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Turbulent wall pressure fluctuations over wavy surfaces

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Abstract

Measurements of the spectral characteristics of the wall pressure fluctuations produced by a turbulent boundary layer flow over solid sinusoidal surfaces of moderate wave amplitude to wave-length ratios have been obtained. The wave amplitudes were sufficiently small so that the flow remained attatched. The results show that the root mean square pressure level reaches a maximum on the adverse pressure gradient side of the wave at a position somewhat before the trough. Spectral analysis of the pressure fluctuations in narrow frequency bands reveals considerable differences in low and high frequency behavior. At low frequencies, the peak fluctuation amplitude was found at the trough whereas at high frequencies, the peak occurs just after the crest and a minimum is found at the trough. Pressure fluctuations having streamwise correlation lengths on the order of or larger than the wavelength of the surface do not return to their equilibrium (crest) amplitudes as they travel the length of a wave. Pressure fluctuations having streamwise correlation lengths about one order of magnitude less than a wavelength return exactly to their equilibrium amplitudes. Two-point correlation measurements show a decrease in longitudinal coherence on the adverse pressure gradient side of the wave at low frequencies and a considerable increase over a broad frequency range on the positive pressure gradient side. No change is found in the lateral coherence.

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Abbreviations

C f :

skin friction coefficient

C p :

pressure coefficient

C n :

Fourier amplitudes of the pressure coefficient

C dp :

pressure drag coefficient

d :

pinhole diameter

f :

frequency

h :

half the crest to trough distance

h + :

nondimensional wave amplitude = \(\frac{{hu^* }}{v}\)

k n :

wavenumber = \(\frac{{2\pi n}}{\lambda }\)

k :

fundamental wavenumber = \(\frac{{2\pi }}{\lambda }\)

l p :

pressure correlation length

p s :

mean surface pressure

P ∞ :

ambient pressure

p :

fluctuating pressure

p 2 :

mean square pressure

q :

dynamic head = 1/2 ϱU ∞ 2

R :

space-time correlation

P λ :

Reynolds number based on wavelength = \(\frac{{U_\infty\lambda }}{v}\)

R θ :

Reynolds number based on momentum thickness = \(\frac{{U_\infty\lambda }}{v}\)

t :

time

R ∞ :

free stream velocity

U :

mean streamwise velocity

U e :

streamwise velocity at the edge of the boundary layer

u * :

friction velocity = \(\sqrt {{{\tau _w } \mathord{\left/ {\vphantom {{\tau _w } \rho }} \right. \kern-\nulldelimiterspace} \rho }} \)

x :

streamwise coordinate

y :

wall-normal coordinate

z :

spanwise coordinate

α+ :

non-dimensional wavelength = \(\left( {\frac{{2\pi }}{\lambda }} \right)\left( {\frac{v}{{u^* }}} \right)\) *)

β:

phase of the cross-spectral density

δ* :

boundary layer displacement thickness

Γ long :

longitudinal coherency

Γ lat :

lateral coherency

λ:

wavelength of wavy surface

v :

kinematic viscosity

ω:

radian frequency = 2 π f

Φ :

spectral or cross-spectral density

φ n :

phase of the Fourier series

ϱ :

density

τ:

time delay

τ w :

wall shear stress

θ :

boundary layer momentum thickness

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Authors and Affiliations

  1. Laboratory for Computational Physics and Fluid Dynamics, Naval Research Laboratory, Washington, DC, USA

    R. A. Handler

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  1. R. A. Handler
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Handler, R.A. Turbulent wall pressure fluctuations over wavy surfaces. Experiments in Fluids 10, 33–40 (1990). https://doi.org/10.1007/BF00187870

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