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Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers

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Abstract

Turbulent wall pressure fluctuation measurements were made in water on a towed model of length 129.8 (m) and diameter 3.8 (cm) for steady speeds from 6.2 (m/s) to 15.5 (m/s). The drag on the model was measured with a strut mounted load cell which provided estimates of the momentum thickness and friction velocity. Momentum thickness Reynolds numbers Re θ varied from 4.8 × 105 to 1.1 × 106. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Re θ. The effectiveness of inner and outer velocity and length scales for collapsing the pressure spectra are discussed. The wavenumber–frequency spectra show a convective ridge at higher frequencies similar to flat plate boundary layers. At low frequencies, energy broad in wavenumber extends outside the convective ridge and acoustic cone, with no characteristic wave speed. Wall pressure cross-spectral levels scaled with similarity variables are shown to increase with increasing tow speed, and to follow decay constants consistent with flat plate cases. The convection velocities also display features similar to flat plate cases.

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Abbreviations

d = 2a :

model diameter (mm)

d s :

pressure sensor diameter (mm)

D :

drag force (N)

f :

cyclic frequency (Hz)

k :

streamwise wavenumber (r/m)

k 2 :

spanwise wavenumber (r/m)

k c = ω/U c :

convective wavenumber (r/m)

p :

fluctuating wall pressure (μPa)

r :

radians

Re θ = U oθ/ν:

momentum thickness Reynolds number

s + = ν/u τ :

viscous length scale (mm)

u τ = (τ/ρ)1/2 :

friction velocity (m/s)

U c :

wall pressure convection velocity (m/s)

U o :

carriage tow speed (m/s)

δ:

turbulent boundary layer thickness (cm)

ϕ = ωξ/U c :

cross-spectra phase (r)

Φ(f) = Φ(ω)(2π):

autospectra (μPa2/Hz)

Φ(ξ, f) = Φ(ξ, ω)(2π):

cross-spectra (μPa2/Hz)

Φ(k, f) = Φ(k, ω)(2π):

wavenumber–frequency spectra (μPa2/(Hz (r/m)))

γ(ωξ/U c):

coherence function (normalized)

ν:

kinematic viscosity (m2/s)

ρ:

fluid density (kg/m3)

θ:

turbulent boundary layer momentum thickness (cm)

τ:

mean wall shear stress (N/m2)

ω:

radian frequency (r/s)

ξ:

sensor streamwise separation (mm)

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Acknowledgments

Funding was provided by the Naval Undersea Warfare Center Division Newport In-House Laboratory Independent Research (ILIR) Program, manager Mr. Richard Philips. Professor Tim Wei at RPI provided many helpful suggestions. The authors are also grateful to Ms. Jane Leous (Cornell University) and Ms. Elizabeth Scales (Georgia Tech.) for their contributions to this project under the Office of Naval Research Naval Research Enterprise Intern Program (NREIP). Mr. David Jasinski of Code 1513 also provided invaluable support on the tests.

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Authors and Affiliations

  1. Sensors and Sonar Systems Department, Naval Undersea Warfare Center, 1176 Howell St., Newport, RI, 02841, USA

    William L. Keith & Kimberly M. Cipolla

  2. Marine and Aviation Department, Carderock Division Naval Surface Warfare Center, 9500 MacArthur Blvd, West Bethesda, MD, 20817-5700, USA

    Deborah Furey

Authors
  1. William L. Keith
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  2. Kimberly M. Cipolla
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  3. Deborah Furey
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Correspondence to William L. Keith.

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Keith, W.L., Cipolla, K.M. & Furey, D. Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers. Exp Fluids 46, 181–189 (2009). https://doi.org/10.1007/s00348-008-0552-y

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  • DOI: https://doi.org/10.1007/s00348-008-0552-y

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