The effect of forward flight on the noise and flow field of inverted profile jets

Journal of Sound and Vibration (1984) 93(l),

39-55

THE EFFECT OF FORWARD FLIGHT ON THE NOISE AND FLOW FIELD OF INVERTED PROFILE JETS R. A. PETERsENt

AND V.

SAROHIA

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, U.S.A. (Received 5 August 1982, and in revised form 3 May 1983)

Noise and flow field measurements are reported for an inverted profile coannular jet (where the annular jet speed exceeds the center jet speed) under simulated flight conditions.

The annular and center jets were cold and both were operated subsonically. Forward flight was simulated by placing the coannular jet inside a larger open jet. Acoustic measurements show the effects of inverted profile shape and simulated flight on far field directivity, total radiated power, and spectral content. Measurements of total acoustic power demonstrate that the acoustic efficiency of inverted profile jets is about 3 dB less than the efficiency of “top hat” profile jets, and that the noise decreases as the seventh power of the relative jet velocity in the limit of small flight velocity, U, Flow measurements demonstrate that the jet spreading parameter A = ( lJj - Vr)/( Vi + Us) scales the thickness of the outer shear layer and the passage frequencies of the large turbulence scales. Comparisons between the turbulence time scales and the noise spectra suggest that coherent noise sources may become more important in forward flight.

1. INTRODUCTION One of the most important advances in jet noise reduction occurred when turbojet engines were superseded by turbofan engines. Whereas the turbojet produces an essentially “top hat” velocity profile, the turbofan bypass introduces a low speed annular flow that

surrounds the center jet. The combined, coannular flow has the effect of increasing the effective jet diameter while decreasing the effective jet speed. Because the acoustic source strength depends on a higher power of velocity than does thrust, the turbofan is able to produce the same thrust at lower noise levels. Recent noise measurements [l] have indicated that inverted profile coannular jets, where the velocity of the annular jet exceeds the velocity of the center jet, also produce less noise than an “equivalent” single jet with a conventional “top hat” velocity profile. Encouraged by the noise measurements, engine manufacturers are considering design concepts that incorporate inverted jet profiles for next generation engines that might power supersonic commercial transports [2,3]. The noise from inverted profile jets is further reduced by forward flight effects. The noise reduction is the same magnitude as observed for top hat profile jets [4]. Consequently the noise reductions caused by profile changes and flight effects seem to be additive. This might indicate that forward flight and inverted velocity profiles affect the fluid dynamics independently. For example, Tanna [l] noted that in the noise producing region the ‘IPresent Address: Tucson,

Arizona

Department

85721,

of Aerospace and Mechanical Engineering,

The University of Arizona,

U.S.A. 39

0022-460X/84/050039+

17 $03.00/O

@ 1984 Academic

Press Inc. (London)

Limited

40

R. A. PETERSEN

AND

V. SAROHIA

centerline velocity and turbulence levels are lower in inverted profile jets than in “equivalent” single jets. He attributed the noise reduction to these effects. By contrast, the most pronounced effects of forward flight involve the outer shear layer of the jet. In the jet co-ordinate system the spreading rate of the shear layer is reduced by the external flow and the jet is “stretched” in the downstream direction. Brown and Roshko [5] demonstrated that the spreading rate for a two dimensional mixing layer scales with the parameter A =(G-

U,)I(U*+

U,),

(I)

where Ui and U, are the velocities of the low and high speed sides (a list of nomenclature is given in the Appendix). Morris [6] found that within the potential core region the spreading rates of axisymmetric mixing layers scale reasonably well with A. The spreading rate measurements indicate that similarity of jet mixing layers with external flow U, can be expressed by defining a stretched co-ordinate x’ = Ax. That is, the stretched spreading rate, 6/x’, within the potential core region should be independent of flight speed UP However, the vorticity and turbulence levels are reduced by the factor ( Ui - U,)/ U, Based on these observations, Crighton, Ffowcs Williams and Cheeseman [7] estimated that forward flight would reduce the acoustic source strength by the factor ( Uj - U,)“/ UF and that the volume of the source region would be increased by the factor l/A. The net acoustic power would then be expected to decrease by (Uj- U,)‘/ U:. In practice, measured reductions in acoustic intensity near 8 = 90” caused by simulated flight are much smaller than that [4,8]. However, there are significant changes in acoustic directivity caused by the external flow and these must be included in order to estimate reductions in total acoustic power. Michalke and Michel[9] have derived a scaling law for estimating the acoustic intensity produced by a jet in flight based on measured intensities from the same jet operated statically. Their scaling law was obtained from a convected form of the Lighthill equation where the axial co-ordinate was stretched by the factor a=l+AUf/(U,-Uf)

(1.5sAs3).

(2)

When the adjustable parameter A = 2, then (Yis the reciprocal of the spreading parameter A. Their estimates agree with jet aircraft flyover measurements [lo]. Monkewitz and Huerre [l’l] and Michalke and Hermann [12] have shown that the spreading parameter is related to the instability of the mixing layer. Monkewitz and Huerre considered two dimensional mixing layers with hyperbolic tangent and Blasius velocity profiles, and they found that the amplification rate per wavelength, -2raJ(~,, where LYis the (complex) wave number of the spatially growing instability, is proportional to A. Michalke and Hermann considered thick, axisymmetric mixing layers with hyperbolic tangent profiles. They reached conclusions similar to those of Monkewitz and Huerre. However, they found that similarity was improved slightly by the choice A = 1.4 in equation (2). Thus, the reduction in spreading rate is consistent with the reduction in linear amplification rate. In what follows results of an investigation of the changes in far field directivity caused by changes in the inverted velocity profile and by simulated flight are described. This information is used to estimate that acoustic efficiency of various inverted profile jets and to determine the reduction in total acoustic power caused by forward flight. Flow measurements are used to determine the limitations of the co-ordinate stretching as a similarity variable for the mean velocity distribution and for the large scale turbulence.

FLIGHT

EFFECTS

2. EXPERIMENTAL

ON INVERTED

PROFILE

JETS

41

FACILITIES AND INSTRUMENTATION

The inverted profile jet was produced by a set of coaxial nozzles, with conical contractions. The exit diameters of the center and annular nozzles were 1.27 and 2.03 cm, respectively, which results in an annular/center jet area ratio of 1.56. The contraction ratios of the center and annular nozzles were 2.25 and 2.05 respectively. Cold nitrogen was delivered to the nozzles through straight coaxial tubing. Stagnation temperatures were generally around 10°C. The pipe flow Reynolds number was in the range 105-106. Consequently, the turbulence levels of the jets were rather high. Measured levels were 3-4%, and are consistent with fully developed pipe flow at these Reynolds numbers and contraction ratios. The annular jet was operated at a local Mach number of 0.91 for most of the measurements. The center jet was operated at Mach numbers ranging from 0 to 0.97. The maximum Reynolds numbers UJA/ v,based on the exit area A, were 2.4 X lo5 and 2.9~ lo5 for the center and annular jets, respectively.

Sound obsorblng

Atrfoll

sectlon Pnmory

nozzle

supply

Figure 1. Sketch of flight simulation

facility.

Forward flight was simulated with the air jet facility shown in Figure 1. The diameter of the flight simulation jet was 17.1 cm. The external boundary layer was thick relative to the nozzle diameter (S/d =0.25 based on 0.95 U,). The coaxial nozzle extended beyond the exit of the flight simulation jet to permit noise measurements in the forward arc. Both jets could be operated continuously. The facility was located inside an anechoic chamber. Noise measurements were made by using electret condenser microphones, 1.27 cm in diameter. The 2 dB frequency response was from 5 Hz to 19 kHz, which was adequate for resolving spectral peaks and for measuring mean square sound pressure. The microphones were distributed along a line parallel to the jet axis and offset 115 jet diameters. Microphone to nozzle distances ranged from 115 to 198 primary jet diameters. A total pressure probe and radial traverse was used for the mean velocity measurements, and a constant temperature hot film probe was used for the turbulence measurements. A digital correlator was used for the autocorrelation measurements. 3. ACOUSTIC MEASUREMENTS

A “top hat” type velocity profile and a purely annular flow are the limiting cases of an inverted profile jet. For any given annular to center jet area ratio there is a profile somewhere between these two extremes that produces the least noise. For the present

42

R. A. PETERSEN

AND

V. SAROHIA

purposes that profile will be referred to as “optimum”. In moving from the “optimum” profile to the top hat profile, the increase in noise is accompanied by an increase in thrust. However, in moving from the “optimum” profile to the pure annular profile, the noise increase is accompanied by a reduction in thrust. This effect is demonstrated in Figure 2, where noise intensity measured at 90” to the jet exhaust is shown as a function of overpressure ratio. The noise intensities are normalized by the noise from the pure annular jet. The noise minimum is reasonably flat over the range 0.05 < Apc/Apa ~0.15. This range of overpressure ratios corresponds to the range of Mach ratios 0.2 < MC/M, -=c 0.4.

Figure 2. Relative OASPL as a function of center jet to annular jet overpressure ratio. Overpressures refer to pitot tube pressures. M, = 0.90; r3= 89”.

In the limit of a “top hat” profile, ApJAp, = 1.0, the noise is 5 dB greater than that produced by the “optimum” shape. Of course, this higher noise level is offset by a 50% increase in thrust. In the limit of a pure annular jet, the center pressures are negative due to recirculation. If base drag in the pure annular jet is neglected then the inverted profile that produces the same noise level produces at least 1.5 times as much thrust. 3.1. ACOUSTIC EFFICIENCY OF INVERTED PROFILE JETS When inverted profile jets are compared with “equivalent” single jets, the apparent noise reduction depends on which parameters are matched. The important operating parameters include thrust, mass flow rate, temperature, and jet diameter. The fact that only three of these variables are independent creates ambiguity in making comparisons. In his measurements, Tanna [l] compared the inverted profile jet to a single jet with the same thrust, mass flow rate, and nozzle exit area. He observed a maximum noise reduction of 2-3 dB. If thrust, area, and temperature were matched the comparison would be less favorable because the “equivalent” single jet speed would be smaller. In fact there is some evidence [4] that the inverted profile jet is actually noisier than the “equivalent” single jet under these circumstances. The question of which parameters, in addition to thrust, should be matched depends on the particular engine designs being compared. The engine manufacturers would be most likely to be interested in a comparison based on equivalent fuel consumption rates and on equivalent engine drag. One way of avoiding some of these problems is to examine the effect of velocity profile on acoustic efficiency. Unless the inverted profile provides a reduction in acoustic efficiency, the quietest engine will be the one that produces the least mechanical power at a given thrust. The acoustic efficiencies of inverted profile jets can be compared to the efficiencies of top hat profiles without having to match flow quantities other than jet Mach number. The ambiguity is reintroduced in trying to establish the “effective” Mach number of the “equivalent” single jet. However, it should be possible to establish an upper bound on apparent noise reduction.

FLIGHT

EFFECTS

ON

INVERTED

PROFILE

43

JETS

Acoustic efficiency is the ratio of acoustic power to mechanical power. Acoustic power is the surface integral of far field acoustic intensity. Axisymmeg is assumed, and the acoustic power, W,,&estimated from the measured directivity, pz( 8)/7(90”), and from the sound intensity, p2(900)/pooam, according to I(M,, MC) =

W, = (2~~2/PmQm) p2(9O”)I(M,, MC),

[2(0)/&90)]

sin f3d0, (374)

where R is the far field distance.

-5

Cl

/

I

I

I

I

I

20

40

60

80

I00

120

I40

e

Figure 3. Far field directivities for various jet profile shapes. Open symbols: Ma = 0.90. MC/Ma:0, no center flow; 0, 0.36; 0, 0.95; ?? , center jet only M,=O.91; -, Ribner [13].

Directivity

measurements

are shown in Figure 3 for various jet profile shapes. The

OASPL’s are referred to 8 = 90” and are corrected for differences in jet exit to microphone

distance. The directivity measurements are compared to Ribner’s basic directivity [13], modified by convective effects, which is defined as [(1+0~3~~)/{(1-~,~0~8)*+0~3~~}]~~~[1+(~0~~e+c0s~8)/2]. h4, is the convective Mach number of the moving sources based on the ambient speed of sound and is generally considered to be 0.5U,-/LG.,. The basic directivity agrees with single jet measurements made by operating the center jet alone. The inverted profile jets are less directional than the single jet. As MC/M, approaches 1.0, the inverted profile directivities would be expected to approach the single jet directivity. The figure suggests that there will be some disagreement in that limit. The reasons are unclear, although the noise produced by the wake of the center jet nozzle lip may be a contributing factor. The mechanical power, W,, is given by d/2 wM=??p(r) U3(r)r dr, (5) I0

where U(r) is the mean velocity profile. For the present configuration efficiency is approximately efficiency={16(R/d)2/p~a,U~}{~(90”)I(M,,M,)/[O~61+0~39(U,/U,)3]}.

the acoustic (6)

In Figure 4, acoustic efficiencies of the inverted profile jets are compared with the single jet efficiency.

44

R.

A. PETERSEN

AND

V. SAROHIA

Using dimensional arguments, Lighthill [14] estimated the acoustic efficiency of single jets to be 0.5 X 10B4( V/U,)~. The Lighthill estimate has shown good agreement with a wide range of measurements [15]. The present measurements show that the efficiencies of the single jet and the inverted profile jet with MC/M, = 1.0 are about the same and are approximately equal to the Lighthill estimate. The lowest efficiencies occur in the range MC/ Ma = 0.2-0.4 and are about half of the single jet efficiency. This reduction in efficiency is of the same magnitude as the 3 dB noise reductions reported by Tanna [l]. In general, the acoustic efficiency of compact quadrupole type radiation is proportional to the fifth power of the jet Mach number. In the case of Figure 4, the acoustic efficiencies were normalized by the fifth power of the annular jet Mach number, which was the same for all cases. In order to compare the efficiency of an inverted profile jet with the efficiency of an “equivalent” single jet it is necessary to define the “equivalent” Mach number of the single jet. For any comparison of practical interest the “equivalent” single jet Mach number is bounded by the Mach numbers of the center and annular flows. The comparison most favorable to the inverted profile is the case where the single jet Mach number matches the annular flow Mach number. In that case a maximum reduction in efficiency of 3 dB was achieved with an inverted profile jet (see Figure 4).

I

0 0

0.2

I

0.4

I 0.6

I 0.8

I I.0

M,'M,

Figure 4. Acoustic efficiencies of inverted profile jets. The annular jet Mach number, U,/a,, was 0.82 for all profiles -- -, Lighthill [14]. +, Center jet only (i14, = 0.91); 0, inverted profile jet (M, = 0.90).

3.2.

FORWARD

FLIGHT

SIMULATION

The disadvantage of using an open jet to simulate forward flight is the presence of the extra shear layer. Noise from the primary jet is modified by its transmission through the shear layer of the flight simulation jet. The sound is refracted by velocity shear and scattered by turbulence. There is also the possibility of coupling between instabilities in the primary and flight simulation jets. This possibility is minimized by assuring that the turbulence scales are well separated. For the present experiment, U,/ D - 500 Hz for the flight simulation jet vs. UJd - 15 kHz for the primary jet. Corrections, based on geometrical acoustics, were made for convection, refraction, geometrical spreading, and for shear layer amplification. The procedure described by Ahuja et al. [16] was used. The effect of forward flight on far field directivity is shown in Figure 5. Directivity is expressed in terms of the “effective” emission angle of the sound, relative to the jet axis, rather than the angle to the observer (inconsistencies between this data and Figure 8 of reference [4] are caused by microphone calibration errors in the earlier measurements). The noise reduction caused by forward flight is greatest at small emission angles. Michalke and Michel [9] have attributed this to directional attenuation of the “effective” Mach number of the source terms.

FLIGHT

EFFECTS

ON

INVERTED

45

JETS

angle, 8

Emsslon

Figure 1.00; 0,

PROFILE

5. Effect of flight simulation on far field directivity. 22, 0.85; 0, 37, 0.77; V, 73, 0.59; 0, 99, 0.48.

M, =0.90;

no center

jet flow. U,(m/s),

A: 0, 0,

These rather large changes in directivity must be taken into account in determining noise reductions due to flight effects. The directivity integral, equation (4), depends on the external flow U, as well as the Mach number of the acoustic sources. The functional dependence of the integral on source Mach number has been described by Chu et ~1. [lS]. Its dependence on external flow was determined by numerical integration of the data in Figure 5. The result is shown in Figure 6, expressed as the ratio of the flight simulation case results to those for the static case.

‘6

I.0

I

s

d 44

2

0.5 -

c

: lo P 3 .

0. 0

I 20

I 60

I 40

I 80

100

U, (m/s)

Figure 6. Relative no center flow.

change in far field directivity

integral

(equation

(4)) caused by flight simulation.

Ma = 0.90;

The reduction in total acoustic power was estimated from the attenuation of the directivity integral and from the reduction in acoustic intensity measured at 0 = 90”. The results are shown in Figure 7 as a function of relative velocity, U, - Up At small values of Ur/ U,, the noise reduction is roughly consistent with the (1 - U,/ U,)’ prediction by Crighton et al. [7]. At larger values of Ur/ U,, however, the noise reduction is substantially less than the (1 - Ur/ U,)’ law. Possible explanations for this deviation include noise directly from the flight simulation jet and shielding by the wake from the nozzle lip. At the highest simulated flight speed the noise from the flight simulation jet was more than 10 dB below the noise from the

46

R. A. PETERSEN

AND

V. SAROHIA

0i

d

Figure 7. Reduction in total acoustic power caused by simulated flight. M, = 0.90; no center flow.

annular profile jet. For that reason, contamination from the flight simulation jet is discounted. Wake effects are a more likely explanation. Sarohia and Massier [17] have shown that increasing the thickness of the external boundary layer over the nozzle results in higher noise levels. Moreover, the wake becomes more pronounced as Ur/ U, increases. 3.3. SPECTRAL MEASUREMENTS Tanna [l] has demonstrated that the power spectra produced by inverted profile jets is shifted towards higher frequencies compared with the power spectra produced by equivalent single jets. This trend is further accentuated by forward flight. Forward flight alters the spectral content of the total acoustic power through small changes in the individual spectral shapes and through the larger changes in directivity. Figure 8 shows the spectral shapes of noise radiated at various emission angles with and without forward flight simulation. The most obvious effect is the shift to low frequencies at angles close to the jet axis. This is characteristic of jets in general, and this general trend is unchanged by forward flight. However, changes in directivity (see Figure 5) caused by forward flight emphasize radiation emitted at larger angles. Consequently, the total power spectrum can be expected to shift to higher frequencies. A secondary effect of the flight simulation is to emphasize a local spectral peak near fd/ U, = 0.7. This peak is examined in more detail in Figure 9, where spectra of noise emitted at 90” are shown for various flight simulation speeds. The spectral peak at fd/ U, = 0.7 is evident at external flow velocities U, greater than 55 m/s; it increases slightly in magnitude as the flight speed is increased. The acoustic source of this peak is still uncertain; however, the secondary peak at low frequency (fd/ U, - 0.1) is considered to be direct radiation from the flight simulation jet.

FLIGHT

EFFECTS

ON INVERTED

PROFILE

JETS

47

-60L

I 0

1

1 0.4

I

1 0.6

1

1 I.2

1

1 I.6

1

1 2.0

fd/U,

Figure 8. Power spectral densities measured at various emission angles with and without flight simulation. U, = 287 m/s; MC/M, = 0.34. Relative levels are not shown; spectra are displaced for clarity.

Ma = 0.91;

u, = 128 m/s III m/s 94 m/s 76 m/s 55 m/s

-60

0 m/s

I

1

1

1

I

1

1

0.8

1

I.2

1

1

0

0.4

I.6

L 0

I

I

I

I

I

5

IO

I5

20

25

I 2.0

fd/u I

f (kliz)

Figure 9. Power spectral densities at emission angles near 90” for various flight simulation speeds. Ma = 0.91;

U, = 287 m/s; MC/Ma = 0.34.

4.

FLOW MEASUREMENT

Tanna [l] attributed most of the noise reduction that occurs in inverted profile jets as compared to equivalent single jets to reductions in centerline velocity and turbulence level. Based on these global differences, his predictive models show good agreement with measurements. Since inverted profile jets also produce substantially less noise than purely annular jets, it is worthwhile to examine the flow fields of those jets as well in order to determine whether similar mechanisms are responsible. The spreading parameter, A = ( uj - iI_+)/
48

R. A. PETERSEN

AND

V. SAROHIA

to be examined for the inverted profile jets in terms of scaling the outer shear layer, the centerline velocity, and the large scale turbulence. 4.1. MEAN VELOCITY MEASUREMENTS A characteristic feature of inverted profile jets is the extra shear layer on the inner edge of the annular jet. Chigier and Beer [18], among others, have demonstrated that entrainment by this shear layer can produce a recirculation vortex and subatmospheric pressures within the center jet. This occurs when the center jet mass flow is small; recirculation ceases when entrainment rates are matched by the center flow.

M, = 0.59

MO z 0.59

M-

MC 0

M, = 0.23

M, = 0.55

M,/M, = 0

MC/M0= 0.39

MC/M0= 0.93

??

??

0.59

Figure 10. Total pressure profiles of three inverted jet profile shapes at r/d =O.l. Retrace displacements are caused by hysteresis and probe response. Traces were averaged for mean velocity measurements.

Total pressure profiles are shown in Figure 10 for a purely annular jet and for two inverted jet profiles with the same annular jet speed. The centerflow for the inverted profiles is sufficiently large that there is no evidence of recirculation. The profile where MC/ Ma = O-39 is optimum from a noise standpoint. When the Mach number ratio became larger than about 0.6, a noticeable wake was shed from the center nozzle lip. In the case MC/Ma =0*93, the wake persisted about two diameters downstream. Total pressure profiles with flight simulation show additional wakes shed by the annular nozzle lip. For example, when Q/ U, = 0.5 the wake persisted for more than six diameters downstream. Chigier and Beer [ 181 characterized the flow fields of annular jets in terms of a merging region, where the annular jet profiles merge together, and a fully merged region with a single velocity maxima located on the jet centerline. Ko and Kwan [19] divided the merging region into an initial region where there are potential cores, and an intermediate region beyond the potential cores where there are two distinct maxima in the velocity profile. In Figure 11, the flow field of an inverted profile jet is compared with the flow field of a pure annular jet in terms of Mach contours. The particular inverted profile jet is the optimum noise profile, MC/ Ma = O-39. The most obvious differences occur within the merging region. Although the recirculation in the annular jet is confined to the first half diameter, its influence is felt for several diameters downstream. Recirculation produces a decrease in diameter of the annular jet in the initial merging region, although the ultimate spreading rates of the two jets are about the same. Also, the presence of recirculation facilitates the merging process. The centerline Mach number increases more rapidly and reaches a higher level than that of the inverted profile jet. The potential core region is also larger and extends farther downstream. The effects of profile and simulated flight on the spreading rate of the outer shear layer are shown in Figure 12. The thickness, S, was measured from the total pressure profiles

FLIGHT

EFFECTS

ON

INVERTED

PROFILE

JETS

49

/ O-

/

.5 -

hf. = o-59 No cenler

flow

.o

.5

0 O-

1.5 L

a .o 4

.5 -

, 0

2

\-,o.l , 4

6

8

I(

x/d

Figure 11. Mach number are indicated on contours.

contours

of annular

jet (top) and an inverted

profile jet (bottom).

Mach numbers

Figure 12. Effect of profile shape and simulated flight speed on the thickness of the outer shear layer. -Brown and Roshko [5]. MC/Ma, A: 0, annular jet, 1.00; Cl, 0.39, 1.00; m, 0.40, 0.39; A, 0.93, 1.00.

-,

50 and

R. A. PETERSEN

AND

V. SAROHIA

is defined by S = r2 - ri, where (7)

M,,, being the Mach number of the local maximum. The virtual origin, x0, was determined from the zero intercept, and the axial co-ordinate is stretched by the spreading parameter, A, which is presently defined in terms of U, and U, as A = (Ua - q,/c

(8)

u, + Uf).

Two different growth rates are apparent: a high growth rate in the merging region, followed by a smaller growth rate in the merged region. The shear layer thickness is insensitive to changes in the profile, except in the intermediate region where the annular jets are in the process of merging. The spreading parameter scales the shear layer growth in the initial merging region but is less successful in scaling the intermediate region. It appears as though the scaling may work again for the merged region, but the measurements were not carried far enough downstream to be certain. The spreading rate S/(x - x0) = 0.18 A reported by Brown and Roshko [5] is shown for comparison. Although the comparison is imprecise because of different definitions of shear layer thickness, there still seems to be general agreement within the merging region.

0.2

I

I 0.4

I

I

lllll I

2

I

I111111 4

IO

I5

[(x-x,)/dlX Figure 13. Distribution of centerline Mach numbers for various center jet speeds and for one flight simulation. Dashed lines indicate distribution of maximum Mach numbers. MC/Ma, A: 0, annular jet, 1.00; ? ,? 0.39, 1.00; ?? , 0.40, 0.34; A, 0.93, 1.00.

Centerline Mach number distributions are shown in Figure 13 for the three profiles from Figure 10. As a consequence of the rapid merging of the potential cores induced by the recirculation, the centerline Mach number for the pure annular jet attains a maximum value almost as high as that of the inverted profile jet with MC/Ma = O-93. This is additional evidence that noise reduction caused by changes in the velocity profile are tied to reductions in the centerline velocity distribution and associated turbulence levels. The effect of simulated flight on the centerline Mach distribution is shown in the lower part of Figure 13. The distributions of maximum Mach numbers are also shown, and they define the length of the potential cores. The axial co-ordinate is stretched by the

FLIGHT

EFFECTS

ON

INVERTED

PROFILE

JETS

51

spreading parameter, and again the stretching does a poor job of scaling the intermediate merging region, This is not surprising because the growth rate of the inner shear layer is not expected to scale with A. The stretching over-corrects the rate of merging of the potential cores, and the consequence is that the outer shearing rate is smaller and the centerline velocity larger than would be predicted by simply scaling axial distances by A. 4.2. TURBULENCE MEASUREMENTS The effect of profile shape on turbulence levels has been reported by Tanna [ 11. Briefly, in the merging region turbulence levels are higher in inverted profile jets than in equivalent single jets. In the merged region, the reverse is true. The effect of forward flight on turbulence levels has been reported by Morris [6]. He found that peak turbulence levels scale with centerline velocity according to (U,-- Uf)“, where IZ varies between O-7 and 1.0 depending on the ratio (U,- C_$)/Up Recent turbulence research [20,21] has indicated that the dynamics of the large scale structures known to dominate turbulent shear flows may play an important role in jet noise. Because the dynamics of these large scales are related to the instabilities of the free shear layer, any scaling predicted from linear stability theory can be expected to have implications for turbulence scales. The stability calculations by Monkewitz and Huerre [ 1 l] for a co-flowing mixing layer show that the frequency of the most unstable disturbance is approximately f=0*03(U,+U,)/6, (9) where U, and U, are the flow speeds. Since the shear layer thickness scales with A, the passage frequency, f, of the large scale structures might be expected to scale according to fdl(u,+

U,)QW(z-x0).

(10)

The motion of the large scale structures were measured by placing a hot film probe outside the inverted profile jet near the edge of the outer mixing layer. The external flight simulation U, provided a polarizing flow for the hot film, which was used to measure axial velocity fluctuations induced by the passage of large concentrations of vorticity. At each downstream location the probe was positioned radially at the edge of the intermittancy region. Figure 14 shows autocorrelations of the hot film signal produced by the x/d

1 -

I.0

1

1

I

- 0.5

0

0.5

Time

delay,

I.0

I

Figure 14. Autocorrelations of signal from a hot film probe located outside the annular jet, at the edge of the shear layer, at various distances downstream. 17, = 101 m/s; M, =0.91; no center flow.

52

R. A. PETERSEN

AND V. SAROHIA

annular jet at a simulated flight speed of 101 m/s. Within the first five jet diameters the autocorrelations are periodic. The autocorrelation periods are constant over the range O-5-1.0 diameters downstream and over the range 1.5-3.0 diameters downstream. Between 1-O and 1.5 diameters there is a subharmonic shift in frequency. This indicates that a pairing has occurred between those positions.

A

_

I

-1.25

x/d = 5.0

x/d = 7.0

A

I

I

0

1.25

T (msi

Figure 15. Effect of profile shape on hot film autocorrelations. In each set, upper trace: annular jet; lower trace: inverted profile jet, MC/M, = 0.34. For both profiles, Ma = 0.91 and f.$ = 50 m/s.

The influence of jet profile shape on the turbulence scales is shown in Figure 15. Hot film autocorrelations measured with an inverted profile jet are compared with autocorrelations measured with a pure annular jet. The annular velocities and flight simulation speeds were the same. At each downstream position the autocorrelations are virtually identical. The fact that the turbulence time scales are independent of the center jet conditions suggests that these scales are associated with the outer shear layer. This interpretation is supported by Figure 12, which shows that the outer shear layer thickness is relatively insensitive to center jet conditions. The frequency scaling with flight simulation is shown in Figure 16. The frequencies are determined from autocorrelation period and are expressed as Strouhal numbers based on annular jet speed. The axial co-ordinate is stretched, and the co-ordinate stretching is successful in collapsing the Strouhal numbers. The Strouhal numbers show general agreement with single jet measurements by Petersen [22]. This lends further support to the notion that these scales are associated with the outer shear layer. The slightly higher Strouhal numbers of the single jet are largely attributed to virtual origin differences. The passage frequencies do not scale with ( U, + 4)/2 as predicted by stability theory, equation (10). Since U, was not varied, the true frequency scaling is uncertain. It is quite possible that the jet was excited at some frequency associated with the facility. The location of the first pairing does seem to scale with A, and occurred near Ax/d = O-6 in both cases. The pairings were localized to within O-2 d/h. It is worth noting the coincidental frequencies associated with the vortex pairing and with the spectral peak in Figures 8 and 9. A local peak at a Strouhal number of 0.7 was evident in some of these spectra. It was strongest at emission angles near 90” and its

FLIGHT EFFECTS ON INVERTED

PROFILE

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(r/d)A

Figure 16. Passage frequency of large turbulence scales in the annular jet mixing layer, expressed as a Strouhal number, as a function of stretched co-ordinate. M. =0.91; no center flow; solid symbols are single jet measurements. U,(m/s), A: 0, 54, 0.68; 0, 101, 0.48; +, 0, 1.00 [22].

relative importance increased with flight simulation speed. The frequency of the peak is in approximate agreement with the 0.6 Strouhal number of the pairing subharmonic. Although no causal relationship has been established it is an intriguing coincidence.

5.

CONCLUSIONS

Measurements were made to demonstrate the effects of profile shape and forward flight on the noise and flowfield of an inverted profile jet. The jet was operated cold and subsonic. The Mach number of the annular flow was maintained constant at O-9 for most of the measurements. The main conclusions are as follows. 1. The apparent noise reduction that can be achieved with the inverted profile jet as compared to an “equivalent” single jet depends on which performance parameters are held constant. However in terms of reductions in acoustic efficiency, measurements indicate that 3 dB is the upper limit. 2. The noise reduction caused by simulated forward flight is independent of inverted profile shape and is approximately (1- L$/ U,)’ in the limit U,/ U, + 0. As Uf/ U, increases the noise reduction is less than (1 - Ur/ U,)‘. 3. Simulated forward flight shifts the peak in the far field directivity pattern away from the jet axis towards the forward arc. 4. Changes in inverted jet profile had little effect on the spreading rate of the outer shear layer. With forward flight simulation the spreading rate was proportional to the spreading parameter, A = (U, - Ur)/( U, + U,,), within the potential core region. 5. The limitations of the stretched co-ordinate, x’ = Ax, as a similarity variable were examined. It is an effective similarity variable for flow quantities associated with the outer shear layer, such as shear layer thickness and turbulence scales. It is not an effective similarity variable for quantities associated with the inner shear layer, such as centerline velocity distribution. ACKNOWLEDGMENT

This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract NAS7-100, sponsored by the National Aeronautics and Space Administration. The authors would like to express

R. A. PETERSEN AND V. SAROHIA

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their gratitude to W. Bixler, B. Green and R. Smither for their assistance in assembling and conducting these experiments.

REFERENCES they 1. H. K. TANNA 1980 Journal of Sound and Vibration 72, 97-118. Coannular jets-are really quiet and why? 2. R. W. HINES 1978 Journal of Aircraft 15,321-325. Variable stream control engine for supersonic propulsion. 3. W. T. ROWE, E. S. JOHNSON and R. A. MCKINNON 1979 Journal of Aircraft 16, 95-101. Technology status of jet noise suppression concepts for advanced supersonic transports. 4. R. A. PETERSEN and V. SAROHIA 1981 American Institute of Aeronautics and Astronautics Paper 81-2026. Noise radiated from inverted profile jets under simulated flight. 5. G. L. BROWN and A. ROSHKO 1974 Journal of Fluid Mechanics 64, 775-816. On density effects and large structures in turbulent mixing layers. 6. P. J. MORRIS 1976 American Institute of Aeronautics and Astronautics Journal 14,1468-1475. Turbulence measurement in subsonic and supersonic axisymmetric jets in a parallel stream. 7. D. G. CRIGHTON, J. E. FFOWCS WILLIAMS and I. C. CHEESEMAN 1976 American Institute

8. 9.

10. 11. 12. 13. 14. 15. 16.

17.

18.

19. 20. 21. 22.

of Aeronautics and Astronautics Paper 76-530. The outlook for simulation of forward flight effects on aircraft noise. V. SAROHIA 1979 American Institute of Aeronautics and Astronautics Paper 79-0616. Flight effects on subsonic jet noise. A. MICHALKE and U. MICHEL 1979 Journal of Sound and Vibration 67,341-367. Prediction of jet noise in flight from static tests. A. MICHALKE and U. MICHEL 1980 American Institute of Aeronautics and Astronautics Paper 80-1031. Prediction of flyover noise from plain and coannular jets. P. A. MONKEWITZ and P. HUERRE 1982 Physics of Fluids 25,1137-1143. The influence of the velocity ratio on the spatial instability of mixing layers. A. MICHALKE and G. HERMANN 1982 Journal of Fluid Mechanics 114, 343-359. On the inviscid instability of a circular jet with external flow. H. S. RIBNER 1969 Journal of Fluid Mechanics 38, l-24. Quadrupole correlations governing the pattern of jet noise. M. J. LIGHTHILL 1963 American Institute of Aeronautics and Astronautics Journal 1,15071517. Jet noise. W. T. CHU, R. A. PETERSEN and K. KAO 1972 Journal of the Acousricul Society of America 51, 830-832. Directivity of jet noise. K. K. AHUJA, B. J. TESTER and H. K. TANNA 1978 NASA CR 3056. The free jet as a simulator of forward velocity effects on jet noise. V. SAROHIA and P. F. MASSIER 1980 American Institute of Aeronautics and Astronautics Journal 18, 630-635. Effect of density on noise radiation from subsonic inverted velocity profile jets. N. A. CHIGIER and J. M. BEER 1964 Journal of Basic Engineering, Transactions of the American Society of Mechanical Engineers 86, 797-804. The flow region near the nozzle in double concentric jets. N. W. M. Ko and A. S. H. KWAN 1976 Journal of Fluid Mechanics 73, 305-336. The initial region of subsonic coaxial jets. J. LAUFER 1974 in Volume in onore di Carlo Ferrari, 449-464. On the mechanism of noise generation by turbulence. Turin: Levrotto and Bella. J. E. FFOWCS WILLIAMS and A. J. KEMPTON 1978 Journal of Fluid Mechanics 84,673-694. The noise from the large-scale structure of a jet. R. A. PETERSEN 1978 Journal of Fluid Mechanics 89,469-495. Influence of wave dispersion on vortex pairing in a jet.

APPENDIX: : d

speed of sound jet exit area outside diameter of jet

NOMENCLATURE

FLIGHT

i P

R

u W x, r X0 8 e A V P

T

0 cc

ON

INVERTED

PROFILE

diameter of flight simulation jet frequency Mach number pressure far field distance mean axial velocity power axial, radial co-ordinates virtual origin mixing layer thickness spherical angle of sound emission relative to jet axis shear layer spreading parameter, = ( lJ2 - U,)/( U, + VI) kinematic viscosity density

Subscripts annular a

; i m s

EFFECTS

jet exit conditions center jet exit conditions flight conditions single jet exit conditions local maxima acoustic source stagnation conditions centerline conditions ambient conditions (external to flight simulation jet)

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