A wind tunnel investigation of panel response to boundary layer pressure fluctuations at Mach 1.4 and Mach 3.5

APPENDIX A ESTIMATION OF BOUNDARY LAYER THICKNESSAND BOUNDARY LAYER PRESSURE FLUCTUATIONSTO BE ENCOUNTERED BY A SUPERSONIC TRANSPORT We assume that the supersonic transport under consideration flies at an altitude of 70,000 ft,in a standard atmosphere.

We confine our attention to a flat panel in a region of unperturbed flow approximately 35 ft from a leading edge.

We obtain the following table of values from our assumptions A,1/ and ARDC standard atmosphere tables.

kinematic coefficient of viscosity 2 12x10-3ft2/sec .

968 ft/sec velocity of sound, c length from leading edge, 4 35 ft Mach number, M 3 -4 1.40x10 slugs/ft3 air density, pa 4.80~10~ Reynolds number R A 2/ to calculate !?le use the well-known fifth power law-t- the boundary layer thickness 6 $ = 0.37(R)-1'5 At Mach 3 the ratio of the displace- and obtain 6 = 4.5".

ment thickness to the boundary layer thickness is-approxi- L9 We use this value to obtain an estimate mately 0.37.

* = 1.6”. This value is of the displacement thickness 6 approximately a factor of five larger than the displacement thickness observed in the Douglas 1' x 1' tunnel at Mach 3.5 (see Table II of the text).

The generally accepted subsonic value for the ratio of overall mean square pressure fluctuations in a turbulent &4,A,5/ boundary layer to the free stream dynamic pressure is

J--

G

= 6x10’~

(A.1)

c4

The associated spectrum may be considered to be flat up to a frequency given by after which the spectrum rolls off at a rate of the order Use of the estimates of or greater than 20 dB per decade.

Mach number and velocity of for displacement thickness, sound given above and (A.2) leads to a value of 3.3 kcps for the roll off frequency.

This value and the assumption of a flat spectrum below 3.3 kcps allows us to estimate the expected boundary Using the layer pressure fluctuation spectrum level.

we obtain for the free stream dynamic values given above, dyne/cm2. Use of (A.l) then gives pressure q = 2.81~10~ 138 dB re .0002 microbar as the overall pressure fluctuation level. Using our assumption of a flat spectrum below 3.3 kcps that rolls off quite abruptly above 3.3 kcps, we may compute the value of the constant spectrum level.

We take the spectrum bandwidth as 3.3 kcps and determine the spectrum level to be approximately 103 dB re .0002 microbar.

There is some evident ,A.5/ which Indicates that the constant in (A.l) may diminish and the constant In (A.2) may increase as the Mach number increases supersonically. The reference cited indicates that the constants may be of the order -3 of 2x10 If these and 3, respectively, at'Mach 3.0.

values are used, the spectrum roll off frequency becomes 9.9 kcps and the overall sound pressure level becomes 128 dB. The corresponding spectrum level in this case is approximately 88 dB re .0002 microbar.

The difference between the two estimates of spectrum level is 15 dB. As a compromise we shall calculate panel response as shown In Fig. 23 of the text using a spectrum level of 100 dB re .0002 microbar. When the matter of spectrum level has been resolved, the data in Fig. 23 may be suitably corrected.

REFERENCES FOR APPENDIX A A.1 The ARDCModel Atmosphere, 1959, AFCRC-TR-59-267.

Boundary Layer Theory (Pergamon A.2 H. Schllchting, Press, New York, 1955).

A.3 D, A, Bles,"A. Brief Investigation of Flight and Wind Tunnel Measurements of Boundary Layer Pressure Fluctuations," Part II of the second quarterly progress report, NASA Contract NASw-932, November 1964.

~,4 J. S. Murphy, D. A. Bies, W. V. Speaker, and P. A. Franken, "Wind Tunnel Investigation of Turbulent Boundary Layer Noise as Related to Design Criteria for High Performance Vehiclesi'NASA TN D-2247, April 1964.

A.5 W, V. Speaker and C, M, Ailman, "Spectra and Space- Time Correlations of the Fluctuating Pressures at a Wall Beneath a Supersonic Turbulent Boundary Layer Perturbed by Steps and Shock Waves," Douglas Aircraft October 1965 (submitted to NASA, Company report, October 1965).

APPENDIX B THEORETICAL CONSIDERATIONS Various reports and papers have presented calculations of the response of a thin elastic plate to sound fields and to convected, decaying pressure fields representative of the induced wall pressure of boundary layer turbulence.

This appendix summarizes those results that are most per- tinent to the interpretation of the panel response experi- ments.

The first part of this appendix summarizes the results relating to panel response to an acoustic field, and the second part summarizes the results relating to panel response to a turbulent boundary layer.

In each of these two parts, we present the results first for free (resonant) response and then for forced (nonresonant) response. We also include some results related to the reradiation of sound by the vibrating panel.

Although these results are not directly applicable to the panel response experiments performed on this program, they are illustrative of the general approach involved in considering sound reradiation to internal spaces.

A. Acoustic Response Consider a statistically homogeneous sound field, with a pressure spectrum Sa(w) measured at some position removed from walls or scatterers. (On a rigid wall large compared to a sound wavelength, "pressure doubling" of nongrazing waves will occur when the field Is isotropic, and this effect produces a spectral density 2S,('u) on the wall.) On a thin flexible panel Immersed In this sound field, the mechanical power Input spectral denslty.IIa to the panel g&/ is given by 2Tf2C2 II, = Q ns Sa(@ (D> (B.1) w2ph where c Is the speed of sound In the fluid, CDIs the cir- cular frequency, p is the density of the panel, h Is the total thickness of the panel, ns is the modal density of the panel, u 1s the radiation effeclency of the panel, and CD> Is an average directivlty factor.

We will assume that the sound field Is Isotropic, and CD> Is therefore unity.

%2/ For a flat plate, the modal density A n (B.2) S =-j where A Is the area of the panel, k is the radius of gyration of the panel cross-section, and ca is the longl- tudinal wave speed of the panel material. For a homogeneous panel, the radius of gyration K= h (B.3) ci The radiation effeciency CT of supported panels has been B. 3/ calculated by Maldanik - when one side of the panel Is exposed to the sound field. When both sides of the panel are exposed to the sound field, his values of radiation effeciency should be doubled. The expression for u appropriate for the wind tunnel test panel exposed on one In terms of side to sound Is presented in Reference B.3 the panel dimensions and cot, the acoustic critical fre- the frequency at which the speed of sound in the quency, surrounding fluid is equal to the speed of sound on the panel.

The resonant velocity response spectrum rv(cu) is found from the resonant input power by requiring that the dissi- pated power equal that absorbed from the sound field, or I1a 'vat4 = (B.4) cuphArltotal Combining (B.l), where qtot is the total panel damping.

B.4) with the expression for accelera- (Be'& (B.31, and tion spectruma (0) = (u2q@) Q (4 (B.5) we obtain

--

a,(w) = 2G; c2

‘3saw

cDPh '.4 %otal -- _1 The nonresonant (forced) "mass law" acceleration spectrum first mode is given by (one side exposed) of a panel above its (B.7) Turbulence Response B.

Several models of the turbulent boundary layer pressure field have been proposed. We use the convected and decaying correlation pattern proposed by Ffowcs Williams B.5/ B 4/ and Lyon.-?- The pressure correlation has the form w3) with a Fourier-transformed power spectrum (B.9)

(P (%‘> = px(z, (@a - klUc)

where UC is the convection speed, and kl and k3 are the wavenumber components conjugate to the spatial separation The direction of convection is Al.

variables Al and h3.

Is called the hydrodynamic The frequency mUh = UC'/ kc, For high-speed aircraft, the frequency‘ critical frequency.

range below the hydrodynamic critical fI?eqUenCy (CD ( ah) iS In this frequency range, the generally of primary interest.

most strongly excited modes are the "hydrodynamically- These modes propagate at an angle coincident" (HC) modes.

6, to the direction of propagation, where (B.10) The mechanical power Input spectral density for HC modes B.51 is given by cot ac (Pl(kp ~0s +c) p3(kp sin '#$I (B.11) = 87rp; G,A IIHC w where we have assumed that the wavenumber spectrum Is separable Into downstream ( PI) and cross-stream (p3) factors, ph is the overall rms turbulent boundary layer pressure.

Go0is the infinite plate input conductance, given by (B.12) kp is the wavenumber for free bending waves on the plate, given by kp = 03.13) J The downstream wavenumber spectrum @,, may be evaluated in terms of the measured fixed-point pressure spectrum PM (B.14) &kp cos oc) = ~&+, = uc @,t@) C This relationship Is based on the hypothesis that the measured spectrum results essentially from the convection in the x1- direction of the eddy pattern over the fixed microphone.

For ol)<wh, there is power Input to "hydrodynamically-fast" "hydrodynamically-slow" (HS), and HC modes.

A measure (J='), of the power input to the W and HS modes Is given by IIHF = p; G,At(kp6*) @a) A 03.15) where At is an effective "correlation area," defined as an B 4/ average of the wavenumber spectrum.& A simple form that Is frequently assumed for the spectrum function 6; IS QUJ) 2e l =- (B.16) 7r 1 + uJ2e2 where 6 is the mean eddy lifetime, related to the convection speed UC and displacement boundary layer thickness B* by the experimentally determined expression * 8 c3 25 6 03.17) uC For CI) "u‘~, only HF modes can be excited, and (B. 15) can be used directly to give the resonant response.

The various expressions for input power spectra may be converted to acceleration spectra by the use of (B.4) and (B.5). Thus, for HC modes, QHC(“) = 2 y” 7T P: cot Qc pl(kp cos Qc) G3(kp sin Oc) ' h 'J'total (~.18) and, for HF modes, P; At'kps*) $$“') (B.19)

(zHF@)= 27 UJ

4P h 'a'ltotal In addition to the HS, HC, and HF modes of resonant response, there is also a nonresonant (forced) response to, turbulent boundary layer pressure fluctuations. A major part of this nonresonant response arises from excitation by wavenumbers smaller than k the wavenumber for free bending waves on P' the plate. The response In this region depends only on the surface. density of the structure and is referred to as "mass-controlled," This response Is somewhat analogous to response of a panel to acoustic excitation.

the "mass-law" B.6/ For o (ah, Lyon has shown that the nonresonant acceleration spectrum Is given by 'i7,(kp cos ac) arctan (2kp6* sin @,), cu < Oh C (B.20) B.4/ where the spectrum suggested by Hodgson's correlation data -- has been used to evaluate the cross-stream wavenumber spec- trum 26* 'p3(k3) = (B.21) I'r[l + (2k36*)2] The ratio of forced to free response for w ( mh is then found by comparing (B.20) with (B.18).

An additional complication enters if we are interested in reradiated sound rather than structural response, since wave- numbers less than the acoustic wavenumber k, radiate sound I The considerably better than wavenumbers greater than k,.

acceleration spectrum corresponding to the good-radiation range is obtained from (B.20), with kp replaced by ko.

: Q(U) = ,z12u <il(ko cos oc) arctan(2 koG* sin @,), ' c (B.22) o,< WI The ratio of forced to free radiation for w < ah is found by comparing a velocity spectrum based on (A.21) (with PC loading) with one based on (B.l8)(with a radiation loss factor q,,d).

J3& has shown that the nonresonant accel- For w > ah, Lyon eration spectrum Is given by L?&JJ) = * A& @$") (B.23) c2h2 where It has been assumed that the wavenumber spectrum Is in agreement with considerable constant at low numbers, The ratio of nonresonant to resonant experimental data.

Is then found by comparing (B.23) with response for cD > oh (B.19).

REFERENCES FOR APPENDIX B B. 1 P. W. Smith and R. H. Lyon, "Sound and Structural Vibration," NASA CR-160, March 1965, Eq. (V.7.4).

B.2 Ibid, Eq. (nr.fj.lg).

"Response of Ribbed Panels to Rever- G. Maidanik, B-3 berant Acoustic Fields," J. Acoust. SW. Am. 34, 809 (1962).

J. E. Ffowcs Williams and R. H. Lyon, "The Sound B.4 Radiated from Turbulent Flows near Flexible Boundaries," (to be published BBN Report No. 1054, August 1963 as an Agardograph).

R. H. Lyon, "Boundary Layer Noise Response Simulation B.5 with a Sound Field," Second International Conference on Acoustical Fatigue, Dayton, Ohio, April 1964.

B.6 R. H, Lyon, BBN Internal memorandum, July 1965.

.-_ _. _ .

I

APPENDIX C

LIST OF SYMBOLS

A area of panel

effective correlation area

At

acceleration spectrum

Qw

spectrum of the mean square acceleration

aa(c0)

due to acoustic excitation

spectrum of the mean square acceleration

due to hydrodynamic coincident mode excitation

spectrum of the mean square acceleration

~J-#d

due to hydrodynamically fast mode excitation

mean square octave band acceleratfon

a

octave band

C speed of sound in air at normal temperatures

C’ speed of sound in tunnel at reduced temperatures

speed of longitudinal waves in material of panel

average directivity index

<D>

f frequency

octave band center frequency

fC

infinite plate input conductance

Gc%l

h thickness of a uniform panel

vector wavenumber describing the turbulent

-ii+

boundary layer

wavenumber associated with flexural wave

kP

propagation

wavenumber component parallel to flow and

kl' k3

normal to flow

acoustic wavenumber

kO a

length from leading edge

M

Mach number

modal density of the panel

nS

root mean square overall pressure fluctuation

ph

pressure correlation function

wavenumber spectrum in direction of flow, and

normal to flow and parallel to wall respectively

fixed-point pressure spectrum

temporal part of the pressure correlation

function

spatial part of the pressure correlation

X

P

function

free stream dynamic pressure

q

R Reynolds number based on length

acoustic pressure spectrum

time delay

t

mean convection velocity of turbulent

uC

boundary layer

free stream air flow velocity

UC0

mean square velocity spectrum

/-I)’

mean square velocity spectrum response to

v

a

acoustic excitation

6 boundary layer thickness

6* boundary layer displacement thickness

loss factor (defined as complex part of

rl

Young's modulus)

total loss factor including radiation loss

%otal

as well as losses in medium

mean eddy lifetime

radius of gyration of a panel of uniform

material

directed flexural wavelength in panel (vector)

components of flexural wavelength parallel

to flow, normal to flow

h

flexural wavelength in panel

P

mechanical power input spectral density

II,

function for acoustic excitation

mechanical power input spectral density

"HC

function for hydrodynamically coincident

modes

mechanical power input spectral density

IIHI?

function for hydrodynamically fast modes

density of uniform panel material

density of air

surface density of panel

radiation efficiency

wall shear stress (skin friction)

critical angle of panel Mach wave propagation

angular frequency

angular frequency at which flexural wave

velocity equals mean turbulent boundary

layer convection velocity

MILLED SLOT 12” DIA .012” OR .022” PANEL SEE DETAIL (1 GRAM ACCELEROMETER) CLEVITE 2E3 .050” GAP O-RING- A-A VIEW FROM OUTSIDE TUNNEL (accelerometer cover plate removed) SHEET STAINLESS STEEL ,005” OR .OlO” .002” TRANSFER ADHESIVE 3M NO. 465 DETAIL FIGURE i. MODEL FOR TESTING PANEL RESPONSE Tc> BOUNDARY LAYER PRESSURE FLUCTUATIONS -;.i ‘.,:, :: ‘; : ,.

., Front View Showing Test Panel, Backing Plate and Retaining Ring Back View Showing Test Panel with Accelerometers Attached, Backing Plate, Cover Plate, and Retaining Ring FIGURE 2.

TEST PANEL ASSEMBLY % . _. ---- .

: --~ -.-.-. - ;‘i:, 1;. . .

.:..p .. .Y ,. 7 .’ .: . .

----..

FIGURE 3. TEST PANEL INSTALLED IN WIND TUNNEL SIDE WALL .2 .l - ..~ .08 c .

b .06 t 1 .04 - F-105 DOOR PANEL LOSS FACTOR SCALED UP IN FREQUENCY BY A FACTOR \ - OF FIVE .02 \ \ /- ASD - TDR - 62 - 237 \, \ LO \ \ 0 ’ \ .Ol .

c .-

T

5 2 al b _-..- 0 1 5 .022” THICK PANEL o .012” THICK PANEL l G -5 .

.I .2 .4 .6 .8 1 2 4 6 8 10 frequency kcps FIGURE 4. LOSS FACTOR 77 AND FLEXURAL WAVELENGTH AS A FUNCTION OF FREQUENCY FOR TWO TEST PANELS 25 FT CABLE / AMPEX B & K 2203 RECORDER CLEVITE 2E3 e a SOUND LEVEL - CP 100 ACCELEROMETER METER 60 ips, 54 kc FM t CALIBRATION SYSTEM I 68.98 C-2 I CLEVITE 2E3 a ACCELEROMETER .

- 620 C2 ACCELERATION DATA ACQUISITION SYSTEM 25 FT CABLE 250 cps , 128 db SPL B & K 2630 B & K 2203 B & K 4136 PISTONPHONE CATHODE SOUND LEVEL .- MICROPHONE FOLLOWER METER AMPEX RECORDER c CP 100 60 ips, dir. rec.

BOUNDARY LAYER PRESSURE FLUCTUATION DATA ACQUISITION SYSTEM FIGURE 5. WIND TUNNEL TEST DATA ACQUISITION SYSTEMS SEE NOTE 1 MH 3172 MH 5203 MH 5113 TAPE REEL c DISCRIM- - g PREAMP TRANSPORT I NATOR I 1 RE-RECORD 1 OUTPUT 54 kc+ 40% MH 5203 * B 8, K 2203 B & K 1613 MH 5113 @ DISCRIM- : , b@ 7 SOUND LEVEL. c OCTAVE BAND * PREAMP I NATOR METER METER I I MH 5203 1 * MH 5113 H-P1 308 D DISCRIM-. = ’ b * PREAMP CR0 ** INATOR TIME DELAY MULTIPLIER COMMUTATI NG INTEGRATOR/ * DRUM SYSTEM * PHILBRICK D SMOOTHER - BBN 600A-W 1 * K5M BB N #302D-Wl SWITCH UP FOR SPECTRUM ANALYSIS SWITCH DOWN FOR CORRELATION ANALYSIS NOTE 1: RE-RECORD OUTPUT IS NOT DISCRIMINATED BUT IS MERELY AMPLIFIED FIGURE 6.

WIND TUNNEL TEST DATA REDUCTION SYSTEMS ANGULAR POSITION DEGREES -90 .

-60 y7 -30 v 0 ODO mm 120 A 150 A 180 oo I 1 I I I I --- -- CALCULATED RESPONSE, SEE -10 TEXT, SECTION Y NASA TN D-2247 l PRESENT TESTS z

A

----- ESTIMATE USED IN CALCULATI NG RESPONSE, SEE TEXT, SECTION P octave band center frequency kcps FIGURE 7a PANEL ACCELERATION LEVELS AND BOUNDARY LAYER PRESSURE FLUCTUATION LEVELS .012” Thick Panel. Mach 3.5. Unoerturbed Flow -60 ANGULAR POSITION DEGREES -90 0 -60 l -30 0 OA 120 W 150 v 180 A ----- CALCULATED RESPONSE, SEE -10 TEXT, SECTION IZ 0.a. .5 1 2 4 8 octave band center frequency kcps FIGURE 7b PANEL ACCELERATION LEVE LS .022” Thick Panel, Mach 3.5, Unperturbed Flow (Boundary Layer Pressure Fluctuation Levels Shown in Part a of Figure) ANGULAR POSITION DEGREES -90 0 -60 V -30 v 0 0 90 0 120 A 150 A

T

180 l

-

-

-10 NASA TN D-2247 l PRESENT TESTS 0 0.a. .5 1 4 8 octave band center frequency kcps FIGURE 8a PANEL ACCELERATION LEVELS AND BOUNDARY LAYER PRESSURE FLUCTUATION LEVELS .012” Thick Panel, Mach 1 .4, Unperturbed Flow ANGULAR

AA

POSITION

?

DEGREES I I I I I w-1-

A

A

-60

w-t-

i I ! !

!

I v -30

y‘ 8 T

0 0 150 A 180 .

1 2 4 8 0.a. .5 octave band center frequency kcps PANEL ACCELERATION LEVELS FIGURE 8b .022” Thick Panel, Mach 1 .4, Unperturbed Flow Pressure Fluctuation Levels Shown in Part a of Figure) (Boundary Layer ANGULAR POSITION DEGREES -90 0 -60 v -30 v 0 0 90 l 120 A 150 A 180 o PRESENT TEST o I I i- -- i I 0.a. .5 1 2 4 8 octave band center frequency kcps FIGURE 9. PANEL ACCELERATION LEVELS AND BOUNDARY LAYER PRESSURE FLUCTUATION LEVELS .012” Thick Panel, Mach 3.5, Thickened Boundary Layer r -- - < --.

L

ANGULAR V POSITION

&

DEGREES -~ -__t -90 0

~- A -60 V

-30 v 0 0 _- -_ 120 A - 150 A 180 l -- -- -~ -- -- - -___ I40 PRESENT TEST o -. - -.~~ - --.-- -- -. -- 0.a. .5 1 2 4 octave band center frequency kcps FIGURE 10~ PANEL ACCELERATION LEVELS AND BOUNDARY LAYER PRESSURE FLUCTUATION LEVELS ,012” Thick Panel, Mach 3.‘5, Aft Facing 3/4” Step ANGULAR POSITION DEGREES

-90

-60 v -30 ?

120 n 150 A 180 l

0.a. 2 4

octave band center frequency kcps FIGURE lob PANEL ACCELERATION LEVELS .022” Thick Panel, Mach 3.5, Aft Facing 3/4” Step (Boundary Layer Pressure Fluctuation Levels Shown in Part a of Figure)

I

ANGULAR POSITION DEGREES -90 0 -60 v -30 v 0 0 90 0 10 120 A 150 A 180 .

, / i --t--~.I---.t-~-.--.I, PRESENT TEST o 0.a. 0.a. .5 .5 1 1 2 2 4 4 8 8 octave band center frequency kcps octave band center frequency kcps FIGURE 11. PANEL ACCELERATION LEVELS AND BOUNDARY LAYER PRESSURE FLUCTUATION LEVELS .022” Thick Panel, Mach 1 .4, Aft Facing 3/4” Step ,67

I

ANGULAR POSITION DEGREES 0 0 la0 ’ NASA TN D-2247 o 1 2 0.a. .5 4 a octave band center frequency kcps FIGURE 12a PANEL ACCELERATION LEVELS AND BOUNDARY LAYER PRESSURE FLUCTUATION LEVELS .012” Thick Panel, Mach 3.5, Mild Shock ANGULAR POSITION DEGREES

-90 0

-60 v -30 D 0 0 120 A 150 n 180 q -10 1 2 4 a 0.0. .5 octave band center frequency kcps L 5 FIGURE 12b PANEL ACCELERATION LEVE C k .022” Thick Panel, Mach 3.5, Mild Sho (Boundary Layer Pressure Fluctuation Levels Shown in Part a of Figure) o&70 ANGULAR POSITION DEGREES 0 ov 180 AD LLV -10 PRESENT TEST o 0.0. .5 1 2 4 a octave band center frequency kcps FIGURE 13a PANEL ACCELERATION LEVELS AND BOUNDARY LAYER PRESSURE FLUCTUATION LEVELS .012” Thick Panel, Mach 3.5, Mi I d Expansion - - _.

- ANGULAR , I I POSITION DEGREES -90 v 0 0 90A 0 180 .

-10

0.a. 1 2 4 8

.5 octave band center frequency kcps FIGURE 13b PANEL ACCELERATION LEVELS Thick Panel, Mach 3.5, Mild Expansion . 022” (Boundary Layer Pressure Fluctuation Levels Shown in Part a of Figure) AIR FLOW %q=Q PERCENT CORRELATION 1 ROLL ANGLE 30’ ROLL ANGLE 60’ 10 - O- -lo- r# ROLL ANGLE 90’ -10 l!bl!

-1.0 -.a -.6 -.4 -.2 0 .2 .4 .6 .a 1.0 time delay - milliseconds FIGURE 14. PANEL ACCELERATION CROSS CORRELATION .012” Thick Panel, Mach 3.5, Unperturbed Flow (For roll angles less than 90°, positive delay corresponds to disturbance propagation with a component in the direction of flow) - AIR FLOW y PERCENT CORRELATION t -10 fl ROLL ANGLE 30’ t t -1,

0 1

-lo- ROLL ANGLE 60’ lo- -10 - 1 ROLL ANGLE 90 -10 B 1.0 .6 .8 .2 .4 -.2 o -.6 -.4 -.a -1-o time delay - milliseconds FIGURE 15, PANEL ACCELERATION CROSS CORRELATION .012” Thick Panel, Mach 1.4, Unperturbed Flow positive delay corresponds to (For roll angles less than 90°, in the direction of flow) disturbance propagation with a component AIR FLOW PERCENT CORRELATION

7-r

ROLL ANGLE 0’ t -10

d---l

ROLL ANGLE 30” \ / r~ - -10 t-i -ROLL ANGLE 60’ 1 1 -10

r

~ -1.0 -.8 -.6 -.4 m-2 . .

1.0 time delay - milliseconds FIGURE 16. PANEL ACCELERATION CROSS CORRELATION .022” Thick Panel, Mach 1,.4, Unperturbed Flow (Positive delay corresponds to disturbance propagation with a component in the directIon of flow) VACUUM CHAMBER SPEAKER BB K4136 MICROPHONE TEST PANEL- + CLEVITE 2E3 B 8, K 2203 ACCELEROMETER SOUND LEVEL METER MANOMETER

lr

B & K 1613 AMPLIFIER - OCTAVE BAND ANALYSER VACUUM 1 I I I PUMP B 8, K 2630 CATHODE FOLLOWER B 8. K 2203 SOUND LEVEL METER B & K 2630 t I I CATHODE FOLLOWER B 8. K 1613 OCTAVE BAND ANALYSER TEST APPARATUS FOR DETERMINING RESPONSE FIGURE 17.

OF TEST PANEL TO REVERBERANT ACOUSTIC FIELD AT VARIOUS STATIC PRESSURE octave band center frequency kcps TYPICAL ACOUSTIC TEST DATA SHOWING PANEL FIGURE 18.

ACCELERATION LEVELS AND SOUND PRESSURE LEVELS .012” Thick Panel with Backing Plate Removed, Static Pressure 7 psia i \ \ \ \ \ \ - WIND TUNNEL TEST, Ml .4 \ \.

\

\ \ ----- ACOUSTIC TEST '\ '\ -me ACOUSTIC TEST WITH \'\ BACKING PLATE REMOVED I \ I

\

‘\ ’

‘h

\\

‘\

-!

-140

2 4 .5 1 a octave band center frequency kcps PRESSURE-FLUCTUATION-TO-ACCELERATION TRANSFER FIGURE 19.

FUNCTION FOR WIND TUNNEL AND ACOUSTIC TESTS Static Pressure 7 psia ,022” Thick Panel, -1 lo- \ \ \ \ t \ \ \

\

\

\

\ \

\

\ -125. WIND TUNNEL TEST, Ml .4

+ -+-

\ \

--B-m- ACOUSTIC TEST \

\

--- ACOUSTIC TEST WITH BACKING PLATE REMOVED ‘\ :\, t \\: -130

--B-s

\

‘\

\

-135 -140* .5 1 4 a octave band center frequency kcps FIGURE 20. PRESSURE-FLUCTUATION-TO-ACCELERATION TRANSFER FUNCTIONS FOR WIND TUNNEL AND ACOUSTIC TESTS .012” Thick Panel, Static Pressure 7 psia -110

--o

-115

-0

r \ -‘\ - ‘\ \ \ -‘\ \ \ WIND TUNNEL TEST, M3.5 ----- ACOUSTIC TEST --- ACOUSTIC TEST WITH BACKING PLATE REMOVED -_ -140

2 4 a

.5 1 octave band center frequency kcps FIGURE 21. PRESSURE-FLUCTUATION-TO-ACCELERATION TRANSFER FUNCTIONS FOR WIND TUNNEL AND ACOUSTIC TESTS .022” Thick Panel, Static Pressure 1.5 pria WIND TUNNEL TEST,M3.5 \ \ ----- ESTIMATED ACOUSTIC \ TRANSFER FUNCTIONS \ \ See Text \ \ \ - - - ESTIMATED ACOUSTIC \ \, TRANSFER FUNCTIONS WITH BACKING PLATE ,+ REMOVED \

- \ It

See Text \ \ - \ \, ?

-

\\

- -

\

\

1 2

..i 4 a

octave band center frequency kcps PRESSURE-FLUCTUATION-TO-ACCELERATION TRANSFER FIGURE 22.

FUNCTIONS FOR WIND TUNNEL AND ACOUSTIC TESTS .012” Thick Panel, Static Pressure 1 .5 psi 0050” PANEL --e-B .lOO” PANEL 800 1600 100 200 400 octave band center frequency cps FIGURE 23. EXPECTED RESPONSE OF TWO PANELS AT MACH 3.5 AT 70,000 FT ALTITUDE Based on Model Tests Scaled By a Factor of Five and Corrected With an Assumed Flat Pressure Fluctuation for Damping Spectrum Level of 100 dB re 0.0002 Mlcrobar (See Appendix A and Test) NASA-Langley, 1966

ai

CR-501