Direct numerical simulation of vortex structures and fluctuating energy transfer in boundary layers with streamwise-adjacent roughness elements

Roughness elements on a smooth surface can promote transition within the boundary layer. It is crucial to elucidate the flow field structure changes for surface heat transfer and flow resistance control. To investigate the impact of streamwise adjacent roughness elements on plate boundary layer, this study conducts direct numerical simulation of flows over upstream roughness element characterized by three distinct shapes and downstream cylinder. The changes of the downstream vortex structures and fluctuating flow field caused by different upstream element shapes are revealed by specifically analyzing the streamwise vorticity stimulating term, first and second moments of velocity, fluctuating kinetic energy distributions and budget, fluctuating velocity anisotropy, and the coherent structures. The findings indicate that both the mixing enhancement of round head and the ramp's intense shear can diminish the wavelength of downstream spanwise vortices resulting in a denser hairpin vortex cluster and make the central low-speed region more compact. The following enhanced downstream streamwise vortex pair exerts a lifting effect on the boundary layer, which weakens the interaction between the energetic structures induced by the upstream roughness element and the downstream cylinder. This reduction is reflected in smaller production and dissipation terms within the fluctuating kinetic energy budget near the roughness element height. In the fluctuating velocity anisotropy contours, the reduction is manifested far downstream as the distinct unidirectional developing regions and the middle isotropic regions. The robust shear of the ramp fosters the generation of spanwise and streamwise vorticity, thereby stimulating the formation of hairpin vortex clusters. Concurrently, the flow encircling the rounded head efficiently blends coherent structures across varying elevations. This blending phenomenon extends its influence into the far downstream region.