Transition Prediction in Hypersonic Boundary Layers Using Receptivity and Freestream Spectra

Abstract

Boundary-layer transition in hypersonic flows over a straight cone can be predicted using measured freestream spectra, receptivity, and threshold values for the wall-pressure fluctuations at the transition onset points. Simulations are performed for hypersonic boundary-layer flows over a 7 deg half-angle straight cone with varying bluntness at a freestream Mach number of 10. The steady and the unsteady flowfields are obtained by solving the two-dimensional Navier–Stokes equations in axisymmetric coordinates using a fifth-order-accurate weighted essentially nonoscillatory scheme for space discretization and using a third-order total-variation-diminishing Runge–Kutta scheme for time integration. The calculated factors at the transition onset location increase gradually with increasing unit Reynolds numbers for flow over a sharp cone and remain almost the same for flow over a blunt cone. The receptivity coefficient increases slightly with increasing unit Reynolds numbers. They are on the order of four for a sharp cone and are on the order of one for a blunt cone. The location of transition onset predicted from the simulation including the freestream spectrum, receptivity, and the linear and the weakly nonlinear evolutions yields a solution close to the measured onset location for the sharp cone. The simulations overpredict transition onset by about 20% for the blunt cone.