Direct numerical simulation of flat-plate transition induced by spanwise adjacent roughness elements and inlet free-stream turbulence

In this research, direct numerical simulation is performed on flat-plate boundary layer flows featuring spanwise adjacent roughness elements and inlet free-stream turbulence (FST). The study explores the combined effects of the element shape and the FST intensity on transition. The findings indicate that sufficient FST intensity leads to the formation of Klebanoff modes (K-modes) with pronounced spanwise modulation, where the spanwise wave number increases with FST intensity, unaffected by the roughness element shape. The enhancement of peripheral K-modes' amplitude and wave number promotes the growth of central low-speed streaks through the lift-up mechanism. The energy transfer from the mean flow to the fluctuating flow is primarily influenced by the configuration of roughness elements, while the spectral characteristics of coherent structures are dictated by the inlet FST. Even with weak FST intensity, the flow spectrum under varying roughness element configurations is predominantly governed by the streamwise component of the mode in fundamental frequency, attribute to the low-frequency and high-amplitude characteristics of K-modes. Roughness element shapes that cause minimal disturbance facilitate the development of harmonics introduced by FST. In the immediate downstream region of the roughness elements, the linear instability of the flow is closely linked to nonlinear coherent structures, whereas no significant linear instability is observed in the high-frequency band of the far downstream region. The adjacent ramps envelop the central low-speed region through coherent structures, effectively minimizing the erosion of the original flow spectrum by FST energy spectrum.