Effect of distributed surface roughness on the stability of Falkner-Skan-Cooke boundary layers

Abstract

Direct numerical simulations (DNS) and large eddy simulations (LES) have been carried out to investigate the impact of surface roughness with various heights on the the most unstable/least stable eigenmode developing in a Falkner-Skan-Cooke boundary layer. Crossflow vortices are excited using a spanwise array of cylindrical roughness elements that are introduced by application of the virtual boundary method (VBM). The height of the roughness elements are in the range of medium to large, meaning that they are completely submerged into the boundary layer but close to the critical roughness height needed to trigger transition to turbulence (roughness Reynolds number, Rek for the investigated roughnesses are about 146 and 284). An impulse response is used to effectively trigger the eigenmodes of the flow, and the most unstable/least stable mode is obtained by using the outflow solution that has been filtered through the fringe region as input perturbation, and iterating the response in time. The method of forcing crossflow vortices using VBM proves to work very well with the present pseudo-spectral code and the results are promising. It turns out that when the height of the roughness is close to the critical height for transition, only a slight increase in roughness height will change the stability characteristics drastically, exciting a high-frequency secondary instability as opposed to an otherwise excited low-frequency mode. Differences in the excited modes are traced back to the shear layers developing in the near-field region of the roughness wake. It is concluded that a critical level of shear stress must be surpassed as the roughness size is increased and that this is responsible for triggering the secondary instability.Validerat; 20121120 (global_studentproject_submitter