PEN00166

SOUND AND FLUCTUATING DISTURBANCE MEASUREMENTS IN THE SETTLING CHAMBER AND

TEST SECTION OF A SMALl" MACH 5 WIND TUNNEL

J. B. Anders and P. C. Stainback NASA Langley Research Center

Hampton, Virginia 23665, U. S .A.·

L. R. Keefe Wy1e Laboratories

Hampton, Virginia 23666, U.S.A.

and

1. E. Beckwith NASA Langley Research Center

Hampton, Virginia 23665, U.S.A.

Presented at the Sixth International Congress on Instrumentation in Aerospace Simulation Facilities

Ot tawa " Canada September 22-24, 1975

SOUh~ AND FLUCTUATING DISTURBANCE MEASUREMENTS IN THE SETTLING CHAMBER AND

TEST SECTION OF A SMALL, MACH 5 WIND TUNNEL

J. B. Anders,* P. C. Stainback,* L. R. Keefe,t and I. E. Beckwithf

NASA Langley Research Center, Hampton, Virginia 23665, U.S.A. and

Wyle Laboratories, Hampton, Virginia 23666. U.S.A.

ABSTRACT

Disturbance measurements were made using a hot-wire anemometer and piezoelectric pressure transducers in the settling chamber and free stream of a small Mach 5 wind tunnel. Results from the two instruments are compared and acousti­cal disturbances in the settling chamber are dis­cussed. The source of the test-section noise is identified as nozzle-wall waviness at low Reynolds numbers and as eddy-Mach-wave radiation from the turbulent boundary layer on the nozzle wall at high Reynolds numbers.

A

B

c

d

D

6e m

f

h

I

K

*

NOMENCLATURE

Constant in Equation (3)

Constant in Equation (3)

Phase or propagation velocity, w/K

Needle spacing on hot-wire probe (Fig. 4)

Wire diameter

Fluctuating hot-wire voltage

Hot-wire sensitivity to mass flow fluctua tions

Hot-wire sensitivity to total temperature fluctuations

Frequency

Heat-transfer coefficient

Mean hot-wire current

Wave number

Aerospace Engineer, Gas Dynamics Section, High-Speed Aerodynamics Division.

tResearch Engineer, Wyle Laboratories, Hampton, Virginia.

f~ Dynamics Section, High-Speed Aer~namics Division.

L-l027l

k

L

M

m

Nu

P

p

R

R r

R z

r

T

t·

u

u s

v

z

s

Thermal conductivity

Nozzle length from throat to exit

Wire length

Mach number

Mass flow

Nusselt number based on wire

diameter, ~

Wire power. r2R w

Pressure

Resistance

Reynolds number at total conditions

ptu"P based on wire diameter,

)..!t

Unit Reynolds number in settling chamber or test section

Cross-correlation coefficient for a radial spacing 6r

Cross-correlation coefficient for a longitudinal spacing 6z

Radial distance in settling chamber

Temperature

Time

Velocity

Source velocity

Mean hot-wire voltage

Axial distance in settling chamber

Coefficient in Equation (1)

C( (y - 1) MZ

y

e

p

T

w

Subscripts

aw

f

t

t,2

w

Superscripts

n n

RatiO' af specific heats

Caefficient in Equatian (1)

Recavery factar, Taw/Tt

Angular caardinate in settling chamber

Viscasity

Density

Time delay

Angular frequency

Adiabatic wall

Reference canditian at 273 0 K

Tatal canditians

Tatal canditians behind a narmal shack

Wire

Settling chamber ar test sectian free-stream canditians

rms value

Mean value

INTRODUCTION

The high naise levels in supersanic and hyper­sanic wind tunnels has became a matter af increas­ing concern in recent years because af the passible influence af naise on certain aeradynamic test data (1-3). The saurces af this naise can be quite varied, but at higher Mach numbers (>2.5) the pri­mary saurce is the turbulent baundary layer an the nazzle wall (4). The mechanism af supersanic baundary-layer naise radiatian was identified in the thearetical wark af Phillips (5) as eddy-Mach­wave radiatian. This phenamenan was further examined by Ffawcs-Williams and Maidanik (6) fer a supersonic shear flaw and their theary was applied to' a supersonic, nazzle-wall baundary layer. Surprisingly gaad agreement with the experimental results of Laufer (7) was abtained. Laufer, in fact, provided same af the first saund measurements in a supersanic wind tunnel and his early experi­ments (8) cancerning the effect af test-section disturbances an baundary-layer transitian led him to' propase a series af investigatians designed to' eliminate naise, varticity, and temperature spotti­ness in the Jet Prapulsian Labaratary 18- by 20-inch supersanic tunnel. He shawed that settling chamber varticity had nO' effect an transitian an a 50 cane when the test-section Mach number was greater than 2.5.

Markavin (9,10) alsO' cansidered varticity, temperature spattiness, and naise in supersanic wind tunnels and, similarly, he cancluded that settling chamber varticity (because it is greatly suppressed by the nazzle expansion (11» has little influence even an such sensitive a phenamenan as baundary-layer transit ian. Markavin alsO' indicated that temperature spattiness may be easily minimized in mast facilities by suitable upstream mixers and affers nO' difficulty. He further cancluded that naise is the largest cantributar to' the free-stream disturbance level in mast supersanic wind tunnels. The naise can be af twa types: [1] quadrapale radiatian ef the type discussed in Reference (5) and measured in References (4) and (12), and [2] "shivering" Mach waves (9,10) caused by nazzle­wall waviness ar raughness. These shivering waves may, in fact, be a majar contributar to' the free­stream disturbance field under certain canditians. In the 18 years since Markovin pointed aut the shivering Mach wave phenamenan, only Laufer has measured their cantributian to' the tunnel disturb­ance level by artificially intreducing a very weak shack. This lack af data is passibly due to the averwhelming effect in mast wind tunnels af saund radiated by the turbulent, nazzle-wall baundary layer (type (1». Hawever, when the baundary layer is laminar, shivering Mach waves shauld be expected to' daminate the test-sectian disturbances.

The present investigatian is part af an angaing pregram at NASA Langley to' develap a quiet wind tunnel (13-15). The main abjective af this pragram is to' develap techniques far substantially reducing the test-sectian disturbances in supersanic/hypersanic wind tunnels at free-stream Reynalds numbers high enaugh to' provide natural transitian and fully turbulent flaws an madels. The achievement af this abjective will require a tharaugh understanding af flaw generated noise and same innavative ideas applied to' wind-tunnel design.

The purpase af this paper is to' present results shawing haw the hat-wire anemameter and the piezaelectric pressure transducer were used to' measure the disturbance levels in a supersanic wind tunnel, and haw the hO't-wire anemameter was used to' identify acoustic disturbances and deduce their or~g~n. Camparisans are made af measurements by bath instruments in the settling chamber and test sectian af a small Mach 5 wind tunnel.

APPARATUS AND TESTS

The measurements presented in this paper were made in the pilat madel "quiet" tunnel (13) at the NASA Langley Research Center. This facility is equipped with a large multicampanent settling chamber and twa interchangeable nazzles (see Fig. 1). One nazzle is af conventianal design and pravides a unifarm Mach 5 exit flaw. The ether nazzle also has an exit Mach number af 5 but is equipped with an annular slat just upstream af the throat (13). The purpase af the slat is to' remeve the turbulent baundary layer that has develaped alang the wall af the settling chamber sa that a new, laminar baundary layer will develap dewnstream

of the slot and delay transition in the supersonic portion of the nozzle.

A detailed drawing of the large settling chamber is shown in Figure 2. This chamber is equipped with various interchangeable screens and diffusers. The conventional nozzle has an addi­tional small chamber just upstream of the nozzle entrance (see Fig. 1) that also may be equipped with various screens and filters as desired (16).

Measurements of the disturbance levels and spectra were made in the free stream of both nozzles and in the large settling chamber with quartz piezoelectric pressure transducers and with hot-wire probes. The settling chamber dis­turbance levels were measured with the slotted nozzle configuration shown in Figure 1 because of the possibility of settling chamber disturb­ances affecting the performance of the annular slot flow and tripping the new, laminar boundary layer downstream of the slot. The probes and calibration procedures for both instruments are described in the following sections.

Hot-Wire Anemometer

The hot-wire anemometer was a constant cur­rent device with a maximum frequency response of 500 kHz. Two types of probes were used: an L-shaped, boundary-layer type probe for measure­ments in the settling chamber, and a sting-mounted probe for the supersonic measurements. Figures 3 and 4 show the construction details of both types of probes.

The sensing element for these probes was a s-~m-diameter platinum wire with a length-to­diameter ratio of 150-200. The wire was manu­factured' by the Wollaston process and the central portion of the wire was etched to expose the platinum core. The unetched sleeves served to strengthen the attachment of the wire to the needles and to space the sensing portion of the wire away from the disturbed flow field around the needles. The photomicrograph in Figure 4 shows the large amount of slack required for the super­sonic probes to eliminate extraneous strain-gage signals (1). The wires for the subsonic probes were mounted with much less slack.

Temperature Calibration. The temperature­resistance characteristics of each wire were determined by oven calibration. A typical cali­bration is shown in Figure Sea). Each calibration was fitted with an expression of the form

However, the temperature range of the present calibrations was insufficient to define accurately the nonlinearity of the data so a value of Yf = -0.044 was taken from Reference (17) for all wires.

Low-Speed Flow Calibration. Most low-speed wind-tunnel testing is done at atmospheric or near atmospheric pressure. At such conditions the

natural convective heat loss from a hot-wire is negligible compared to the forced convective heat loss, even at velocities as low as 4 cm/s (18). However, as the stream density is increased, the natural convective heat loss can easily become a significant fraction of the total heat loss since the Grashoff number increases as p2. For example, at a pressure of 6.7 atmospheres and with a sixty­fold increase in velocity to 240 cm/s the natural convective heat loss is almost 5% of the total for a S-~m-diameter wire. This heat loss can be mini­mized by orienting the wire vertically instead of horizontally but the only way to completely account for the natural convective loss is to calibrate the wire in the same environment as the measurement. For this reason, the low-speed flow calibrations for the present settling chamber measurements were done in the settling chamber by replacing the supersonic slotted nozzle with a smoothly contoured sonic throat. The discharge coefficient of the sonic throat was assumed to be unity and the center­line velocity in the settling chamber was calcu­lated from the geometric chamber-to-throat area ratio. This calculation ignores the effect of the boundary layer in the settling chamber and nozzle throat, but subsequent boundary-layer measurements have indicated that the resulting error in the center-line velocity is negligible.

The theoretical heat-loss characteristics of a wire in low-speed flow are determined by per­forming a steady-state heat balance between the heat generated in the wire, r2Rw' and the forced convection heat loss from the wire, Nun9,k (Tw - Tt ). This heat balance gives

Nu = (~::~ ~ : Tt

) \. / ,-W

(2)

Combining Equations (1), (2), and the empirical expression given in Reference (18) for forced con­vection from a cylinder perpendicular to the flow results in the following relation (Yf assumed zero):

R w

r2R _; =A+B~

aw (3)

The low-speed calibration consists of determining the constants A and B. Evaluating A and B experimentally accounts for any heat losses not included in Equation (2) (conduction, radiation, natural convection). The experimental values of A and B are then used to determine the wire sensitivity to velocity fluctuations (see Ref. (18». The wires were oriented vertically and normal to the mean velocity direction near the center line of the settling chamber for calibration. A typical calibration is shown in Figure S(b).

Supersonic Flow Calibration. The hot-wire calibrations for high-speed flow were done in the free stream at the exit of the M = S nozzle during the same time the fluctuating measurements were made. The technique has been previously reported (14,16,17) and consists of measuring the wire Nusse1t number for zero heating current over a range of Reynolds numbers. The Nusselt number is determined from

(4)

The recovery factor for each probe was also meas­ured and typical results are shown in Figure 6. The data are fitted with the best power-law curve over the complete Reynolds number range. The wire sensitivity to mass flow and total temperature fluctuations is then determined from known wire characteristics and the calibration curves (see Ref. (17)).

Pressure Transducer

A piezoelectric pressure transducer, converted to operate in the piezotron mode (i.e., converted to a low output impedance device so as to be more compatible with conventional electronic data proc­essing equipment), was used to measure the fluc­tuating pressure on the settling chamber wall. The 1.OS-cm-diameter transducer was mounted flush with the settling chamber wall with its sensing surface exposed to the flow. A second transducer was also mounted on the settling chamber wall but with its sensing element shielded from the flow. Since the fluctuating pressure levels are so small and since the transducers are sensitive to accel­eration, the mean square of the shielded transducer signal provides an acceleration "noise" that can be subtracted from the mean square of the exposed transducer signal to give the correct fluctuation level of the flow. In order for this technique to be correct, the two transducers must be matched to give identical outputs for given acceleration levels. This was accomplished by varying the sensitivity of the Kistler 504D charge amplifier to match the output of the two transducers due to vibration. The resolution of these transducers is 0.S76 N/m2 and the axial vibration sensitivity is given as 0.175 N/m2/g. The resonant frequency is l30 kHz.

The fluctuating measurements in the supersonic free stream were made by mounting a 0.3lS-cm­diameter PCB piezoelectric transducer flush with the front fmrface of a pitot pressure probe. Figure 7 shows the construction details and a photo­graph of the pitot probe. Again, a second covered, matched transduc:er was used to measure the accel­eration component of the signal. The resolution of these transducers is 0.S76 N/m2 with an axial vibration sensitivity of 1.75 N/m2/g and a resonant frequency of 300 kHz. Since the pressure is almost constant across the center of a flat-face disc in supersonic flow, the probe diameter was designed to be twice that of the transducer.

Typical calibrations for both transducers are shown in Fig~re S. The calibrations were assumed to be linear as indicated on the figure.

RESULTS AND DISCUSSION

Settling Chamber Measurements

Measurements of fluctuating pressure and velocity were made in the settling chamber using both a hot-wire probe and a wall-mounted

piezoelectric pressure transducer. All measure­ments reported here were made at the downstream instrumentation port just upstream of the converg­ing nozzle inlet (see Fig. 2). The hot-wire probes were mounted so that the sensing wires were in the settling chamber free stream. The pressure trans­ducer was mounted in a steel block and the dia­phragm of the transducer was faired flush with the inside wall of the chamber using silicon rubber. The fluctuating signals from both instruments were processed as described in References (14) and (16). The rms values were measured and recorded. The frequency compensation of the hot-wire signal was performed by the usual square-wave technique (19) to achieve a flat response to 100 kHz. Subse­quently, the signal was low-pass filtered at 50 kHz to improve the signal-to-noise ratio. The wall pressure signal was filtered at 70 kHz.

For incompressible flow, variations in hot­wire output voltage are a function only of the velocity fluctuations (IS). Figure 9 shows the rms velocity fluctuations on the settling chamber center line compared with the rms static pressure fluctuations measured at the wall by the pressure transducer. The difficulty in comparing the two results lies in the fact that the velocity fluctua­tions measured by the hot-wire may be composed of vorticity and sound and no simple way of separating the two contributions exists (17). Previous meas­urements in this facility (14) have indicated no temperature spottiness. The flagged symbols and dashed line of Figure 9 indicate the pressure fluctuation level obtained from the hot-wire data by assuming that all of the velocity fluctuations are due to acoustic disturbances. The relation between velocity and pressure for acoustic waves normal to the tunnel axis is given by

- -~ = YM::- (5) p u

The surprisingly good agreement with the wall pres­sure measurements suggests that the vorticity con­tribution to the hot-wire signal may be small. This possibility gains additional support when it is recognized that the measurements were made many thousands of mesh diameters downstream of the last screen. At this distance downstream in a gradient­free flow one might expect most of the vorticity to have been dissipated by the action of viscosity (20).

Since the boundary layer on the wall of the settling chamber could possibly influence the mag­nitude of the wall fluctuations, estimates were made of the wall pressure fluctuations under a tur­bulent boundary layer. For the present conditions, the contribution of the turbulent boundary layer was less than 1% of the measured values of pip.

Several frequency spectra of the hot-wire and wall pressure transducer are shown in Figure 10. The spectra are shown only to 2 kHz since no appreciable signal could be measured with either instrument beyond this frequency. The wall spectra show a strong 60-Hz component at the lower unit Reynolds numbers that is probably not due to the flow but is due to the electronic noise of the charge amplifier since the amplifier was operated

at maximum gain for the low Reynolds number tests. A strong component near 1600-1700 Hz is also noted in the wall spectra with a corresponding, somewhat broader group of peaks in the hot-wire spectra. In the case of the hot wire, this component seems to decrease significantly with increasing Reynolds number. Spectra for both the hot-wire and the pitot probe show that the peaks near 1600-1700 Hz shift slightly toward higher frequencies (1700-1800 Hz) as Reynolds number increases. (The hot-wire spectra also show a new, lower frequency component (380 Hz) appearing at the higher Reynolds numbers.) 'Because of the relatively narrow band­width of the l600-1700-Hz disturbance and because it appeared on the settling chamber center line as well as the wall, it was thought to be an acoustic Jave rath,,,r than any turbulence phenom­enon. In a further attempt to classify this disturbance, cross-correlation measurements were made with two hot-wire probes. The probes were positioned at the same axial station, one on the chamber center line and the other spaced a known radial distance away. The results for two such spacings are shown in Figure 11. A periodic correlation for r = 5.1 cm is noted with a period of about 600 )Js (1667 Hz) which corresponds to the spectral peaks in Figure 10. This corre­lation is strong evidence that the periodic dis­turbance is acoustic since it is unlikely that the vorticity would correlate over, this large a spacing. A maximum in the correlations occurs at zero time delay indicating that the phase shift over the 5.l-cm probe spacing is zero. The corre­lation at 10 cm is much less distinct, and at the higher Reynolds numbers the correlation for both spacings decays, again in agreement with the spectral data. The forcing function for this dis­turbance is probably aerodynamic since it is strongly Reynolds number dependent. Examples of many such aerodynamic forcing mechanisms exist in the literature (20); perhaps the earliest being Lord Rayleigh's discussion in 1894 of Reynolds number effects on the generation of Aeolian tones produced by vortex shedding from wires (21).

As a further check on the character of the periodic disturbance, longitudinal cross­correlation measurements were made to determine its propagation velocity. Two wires were spaced 18.4 cm apart along the flow direction with the upstream probe situated on the tunnel center line and with the downstream probe approximately 4 cm below the center line. This vertical displacement was necessary to insure that the downstream probe was not in the wake of the upstream probe. The results are shown in Figure 12. The first peak in the correlation occurs at approximately 300 jJs with successive peaks occurring approximately every 600 )Js. Because of these periodic peaks, the common method of determining convection velocity from the transducer spacing divided by the time delay to the first correlation peak is inapplicable. Clearly, any periodic disturbance of the form

p(r,e,z,t) = fer,e) cos (wt - Kz) (6)

will give a periodic cross-correlation function (between two longitudinally spaced points) of the form

Rz = cos (WT + Kb) (7)

where b is the longitudinal spacing of the points and T is the time delay. Consider the value of this function at T = 0

Rz (6,0) = cos (Kb) (8)

Because of the periodic nature of the cosine func­Uon, there exists an infinite family of K values that will satisfy (8). Thus, since the propagation velocity of a disturbance of the form given by (6) can be shown to be

W C = K (9)

there exists a family of propagation velocities at any given frequency corresponding to the set of K values. From a mathematical standpoint, there are no reasons to favor one value of K (or c) over another one as being the "correct" value. However, on the basis of physical arguments, the set of values can usually be narrowed to a much smaller range.

For a disturbance with a measured period of 600 I-lS (see Fig. 11) and a measured phase shift of 300 I-lS (see Fig. 12) a family of propagation velocities was calculated from (9). Only one of this family (614 m/s) is above the acoustic veloc­ity (370 m/s). It is known from the theory of sound propagation in ducts that the phase velocity of any acoustic disturbance must be greater than or equal to the local acoustic velocity. Thus, only one propagation velocity in the calculated family is permissible (the highest one) if the disturbance is truly acoustic. Circular duct theory (22) also predicts the phase speed at which a particular duct mode W1LL propagare. In this case it is found that the (2,0) mode propagates at 569 mis, and that no other mode propagates near this velocity. While the agreement between the measured and computed phase velocities is not perfect (measured value is 8% too high), it does tend to confirm that the spectral peaks near 1600-1700 Hz in Figure 10 are acoustic disturbances.

An examination of the components and physical arrangement of the settling chamber revealed the source of these disturbances. Since the disturb­ances tended to decay with increasing Reynolds number (see Fig. 11) it seemed likely that the generating mechanism originated in a region of the flow that was Reynolds number dependent. The entrance section of the settling chamber was just such a region since the fluid mechanical processes in the elbow (see Fig. 2) are strong functions of the Reynolds number. The interaction of the flow from the elbow with the upstream, domed Rigimesh plate in the settling chamber was considered the most likely noise generator. When this hemi­spherical, sintered metal plate was replaced with a conical-shaped piece of the same material (see Fig. 2) the spectral peaks at 1600-1700 Hz vanished. Apparently this change modified the flow­acoustics interaction enough to destroy the gener­ating mechanism.

The above results ilfustrate the sort of information the hot wire can provide about the character of disturbances in low-speed flow. How­ever, actual separation of broad-band sound from vorticity is, in general, not possible. In the special case of plane sound waves, the cross­correlation coefficient can be used to deduce the magnitude of the noise and vorticity components from the overall fluctuation level. In the present situation, the plane-wave assumption does not apply, both because the complex mode shape indicated pre­viously is certainly not planar and because the reflection process at the converging nozzle entrance must further complicate the sound field at the meas­urement station.

Supersonic Free-Stream Measurements

The test-section disturbance levels were measured by the hot wire and pressure transducer using the probes shown in Figures 4 and 7. Both probes were positioned on the tunnel center line at the nozzle exit. In supersonic flow, acoustic disturbances cannot travel ahead of the local Mach line so the acoustic signals sensed by either probe must originate far upstream in the nozzle. Figure 13 shows the acoustic origin in the conven­tional nozzle, located by following a Mach line upstream from the probe to the nozzle wall. The acoustic origin in the slotted nozzle is found in a similar way but since it is a shorter, more rapidly expanding nozzle the acoustic origin for the same probe location occurs at about 0.4L instead of about 0.5L as in the conventional nozzle.

Conventional Nozzle. Figure 14 shows the variation of the rms pitot pressure with free­stream Reynolds number. The hot-wire data are plotted in terms of the fluctuating pitot pressure, utilizing the method of Reference (16), in order to facilitate comparison with the pitot probe data. The relation between the static pressure fluetua.­tions (as measured by the hot wire) and the pitot pressure fluctuations is given in Reference (16) as

(10)

This relation can be used because the hot-wire signal in the free stream of this tunnel has pre­viously been shown to be purely acoustic (14). The present data confirm this.

A detailed discussion of the data in Figure 14 will be postponed until the discus.sion of the hot­wire mode diagrams in Figure 15. In general, how­ever, the increase in the rIDS level in Figure 14, up to Rew/m = 10.5. x 106 , occurs with a laminar nozzle wall boundary layer" Above Rew/m = 10.5 x 106 the boundary layer becomes transitional and the rms level increases rapidly to a peak value. The decreasing rms levels at the higher Reynolds numbers are characteristic of a fully turbulent.boundary layer.

The hot wire and pitot probe generally indi­cate the same trend and level with respect to the Reynolds number. This agreement is of great prac­tical importance since the piezoelectric pitot probe is a much more rugged instrument with Simpler data reduction procedures than the hot-wire probe. For diagnostic studies, the pitot probe can provide essentially the same information as the hot-wire probe with much less effort. However, the hot wire does have one particular advantage in the present investigation. That is, in a pure sound field the hot wire can distinguish between moving sources and fixed sources (4). For the present investiga­tion, it is important to differentiate between the two types of sources so that the most appropriate methods of reducing the test-section disturbance levels can be developed and applied.

Figure 15 shows typical mode diagrams for several Reynolds numbers. The hot-wire mode vari­ables (17,19) are reasonably well known and their derivation will not be discussed in detail here. Briefly, the basic hot-wire equation for supersonic flow may be written as

where iUT

t

roT t

The linear mode diagrams of Figure 15 are consist­ent with the assumption that the hot-wire signal is either sound or temperature spottiness (4). For pure temperature spottiness, it can be shown that b~/beT = -a when b~/V6eT = O. For the present data a = 0.167 and none of the mode diagrams pass through -a, hence, temperature spottiness can be eliminated. For sound radiated at the Mach angle, the pressure and velocity are perfectly anticorrelated which can be shown to result in RmT = -1. Equation (11) can then be written as

(12)

Equation (12) is entirely consistent with the meas­ured mode diagrams. The positive slopes of the diagrams are the mass flow fluctuations and the positive ordinate intercepts are the "apparent" total temperature fluctuations. It should be emphasized that these "apparent" total temperature fluctuations are not due to temperature spottiness but are the result of the acoustic waves. The velocity of the radiating sources can be shown to be

Ei+ (iJ =t u m s 1 -

. Tt

(13) u co ~ + (~2)

Tt

It

Thus, for TtlTt = 0 (mode diagrams with an orLgLn intercept) the source velocity must be zero, indi­cating fixed sources of sound'. These fixed source disturbances are the shivering Mach wave phenomena of References (9) and (10). The origin of these waves is most likely nozzle-wall waviness (9). The mode diagram slopes are approximately propor­tional to the pressure fluctuation levels and it is seen that these levels begin to increase even before the appearance of turbulent spots (see Figs. 14 and 15). This increase in noise level, even when the boundary layer is laminar, is attrib­uted to the thinning of the laminar boundary layer with increasing Reynolds number. This thinning heightens the effect of any waviness or roughness on the nozzle wall and results in the increasing rms levels. with increasing Reynolds number.

The first occurrence of turbulent bursts in the output' signal (see Fig. 14) is always accom­panied by a change in the mode diagram from an origin intercept to a positive ordinate intercept (see Fig. 15). This indicates radiation from a moving source and marks the beginning of the boundary-layer transition process. The moving sources are local turbulent spots moving at super­sonic velocities with respect' to the free stream and radiating at or near the Mach angle.

Figure 16 shows a comparison of the measured spectra from the hot-wire and pitot probe. The Reynolds number corresponds approximately to the peak rms region of Figure 14. The pitot probe spectra appear to be characteristic of a well­developed turbulent boundary layer while the hot­wire spectra are more transitional in nature (14). Transitional spectra are characterized by a pre­dominance of energy at lower frequencies. More energy shifts to higher frequencies as transition progresses until the fully turbulent shape, as shown by the pitot spectra in Figure 16, is achieved. Because of the sensitivity of the transition process in the peak rms region to small changes in wall roughness, the difference in the two spectra at the same Reynolds number is not viewed as a serious discrepancy. Most likely, since the pitot and hot-wire tests were conducted at different times, a small degradation in surface finish in the nozzle throat region caused the pitot spectra to be more nearly turbulent. In fact, the surface in the throat region required constant cleaning and polishing to maintain transi­tion at a fixed Reynolds number.

It should be remarked that the higher Reynolds number hot-wire data (Re 1m > 15 x 106) for the conventional nozzle show~d some strain-gage sig­nals (18), generally beyond 100 kHz. The contri­bution of the strain-gage signals was believed to be less than 10% of the overall rrns values.

Slotted Nozzle. Figure 17 shows hot-wire rms pressure fluctuations in the slotted nozzle for two different wall finishes. The original finish resulted in disturbance levels somewhat higher than for the conventional nozzle (compare Figs. 14 and 17). Inspection of the nozzle revealed a strong pattern of waviness on the interior wall. The nozzle was re-machined in an effort to reduce

the waviness but the resulting finish was generally no better than before. Unfortunately, an annular depression was inadvertently machined just down­stream of the throat and although transition occurred at essentially the same Reynolds number as before the laminar disturbance levels were much higher.

Figure 18 shows the mode diagrams for the re·-machined nozzle. As before, the mode plots indicate that shivering Mach waves are dominating the test-section noise level until the transition process begins. It is interesting to note that the measurement at Roolm = 8.2 x 106 resulted in an rms level considerably above the turbulent level. This is a prime example of how an incor­rectly machined nozzle can result in a large test­section noise level even when the nozzle-wall boundary layer is laminar. This nozzle is cur­rently being replaced with a nozzle made by electroplating on a highly polished mandrel.

CONCLUDING REMARKS

Disturbance measurements were made with hot­wire probes and piezoelectric pressure transducers in the settling chamber and test section of a small, Mach 5 wind tunnel. The measurements in the settling chamber indicated that the rrns level of the hot-wire signal on the chamber center line generally agreed with the rrns level of the wall pressure fluctuations when the hot-wire signal was interpreted as purely acoustic. Further, cross­correlation of the signal from two hot-wire probes confirmed the acoustic nature of a particular narrow-band spectral component and tentatively identified this disturbance as a duct mode.

The data from the hot-wire probe and piezo­electric pitot pressure probe in the supersonic free stream of the conventional, Mach 5 nozzle were in good agreement. This agreement indicates that the pitot probe can be used for quantitative as well as diagnostic data at conditions similar to the present experiment. Because the piezoelectric probe is much more rugged than the hot-wire probe and because the data reduction procedure is much more straightforward, the piezoelectric probe offers a distinct advantage for free-stream dis­turbance measurements.

The hot-wire anemometer, although more diffi­cult to use than the pitot probe, has the unique capability to distinguish between fixed noise sources and moving noise sources for pure sound fields in supersonic flow. This capability was u;3ed in the present investigation to identify "shivering" Mach waves caused by nozzle-wall wavi­ness as strong contributors to the tunnel test­section disturbance level when the nozzle-wall boundary layer was still laminar. Accurate meas­urements of these shivering wave disturbances were obtained and their magnitude was found to be related to the degree of finish and machining accuracy of the nozzle contour and to the relative thickness of the laminar boundary layer. The first appearance of moving sound sources in the hot-wire signal provide a convenient way of determining the beginning of boundary-layer transition.

REFERENCES

(1) Wagner, R. D., Jr., Maddalon, D. V., and Weinstein, L. M., "Influence of Measured Free Stream Disturbances in Hypersonic Boundary Layer Transition," AIM JOURNAL, VOL. 8, NO.9, pp. 1664-1670, Sept. 1970.

(2) Pate, S. R., and Schueler, C. J., "Radiated Aerodynamic Noise Effects on Boundary Layer Transition in Supersonic and Hypersonic Wind Tunnels," AIM JOURNAL, VOL. 7, NO.3, pp. 450-457, March 1969.

(3) Dods, J. B., Jr., and Hanley, R. D., "Evaluation of Transonic and Supersonic Wind Tun­nel Background NOise and Effects of Surface Pres­sure Fluctuation Measurements," AIM PAPER NO. 72-1004, Sept. 1972.

(4) Laufer, J., "Aerodynamic Noise in Supersonic Wind Tunnels," J. AERO. SCI. VOL. 28, NO.9, pp. 685-692, Sept. 1961.

(5) Phillips, O. M., "On the Generation of Sound by Supersonic Turbulent Shear Layers," J. FLUID MECH. VOL. 21, PART 4, pp. 641-657, 1965.

(6) Ffowcs-Williams, J. E., and Maidanik, G., "The Mach Wave Field Radiated by Supersonic Turbulent Shear Flows," J. FLUID MECH. VOL. 21, PART 4, pp. 641-657, 1965.

(7) Laufer, J., Ffowcs-Williams, J. E., and Childress, S., "Mechanisms of Noise Generation in the Turbulent Boundary Layer," AGARDograph 90, Nov. 1964.

(8) Laufer, J., "Factors Affecting Transi­tion Reynolds Number on Models in Supersonic Wind Tunnels," J. AERO. SCI., VOL. 21, NO.7, pp. 497-498, July 1954.

(9) Morkovin, M. V., "On Transition Experi­ments at Moderate Supersonic Speeds," J. AERO. SCI., VOL. 24, NO.7, pp. 480-486, 1957.

(10) Morkovin, M. V., "On Supersonic Wind Tunnels With Low Free Stream Disturbances," J. APP. MECH., VOL. 26, NO.3, pp. 319-323, Sept. 1959.

(11) Uberoi, M. S., "Effect of Wind Tunnel Contraction on Free Stream Turbulence," J. AERO. SCI., VOL. 23, NO.8, pp. 754-764, Aug. 1956.

(12) Laufer, J., "Some Statistical Proper­ties of the Pressure Field Radiated by a Turbulent Boundary Layer, II PHYS. OF FLUIDS, VOL. 7, NO.8, pp. 1191-1197, Aug. 1964.

(13) Beckwith, I. E., "Development of a High Reynolds Number Quiet Tunnel for Transition Research," AIM JOURNAL, VOL. 13, NO.3, pp. 300-306, March 1975.

(14) Harvey, W. D., Stainback, P. C., Anders, J. B., and Cary, A. M., "Nozzle Wall Boundary Layer Transition and Freestream Disturbances at Mach 5," AIM JOURNAL, VOL. 13, NO.3, pp. 307-314, March 1975.

(15) Harvey, W. D., Berger, M. H., and Stainback, P. C., "Experimental and Theoretical Investigation of a Slotted Noise Shield for Wind Tunnel Walls," AIM PAPER NO. 74-624, July 8-10, 1974.

(16) Stainback, P. C., and Wagner, R. D., "A Comparison of Disturbance Levels Measured in Hypersonic Tunnels Using a Hot-Wire Anemometer and a Pitot Pressure Probe," AIM PAPER NO. 72-1003, Sept. 13-15, 1972.

(17) Morkovin, M. V., "Fluctuations and Hot-Wire Anemometry in Compressible Flows," AGARDograph 24, -Nov. 1956.

(18) Hinze, J. 0., "Turbulence," McGraw-Hill Book Company, Inc., 1959.

(19) Kovasznay, L. S. G., "Hot-Wire Method," VOL. IX of High Speed Aerodynamics and Jet Propul­sion, Article F, 2, R. W. Ladenburg, B. Lewis, R. N. Pease, and H. S. Taylor, eds., Princeton University Press, 1954.

(20) Loehrke, R. I., and Nagib, H. M., "Experiments on Management of Free Stream Turbulence," AGARD-R-598, Sept. 1972.

(21) Rayleigh, J. W. S., "The Theory of Sound," Dover Publications, New York, 1945.

(22) Skudrzyk, E., "The Foundations of Acoustics," Springer-Verlag, New York, 1'971.

Conventional settling chamber and nozzle

30.48

--.

13.97

II Vacuum box ~ tt II

Large settling chamber and slotted nozzle tt 1130.48 39.37

I.. 104.1 . .,.j.. 154,,3 .,... .,.1.. ..I

Large 6.p baffles

--f---lit - ---- III

Perforated plate

Settling chamber

Figure 1.- General arrangement of test facility (dimensions in cm).

-11-11 '( -...... Vacuum

Alternate arrangement for settling chamber entrance

Steel wool,

Instrumentation T~ 1TW-15.24 port

I ...... '" 59.1 .. I ~ 104.1 1\\ ... 1... ·154.3 --I

Instrumentation ports

I.... 1 Screens-I I JIOooj Flow

I~.J .I.~Jj.l.J t 135.4 '"I'. I-I Filter paper on upstream side of Rigimesh

Figure 2.- Schematic of settling chamber.

f.. ~t--------4.190------~....r 0.127 I I

+~:' ... ~%(~= .. ~O=:;~~J . . Jewelers broaches

1.91

....... -1.27 -.-...t

Electrical leads (4)

Figure 3.- Hot-wire probe for settling chamber measurements (dimensions in em.).

0.S2 mm teflon coated wire I (2 leads per needle) :::= ~-L-' --O~...,......,..--tc? ~tainless steel I Heat shrinkable S.18 mm s.s. tubing L Bakelite insulator

needles insulation

(a) Probe construction

d = 0.25 ern-I

(b) Wire mounting (SOX)

Figure 4.- Hot-wire probe for high-speed measurements.

5.0

4.0

3.0 ~----~----------~------------~------------~ 300 350 400 450

(a) Oven calibration

2.5 x 104

2.0

12l\.v 1.5

R - R w aw

Q 1.0

.5 ~----~------~------~------~------~----~ 1 2 3 4

~Ret (b) Low-speed flow calibration

Fig:ure 5.- Hot-wire probe calibrations.

~

~

::I Z

o o If':)

0 0 ...-I

0 If':)

~

OJ p:;

If':)

II g ~ ....., C1:!

= 0 ......

~ ,Q ...... ~ 0

~ 0 ..... ~

OJ M ...... ~ I ~ 0 ~

I . (.0

OJ M

~ ...... ~

Exposed transducer

t RUbber~ ~ . Nylon ~covered transduer

t 1iP::Y¢1~'\ ~@f-2t4~;£$llWEZ/21 0.635

I... 2.54 ·1 RTV rubber

10n spacers

Rubber sleeves

Figure 7.- Construction details of pitot probe (dimensions in em.).

1000

p, N/m2 100

10

0.318 cm PCB transducer '"

100

e, mv

~.08 cm PCB transducer

! ,

1000

Figure 8.- Calibration of pressure transducer using Photo con Research Products Model PC-120 Pressure Calibrator and Kistler Model 504D Dual Mode Charge Amplifier (Range 1).

u -u

_.2_ p

-2 10

Data C) Hot wire on centerline

[] Pressure transducer on wall

--0-- Pressure fluctuations from hot-wire data using eqn. 10

Figure 9.- Pressure and velocity fluctuations in settling chamber.

5 Reoolm =, 7.44 x 10

Reo:!m = 15.85 x 105

~ Re~/m" 23.60 x 105

[

o 1000

Frequency, Hz

(a) Hot 11ire

2000

o

Figure 10.- Concluded.

Reoo/m = 6.93 x 105

Reco/m = 14.83 x 105

ReDO/m = 28.50 x 105

1000

Frequency, Hz

(b) Pressure transducer

2000

1.0t-.6omBA ~ ~ ~ O~7 p::

.. ~ 2 s:; Q) ..... () ..... :::: Q) o ()

s::: o ..... .+j

ca -. Q) ~ ~ o () I

Ul Ul o H U

.1

o I \aid .. pW I \a. Al' \_ .l''' '" .2

.1

o I . \A :Ii"'!' ~ I V\ IA. rlf \\. xlV', ...

.1i+-.6om~

O~~It~ LIncreasing time delay, T ......... C

.6.r = 5.1 cm

.5~ Reoo/m = 1.67xl05 O~

.1

b Reoo/m = 7.44XI05 0 ~1I1a~"~ AAK ... A,.,A

.1

b Reoo/m = 1.59x106 O~.~MvV", •• ",,· ..

.1 .

Re",/m = 2.32x106 O~a~_J\"""""""'''''' ... """" • i- Increasing time delay,. T--JIIiII'-

.6.r = 10.2 cm

Figure 11.- Cross~correlation of signals from two hot-wires spaced transverse to mean flow direction, setting chamber, U ~ 2.4 m/sec.

T :-0

300 iJ.s

J-----Increasing time delay )!III»

Figure 12.- Cross-covariance of two longitudinally-spaced hot-wires in settling 6 chamber, 6.z::= 18.4 cm, Ar =3.8 cm, Reoo/m = 3.3 x 10 .

I

l/NOZZle 26.8 ---j ,:>>,'0,'0,>,0,>,>,"0,">'> >0> > > > ,

• .::::::. '> '> '> '> r2::2::: _ _ _ _

exit

rProbe

~at ,/

Acoustic origin J ~ Nozzle contour

Figure 13.- Schematic of conventional nozzle showing acoustic origin (dimensions in cm).

5 x 10-2 I

Pt,2

Pt,2

10-2 rl ---

Fully turbulent nozzle wall boundary layer

o PUot

o Hot wire

10-3 I ~ II First appearance of-------I -turbulent spots

106

Reoo/m

Figure Free-stream pressure fluctuations at exit of conventional nozzle, IV! ::::

1.0

.9

.8

.7

'"V

Ae ---VAe T .6

Symbol Reoo/m .5

0 5.25 x 106 Laminar

0 7.87Xl06

.4 010. x 106 { 6 117

..I. I • X Peak . 3

.2

-0' .1

-.2 -.1 o .1 .2 .3 .4 .5 ,6 .7

Figure 15.- Hot wjre mode diagrams

<!.l ....-4 ro u Ul

~ ro M

-l-> -.-I

£ ~

<!.l ....-4 ro C,)

00

---o

Reoo/m = 2.87xlO 7

Electronic noise ------

Hot wire anemometer

Re oo / m = 2.87xl07

transducer

in the stream, Moo = 5.

"" Pt 2 , I\,2

10-1 , =-----,--

10-2

o Original finish

o Remachined finish

First appearance of -turbulent spots

10-3 ~~~!!1-! ~~L 107 I I

Re~ 1m 10

8

Figure 17. stream pressure fluctuations at exit of slotted nozzle, Moo::: 5.

y)

1.0 x 10-2

.9

.8 .

. 7

.6

~

6 ~e

V~eT .5

.4

Be Symbol

00

.3 0 5.25 x 106

0 6.23 x 106

,2 0 8.20 x 1

6 9.84 x 106 First appearance

.1 ~ 11.16 x 106 turbulent spots

-0' Transitional

~ 6 Peak RMS D 12.80 x 10

I I I I -.2 -.1 0 .1 .2 .3 .4 .5 '(1. .7

~em

~eT

Figure 18 • .;. Hot wire mode diagrams for slotted nozzle.