
72 

c 

::l 

~ Q) 

::2 

0::: 

W 

m 

L 

::> 

z 

I 

0 

<t: 

~ 

w 

> 

.....l 

~ 

w 

0::: 

EXCiTATION STROUHAL NUMBER EFFECTS ON RELA TlVE MACH 

1.1 

0.9 

0.8 

0.7 

0.6 

o 

NUMBER ON JET AXIS AT X/D j = 9 

o REL. MACH NUMBER 

6 EXCITATION LEVEL 

M M 'h 

b. 6 66 

6 M 

Il 

11 6 

A 

0.5 1 

STROUHAL NUMBER, St· J 

180 

170 

160 

150 

140 

130 

120 

1.5 

FLOW CONDITIONS: Mj = 0.806 Tt/T 0 = 229 

Tt = 671.8 K 

Figure 6.10 

-1 Uj = 392.1 m . S 

Rej = 380,206 

High Mach number heated jet. 

Smooth nozzle, Test Point 4. 

--.. 

(1) 

'"0 

"--" 

<L> .....l 

.....l 

w 

> W 

.....l 

Z 

0 

~ l::: 

U 

X 

W 
c 

~ x 

(l) 

2 

~ 

w 

en 

2 

::> 

Z 

I 

() 

« 

~ 

W 

> 

~ --I 

w 

0::: 

EXCITATION STROUHAL NUMBER EFFECTS ON RELA TlVE MACH 

NUMBER ON JET AXIS AT X/Oj = 9 

1.1 180 

o REL. MACH NUMBER 

I::.. EXCIT A liON LEVEL 

170 

160 

0.9 

A A I::..Af I::.. 150 

1:.. A A I::.. 

A I::.. 

0.8 

A Af 

I::.. 140 

0.7 

130 

0.6 I.-_ ........ __ .....I.. __ ...io-__ ...... __ ....... _ ....... 120 

o 0.5 1 1.5 

STROUHAL NUMBER, St· . J 

FLOW CONDITIONS: Mj = 0.481 Tt/To = 1.67 

Tt = 487.9 K -1 Uj = 207.7 m . S 

Rej = 305,586 

Figure 6.11 Intermediate Mach number heated jet. 

Smooth nozzle, Test Point 6. 

,.-... 

en 

"'0 

"-" 

<I.> 

~ 

~ 

w 

> w 

~ 

Z 

0 

~ 1= 

0 

X 

W 

73 
74 

o 

EXCITATION STROUHAL NUMBER EFFECTS ON RELA TlVE MACH 

NUMBER ON JET AXIS AT X/Oj = 9 

1.1 

0.9 

~--~----~----~----~--~-----, 180 

A 

o REL. MACH NUMBER 

A EX CIT A TION LEVEL 

A 

170 

160 

150 

« 0.8 ~ 

A 

~ 

~ 

140 

-...I 

W 

a::: 0.7 A 130 

0.6 ----------~----~----~---------- 120 

o 0.5 1 

STROUHAL NUMBER 1 St· J 

FLOW CONDITIONS: Mj = 0.306 

-1 Uj = 170.6 m . S 

Rej = 103,263 

1.5 

Tt/T 0 = 2.68 

Tt = 812.8 K 

Figure 6.12 Low Mach number heated tripped jet. 

Tripping device A. 

....J 

W 

> 

~ 

z 

o 

~ 1= 

U 

>< w 
F1.0W CONDITIONS: Mj = 0.810 T tiT 0 = 2.66 

Uj = 431.0 m . S-1 Tt = 810.6 K 

Rej = 306,878 

Figure 6.13 High Mach number heated tripped jet. 

Tripping device A. 

75 
76 

c 

::l 

~ Q) 

~ 

0::: 

W 

en 

~ 

::::> 

z 

I 

() 

<{ 

~ 

w 

> 

~ ....I 

w 

0::: 

EXCITATION STROUHAL NUMBER EFFECTS ON RELATIVE MACH 

1.1 

0.9 

0.8 

0.7 

0.6 

NUMBER ON JET AXIS AT X/Dj = 9 

180 

o REL. MACH NUMBER 

t,. EXCITATION LEVEL 

170 

160 

.t- ~Mt,. t,.t,. 150 

At,. 

t,. t,. 

140 

t,. 

t,. 

130 

~ __ ~ ____ -h ______________ ~______ 120 

o 0.5 1 

STROUHAL NUMBER J St· J 

1.5 

FLOW CONDITIONS: Mj = 0.806 Tt/T 0 = 2.28 

-1 U j = 391.9 m . S T t = 671.2 K 

Re· = 381614 J J 

Figure 6.14 . High Hachnumberheated' tripped jet. 

Tripping device B. 

,..-... 

(l) 

"'0 

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

Q) 

....I 

....I 

w 

> W 

....I 

Z 

0 

~ I:::: 

() 

X 

W 
on the excitability of heated jets could not be investigated to provide a 

full understanding of this problem. Evidently, further work was needed and 

is covered in Part II of this report. 

6.1.3 Supersonic Jets 

These experiments were aimed at revealing the effects of upstream acoustic 

excitation on a supersonic, fully expanded, heated jet. The jet operating 

conditions were Mj = 1.2 and Tt 489 K. Jet-noise spectra measurements 

revealed that shockless expansion, for the nozzle used, occurred actually 

at a jet Mach number of Mj = 1.16, which was slightly lower than the 

nominal Mach number 1.2 given by Test Point 7 in the Test Matrix in Section 

3.0. The spectra were measured by a microphone placed at an angle ~ = 90 

degrees, with respect to the jet axis at a distance R* = 100 mm from the 

nozzle axis in the nozzle exit plane. The spectra for three different Mach 

numbers are shown in Figures 6.15 through 6.17. Although these 

measurements were not carried out in an anechoic chamber, it was assumed 

that the spectrum at Mj = 1.16 was that for a fully expanded jet, since it 

contained the smallest contribution of screech-related discrete tones. The 

measurements for supersonic conditions were, therefore, carried out at a 

Mach number of Mj = 1.16. 

The Strouhal number optimization experiments show that a supersonic heated 

jet of,Mj = ~.16, and Tt 489 K is practically unaffected by upstream 

acoustlc excltatlon, as seen in Figure 6.18. Additional Strouhal number 

optimization experiments were carried out for supersonic unheated jets. As 

shown in Figure 6.19, the unheated supersonic, fully-expanded jet response 

to upstream acoustic excitation is similar to that of high-speed subsonic 

jets. In accordance with previously acquired results for high-speed 

subsonic jets, it appears that excitation levels achievable in our test 

facility may not be high enough to enhance mixing of supersonic jets heated 

above the total temperature of Tt ~ 500 K in the range of excitation 

Strouhal numbers up to Stj = 0.6. 

6.2 EXCITATION LEVEL EFFECTS 

The excitation-Ievel-effect experiments were carried out only for some of 

the jet operating conditions given in the Test Matrix in Section 3.0. 

Similar to the Strouhal number optimization experiments, the excitationlevel-effect experiments vTere also based on the changes of the centerline 

local Mach number at X/D = 9 as described in Section 6.1. The excitation 

Strouhal number (Stj) at E~ach test point was selected in accordance with 

77 
'J 

00 

.-.... 

CO 

-a 

-l 

.. -l 

w 

> 

w 

-l 

w 

0::: 

::::> 

(/) 

(/) 

w 

0::: 

0.. 

0 

:z: 

::::> 

0 

(/) 

0 

:z: 

« 

en 

J 

:3 

0 

I- 0::: 

0::: 

« 

:z: 

I I llf = 20 Hz 

II a = 90 deg - l 1\ R*= 100 mrn 10 dB 

t II 

/I 

J\ " - " rV\jlv~~ ~~~ 

I 

I 

0 2 4 6 8 10 

FREQUENCY, f (kHz) 

Figure 6.15 Jet-noise frequency spectrum for M. 

J 

1.12. 
-....I 

\0 

......-

co 

-0 

....l 

....l 

W 

> 

W 

.....l 

W 

0:: 

::::> 

U') 

U') 

W 

0:: 

0.. 

£::) 

Z 

::::> 

o 

U') 

£::) 

z 

« 

co 

I 

3: 

o 

0:: 

0:: 

« 

z 

10 • dB 

L n} 

~f = 20 Hz 

a = 90 deg 

R""= 100 mm 

~J~iJ~~\ "J\, iV' 0,/\j'v/'\, - r J,,,/ V 'vJ' ',-

o 2 4 6 10 

FREQUENCY, f (kHz) 

Figure 6.16 Jet-noise frequency spectrum for M. 

J 

1.16. 
(Xl 

o 

~ ,- -- - --- -, ~ ~ f = 2 0 Hz 

--' II a = 90 deg 

r- R*= 100 mm ~ 10 dB I 

~ j )\ of\ ! 

~ ;rrv V~ ~y~~~ 

Cl I-

§ 

o 

U') 

~ I-

<C 

co 

I 

:3 

~ l- e::: 

<C 

:z 

I I 

o 2 4 6 8 10 

FREQUENCY, f (kHz) 

Figure 6.17 Jet-noise frequency spectrum for M. 1.22. 

J 
EXCITATION STROUHAL NUMBER EFFECTS ON RELATIVE MACH 

NUMBER ON JET AXIS AT X/O j = 9 

1.1 180 

o REL. MACH NUMBER 

A EXCIT A liON LEVEL 

c 170 

i: x 

Q) 

:2: 

160 

0::: 

w 0.9 

CD 

:2: 

:::> 

z L\ 150 

I 

0 

« 0.8 ~ ~ 

W t::.l:A 140 

> /:::,.A 

~ A 

....J 

W At:. A 

0::: 0.7 

A 130 

0.6 1....-__ ........ __ ""--_ ........ ___ ""'--_ ....... __ .... 120 

o 0.5 1 1.5 

STROUHAL NUMBER. ,Stj 

FLOW CONDITIONS: Mj = 1.138 Tt/To = 1.70 

Tt = 488.8 K -1 Uj = 449.4 m . s 

Rej = 892,030 

,.-.. 

en 

""0 

......... 

(J) 

....J 

• ...J 

w 

> W 

....J 

Z 

0 

~ 1= 

0 

X 

W 

Figure 6.18 Supersonic heated jet. Test Point 7. 

81 
82 

c 

:J 

~ x 

Q) 

:::E 

0:::: 

W 

m 

:::E 

:::> 

Z 

I 

0 « 

~ 

W 

> 

--l 

~ 

W 

0::: 

EXCITATION STROUHAL NUMBER EFFECTS ON RELATIVE MACH 

1.1 

0.9 

0.8 

0.7 

0.6 

o 

NUMBER ON JET AXIS AT X/Dj = 9 

AA 

All. 

A 

o REl. MACH NUMBER 

A Exerr A TION LEVEL 

A 

AAM 

AA A 

A 

0.5 1 

STROUHAL NUMBER, St· J 

180 

VO 

160 

150 

140 

130 

120 

1.5 

FLOW CONDITIONS: Mj = 1.149 Tt/To = 1.01 

Tt 6 = 2852 K -1 Uj = 34 .2 m. s 

Rej = 1,811,034 

Figure 6.19 Supersonic unheated jet. 

,.........,. 

ill 

"'0 

'-" 

Gi 

--l 

--l 

w 

> w 

--l 

Z 

0 

~ I:::: 

U 

X 

W 
the results of the Strouhal number 

above. 

optimization experiments, presented 

The excitation level effects on jets of different total temperatures are 

shown in Figures 6.20 through 6.23. When these figures are examined 

collectively, it appears that higher temperature jets require higher 

excitation levels for the flow to respond to this excitation. Probably due 

to this trend, no effects of upstream acoustic excitation were observed at 

jet operating conditions corresponding to Test Points 4, 5, 7, and 8 in the 

Test Matrix (Section 3.0). The maximum excitation 1ev51 which could be 

generated in our test facility was 150 dB (reI. 2 x 10 Pa) or lower at 

high Mj and Tt , and this may not be high enough to produce measurable flow 

changes at the high velocity, high temperature conditions. 

In summary, it has been found that the effect of upstream acoustic 

excitation on mixing of heated jets strongly varies with the jet operating 

conditions. At low Mach numbers, the heated jets were found to be highly 

excitable by sound. At high Mach numbers, however, little effect of sound 

was noticed for heated jets (above 600 K) even though the unheated jets 

were noticeably excitable at the same Mach number as seen in Figure 6.24. 

The preferential excitation Strouhal number does not change significantly 

with a change of the jet operating conditions. The effects of changing 

the nozzle exit boundary layer thickness were found to be similar, for 

both, heated and unheated jets at low Mach numbers in that the thicker the 

boundary layer, the less excitable was the jet. Finally, for heated high 

Mach number jets the effects of upstream acoustic excitation diminish 

significantly, regardless of the nozzle exit boundary layer thickness. 

Bear in mind, however, that the effects of nozzle exit boundary layer 

conditions were not investigated in full detail in this phase of the 

program due to a program funding limitation. 

Based on the results of the optimization exercise, the proper excitation 

conditions were selected for each of the test points in the Test Matrix 

(Figure 3.1) to conduct detailed measurements of the entire flowfield. 

The results of these measurements are presented in the Part III of this 

report. 

83 
84 

r::r: 

w 

(l) 

~ 

:::) 

Z 

I 

0 « 

~ 

w 

> 

-l 

~ 

LU 

r::r: 

EXCITATION LEVEL EFFECTS ON RELATIVE MACH NUMBER 

ON JET AXIS AT X/Oj = 9 

1.1 

o EXCITED JET 

!:l. UNEXCITED JET 

0.9 

0.8 

0.7 

0.6 "-_ ....... _od.-_-'--_ ..... _...&..._--'-_--'-_-"" 

120 130 140 150 160 

EXCITATION LEVEL, Le (dB) 

FLOW CONDITIONS! Mj = 0.798 Tt/To = 0.99 

Tt = 291.1 K 

Stj = 0.41 

-1 Uj = 257.3 m . S 

Rej = 1,069,519 

Figure 6.20 High Mach number unheated jet. 

Test Point 1. 
0:::: 

w 

m 

::2: 

:) 

Z 

I 

u « 

:2 

w 

> 

~ .....J 

w 

0:::: 

EXCITATION LEVEL EFFECTS ON RELATIVE MACH NUMBER 

ON JET AXIS AT X/Oj = 9 

o EXCITED JET 

A UNEXCITED JET 

0.9 

0.8 0 

0.7 

0.6 L-_&.. __ .L..-._.l..-_.r....-_ooI....-_ooI....-_...I..-.--II 

120 130 140 150 160 

EXCITATION LEVEL, Le' (dB) 

FLOW CONDITIONS: Mj = 0..800 Tt/To = 1.25 

Tt = 366.5 K 

Stj = 0.39 

-1 Uj = 289.1 m . S 

Rej = 797,476 

Figure 6.21 High Mach number heated jet. 

Test Point 2. 

85 
86 

cr: 

w 

en 

:.:2 

:::> 

Z 

I 

0 « 

:.:2 

w 

> 

~ w 

cr: 

EXCIT A nON LEVEL EFFECTS ON RELATIVE MACH NUMBER 

ON JET AXIS AT X/Oj = 9 

1.1 ---.,....--..,..--...,....-..,....-....,--...,..-...,..---. 

o EXCITED JET 

b. UNEXCITED JET 

1 A 

0.9 

O.B 

0.7 

0.6 ...... -----"""---'------...... ------""'---

120 130 140 150 160 

EXCITATION LEVEL J Le (dB) 

FLOW CONDITIONS: Mj = 0.B01 Tt/To = 1.66 

Tt = 4BB~2 K 

Stj = 0.35 

-1 Uj = 333.7 m . S 

Re· = 559490 J I 

Figure 6.22 High Mach number heated jet. 

Test Point 3. 
0::: 

w 

IT) 

:E 

:::::> 

Z 

:r: 

U « 

~ 

w 

> 

-l 

~ 

W 

n:::: 

EXCIT A nON LEVEL EFFECTS ON RELATIVE MACH NUMBER 

ON JET AXIS AT X/Oj = 9 

1.1 

1 I-A 

0.9 I0.8 I0.7 I0.6 

120 

I I I 

o EXCITED JET 

A UNEXCITED JET 

-

-

-

-

I I I 

130 140 150 160 

EXCITATION LEVEL, Le (dB) 

FLOW CONDITIONS: Mj = 0.807 Tt/To = 229 

Tt = 6716 K 

Stj = 0.40 

-1 Uj = 392.5 m . S 

Re· = 380934 J ' 

Figure 6.23 High Mach number heated jet. 

Test Point 4. . 

87 
7.0 FLOW VISULAIZATION 

Flow visualization studies of the jet nearfield started with low-speed jet 

conditions. For a Mach number of 0.3, however, the sensitivity of the 

schlieren system was not high enough to make good-contrast pictures. 

Therefore, the Mach number was raised to increase the density gradients in 

the flow and thus to improve the contrast of the schlieren pictures. In 

order to visualize the development of the large-scale structure in detail, 

the schlieren pictures were taken with a "corner" knife edge to utilize the 

effects of both horizontal as well as vertical knife edge orientation in a 

single picture. Each of the presented pictures consists of about 20 

repeated 5-ps-exposures. 

7.1 UNHEATED JETS 

Figure 7.1 shows the response of the unheated jet to upstream acoustic 

excitation at three Mach numbers 0.39, .41, and 0.43. As seen in the 

figure, the vorticity shed from the nozzle lip appears to be in the form of 

vortex rings. The vortex rings are obviously very stable, keeping their 

form until they diffuse some 5 nozzle diameters downstream of the nozzle 

exit. The essential features of the vortex movement and mutual interaction 

can be observed in Figure 7.2 where a series of pictures with a constant 

phase shift of 60 deg is shown. Two vortex structures are traceable in 

this series. The main structure, highlighted by solid lines, tends to 

maintain its formation in the flow and is convected relatively far down the 

flow with a velocity of 0.67U·. The secondary structure, highlighted by 

broken lines, has a shorter lifetime, because it is convected with a lower 

velocity, 0.45Uj, and its vortices are overtaken and absorbed by the 

vortices of the main structure (Figure 7.2f). For the sake of 

completeness, the picture of the unheated, unexcited jet of Mj = 0.48 is 

shown in Figure 7.3 

At high Mach number, a considerable distortion of the vortex structure in a 

tone excited jet was observed. As seen in Figure 7.4, the vortex rings at 

this Mach number were no longer perpendicular to the jet axis. Also, it 

appears that vortices diffused faster than in the low-speed tone excited 

jet. The picture of the unexcited, unheated, high-speed jet is shown in 

Figure 7.5. 

88 
a. 

Mj 0.39 

Tt 292 K 

Stj = 0.39 

Le = 142 dB 

b. 

Mj 0.41 

Tt 292 K 

Stj = 0.50 

Le = 145 dB 

c. 

Mj 0.43 

Tt 292 K 

Stj = 0.43 

Le = 144 dB 

Figure 7.1 Ensemble-averaged photographs of tone-excited? unheated, low Mach 

number jets. 

89 
\0 

o 

[>t-h [>0.. -e- • [>ro [>0 [>0' 

-e- • -e- • -e- • -e- • 

w 

0 N ..... ..... 0'\ 

0 +:-- 00 N 0 

0 0 0 0.- 0.-

ro 0.- 0.- 0., ro 

Q'q ro ro ro Qq 

Qq Qq (Jq 

Figure 7.2 Phase-locked ensemble-averaged photographs of large-scale 

structure development in a tone-excited, unheated free jet. 

(Mj = 0.43, Tt = 292 K, Stj = 0.61, Le = 145 dB) 

[>P> 

-e- • 

0 

0.-

ro 

Q'q 
Figure 7.3 Photograph of an unexited, unheated, low Mach number jeto 

(Mj = O.48 y Tt = 292 K) 

91 
a. 

Mj ::: 0.76 

Tt = 291 K 

Stj := 0.28 

Le := 143 dB 

b. 

Mj 0.80 

Tt 295 K 

Stj := 0.37 

Le :::: 142 dB 

c. 

Mj 0.80 

Tt 293 K 

Stj == 0.48 

Le == 138 dB 

Figure 7.4 Ensemble-averaged photographs of tone-excited, unheated, high 

Mach number jets. 

92 
7.2 HEATED JETS 

The unexcited low Mach number jet, heated up to a total temperature of 670 

K is shown in Figure 7.6. Due to the heating of the flow, the schlieren 

pictures have much better contrast. As mentioned in the previous section, 

heating of the low Mach number jet significantly improved its excitability. 

A similar conclusion may be drawn also from the flow visualization study. 

As seen in Figure 7.7, there is a well defined ring-vortex structure in the 

flowfield of a heated low Mach number jet acoustically excited in the range 

of Strouhal numbers from 0.25 to 0.45. 

The vortex structure in the heated jet appears to diffuse faster than in 

the unheated, low-speed, tone-excited one. It diffuses at approximately 4 

exit diameters downstream from the nozzle exit plane. At an excitation 

Strouhal number of 0.25, pairing of two vortex structures was observed. As 

seen in Figure 7.8, two vortex structures are present in the flow. The 

main one (solid lines) is convected with a velocity of 0.35Ujo The 

secondary structure (broken lines) is convected with a higher velocity of 

0.59Uj; its vortices thus catch up and fuse with the vortices of the main 

structure (Figure 7.8 a through e). At the higher excitation Strouhal 

number of 0.45, no vortex -pairing was observed. As seen in Figure 7.9, 

vortices are convected with a velocity of 0.30Uj and keep a constant 

distance from each other. 

At a high Mach number of 0.8, the jet heated to 670 K did not respond to 

upstream excitation at the maximum allowable level of 136 dB. As seen in 

Figures 7.10 and 7.11, there is no visible difference between the tone 

excited and unexcited jets at given jet operating and tone excitation 

conditions. This observation agrees with the conclusion drawn from the 

results of the optimization experiments. Perhaps, much higher levels are 

needed to excite high Mach number, heated jets. Further work to excite 

such jets using external excitation is described in Part 2 of this report. 

93 
Figure 7.5 Ensemble-averaged photograph of an unexcited, unheated, high Mach 

number jet. 

(Mj = 0.8, Tt = 291 K) 

Figure 7.6 Ensemble-average photograph of an unexcited, heated, low Mach 

number jet. 

(Mj = 0.3, Tt = 666 K) 

94 
a. 

Mj 0.29 

Tt 673 K 

Stj = 0.25 

Le = 144 dB 

b. 

Mj = 0.30 

Tt = 672 K 

Stj = 0.35 

Le = 142 dB 

c. 

Mj 0.30 

T t 671 K 

Stj = 0.45 

Le = 145 dB 

Figure 7.7 Ensemble-averaged photographs of tone-excited 9 heated 9 low Mach 

number jets. 

95 
\0 

'" 

C>1'""n 

-e- • 

w 

0 

0 

0-

(J) 

()q 

C>o.. C>(J) C>() C>t:r 

-e- • -e- • -e- • -e- • C>Pl 

II 

-e- • 

N ~~ ~ 0'\ 

+:-- 00 N 0 0 

0 0 0 

0-

0- 0-

0-

0- (J) (J) 

(J) (J) (J) ()q ()q 

()q ()q ()q 

Figure 7.8 Phase-locked ensemble-average photographs of large-scale 

structure development in a tone-excited, heated free jet. 

(Mj = 0.29, Tt = 673 K, Stj = 0.25, Le = 144 dB) 
\0 

........ 

[>t-n 1>(1) [>0.. [>() [>0'" -e- c -e- • -e- • -e- • -e- • 

w N f-> f-> (j'\ 0 ,J::-. (X) N 0 0 0 0 0 

0.. 0.. 0.- 0.- 0.- (1) (1) (1) (1) (1) Qq Qq Qq ()q Qq 

Figure 7.9 Phase-locked ensemble-averaged photographs of large-scale 

structure development in a tone-excited 9 heated free jet. 

(Mj = 0.30, Tt = 672 K, Stj = 0.45, Le = 145 dB) 

t>Pl 

-e- • 

0 

0.-

(1) 

Qq 
Figure 7.10 Ensemble-averaged photograph of an unexcited 9 heated, high Mach 

number jet. 

(Mj = 0.80, Tt = 663 K) 

Figure 7.11 Ensemble-averaged photograph of a tone-excited, heated, high Mach 

number jet. 

(Mj = 0.80, Tt = 674 K, Stj = 0.32, Le = 136 dB) 

98 
8.0 THEORY AND COMPARISONS WITH EXPERIMENT 

The initial formulation of the analysis is contained in Reference F.1. In 

this section of the report we will examine extensions to that analysis 

without reviewing the previous work. The new developments have enabled the 

predictions of the jet development to be extended beyond the end of the 

potential core. This means that the centerline velocity decay may be 

predicted. The slight decrease in the jet centerline velocity in the 

potential core itself, which is observed experimentally at high levels of 

excitation, is also now predicted by the analysis. These extensions to the 

analysis have involved several separate efforts. These are described in 

the next section. 

8.1 STABILITY OF THE JET IN THE DEVELOPED JET REGION 

In order to evaluate the local rate of growth or decay of the instability 

wave at any location in the jet, it is necessary to solve the OrrSommerfeld equation. The boundary conditions to be satisfied by the 

instability wave are relatively easy to specify, for the purposes of 

numerical calculation, in the potential core region of the jet. This 

analysis is given in Reference F.9 where it is shown that the wave depends 

on modified Bessel functions in the potential core and on Hankel functions 

outside the jet in the ambient fluid. This latter condition still applies 

downstream of the potential core, but close to the jet centerline, a series 

solution to the Orr-Sommerfeld equation must be sought. At high Reynolds 

numbers, in free shear flows, the stability characteristics of the waves 

may be obtained from the inviscid Rayleigh equation. The only difficulty 

with solutions to this equation is that, for decaying solutions, the 

solution is not valid at all real radial locations, Reference F.16. 

Because of this the full viscous Orr-Sommerfeld equation was solved in the 

potential core region, since the calculations of the coupling coefficients 

required the values of the eigen solutions at all real radial locations. 

However, downstream of the end of the potential core, as no further 

coupling of any significance occurs between the exciting acoustic wave and 

the excited instability wave then, since the calculations only require the 

local growth rate, the inviscid Rayleigh equation may be solved. A series 

solution is sought where the mean velocity and density are written 

99 
+ ..... 

and 

The instability wave pressure p(r) is written, 

These forms are substituted into the Rayleigh equation and the coefficient 

a2n evaluated for given b2n and c2n' The terms were evaluated up to a4' 

The mean velocity profile is assumed to take a Gaussian form: 

u _a*.r 2 / 

where Uc is the centerline velocity, b is the jet half-width and a* = 

0.69315. The jet density is related to the axial mean velocity using 

Crocco's relationship [F.17]. The coefficients b2n and c2n are then 

readily obtained. For example, 

c 

o 

*- / b 2 - a.u • 

c 

The local growth rate of the instability wave is then obtained by 

integrating the Rayleigh equation subject to the series solution for small 

radius and matching with the Hankel function solution outside the jet flow. 

100 
As is the case in the annular mIxIng region of the jet, the downstream 

development of the jet flow beyond the end of the potential core is 

determined from the solution of the integral equatiohs. These are the 

momentum integral equation, the mean mechanical energy equation, and the 

turbulent kinetic energy equation. Using the notation of Reference F.1, 

these equations may be written, 00 

d Joo u3 

- . p. - .. r . dr dx 2 

00 

f~·r.dr o o 

and 00 00 - 2 f P . € ~.( ~ ~ ) • r . d r + 

00 00 

dx d J p.u.q.r.dr - f ~. r . d r - J €"'; r . d r 

o o o o 

Here, • (r) represents the interaction between the instability wave and the 

fine-scale turbulence, t* denotes the viscous dissipation, and q represents 

the turbulent kinetic energy. Models are proposed for all the terms in the 

integrals on the basis of experimental observations. Thus, we write 

u = uc.exp [ _a~r2 / b 2 ] 

q = q(x) exp [_1.7946 

0.05 

and 

; c

2 = 1.5 

Using the same arguments as proposed in Reference F.1, the wave interaction 

term may be written, 

The constant c3 is an unknown empirical constant which sets the level of 

coupling between small scale turbulence and the instability waves. In this 

equation L (x) is a local length scale defined as the radial distance 

between points where u is 0.9 Uc and 0.1 uc ' respectively. In this case, 

101 
for the Gaussian velocity profile, 

1= 1.43274 b. 

With these assumptions the integral equations reduce to a system of 

ordinary differential equations for uc ' b, and q as functions of downstream 

distance. The equations are solved numerically using a variable step-size 

fourth-order Runge-Kutta integration scheme. 

The final extension to the previous analysis permits the effect of the 

finite amplitude instability wave on the jet centerline velocity, in the 

potential core region, to be determined. In the potential core region, the 

centerline velocity had been constrained to be equal to the jet exit 

velocity. However, for sufficiently high levels of excitation, the 

centerline velocity is observed experimentally to vary. This is due to the 

effect of finite amplitude instability waves growing rapidly along the jet. 

Their influence is felt on the jet axis. Consider the instantaneous 

momentum equation for axisymmetric disturbance and mean flow. 

dU 

+ 

dV 1 1 d p.u.-dX p.v·-dr Re . -

r . a r (r.~; I 

Close to the jet centerline 

u = u (x) + u 

c c 

V = 0 

P P (x) + p c c 

Thus, on averaging, the axial momentum equation reduces to 

du du du 

c c + 

c 0 Pc u + Pc u ~ P u c dx c c c dx 

For the sake of simplicity, it 

correlation is much smaller than 

the momentum equation reduces to, 

will be assumed that the density/velocity 

the velocity/velocity correlation. Thus, 

102 
Integrating, and assuming the instability wave has zero amplitude at the 

jet exit gives, 

-2 

u 

c 

1 ~2 

- u 

c 

If we introduce the 

wave, such that 

obtain 

wave-like form of the solution for the instability 

-2 

u 

c 

---=-z 

u 

c 

1 / (l + 

1

2 -2 

• u 

c 

we 

Clearly, as the amplitude of the instability wave increases, the jet 

centerline velocity decreases. For example, IAI?IOcI2 reaches a typical 

maximum amplitude of 0.025, for high excitation levels. This means that U c falls to 98 percent of the exit velocity. This is typical of the earlier 

experimental observations. 

The presented prediction scheme is based on the assumption that the initial 

boundary layer is turbulent and the only influence of the boundary layer is 

through its thickness at the jet exit. To include the influence of the 

type of the initial boundary layer in the prediction scheme would require a 

more detailed modeling of the initial flow development including the 

transition of the mean velocity profile from a laminar boundary layer to a 

turbulent mixing layer. Tough this would be possible, it is beyond the 

scope of the present prediction scheme. 

All of the preceding extensions to the earlier 

incorporated into a computer program, which also 

representation of the downstream jet development. 

analysis have been 

provides a graphical 

8.2 COMPARISON WITH THEORETICAL PREDICTIONS 

8.2.1 Typical Predictions 

The 'computational program, based on the 

distributions of four basic parameters 

upgraded theory, generates axial 

of a tone excited jet. These 

103 
characteristics are: (1) mean velocity, (2) jet half width, (3) peak 

turbulent kinetic energy, and (4) peak pressure level. Figures 8.1 through 

8.4 show typical predicted distributions for a heated, excited jet at a 

Mach number of Mj 0.48, total temperature of Tt = 488 K, excitation 

Strouhal number of Stj = 0.48, and excitation level Le = 151 dB. Similar 

sets of plots were acquired for the other jet excitation and operating 

conditions also. 

8.2.2 Typical Comparisons 

The results of theoretical predictions were compared with experimentally 

acquired data. However, since the turbulence and acoustic pressure data 

were not obtained under this contract, only the mean velocities were 

compared. The comparison of mean velocities was based on the behavior of 

local Mach number on the jet centerline at nine nozzle exit diameters 

downstream of the nozzle exit plane. As described in Section 6.0, the Mach 

number at this location was found to strongly depend on the excitation 

Strouhal number. Because of the time consuming nature of the computer 

programs, the comparisons between prediction and measurements were made 

only at one jet Mach number. A moderate jet Mach number of Mj = 0.48 and 

jet total temperature of Tt = 488 K were selected for this comparison. As 

shown in Figure 8.5 at this jet operating condition, the agreement between 

predicted and measured behavior of the local Mach number was found to be 

excellent. The particular excitation levels used for the theoretical 

predictions were the same as the measured ones, and were presented earlier 

in Figure 6.11. 

Because of the funding limitations, only a limited number of calculations 

have been made at other jet operating conditions. However, the preliminary 

results indicate that for the highly heated jets the predicted mean 

velocities somewhat differ from measured ones. It appears that for the 

high Mach number heated jets, the theory predicts faster velocity decay 

along the centerline than the measured one. On the other hand, for the low 

Mach number heated jets, the theory predicts more gradual velocity decay 

compared to the measured one. 

On the whole, it may be concluded that the theory works satisfactorily, 

particularly for the moderate jet Mach numbers and moderate jet total 

temperatures. However, further calculations are necessary to verify the 

theory for highly heated jets at low and high jet Mach numbers. 

104 
. ., 

:::::> 

........ 

:::::> 

., 

0 

I-

« 

0:::: 

>- Iu 

0 

.-J 

LJ..I 

> 

1.0 

0.8 

0.6 

0.4 

M. = 0.481 

TJ IT = 1.67 t 0 

St· = 0.479 

L J = 151 dB e 

DIMENSIONLESS DISTANCE, X/D 

Figure 8.1 Mean velocity centerline distribution. 

105 
CY.: 

"-.0 

::r: 

Ia 

3: 

lJ... 

....J 

c::( 

::r: 

Iw 

--, 

106 

St· = 0.479 J L = 151 dB e 

2.0 ~----~------~------~------~----~ 

1.6 

1.2 

0.8 

0.4 

2 4 6 8 10 

DIMENSIONLESS DISTANCE, X/D 

Figure 8.2 Half-jet width centerline distribution. 
, 0-

>-

(,!J 

a::: 

L1J 

:z 

L1J 

u 

IL1J 

:z 

~ 

L1J 

U 

:z 

L1J 

-I 

:::> 

co 

0::: 

:::> 

I-

~ 

<C 

L1J 

D.. 

Mj = 0.481 

Tt/To = 1.67 

St· = 0.479 

L; = 151 dB 

0.040----·--~----~------,------r-----, 

0.036 

0.032 

0.028 

0.024 

0.020 L-__ , __ ~ ____ ~ ______ ~ ____ ~ ____ ~ 

o 2 4 6 8 10 

DIMENSIONLESS DISTANCE, X/D 

Figure 8.3 Peak turbulent kinetic energy centerline distribution. 

107 
108 

160 

,.-.. 

co 

'"0 

10- 140 

W 

0::: 

::::> 

(/) 

U) 

W 

0::: 

0-

W 

z 120 ....J 

0::: 

W 

Iz 

w 

u 

100 

o 

Mj = 0.481 

T tiT 0 = 1.67 

2 4 6 

Stj = 0.479 

L = 151 dB e 

8 

DIMENSIONLESS DISTANCE, X/D 

10 

Figure 8.4 Peak pressure level centerline distribution. 
c 

:::J 

~ x 

(]) 

~ 

... 0:: 

w 

CD 

~ 

::::J 

Z 

I 

() 

<{ 

~ 

.-J 

w 

a:::: 

EXCITATION STROUHAL NUMBER EFFE8TS ON REL..1.T;VE MACH 

NUMBER ON JET AXIS AT X/'Dj - 9 

1.1 

1 

o 0 

0.9 

0.8 

0.7 

a 

o EX?ER[M::~'ljT 

TH::::ORY 

o ocfJ 

'00 0 

0.5 1 1..5 

STROUHAL NUMBER, St· J 

FLOW CONDITIONS: Mj = 0.481 

Uj = 207.7 rr/s 

Rej = 305586 

T tiT v = 1.37 

T - /';;;''79 K . t - "'Ui. ' 

Figure 8.5 Comparison between theory and experiment. 

The particular excitation levels for each 

test point are in Figure 6.11. 

109 
9.0 CONCLUSIONS FOR INTERNAL EXCITATION 

To obtain a fundamental understanding of the effects of relatively strong 

upstream acoustic excitation on the mixing of heated jets, a fairly 

detailed experimental study has been carried out. A theoretical model has 

been extended to consider the region downstream of the jet potential core. 

A limited comparison between theoretical prediction and experimental 

results has also been made. 

A summary of key observations is given below. Of course, the validity of 

the conclusions, presented here, is restricted to the range of investigated 

jet operating and flow excitation conditions. 

o 

o 

o 

o 

110 

The sensitivity of heated jets to upstream acoustic excitation 

strongly varies with the jet operating conditions. 

A low Mach number jet (Mj = 0.3) shows increased sensitivity to 

upstream excitation as the jet temperature is raised, but the 

high Mach number jet (M' = O. 8) exhibits a decrease in the jet 

excitability as the jet temperature rises, as shown in Figure 

9.1. This figure is based on the results presented in Section 

6.0. 

Preferential excitation Strouhal number does not change 

significantly with a change of the jet operating conditions. 

The excitation Strouhal number that produces the maximum changes 

in the jet flowfield practically does not depend on the jet 

operating conditions. As shown in Section 6.0, the most 

effective excitation Strouhal number remained in the range of Stj 

= 0.35 - 0.5 at all examined jet operating conditions. 

The effects of the nozzle exit boundar were 

found to e similar for oth heated and un Mach 

number. 

The excitability of both heated and unheated low speed jets 

decreases as the nozzle exit boundary layer thickens. The 

artificially generated thicker nozzle exit boundary layer at low 

Mach numbers depressed the effects of upstream acoustic 

excitation regardless of the jet temperature. This outcome was 

demonstrated in Sections 5.0 and 6.0. 

The experiments with a tripped boundary layer for the heated high 

speed jets did not help to clarify the effect of nozzle exit 
1.1 

c X/D. = 9 ;:i J 

~ To = 297 K 

x 

Q) 

::2 A Mj = 0.80 

1 Stj = 0.35 - 0.42 

Le = 145 - 150 dB 

a:: 

w 

m 

:2 

::) 0.9 z 

I 

~ .. ~ .. .. ~ .. ::2 ... ..,"'-'" ..., ......... ~ 

w 0.8 " .................... 

> .... " ... " 

o Mj = 0.30 ............... 

~ Stj = 0.35 ---.,." .. 0 

-I 

W Le = 150 - 153 dB a:: 

0.7 

1 1.5 2 2.5 3 

TEMPERATURE RATIO, Tt/To 

Figure 9.1 Temperature effects on acoustically excited jets. 

111 
boundary layer profile (laminar or turbulent) on heated jet 

excitability. The tripping device used in our experiment 

generated a boundary layer which was too thick. Jet excitability 

depends also on nozzle exit boundary layer thickness, as 

discussed above, thus the possible effect of the changed boundary 

layer profile was hidden by the effect of increased boundary 

layer thickness. No firm conclusions were drawn about effects of 

nozzle exit boundary layer profile on the excitability of heated 

jets at this point. Further experiments on boundary layer 

effects ate described in Part II. 

o This study has further confirmed the earlier Lockheed findings 

that a 'et can be excited even if it is turbulent and is operated 

at high Reynolds num ers. 

Because a majority of the studies in this field have been carried 

out for low Reynolds number jets (and also ~ostly for laminar 

jets), there appear to prevail common misgivings amongst many 

members of the research community about the validity of the 

acoustic excitation effects for turbulent and high Reynolds 

number jets. The present studies categorically confirm earlier 

Lockheed findings (References D.2 and D.3) that a jet can be 

excited even if it is turbulent and is operated at high Reynolds 

numbers (see Figures 5.3 and 6.2). 

o The upgraded theory has been verified at moderate jet Mach number 

and moderate jet total temperatures. 

o 

112 

Good agreement has been found between the theory and the 

experiments in moderately heated jets. However, the theory has 

not yet been fully confirmed for highly heated jets, and a range 

of excitation conditions. 

Further ex erimental and theoretical work is needed to obtain 

better understandIng of heated jets under inf uence of 

acoustic excitation. 

Further comparison of predicted results with the measured data 

needs to be made for a range of test conditions. The areas where 

disagreements are found need to be examined closely by way of 

measurements of the turbulence intensities in the heated, excited 

jets. Also, the sound source used for the present tests needs 

to be upgraded so as to produce much higher excitation levels at 

the jet exit. Finally, if needed, the assumptions made in the 

theory need to be reassessed in the light of measurements that 

may be generated in any future program. 
The results obtained in this experimental investigation have pointed out 

some differences between heated and unheated jets, as far as their 

excitability and consequently their rates of mixing are concerned. In 

addition, it has provided an extensive experimental data base on heated 

jets under the upstream acoustic excitation, as well as without 

excitation. 

It was these results that prompted the addition of an external excitation 

source, the results for which are described in Part 2 of this report. It 

is shown in Part 2 that heated, supersonic jets are excitable, but to 

understand the effects properly, further work is still needed. 

113 
a 

A 

a*,aO,a2,a4 

b 

bO,b2,b4 

cO,c2,c4 

D 

f 

H 

K 

k 

L 

I 

M 

m 

mw 

n 

p 

q 

r 

R 

R* 

Re 

St 

T 

U,u 

u' 

V,v 

v' 

x 

Y 

Z 

114 

LIST OF SYMBOLS 

sound velocity 

instability wave amplitude function 

constants 

half jet width 

constants 

constants 

nozzle exit diameter 

frequency 

shape factor 

dynamic correction ratio 

wave number 

level 

length scale 

Mach number 

exponent 

circumferential mode number 

nth term 

pressure 

turbulent kinetic energy 

radius 

nozzle exit radius 

distance 

Reynolds number 

Strouhal number 

temperature 

axial velocity 

axial fluctuating velocity 

radial velocity 

radial fluctuating velocity 

axial coordinate 

radial coordinate 

radial coordinate 

angle 

specific heat ratio 

displacement thickness 

energy thickness 

viscous dissipation 

kinematic eddy viscosity 

interaction term 

density 

momentum thickness 

pressure ratio 

boundary layer thickness 
Subscripts 

c 

e, ex 

j 

p 

s 

t 

un 

o 

cS 

£ 

e 

Overbars 

centerline 

excited 

jet, based on nozzle diameter 

probe 

static 

total 

unexcited 

ambient 

based on displacement thickness 

based on energy thickness 

based on momentum thickness 

time average 

phase average 

instability wave 

115 
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0.49 

Zaman, K.B.M.Q.; and Hussain, 

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CR-3538, 1982. 

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F.15 

F.16 

F.17 

Tam, C.K.W.; and Chen, K. C.: 

in Two-Dimensional Mixing Layers. 

303-326,_1979. 

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P. J.: The Radiation of Sound by the 

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with Experiment. J. Sound and 

129 
NI\S/\ 

National ,Aeronautics and 

Space Administration 

1. Report No. 

NASA CR-4129, Part I 

4. Title and Subtitle 

Report, Documentation Page 

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

5. Report Date 

June 1988 

Acoustically Excited Heated Jets 

I - Internal Excitation 6. Performing Organizati;~ Code 

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

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

M. Salikuddin, and P.J. Morris 

9. Performing Organization Name and Address 

Lockheed Aeronautical Systems Company - Georgia 

Dept. 72-74, Zone 403 

LGB6ER0022 (E-4001> 

10. Work Unit No. 

505-62-91 

11. Contract or Grant No. 

NAS3-2370B 

Marietta, Georgia 30063 13. Type of Report and Period Covered 

r1-2.-s-po-n-sO-rin-g-A-ge-n-CY-N-a-me-a-n-d-Ad-d-re-ss------------------------------~ Contractor Report 

Final 

National Aeronautics and Space Administration 

Lewis 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. Salikuddin, 

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

University, University Park, Pennsylvania. 

16. Abstract 

A detailed, mostly experimental, study to understand the effects of relatively 

strong upstream acoustic excitation on the mixing of heated jets with the surrounding air was carried out. To determine the extent of the available information on experiments and theories dealing with acoustically excited heated jets, 

an extensive literature survey was carried out at the outset of this program. The experimental program consisted of flow visualization ~nd flowfield velocity and temperature measurements for a broad range of jet operating and flow excitation conditions. A 50.B-mm-diam nozzle was used for this purpose. Parallel 

to the experimental study, an existing theoretical model of excited jets was 

refined to include the region downstream of the jet potential core. Excellent 

agreement was found between the theory and the experiments in moderately heated 

jets. However, the theory has not yet been confirmed for highly heated jets. 

It was found that the sensitivity of heated jets to upstream acoustic excitation 

varies strongly with the jet operation conditions and that the threshold excitation level increases with increasing jet temperature. Furthermore, the preferen- tial Strouhal number is found not to change significantly with a change of the 

jet operating conditions. Finally, the effects of the nozzle exit boundary layer 

thickness appear to be similar for both heated and unheated jets at low Mach 

numbers. 

17. Key Words (Suggested by Author(s» 

Sound-flow interaction; Jet mixing; Flow 

visualization; Velocity and temperature 

measurement; Large-scale structures 

18. Distribution Statement 

Unclassified - Unlimited 

Subject Category 02 

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

Unclassified Unclassified 134 

NASA FORM 1626 OCT 86 *For sale by the National Technical Information Service, Springfield, Virginia 22161 

22. Price' 

A07 

NASA-Langley, 1988 
End of Document