Surface pressure fluctuations on steps immersed in turbulent boundary layers

Abstract

AbstractSurface pressure fluctuations induced by turbulent boundary-layer flow at ${\mathit{Re}}_{\theta } = 4755$ over small backward- and forward-facing steps are studied with large-eddy simulation. Four step heights that are 53, 13, 3.3 and 0.83 % of the boundary-layer thickness are considered to investigate the effects of step height on surface pressure characteristics and pressure-source mechanisms. The extent to which turbulent velocity fluctuations in the boundary layer and the separated shear layer contribute to the surface pressure fluctuations is examined with scaling of various pressure statistics and two-point correlations. For larger steps, vortical structures develop in the shear layer and the associated intense velocity fluctuations are the dominant source. Downstream of slightly less than one reattachment length from the step, the root-mean-square pressure is found to scale with the local maximum cross-stream Reynolds normal stress ${ \overline{{v}^{\ensuremath{\prime} \hspace{0.167em} 2} } }_{\mathit{max}} $. The pressure frequency spectrum at the maximum ${p}_{\mathit{rms}} $ location consists of an energy-containing range that scales with the mean reattachment length ${x}_{r} $ and a higher frequency range that rolls off with a slope close to $\ensuremath{-} 7/ 3$. As the step height decreases, the boundary-layer turbulent fluctuations become the dominant source, the ${ \overline{{v}^{\ensuremath{\prime} \hspace{0.167em} 2} } }_{\mathit{max}} $ scaling of ${p}_{\mathit{rms}} $ is no longer valid and the roll-off slope of the frequency spectrum becomes steeper. The downstream recovery of a step-perturbed boundary layer towards an equilibrium boundary layer is investigated from the point of view of surface pressure fluctuations. For steps with a strong separated shear layer, pressure fluctuations are found to decay rapidly for up to three reattachment lengths downstream of the step, within which approximately 60 % of the peak ${p}_{\mathit{rms}} $ is dissipated. Farther downstream, recovery is much slower. The pressure-recovery distances estimated for the largest backward and forward steps are 175 and 295 step heights, respectively.