Transmission of a turbulent boundary layer wall pressure field through an elastomeric coating

Ocean Engineering 47 (2012) 43–49

Contents lists available at SciVerse ScienceDirect

Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng

Transmission of a turbulent boundary layer wall pressure field through an elastomeric coating William L. Keith n, Alia W. Foley, Kimberly M. Cipolla Devices, Sensors, and Materials Research and Development Branch, Naval Undersea Warfare Center, Newport, RI 02841

a r t i c l e i n f o

abstract

Article history: Received 3 May 2011 Accepted 12 March 2012 Editor-in-Chief: A.I. Incecik Available online 4 April 2012

The wall pressure fluctuations beneath a turbulent boundary layer introduce flow-induced noise and vibration which limits the performance of acoustic arrays. One method for mechanically filtering this energy is to separate the acoustic sensors from the fluid–solid interface with an elastomeric coating. Long wavelength acoustic energy is transmitted across the coating, and shorter wavelength energy from convected turbulence is attenuated. Experiments were conducted in an acoustically quiet water tunnel to measure the wall pressure fluctuations under 0.635 mm and 1.27 mm thick elastomeric coatings. Autospectra, magnitude and phase of the coherence, and convection velocities are presented for the range of Reynolds numbers 7540 o Rey o 16,100. The autospectra display an exponential decay which increases with increasing frequency and coating thickness. A modified model of that given by Blake (1984) is shown to accurately predict the attenuations in the autospectra. The cross-spectral model given by Corcos (1963) is shown to be valid for measurements of the wall pressure coherence beneath the coatings. Published by Elsevier Ltd.

Keywords: Flow noise Turbulent boundary layer SONAR

1. Introduction Turbulent boundary layers at moderate to high Reynolds numbers and low mach numbers are a primary source of direct flow noise and flow-induced noise for hull-mounted and towed undersea acoustic sensors. The fluctuating wall pressure and wall shear stress at the fluid–solid interface generate a stress field which is transmitted to the acoustic sensors. Efforts aimed at active or passive control of the turbulent field for noise reduction are often impractical due to cost and physical constraints. Elastomeric coatings offer a passive mechanical filtering approach which leads to significant attenuation in the wall pressure field. At moderate to low frequencies, acoustic waves of interest are transmitted through the coating which is designed to have approximately the same acoustic impedance as water (Ramotowski and Jenne (2003)). The smaller wavelength (or higher wavenumber) wall pressure fluctuations are attenuated, typically decaying exponentially across the coating as shown in Fig. 1. A significant amount of research was focused on the use of compliant coatings for drag reduction during the 1970s and 1980s (Bushnell et al. (1977), Gad-el-Hak (1986, 1987), Voropayev and Babenko (1978), Kanarskiy and Teslo (1980); Semenov et al. (1985)). Hess (1990) found that soft, highly compliant coatings

n

Corresponding author. Tel.: 401 832 5191. E-mail address: [email protected] (W.L. Keith).

0029-8018/$ - see front matter Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.oceaneng.2012.03.011

in water could lead to reductions in mean wall shear stress of approximately 5% at most. Keith (1987) found no effect of a urethane coating in water on the wall pressure autospectra measured at the fluid–solid coating interface, in comparison to the rigid wall case. The coatings used there were similar to those of the present investigation, with approximately the same acoustic impedance as water but of significantly greater thickness (16 mm). For the elastomeric coatings of practical use in undersea applications, the effects of the coating on the turbulent boundary layer are therefore assumed to be negligible. Changes in the wall pressure field measured beneath the coatings are therefore due primarily to the mechanical response of the coating and resulting stress field transmitted across the coating. The use of a coating to mechanically filter wall pressure fluctuations was first addressed by Maidanik and Reader (1967). Coating thicknesses can vary over a wide range depending on the specific undersea application. Recently, Capone and Bonness (2008) considered this problem and presented theoretical predictions for thick elastomeric coatings on the order of 30 mm. The purpose of the present investigation was to make detailed measurements in the wavenumber regime dominated by convective energy. Therefore, thin coatings, on the order of 1 mm, were investigated to determine how the wall pressure field is transmitted across them. The pressure sensors used were sufficiently small to measure convective energy. The results are required for validation of theoretical and finiteelement analyses aimed at improving future hull-mounted and towed acoustic sensor array designs.

44

W.L. Keith et al. / Ocean Engineering 47 (2012) 43–49

Nomenclature c acoustic wave speed m/s d¼2r pressure sensor diameter mm d þ ¼dut/n pressure sensor diameter scaled on viscous lengths f cyclic frequency Hz h coating thickness mm p(x,z,t) fluctuating wall pressure mpa R1 PðoÞ ¼ ð1=2pÞ 1 pðtÞeiot dt Fourier transform pair mpa/(rad/s) Rey ¼Uoy/n momentum thickness Reynolds number u(y) mean streamwise velocity m/s ut ¼(tw/r)1/2 friction velocity m/s u þ ¼u(y)/ut mean streamwise velocity scaled on friction velocity Uc wall pressure convection velocity m/s Uo free stream velocity m/s x streamwise coordinate mm y wall normal coordinate mm

2. Experimental setup The Quiet Water Tunnel Facility at the Naval Undersea Warfare Center, Division Newport, is ideally suited for this investigation due to its low acoustic noise and test section design, as discussed by Keith and Kiser (2011). The facility is a closed-loop water flow system driven by a dual suction centrifugal pump. The tunnel contains two test sections, a 102 mm by 305 mm cross section rectangular section and an 89 mm inner diameter circular test section. The rectangular test section, used for this test, increases in height from 102 mm to 112 mm over its 2.11 m length to allow zero pressure gradient turbulent boundary layers to develop on the channel walls. Transition takes place in the contraction nozzle upstream of the test section. Six wells in the top of the test section accommodate instrumented port plugs designed to accept different types of transducers and materials for testing as shown in Fig. 2. For this experiment, two port plugs were manufactured to accept coatings of 0.635 mm and 1.27 mm, as illustrated in Fig. 2. The coatings used were a polyurethane (Composite Polymer Design 9130, Polymer Design MN) elastomer with an 85 shore A hardness and were hydraulically smooth with respect to the port plug. Pairs of wall pressure sensors were mounted beneath the coatings in the center of each port plug. The experiment was designed to measure the energy transmitted through the

y þ ¼ yut/n wall normal coordinate scaled on viscous lengths z spanwise coordinate mm a empirical coating attenuation parameter b cross spectral decay parameter g(f) coherence¼ ((9(F(x,f))9/(O(Fo(f))O(F1(f))) d turbulent boundary layer thickness mm y turbulent boundary layer momentum thickness mm n kinematic viscosity m2/s x sensor streamwise separation mm r fluid density kg/m3 t mean wall shear stress N/m2 f phase angle rad F(o)¼ F(f)/2p autospectrum mpa2/(rad/s) Fa(o) autospectrum measured at the fluid–solid interface mpa2/(rad/s) Fb(o) autospectrum measured at the sensor mpa2/(rad/s) F(x,o) ¼ F(x,f)/2p cross spectrum mpa2/(rad/s) o ¼2pf radian frequency rad/s

material, rather than the stress field in the material itself. Seating the sensors below the coating material mitigates the development and measurement of resonances and modal energy within the coating itself. An additional reference pressure sensor was mounted near the outer edge of each of the port plugs, at the fluid–solid interface. The wall pressure sensors were custom-made, end-capped, air-filled piezoelectric cylinders, 2.03 mm in sensing diameter. The analog voltage signals from these sensors were sampled at 2 kHz using a National Instruments PC-based analog-to-digital system with anti-aliasing filtering. To compute the spectra, 1000 or more ensemble averages were used, with 1024 samples per record, resulting in an uncertainty of þ/  0.1 dB in the autospectra. Background acoustic noise related to the pump was negligible for frequencies greater than 28 Hz. Velocity profiles were obtained using a total head pitot tube probe and static pressure ports on the top wall of the test section. During testing, the water temperature was 23.9 1C, and the static pressure in the test section was 206.8 kPa.

3. Experimental results Velocity profile measurements made in well 5 of the water tunnel’s rectangular test section are shown in Fig. 3, scaled on inner boundary layer variables. Also shown is Clauser’s log law (1956), given as u þ ¼ 2:44 lnðy þ Þ þ 4:90

Fig. 1. Acoustic pressure sensor beneath an elastomeric coating excited by a turbulent boundary layer.

ð1Þ

Values for the friction velocity ut were determined by fitting the data points closest to the wall to Clauser’s Eq. (1). Measurements in the viscous sublayer for y þ o10 were not possible due to the size of the pitot tube. The measured and computed turbulent boundary parameters are given in Table 1. Also given are values for sensor diameter d þ and the coating thickness h. Schewe (1983) conducted measurements in air and concluded that wall pressure sensors 20 viscous lengths (or less) in diameter were required to resolve the highest frequencies of turbulent wall pressure energy. The sensors used here are an order of magnitude greater in size (in terms of viscous lengths) due to the requirements for use in water at moderate to high Reynolds numbers. As a result, the roll-off of the wall pressure autospectra at higher frequencies is more rapid than for a perfectly spatially resolved

W.L. Keith et al. / Ocean Engineering 47 (2012) 43–49

45

177.80 mm 6.35mm 92.10 mm

Port Plug Fitted with Elastomeric Coating and Pressure Sensors.

Rectangular Test Section

wall pressure fluctuations wall shear stress fluctuations

turbulent boundary layer flow coating

sensors

port plug Fig. 2. Quiet water tunnel rectangular test section and instrumented port plug.

135

30

125 10Log(Φ(f)/(μPa2/Hz))

35

25

u+

20 15 Uo = 2.89 (m/s) Uo = 4.40 (m/s) Uo = 6.15 (m/s) Clauser (1956)

10 5

115 U1, h0 U1, h1 U1, h2 U2, h0 U2, h1 U2, h2

105 95

U3, h0 U3, h1 U3, h2

85 75

0 100

101

102

103 y

104

105

20

40

60

+

100

200

400 600

1000

f (Hz) Fig. 4. Dimensional wall pressure autospectra.

Fig. 3. Mean velocities scaled with inner variables.

Table 1 Turbulent boundary layer and coating parameters.

10

utm/s

ut/Uo

d mm

y mm

Rey

dþ

h mm

U1 ¼ 2.89 U2 ¼ 4.40 U3 ¼ 6.15

0.10 0.15 0.21

0.035 0.034 0.034

24.2 23.9 24.3

2.42 2.39 2.43

7,540 11,300 16,100

218 328 459

ho ¼ 0.000 h1 ¼0.635 h2 ¼1.270

measurement. Corrections for the effect of sensor size on the measured spectra are presented in Appendix A. The autospectra measured at the fluid–solid interface (ho) and beneath the two coating thicknesses (h1 ¼ 0.635 mm and h2 ¼1.27 mm) are shown in Fig. 4. The attenuations due to the coating increase with coating thickness and also increase with frequency. At low frequencies the spectra measured beneath the coatings generally converge with the baseline spectra. At the two higher speeds, the levels beneath the coating are slightly lower than the baseline at the lowest frequencies measured. Shown in Fig. 5 are the autospectra scaled with mixed variables, as discussed by Keith et al. (1992). For nondimensional

0 10Log(Φ(ω) Uo/(τ2θ))

Uo m/s

-10 -20 -30 -40

U1, h0 U1, h2 U2, h0 U2, h2 U3, h0 U3, h2

-50 0.1

1.0 ωθ / Uo

Fig. 5. Nondimensional wall pressure autospectra scaled on mixed variables.

46

W.L. Keith et al. / Ocean Engineering 47 (2012) 43–49

-50

1.0

0.8

-70

Uc/ Uo

10Log(Φ(ω) /(ρ2θUo3))

-60

-80 -90

-100

0.6

0.4

U1, h0 U1, h2 U2, h0 U2, h2 U3, h0 U3, h2

U1, h1 U1, h2 U2, h1 U2, h2 U3, h1 U3, h2

0.2

-110

0.0 0.1

1.0

0.0

0.5

1.0 ωθ/ Uo

ωθ / Uo Fig. 6. Nondimensional wall pressure autospectra scaled on outer variables.

1.5

2.0

Fig. 8. Wall pressure convection velocities scaled on outer variables.

40 35 30

U1, h1 U1, h2 U2, h1 U2, h2 U3, h1 U3, h2

0.8

0.6

25

γ(f)

Uc/ Uτ

1.0

U1, h1 U1, h2 U2, h1 U2, h2 U3, h1 U3, h2

0.4

20

0.2

15 10

0.0

0.5

1.0 ωθ/ Uo

1.5

2.0

Fig. 7. Wall pressure convection velocities scaled on mixed variables.

frequencies oy/Uo o0.7, the spectral levels for the baseline and thicker coating collapse well at lower frequencies, with slight scatter. At higher frequencies, the baseline spectra collapse well for all speeds, and the spectra beneath the thicker coating also collapse well, at a lower level. The spectra scaled on outer variables are shown in Fig. 6, demonstrating the same trends as those scaled on mixed variables. A slightly improved collapse is seen, but to within the uncertainties in the scaling parameters and spectra, the mixed and outer scalings appear to work equally well. The measured wall pressure convection velocities are given in non-dimensional form in Figs. 7 and 8. The trend shown is increasing convection velocity with increasing free stream velocity at a given frequency. The two higher speeds display decreasing values with increasing frequency; this reflects that smaller-scale, turbulent energy-producing structures propagate slower than those of larger scales due to the proximity to the wall. The convection velocities show that all of the measured energy propagates at speeds directly related to turbulence in the boundary layer, as opposed to wavespeeds associated with any structural response of the coating material. The wall pressure coherence between sensors separated by 6.35 mm is plotted as a function of frequency for both coating thicknesses in Fig. 9. At the highest speed there is no measurable change in the coherence due to the thicker coating. At the two

0

200

400

600

800

1000

f (Hz) Fig. 9. Wall pressure coherence vs. frequency, sensor spacing 6.35 (mm).

8 7 6 5 φ (rad)

0.0

4 U1, h1 U1, h2 U2, h1 U2, h2 U3, h1 U3, h2

3 2 1 0 0

200

400

600

800

1000

f (Hz) Fig. 10. Wall pressure phase vs. frequency, sensor spacing 6.35 (mm).

lower speeds there is a small but measurable increase resulting from the thicker coating. For any given frequency, the coherence levels increase with increasing speed, due to the effective larger wavelengths being correlated over longer distances. Fig. 10 shows the wall pressure phase versus frequency between sensors

W.L. Keith et al. / Ocean Engineering 47 (2012) 43–49

The coherence function g(ox/Uc) is the magnitude of the normalized cross-spectra expressed as a function of the similarity variable ox/Uc, where the convection velocity Uc varies with frequency and sensor separation. The similarity variable ox/Uc is by definition the phase of the cross spectrum. Farabee and Casarella (1991) and Keith and Barclay (1993) have shown that the similarity scaling breaks down at very low frequencies. The form of the coherence function for flat plate turbulent boundary layers is

gðox=U c Þ ¼ ebðox=Uc Þ

ð3Þ

where the decay constant b varies with flow parameters. Farabee and Casarella (1991) stated that values for b ranging from 0.10 to 0.19 were reported for flat plate investigations, and noted the trend of a decrease in decay constant b with increase in Ry. They found b decreased from 0.145 to 0.125 as Ry increased from 3386 to 6025. Bull (1967) reported a decay constant of 0.100 for an Ry value of 10,000. A value of 0.125 may be interpreted as a 90% loss of coherence as turbulent pressure producing structures convect over three of their own wavelengths. A value of 0.1 was found to provide the best fit to the data under consideration here, as shown by the dashed line in Fig. 11. The trend of increased levels with increasing speed (or equivalently, Reynolds number) is observed, which is consistent with other investigations. The small increases in coherence levels due to the thicker coating noted in Fig. 9 are much less apparent in Fig. 11. The Corcos model of the coherence effectively collapses the data for the two coating thicknesses at each respective speed. The attenuation of the autospectra due to the coating can be approximated by the exponential decay model (Blake, 1984):

Fb ðoÞ ¼ Fa ðoÞe2aoh=Uc

due to stand-off increases with both frequency and material thickness. The relevance of the frequency and spatial dependence of convection velocity (Uc) was discussed by Keith and Abraham (1997). Here, only frequency dependence is considered, and both a fixed and a frequency-dependent value of Uc are chosen. For the fixed value, Uc ¼0.75Uo is taken, chosen as the best approximation for the frequency range of interest here (see Keith and Abraham (1997)). The frequency-dependent Uc was computed from the measured phase, using the expression f(o)¼ ox/Uc(o). Fig. 12 presents the autospectra measured under the 0.635 mm coating and the predictions of these autospectra using the fixed and frequency-dependent values of Uc in Eq. (4), where the autospectra measured by the reference sensor at the fluid– solid interface are used for Fa(o). The autospectra measured under the 1.270 mm coating and their respective predictions are given in Fig. 13. A value of a ¼ 0.4 was used for the predictions for each coating thickness, leading to a good agreement with the measured data over its frequency range. There is little apparent difference between the predictions made using a fixed value for convection velocity and those made with a frequency dependent value. At the highest speed, the measured and predicted data diverge slightly at very low frequencies. Similarly, at the lowest

135 125 10Log(Φ(f)/(μPa2/Hz))

separated by 6.35 mm under both coating thicknesses. For any given frequency, the phase decreases with increasing speed. Comparing coating thicknesses, the changes in the phase are very small, consistent with the magnitude of the coherence. The Corcos (1963) model of the streamwise cross-spectra of the wall pressure field may be expressed as   Fðx, oÞ ¼ FðoÞg ox=U c eiox=Uc ð2Þ

115 U1, Coated U2, Coated U3, Coated U1, Modeled with Fixed Uc U2, Modeled with Fixed Uc U3, Modeled with Fixed Uc U1, Modeled with Uc(f)

105 95 85

U2, Modeled with Uc(f) U3, Modeled withUc(f)

75

ð4Þ

where Fb(o) denotes the wall pressure autospectrum measured by a sensor beneath a coating of thickness h, Fa(o) denotes the baseline wall pressure autospectrum which exists at the fluid– solid interface, and a is an empirical parameter. The form of this equation was derived for the hypothetical case of a layer of quiescent fluid between a pressure sensor and the turbulent boundary layer and demonstrates that, in general, attenuation

47

20

40

60

100

200 f (Hz)

400 600

1000

Fig. 12. Measured and modeled wall pressure autospectra for coating h1 ¼ 0.635 mm. Predictions were made using both fixed (‘fixed Uc’) and frequency dependent (‘Uc (f)’) values for convection velocity in Eq. (4).

135

1.0 10Log(Φ(f)/(μPa2/Hz))

125

0.8

γ (φ)

0.6 U1, h1 U1, h2 U2, h1 U2, h2 U3, h1 U3, h2 Corcos Model

0.4

0.2

115 U1, Coated U2, Coated U3, Coated U1, Modeled with Fixed Uc U2, Modeled with Fixed Uc U3, Modeled with Fixed Uc U1, Modeled with Uc(f)

105 95 85

U2, Modeled with Uc(f) U3, Modeled withUc(f)

75 20

0.0

40

60

100

200

400 600

1000

f (Hz)

0

1

2

3

4

φ (rad)

5

6

7

Fig. 11. Wall pressure coherence vs. phase, sensor spacing 6.35 (mm).

8 Fig. 13. Measured and modeled wall pressure autospectra for coating h2 ¼ 1.270 mm. Predictions were made using both fixed (‘fixed Uc’) and frequency dependent (‘Uc (f)’) Values for convection velocity in Eq. (4).

W.L. Keith et al. / Ocean Engineering 47 (2012) 43–49

4. Conclusions Turbulent wall pressure energy attenuation due to an elastomeric coating is shown to increases with both frequency and coating thickness. The measured autospectra collapse equally well when using mixed or outer scaling variables. The levels of the attenuation are well predicted by the model of Blake (1984) for the measured data as well as that corrected for sensor spatial averaging effects. For these approximations, the fixed value of convection velocity Uc is as effective as the frequency dependent value and can be used to simplify further modeling efforts. Small increases in coherence levels at the two lower speeds were measured for the thicker of the two coatings tested. These increases were not apparent using the Corcos model of the coherence. The similarity scaling g ox/Uc is therefore shown to be effective for accounting for small changes in the coherence levels due to the elastomeric coatings. The data also indicate that the energy measured beneath the coating is exclusively transmitted turbulent energy and does not contain any structural modes which may have developed in the coating material itself. The use of a urethane coating over a sensor array provides significant passive control of flow noise for undersea acoustic sensors. In addition to increasing array performance, this method may also lead to improvements in array durability. For specific applications, coating thicknesses could vary from fractions to hundreds of millimeters. The effect of coating material properties on the attenuations can be investigated to optimize the desirable effects. Refinements in the modeling which take into account material properties, including moduli and wavespeeds, will extend the applicability of the models to other materials.

Acknowledgments

135 125 10Log(Φ(f)/(μPa 2 /Hz))

speed, the measured and predicted data diverge slightly at very high frequencies. The reason for all of these disparities is unclear, but the order to which they occur is within the uncertainty of the measurements themselves, and the dominant trend is that the measurement under the coating is well predicted by Eq. (4), independent of coating thickness and flow velocity.

115 105

U1, Measured U1, Corrected U2, Measured U2, Corrected U3, Measured U3, Corrected

95 85 75 20

40

60

100

200 f (Hz)

400 600

1000

Fig. A1. Wall pressure autospectra corrected for sensor spatial averaging (no coating).

135 125 10Log(Φ(f)/(μPa2 /Hz))

48

115 105 U1, Corrected U1, Corrected and Modeled with Uc(f) U2, Corrected U2, Corrected and Modeled with Uc(f) U3, Corrected U3, Corrected and Modeled with Uc(f)

95 85 75 20

40

60

100

200

400 600

1000

f (Hz) Fig. A2. Measured and predicted wall pressure autospectra for coating h1 ¼ 0.635 mm. Predictions were made using the frequency dependent (‘Uc (f)’) values for convection velocity in Eq. (4). All measurements were corrected for sensor spatial averaging.

This work was funded under the Naval Undersea Warfare Center In-house Laboratory Independent Research (ILIR) Program, Manager Dr. A. Ruffa.

135

Corcos (1963) addressed the problem of spatial resolution of finite size pressure sensors. Using his model for the crossspectrum, he showed that the attenuation in the measured autospectra may be expressed as a function of the quantity or/Uc, where r¼d/2 is the radius of the pressure sensor. Here, we fit a third order polynomial to the attenuation function given by Corcos (1963) in the form Fm(o)/Ft(o) vs. or/Uc, where subscripts m and t denote measured and true quantities. The measured values for convection velocity Uc as a function of frequency were used to determine the attenuations. The measured and corrected baseline (no coating) autospectra are shown in Fig. A1. The attenuations increase with frequency, which reflects the higher convective wavenumbers (smaller convective wavelengths) which contain the dominant energy at the higher frequencies. The data in Figs. 12 and 13 are shown in Figs A2 and

10Log(Φ(f)/(μPa2/Hz))

125 Appendix A. Effects of sensor spatial averaging on the measured autospectra

115 105 U1, Corrected U1, Corrected and Modeled with Uc(f) U2, Corrected U2, Corrected and Modeled with Uc(f)

95 85

U3, Corrected U3, Corrected and Modeled with Uc(f)

75 20

40

60

100

200

400 600

1000

f (Hz) Fig. A3. Measured and modeled wall pressure autospectra for coating h2 ¼1.270 mm. Predictions were made using the frequency dependent (‘Uc (f)’) values for convection velocity in Eq. (4). All measurements were corrected for sensor spatial averaging.

W.L. Keith et al. / Ocean Engineering 47 (2012) 43–49

A3 respectively, where corrections for spatial averaging have been applied. Here we only show the coating attenuations for the cases of convection velocity varying with frequency. The results confirm that the modeling approach for the coating thickness works very well when the spectra are corrected for spatial averaging.

References Blake, W.K., 1984. Aero-Hydroacoustics for Ships. David Taylor Naval Ship Research and Development Center, Bethesda, MD Ch.7 p.781. Bull, M.K., 1967. Wall-pressure fluctuations associated with subsonic turbulent boundary layer flow. J. Fluid Mech. 28 (4), 719–754. Bushnell, D.M., Hefner, J.N., Ash, R.L., 1977. Effect of compliant wall motion on turbulent boundary layers. Phys. Fluids 20 (10). pt.2. Capone, D.E., Bonness, W.K., 2008. The transmission of turbulent boundary layer unsteady pressure and shear stress through a viscoelastic layer. J. Fluids Struct. 24, 1120–1134. Clauser, F.H., 1956. The turbulent boundary layer. Adv. Appl. Mech. 4. Corcos, G.M., 1963. Resolution of pressure in turbulence. J. Acoust. Soc. Am. 35 (2), 192–199. Farabee, T.M., Casarella, M.J., 1991. Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluids A 3 (10), 2410–2420. Gad-el-Hak, M., 1986. Boundary layer interactions with compliant coatings: an overview. Appl. Mech. Rev. 39 (4). Gad-el-Hak, M., 1987. Compliant Coatings Research: A Guide to the Experimentalist. J. Fluids Struct. 1 (1).

49

Hess, D.E., 1990. An Experimental Investigation of a Compliant Surface Beneath a Turbulent Boundary Layer. Ph. D. Thesis Johns Hopkins University, Baltimore, MD. Karnarskiy, M.V., Teslo, A.P., 1980. Turbulent flow over a plate with a compliant surface. Fluid Mech. Sov. Res. 9 (5). Keith, W.L., 1987. Turbulence Measurements on Isotropic and Nonisotropic Compliant Slabs. NUSC-TR-8143, New London, CT, December 7. Keith, W.L., Hurdis, D.A., Abraham, B.M., 1992. A comparison of turbulent boundary layer wall pressure spectra. J. Fluids Eng. 114 (3), 338–347. Keith, W.L., Barclay, J.J., 1993. Effects of a large eddy breakup device on the fluctuating wall pressure field. J. Fluids Eng. 115 (3), 389–397. Keith, W.L., Abraham, B.M., 1997. Effects of Convection and decay of turbulence on the wall pressure wavenumber–frequency spectrum. ASME J. Fluids Eng. 119, 50–55. Keith, W.L., Kiser, J.R., June 7–9, 2011. Capabilities of the Quiet Water Tunnel. In: Proceedings of the Undersea Defence Technology Conference and Exhibition. Clarion Defence and Security Ltd., London, UK. Maidanik, G., Reader, W.T., 1967. Filtering action of a blanket dome. J. Acoust. Soc. Am. 44 (2), 497–502. Ramotowski, T., Jenne, K., 2003. NUWC XP-1 Polyurethane-Urea: A New, ‘‘Acoustically Transparent’’ Encapsulant for Underwater Transducers and Hydrophones. In: Proceedings of MTS/IEEE Oceans 2003, n, San Diego, CA, September 22–25. Schewe, G.S., 1983. On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary layer flow. J. Fluid Mech. 134, 311–328. Semenov, B.N., Kulik, V.M., Lopynev, V.A., Mironov, B.P., Poguda, I.S., Yashmanova, T.I., 1985. The combined effect of small quantities of polymeric additives and pliability of the wall on friction in turbulent flow. Fluid Mech. Sov. Res. 14 (1). Voropayev, G.A., Babenko, V.V., 1978. The turbulent boundary layer on an elastic surface. Fluid Mech. Sov. Res. 7 (6).