Verification Of Local Scattering Theory As Is Applied To Transition Prediction In Hypersonic Boundary Layers

The e~Nmethod is the most widely used transition-prediction approach in aerospace engineering,but it fails to take into account the effects of surface abrupt changes,such as roughness elements,gaps,steps,etc.,in boundary-layer flows.However,the latter appear frequently on the surface of flying vehicles.A recently developed local scatter-ing framework provides an effective means to address this issue.Based on the phys-ical mechanisms of transition,the theoretical framework quantitatively describes two regimes,the local receptivity and linear-mode scattering,leading to a modification of the transition criterion by the parameterized receptivity and transmission coefficients.In order to confirm the effectiveness of the theoretical framework,a pair of direct numer-ical simulations of hypersonic boundary-layer flows are designed,namely,introducing the same inflow modal perturbations for two cases with a smooth and a rough surfaces,respectively.The transition processes are simulated,and the roughness effect on transi-tion is quantified.It is inferred from the numerical results that roughness strips in hyper-sonic boundary layers can enhance the Mack instability modes when their frequencies are lower than the synchronization frequency,but suppress the supercritical frequen-cies.Therefore,carefully designs of the numerical configurations can show phenomena of transition delay,which is a distinguished feature of transition in hypersonic bound-ary layers against that in low-speed flows.The numerical result are compared with the theoretical predictions of the linear-mode scattering regime in detail.The numerical results confirm that the local scattering phenomena would appear when oncoming per-turbations with different frequencies propagate over roughness strips,and the distortion of their amplitudes can be readily predicted by the local scattering theory.Even when the perturbations evolve to weakly nonlinear phase,the change of their amplitudes stil-l agree with the theoretical predictions,indicating that the local scattering process is weakly dependent on the nonlinearity.