Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer

Abstract

Measurements of the turbulent pressure field at the wall beneath a thick (5-inch) turbulent boundary layer produced by natural transition on a smooth surface are reported. The data include the mean-square pressure, parallel to the stream, and spatial correlation of the pressure transverse to the stream.The root-mean-square wall pressure was 2.19 times the wall shear stress. The power spectra of the pressure were found to scale with the free-stream speed and the boundary-layer displacement thickness. A few tests with a rough surface showed that the increase in root-mean-square wall pressure was greater than the increase in wall shear stress.The space-time correlation measurements parallel to the stream direction exhibit maxima at certain time delays corresponding to the convection of pressure-producing eddies at speeds varying from 0.56 to 0.83 times the stream speed. The lower convection speeds are measured when the spatial separation of the pressure transducers is small, or when only the pressure fluctuations at high frequencies are correlated. Higher convection speeds are observed when the spatial separation of the pressure transducers is large, or when only low frequencies are correlated. The result that low-frequency pressure fluctuations have the highest convection speed is in agreement with the measurements of Corcos (1959, 1962) in a fully turbulent tube flow. Analysis of these measurements also shows that both large- and small-scale pressure-producing eddies decay after travelling a distance proportional to their scale. More precisely, a pressure-producing eddy of large or small wavelength λ decays and vanishes after travelling a distance of approximately 6λ.The transverse spatial correlation of the wall-pressure fluctuations was measured and compared with the longitudinal scale. Both the transverse and the longitudinal scale of the pressure fluctuations were of the order of the boundary-layer displacement thickness. The transverse and longitudinal scales of both large- and small-scale wall-pressure fluctuations were also measured and were also found to be approximately the same.

Numerical investigation of the wall pressure fluctuations in channel flows

“…2 The result <p2)qz/(r w) ~ 2.4 -+ 0.2 for the plane channel is in accordance with a large number of measurements [12]. This ratio is remarkably smaller at the inner wall of the annulus, however.…”

“…7). Oscillations of the same order of magnitude have been found by Gorman [5] in an annulus (R2/R~ = 1.67) and even larger ones by Bakewell [13] for a pipe, but they did not appear in a boundary layer flow [12]. Hence, it must be concluded that these oscillations are strongly geometry-dependent and equations based on measurements for one specific geometry, such as those used by Reavis [4], are not sufficient.…”

Turbulent structure of high-amplitude pressure peaks within the turbulent boundary layer

“…The remains are the structures with a longer lifetime (lower frequency) that travel at a higher velocity at locations further away from the wall. The increase in the advection velocity with streamwise separation has also been observed by Willmarth & Wooldridge (1962) and Bull (1967) using arrays of pressure transducers. For two transducers of small streamwise separation (∼θ ), Willmarth & Wooldridge (1962) observed an advection velocity of 0.56U ∞ and Bull (1967) observed 0.53U ∞ while both estimated 0.83U ∞ for transducers of larger streamwise separation (∼8θ, beyond the measurement field of the current experiment) and attributed the trend to the decay of the high-frequency pressure fluctuations.…”

“…The broad range of pressure fluctuations within the turbulent boundary layer was initially classified into low-and high-frequency fluctuations by Willmarth & Wooldridge (1962). They conducted a comparison and associated the low-frequency fluctuations with a high advection velocity using space-time correlation of wall pressure.…”

“…The previous experiments on turbulent boundary layer have been obliged to use miniaturized pressure transducers (Willmarth & Wooldridge 1962;Bull 1967) or condenser microphones (Blake 1970) which are intrusive and provide point-wise diagnostics. The shortcomings can be addressed by the recent advances in the PIV technique in combination with the Poisson pressure equation.…”