The vortical structures in shear layers govern many dynamic aspects of the jet, including entrainment of mass, transfer of momentum and noise generation. These structures develop from instability waves and undergo a merging process. Vortex merging reduces the time scale and increases the length scale of the shear layer. At the same time pressure fluctuations are induced by the unsteady motion. These pressure perturbations can exert high level dynamic loading on nearby structures, and radiate to the far field as noise. In this study, the generation mechanism of the pressure fluctuations and the radiation process are examined

Ho, C. M.

English

NASA Technical Reports Server

- c.’ 
FINAL REPORT 
I: TITLE: 
Near Field Pressure Fluctuations in a Circular Jet 
II: CONTRACT NUMBER: 
NAG- 1-420 
III:PRINCIPAL INVESTIGATOR: 
Ho, Chih-Ming 
IV: PERIOD: 
/6p 
November 4, 1983 - November 3, 1985 
V-PUBLISHED PAPERS: 
1. Ho, C. M., and Lafouasse, B., “Hydrodynamic Pressure Field of an Axisymmetric 
Jet”, AlAA paper No. 84-2316, 1984. 
2. Lafouasse, B., Chan, A., and Ho, C. M., “Near Field Pressure Fluctuations of a 
Circular Jet”, Proceedings of IUTAM Symposium on Aero- and Hvdro-Acoustics, 1985. 
3. Chan, A., Lafouasse, B., and Ho, C. M., ”Modal Distributions of a Pressure Field 
Generated by a Circular Jet”, AlAA paper No. 86-1910, 1986. 
VkGRADUATE DEGREE GRANTED UNDER THIS CONTRACT: 
Benoit Lafouasse, M. S., 1984 
Anthony Chan, M. S., 1985 
[NASa-CR- 179647) Y E B E  FIELD P R E S S U R E  N87- 102 49 
E L U C ‘ I D A T I O N S  IN A C I R C U L A R  JET F i n a l  
fi€Fort, 4 Nov. 1’323 - 3 NOV. 1985 
[ U n i v e r s i t y  of Southern C a l i f c r x i a )  t 6  p Unclas 
CSCL 20D G3/34 114337 
https://ntrs.nasa.gov/search.jsp?R=19870000816 2020-03-20T13:56:36+00:00Z
2 
TECHNICAL REPORT 
ABSTRACT 
The vortical structures in shear layers govern many dynamic aspects of the jet, 
including entrainment of mass, transfer of momentum and noise generation. These 
structures develop from instability waves and undergo a merging process. Vortex 
merging reduces the time scale and increases the length scale of the shear layer. At the 
same time pressure fluctuations are induced by the unsteady motion. These pressure 
perturbations can exert high level dynamic loading on nearby structures, and radiate to 
the far field as noise. In this study, we examine the generation mechanism of the 
pressure fluctuations and the radiation process. 
I: INTRODUCTION 
In the vicinity of a shear layer, pressure fluctuations are produced by the unsteady 
evolving vortices. Near the flow, the pressure fluctuations are of a hydrodynamic nature. 
The perturbations propagate in the order of the flow velocity and the amplitude is 
proportional t o  the magnitude of the flow velocity. The perturbations can cause high 
level dynamic loading on a nearby solid surface (e.g. VSTOL aircraft)lS2 and as a result, 
structural considerations are required. At the far field, the radiated pressure propagates 
a t  acoustic speed. The noise can be a health hazard and can create problems in many 
practical applications. 
The shear layer of a jet is unstable and amplifies the disturbances exponentially3. 
The growing stability waves roll up into large-scale coherent vortical structures which 
dominate the dynamics of the flow4. The structures themselves are not stable and 
undergo merging5, a n  unsteady process which produces noise6*’ and near field pressure 
f l u c t ~ a t i o n s ~ ~ ~ .  The frequencies of the pressure perturbations are the fundamental 
instability frequency (corresponding to  the formation of the primary vortex) and its 
subharmonics (corresponding to the subsequent vortex mergings). 
I 
3 
,d 
In jet studies, the flow field3 and the far field noise’0~’’~’2 have been extensively 
investigated. However, information regarding the crucial link, i. e. the near field pressure 
fluctuations, is very scarce. The present effort is to explore the missing link in order t o  
understand the generation and the radiation of the pressure fluctuations. 
This report is a summary of our findings over the past two years8, 9* 21. The 
relation between the generation of fluctuating pressure and the evolution of vortices is 
clarified first. The modal distributions of the near pressure fluctuation are then 
determined. Finally, the length scales associated with the transition from the near field to  
the far field are identified. 
II: FACILITY AND INSTRUMENTATION 
The jet nozzle has a diameter, D, of 5.08 cm and is connected to  the stagnation 
chamber with a fifth order polynomial contraction. The contraction ratio is 56 : 1. 
Honeycomb and several layers of screens are used to  reduce the background turbulence 
level to approximately 0.1%. A small angle diffuser connects the stagnation chamber to  a 
20 cm diameter pipe which leads to the compressed air tanks. The compressed ai r  flows 
through a dryer before entering five large storage tanks. The operating pressure is 
regulated by a low noise valve. Extreme care has been taken to remove possible 
upstream disturbances. Acoustic forcing i s  provided by eight loudspeakers placed in a 
cavity near the jet nozzle. The acoustic waves which emit from a thin slit around the 
nozzle can perturb the thin shear layer in desired manners. The jet is located in an 
anechoic chamber measuring 7.42 m long, 4.79 m wide and 3.63 m high. The low cut-off 
frequency is 150 Hz. The chamber is suspended o 
Hz are isolated. 
The origin of spherical coordinate is defined 
diameter downstream from the nozzle exit. r = 17 
springs and vibrations higher than 1 
a t  the point on the jet axis and five 
is the distance away from the origin 
, 
4 
and is the angle between ? and the jet axis. 8 is the azimuthal angle. 
Multi-channel hot-wires, pressure transducers (Panasonic type wm-32) and 
microphones (B & K 0.32 cm dia.) are used to  record the instantaneous velocity and 
pressure signals. The data are digitized and processed by a PDP 11-23 microcomputer. 
The computer is equipped with an ADAC 100 kHz analog-to-digital converter and a SKY 
array processor. 
111: EXPERIMENTAL RESULTS 
Preferred Mode and Facilitv Dependence: 
More than a decade ago, Crow and Champagne13 found that a je t  with a top-hat 
profile was most susceptible to a forcing a t  a frequency of fpD/Ui = 0.3 which is known 
as the preferred mode. Since then, a fundamental question has been raised; is the 
preferred mode a subharmonic of the init ial most amplified frequency or a frequency 
independent of the initial instability? This question was not solved until Kibens’ 
performed an experiment in a clean circular jet presumably free of any upstream 
disturbances. He found that the preferred mode is related to the initial instability in the 
low speed range and a t  high speeds has a constant value of 0.44 independent of the 
initial instability frequency. 
Gutmark and HoI4 conducted a special study of the facility influence on the values 
of the preferred mode. They found that the residual noise from the facility could cause 
the values of the preferred mode to change in a stepwise manner rather than remaining 
constant. Therefore, whether the preferred mode is constant or not can be used as a n  
indication of the cleanliness of the facility. As a matter of fact, the existing data collected 
over the past two decades have a scatter of 100°/~, from 0.25 to 0.5, which is presumbly 
due to the residual noise of individual facilities. In the present facility, tedious t r ia l  and 
error tests and improvements have been carried out until finally, the measured preferred 
5 
mode over a wide range of velocities has values of about 0.44 (Fig. 1). The data has 
small scatter but definitely no stepwise behavior. After having achieved this condition, it 
is believed that the jet is clean and the far field noise as well as the near field pressure 
fluctuations are free from the influence of the facility. 
Sources of Pressure Fluctuations: 
Measurements of far field noise 6*7 have shown that the frequencies of the peaks 
are the same as the initial instability frequency or their subharmonics. The results 
suggests that the noise sources are fixed in space because there is no Doppler shift. The 
coherent structures convect in the streamwise direction, but the merging positions are 
more or less stationary in space Is. This implies, therefore, that the unsteady motion of 
the merging vortices produces the noise. In this section, we examine the generation 
mechanism from the amplitude contours of the near field pressure. 
Approximately one thousand measuring stations were used to  survey the near field 
pressure in the vicinity of the jet edge. The jet had a Mach number of 0.088 and was 
forced at the initial most amplified frequency, fo. The spectrum at each station was 
measured. Near the nozzle exit, the spectra have a sharp peak a t  the most amplified 
frequency. At downstream locations, the peak at fo decays as the first subharmonic, f,, 
emerges. The grow-decay cycles of f,, and higher harmonics, f, f, etc., take place with 
increasing streamwise distance. The constant spectral density contours can be 
constructed from the measured spectra and are shown in Fig. 2. The jet edge in the 
figure is defined as the location where the local mean velocity is five percent of the jet  
exit speed. The pressure contour map clearly indicates that the pressure perturbations 
originate from the corresponding vortex merging position. The result is the same as that 
found in an elliptic jet16. The zone of the same pressure intensity increases with 
decreasing frequency. For example, the lo-' Pa2/Hz2 contour covers a narrow region near 
the first vortex merging pcjsition, but extends far from the jet edge for the preferred mode 
6 , 
case. 
Modal Distribution 
The geometrical shapes of the coherent structures have many forms, including 
axisymmetric rings, helix or other asymmetric configurations. The stability a n a l y s i ~ ' ~ ~ ~ ~  
shows that the amplification rates of the symmetric mode [mode 01 and the helical modes 
[mode 2 11 are about the same in the potential core region. The data show that the 
instability waves intermittently change among the mode 0 and the modes 21. When the 
shear layer thickness becomes appreciable, the amplification rate of the helical mode 
dominates. At the end of the potential core, the mean velocity profile has a bell shape; 
only the helical mode amplifies''. It is expected that the vortex merging process will also 
be of different modes. It is therefore interesting t o  investigate the modes of the pressure 
fluctuations. 
Eight pressure transducers are evenly distributed in the azimuthal direction. They 
are placed in the 8 = 90' plane and r = 10.8 cm, 11.4 cm, 12.1 cm & 15.2 cm. The Mach 
numbers are varied from 0.12 to  0.58. These transducers are near the end of the 
potential core and are about two preferred mode instability wavelengths away from the 
jet edge. Most of the signals are dominated by the pressure generated by the preferred 
mode. The outputs are Fourier decomposed in azimulthal spatial modes. 
The axi-symmetric mode and the helical modes all increase with increasing Mach 
number, but it is not a strong function (Fig.3). As expected, the +1 mode has the same 
magnitude as the - 1  mode since the jet should have no preferrence regarding the right 
hand or left hand helix. The magnitude of axi-symmetric mode is higher than the 
magnitude of each + 1  mode or -1 mode, but is about 25% lower than the sum of the +1 
modes. This is different from the measurement by Fuchs and Miche12', which showed 
that the most dominant mode in their jet  was the axi-symmetric mode. Figure 4 shows 
7 . 
the changes of the magnitude as a function of the radial distance. The axi-symmetric 
mode decreases sharply with the distance. Helical modes have much milder variation in 
the measured range. 
The Hydrodynamic Near Field: 
Figure 2 shows that the pressure fluctuations decrease rapidly with the distance 
away from the jet edge. The fluctuating levels in the hydrodynamic region decay 
exponentially with distance normal to the jet edge and change to algebraic decay in a 
short distance (Fig. 5). A length scale, R-RE, was defined as a measure of the 
exponentially decaying region. The scale is determined from the jet edge to the point 
where the decay curve deviates from the exponential decay line (Fig. 5). The scale at a 
specific frequency was measured at the streamwise locations where the vortex mergings 
O C C U ~ ~ " ~ .  R is the distance measured normal from the jet edge at these streamwise 
locations. When the scales, R-R,, are normalized to the instability wavelength a t  the 
specific frequency X = Uj/2f, the normalized values are almost the same for all 
frequencies and are about half of the local instability wavelength (Fig. 6). Hence, the 
exponential decay region of the hydrodynamic pressure fluctuations extends only in the 
order of one instability wavelength away from the jet edge. This result agrees with the 
measurements made in an elliptic jet.16 
The Acoustic Near Field: 
In the hydrodynamic near field, the length scale is the instability wavelength. At the 
far field, the length scale has to be the acoustic wavelength. In the low Mach number 
range, the two length scales are one order of magnitude apart. In other words, there 
must be another transitional layer between the hydrodynamic exponential decay region 
and the far field. In order to examine this region, the pressure fluctuations were 
measured around a chosen location, ro 9 127 cm. This location is far from the 
hydrodynamic field but only a few acoustic wavelengths from the source, so that we can 
a 
- -N 
explore the transition process. The acoustic wavelength, X,(M), used here is the 
wavelength a t  the preferred mode of a jet a t  Mach number M. The pressure intensity 
decreases algebraically with distance in this region as 
The values of k are shown in Fig. 7. At B = 50' and 30°, the values of k vary with 
Mach number and reach the asymptotic value of -2 a t  M = 0.74. However, this is not a 
Mach number effect. It actually indicates that an acoustic near field exists outside the 
hydrodynamic field, since ro = 127 cm is about ten acoustic wavelengths from the jet a t  
high Mach number (ro/Xa(M) = 7.48 at M = 0.75), and is only about one wavelength from a 
low Mach number jet (ro/Xa(M) = 1.51 at M = 0.15). The angular dependence can be 
explained as follows: the long wavelength waves propagate in the direction of small B, a t  
a larger angle, e.g. B = 75', the spectrum contains more high frequency wave than that a t  
a lower angle. Therefore, the peak level acoustic waves a t  larger angles are a few more 
acoustic wavelengths away than those a t  smaller angles. 
The existence of an acoustic near field can be further substantiated by the 
measurements of acoustic intensity dependence on the Mach number for 0' 5 r 1. 127 
cm. 
The values of N are plotted against r/Xa(M) in Fig. 8. It takes about ten acoustic 
wavelengths to reach the eighth power dependence on Mach number. The low Mach 
number measurements have low power dependence, 4 5 N 1. 6, because of their long 
acoustic wavelengths. If the set of data is plotted as the parameter of the angle with 
9 
respect to  the jet axis (Fig. 9), a slight angular dependence can be observed especially 
between 6 = 30' and 75'. 
The traditional acoustic far field is defined at about fifty jet diameters from the 
nozzle. This scaling is essentialy based upon the length scale of the preferred mode 
wavelength. Let R, be the distance from the nozzle t o  the far field, then 
R, / D = 50 (3) 
The present experimental results suggest that the proper acoustic far field should 
be ten A,(M) away from the jet. 
R, / A,(m) = 10 (4) 
or 
R, / D = 25 / M (5) 
Therefore, Eq. (3) only holds for M > 0.5. Eq. (5) indicates that special care is 
needed for low Mach number jet noise research because a fairly large anechoic chamber 
is required. 
IV: CONCLUSION 
The near field pressure contours of a clean jet show that the pressure fluctuations 
are produced by the vortex merging process. The different geometical configurations of 
the coherent structures are also reflected in the hydrodynamic pressure fluctuations. The 
magnitudes of the axi-symmetric mode and the helical modes are of the same order and 
increase with Mach Number. 
Two length scales govern the radiation precess, the instability wavelength and the 
acoustic wavelength. The hydrodynamic pressure fluctuations extend only about one 
instability wavelength from the jet edge. It takes ten acoustic wavelengths to reach the 
acoustic far field. 
REFERENCES 
10 
/ 
1. Yu, J.C., Reddy, N.N. and Whitesides, J.L., "Noise and Flow Characteristics of an 
Externally Blown Flap", Proc. of Second Interagency Symp. on Univ. Res. in Transportation 
Noise, 1 :2 19-37, 1974. 
2. Ho, C.M., and Nosseir, N.S., "Dynamics of an Impinging Jet", Part I, the Feedback 
Phenomenon, J. Fluid Mech., 1051 19-42, 1981. 
3. Ho., C.M., and Huerre, P., "Perturbed Free Shear Layers", Ann. Rev. Fluid Mech., 
16:365-424, 1984. 
4. Brown, G.L., and Roshko, A., "On Density Effects and Large Structure in Turbulent 
Mixing Layers", J. Fluid Mech., 64:775-816, 1974. 
5. Winant, C.D., and Browand, F.K., "Vortex Pairing, the Mechanism of Turbulent Mixing 
Layer Growth at Moderate Reynolds Numbers", J. Fluid Mech. 63:237-55, 1974. 
6. Laufer, J., and Yen, T.C., "Noise Generation by a Low Mach Number Jet", J. Fluid 
A* Mech 134:1-3 1, 1983. 
7. Kibens, V., "The Limit of Initial Shear Layer Influence on Jet Development", AlAA Paper 
NO. 81-1960, 1981. 
8. Ho, C.M., and Lafouasse, B., "Hydrodynamic Pressure Field of an Axisymmetric Jet", 
AlAA Paper No. 84-2316, 1984. 
9. Lafouasse, B., Chan, A., and Ho., C.M., "Near Field Pressure Fluctuations of a Circular 
Jet", Proc. of IUTAM Symp. on Aero- and Hydro-Acoustics, 1985. 
10. Ffowcs Williams, J.E., "Aeroacoustics", Ann. Rev. Fluid Mech., 9:447-68, 1977. 
11. Goldstein, M.E., "Aercdynamic Noise", Ann. Rev. Fluid Mech., 16:263-85, 1984. 
11 
12. Huerre, P., and Crighton, D.G., "Sound Generation by Instability Waves in a Low Mach 
Number Jet", AlAA Paper No. 83-0661, 1983. 
13. Crow, S.C., and Champagne, F.H., "Orderly Structure in Jet Turbulence", J. Fluid Mech., 
48:547-9 1, 197 1. 
14. Gutmark, E., and Ho, C.M., "On the Preferred Modes and the Spreading Rates of Jets", 
Phys. Fluids, 26:2932-38, 1983. 
15. Ho, C.M., and Huang, L.S., "Subharmonics and Vortex Merging in Mixing Layers", 3, 
FLuid Mech., 119:443-73, 1982. 
16. Gutmark, E., and Ho, C.M., "Near Field Pressure Fluctuations of an Elliptic Jet", AlAA 
Paper No. 83-0663, 1983. 
17. Plaschko, P., "Helical Instabilities of Slowly Diverging Jets", J. Fluid Mech. 92:209-15, 
1979. 
18. Cohen, J., and Wygnanski, I., "The evolution of Instabilities in the Axisymmetric Jet", 
Submitted to J. Fluid Mech., 1986. 
19. Batchelor, G.K., and Gill, A.E., "Analysis of the Stability of Axisymmetric Jets", J. Fluid 
/# Mech 14:528-551, 1962. 
20. Fuchs, H.V., and Michel, U., "Experimental Evidence of Turbulent Source Coherence 
Effecting Jet Noise", AlAA Paper No. , 1977. 
21. Chan, A., Lafousse, B., and Ho, C. M., "Modal Distribution of Pressure Field Generated 
by a Circular Jet", AlAA PAPER No. 86-1910, 1986. 
Figure 1: Preferred Mode 
Figure 2: Near Field Pressure Contours 
I.. .-. - . First Subharmonic 
-.e- Preferred Mode 
Second Subharmonic 
mode 0 
H mode +1 
0 mode -1 ' I  
Figure 3: Modal Distribution as a Functions 
of Mach Number, r - 10.8 cm. 
Omode 0 
Figure 4: modal Distribution as a Function 
of Radial Distance, M - 0.58. 
2 Pa 
7 
lo2 
3 4 
R cm 
5 
Figure 5: Decay of Hydrodynamic Pressure 
Fluctuations, M - 0.087, 
First Subharmonic. 
0 . 1  3 
e l l i p t i c  jet 
0 '  . A .  I 
10 10. l o 3  lo4 
Figure 6: The Normalized Length Scale of 
Hydrodynamic Near Field, M = 0.087, 
1,: First Subharmonic 
f2: Second Subharmonic 
0 f3: Third Subharmonic 
: Data of the Elliptic Jetts 
0 015 .5  0 75 
M 
Figure 7: Variation of k with respect to 
Mach Number, 
m 8 = 75q  0 .  8 - 50°, 0 8 = 30°. 
8 
N 
6 
4 
2 
Figure 8 Variation of N with respect to 
Normalized Distance, 
0 M = 0.15. 0 M - 0.45, 0 M - 0.74. 
8 
N 
6 
4 
2 
Figure 9: Variation of N with respct to 
Normalized Dist snce, 
rn B = 75'. 0 6 -  50°, 0 8 - 306 . 


Near field pressure fluctuations in a circular jet

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