PNNL

Abstract

Random rougness is omnipresent in engineering applications and may often affect performance in unexpected way. Here, we employ synergistically stochastic simulations and second-order stochastic perturbation analysis to study supersonic flow past a wedge with random rough surface. The roughness (of length $d$) starting at the wedge apex is modeled as stochastic process (with zero mean and correlation length $A$) obtained from a new stochastic differential equation. A multi-element probabilistic collocation method (ME-PCM) based on {\em sparse grids} is employed to solve the stochastic Euler equations while a WENO scheme is used to discretize the equations in two spatial dimensions. The perturbation analysis is used to verify the stochastic simulations and to provide insight for small values of $A$, where stochastic simulations become prohibitively expensive. % We show that the random roughness enhances the lift and drag forces on the wedge beyond the rough region, and this enhancement is proportional to $(d/A)^2$. The effects become more pronounced as the Mach number increases. These results can be used in designing smart rough skins for airfoils for maxiumum lift enhancement at a minimum drag penalty.