The noise from normal-velocity-profile coannular jets

Journal ofSound

THE

and Vibration (1985) C%(2), 213-234

NOISE

FROM

NORMAL-VELOCITY-PROFILE

COANNULAR H. K. TANNA

AND

JETS? P.

J. MORRISI

Lockheed-Georgia Company, Marietta, Georgia 30063, U.S.A. (Received 5 January 1983, and in revised form 29 February 1984)

The noise from subsonic coannular jets with normal velocity profiles (to represent typical high-bypass-ratio turbofan engines) is studied experimentally and theoretically. The ‘source alteration” effects and the “flow-acoustic interaction” effects are isolated as far as possible for all jet conditions. In the acoustic experiments, the effects of fan-to-primary velocity ratio and static temperature ratio are quantified explicitly. Furthermore, the coannular jet noise levels are compared directly with the equivalent single jet noise levels for fixed aerodynamic performance of the engine. Previous theoretical work on single-stream jet

noise conducted at Lockheed is used to develop an analytical model, based on geometric acoustics, to link the acoustic and flow characteristics of coannular jets. The predictions based on this model provide very good agreement with measured results in most cases.

1. INTRODUCTION

While the noise from a conventional single-stream jet is relatively well understood, a fundamental study of the noise radiated by coaxial or coannular jet flows is required before the basic noise generating mechanisms can be quantitatively specified and noise reduction measures can be effectively implemented. Two categories of coannular jets are practically relevant: (a) the normal-velocity-profile coannular jets, representing turbofan engines, in which the primary jet velocity is greater than the secondary jet velocity, and (b) the inverted-velocity-profile coannular jets (for possible application in advanced supersonic transports), in which the outer stream is discharged at higher velocity than the inner stream. Fundamental research on the noise from both classes of coannular jets has been on-going at Lockheed over the last four years. In particular, as a result of two NASA Langley contracts on the noise of inverted-velocity-profile (IVP) coannular jets, the mechanisms of (a) jet mixing noise reduction in subsonic IVP coannular jets, and (b) shock-associated noise reduction in supersonic IVP coannular jets have now been identified and essentially understood. The results from these studies are documented in references [l] and [2], respectively. The present paper describes the findings of the recently completed experimental and theoretical work dealing with the noise from subsonic normal-velocity-profile (NVP) coannular jets. To maintain a proper perspective of the various physical phenomena which give rise to the total noise from a coannular jet, the technical approach must isolate the major t A firstreport on this work was presented at the AIAA 7th Aeroacoustics October 1981 (Paper No. AIAA-81-1992). $ Permanent address: Department of Aerospace Engineering, Pennsylvania Pennsylvania 16802, U.S.A.

Conference,

Palo Alto, California,

State University,

University

Park,

213 0022-460X/85/020213+22

%03.00/O

@ 1985 Academic

Press Inc. (London)

Limited

214

H. K. TANNA

AND

P. J. MORRIS

effects. In particular, for turbulent jet mixing noise, it is now well established that the changes in the noise characteristics as a function of jet operating condition and/or nozzle geometry are the net result of two effects. The first effect, termed “source alteration”, describes the changes in source strength and/or character. The second effect, commonly referred to as “flow-acoustic interaction”, describes the changes in radiation efficiency of the sources that occur when sound generated from a given source has to propagate through the mean velocity and temperature field in the jet exhaust flow, before reaching the surrounding ambient medium. To obtain a basic understanding of the complete noise generation and radiation process, these two effects are quantified separately in the present work. In other words, the theoretical and experimental efforts are structured in a manner which isolates, as much as possible, the source “strength” changes from the “shrouding” influence of the surrounding flow field. In this paper, the acoustic experiments and results are described in sections 2 and 3, while the theoretical work is discussed in section 4. Following this, some typical comparisons between theory and experiment are presented in section 5. Finally, the main conclusions from this study are stated in section 6.

2. ACOUSTIC EXPERIMENTS The experimental program to obtain the far field noise characteristics of normal-velocityprofile coannular jets is described in this section in two parts. The first part deals with the facilities and the data acquisition and reduction procedures used in the experiments, while the second part gives the details of the coannular jet test conditions. 2.1.

FACILITIES

AND

DATA

ACQUISITION

acoustic experiments were conducted in the Lockheed anechoic facility, which has been used extensively in the past to conduct both single jet and coannular jet noise measurements. A detailed description of this facility is given in reference [3], and the salient features are summarized below. The anechoic chamber provides a free field environment at all frequencies above 200 Hz, and incorporates a specially designed exhaust collector/muffler which (i) provides adequate quantities of jet entrainment air, (ii) distributes this entrainment air symmetrically around the jet axis, and (iii) keeps the airflow circulation velocities in the room to a minimum. The air supply for the primary and secondary jets originates from the main compressor, which provides up to 9 kg/s of clean dry air at 2.07 x lo6 N/m’. This air is heated by a propane burner to approximately 1100 K. Downstream of the burner, the primary and secondary air supplies are controlled independently, and each has a hot and a cold valve so that any desired jet operating conditions can be achieved within the pressure and temperature limitations of the system. Each airstream is then directed through a diffuser and a muffler to minimize internal noise levels. The two streams finally enter their respective plenums, which are located upstream of the coannular nozzle section. Special attention has been paid to flow conditioning. Downstream of the mufflers, the flow area to nozzle exit area is maintained greater than 36: 1 up to the nozzle inlet. This ensures that no additional noise or turbulence is generated, since the flow velocities are very low. To ensure that the relative axial positions of the exit planes of the two nozzles do not vary, a special expansion coupling has been incorporated in the primary ductwork, with a corresponding spacer in the secondary ductwork. This provides for expansion or The

COANNULAR

215

JET NOISE

contraction of the inner duct relative to the outer duct of *4 mm from center, which is adequate for the thermal expansion associated with the probable temperature differentials between primary and secondary flows. Finally, to maintain concentricity of the two nozzles at all times, a special spoked nozzle attachment flange is included. A model-scale, coplanar, coaxial nozzle configuration of equivalent diameter Deq = 7.77 cm and fan-to-primary nozzle area ratio A//A, = 2.93 was used to represent typical high-bypass-ratio turbofan engines. The acoustic measurements were conducted on a polar arc of radius 3.66 m (12 feet). Ten 6.35 mm ($ inch) Briiel and Kjaer (B & K) microphones were positioned from 20” to 110” to the downstream jet axis at intervals of 10”. The sound pressure data were recorded on a multi-channel Honeywell tape recorder for subsequent analysis. The recorded data were analyzed on a General Radio one-third octave band analyzer over the frequency range from 200 Hz to 80 kHz, and the results were recorded on a digital tape recorder. The recorded levels were subsequently processed on a digital computer using a data reduction program which applies microphone frequency response corrections and atmospheric attenuation corrections, and computes overall sound pressure levels over the frequency range 200 Hz-80 kHz. It should be noted that all sound pressure and sound power results presented in this paper are lossless (that is, with zero atmospheric attenuation), and the levels are expressed for a common observer distance of R = 47 Deq (i.e., R = 3.66 m) from the nozzle exit. 2.2.

TEST

PROGRAM

To evaluate the noise benefit of coannular jets, it is desirable to have a means of comparing different coannular jet noise levels which takes realistic account of the aircraft propulsion design constraints. Significant parameters in this context include nozzle gross thrust, mass flow rate, total enthalpy change, and exit area. A constant-thrust comparison is obviously essential; which two other parameters should be kept constant is to some extent arbitrary. In the Lockheed work, area and mass flow rate have been chosen for the time being, and it is believed that the final conclusions are not expected to differ significantly if mass flow rate and total energy are kept constant instead (with area as the floating parameter). As a basis for quantifying the noise reductions, therefore, the fully mixed equivalent single jet, defined as having a uniform exit profile and the same exit area, mass flow rate, and thrust as the actual coannular jets, is used. Comparison on TABLE

1

Test matrix for acoustic measurements

1.0

1t

9

17

25

0.9

2

10

18

26

0.8

3

11

19

27

0.7

4

12

20

28

0.6

5

13

21

29 30

0.5

6

14

22

0.4

7

15

23

31

0.3

8

16

24

32

i Reference

or equivalent

jet condition

1.ooo o-900 0.800 o-700 O-600 0.500 0.400 0.300

1*ooo 0.900 O-800 0.700 0.600 0.500 0.400 0.300

1.ooo 0.900 0.800 0.700 0.600 0.500 0.400 0.300

9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24

25 26 27 28 29 30 31 32

Vrl v,

1.000 0.900 O-800 o-700 0.600 o*soo o-400 0.300

-

I 2 3 4 5 6 7 8

TP

o-500 0.500 o-500 0.500 0.500 0.500 0.500 0*500

0.700 0.700 0.700 O-700 0.700 0.700 o-700 o-700

0.850 0.850 0.850 0.850 0.850 0.850 0.850 0.850

1.ooo ldM0 1 *ooo 1.ooo 1.ooo 1 .ooo I*000

1400

TWTp

0.553 0.543 0.53 1 0.515 0.492 0.46 1 0.416 0.351

0.391 O-427 o-470 O-520 0.580 O-652 o-735 O-828 0.649 O-708 0.777 0.855 0.942 1.034 1.119 1.171

0.649 0.704 0.767 O-835 0.908 0.980 1.039 I.063

0.649 O-702 0.760 0.823 O-888 0.949 0.994 1.007

0.526 0.513 O-496 0.474 0445 0407 0.356 0.29 1 0.537 0.525 0.510 0.490 0.464 0.428 0.379 0.313

0.649 0.699 0.754 O-812 O-870 O-923 o-959 0.964

VP/a0

0.516 0.501 0.483 o-459 0.428 0.389 0.338 0.273

Mf

0449 0.488 0.534 0.586 0.646 o-715 0.792 0.872

0.485 0.526 O-572 0.624 0.684 0.750 0.822 0.894

O-516 o-557 O-604 O-656 0.714 0.777 0.844 O-910

MP

2

0.649 0,637 0.62 1 O-598 O-565 o-517 0448 0.351

0.649 0.634 0.613 0.585 0.545 0.490 0.415 o-319

0.649 0.63 1 0.608 0.576 0.533 0.474 0.398 0.302

O-649 0.629 O-603 0.569 0.522 0.461 0.384 O-289

Vflao

2.755 2.75 1 2.735 2.700 2,634 2.517 2.318 2.000

2.083 2.079 2.064 2.033 1.975 1.877 1.720 1,484

1.786 I.782 1.769 1.740 1.687 1.600 1.465 1.268

1.578 1.575 1.562 1.535 I.487 l-409 1.290 1.122

Tp/ To

Test conditions

TABLE

1.378 1.376 1.368 1.350 1.317 1.258 I.159 1.ooo

1.163 1.203 1.256 1.330 l-432 1.568

1.149 1.177 I.214 .262 .324 .406 .512 .642

1.175 I -207 1.248 1.300 1.367 1.452 I.558 1.680

1.518 1.515 1.503 1 *479 1 .434 1.360 1.245 1.078 1.458 1.455 1445 1.423 1.383 1.314 1.204 1.039

.I99 ~235 -279 .335 -405 *491 .594 .710

6

1 -578 1 .575 1~562 1 .535 1.487 I .409 1 .290 1 .122

Tf/ G

l-231 1.222 1.212 1.198 I.180 1.157 l-126 1.089

1.217 1.207 1.194 I.179 I.159 1.134 1.104 1.070

1.208 I.197 1.183 1.166 1.146 I.121 1.092 1.060

1.199 1.187 1.173 1.155 1.134 1.110 I.082 1.053

k -

2.839 2.851 2.856 2.847 2.81 I 2.730 2.568 2.274

2.167 2.178 2.182 2.173 2.140 2.069 1.936 1.710

1.870 1.881 I.884 1.875 1.845 1.780 1.663 1.471

1.663 1.673 l-676 1.667 1.638 1.579 I.474 1.308

TJ To

z 5 p

I ,277 1,405 I.096

1.462 I .457 1445 I.422 I.381 1.312 I.199 1.025

1.520 1.492 1.442 1.362 I .239 1.059

$ G;

;

s 1.577 1.545 I .491

1.542 1.536

;r: -(

3 I.602 l-595

1.663 1.654 I .635 1.600 1.541 I.451 1.319 I.139

T,,l To

COANNULAR

JET

NOISE

217

this basis indicates where particular coannular configurations hold promise of useful noise reductions in an actual propulsion application. In the previous Lockheed studies on coannular jets [ 1,2], the noise reductions from IVP coannular jets were quantified and understood on the basis discussed above. The same criteria are used here, with the emphasis placed on noise from NVP coannular jet flows. A matrix of test conditions was designed which not only satisfies the constant thrust, mass flow rate, and area requirements discussed earlier, but also enables the isolation of fan-to-primary velocity ratio effects from temperature ratio effects. This test matrix, consisting of 32 test points (TP), is shown in Table 1. The actual test conditions for the entire experimental program are given in Table 2, where M is the Mach number, V is the velocity, T is the static temperature, T, is the total temperature, 5 is the pressure ratio, and a is the speed of sound. The subscripts p and f indicate exit conditions for the primary and fan jets, respectively, and the subscript 0 stands for ambient conditions. The fully mixed equivalent single jet velocity (or specific thrust) for each point in the test matrix is 230 m/s (755 ft/s). It can be seen that along each of the four columns of the matrix in Table 1 the static temperature ratio at the nozzle exit (T,/ T,) is held constant while the velocity ratio (V,/ VP) is decreased from 1.0 to 0.3. Conversely, along each row of the matrix, the effects of T,/ Tp can be examined for a fixed value of y,/ VP. Two more comments regarding this test plan are worth noting. First, it should be recognized that although the velocity and temperature ratios ( V,/ V,, T,/ T,) are kept constant, the absolute values of velocity and temperature (V, T) for the two streams vary from one test point to another. Second, TP 1 (V’/ VP = 1, T,/ T, = 1) represents the fully mixed equivalent jet corresponding to the remaining 31 test conditions, and it is therefore referred to as the “reference” or “equivalent” jet in the rest of this paper. In this manner, the noise measurements at any test point can be compared directly with the reference jet noise levels to determine the noise changes for fixed aerodynamic performance of the engine. In addition to the acoustic experiments, aerodynamic measurements of NVP coannular jets were conducted with use of the Lockheed laser velocimeter system. At selected test points, the jet flow was mapped in detail from the nozzle exit plane to approximately 20 equivalent nozzle diameters (D,,) downstream. The measurements were processed to yield mean velocity and turbulence intensity distributions. The data from these experiments are documented in reference [4]. In the present work, these data were used in the theoretical modeling

to be described

in section

4.

3. MEASURED

RESULTS

The results from the acoustic experiments are presented in this section in sufficient detail to show the major effects of velocity ratio and temperature ratio on the jet mixing noise from subsonic normal-velocity-profile coannular jets. In addition to the results presented in this paper, the data from the entire experimental program can be obtained from reference [5].

3.1. SOUND PRESSURE LEVEL RESULTS The effects of fan-to-primary velocity ratio ( V,/ VP) on one-third octave SPL spectra at 90” and 30” to the jet exhaust are shown in Figure l(a) and (b), respectively. Here, the static temperature ratio (T,/ T,) is held constant at unity. Hence, the velocity ratio effects are examined explicitly here. At and around 90” to the jet axis, Figure l(a) indicates the noise levels at low frequencies. In contrast, at frequencies

that there is little change in above approximately 1 kHz,

218

H.

N;

60-

1 0

70-

K. TANNA

AND

P. J. MORRIS

b x 60N _ 3

50.

3 5

40. 30

~a’~~!ll!ll!~~!~~!~~!~~!~~:~ 0.25 1.00 4m 16.60 63.00 050 2.00 6.00 31.50

One-third

octave center

frequency

(kHz)

Figure 1. Variation of SPL spectra at (a) ~9= 90” and (b) 0 = 30” with V’/ VP for fixed T’/ TP = I .O

the noise levels first decrease as V,/ VP is reduced from 1a0 to 0.7, and then the noise levels increase by as much as 8 dB as V,/ VP is further reduced from 0.7 to 0.3. Since refraction and source convection effects are minimum around 90” to the jet axis, the noise level changes are essentially governed by the changes in the source strength, and therefore the above observations indicate that at the middle and high frequencies of the spectra, the integrated strength of the noise sources is strongly influenced by the velocity ratio. As the velocity ratio is reduced, the source strength initially decreases and reaches a minimum value beyond which it increases significantly. At 0 = 30” (Figure l(b)), the changes in noise levels with velocity ratio are greatly enhanced, especially in the mid-frequency range where the spectral peaks occur. In this case, the noise levels increase systematically as the velocity ratio is decreased. The peak frequency levels increase by over 10 dB as the velocity ratio is reduced from 1.0 to 0.3. The behavior at very low frequencies and high frequencies is similar to the variation with velocity ratio observed at 8 = 90”. That is, velocity ratio has an insignificant effect on the low frequency noise levels, whereas at the high frequencies the noise levels first decrease and then increase as V,/ V, is gradually reduced from 1.0 to 0.3.

0 ; ;

60

60-

*

t

70

50

0

t

2 40 v)

I (0) JOI,!,,!,,!,,!,,!,,!,,!,,!ll!lJ 0.25 l-00 4.00 16.00 63.00 0.50 2.00 600 31.50 One

-third

-I -1

6”t

t

(b)

5oli!ll!~~!~~!~~!~~!~~!~~!~~!~l 025 1.00 4.00 16.00 63.00 0 50 2.00 6.00 31.50

octave center frequency

CkHz)

Figure 2. Variation of SPL spectra at (a) 0 = 90” and (b) 6 = 30” with V’/ VP for fixed T,/ TP= 0.5.

COANNULAR

JET

NOISE

219

To show that the effects of velocity ratio discussed above for a fixed value of the static temperature ratio, TI/ Tp = 1.O, are generally present at all temperature ratios, the corresponding results at another constant value of T,/ Tp equal to 0.5, are presented in Figure 2(a) and (b). When these results are compared with the Tf/ Tp = 1-O results shown in Figure l(a) and (b), it becomes evident that not only are the velocity ratio effects qualitatively similar in both cases, but additionally the influence of velocity ratio V,/ V, is even greater at T,/ Tp = 0.5. At 0 = 30”, Figure 2(b) indicates that the peak spectrum levels now increase by over 12 dB as the velocity ratio is reduced from 1a0 to 0.3. The effects of fan-to-primary static temperature ratio (T,/ Tp) on one-third octave SPL spectra are illustrated typically in Figure 3(a) and (b), where the velocity ratio (V’/ V,) is held constant at 1.0. That is, the temperature ratio effects are examined independently here. Unlike velocity ratio, temperature ratio does not appear to be a significant parameter when the noise levels are compared at constant thrust, mass flow rate, and jet exit area. In other words, the velocity ratio effects are much more powerful than the temperature ratio effects. For a fixed velocity ratio of 1.0, the only noticeable effect of decreasing the temperature ratio from 1.0 to 0.5 is that the low frequency noise levels are increased by about 2 dB at both 90” and 30” to the jet exhaust.

0 x N

60~~

z50.

-

70..

-

60.

-

50-

9 $40~ v)

I 30~!0),,!,,!,,!,,!,,!,,!,,!,,!,.

0.25

1.00 0.50

400 200

4O,!ll!ll!li!ll!ll!il!li!illL 16 00 63.00 0.25 100 4.00 16.00 63-00 6.00 31-50 0 50 2 00 8 00 31 50 One- third octave center frequency (kHr)

Figure 3. Variation of SPL spectra at (a) 0 = 90” and (b) 0 = 30” with Tf/ T, for fixed V,/ V,,= I ,O.

The overall sound pressure levels of jet mixing noise for all velocity ratios and three out of the four temperature ratios defined in Table 1 are plotted on a relative basis in Figure 4. Here the difference AOASPL between the normal-profile coannular jet OASPL (i.e., V,/ V, < 1 and/or T,/ Tp < 1) and the flat-profile reference jet OASPL is plotted against V,/ V, at five angles to the jet exhaust ranging from 30” to 110”. That is, a positive AOASPL indicates a noise increase, whereas a negative AOASPL indicates a noise reduction relative to the “reference” or “equivalent” single jet. At large angles to the jet exhaust, for example 8 =90” (Figure 4(d)), the noise levels do not change appreciably as the velocity ratio is reduced from 1-O to O-5. However, a further reduction of V,/ V, to 0.3 causes the noise levels to increase by about 5 dB. In contrast, at small angles to the jet exhaust, for example 0 = 30” (Figure 4(a)), the noise levels increase continuously as the velocity ratio is reduced from 1.0 to 0.3, and at the lowest velocity ratio, the OASPL values increase by over 10 dB relative to the reference condition. In searching for any noise reductions in Figure 4, it becomes apparent that these occur only at large angles to the jet exhaust for the Tf/ Tp = 1 test series; furthermore,

220

H. K. TANNA

AND

P. J. MORRIS

‘Ii/ 0.3

0.5

0.7

0.9

b/v,

Figure 4. Variation of AOASPL with V’/ V, and Tfl Tp T,/Tp: 0, ( V,/ V,, T,/ T,) = OASPL ( V/l V,, T/f T,) - OASPL ( V,/ VP = 1, Tf/ Tp = I ).

1.0;

0,

0.7;

0,

0.5.

AOASPL

when the noise reductions do occur, the maximum value is only of the order of 2 dB, which is observed around V’/ VP= 0.7. 3.2.

SOUND

POWER

LEVEL

RESULTS

polar sound presssure level results (lossless data) obtained from the present experiments were used to compute the corresponding sound power level (PWL) spectra for all test points, by using conventional procedures. The overall sound power levels (OAPWL) were then calculated by adding the one-third octave band sound power levels. The variation of sound power level spectrum with velocity ratio V,/ V, is shown in Figure 5 for a constant value of temperature ratio, Tf/ Tp = 1.00. The results are quite similar to the SPL spectrum results at 8 = 30” presented earlier in Figure 1(b). At low frequencies below 500 Hz, the levels are not influenced by velocity ratio. In contrast, in the middle frequency range between 500 Hz and 2.5 kHz, where the spectrum peaks occur, the sound power levels increase systematically by as much as 10 dB as the velocity ratio is gradually reduced from 1-O to 0.3. Finally, at high frequencies above 2.5 kHz, the sound power levels first decrease slightly as V’/ VP is reduced from 1.0 to 0.7, and then increase by significant amounts as V,/ V, is further reduced from O-7 to 0.3. The effect of temperature ratio T,/ Tp on the PWL spectrum is shown explicitly in Figure 6, where the velocity ratio is kept constant at unity. As observed previously in the The

COANNULAR I

221

NOISE

JET

I

1

120

0°0 0

0

0

0 0

0 &a OOA,

0

AA

OA

Q B,O

T-

0

0

00

o:;nn

-

Oo ??

10 dB

Q

110

8 3

0

s 4

08 QoO

Ooo

A

’ 0

I_

AO” A00

OO

- 100 0

boo A000 A

AA0

00

0 00

A~ 1

0.2

I

,

0.4

0 0

1.6

3.15

6.3

A 1

I

12.5

25.0

90

50.0

Frequency (kHz) Figure 5. Variation 0, oT3.

of PWL spectrum

with V,/ VP for constant

T,/ T, = I .OO. Vf/ V,: 0, 1.0; A, 0.7;

T

0,

0.5;

110

10 de

i 100 z;

1

ps

90

0.2

Figure 6. Variation

0.4

of PWL spectrum

0.0

1.6 3.15 Frequency

6.3 (kHz)

with T,/ T, for constant

125

25.0

50.C

V,/ V, = I .OO. T,/ T,: 0,

I .OO; 0, 0.50.

SPL results, temperature ratio has little effect on turbulent mixing noise from a coannular jet for fixed aerodynamic performance of the nozzle configuration. The overall sound power level results from the entire test program are presented in Figure 7 on a relative basis, in a manner similar to that used for the OASPL plot of Figure 4. The figure shows that normal-velocity-profile coannular jets at subcritical conditions radiate more acoustic energy compared to that radiated from a fully mixed equivalent single jet at identical thrust, mass flow rate, and exit area. Furthermore, the magnitude of this extra acoustic energy increases as the velocity profile at the coaxial jet exit plane deviates more and more from the fully mixed or flat-velocity profile (i.e., as the velocity ratio V,/ V, decreases from unity).

222

H. K. TANNA AND P. J. MORRIS

E 3

6-

% 6% 2 42-

-22 0.3

0,4

0.5 0.6 0.7 0.0

0.9

1.0

“f ‘“, Figure 7. Variation of AOAPWL with V,J V, and T//TV AOAPWL (v/f V,,, Tff T,) = OAPWL ( V,l V,, T,/ T, ) - OAPWL ( v,/ V,, = 1, T,/ T, = 1). T,/ T,: 0, 1.00; A, 0.85; 0, 0.70; 0, O-50.

I

1

I

I

,

,

,

110

,

(Cl

100

)

0

90

A \

!$ kg

f Cl

A

I!

0

__+

_

--a-0

0

0

(c.1-I 60

I

A

__b_ I

I

0.3

0.4

I

I

,

0.5 0.6 0.7 “f 1%

1

,

0.0

0.9

-7 ‘0

,

1.0

Figure 8. Variation of static peak PNL with V,/ V, and T//T, at several sideline distances. (a) 61m (200 ft) sideline; (b) 244m (800ft) sideline; (c) 649 m (2128 ft) sideline. T,/ Tp: 0, 140; A, 0.85; 0, 0.70: V, O-50.

COANNULAR

3.3.

PERCEIVED

NOISE

LEVEL

JET

NOISE

223

RESULTS

The model-scale acoustic data presented above were finally transformed to larger scale conditions by using standard scaling procedures for jet noise. Although a scale factor of 20 would have been more appropriate to obtain results for a typical full scale turbofan engine, such a large scale factor would reduce the maximum frequency of 80 kHz in the model scale to 4 kHz in the full scale, which is rather low. A scale factor of 10 was, therefore, used for this purpose, and this resulted in the following specifications for the larger scale configuration: equivalent nozzle diameter = O-777 m (30.6 in) ; total exit area = 0.475 m* (5.11 ft”); total thrust = 17 925 N (4030 lbf); total mass flow rate = 78 kg/s (172 lb/s). The lossless larger scale data were then subjected to atmospheric attenuation corrections for a standard FAA day (25°C 70% relative humidity), and static perceived noise levels (PM%) in PNdB were calculated for three sideline distances of 61 m (200 ft), 244 m (800 ft), and 649 m (2128 ft). The variation of (static) peak PNL with velocity ratio and temperature ratio for the 32 test points specified in Table 1 is shown in Figure 8. Once again, the PNdB levels for the coannular jet are plotted relative to the “reference” jet level (which is shown by the broken line) at each sideline distance considered. The results for T,/ Tp = 1.O indicate that although the normal-velocity-profile coannular jet radiates more acoustic energy compared to the fully mixed equivalent single jet, the coannular jet is subjectively quieter at velocity ratios around 0.7-0.8. However, the noise reductions are rather small, the magnitudes being less than 2 PNdB at the most. This result is a direct consequence of the high frequency noise reductions around V,/ V, = O-7 in NVP coannular jets, which are weighted higher in the standard PNL calculation procedures. As the velocity ratio is reduced further, these reductions disappear, and the coannular jet becomes noisier than the “reference” jet. In contrast, the results for T,/ Tp = 0.5 indicate that the NVP coannular jet is subjectively noisier than the “reference” jet at all velocity ratios. In this case, although the peak PNL values do not change significantly as the velocity ratio is reduced from 1a0 to 0.7, the PNdB increments relative to the reference jet become quite large as the velocity ratio is reduced further down to V,/ V, = 0.3.

4. THEORETICAL

WORK

The purpose of this section of the paper is to provide an explanation of the observed variations in the radiated noise. However, this is not intended to be an empirical correlation but rather an attempt to provide a physical explanation of the observed phenomena. Although it will be necessary to make use of some experimental data to develop the noise prediction model, these will be concerned with the turbulence characteristics of the coannular jet flow and not the noise measurements themselves. The philosophy to be adopted here is that, in order to model the noise radiation from the coannular jet, it is necessary to model the jet’s turbulent structure. The state of the art in the prediction of turbulent flows is that the single-point time-averaged properties of the coannular jet could be obtained for a given set of initial conditions, such as the jet operating conditions and the nozzle exit boundary layer profiles. Predictions of the radiated noise could then be made on the basis of scaling laws, with the assumption of localized sources. The directivity of the radiated noise could also be calculated from a flow/acoustic interaction model such as one based on Lilley’s equation. Such a procedure has been applied by Balsa and Gliebe [6]. However the repeated solution, based on this approach, for a wide range of operating conditions, is likely to be computationally time-consuming.

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With this in mind, in the present approach the noise sources in the coannular jet are modelled as if they were contained in a composite jet consisting of three equivalent single jets. The properties of these single jets are described below. The noise radiation and directivity may then be calculated on the basis of a geometric acoustics model proposed by Morfey and Szewczyk [7] and Morfey et al. [8]. A computer program that applies this technique to the prediction of noise from a single round jet is described in reference [9]. The calculations based on the source scaling proposed in this paper provide a remarkably accurate prediction of the absolute levels of radiated noise. This scaling is described below. During the review of this paper the authors’ attention was drawn to similar work by JuvC et al. [lo]. These authors also attempted to explain the changes in the noise of coannular jets on the basis of observed aerodynamic changes. However, an estimate of only the overall radiation efficiency was attempted. The present calculations, on the other hand, provide an extensive prediction capability including variations in the noise spectra and directivity of coannular jets as well as predictions of absolute levels of radiated noise. The modelling of the coannular jet flow is described in the next sub-section. The geometric acoustics model will then be described briefly. Finally, the predictions of the radiated noise will be compared with the measured values. 4.1. JET FLOW MODEL In order to model the coannular jet flow field, for the purposes of noise prediction, it is necessary to describe the following properties of the flow in each region. The scaling of the velocity and temperature fluctuations and mean velocity and static temperature must be described. For this purpose the coannular jet is divided into three parts: (i) an outer mixing region which separates the fan potential core from the ambient fluid, (ii) an inner mixing region which separates the fan and primary potential cores, and (iii) the flow region downstream of the end of the primary potential core. These three regions are shown in Figure 9. In a normal-velocity-profile coannular jet the outer potential core, generated by the fan jet, is shorter than the inner potential core of the primary jet. However, it is assumed that the two annular mixing regions extend to the end of the primary potential core. This is equivalent to assuming that, along a surface

Coonnulor

iet *

Pre-merged section

Transition section

Figure 9. Schematic

Fully-developed section

of coannular

jet flow field.

COANNULAR

JET

NOISE

225

separating the two layers, the mean axial velocity is equal to the fan jet velocity. This enables the flow field up to the end of the primary potential core to be considered as two separate jet flows. It is recognized that this is an over-simplification of the actual conditions. However, this will affect mostly the development of the primary jet towards the end of the primary potential core. It is shown below that some corrections for this effect are necessary in estimating, for example, the length of the primary potential core. It is also recognized that this simplification involves superposition of turbulent flows from the inner and outer mixing layers, modelled as separate jets, in the region downstream of the fan potential core. However, unless the area ratio, p = A,/A,, is very small, the regions of highest turbulence intensity do not fall in the overlapping region. Thus, if it is argued, for the purposes of noise prediction, that the greatest noise is generated close to the regions of highest turbulent fluctuations, the present model should be adequate for area ratios of practical importance. Each of the separate regions of the coannular jet flow, described in the preceding paragraphs, is now to be modelled individually. (i ) The outer shear layer. The outer layer is modeled by assuming that it is equivalent to a single jet with exit diameter equal to the fan jet outer diameter and exit velocity and static temperature equal to the fan exit conditions. This appears to be the simplest region to model and the results indicate that such a model is adequate. (ii) The inner shear layer. This region is taken as equivalent to a single jet, with exit conditions and diameter equal to those of the primary jet, exhausting into a uniform moving stream with the velocity and temperature equal to the fan jet exit conditions. The properties of these two model jets may be used to estimate properties of the coannular jet such as the length of the primary potential core and the characteristic turbulence levels in the mixing layers, As a basis for evaluating these estimates the experimental data of Ko and Kwan [I I] and Lau [4] will be used. The length of the potential core of a jet exhausting into a coflowing stream was found by Morris [12] to be proportional to (1 -0.92A)- ‘, where A is the ratio of the free stream velocity to the jet velocity. The variation of potential core length with jet Mach number and static temperature ratio was found by Lau [13] to be given by x,/d

=(4.2+1Wj)(?;/T,)-“”

for subsonic flows, where x, is the potential core length, d is the jet diameter, Mj is the jet exit Mach number, and T, and T, are the jet exit and ambient static temperatures, respectively. Equations (1) and (2) may be used to predict the primary potential core length for a coannular jet. The primary potential core length, xCP which has been found to be an important parameter in the noise prediction scheme, may be taken as

where A is now the coannular jet velocity ratio, given by A = V,/ VP a is the coannular jet static temperature ratio, given by (Y= T,/ T, and the subscripts f and p refer to the fan and primary jets respectively. However, a comparison with the data of Ko and Kwan [l l] and Lau [4], as shown in Table 3, indicates that equation (3) consistently overpredicts the value of xCP As discussed above, this is due to the disappearance of the uniform external stream beyond the end of the fan potential core. To allow for this the primary

226

H. K. TANNA

AND

TABLE

P. J. MORRIS

3

Predicted and measured variation of primary potential core length

I

A

ff

0.70 0.67 0.67 0.67 0.67 0.67

1.000 0444 0444

MP

1 ,000 1.ooo 1.020

Measured [ref.]

0.17 0.80 0.50 O-80 0.75 0.50

9.5 9.1 8.0 10.9 10.9 11.7

Equation (3)

[ll] [4] [4] [4] [4] [4]

4x,/x,) 2.40 1.77 1.02 1.88 1.15 0.03

11.90 10.87 9-02 12.78 12.05 11.73

potential core length is modeled by (4.2+ lU4;)a0’2/(1 -0*92A)-2.4A, xcp’dp= { (4.2+11M;)(TJT,)-0’2(d,/dp),

A s 0.8, A > 0.8.

(4)

The use of the second part of equation (4) reflects the dominance of the outer jet flow for high values of A. The peak turbulence intensity for a jet exhausting into a collowing stream was found by Morris [ 121 to be given by u,&,/ y - (1 -A)‘.‘,

(1 -A)>0.163.

(5)

A different scaling was found for higher velocity ratios. However, in the present case, only equation (5) is of interest since the noise sources in the inner mixing region are found to make a negligible contribution to the noise radiation for ( 1 - A) < O-163. On the basis of equation (5) the characteristic velocity fluctuation in the inner mixing layer is assumed to vary as ~;/V~-(l-h)~.

(6)

The factor 6 would be expected to vary from a value of 0.7 close to the jet exit to some lower value at the end of the potential core, to reflect the non-uniformity of the secondary stream. This axial variation has been modeled by 6 = 0.7 -0.3x/x,,

(7)

According to the mode1 proposed above for the outer shear layer characteristics, it is clear that the characteristic velocity fluctuation in this layer, relative to the primary jet velocity, is given by v;l Vp = Cv;l V-)( V’l Vp) - A,

(8)

since v;/ V, is a constant. The ratio of the velocity fluctuations in the outer and inner mixing layers may now be written as v;/v;=A/(l-A)S.

(9)

Thus, the turbulence level in the inner mixing layer is greater than that in the outer layer when (1 - A)’ > A. For 6 = O-7this gives A < 0.5615. It might be expected that for A < 0.5615 the inner mixing layer contributes most of the noise from the initial region of the jet. For A = 0.7, Ko and Kwan [l 11found (v;),,,/ VP= 0.105 and ( v&,~.J VP= 0.06, which gives vb/ v).;= O-57. For A = O-67, and a higher Mach number, Lau [4] found vb/ vi= 0.67.

COANNULAR

227

JET NOISE

Equation (9), with A = O-7 and S = 0.7 gives vi/u; = O-62. Thus the scaling proposed by equations (6) and (8) provides a reasonable correlation of-the experimental data. For the purposes of noise predictions in single jets Tester et al. [9] modeled the temperature fluctuations as proportional to the difference between the static temperatures at the source location and in the ambient medium. Thus in the outer and inner mixing layers it is proposed that, T;-(TX-T,)

and

Tb-(T,-Tf),

(lOa, b)

where T, is the mean static temperature at the source location. It has been assumed that in each of the annular mixing regions, the static temperature is only a function of the mean axial velocity. Then, for a Prandtl number of unity and zero axial pressure gradient, a Crocco relationship [14] may be developed for each mixing layer. For example, in the inner mixing layer

( )L

$=I+ G-1 -(l-4+w)M* P

P

(1-A)

( )I. *_J

2

VP

p

(11)

The velocity profiles in the annular mixing layers are assumed to take an error function form, such that V/V,=h+0.5(1-h)[l-erf(Gr/&)], V/ V, = 0+5[ 1 - erf (JYr/

r<(d,+&)/4, a,)],

r>(d,+&)/4,

(12a) (12b)

where S, is the thickness of the mixing layer at the source location. The variation of S, with source frequency was given by Morfey et al. [8] and has not been altered for the present calculations. (iii) 7he deuelopedjetflow. It is important in modeling this region of the flow to ensure that a reasonable model for both the flow and acoustic source properties is proposed. Far downstream the jet develops as a single equivalent jet (SEJ) with operating conditions that must be determined. One possible model, that has been tried, can be obtained by assuming that the SEJ has an exit velocity equal to the primary jet velocity, with static temperature and area set by requiring that its thrust and mechanical energy output be the same as those of the coannular jet. This leaks to equivalent jet properties, denoted by an asterisk, of T*/Tp=(~6y-“‘y+h/3,$-‘)‘y)/(l+h2~/~)-O~5(~-l)M;

(13)

and A*/Ap=(1+h2/3/a)T*/Tp,

(14)

where 5 is the total pressure ratio, relative to the ambient pressure. Equation (14) arises from the equal thrust constraint alone. A jet operating with these conditions is likely to give the correct asymptotic behavior. However, the noise produced in the flow far downstream is of little consequence. The important noise-producing region for the merged jet is just downstream of the end of the primary potential core. Equation (13) results in a value of T* that exceeds either Tf or Tp or both. This results in a characteristic temperature difference at the end of the potential core which exceeds the actual maximum value. Since the strength of the noise sources, associated with density inhomogeneities, have been assumed by Morfey et al. [8] to be dependent on this temperature difference, an overestimate of the noise from these sources is expected to result.

H. K.

228

TANNA

AND

A better model for the noise-producing given by

v* = VP,

P. J. MORRIS

properties

TP, Tfi

T*=

of the SEJ has been found to be

Tp> T,;

(15)

Zj.> Tp

In addition equation (14) is used to give an exit area for equal thrust, and the end of the potential core of the SEJ is set at the same location as the actual end of the primary potential core. This final requirement leads to an exit plane for the SEJ which is not the same as the coannular jet exit plane. The decay of jet centerline velocity with axial distance may be calculated from the relationship used by Lau [ 131:

( vl

Vp)centerline

=

1 -exp [l-4/(1 -x/xc,)].

(16)

A comparison of the decay characteristics of the SEJ and the values measured by Lau [4] is shown in Figure 10. For the initial region of decay the prediction is reasonable; however, the decay is too rapid downstream. Thus the important noise-producing region has been modelled.

0.01 0

5

10

15

20

25

I

x/do

Figure 10. Prediction of centerline velocity decay: A = 0.7, (2 = 1.0. 0, Measured (Lau [4]); -, (equation (16)).

predicted

An important difference between the SEJ and the merged region of the coannular jet is that the initial characteristic turbulence level at the end of the potential core is less in the coannular case. To allow for this the turbulence level in the SEJ has been smoothed between a value appropriate to that at the end of the primary potential core and the single merged jet value far downstream. If the characteristic turbulence level at the end of the potential core is denoted by u: then, in the SEJ, the characteristic level is assumed to vary with axial distance as (r&J

-

u:+(1-u:)exp[5/(1-xlx~)l,

(174

where l(A) = (4*2h - l)A,

(17b)

and XT is the length of the potential core of the SEJ. The variation of the factor 5 with A shows that for small values of A the turbulence levels in the merged jet adjust rapidly to the single jet values, whereas if the velocity ratio A is large the transition is slower. The value of u: is taken to be the larger characteristic fluctuation of either the inner or the outer mixing layer. A similar transition is assumed

COANNULAR

for the temperature

JET

NOISE

229

fluctuations,

(T’)SEJ=T~+(1-T:)exp[5/(1-xlxr)l.

(18)

Now the characteristic temperature differences in the inner and outer shear layers are (TP- T,) and (T,- T,), respectively. If the fluctuations scale with these differences then the ratio of the temperature fluctuations in the inner and outer layers is

Tb/T;=(l-n)/((Y-T,/Tp).

(19)

In modeling the flow downstream of the end of the potential core, the characteristic temperature difference is ( Tp - T,) or (T, - T,), whichever is greater. In the latter case no transition is required. However, if a < 1, the fluctuations may be overestimated. There are two cases: (i) if (1 - a) > (a - Ta/ Tp) the inner shear layer has the greater fluctuations and 7-Y ( 7%~ = (1-a)/(l-K/T,);

(20)

(ii) if (1 - a) < (0 - T,/ T,) the outer shear layer has the greater temperature fluctuations and T:l( T’)ss, = (a - L/ T,)/( I- To/ &I.

(21)

On the basis of these scaling relationships the radiated noise may be calculated for each model jet, and the total noise radiation can be predicted. Though it may not be apparent at first sight, the small number of model equations should be emphasized. In the next section a brief description is given of the noise prediction scheme. 4.2.

NOISE

RADIATION

MODEL

The noise radiation model for a single jet has been described in detail by Tester et al. [9] and only a brief description of the model and some minor modifications necessary to treat the coannular jet need be given here. The model includes two independent noise sources, a “quadrupole” source associated with the velocity fluctuations and a “dipole” source associated with the density inhomogeneities or temperature fluctuations. As it is a geometric acoustics model the radiation to regions inside and outside the “cone of silence” are treated separately. In the former case it is assumed that disturbances associatded with the source decay exponentially through the shear layer until they may propagate freely. The radiated noise associated with each source is the sum of several different components: (i) a “master spectrum” of the radiated noise; (ii) an inverse square law based on the effective source location; (iii) the Lighthill scaling law, either the 6th or the 8th power of the jet velocity ratio, depending on the dipole or quadrupole nature of the source ; (iv) a convective amplification factor; (v) a directivity factor based on high frequency solutions of Lilley’s equation. The reasoning behind these contributing factors has been given in references [7-91. Several modifications to the single jet noise radiation model are required to deal with the noise radiation from the three component jets of the coannular jet. Two straightforward but significant alterations are described here. Consider first the determination of the source location for the SEJ. The operating conditions for the SEJ were determined in the previous section and the jet diameter may be determined from equation (14). The location of the jet exit is determined by calculating the length of the SEJ potential core, xz, by using equation (4). The location of the SEJ exit, x8, is then taken to be at xg*--x,-xx,. *

(22)

230

H. K. TANNA

AND

P. J. MORRIS

Second, the source location for a particular modified Strouhal number (see reference [9]) is then given by x:/d*

= (0.057 S*,+O.O21 S;z)-“2,

(23)

with S*, = fd*/ VP Since the observer in the far field is positioned with respect to the exit of the coannular jet and the source is also downstream of this location, it is necessary to modify the relationship between the measurement angle 8,, the radius R,, the source radiation angle &,, and the radiation distance R, By using the definition of distances and angles in Figure 11 it can be readily shown that R,/d*={(R,/d*)*+[(xf+x~)/d*l2-2[(x~+x8)/d*](R,/d*)

cos 19,,,}“~,

co~(~,-e,)={(R,/d*)*+(R,/d*)~-[(x~+x~)/d*]~}/2(R,/d*)(R,/d*).

(24) (25)

Additional minor modifications are required to reflect the scaling of velocity and temperature fluctuations given by equations (9) and (17)-(21). Details of these minor modifications are given in reference [5]. The coannular jet noise predictions and comparisons with the measured noise radiation levels are described in the next section. \

\

\

\

‘\

Microphone

\

\

\ Measurement OK centered on nozzle

(SEJ) Exit

Figure Il.

Definition

5.

of angles and distances

COMPARISON

BETWEEN

used in the analysis

THEORY

AND

and prediction

of jet mixing noise.

EXPERIMENTS

The predictions will be compared with measurements on the basis of the variation with velocity ratio V,/ VP at a fixed temperature ratio Tf/ Tp Variations with temperature ratio were found to be of secondary importance. It should be emphasized that all predictions are of absolute sound pressure levels and are not presented as relative changes with respect to an arbitrary base condition. Only a limited number of representative comparisons will be shown here due to the constraints of space. However, a complete set of comparisons is contained in reference [5]. Figure 12(a)-(c) shows a comparison of measured and predicted levels, at 30” and 90” to the downstream jet axis, for velocity ratios of approximately 0.7, 0.5 and 0.3. The agreement between the predictions and the measurements at all frequencies is good. The

COANNIJLAR

\

0

z 9 -.I

B

231

JET NOISE

:I 0

80

.

70

.

.

. .

.

\ ??

.*

-..*o . -.*..x

-

??

I

60 L

60. 02

04

0.6 One-ihlrd

1.6 octave

315 center

63 frequency

12.5 (kliz)

25

Figure 12. Comparison between measured and predicted coannular jet noise spectra. (a) VJ/ VP = 0.7, T,/ T, = I .O; (b) V,/ VP = 0.5, Tf/ T, = 1.O; (c) V,/ VP = 0.3, T,/ T, = I .O. 0, Measured, 0 = 30”: 0, measured, 0 = 90”; -, predicted; - - -, interpolation.

agreement at 90” indicates that the source strength alterations have been correctly modelled, since at this location the effects of convection and refraction are negligible. The predictions at 30” at higher frequencies and Vj/ VP= 0.5 and 0.3, in Figure 12(b) and (c) respectively, show some problems. At these velocity ratios, the highest turbulence levels, upstream of the end of the primary potential core, occur in the inner mixing layer. At these radiation angles and frequencies, the observer is within the geometric acoustics “cone of silence.” In using the model proposed by Morfey et al. [8] one determines the radiation level within the cone of silence by allowing for the exponential decay of the sound radiation close to the source out to some “transition point” at which, according to Lilley’s analysis, acoustic radiation occurs. The location of the transition point for a

232

H. K. TANNA

AND

P. J. MORRIS

single jet depends on the mean velocity and temperature profiles and its determination is described in reference [9]. For the more complicated mean velocity profiles of the coannular jet, it is not always as readily predictable. Since the measured levels at the high frequencies and small angles are at least 20 dB below the peak spectrum levels, it was felt to be unnecessary to determine the transition point in these cases. An example of the manner in which the three single model jets contribute to the total noise is shown in Figure 13(a) and (b). Only the 90” predictions are shown since they provide the best indication of source strength. At the higher velocity ratio V,/ VP = 0.7 in Figure 13(a) the maximum contribution at all frequencies is made by the outer shear layer. The single equivalent jet contributes at low frequencies, and the inner mixing layer makes only a small contribution at high frequencies. At the lower velocity ratio V’/ VP = 0.3 shown in Figure 13(b), the roles of the inner and outer mixing layers are reversed. The outer mixing layer makes an insignificant contribution, the SEJ dominates the noise radiation at low frequencies, and the inner mixing layer makes the high frequency contributions. At an intermediate velocity ratio of about 0.4, all three model jets make similar levels of contributions to the radiated noise.

90

(0)

60

‘._ Inner shear

$90

layer /+--...

(bl

1

.

.

Inner

Outer

shear

shear

layer

layer

/

/---

50 02

0.4

08 One-thrd

1.6 octave

3.15

6.3

center

frequency

Figure 13. Contributions from single model jets. (a) V’/ VP= 0.7, 0, Measured,

12 5

25

3

ktiz)

T,/ T, = 1 .O; (b) v,/ v, = 0.3, T,/ T, = 1.O,

0 = 90”.

The predicted effect of variation in the static temperature ratio on noise is not shown here. As has been noted in the experimental results, the noise changes due to temperature effects at a fixed velocity ratio are small in comparison to the effects of changes in the velocity ratio.

COANNLJLAR

JET

233

NOISE

6. CONCLUSIONS The jet mixing noise from normal-velocity-profile (NVP) coannular jets representing typical high-bypass-ratio turbofan engines has been studied experimentally and theoretically. In particular, the effects of fan-to-primary velocity radio V,/ VP and static temperature ratio T,/ Tp have been isolated, and the experimental results have been correlated with a theoretical model that allows the source alteration effects and the flow-acoustic interaction effects to be assessed separately. The main conclusions are as follows. (1) For constant thrust, mass flow rate, and nozzle exit area, the NVP coannular jet noise levels increase as the velocity ratio Vj/ VP decreases. The noise increase is particularly evident in the mid-frequency parts of the sound power level spectra where the spectral peaks occur. At very low frequencies, the radiated noise energy is essentially independent of the velocity ratio. (2) The effect of temperature profile (or temperature ratio) is insignificant relative to the effect of velocity profile (or velocity ratio). (3) The previous theoretical work on single-stream jet noise conducted at Lockheed has been extended to develop an analytical model, based on geometric acoustics, to link the acoustic and flow characteristics of coannular jets. The predictions obtained by using this model provide very good agreement with measured results in most cases. The good agreement at 90” to the jet axis indicates that the source strengths have been correctly modeled, since at this angle, convective and refractive effects are negligible. At small angles to the jet axis such as 30”, the good agreement strongly indicates that the flowacoustic interaction effects are being correctly predicted, since it is mainly these effects, and not source alteration effects, that lead to the differences in the sound pressure level spectra at all angles. The good agreement between theory and experiment obtained in this study also strongly indicates that this knowledge can in the future be applied with confidence to study the acoustic behavior of more complex suppressor nozzle geometries. (4) Finally, when the noise and jet flow data on normal-velocity-profile and invertedvelocity-profile coannular jets are analyzed collectively, it becomes evident that, relative to the equivalent single jet, the two types of coannular jets display opposite trends in

00

05

1.0

15

2.0

Fan- to- pr,mary velocdy rotlo Cv,/v,,

Figure basis).

14. Schematic

representation

of coannular

jet noise relative to equivalent

single jet noise (on OAPWL

234

H. K. TANNA

AND

P. J. MORRIS

almost all respects. The acoustic performance of shock-free coannular jets, on the basis of total radiated noise energy, is summarized in Figure 14.

ACKNOWLEDGMENTS This work was conducted with Lockheed internal research and development funding. The authors gratefully acknowledge the contributions made by Mr R. H. Burrin and Mr D. F. Blakney during the acoustic measurements and data reduction. The jet flow measurements were conducted by Dr J. C. Lau. REFERENCES 1. H. K. TANNA, B. J. TESTER and J. C. LAU 1979 NASA-CR-158995. The noise and flow characteristics of inverted-profile coannular jets. 2. H. K. TANNA, C. K. W. TAM and W. H. BROWN 1981 NASA-CR-3454. Shock-associated noise reduction from inverted-profile coannular jets. 3. R. H. BURRIN and H. K. TANNA 1977 Lockheed-Georgia Company Report LG77ERQ243. The

Lockheed-Georgia coannular jet research facility. 4. J. C. LAU 1980 Lockheed-Georgia Company Report LG80ER0017. A study of the structure of the coannular jets. 5. H. K. TANNA and P. J. MORRIS 1981 Lockheed-Georgia Company Report LG81 ER0224. The noise from normal-velocity-profile coannular jets. 6. T. F. BALSA and P. R. GLIEBE 1977 American Institute of Aeronautics and Astronautics Journal 15, 1550-1558. Aerodynamics and noise of coaxial jets. 7. C. L. MORFEY and V. M. SZEWCZYK 1977 University of Southampton, ISVR Technical Reports Nos 91, 92 and 93. Jet noise modelling by geometric acoustics, Parts I, II and III. 8. C. L. MORFEY, V. M. SZEWCZYK and B. J. TESTER 1978 Journal of Sound and Vibration 73, 255-292. New scaling laws for hot and cold jet mixing noise based on a geometric acoustics model. 9. B. J. TESTER, P. J. MORRIS, J. C. LAU and H. K. TANNA 1978 U.S. Air Force Aero-Propulsion Laboratory Technical Report No. AFAPL-TR-78-85. The generation, radiation and prediction of supersonic jet noise. 10. D. JUVE, J. BATAILLE and G. COMTE-BELLOT 1978 Journalde MecaniqueAppliquee 2,385-398. Bruit de jets coaxiaux froids subsoniques. 11. N. W. M. Ko and A. S. H. KWAN 1976 Journal of Fluid Mechanics 73, 305-332. The initial region of subsonic coaxial jets. 12. P. J. MORRIS 1976 American Institute ofAeronautics and Astronautics 14, 1468-1475. Turbulence measurements in subsonic and supersonic axisymmetric jets in a parallel stream. 13. J. C. LAU 1978 American Institute of Aeronautics and Astronautics Paper No. 78-1152. Mach number and temperature effects on jets. 14. H. SCHLICHTING 1968 Boundary Layer Theory. New York: McGraw-Hill: sixth edition. See pp. 314-315.