The stability analysis and transition prediction are proceeded for one-order compression ramp,which is the valuable configuration for the hypersonic vehicles.The finite volume method is used to solve the NS equations to get the basic flow field.The solution of the eigenvalue problem is obtained by using the linear stability theory under the assumption of local parallel flows.The first mode and the second mode unstable waves are found at the Mach number of 6.With the relation of the temporal and spatial amplification rates,the transition position is predicted by the EN method.

Numerical method for stability analysis and transition prediction for supersonic flow around a blunt cone is investigated. In order to meet the required accuracy of the numerical values in the basal flow field, the result of the flow field is obtained by solving Euler equations where the pressure attribution on the surface of the cone is used as the outer edge pressure attribution of the viscous boundary layer. The Rayleigh inverse-iteration method and boundary layer asymptotic expansion method are used to solve the blunt cone boundary layer stability equation to get reliable boundary layer transition data. This method improves the numerical precision, and saves the computation time. It is also useful for stability analysis of blunt cone supersonic flow.

The Orr-Sommerfeld equation is solved numerically using a finite element method and the LR matrix eigenvalue algorithm.The results of great accuracy are obtained, by choosing higher order Hermite polynomials to be basis functions and making element distribution according to the physical character of the flow existed in the region.The method is applied to the stability of plane Poiseuille flowi It is found that the critical Reynolds nnmber is 5772.2218 and, it is computed that the neutral curve in the range of Reynolds number from Rc to 1010 farabove than those obtained before