Measurements of V/STOL aircraft noise mechanisms using pressure cross-correlation techniques in a reverberant wind tunnel

APPENDIX A. REMARKS ON THE CONSTANT C tN EQ, (5.).

Begin by squaring (5); then substitute from (1) in (3) and in (the square of) (5) to find C P (Al) where we assume for the correlation in (5) that the maximum value occurs for r = 0.

We suppose that the various correlation volumes are approximately equal. The process po is statistically stationary so we find <P P.p>

-<P >

and (Ai) can be written c = P.

(A2) By differentiating po it would appear that (A2) would yield a simple method to determine C. Unfortunately the static pressure has errors in it at higher frequency.

Two which can be named are the following.

First, the fact that turbulent flow is being convected past the probe means that part of the time variation in po is due to this convection: That part of the time variation would not be observed in a system moving with the mean-flow--what is really desired for (1) (see discussion after (1)). Secondly for the higher frequency portions of po there is some reason to believe that the propagating sound is an important contributing element.

As described in the theory section (and in associated references) po should be that portion of the static pressure which is 'hydrodynamic', i.e., which would occur if the fluid were truly incompressible.

For the important frequency components In Po there is no difficulty on this question.

The difficulties just described do not in general permit a sensible determination of the RMS values of derivatives, such as those required for the expression (A2).

It is hoped that in the futur'e these difficulties can be overcome.

A-i

APPENDIX B. ELIMINATION OF REVERBERANT EFFECTS, FROM NORMALIZED CORRELATIONS.

The 7'x10O' wind tunnel acts like a semi-reverberant chamber and therefore it is necessary to use a correction factor in order to simulate an experiment being conducted in a free field environment.

In particular when normalizing the cross correlations the effects of reflections (and other non-correlated noises) enter into the normalization process.

In the present experiment we are concerned with calculating the normalized cross-correlation between the output of the static-pressure probe microphone and that of the far field microphone.

Recall that a prime represents an RMS value. Use the standard definition of a normalized correlation, c (r,r) = PP > (B1) where P is the pressure signal seen at the probe microphone and p o is the signal sensed at a -articular far field position.

Hereris the distance from the probe to the far field position and r is the time delay in the correlation.

When operating in the 7'xlO' wind tunnel p consists of not only the direct signal from the source but also the reverberant field, those signals which initially were propagated in different directions but due to reflections were sensed at the far field microphone position. In addition p contains the tunnel background noise. We have p '*? e t*i"' ~.f , ij, ~ (82) where poo is the pressure due to the direct signal and the other terms reflections, numbered chronologically. For pol' P etc. are the various o 2 higher order reflections, the reflections in the correlations are no longer discrete and of course become smaller and lost in the noise; we lump those signals together and call their sum PoH.O.* The uncorrelated (with the jet noise) background noise, including local noise effects caused by turbulence B-1 at the microphone, is called pN. Using (82), (8B1) can be written (B3) recalling that po and pN are independent. So we should observe n+l peaks with n the number of separately discernible reflections.

For p' use (82), square and average, e p+.

+ +tP. . .O. +P, (B) + Cross terms All cross terms like <( Pt. , > (B5) vanish because the tunnel background noise is statistically independent of the jet noise. Further the first n reflections contained in the correlation are by hypothesis separated from one another so their cross terms vanish: Hence all the cross terms in (B4) vanish.

Now we look at a particular time dealy (t) in the cross-correlation process, for example that time r equal to the time required for the signal to propagate directly from the probe microphone to the far field microphone.

All of the cross-correlations represented in (B3) vanish except one and we have, using (B4) and neglecting cross terms, ( .

>, C Cy. r) rCP.

If the same experiment were being conducted in a free field environment, e.g. an anechoic room, the "correct" normalized cross-correlation function, cc would be C. (r' r = r./.

.* (B7) We must multiply (86) by a correction factor, K, in order to obtain (87).

Before doing this we examine the higher order reflection terms and the effects of acoustic losses.

To calculate K we use source images in the tunnel walls to replace reflections. The mean square sum of relfection_ is ) .

- a m/ (A+B) B-2 (88) ,-2 -where = rod distance from real source to far field microphone.

ro= distance from image source to far field microphone.

=D average source directivity constant (would be equal to one for a true simple source).

A&B= cross-sectional dimensions of wind tunnel.

aa average absorption coefficient of wind tunnel walls for the acoustic reflections.

Expanding the summation and dividing (B8) by po , we have o /".

AB Y (AB (B) where E is an exponential integral,

) Xe (BIO)

E (AtB) The ambient speed of sound is defined as a and T is the time delay o n required for the signal from the furthest image (reflection) which can be identified in the cross-correlation data. Therefore aoTn is the distance from that image source to the far field microphone.

The integral approximates the effects of the signals from the image sources which are not clearly identifiable in the cross-correlation data. Therefore the correction factor to be applied to (B6) to obtain (B7) is The values Pon/Po for the image sources which are identifiable from the cross-correlation data can be approximated by the ratio of the values of the cross-correlations (normalized) of the particular peaks.

The average source directivity constant is calculated from the anechoic source directivity if available; if not it must be estimated from other data.

li nff F (Ok) stinO dO

$ (812) 4 00 e0 Co, O) The average absorption coefficient a used in the calculation of K was 8-3 .02, obtained from measurements o reflection losses as reported in standard references.

Using-this correction technique a number of cross-correlation measurements .made in the 7'xlO' wind tunnel were corrected; the tunnel was off so p = 0.

n The results of this correction prcess are shown in Tablei-D, where the corrected values for the wind turnel measurements are compared to similar measurements made in an anechoic chamber. The results show good agreement for the two sets of measurements, except for the case of microphone #1 when the source is canted. In this orientation the source is pointing directly at microphone #1.

In actual applications the wind tunnel would of course be operating so that one would have to determire, p'; this is easily done by operating ,the wind tunnel without the jet -and taking the sound levels. This pressure level is then used in (811).

The successful use of this nathod depends upon having a sufficient number of reflection components i~ the cross-correlations so that the integral approximation for the higer order terms (those called PoH.0. here) is valid. In our work with the wind tunnel, we could not process the data for a sufficient period of time so that was the case.

It is expected that in other applications it would bea possibility.

B-4

APPENDIX C. SOUND SOURCE IEASUREMENTS IN ANECHOIC CHAMBER AND WIND TUNNEL In order to study the influence of the 7'xlO' wind tunnel reflections surfaces on cross-correlation.functions initial, measurements were made using a sound source (Altec 802D driver). The measurements were first made in an anechoic chamber and then repeated in the 7'xl0' tunnel.

A test was used consisting of a source with four far field microphones in different directions. In addition a probe-type microphone was positioned approximately 26.7 cm from the source. The sound source was driven by a white noise generator.

Two basic experiments were conducted: one, the sound source in a vertical orientation, and two, the source slanted toward one of the far field microphones. The slanting was intended to give directional effects. The outputs of the far field microphones and the probe micro- phones and the probe microphone were recorded.

Auto correlations and cross-correlations of the recorded signals were made. The main interest centered on the cross-correlation between the probe (near field) microphone signal and the various far field microphones.

In the anechoic chamber the normalized cross-correlations between the probe microphone and the different far field microphones varied between 0.82 and 0.89.

When the experiment was rerun in the 7'x10' wind tunnel a significant degradation of the normalized cross-correlation values occurred, the values varying between 0.41 and 0.59.

Our first cross-correlation ideas, as described in Appendix B, treated the normalized cross-correlation functions calculated for the wind tunnel data in such a way that the results would approximate a

0-1

free field condition. As a step in calculating this formula, it was necessary to measure the directivity pattern of the sound source (Altex 802D driver). This directivity pattern, measured in anechoic chamber, is shown in Fig. 1-C.

Employing the data from the directivity pattern and using an average absorption coefficient 0.02 for the wind tunnel walls, a number of cross-correlations made in the 7'x10' wind tunnel were corrected.

The results of this correction process is shown in Table 1-C, where the corrected values for the wind tunnel measurements are compared to similar measurements made in an anechoic chamber.

The results show good agreement for the two sets of measurements, except for the case of microphone #1 when the source is canted.

In this orientation the source points directly at the microphone.

In addition to the cross-correlation measurements, frequency spectra of the far 'field signals were made for both the anechoic chamber and wind tunnel tests. Fig. 2-C shows the results of such measurements.

For this particular plot the far field microphone was located approximately 1.3 meter from the source and at an angle of 400 from the source axis.

In the wind tunnel this microphone was located in front of one of the side walls.

These spectra were made with a constant bandwidth of 50 Hz. As expected, due to reflections, the signal inside the tunnel shows high amplitude and a larger number of irregularities.

C-2

APPENDIX D. MUFFLER FOR MODEL JET One .of the preliminary tests conducted during the course of this program was made to insure that the sound generated by the model jet was true aerodynamic noise and not noise originating in valves, etc., upstream from the jet nozzle exit.

This test consisted of replacing the 3. cm.

diameter jet nozzle with a 10.2 cm. diameter pipe with all controls kept constant to approximate equal mass flow.

Far field sound measurements were recorded and analyzed for both conditions. Fig.

1-D shows the spectra of the far field microphone signals with the microphone located at an angle of 300 and a distance of 1.5 m from the jet.

The dominant peak in the vicinity of 1850 Hz, clearly results from a noise mechanism located upstream from'the jet exit (such as valve noise). The same peak was evident in a spectrum made for a static pressure fluctuation probe inserted in the jet wake.

It was decided that an acoustic muffler would be designed and built prior to any further testing.

This muffler, shown in Fig. 2-D is a reactive - dissipative device with an effective length of approximately 4.4 meters.

It has an input and output area ratio of 5.44. It includes two right angle bends. The inner portion of the muffler consists of a perforated pipe with a 44.4% opening. This pipe is covered with a 10.2 cm. thick foam blanket.

The random signal absorption for this foam'is shown in Fig. 3-D.

With this acoustic muffler inserted in the system, the above test was repeated. Fig. 4-D shows the result for the muffler, for 3.8 cm.

and 10.2cm diameter jets.

These curves show that the muffler provides considerable attenuation for 900 Hz and above. As expected, due to the dimensions of the muffler the attenuation below 600 Hz becomes small (but of course .is not needed).

D-1 The spectra for the far field sound forthe 10.2 cm.

-diameter nozzle with and without muffler are shown in Fig. 5-D.

Considerable attenuation is evident, in particular at 1850 Hz. where the attenuation is approximately 33 dB: the dimensions for the right angle bends were chosen to give maximum attenuation for this frequency.

The spectra for the static pressure fluctuation and the far field radiated sound for the 3.8 cm. diameter jet running at Mach 0.63 ,with and without the acoustic muffler are shown in Figs. 6-D and 7-D respectively.

For both cases the muffler has eliminated the peak at 1850 Hz.

In addition to the narrow band spectra, cross-correlations and autocorrelations were made. In all cases the periodicity in the functions which was present when similar measurements were made before the acoustic muffler was installed, no longer appeared. The cross-correlations between the pressure probe and the far field microphones resembled those functions measured in an anechoic chamber with the addition of reflected pulses as expected.

D-2

APPENDIX E. PARALLEL JET The main purpose of this portion of the study was to use the results as a reference for the interpretation of the results of the perpendicular jet experiment. It was anticipated that the parallel jet experiment would be an intermediate step between a model jet in an anechoic chamber (about which much l information is available) ' and a model jet oriented normal to the flow, in a wind tunnel. Due to experimental problems the results were not as helpful as had been hoped.

E.1 Experiment The parallel jet experiment employed a model' jet aligned parallel to the wind tunnel flow. A diagram of the test configuration is shown in Fig. I-E.

The model was a circular jet with a 3.8 cm. diameter. In order to insure that the noise generated by this jet was aerodynamic noise (to eliminate up- stream noise in the air supply) it was necessary to design and install a dissipative-reactive muffler with an effective length of 4.4 meters ahead of the jet exit. The design and the acoustic properties of this muffler are describedin Appendix D of this report.

The jet was positioned so that its centerline coincided with the centerline of the wind tunnel.

Two far field microphones were employed. These transducers were at positions 1.5 meters (40 jet diameters) from the jet exit at 300 and 500, measured from the centerline. They were attached to the side wall of the wind tunnel at the same height as the jet centerline and used B&K 1.3 cm.

condenser microphones, with nose cones, as active elements. In addition a pressure probe (a 0.32 cm. microphone of the same type) was employed to measure and record the static pressure fluctuations within the turbulent volume.

*Errors made, when measuring static pressures in this way,.have been discussed 4 - 7 previously For the most part such errors are not important here.

E-l The coordinate system defined for this pressure probe, for this experiment is shown in Fig. 2-E.

All hardware employed inside the 7'x10' wind tunnel was designed and constructed to minimize noise generation arising from the tunnel flow interaction.

The basic experiment conisted of running the model jet at a Mach number of 0.62 and varying the wind tunnel-conditions. Three different conditions were used in the wind tunnel. They were: a. Static case--no flow--Q (dynamic pressure) = 0, resulting in a velocity ratio of zero.

b. Q = 19, flow speed approximately 38.4 m/sec giving a velocity ratio of 0.18.

c. Q = 47, flow speed approximately 60.4 m/sec giving a velocity ratio of 0.28.

The velocity profiles at the jet exit for both the Y and Z axes for the model jet running at Mach 0.62 with the wind tunnel in a static condition (no flow) are shown in Fig. 3-E. These profiles show the typical "top hat" characteristics, with good symmetry for both axes.

With the wind tunnel running with a Q of 19 a velocity profile along the Z axis, was made at X/D equal 3 and Y/D equal zero. This profile and the exact profile for the wind tunnel in a static (Q=0) condition are shown in Fig. 4-E. The tunnel flow seems to have little effect on the velocity profile except of course near the skirts where the velocity does not -reach zero as in the static case but rather approaches the velocity of the tunnel flow. This perhaps surprising lack of effect internal to the jet is noteworthy.

The experiment consisted of recording the fluctuations at seven pressure probe positions and at the two far field microphones, for test conditions previously described.

E-2 E.2 Analysis The data analyses consisted of doing narrow band (50 Hz) frequency analyses of the signals recorded and calculating the cross-correlation functions for the various probe positions and for the two far field microphones. A block diagram of the electronic equipment used in the data analysis is shown in Fig. 6 of the report.

E.2.1 Frequency Analyses Narrow band (50 Hz) frequency spectrums were made of the pressure signals.

The frequency spectrums for the far field microphone position #2 are shown .in Fig. 5-E. For the tunnel running with a Q of 19 and of 47, the background noise (tunnel noise) shows two dominant peaks, each with their first harmonics.

The main peak for Q equals 19 is located at approximately 750 Hz while the main peak for Q equals 47 has a frequency.of approximately 1200 Hz. The ratio between these two frequencies is 1.6 which turns out to be the ratio of the tunnel velocities for the wind tunnel operating at a Q of 19 and 47.

Since these frequencies are much too high for the fan noise generated by the wind tunnel drive mechanism, it is believed that these peaks are generated by some type of a whistle created by the flow interaction with some artifact in the tunnel (e.g.

hole, strut, etc.).

The aerodynamic noise generated by the model jet is typically 10 to 15 dB higher than the tunnel noise for Q equal.19, except at the fundamental peak which rises 10 db above the jet noise. For the tunnel running at a Q of 47, the difference is more like 2 or 3 dB with the peak frequency and its first harmonic being about 15 dB above the jet noise. To sum up, for the higher tunnel speed there is difficulty with tunnel noise; correlation methods are used).

needed (and are E-3

E.2.2 Cross-Correlation measurements As described in the theory section of this report the raw cross- correlates-between the far field microphones and the static pressure probe, at various positions, were measured. The (maximum) measured cross-correlation, times the square of the distance from the pressure probe to the far field microphone, and divided by the RMS value of the static pressure fluctuations are plotted against the velocity ratio (Voo/V.)

in Fig. TE and 7E. Such a plot, see Section 2, shows the effect of tunnel speed variation upon the sound radiated from the eddy at the probe position. The dB values are referenced to an arbitrary number and are to be used to give relative values for different positions or different speeds. It should be understood that the curves are rough approximations since they are derived from only three points (velocity ratios of 0, 0.18, and 0.28). The error flags on these curves are calculated from the noise seen on the cross-correlation functions. Since a finite averaging time is employed in the calculation of the cross-correlation functions there exists a noise fluctuation (see Section 2) which gives rise to an uncertainty in the true value, the lower the amplitude of the function the higher the uncertainty. This is especially noticeable in the curves for microphone #2 where the errors increase as the background noise of the tunnel increases.

From work done previously on a model jet in the anechoic chamber, the eddies in the vicinity of the probe positions, for the various curves shown in these two figures, are known to be strong noise radiators for smaller far field angles (microphones #2). For larger far field angles (microphone #1) the shear region is also a very active noise-radiating region.

Probes were placed in the shear region but (ossibly due to a large mechanical vibration experienced by the probe, over a frequency region of 2200 to 3800 Hz) the data could not be analyzed. This noise, which appeared on all the recordings for the parallel jet experiment, required the use of a band E-4 ;rejectifilter in the determination of the cross-correlation functions.

This significantly contributed to the errors since it tended to reduce the true value of the cross-correlation function especially for the higher far field angles (microphone #1) where the sound field shows higher frequency content that at the lower angles. Taking these two factors into consideration plus the fact that the tunnel noise is more important at microphone #1, as previously stated, it is undertandable that the error flags are so large for this position--even for a velocity ratio of zero. The large errors for curves for far field position #1 (in Fig. 6E and 7E) make interpretation difficult. It is noted that in Fig. 6E the probe is located just off the jet axis (Y/D = +0.3 and -0.13), 5.5 diameters from the jet exit. These two positions are in the same plane as the far field microphones and the jet centerline (X-Y Plane). For Y/D equal -0.13 the sound generated at this position and experienced at the far field position #2 is reduced from 6 to 11 dB (limits of the error flags) when the velocity ratio goes from zero to 0.18. As the velocity ratio is further increased the reduction lies: between 2 to 8 dB. Whether a minimum actually occurs at Voo/V equal 0.18 j cannot be accurately determined from the curve due to the relatively large error flags and to the fact that only three velocity-ratio points were measured. For Y/D equal + 0.3 the results are very similar to those just described.

For far field microphone position #1 no trend can be inferred from the curves for the reasons just mentioned.

The top curves in Fig. 7E represent the results for the static pressure probe located at X/D equal 5.5 and Z/D equal -0.3: The probe is located in the X-Z plane. Increasing the velocity ratio from zero to 0.18 results in a sound reduction of 2 to 5.5 dB at far field position #2. As the velocity ratio is further increased the errors are too large to determine the effect. Therefore, no definite trend can be stated when the velocity increases from 0.18 to 0.28, For far field position #1 no definite trend E-5 can be observed for the reasons just mentioned in connection with Fig. 6-E The lower curves in Fig. 7-Ewere calculated for the pressure probe located on-the jet axis (centerline), 7.5 diameters from the jet exit.

For the far field position #2, an increase in the velocity ratio from zero to 0.18 results in a reduction from 2 to 6.5 dB. The effect of a further increase in the velocity ratio cannot be determined because of the error flags.

Similar problems are met for position #1.

E-6