Progress Report 

Pressure Measurements of Impinging Jet with Asymmetric Nozzle 

Grant No. NAG-1-819 

submitted to 

NASA Langley Research Center 

Hampton, VA 23665 

Attention: J. M. Seiner 

Department of Aerospace Engineering 

University of Southern California 

University Park 

Los Angeles, California 90089-1191 

(NASA-CR-182759) PRESSURE HEASUREHENTS OP N 88- 220 11 

IHPINGING JET WITH ASYHHETRIC NOZZLE 

Progress Report (University of Southern 

California) 24 p CSCL 018 Unclas 

G3/02 0140735 

Principal Investigator: 

Ho, Chih-Ming, Professor 

(213)743-6560 

Date: May 1988 
THE NEAR-FIELD PRESSURE FLUCTUATIONS OF AN 

IMPINGING ELLIPTIC JET 

Principal Investigator: Ho, Chih-Ming, Professor 

Department of Aerospace Engineering 

University of Southern California 

Los Angdes, California 90089-1191 

ABSTRACT 

For modern aircraft, impinging surfaces are commody used as a device for obtaining vector 

thrust from engine exhaust. The nature of dynamic loading is important to understand 

for design purposes. In this study, we examine the frequency, mode and level of pressure 

fluctuations generated by an elliptic jet. The elliptic jet is used because it has several 

operational advantages over a circular jet. 

1 INTRODUCTION 

When a jet issues from the nozzle, a thin shear layer forms between the high speed stream 

and the ambient. The shear layer is unstable and develops Kelvin-Helmholtz instability 

waves. Eventually, the vorticity lumps into large vortical structures.' When the structure 

convects with the free stream flow, it generates pressure fluctuations. Near the jet, the 

pressure fluctuations am of the hydrodynamic type. The propagation speed and the amplitude of the pressure waves scale with the jet speed. Far away from the jet, the pressure 

1 
waves propagate at sonic speed and the intensity is proportional to the eighth power of 

the jet speed. In the past, flow generated acoustic waves have been extensively studied 

for the purpose of better environmental pr~tection.~,~~~~~ On the contrary, the hydrodynamic pressure field is not fully explored. 6 Recently, due to the applications of composite 

materials and the use of vectored thrust devices, an accurate pressure loading has become 

necessary for proper design of the loading surface. 

Most conventional jets have a circular exhaust. The instability waves and coherent 

structures can develop in axisymmetric or higher mode^.^,^,^ The near-field pressure fluctuations induced by these structures also exhibit a combination of many modes, but the 

axisymmetric is the strongest. Recently, it has been found that the jet with an ellip10 tic nozzle can entrain surrounding fluid much more effectively than the circular nozzle. 

The main mechanism of the large entrainment is the axis switching of the elliptic vortex 

ring caused by the self-induction. Obviously, the near-field pressure fluctuations will be 

greatly influenced by the axis switching process. Asymmetric node becomes a common 

configuration in some modern airplanes. An understanding of the pressure loading is in 

demand. 

When a plate is placed ne= the jet, the development of the coherent structures will 

be modified by the feedback of the pressure generated by the impinging vortices. Zn the 

case of an elliptic jet, one extra factor is the ratio between the axis switching distance and 

the nozzle to plate distance because this ratio determines the phase of feedback pressure 

waves in the plane normal to jet axis. The formation of the vortices will be determined 

2 
by the feedback forcing and the dynamic loading is then modified. Therefore, the location 

and the orientation of the plate is a major parameter in studying the near-field loading 

problem. 

In this project, we studied the pressure fluctuations of both a free and an impinging elliptic jet. The levels of loading, the spectral information and the azimuthal phase 

distribution are examined. 

2 FACILITY AND INSTRUMENTATION 

Measurements were pedormed in a small-aspect-ratio elliptic jet located inside the USC 

anechoic chamber, which has a working dimension of 7.4 x 4.8 x 3.6 m and a low frequency 

cut-off of 150 Hz. The majgr diameter of the nozzle 2u was 50.8 mm and the minor 

diameter 2b was 25.4 mm. The settling chamber of the nozzle assembly (Fig. la) had an 

inside diameter of 0.38 m. The totd contraction ratio was 112:l. Jet flow was driven by a 

blow-down system and was maintained at a speed of 21.9 m/sec or Re% = 7.8 x lo4 in the 

present experiment. Together with the low poise control valve downstream from the highpressure storage vessel and silk-screens in the settling chamber, the 5th order polynomial 

nozzle contour provided an initially laminar boundary layer and a low turbulence level 

such that the dominating fundamental instability of the jet satisfied linear theory and had 

a frequency proportional to Via. z 

Eight Panasonic WM-063X electret microphones were selected for the near-field me& 

surements. The dymxnic response of the microphones, which had a physical dimension 

3 
of 6 mm and were equiped with a home-made power-supply/amplifier, were calibrated locally and shown to have a linear response up to 5 kHz. The impinging plate was mounted 

vertically at a distance Sa from the jet exit. 

Measurements were digitized on line with a PDP11/23 microcomputer. Data reduction 

was performed with this microcomputer or with a larger VAX/750 computer. 

3 EXPERIMENTAL RESULTS 

3.1 Loading Level: 

We placed eight pressure transducers around the jet, at an equal distance from the axis 

(Fig. lb) to measure the fluctuating pressure. At the nozzle, they are located at the jet 

edge of the major axis side. When they are placed at downstream positions, each transducer is moved along a ray at 12" with respect to the axis. The near-pressure level drops 

from the jet edge exponentially and then changes to algebraic decay. The exponentially 

decaying region extends about one hydrodynamic instability wavelength from the jet." 

The surveyed region of these transducers is within the hydrodynamic near field. 

The streamwise fluctuating pressures are shown in Fig. 2. The level of fluctuations increases with distance as the instability wave amplifies. F'urther downstream, the intensity 

drops. The measurements near the major axis have higher readings than other positions 

because the transducers are placed closer to the jet edge. The interesting point is that 

the level of fluctuations for the impinging case are in general lower than those for the 

4 
free jet case. The difference is about as much as 50% before the peak of the distribution. This result indicates that the near field pressure can be altered dramatically by the 

presence of a nearby structure. It is a significant finding and can be an important factor 

for design considerations. We will examine the effects of orientation of the impingement 

and other parameters in more detail. Identifying the physical mechanism of this change 

is probably the major task for the near future. We speculate that the feedback generated 

by the impinging vortices delays the development of the vortices in the shear layer. The 

exact process remains to be clarified. The akmuthal distributions of the free jet and the 

impinging cases are shown in Fig.3. The lower fluctuation level for the impinging jet is 

observed around the jet. 

The flip-flop between the major and the minor axis is caused by the self-induction of the 

asymmetric vortex rings. The near field pressure reflects the axis switching phenomenon. 

At x/u = 0.48, the azimuthal profile shows high levels of disturbances near the major 

axis area because the sensors are closer to the jet (Fig. 4). A t/u = 5.76, the switching 

becomes apparent and the azimuthal distribution of the pressure is opposite, in phase, to 

the one near the nozzle. 

3.2 Spectral and Phase Information 

The spectrum taken at the major axis near the nozzle (x/a = 0.48, Fig. 5) shows peaks of 

the fundamental (-2 kHz), the first subharmonic (-1 k Hz) and a strong beat at frequency 

about 1.5 kHz. The pressure spectrum at the minor axis has a different form; the second 

5 
subharmonic is dominating and the fundamental is not observable. We have found that the 

extents of the fundamental and the subhannonics are scaled with their own wavelength.ll 

The transducer placed near the minor axis is more than one fundamental wavelength away 

from the jet and therefore the pressure fluctuations at the fundamental frequency are not 

strong. The dashed lines are the spectra for the impinging jet. The spectra of the free jet 

have almost the identical shape of the impinging case, but the spectral density is uniformly 

higher. 

At a downstream station (z/u = 0.85), the transducers are at about four initial instability wavelengths from the node. This is the location where the &st vortex merging 

takes place (Eo and Gutmarklo). Near the major aSs, the spectra of both free jet and 

impinging jet are dominated by the peak at the first subharmonic (Fig. 6). The peak at 

the second subharmonic dominates the spectra near the minor axis. 

The elliptic vortex ring not only switches the major and minor axes while it convects 

with the free stream velocity, but also bends from the plane normal to the jet axis. The 

phase codations of the transducers placed in the same plane can reveal the deformation. 

For example, the two transducers placed at two sides across the major axis have their 

phase spectrum shown in Fig. 7. The phase differences at all frequencies are close to zero 

because the rings distort in the same fashion across the jet. The phase spectrum between 

the two transducers placed at the major and the minor axes have very different forms. 

The phase difference between the first and the second subharmonics is very large due to 

the azimuthai deformation of the eiiiptic vorticai structures. 

6 
3.3 Pseudo-visualization of the Elliptic Vortices 

To construct a display to vbuolize the passage of the vortical structures of an elliptic jet, 

pressure measurements were acquired from eight microphones mounted on a rack such 

that the measuring points were evenly distributed azimuthally at a fixed radial location 

at a plane downstream and parallel to the exit plane. At a certain time to, their pressure 

fluctuations p were plotted versus azimuthal angle 4 and connected by means of a straight 

forward interpolation scheme. The measurement at the first azimuthal location was repeated as the ninth measurement in the interpolation because of the circular geometry of 

the microphone array. Qualitatively, this curve represented the global instantaneous pressure fluctuations at the measuring plane. When the same types of curves were constructed 

at t > to with constant time increments, the resulting imprint showed the passage of the 

hydrodynamic waves at this imaginary plane. Since the microphones were submerged in 

the expontentially decaying region of the jet, these imprints also represented the passage 

of the vortical structures in the jet. 

Since microphones would sense waves generated in a fixed neighborhood around themselves, these signals were contaminated and had to be filtered before the pseudo-display 

scheme could be applied. To avoid phase distortion, a FIR (finite impulse response)’digital 

bandpass filter was applied to the microphone signals. Results were plotted in Figs. 8 

to 13. The solid lines were arbitrarily designated for positive pressure fluctuations while 

the dashed lines were used when fluctuations were negative. For Fig. 8 to 11, the center 

frequency of the bandpass filter was set at the first subharmonic fi such that the distortion 

7 
of these structures during the pairing process could be visualized. The azimuthal distortion 

of the imprint at x/a = 0.85, Fig. 9, symbolized the deformation of the vortical structures 

during the pairing process. However, by comparing the imprints of Figs. 10 and 11 to Fig. 

9, it was shown that the same types of distortion, hence, the pairing process, were actually 

delayed by the presence of the impinging plate. 

The slight distortion of the structures in Fig. 8 demonstrated the phase deformation 

caused by the mismatch between the circular microphone-array and the elliptic sound 

generating region of the jet. Figs. 12 and 13 show the imprints of the vortical structures 

near the first axis switch location (z/a rv 5).1° At this location, the cross section of the 

jet flow turned quite circular and the distortion of the structures in these imprints, unlike 

the case in Fig. 8, became azimuthally independent. As a matter of fact, the presence of 

the impinging plate produced more organized vortical structures at this location. However, 

a quantitative verification of this observation is required. . 

4 CONCLUSIONS 

The important finding in this preliminary study is that the near-field pressure fluctuations 

for an impinging jet are much lower than those of a free jet. The exact physical mechanism 

is still under investigation but the importance of this finding to the design of an asymmetric 

jet nozzle with a nearby structure is obvious. 

The near-field pressure fluctuation is a strong function of the location away from the jet 

because their ievei decays exponentidy with &stance and the length scale is the bydrody8 
namic instability wavelength. The instability wavelength is about one order of magnitude 

shorter than the acoustic wavelength in the low Mach number range. Therefore, the spatial structures of near-field pressure are much more convoluted than the acoustic field. 

The elliptic vortex ring undergoes deformations in and out of the plane normal to the jet 

axis. The ne=-field pressure fluctuations are influenced by these distortions. The spatial 

structure of the fluctuating pressure ie further complicated by the deformations. 

9 
References 

[l] C. M. Ho and P. Huerre, Annual Review of Fluid Mechanics 16,365 (1984). 

[2] J. E. Ffowcs Williams, 255,469 (1963). 

[3] D. G. Crighton, Progress in Aerospace Science 16, 31 (1975). 

[4] D. G. Crighton, Journal of Fluid Mechanics 106, 261 (1981). 

[5] M. E. Goldstein, Annual Review of Fluid Mechanics 16,263 (1984). 

[6] B. Lafouasse, A. Chan, and C. M. Ho, Near field pressure fluctuations of a circular 

jet, in Aero- and Hydro-Acoustic, pages 403, Springer, Berlin Heidelberg, (1986). 

[7] J. Cohen and I. Wygnanski, Journal of Fluid. Mechanics 176,191 (1987). 

[8] J. Cohen and I. Wygnanski, Journal of Fluid Mechanics 176,221 235 (1987). 

[9] J. K. Wat and R. E. Kaplan, AIAA-86-1911 (1986). 

[lo] C. M. Ho and E. Gutmark, Journal of Fluid Mechanics 179,383 (1987). 

[ll] C. M. Ho and B. Lafouasse, AIAA-84-2316 (1984). 

10 
Screens 

I 0.585 m 0.813 in 0.533 m ' 

A 1 

Figure 1: (a) The settling chamber and nozzle assembly and (b) the relative positions 

between microphones and nozzle outlet. 

11 
5 

4 

3 

2 

1 

A, majordo 

v, miiror axis 

0 

0 1 2 3 4 5 6 

Figure 2: Axial distributions of the average over-all pressure amplitude. 

12 
1 

-k 

1 I I I I I I I I 

0 ir 27r 31 

2 

‘T - - 2 

wimuthal angle, -6 

Figure 3: Azimuthal distributions of the over-all pressure amplitude at x/a= 1.28: +, 

without impinging plate and X, with impinging plate. 

13 
1 I I I I I I I I 

d 

pc 

k 

c 

6 

5 

4 

3 

2 

1 

0 

--A 0 

‘IC : 

azimuthal angle -4 

Figure 4: Azimuthal distributions of the over-all pressure amplitude: x, z/a = 1.28 and 

0, =/a = 5.76. Measurements were performed without the impinging plate installed. 

14 

f 
w" 

d 

f 

\ 

m 

t5 

10' 104 

Figure 5: Near-field pressure spectra at t/a = 0.48. Microphones were located at 4 = (a) 

x and (b) 5: - , without plate case and -0 , with plate case. 

15 
I I I I IIIII n I I I I IIII 

I I I 11I1Ul I 1 1 I1 IIUI 

lo-a 

103 f, Hz lof 104 

Figure 6: Near-field pressure spectra at z/a = 0.85. Microphones were located at 4 = (a) 

A ad (b) : - , without plate case and -.. , with plate case. 

16 
A 

c 

6 

U 

- 3.rr 

10 10’ 103 104 

Figure 7: Relative phase difference of the pressure fluctuations measured between t$ = 0 

and A (-) and between t$ = and A (.om). 

17 
b 

-Tr azimuthal angle -4 

400t 

Figure 8: Azimuthal imprints of the vortical structures at z/a = 0.32. Signals were 

bandpass filtered with a f-octave FIR filter with fe = fi. 

18 
azimuthal angle -4 A 

--A 

MOL 

Figure 9: Azimuthal imprints of the vortical structures at z/a = 0.85. 

bandpass filtered with a $-octave FIR filter with fe = fi. 

Signals were 

19 
I 

Y 

Figure 10: Azimuthal imprints of the vortical structures at x/a = 

bandpass filtered with a $octave FIR filter with fc = ft. Impinging p 

0.85. Signals were 

llat e was inst ded in 

this case. 

20 
1 

azimuthal angle -4 

-A A 

Y 

400t 

Figure 11: Azimuthal imprints of the vortical structures at z/a = 1.06. Signals were 

bandpass filtered with a f-octave FIR filter with fc = fi. Impinging plate was installed. 

21 
400t 

- azimuthal angle -4 

-7r 

7r 

Figure 12: Azimuthal imprints of the vortical structures at z/a = 5.76. Signals were 

bandpass filtered with a $-octave FIR filter with fe = 70 Hz. 

22 
I u 

.LI s" Y 

400t 

,-> azimuthal angle -4 

--A 

Figure 13: Azimuthal imprints of the vortical structures at x/a = 5.76. Signals were 

bandpass filtered with a $octave FIR filter with fc = 70 Hz. Impinging plate was installed. 

23