Predictive capability of the logarithmic law for roughness-modeled large-eddy simulation of turbulent channel flows with rough walls

Abstract

Direct numerical simulation (DNS) and large-eddy simulation (LES) resolving roughness elements are computationally expensive. LES employing the logarithmic law as the wall model, without the need to resolve the flow at the roughness element scale, provides an efficient alternative for simulating turbulent flows over rough walls. In this work, we evaluate the predictive capability of the roughness-modeled LES by comparing its predictions with those from the roughness-resolved DNS for turbulent channel flows with rough walls. A good agreement is observed for the mean streamwise velocity. The Reynolds stresses predicted by the roughness-modeled LES also reasonably agree with the roughness-resolved predictions. Differences, on the other hand, are observed for the dispersive Reynolds stresses, integral scales, and space-time correlations. The roughness-modeled LES fails to predict the dispersive stresses as one can expect. In the outer layer, the integral length scale predicted by the roughness-modeled LES is lower than the roughness-resolved prediction, which cannot be improved by refining the grid. As for the space-time correlations, discrepancies are shown for the streamwise velocity fluctuations, with a faster decay of the correlation in the outer layer observed in the roughness-modeled predictions. Examination of the space-time correlation using the elliptic approximation model shows that the roughness-modeled LES underpredicts the convection velocity in the near wall region while overpredicting the sweeping velocity in the outer layer with no improvements observed when refining the grid.