Parameter Effects of Spanwise-arrayed Cylindrical Roughness Elements on Transition in the Falkner-Skan-Cooke Boundary Layer^*

The effects of roughness parameters, including height, diameter, and spacing of the cylindrical roughness elements, on turbulent transition are investigated in a three-dimensional boundary layer using direct numerical simulation. There are two types of transition process, classified as gradual and forced. The former is caused by a linear development of crossflow vortices and their secondary instability, while the latter is an immediate breakdown to turbulence behind the roughness without any crossflow vortex. These processes are only demarcated by the roughness height. The diameter and the spacing affect the initial creation processes of the crossflow vortex as well as the onset of the secondary instability in the gradual transition. With a fixed roughness volume, the greater height induces larger initial disturbances and causes earlier transition than a larger diameter. The aforementioned observations apply when the most unstable crossflow mode is induced. When the unstable mode is absent or is secondarily induced, the disturbance decays or the transition point shifts downstream. Therefore, when considering the critical parameter between the gradual and forced transitions, only the height is crucial. However, for a gradual transition, roughness parameters affect the transition point and we should consider the flow alternation caused by the roughness.