Direct numerical simulation of the effects of a smooth surface hump on transition in swept-wing boundary layers

Abstract

The effect of a smooth surface hump on laminar–turbulent transition over a swept wing is investigated using direct numerical simulation (DNS), and results are compared with wind tunnel measurements. When the amplitude of incoming crossflow (CF) perturbation is relatively low, transition in the reference (without hump) case occurs near 53% chord, triggered by the breakdown of type I secondary instability. Under the same conditions, no transition is observed in the hump case within the DNS domain, which extends to 69% chord. The analysis reveals a reversal in the CF velocity component downstream of the hump’s apex. Within this region, the structure and orientation of CF perturbations are linearly altered, particularly near the wall. These perturbations gradually recover their original state further downstream. During this recovery phase, the lift-up mechanism is weakened, reducing linear production, which stabilises the stationary CF perturbations and weakens spanwise gradients. Consequently, the neutral point of high-frequency secondary CF instability modes shifts downstream relative to the reference case, leading to laminar–turbulent transition delay in the presence of the surface hump. In contrast, when the amplitude of the incoming CF perturbation is relatively high, a pair of stationary counter-rotating vortices forms downstream of the hump. These vortices locally deform the boundary layer and generate regions of elevated spanwise shear. The growth of secondary instabilities in these high-shear regions leads to a rapid advancement of transition towards the hump, in agreement with experimental observations.