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Pressure Power Spectra Beneath a

Supersonic Turbulent Boundary Layer

Steven J. Beresh,* John F. Henfling, Russell W. Spillers,, and Brian O. M. Pruett

Sandia National Laboratories, Albuquerque, NM, 87185

Wind tunnel experiments up to Mach 3 have provided fluctuating wall-pressure spectra

beneath a supersonic turbulent boundary layer to frequencies reaching 400 kHz by

combining signals from piezoresistive silicon pressure transducers effective at low- and mid-

range frequencies and piezoelectric quartz sensors to detect high frequency events. Data

were corrected for spatial attenuation at high frequencies and for wind-tunnel noise and

vibration at low frequencies. The resulting power spectra revealed the -1 dependence for

fluctuations within the logarithmic region of the boundary layer, but are essentially flat at

low frequency and do not exhibit the theorized 2

dependence. Variations in the Reynolds

number or streamwise measurement location collapse to a single curve for each Mach

number when normalized by outer flow variables. Normalization by inner flow variables is

successful for the -1 region but less so for lower frequencies. A comparison of the pressure

fluctuation intensities with fifty years of historical data shows their reported magnitude

chiefly is a function of the frequency response of the sensors. The present corrected data

yield results in excess of the bulk of the historical data, but uncorrected data are consistent

with lower magnitudes. These trends suggest that much of the historical compressible

database may be biased low, leading to the failure of several semi-empirical predictive

models to accurately represent the power spectra acquired during the present experiments.

Introduction

The accurate measurement of the fluctuating wall-pressure spectrum beneath a supersonic turbulent boundary

layer has proven elusive for many decades. Dolling and Dussauge [1] discuss many of the reasons why this is the

case. The principal problem is sensor frequency response; the temporal frequencies of interest in high-speed flows

typically extend beyond the capability of most pressure sensors. Moreover, resonance of both the sensor diaphragmand the cavity often occurs at frequencies that contaminate the measurement. Spatial resolution of the sensors also

poses a problem, as the spatial scales of the flow in which significant energy is contained are commonly much

smaller than the sensor size, leading to a low-pass filtering of the signal. Electronic noise also is a routine difficulty

in wind tunnel environments, hindering the detection of subtle effects. The combination of these difficulties oftenlimits measurement frequencies to those below about 100 kHz, and sometimes considerably less.

Despite these challenges, numerous efforts have been made to acquire unsteady wall pressure data for

supersonic boundary layers, on a variety of geometric surfaces. Many such experiments have been cited by Dolling

and Dussauge [1], Dolling and Narlo [2], and Laganelli and Hinrichsen [3], but the results they report exhibit analarming degree of scatter for nominally compatible measurements. Partly, differences may arise because the

experimental conditions themselves are dissimilar or insufficiently reported, or are influenced by unknown effects.

But some of the data scatter certainly results from the variety of measurement errors discussed earlier. As a result,

universal trends in the data may be obscured, and the development of engineering models and computational

*Principal Member of the Technical Staff, Engineering Sciences Center, Associate Fellow AIAA, correspondence to: P.O. Box5800, Mailstop 0825, (505) 844-4618, email: [email protected]

Distinguished Technologist, Member AIAA

Senior Technologist

Senior Technologist

This work is supported by Sandia National Laboratories and the United States Department of Energy. Sandia is amultiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of

Energys National Nuclear Security Administration under Contract DE-AC04-94AL85000.

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simulations may be hampered by an incomplete understanding of the behavior of supersonic wall pressure

fluctuations.

Experiments have been conducted in Sandias Trisonic Wind Tunnel up to Mach 3 to provide fluctuating wall

pressure data under well-characterized flow conditions to frequencies exceeding 100 kHz. Carefully acquired, these

data can play an important role in reconciling the conflicts present in the historical data. An earlier document [4]has detailed improvements in the pressure sensor capability by developing an innovative technique to merge

measurements from three sensors. Data have been acquired using piezoresistive silicon pressure transducers

effective at low- and mid-range frequencies, then supplemented by piezoelectric quartz sensors capable of detectingvery high frequency events. The two sensor types were dynamically calibrated against a condenser microphone

reference standard, then combined into a single curve describing the wall pressure spectra. The effects of wind

tunnel noise and vibration at low frequencies were reduced using an adaptive filter technique similar to Naguib et al

[5] and the effects of spatial attenuation at high frequencies were compensated using the Corcos correction

technique [6]. Using this approach, measurements were shown to be accurate to 400 kHz and to produce resultsconsistent with more reliable incompressible experiments, but at the same time they suggested that the historical

database of supersonic pressure fluctuation intensities is biased low.

The present paper utilizes this improved measurement capability to acquire pressure power spectra under avariety of flowfield conditions, then compares the results with the historical database and common engineering

models. Though even unsteady pressure measurement often is regarded as routine in wind tunnel experimentation,

unrecognized error sources have repeatedly contaminated past experiments, and thus careful conduct of the present

study can yield results that will clarify murky trends in the historical literature.

Historical Database

The intensity of the pressure fluctuations is commonly characterized by the r.m.s. of the unsteady signal, p,

and normalized by either the edge (or freestream) dynamic pressure qe or the wall shear stress w. High-speedexperiments generally have preferred normalization to qe because of its ease of measurement in comparison to w

and its practicality in engineering applications. The theoretical justification for normalization to w is stronger, but

the measurement uncertainty (or predictive inaccuracy) usually is considerably greater, and furthermore a

dependence upon Reynolds number is known.

Even the measurement of incompressible fluctuating pressure intensities on a smooth flat plate has posed aformidable challenge. Numerous efforts to compile a database of high-speed pressure fluctuations have cited an

incompressible value ofp/qe=0.006 [e.g., 7-9], a value apparently originally attributable to the work of Willmarth

[10, 11] and Bull [12] and Shattuck [13]. Although it was widely accepted for a long time, evidence accumulated tosuggest that this value was biased low due to insufficient sensor spatial resolution [6, 14, 15]; see reviews by

Willmarth [16] and Bull [17]. Subsequent experiments gradually raised the pressure intensity value. Bull andThomass study [14] suggests a correct value near p/qe=0.008 but may suffer from perturbations induced by a

pinhole microphone [17]. Schewe [15] shows that a sufficiently small microphone will return p/qe=0.010, a resultsupported by Lueptow [18]. Gravante et al [19] find p/qe varies from 0.008 to 0.010 asRe decreases, and Goody

et al [20] find about 0.009. Farabee and Casarella [21] integrate their measured power spectra and the estimated

spectra beyond their measurement capability to determine p/qe=0.009, which, in the view of both Bull [17] and the

present author, probably is the most correct estimation of the incompressible value ofp/qe.

Supersonic and hypersonic measurements of p/qe are considerably more challenging. The difficultiesencountered for incompressible measurements regarding spatial resolution and frequency response only become

more acute as freestream velocities rise and boundary layer thicknesses typically diminish due to the smaller size ofmost testing facilities. Nonetheless, the importance of pressure fluctuations to flight vehicle performance has

motivated numerous experiments, which are collected in Fig. 1. Data are given in terms of the edge Mach number,

Me, as the compilation includes experiments conducted on cones and sting-mounted flat plates, but for

measurements on a wind tunnel wall, this is equivalent to the freestream Mach number, M. The range ofincompressible values is based upon the discussion in the previous paragraph and is summarized by a single data

bar. Most data have been obtained on a wind tunnel wall to yield the thickest boundary layers, as in the present

experiment, but nominally compatible measurements from flat plates, cones, and ogive cylinders are included as

well. Given that the data from these latter geometries may be subject to additional influences or uncertainties such

as post-bow-shock conditions, transitional/turbulent flow state, thinner boundary layers, and leading edge effects,these measurements have been displayed as hollow data points; measurements on wind tunnel walls are denoted by

solid data points. Some of the supersonic data are obtained from experiments nominally concerned with

shock/boundary-layer interactions, but also contain data in an undisturbed flowfield that may be included here. The

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Fig. 1: Historical database of pressure fluctuation intensity as a function of Mach number, normalized by

dynamic pressure. Solid points show data measured on a wind tunnel wall; hollow points measured on a

flat plate, cone, or ogive cylinder. Four semi-empirical predictive equations are shown as well.

bulk of the measurements presented in Fig. 1 were obtained in the 1960s and 1970s and did not have available the

measurement technology now commonplace. Most of the more recent measurements are extracted from the

shoc

diffe

dictions well represents the experimental data, which hardly is surprisinggive

/q falls asRe -1/4 [33]. Kistler and

Che

k/boundary-layer database and are limited in Mach range.

Figure 1 dramatically illustrates the impressive scatter of several decades of nominally compatible

measurements. In fact, nearly the only conclusion that may be drawn with any confidence is that the pressure

fluctuation intensity diminishes with rising Mach number, and even then the strength of this trend is ambiguous. Norences are evident between the data acquired on a wind tunnel wall and those measured on other surfaces.

Also shown in Fig. 1 are curves for several semi-empirical predictive equations for the pressure fluctuationintensity. The simplest is Lowsons equation, which is solely a function of the Mach number [8]. Chaump et al [35]

later found that Lowsons prediction was consistent with the data for supersonic Mach numbers, but developed an

extension to his curve for Mach numbers exceeding 5, also based solely upon the Mach number. A more complexpredictive equation was developed by Laganelli et al [50] that incorporated effects due to the wall temperature. Two

curves are shown for the Laganelli prediction to account for this dependence, one for Tw=Taw and one for the

bounding condition ofTwTaw. Wall temperature effects within the historical data are discussed subsequently.Generally speaking, however, none of pre

n the broad scatter of the data points.

The scatter of the data in Fig. 1 may arise from trends not taken into account, such as those due to varying

Reynolds number. In incompressible flow, no evidence has been found of a relationship between p/qe and the

Reynolds number based either on boundary layer thickness, Re, or momentum thickness, Re; however, somevariation may exist for small values ofRe orRe but vanish once moderate Reynolds numbers are reached [19].

Conversely, a trend with Reynolds number may be present for high-speed flows. Raman convincingly finds that

p/qe falls as a function ofRe*-0.2 [43, 44] when the Mach number is constant, where * is the boundary layer

displacement thickness, which is quite close to Maestrellos assessment that p e n also find a decreasing p/qe asRe* falls at constant Mach number [32].

To ascertain whether a Reynolds number effect is present in the historical database and may account for the

scatter, the data points of Fig. 1 have been recast in Fig. 2 with their color a function of their Reynolds number.Data points have been excluded for which the Reynolds number was not provided or could not be reasonably

estimated. Figure 2a shades the points based uponRe and Fig. 2b based uponRe. ThoughRe is not as descriptive

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(a) (b)

Fig. 2: Data points from Fig. 1 shaded by the Reynolds number based upon: (a) 99%-velocity boundary layer

thickness; (b) boundary layer momentum thickness.

(a) (b)

Fig. 3: Data points from Fig. 1 shaded by characteristic sensor parameters; (a) non-dimensional cutoff frequency;

(b) cutoff frequency due to spatial resolution.

of the boundary layer state as Re, is more commonly measured and, arguably, also is easier to evaluate in a

compressible flow as compared to * or. Trends as a function ofRe* generally track those as a function ofRe,

and hence are omitted for brevity. Unfortunately, any pattern is difficult to identify. It appears in Fig. 2a that some

lower values ofp/qe correspond to greaterRe, but this only is definitive for the Raman data points [43, 44].Similarly, Fig. 2b appears to show a cluster of data points at lower /q whenRe is larger, but again this is hardly

defi

p e

nitive.Another possibility is that any trends found in Fig. 1 are not due to the physics, but rather, due to measurement

limitations. The frequency response of a pressure sensor can be described in non-dimensional form by /U, where

is the cutoff frequency characteristic of the sensor [1]. The spatial resolution of a sensor induces a cutofffrequency as well due to attenuation of wavelengths smaller than the sensors sensitive area, which can becharacterized by Uc/d [6], where Uc is convection velocity near the wall and can be reasonably approximated as

Uc/U=0.6 [1] and d is the sensor diameter. Figure 3 recasts the data of Fig. 1 based upon these two sensor

parameters, shown in Figs. 3a and 3b respectively, excepting those data points for which insufficient information

was available to determine either/U orUc/d. A calculation of values for/U is complicated by the fact that

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Fig. 4: Historical database of pressure fluctuation intensity as a function of Mach number, normalized by

wall shear stress. Solid points show data measured on a wind tunnel wall; hollow points measured on a flat

plate, cone, or ogive cylinder.

in many cases the frequency response is an estimaterather than a rigorously determined value, but

nevertheless a clear pattern emerges. Figure 3a does in

fact show an identifiable trend of larger values ofp/qe

arising from sensors with larger cutoff frequencies.This is not surprising, as it stands to reason that sensors

capable of measuring a broader portion of the frequency

spectrum will be sensitive to more pressure fluctuationsand hence record a greater total intensity. It also is

worth recognizing that achieving a better frequency

response can be accomplished not only by fast-response

sensors, but alternatively by obtaining measurements in

a fa

lution is less than the high-frequency limit of the

irly thick boundary layer; this appears to have beenkey to the apparent success of some of the earliest

experiments.

On the other hand, Fig. 3b does not indicate anydistinct trend ofp/qe as a function of spatial resolution,

which suggests that sensor frequency response is thedominant issue for high-speed flows. This observationis initially surprising given the clear need in

incompressible flow for adequate spatial resolution [15, 18] or corrections for spatial attenuation [6]. However,

what is actually demonstrated is that improvements in spatial resolution are not useful without corresponding

improvements in sensor frequency response. For example, the lines of the Raman [43, 44] data points at Machs 5.2,

7.4, and 10.4 have large values of both /U and Uc/d, and hence return the largest hypersonic values forp/qe.

Conversely, the cluster of Harvey et al [26] data points between Mach 8 and Mach 9 shows a large value of Uc/d,

but without a similarly large value of/U to match, lower values ofp/qe are returned. In a small number of

cases, the effective high-frequency limit due to the spatial reso

Fig. 5: Data points from Fig. 4 shaded by sensor non-

dimensional cutoff frequency.

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sens

d similarly, the Chung and Lu [22] data point corresponds to T /T =0.39. The other hypersonic

expe

w, and Fig. 3b illustrates this point.

Nev

las prediction would raise p/w only to about 3.9; this range of values is shown in Fig. 4 as the

inco

evity. Figure 5 supports the earlier

indication that the dominant influence upon the measured pressure fluctuation intensities is the frequency responseof the sensor, and that larger values ofp/ rate.

2K by heating in the storage tanks, and the wall

tem

or itself; inserting the lower values due to spatial attenuation into Fig. 3a does not appreciably change the

results.

Some of the data scatter in Fig. 1 may be attributed to wall temperature differences between the experiments, as

suggested by the range of results predicted by Laganelli et al [50] as Tw/Taw varies. In practice, however, for most

moderate values of Mach number, Tw/Taw is fairly close to unity, and therefore the wall temperature is not asatisfying explanation for those data points exhibiting large values ofp/qe at Me

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at each of the three streamwise stations, then fitted to

the method of Sun and Childs [51] to provide the

freestream velocity U, the 99%-velocity boundary

layer thickness , the displacement thickness *, and the

momentum thickness . The skin friction coefficient cfalso may be determined by the Sun and Childs fit.

measurement stations, the

bou

position is not significant, as determined by

wind

nsor

rang

is flat to

appr

low as 0.01 Pa. Of the sensors utilized in the present work, only the B&K

4138 is provided by the manufacturer with a calibration curve of amplitude response as a function of frequency up to

se in the current study is to function as a reference standard in sensor calibrations performed

acou

Within the range of these

ndary layer has been shown to be in equilibrium, asdiscussed by White [52] based upon Clausers classic

argument [53].

Pressure InstrumentationThree different types of pressure sensors were

used: Kulite MIC-062, PCB 132A31, and Brel &Kjaer (B&K) 4138. Additionally, two Kulite screen

types were tested, and two of each sensor were

employed, bringing the total number of sensors to eight.

The present document utilizes only those sensors that

proved most successful; the others are discussed in [4].

The eight sensors were installed in the wind tunnel

simultaneously, mounted in an insert block that placedall sensors at the same axial station within the test

section, as indicated in Fig. 6. The spanwise variationin sensor

tunnel calibration data. The insert block

containing the eight installed sensors could be placed at

any of the three streamwise stations, leaving the other

two locations to be plugged by a blank containing no sensors.The Kulite MIC-062 is a piezoelectric silicon sensor based upon the widely used XCQ-062 product line and is

essentially a 7 kPa pressure transducer with a specified sensitivity of 2 Pa and a diaphragm resonance frequency of

approximately 125 kHz in a cylindrical housing of 1.62 mm diameter. Data reported herein used an A-screen to

protect the diaphragm, which is simply a 1.02 mm hole at the sensor face, as opposed to the more conventional B-screen consisting of a ring of 0.15 mm holes around the periphery of the sensor face. The B-screen offers better

protection against damage and particulates, but its dynamic response is flat only to about 20% of the diaphragmresonance frequency whereas the A-screen provides superior frequency response to about 30-40% [4, 54].

However, the geometry of the A-screen introduces cavity resonance at a much lower frequency. The Kulitemicrophones are differential pressure transducers and have a vent tube extending from their rear, which was

plumbed to a surge tank whose pressure could be set prior to each wind tunnel run to a value within the se

Fig. 6: Sketch of the three sensor stations within the

Trisonic Wind Tunnel, and the sensor mounting block

that may be installed at any station.

e; venting to the tunnel plenum led to saturation of the pressure signal. Since the pressure signals are recorded

with no DC response (see below) to focus solely upon the fluctuations, it is not necessary to accurately measure the

surge tank pressure or even to carefully set this value.

The PCB 132A31 is a piezoelectric quartz sensor intended by the manufacturer to be a time-of-arrival sensor,but has been used successfully to detect very high frequency events in hypersonic wind tunnel experiments [54-56].

Its performance at low frequencies is limited by a cutoff of 11 kHz but its high-frequency performance exceeds

1 MHz with a specified sensitivity of 7 Pa. The manufacturer suggests the high-frequency response

oximately one-third of its maximum, or roughly 300 kHz. The quartz crystal is bonded to the underside of the

sensing surface and hence does not require exposure to the flow through a screen as do Kulite sensors, preventingthe occurrence of a cavity resonance. The effective sensing area is stated by the manufacturer as 1.6 mm2.

Finally, the B&K 4138 is a pressure-field condenser microphone of diameter 3.2 mm ordinarily used as acalibration standard with a sensitivity as

140 kHz. Its purpo

stically outside of the wind tunnel.

Signal ProcessingThe Kulite sensors were supplied a 10 V excitation from an Endevco Model 136 Amplifier, which also provided

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the first stage of signal gain for the sensor output. The Kulite signals then were low-pass filtered at 200 kHz by a

Krohn-Hite Model 3384 active filter, which is able to provide 48 dB attenuation per octave. Meanwhile, the

PCB132 sensors use a combined power supply and signal conditioner (PCB 482A22), then their signals were low-

pass

ling frequencies were 1 MHz, well below the 10 MHz bandwidthprovided by the PXI-6133 cards, and were recorded at 14 bits depth for typically 1 second of length. These A-to-D

been shown to have excellent low-noise characteristics despite their large bandwidth and performed

bet

d by each sensor to be calibrated. The sensors areexc

cting this noise signal from an original Kulite signal, a

noi

gnal attenuation becomes a concern. The Corcos correction has been

use

filtered at 500 kHz by a Krohn-Hite Model 3944 active filter; though it only offers 24 dB attenuation per octave

in comparison to the Model 3384, it is capable of reaching significantly higher frequency cutoffs and hence isnecessary for the high-frequency signals of the PCB 132 sensors.

All signals, once amplified and filtered, were sampled using a National Instruments PXI-6133 analog-to-digital

converter housed in a PXI-1042 chassis. Samp

converters have

ter than other available sampling electronics.

Data Analysis

To properly analyze fluctuating pressure data, the sensors first must be dynamically calibrated to provide the

amplitude response as a function of frequency. The Kulite sensors are intended for use up to 40 kHz, a range over

which their frequency response should be approximately flat, and a conventional static calibration proved sufficient.Conversely, the PCB sensors are intended for use above 20 kHz and should have a flat response to roughly 300 kHz,

but their amplitude response is poorly characterized and a static calibration is impossible due to their low-frequency

cutoff. A dynamic calibration similar to the one conducted by Zuckerwar et al [57] is used in the present case, with

the principal difference that Zuckerwar et al performed a free-field calibration for acoustic measurements whereas

the current implementation is a pressure-field calibration for wall-mounted sensors. The calibration is based uponthe substitution method, where the B&K 4138 reference standard is flush-mounted in the center of a nearly infinite

wall within an anechoic chamber, then subsequently replace

ited by an ultrasonic speaker reaching 45 kHz. By maintaining constant output of the speaker and constantambient conditions within the calibration site, the signal from the calibrated sensor may be compared to that from

the B&K reference and hence a calibration curve is produced.

Additionally, the low-frequency data from the Kulite sensor are corrected for the effects of wind tunnel noise

and vibration using an adaptive filtering scheme much like that described by Naguib et al. [5]. Two identical Kulite

sensors are installed into the wind tunnel separated by 8-12 boundary layer thicknesses. At this distance, the sensorscan be expected to return statistically identical signals but are sufficiently separated as to observe independent

turbulent events. Thus, the correlated portion of the two signals is due only to wind tunnel noise and the adaptive

filter yields a signal approximating the noise. By subtrase-cancelled signal is produced and its power spectrum reflects the true turbulence of the flow. See [4] for

details. This procedure was implemented only on the Kulite A-screen sensors, since it is these that produce thesignal used for the low-frequency portion of the spectrum.

One of the great difficulties with measuring fluctuating wall pressures in high-speed flows is the small spatial

scale associated with the high-frequency fluctuations relative to the size of the sensors themselves. Corcos [6]provides the most widely known analysis of the attenuation of pressure signals due to limited spatial resolution, in

which he characterizes the severity of the problem based upon the nondimensional sensor size, d/2Uc, where dis

the diameter of the sensors sensitive area and Uc is the convective velocity. Corcos finds that a nondimensional

sensor size of unity represents the 3-dB point of spatial attenuation; hence, when d/2Uc < 1 minimal signalattenuation occurs, and when d/2Uc > 1, si

d widely for incompressible flows and found to return useful results [1, 16, 17], though with limits. Lueptows

[18] analysis of a numerical simulation suggested that the Corcos correction is effective if roughly d/2Uc < 4,

which is consistent with Schewes [15] data.

In the present case, the 3-dB damping point for the Kulite A-screen sensor is 140 kHz based on the 1.02 mm

cavity in the sensor face; given that this sensor is effective only to about 40 kHz, spatial attenuation does not presenta difficulty. Conversely, the 3-dB damping point for the PCB132 based on the 1.6 mm2 sensitive area is 100 kHz,

which poses a considerable problem given that this sensor has a frequency response reaching 1 MHz. (The sensitivearea of the PCB132 actually is a rectangle 1.0 mm 1.6 mm, but its orientation is not marked on the sensor housing

and is indeterminate; satisfactory results have been obtained assuming a circular sensitive area of 1.6 mm2.) Corcos

[6] provides both a semi-empirical formula and tabulated values for the signal attenuation as a function ofd/2Uc,

which then can be used to correct measured values. However, to further complicate the problem, Uc is a function of because high-frequencies typically result from small-scale turbulent eddies near the wall, which convect at a

slower velocity than larger eddies further from the wall. Therefore, the convection velocity must first be known as a

function of the pressure fluctuation frequency, which can be difficult to directly measure for the small spatial scales

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at which it is most necessary. Corcos himself used a curve yielding Uc/U=0.8 for low frequencies and asymptoting

to 0.6 at high frequencies. In the present case, an equation fit to his curve has been adjusted to return Uc/U=0.85 at

low frequencies because cross-correlations between streamwise arrays of pressure sensors show this to be the correct

value at large wavelengths. Practically speaking, however, the Corcos correction is significant only at high

fre

cy range from 100 Hz to 400 kHz; the low frequency limit is determined by practical data processingrestrictions, and the high frequency limit is determined by the validity of the Corcos correction. This procedure

yields spectra over a much larger frequency provide alone, and it is explained in detail

in [

range of wind tunnel unit Reynolds

numbers ofRe=24 - 44 10 m for Machs 1.5, 2.0, and 2.5, andRe=32 - 44 106

m-1

for Mach 3.0 because theer values. This corresponds to values ofRe ranging from 24000 to 51000, depending

upo

quencies, where a constant Uc/U=0.6 is a reasonable approximation. However, the Lueptow [18] and Schewe[15] analyses limit the validity of the Corcos correction to 400 kHz for the PCB132; this represents the effective

high-frequency limit of measurements in the present study.

Once the data from the Kulite A-screen and PCB132 sensors have been calibrated, filtered, and corrected forspatial attenuation, they agree with each other quite well in their overlap range from about 20-40 kHz in fact, their

difference lies within the measurement uncertainty [4]. To create a spectrum ranging from the lowest to highest

measurable frequencies, these two signals can be merged by weighted averaging in the 20-40 kHz range, then using

the Kulite-A data below 20 kHz and the PCB132 data above 40 kHz. The result is a spectrum spanning the

frequen

range than either sensor can

4].

Results and Discussion

Data have been acquired at all three streamwise stations for six different values of freestream Reynolds numbers

at all four supersonic Mach numbers within the capability of the TWT. The complementary Pitot probe surveys atidentical conditions and stations provide the boundary layer thickness, the displacement thickness, and themomentum thickness. Inner boundary layer variables have been determined based upon the skin friction coefficient

found from the Sun and Childs [51] fit. Data have been acquired within a6 -1

TWT will not start at low

n station and Mach number. Run conditions are summarized in Table 1.

Pressure Power Spectra

Representative examples of the power spectral density of the pressure fluctuations are shown in Fig. 7 for each

of the four Mach numbers. Data are provided at the downstream station for a mid-range Re of about 35000,varying by 1000 between the Mach numbers. Data are given as a function of the angular frequency and have

been normalized based upon the freestream velocity U, the freestream dynamic pressure q, and the boundary layer

displacement thickness *. The pressure spectra clearly show that an increase in Mach number produces a reduction

Table 1: Experimental parameters.

Mach P0 (kPa) U (m/s) station (mm) *

(mm) (mm) cf(10-3

) Re

1.47 182 - 334 441 upstream 12.0 - 12.5 1.88 - 2.04 0.89 - 0.95 1.80 - 1.98 23000 - 39000

middle 13.9 - 14.4 2.16 - 2.34 1.02 - 1.09 1.76 - 1.92 26000 - 45000

downstream 16.0 - 16.5 2.45 - 2.63 1.16 - 1.24 1.73 - 1.88 30000 - 51000

1.98 217 - 398 537 upstream 10.0 - 10.3 1.81 - 1.97 0.64 - 0.69 1.77 - 1.93 17000 - 28000

middle 11.8 - 12.0 2.28 - 2.49 0.81 - 0.87 1.65 - 17.8 21000 - 36000

downstream 13.6 - 14.3 2.68 - 2.91 0.96 - 1.02 1.58 - 1.73 24000 - 42000

2.50 277 - 507 603 upstream 10.3 - 10.4 2.26 - 2.45 0.61 - 0.64 16.0 - 17.3 15000 - 27000

middle 12.4 - 12.5 2.81 - 3.06 0.76 - 0.80 15.1 - 16.4 19000 - 33000

downstream 14.7 - 15.0 3.46 - 3.76 0.94 - 0.99 14.5 - 15.5 24000 - 41000

3.02 478 - 660 649 upstream 11.3 - 11.4 3.13 - 3.26 0.64 - 0.66 13.8 - 14.4 21000 - 28000

middle 13.7 - 13.9 3.92 - 4.12 0.80 - 0.83 13.0 - 13.4 27000 - 35000

downstream 16.8 - 16.9 4.78 - 4.93 0.98 - 1.04 12.5 - 12.8 33000 - 43000

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Fig. 7: Power spectral densities of the wall pressure fluctuations at Re=35000 and the

downstream station. The light blue line shows data for Mach 2.0 prior to correction for spatial

attenuation. The thin black lines show data prior to compensation for wind tunnel noise.

in the normalized magnitude, though the shape of the spectra remains similar, which is consistent with the datacompiled by Laganelli et al [50]. The normalized frequency at which the rolloff becomes appreciable,

app

e large magnitude of the correction at high frequencies. Unfortunately, the

ele

fects are relatively mild in comparison to the magnitude of the

bou

roximately a value of 1, also is consistent with the spectra reported in [50]. In the Mach 2.5 spectrum, a small

spike may be seen near*/U = 0.6, which probably is attributable to an unsteady Mach wave disturbance residualfrom the nozzle expansion.

Additionally plotted in Fig. 7 is the slope defined by -1. Bradshaw [58] predicted that the lower frequency

range of the pressure spectra is induced by eddies in the logarithmic layer of the boundary layer and should exhibit a

-1 dependence. Panton and Linebargers [59] and Blakes [60] analyses each draw the same conclusion, but some

measurements have suggested that the slope actually is a little less than -1 if the Reynolds number is not sufficiently

large [19, 61]. In the present case, the Corcos-corrected spectra indicate a slope very close to -1 in the region where

the logarithmic layer is influential. The consistency of the present data with the predicted slope bolsters the

reliability of the present measurements and the approach taken to merge sensor signals. The light blue curve inFig. 7 is the power spectrum for Mach 2.0 prior to the implementation of the Corcos correction for spatial

attenuation, which highlights th

ctronic noise present at high frequencies becomes amplified as well, but this is an unavoidable consequence of an

otherwise successful application of the Corcos correction. It is evident that the -1 slope cannot be detected withoutthe use of the Corcos correction.

The thin black lines in Fig. 7 are the original noisy power spectra prior to the use of the adaptive filter for wind

tunnel noise cancellation. Clearly, the noise ef

ndary layer fluctuations and are constrained to frequencies below 1 kHz (and mostly below 500 Hz). The Mach1.5 and 2.0 data show a small but noteworthy reduction in amplitude once noise cancellation is implemented, but no

appreciable effect is found for Mach 2.5 and 3.0.

Another significant conclusion from the power spectra in Fig. 7 may be observed near the low-frequency limit.

The low-frequency behavior of boundary layer wall pressure spectra has proven to be somewhat controversial, withsome theories predicting a 2 dependence whereas others propose a slower decrease in the power as frequency

drops, or even a flat response (see Bulls summary in [17]). Experimentally, it is especially difficult to obtain

reliable measurements in this frequency range owing to the influence of facility noise and the limits ofinstrumentation. Of experiments that employed a noise-cancellation scheme, it would appear that only Farabee and

Casarella [21] have demonstrated the existence of the 2 regime; however, other such experiments [19, 20] that do

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(a) (b)

Fig. 8: Power spectra for Mach 2.0 at the downstream station for all six values ofRe; (a) absolute units; (b)

normalized units.

not support the

2

dependence do not reach as low a normalized frequency as do Farabee and Casarella.Significantly, glider experiments have returned mixed results [16, 62, 63] and atmospheric boundary layer

measurements [64] do not find the 2

regime, but again, these may not explore a sufficiently low frequency range.In the present case, the data clearly show no 2 dependence at low frequencies, instead indicating a flat or slightly

decreasing spectra except at Mach 1.5. A comparison of noise-cancelled signals to those prior to the adaptive

filt

oncerning the

ver

provides supporting evidence that the wall boundary layer

ering algorithm shows that only a small portion of the power spectrum amplitude is attributable to wind tunnelnoise, suggesting that a more finely tuned noise-cancellation filter would not be beneficial; similar results were

found when instead employing a subtractive noise-cancellation scheme like that of Simpson et al [65].

The measurement uncertainty is composed of the data repeatability and biases in the calibration and data

corrections. Three repeat runs were conducted for the Mach 2.0 conditions, providing a total of eight redundant data

sets since two sets of all the sensors were employed in each case. The uncertainty due to repeatability, found as the95% confidence interval, was determined from the scatter between these eight cases as 6 10-6, in normalized units.

The scatter was computed using a narrow rolling average across the spectra to remove the effects of the noise

between adjacent frequency bins, which shows that the difference between repeated measurements is quite small in

comparison to the routine noise in computing the spectra. The bias error principally lies in the sensor calibrations.Based upon repeated calibrations using the ultrasonic speaker, a range of calibration coefficients was established and

the extreme values used to re-reduce the data. This yielded a bias error of about 6 10-6, coincidentally the same as

the repeatability. Combining the two error sources leads to an uncertainty estimate of 8 10-6, which is the value plotted as an error bar in Fig. 7. Of course, additional uncertainty exists at higher frequencies c

acity of the Corcos correction. Lueptows work [18] suggests that the error will be considerably less than the 8

10-6 value already cited until the limit of the Corcos correction is approached, and hence can be neglected below thehighest measured frequencies, at which point the electronic noise becomes a greater concern anyway.

Data acquired at Mach 2.0 in the downstream station are shown in Fig. 8 for all six Reynolds numbers, where

Fig. 8a provides the results in absolute units and Fig. 8b shows them normalized. Even for this relatively mild

variation in Re, the gradual increase in magnitude of the power spectra is visible in Fig. 8a. However, once

normalized, all six cases collapse neatly into one curve. Results at other Mach numbers and streamwise stations aresimilar. Spectra at the three streamwise stations are given in Fig. 9, again with absolute units in Fig. 9a and

normalized units in Fig. 9b. The boundary layer thickness changes from 10.0 mm to 12.0 mm to 14.3 mm, fromupstream to middle to downstream stations, respectively. As the boundary layer thickens, the power spectrumdiminishes in amplitude slightly and shows the beginning of rolloff to the -1 slope at a lower frequency. Such

behavior may be attributed to the decrease in dynamic pressure required to maintain a constant Reynolds number

while the boundary layer thickness rises. The strength of the pressure fluctuations is proportional to the dynamic

pressure, so this change in freestream conditions is reflected in the power spectra. However, as Fig. 9b makes clear,the three power spectra appear to be identical in normalized form. Although differences near the high-frequency

limit are difficult to ascertain because of the prominence of sensor noise, the three curves collapse well throughout

the measurable spectrum. This successful normalization

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(a) (b)

Fig. 9: Power spectra for Mach 2.0 at the three streamwise stations for Re=28000; (a) absolute units; (b)

normalized units.

(a) (b)Fig. 10: Power spectra for Mach 2.0 normalized on inner variables; (a) varying Re at the downstream station; (b)

all three streamwise stations for constantRe=28000.

und

od using either approach. In contrast, Fig. 10b shows as good collapse across theentire measured spectrum for inner variables as for outer variables in Fig. 9b. The differing behavior of Fig. 10b

because the Reynolds number is held constant in the data of Fig. 10b whereas it

vari

od using either approach. In contrast, Fig. 10b shows as good collapse across theentire measured spectrum for inner variables as for outer variables in Fig. 9b. The differing behavior of Fig. 10b

because the Reynolds number is held constant in the data of Fig. 10b whereas it

vari

er investigation is in equilibrium. Once appropriately normalized, the Reynolds number, freestream conditions,

and streamwise station cease to influence the power spectra within the measurable frequency range; the only

parameter with an effect is the freestream Mach number.

The normalizations used in Figs. 8 and 9 are based upon outer flow variables, but have been quite successful to

the highest frequencies measurable in the present experiment, though these are considered to be mid-rangefrequencies within the hierarchy of boundary layer turbulence. Another nondimensionalization is based upon inner

flow variables and is shown in Fig. 10, where Fig. 10a shows inner variable normalization of the Mach 2.0 data at

multiple Reynolds numbers from Fig. 8 and Fig. 10b shows the analogous results using the Mach 2.0 data from thethree streamwise stations from Fig. 9. Figure 10a shows some degree of greater spread at low frequencies than the

outer variable scaling of Figs. 8b, which is as expected, but the collapse of the curves at higher measured

frequencies appears equally go

uilibrium. Once appropriately normalized, the Reynolds number, freestream conditions,

and streamwise station cease to influence the power spectra within the measurable frequency range; the onlyparameter with an effect is the freestream Mach number.

The normalizations used in Figs. 8 and 9 are based upon outer flow variables, but have been quite successful to

the highest frequencies measurable in the present experiment, though these are considered to be mid-rangefrequencies within the hierarchy of boundary layer turbulence. Another nondimensionalization is based upon inner

flow variables and is shown in Fig. 10, where Fig. 10a shows inner variable normalization of the Mach 2.0 data at

multiple Reynolds numbers from Fig. 8 and Fig. 10b shows the analogous results using the Mach 2.0 data from the

three streamwise stations from Fig. 9. Figure 10a shows some degree of greater spread at low frequencies than theouter variable scaling of Figs. 8b, which is as expected, but the collapse of the curves at higher measuredfrequencies appears equally go

compared with Fig. 10a may becompared with Fig. 10a may be

es for the data of Fig. 10a.

Pressure Fluctuation Intensity

The intensity of the measured pressure fluctuations can be reduced to a single defining parameter as the r.m.s. ofthe unsteady signal, p, just as in the historical data of Fig. 1. Ordinarily, this value simply is calculated from the

es for the data of Fig. 10a.

Pressure Fluctuation Intensity

The intensity of the measured pressure fluctuations can be reduced to a single defining parameter as the r.m.s. of

the unsteady signal, p, just as in the historical data of Fig. 1. Ordinarily, this value simply is calculated from the

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(a) (b)

Fig. 11: Pressure fluctuation magnitude as a function of Mach number. Filled gray points show the currentexperiment, colored points and lines show the historical database as in Figs. 1 and 4. Data are normalized by: (a)

dynamic pressure; (b) wall shear stress.

time-series pressure signal, but in the present case of merged data from multiple sensors combined with the Corcos

correction, p is found by integrating the power spectral density curves. Figure 11 plots the present results againstthe historical data of Figs. 1 and 4, using data at Re=35000 and the downstream station as representative of the

larger data set. The data are shown normalized by qe in Fig. 11a and by w in Fig 11b. The current measurements

are shown in three capacities; in one case, the corrected spectra (gradient triangles) are used to compute p, and in asecond case (delta triangles), the originally recorded data are used instead, without the Corcos corrections or the

noise cancellation. The third set of points (diamonds) will be explained subsequently. The corrected data yield

results somewhat in excess of the bulk of the historical data, but the uncorrected data fall towards the lower end of

its wide scatter; this is true whether normalized by freestream dynamic pressure or wall shear stress. Few of thehistorical experiments have employed the Corcos correction that has proven key to providing correct power spectra

at high frequencies in the present work. Given that the current measurements agree fairly well with the bulk of thehist

ofp and those ofthe

orical data when no corrections are used but rise appreciably above it with corrections, it would appear that much

of the historical database for supersonic and hypersonic pressure fluctuations may be biased low. The sameconclusion is evident regardless of normalization parameter.

The nondimensional frequency of the measurements in TWT, /U, was calculated using the cutoff frequency

due to spatial resolution, =Uc/d. This must be done twice, once for the uncorrected TWT measurements and again

for the Corcos-corrected measurements. Figure 12 displays the results superposed over the corresponding valuesfrom Figs. 3a and 5 for the historical database. The current frequency limitations well fit those of the historical data,

with the corrected data points possessing nondimensional frequencies equivalent to other experiments returning the

largest values of pressure fluctuation intensity. Similarly, the reduced values of the nondimensional frequencies for

the uncorrected TWT data points are close to those of the historical data clustered nearby. These observations are

true whetherp is normalized by qe orw. The consistency of the TWT results, both the valuesfrequency response /U used to obtain them, with those of the historical data provide further support for the

notion that the largest values ofp are more likely to be correct and the bulk of the historical data is biased low just as the limited frequency response of the uncorrected TWT data bias low their values ofp.

Even with the data corrections and measurements extending to 400 kHz, the full range of energy-containing

turbulent eddies has not been captured by the present measurements. Somewhere beyond the -1 dependence of thelogarithmic layer, the spectra can be expected to transition to a steeper slope and become proportional to -5 as small

wavelength eddies very near the wall and viscosity effects become dominant [60]. This high-frequency region has

been confirmed in such incompressible experiments as [19, 20] and its onset can be expected at about /u2=0.3

[21], which translates to about =350-500 kHz in the current experiment depending upon conditions. The spectrum

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(a) (b)

Fig. 12: Data points shaded by sensor non-dimensional cutoff frequency, normalized by: (a) dynamic pressure; (b)

wall shear stress. Circles represent the historical database as from Figs. 3a and 5, delta triangles the TWT

uncorrected data points from Fig. 11a, and gradient triangles the TWT corrected data points from Fig. 11b.

is believed to pass through a region proportional to -7/3

as it transitions from -1 to -5 [15, 66], fully reachingthe -5 dependency at about /u

2=1.0 [60]. Effects of

the high-frequency portion of the spectrum have been

appended to the present data by extending the

logarithmic region to its limit at /u2=0.3, then

following the -7/3 dependence until /u2=1, at which

point the -5 dependence is obeyed until the spectra has

fallen to such low levels that it contains no significant

energy. This extended spectrum is sketched in Fig. 13

for the Mach 2 case. Integration over the augmentedcurve yields a value forvalue forp that estimates the increased

inte

spe

p that estimates the increased

inte

spe

nsity when the entire spectrum is accounted; thesevalues are shown in Fig. 11 as the TWT extended

data points (diamonds). The integrated value of the

estimated high-frequency region is within about 10% of

that calculated by Farabee and Casarella [21], which

lends some confidence to the utility of this exercise.Clearly, Fig. 11 shows that additional energy is contained in the immeasurable portion of the spectrum,

providing further evidence that the historical database is biased low from the true value of pressure fluctuation

intensity. The exact values of the extended spectra are no better than an estimate, since they extrapolate from

generalized behavior found for incompressible flows rather than providing any new data at such extraordinarilylarge frequencies, but they do indicate that substantial energy is missed by any achievable supersonic measurement.

However, in many practical cases for flight vehicle design, the neglected fluctuation energy may be of minimal

concern. Between the Corcos correction and the unmeasured -5 region, the great majority of the lost energy lies atvery high frequencies. Most fluid-structure interactions occur at considerably lower frequencies and the linear, or

nearly so, structural response of most vehicle components indicates that the behavior at the lower portions of the

nsity when the entire spectrum is accounted; thesevalues are shown in Fig. 11 as the TWT extended

data points (diamonds). The integrated value of the

estimated high-frequency region is within about 10% of

that calculated by Farabee and Casarella [21], which

lends some confidence to the utility of this exercise.Clearly, Fig. 11 shows that additional energy is contained in the immeasurable portion of the spectrum,

providing further evidence that the historical database is biased low from the true value of pressure fluctuation

intensity. The exact values of the extended spectra are no better than an estimate, since they extrapolate from

generalized behavior found for incompressible flows rather than providing any new data at such extraordinarilylarge frequencies, but they do indicate that substantial energy is missed by any achievable supersonic measurement.

However, in many practical cases for flight vehicle design, the neglected fluctuation energy may be of minimal

concern. Between the Corcos correction and the unmeasured -5 region, the great majority of the lost energy lies atvery high frequencies. Most fluid-structure interactions occur at considerably lower frequencies and the linear, or

nearly so, structural response of most vehicle components indicates that the behavior at the lower portions of the

Fig. 13: Data for Mach 2 extended to higher

frequencies by estimating the power spectrum shape.

ctrum is of greater importance. Conversely, other flight applications, particularly those motivated by

aeroacoustics, are concerned with much higher frequency events, and therefore accurate prediction across the entirespectrum may be more relevant.

The dependence of the measured pressure fluctuation intensities on Reynolds number was examined to compare

with the limited results from the compressible historical database. Figure 14 shows trends againstRe for both p/qe

and p/w, given in Figs. 14a and 14b respectively using the corrected power spectra. Values ofp resulting from

ctrum is of greater importance. Conversely, other flight applications, particularly those motivated byaeroacoustics, are concerned with much higher frequency events, and therefore accurate prediction across the entire

spectrum may be more relevant.

The dependence of the measured pressure fluctuation intensities on Reynolds number was examined to compare

with the limited results from the compressible historical database. Figure 14 shows trends againstRe for both p/qe

and p/w, given in Figs. 14a and 14b respectively using the corrected power spectra. Values ofp resulting from

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(a) (b)

Fig. 14: Pressure fluctuation intensity as a function of momentum thickness Reynolds number, normalized by: (a)

dynamic pressure; (b) wall shear stress. Delta triangles represent the upstream station, squares the middle station,

and gradient triangles the downstream station. Power-law curve fits also are shown.

the extended spectra are not considered because these are approximate estimates based upon theory andincompressible experiments rather than measured data. Data from the three streamwise stations are shown using

different symbols, from which it can be seen that the three stations collapse well into one curve for each Mach

number when p is normalized by qe. At Mach 1.5, the pressure fluctuation intensity s

from the three streamwise stations are shown using

different symbols, from which it can be seen that the three stations collapse well into one curve for each Mach

number when p is normalized by qe. At Mach 1.5, the pressure fluctuation intensity shows a very slight increase

wit

e Pitot probe surveys in comparison to the easily obtained values of q.

Nevertheless, the data show a clear trend of rising p/w asRe increases for all Mach numbers, though the strengththe w-normalized results at each streamwise station may contribute to the

stre

d tunnel testing, and the Goody [68] model for a broad range of Reynolds numbers in

inc

hows a very slight increase

wit

e Pitot probe surveys in comparison to the easily obtained values of q.

Nevertheless, the data show a clear trend of rising p/w asRe increases for all Mach numbers, though the strengththe w-normalized results at each streamwise station may contribute to the

stre

d tunnel testing, and the Goody [68] model for a broad range of Reynolds numbers in

inc

h Reynolds number, but at the other three Mach numbers, clear decreasing trends are seen consistent withprevious high-speed studies [32, 33, 43, 44]. A power-law curve fit to each Mach number also is provided, from

which a dependency for the three larger Mach numbers of about p/qe ~Re-0.1 emerges.

When scaled by w in Fig. 14b, the results become considerably more jumbled. More scatter is observedbetween points acquired at different streamwise stations and three of the four Mach numbers exhibit significant

overlap. The contrast of this variability with the smooth and consistent curves of Fig. 14a may indicate difficulties

in the measurement of w from th

h Reynolds number, but at the other three Mach numbers, clear decreasing trends are seen consistent withprevious high-speed studies [32, 33, 43, 44]. A power-law curve fit to each Mach number also is provided, from

which a dependency for the three larger Mach numbers of about p/qe ~Re-0.1 emerges.

When scaled by w in Fig. 14b, the results become considerably more jumbled. More scatter is observedbetween points acquired at different streamwise stations and three of the four Mach numbers exhibit significant

overlap. The contrast of this variability with the smooth and consistent curves of Fig. 14a may indicate difficulties

in the measurement of w from th

of the trend varies. Differences inof the trend varies. Differences in

ngth of the rising trend in p/w.

Comparison to Predictive Models

During the many decades in which wall pressure spectra have been measured and analyzed, a number of semi-

empirical engineering models have been developed. Such models may be compared to the present data as a means

of assessing their robustness and applicability to the current flow conditions. To date, the present data have beencompared to the Maestrello [33] model that was derived from supersonic wind tunnel wall measurements, the

Laganelli [50] model designed for supersonic and hypersonic attached boundary layers, the Efimtsov model [67]

based on aircraft win

ngth of the rising trend in p/w.

Comparison to Predictive Models

During the many decades in which wall pressure spectra have been measured and analyzed, a number of semi-

empirical engineering models have been developed. Such models may be compared to the present data as a means

of assessing their robustness and applicability to the current flow conditions. To date, the present data have beencompared to the Maestrello [33] model that was derived from supersonic wind tunnel wall measurements, the

Laganelli [50] model designed for supersonic and hypersonic attached boundary layers, the Efimtsov model [67]

based on aircraft win

ompressible boundary layers. The Goody model is of interest despite its lack of compressibility effects becauseHwang et als [69] recent review of several models finds it demonstrates the best performance, perhaps in part due

to its recent pedigree.Figure 15 shows the present data at all four Mach numbers compared to the aforementioned models. The data

are shown for the downstream station and a common Re=35000 (same as Fig. 7), but given the normalized

parameters, any of the data acquired in the present work will collapse to one of these four curves depending upon

Mach number. A common trend immediately identifiable in Fig. 15 is that every model returns amplitudes

considerably less than the measurements. For the Maestrello, Laganelli, and Efimtsov models, which are based

upon experimental data in the compressible regime, this may be a reflection of the low magnitudes returned formuch of the historical database in comparison to the present work. The Goody model, on the other hand, is built

upon more recent data believed to exhibit greater accuracy, so instead may be due to differences between the

incompressible and compressible flow regimes. The Laganelli and Efimtsov models do not return a 2 dependence,

ompressible boundary layers. The Goody model is of interest despite its lack of compressibility effects becauseHwang et als [69] recent review of several models finds it demonstrates the best performance, perhaps in part due

to its recent pedigree.Figure 15 shows the present data at all four Mach numbers compared to the aforementioned models. The dataare shown for the downstream station and a common Re=35000 (same as Fig. 7), but given the normalized

parameters, any of the data acquired in the present work will collapse to one of these four curves depending upon

Mach number. A common trend immediately identifiable in Fig. 15 is that every model returns amplitudes

considerably less than the measurements. For the Maestrello, Laganelli, and Efimtsov models, which are based

upon experimental data in the compressible regime, this may be a reflection of the low magnitudes returned formuch of the historical database in comparison to the present work. The Goody model, on the other hand, is built

upon more recent data believed to exhibit greater accuracy, so instead may be due to differences between the

incompressible and compressible flow regimes. The Laganelli and Efimtsov models do not return a 2 dependence,

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(a) (b)

Fig. 15: Comparison of current data from Fig. 7 to engineering models; (a) Maestrello [33] and Laganelli [50]

models; (b) Efimtsov [67] and Goody models [68].

by design, which matches the present experimentalobservations; if a 2 dependence does exist, the

Maestrello and Goody models predict it to reach toohigh a frequency. The Maestrello and Laganelli models

do not display an appropriate -1 trend at the highest

measurable frequencies, but the Efimtsov and Goody

models appear to come close. The Goody modelactually is designed -0.7to reach a dependence for

suf

but still do not accurately reflect the measurements. The magnitudes of the modified Laganelli

pre

onsideration returns robust and accurate results in comparison tothe present measurements. This may be partly explained by their basis in historical measurements likely to have

been biased towards lower magnitudes and suffer cy response limitations. Further development ofsuc

ficiently large Reynolds number, which is consistent

with some incompressible data [68]. Finally, all models

show the correct trend of a reduced fluctuation

magnitude as the Mach number increases, although theymay not well predict the spread in magnitudes as the

Mach number varies (most notably, Laganelli).

The Laganelli model was developed assuming the

incompressible pressure fluctuation intensity ofp/qe=0.006, which now is believed to be more

accurately stated as p/qe=0.009. Laganelli himself

recognized the evolution of the accepted incompressible value and used p/qe=0.0078 in a subsequent model [3].Laganellis original model [50] is easily adjusted to incorporate the p/qe=0.009 value and is shown in Fig. 16.

Similarly, a compressible adjustment to Goodys model [68] may be attempted by introducing Laganelliscompressible correction factor to the magnitude of the incompressible skin friction coefficient. These two modified

predictions are displayed in Fig. 16, demonstrating that each returns results nearer the data than their original

formulations,

Fig. 16: Comparison of current data from Fig. 7 to themodified Laganelli and Goody models.

dictions reside nearer the group average at low frequencies, but still fail to exhibit the spread between Mach

numbers found in the data. The modified Goody model continues to return magnitudes well below that of the

present data.

Clearly, none of the predictive models under c

ed from frequenh models for compressible flows is warranted.

Conclusions

Accurate measurement of fluctuating wall pressure spectra beneath a supersonic turbulent boundary layer has proven elusive, such that a compilation of past efforts exhibits an alarming degree of scatter and hinders the

development of engineering models. Recent experiments conducted in Sandias Trisonic Wind Tunnel up to Mach 3

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have provided wall pressure data to frequencies reaching 400 kHz to help reconcile conflicts in the historical data

and promote the reliability of predictive modeling and simulation. Data were acquired using piezoresistive silicon

pressure transducers effective at low- and mid-range frequencies, then supplemented by piezoelectric quartz sensors

capable of detecting very high frequency events. The two sensor types were calibrated based upon a condenser

mic

existent. Variations in the Reynolds number of the

flo

ase for supersonic

and hypersonic pressure fluctuations may be biased low. Several semi-empirical predictive models have beendeveloped based upon historical data subject t mitations, but none of those considered in the

pre

ntryvehicles. The compilation of the historical database was begun by Fred Blottner, now retired from Sandia, and the

authors are grateful for his contribution. He also plementations of three of the four power spectra

References

rophone reference standard, then their resulting data combined into a single curve describing the wall pressurespectra. Data were corrected for spatial attenuation at high frequencies using the Corcos correction and for wind-

tunnel noise and vibration at low frequencies using a noise cancellation algorithm based upon adaptive filtering.

The resulting data revealed the -1 dependence for fluctuations within the logarithmic region of the boundarylayer, as predicted by theory and found in some incompressible experiments. The power spectra are essentially flat

at low frequency and do not exhibit the theorized 2 dependence; measurements reached sufficiently low

frequencies that this region should have been evident were it

w or the streamwise location of the measurement are observable in absolute units but collapse to a single curvefor each Mach number when normalized by outer flow variables. Normalization by inner flow variables is

successful for the -1 region but less so for lower frequencies.

The overall magnitude of the pressure fluctuation intensity was calculated by integrating each power spectrum

and comparing the results to the historical database of compressible boundary layer measurements. A power-lawdependence was found of decreasing intensity as the Reynolds number was raised when normalized by the

freestream dynamic pressure, but increasing intensity when normalized by the wall shear stress. Data employing the

Corcos correction yield results somewhat in excess of the bulk of the historical data, but the uncorrected data falltowards the lower end of its wide scatter; this is true whether normalized by freestream dynamic pressure or wall

shear stress. The effect becomes considerably greater when an estimate is made for the very high frequencyfluctuations beyond the reach of the measurement capability. A detailed examination of fifty years of historical data

reveals that the reported magnitude of the pressure fluctuation intensity chiefly is a function of the frequency

response of the sensors used. When the present results are considered without the Corcos correction, the resulting

frequency response is consistent with prior experiments that produced similarly low pressure fluctuation intensities;conversely, when the Corcos correction is used, the frequency response matches those experiments that returned

elevated pressure fluctuation intensities. These trends suggest that much of the historical datab

o these measurement li

sent study accurately represents the power spectra acquired during the present experiments.

Acknowledgments

The authors would like to thank Ryan Bond, Larry DeChant, Rich Field, Keith Miller, Jeff Payne, and Jerry

Rouse for numerous invaluable conversations regarding the physics of pressure fluctuations relevant to re-e

developed im

predictive models used herein. Tom Grasser designed much of the mounting hardware for the pressure sensors.

[1] Dolling, D. S., and Dussauge, J. P., Fluctuating Wall Pressure Measurements, AGARD-AG-315: A Survey of

Measurements and Measuring Techniques in Rapidly Distorted Compressible Turbulent Boundary Layers, May 1989, pp. 8-1 to 8-18.Dolling, D. S., and Na[2] rlo, J. C., Driving Mechanism of Unsteady Separation Shock Motion in Hypersonic InteractiveFlow, AGARD-CP-428:Aerodynamics of Hypersonic Lifting Vehicles, April 1987.

Laganelli, A. L., and Hinrichsen, R. L., Surface Pressure Fluctuation Correla[3] tions for High-Speed Flow, AIAA Paper2000-2039, June 2000.

Beresh, S. J., Henfling, J. F., Spillers, R. W., and Pruett, B. O. M., Measurem[4] ent of Fluctuating Wall Pressures Beneath aSupersonic Turbulent Boundary Layer, AIAA Paper 2010-0305, January 2010.Naguib, A. M[5] ., Gravante, S. P., and Wark, C. E., Extraction of Turbulent Wall-Pressure Time-Series using an OptimalFiltering Scheme,Experiments in Fluids, Vol. 22, No. 1, 1996, pp. 14-22.

Corcos, G. M., Resolu[6] tion of Pressure in Turbulence,Journal of the Acoustical Society of America, Vo.. 35, No. 2, 1963,pp. 192-199.Houbolt, J. C., On the Estimation of Pr[7] essure Fluctuations in Boundary Layers and Wakes, General Electric Report TIS66SD296, April 1966.

Lowson, M. V., Prediction of Boundary Layer Pre[8] ssure Fluctuations, Air Force Flight Dynamics Laboratory TechnicalReport AFFDL-TR-67-167, April 1968.

-17-


8/9/2019 Man 224989

18/19

[9] Laganelli, A. L., Martellucci, A., and Shaw, L., Prediction of Surface Pressure Fluctuations in Hypersonic TurbulentBoundary Layers, AIAA Paper 76-409, July 1976.

[10] Willmarth, W. W., and Wooldridge, C. E., Measurements of the Fluctuating Pressure at the Wall Beneath a ThickTurbulent Boundary Layer,Journal of Fluid Mechanics, Vol. 14, 1962, pp. 187-210.

Journal of Fluid Mechanics, Vol. 22, Part 1, 1965, pp. 81-84.

54.

o. 4, 1976, pp. 597-599.

l. 36, No. 10, 1998, pp. 1808-1816.

rs,AIAA Journal, Vol. 38, No. 10, 2000, pp. 1822-1831.

Paper 68-77, January 1968.

AIAA Paper 73-996, October 1973.

ASA CR-2449, 1974.

ds, AIAA Paper 77-113, January 1977.

1181.

SA TN-D-2247, 1964.

per 81-1287, June 1981.

[11] Willmarth, W. W., and Roos, F. W., Resolution and Structure of the Wall Pressure Field Beneath a Turbulent BoundaryLayer,

[12] Bull, M. K., Wall-Pressure Fluctuations Associated with Subsonic Turbulent Boundary Layer Flow, Journal of Fluid

Mechanics, Vol. 28, Part 4, 1967, pp. 719-7[13] Shattuck, R. D., Sound Pressures and Correlations of Noise on the Fuselage of a Jet Aircraft in Flight, NASA TN-D-1086,1961.

[14] Bull, M. K., and Thomas, A. S. W., High Frequency Wall-Pressure Fluctuations in Turbulent Boundary Layers,Physics ofFluids, Vol. 19, N

[15] Schewe, G., On the Structure and Resolution of Wall-Pressure Fluctuations Associated with Turbulent Boundary-Layer

Flow,Journal of Fluid Mechanics, Vol. 134, 1983, pp. 311-328.[16] Willmarth, W. W., Pressure Fluctuations Beneath Turbulent Boundary Layers,Annual Review of Fluid Mechanics, Vol. 7,

1975, pp. 13-38.

[17] Bull, M. K., Wall-Pressure Fluctuations Beneath Turbulent Boundary Layers: Some Reflections on Forty Years ofResearch,Journal of Sound and Vibration, Vol. 190, No. 3, 1996, pp. 299-315.

[18] Lueptow, R. M., Transducer Resolution and the Turbulent Wall Pressure Spectrum, Journal of the Acoustical Society ofAmerica, Vol. 97, No. 1, 1995, pp. 370-378.

[19] Gravante, S. P., Naguib, A. M., Wark, C. E., and Nagib, H. M., Characterization of the Pressure Fluctuations Under a FullyDeveloped Turbulent Boundary Layer,AIAA Journal, Vo

[20] Goody, M. C., and Simpson, R. L., Surface Pressure Fluctuations Beneath Two- and Three-Dimensional TurbulentBoundary Laye

[21] Farabee, T. M., and Casarella, M. J., Spectral Features of Wall Pressure Fluctuations Beneath Turbulent Boundary Layers,Physics of Fluids A, Vol. 3, No. 10, 1991, pp. 2410-2420.

[22] Chung, K. M., and Lu, F. K., An Experimental Study of a Cold-Wall Hypersonic Boundary Layer, AIAA Paper 92-0312,January 1992.

[23] Chyu, W. J., and Hanly, R. D., Power and Cross-Spectra and Space-Time Correlations of Surface Fluctuating Pressures atMach Numbers Between 1.6 and 2.5, AIAA

[24] Coe, C. F., Chyu, W. J., and Dods, J. B. Jr., Pressure Fluctuations Underlying Attached and Separated SupersonicTurbulent Boundary Layers and Shock Waves,

[25] Coe, C. F., Surface-Pressure Fluctuations Associated with Aerodynamic Noise, Basic Aerodynamic Noise Research,NASA Report SP-207, 1969, pp. 409-424.

[26] Harvey, W. D., Bushnell, D. M., and Beckwith, I. E., Fluctuating Properties of Turbulent Boundary Layers for MachNumbers Up to 9, NASA TN D-5496, 1969.

[27] Heller, H. H., and Clemente, A. R., Unsteady Aerodynamic Loads on Slender Cones at Free-Stream Mach Numbers from 0

to 22, AIAA Paper 73-998, October 1973.[28] Heller, H. H., and Clemente, A. R., Fluctuating Surface-Pressure Characteristics on Slender Cones in Subsonic,

Supersonic, and Hypersonic Mach Number Flow, N[29] Howe, J. R., and Laganelli, A. L., Surface Pressure Fluctuation Measurements in Attached Transitional/Turbulent

Boundary Layers at Supersonic and Hypersonic Spee[30] Laganelli, A. L., and Howe, J. R., Prediction of Pressure Fluctuations Associated with Maneuvering Re-Entry Weapons,

Air Force Report AFFDL-TR-77-59, Vol. 1, 1977.[31] Garg, S., and Settles, G. S., Unsteady Pressure Loads Generated by Swept-Shock-Wave/Boundary-Layer Interactions,

AIAA Journal, Vol. 34, No. 6, 1996, pp. 1174-[32] Kistler, A. L., and Chen, W. S., The Fluctuating Pressure Field in a Supersonic Turbulent Boundary Layer, Journal of

Fluid Mechanics, Vol. 16, No. 1, 1963, pp. 41-64.[33] Maestrello, L., Radiation from and Panel Response to a Supersonic Turbulent Boundary Layer, Journal of Sound and

Vibration, Vol. 10, No. 2 1969, pp. 261-295.[34] Martelucci, A., Chaump, L., and Rogers, D., Experimental Determination of the Aeroacoustic Environment about a Slender

Cone,AIAA Journal, Vol. 11, No. 5, pp. 635-642, 1973.[35] Chaump, L. E., Martellucci, A., and Monfort, A., Aerodynamic Loads Associated with High Beta Re-Entry Vehicles, Air

Force Report AFFDL-TR-72-138, Vol. 1, 1973.[36] Murphy, J. S., Bies, D. A., Speaker, W. V., and Franken, P. A., Wind Tunnel Investigation of Turbulent Boundary Layer

Noise as Related to Design Criteria for High Performance Vehicles, NA[37] Dolling, D. S., and Bogdonoff, S. M., An Experimental Investigation of the Unsteady Behavior of Blunt Fin-Induced

Shock Wave Turbulent Boundary Layer Interactions, AIAA Pa

[38] Dolling, D. S., and Murphy, M. T., Unsteadiness of the Separation Shock Wave Structure in a Supersonic CompressionRamp Flowfield,AIAA Journal, Vol. 21, No. 12, 1983, pp. 1628-1634.

[39] Dolling, D. S., and Or, C. T., Unsteadiness of the Shock Wave Structure in Attached and Separated Compression Ramp

Flows,Experiments in Fluids, Vol. 3, No. 1, 1985, pp. 24-32.

-18-


8/9/2019 Man 224989

19/19

-19-


-21.

,AIAA Journal, Vol. 26, No. 2, 1988, pp. 179-187.

at Re =2400,AIAA Journal, Vol. 47, No. 2, 2009, pp. 373-385.

urbed by Steps and Shock Waves, NASA CR-486, 1966.

ry 1991.

ents in Fluids, Vol. 18, No. 1-2, 1994, pp. 69-81.

ttached Boundary-Layer Flow, AIAA

[53] in Applied Mechanics, Vol. 4, 1956, pp. 1-51.

054, June 2009.

, AIAA Paper 2008-1153, January 2008.

coustical Society of America, Vol. 119, No. 1, 2006, pp. 320-329.,

[59] Layers, Journal of

[60] anics of Flow-Induced Sound and Vibration, Academic Press, New York, 1986, pp. 497-594.

anics, Vol. 97, Part 2, 1980, pp. 299-319.Wall Pressure and its

[65] Surface Pressure Fluctuations in a Separating Turbulent Boundary

[66] A. S., and Yaglom, A. M., Statistical Fluid Mechanics, Vol. 2, MIT Press, 1975, pp. 375-377.

8] Goody, M., Empirical Spectral Model of Surface Pressure Fluctuations, AIAA Journal, Vol. 42, No. 9, 2004, pp. 1788-1794.

[69] Hwang, Y. F., Bonness, W. K., and Hambric, S. A., Comparison of Semi-Empirical Models for Turbulent Boundary Layer

Wall Pressure Spectra,Journal of Sound and Vibration, Vol. 319, No. 1-2, 2009, pp. 199-217.

[40] Tan, D. K. M., Tran, T. T., and Bogdonoff, S. M., Wall Pressure Fluctuations in a Three-Dimensional Shock-Wave /Turbulent Boundary Interaction,AIAA Journal, Vol. 25, No. 1, 1987, pp. 14

[41] Muck, K. C., Andreopoulos, J., and Dussauge, J. P., Unsteady Nature of Shock-Wave/Turbulent Boundary-LayerInteraction

[42] Ringuette, M. J., Bookey, P., Wyckham, C., and Smits, A. J., Experimental Study of a Mach 3 Compression RampInteraction

[43] Raman, K. R., Surface Pressure Fluctuations in Hypersonic Turbulent Boundary Layers, AIAA Paper 73-997, October

1973.[44] Raman, K. R., A Study of Surface Pressure Fluctuations in Hypersonic Turbulent Boundary Layers, NASA CR-2386,1974.

[45] Speaker, W. V., and Ailman, C. M., Spectra and Space-Time Correlations of the Fluctuating Pressures at a Wall Beneath aSupersonic Turbulent Boundary Layer Pert

[46] Dolling, D. S., and Smith, D. R., Unsteady Shock-Induced Turbulent Separation in Mach 5 Cylinder Interactions, AIAA

Paper 88-0305, January 1988.[47] Unalmis, O. H., and Dolling, D. S., Decay of Wall Pressure Field and Structure of a Mach 5 Adiabatic Turbulent Boundary

Layer, AIAA Paper 94-2363, June 1994.

[48] Gibson, B., and Dolling, D. S., Wall Pressure Fluctuations Near Separation in a Mach 5 Sharp Fin-Induced TurbulentInteraction, AIAA Paper 91-0646, Janua

[49] Thomas, F. O., Putnam, C. M., and Chu, H. C., On the Mechanism of Unsteady Shock Oscillation in ShockWave/Turbulent Boundary Layer Interactions,Experim

[50] Laganelli, A. L., Martelucci, A., and Shaw, L. L., Wall Pressure Fluctuations in AJournal, Vol. 21, No. 4, 1983, 495-502.

[51] Sun, C-C., and Childs, M. E., A Modified Wall Wake Velocity Profile for Turbulent Compressible Boundary Layers,Journal of Aircraft, Vol. 10, No. 6, 1973, pp. 381-383.

[52] White, F. M., Viscous Fluid Flow, 2nd Ed., McGraw-Hill Inc., 1991, pp. 415-417.Clauser, F. H., The Turbulent Boundary Layer, Advances

[54] Casper, K. M., Beresh, S. J., Henfling, J. F., Spillers, R. W., and Schneider, S. P., Pressure Fluctuations in Laminar,Transitional, and Turbulent Hypersonic Boundary Layers, AIAA Paper 2009-4

[55] Fujii, K., Experiment of the Two-Dimensional Roughness Effect on Hypersonic Boundary-Layer Transition, Journal of

Spacecraft and Rockets, Vol. 43, No. 4, 2006, pp. 731-738.[56] Estorf, M., Radespiel, R., Schneider, S. P., Johnson, H. B., and Hein, S., Surface-Pressure Measurements of Second-Mode

Instability in Quiet Hypersonic Flow

[57] Zuckerwar, A. J., Herring, G. C., and Elbing, B. R., Calibration of the Pressure Sensitivity of Microphones by a Free-FieldMethod at Frequencies up to 80 kHz,Journal of the A

[58] Bradshaw, P., Inactive Motion and Pressure Fluctuations in Turbulent Boundary Layers, Journal of Fluid MechanicsVol. 30, No. 2, 1967, pp. 241-258.

Panton, R. L., and Linebarger, J. H., Wall Pressure Spectra Calculations for Equilibrium Boundary

Fluid Mechanics, Vol. 65, No. 2, 1974, pp. 261-287.Blake, W. K., Mech

[61] Tsuji, Y., Fransson, J. H. M., Alfredsson, P. H., and Johansson, A. V., Pressure Statistics and their Scaling in High-Reynolds-Number Turbulent Boundary Layers,Journal of Fluid Mechanics, Vol. 585, 2007, pp. 1-40.

[62] Hodgson, T. H., On the Dipole Radiation from a Rigid and Plane Surface, Proceedings of the Purdue Noise ControlConference, 1971.

[63] Panton, R. L., Goldman, A. L., Lowery, R. L., and Reischman, M. M., Low-Frequency Pressure Fluctuations inAxisymmetric Turbulent Boundary Layers,Journal of Fluid Mech

[64] Klewicki, J. C., Priyadarshana, P. J. A., and Metzger, M. M., Statistical Structure of the FluctuatingIn-plane Gradients at High Reynolds Number,Journal of Fluid Mechanics, Vol. 609, 2008, pp. 195-220.

Simpson, R. L., Ghodbane, M., and McGrath, B. E.,Layer,Journal of Fluid Mechanics, Vol. 177, 1987, pp. 167-186.Monin,

[67] Efimtsov, B. M., Similarity Criteria for the Spectra of Wall Pressure Fluctuations in a Turbulent Boundary Layer, Soviet

Physics Acoustics, Vol. 30, No. 1, 1984, pp. 33-35.[6

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