Numerical simulations of transition due to isolated roughness elements at Mach 6

An accurate prediction of transition onset behind an isolated roughness element has not yet been established. This is particularly important in hypersonic flow, where transition is accompanied by increased surface heating. In the present contribution, a number of direct numerical simulations have been performed of a Mach 6 boundary layer over a flat plate with isolated roughness elements. The effects of roughness shape, planform, ramps, and freestream disturbance levels on instability growth and transition onset are investigated. It is found that the frontal shape has a large effect on the transition onset, which is in agreement with previous studies, whereas the roughness element planform has a marginal influence. A new result is that the roughness shape in the streamwise direction (in particular, the aft section) is also an important characteristic, since an element with a ramped-down aft section allows the detached shear layer to spread out and weaken, leading to a lower instability growth rate. Above a critical value, the instability growth rate is found to be correlated with the amplitude of the low-speed streak formed by the roughness element, suggesting that a more physically based transition criterion should take account of the local liftup effect of the particular roughness shape.