Direct Numerical Simulations of Flow Past an Array of Distributed Roughness Elements

Abstract

Direct numerical simulation was used to describe the subsonic flow past an array of distributed cylindrical roughness elements mounted on a flat plate. Solutions were obtained for element heights corresponding to a roughness-based Reynolds number (Re k ) of both 202 and 334. The numerical method used a sixth-order-accurate centered compact finite difference scheme to represent spatial derivatives, which was used in conjunction with a tenth-order low-pass Pade-type nondispersive filter operator to maintain stability. An implicit approximately factored time-marching algorithm was employed, and Newton-like subiterations were applied to achieve second-order temporal accuracy. Calculations were carried out on a massively parallel computing platform, using domain decomposition to distribute subzones on individual processors. A high-order overset grid approach preserved spatial accuracy on the mesh system used to represent the roughness elements. Features of the flowfields are described, and results of the computations are compared with experimentally measured velocity components of the time-mean flowfield, which are available only for Re k = 202. Flow about the elements is characterized by a system of two weak corotating horseshoe vortices. For Re k = 334, an unstable shear layer emanating from the top of the cylindrical element generated nonlinear unsteady disturbances of sufficient amplitude to produce explosive bypass transition downstream of the array. The Re k = 202 case displayed exponential growth of turbulence energy in the streamwise direction, which may eventually result in transition.