We study the logarithmic behavior of the pressure variance p + 2 from the datasets obtained from direct numerical simulations of turbulent channel flow for friction Reynolds number Re τ up to 4000. The higher-order moments of p were found to follow logarithmic behaviors at the same distances from the wall where p + 2 shows its log profile. The same results have been confirmed for the spanwise velocity fluctuations w at the same Reynolds numbers, with both p and w following a super-Gaussian behavior. The minimum Reynolds number for p + 2 and w + 2 log profiles to appear is Re τ ≈ 500, where flow structures O(h) or less were found to significantly contribute to these profiles. The configuration of the hairpin eddy structures obtained from the conditional sampling at different wall-normal locations showed a strong link between p and w fluctuations. Positive pressure fluctuations are located between the legs of the hairpin eddy, while the negative pressure fluctuations are consistent with the head part of the hairpin eddy. Positive and negative spanwise velocity fluctuations are strongly positioned with the legs of the hairpin eddy, consistent with the counter-rotating motion resulting from the eddy legs. The structures were also found to be geometrically self-similar such that their length and their width increase linearly with the distance from the wall.
We investigate the turbulent structures associated with positive and negative high-amplitude wall pressure peaks in fully developed turbulent channel flows. The analysis is performed by conditional sampling of a channel flow dataset computed in direct numerical simulations. The Reynolds number was varied from 180 to 4000 based on the channel half-depth h and the friction velocity u τ . Positive and negative wall pressure events were associated with small-scale vortex structures identified by Q-criterion. When scaled in wall units, the overall size of the structure was independent of Reynolds number. Positive and negative wall pressure events were also associated with a large-scale sweep motion (of O( ) h ) from the outer layer, which constitutes a shear layer in the near-wall region. In a statistical analysis of the instantaneous pressure field, a sequence of negative and positive pressure peaks was found to predominate at the wall. The relative contributions from the large-and small-scale structures were qualitatively assessed by investigating the rapid and slow pressure terms from Poisson's equation. Both terms contributed nearly equally to the positive wall pressure peaks, but the slow term dominated the negative pressure peaks (with a relative contribution of approximately 60%).
Turbulent flow at high Reynolds number introduces large scale structures in the outer region which affect the turbulent motions. Reynolds number dependence on the pressure fluctuations is studied from Direct Numerical Simulations (DNS) data set at Reynolds number 180, 400, and 1000. The results indicate that the peak of root mean square value (r.m.s) of total, slow, and rapid pressure fluctuations depend on the logarithmic Reynolds number. Probability density function (PDF) for the total pressure shows slice difference between the studied range of Reynolds number. Power spectra are similar for the three pressures close to the wall, and at the center of the channel, rapid pressure shows different behavior in the intermediate and the high wavenumber range. Scale structures associated with total, slow, and rapid pressures introduce variation with the Reynolds number suggesting for more work in the scaling analysis.
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