Theoretical Analysis of Second Mode in Hypersonic Boundary Layer Above Porous Wall

Abstract

The porous wall can delay hypersonic boundary layer transition by suppressing the second mode instability, which helps in reducing the weight, cost and complexity of thermal protection systems of hypersonic vehicle. A linear stability theory model is developed to investigate the performance of suppressing second mode instability. Based on the fourth Runge-Kutta scheme, the basic flow of hypersonic boundary layer is obtained using a shooting technique. The admittance of porous wall is considered in the boundary condition of stability equations. The second mode growth rate in temporal stability problem is solved by the Chebyshev spectral method. The prediction results agree well with the existing data. The porous walls with high porosity and relatively high aspect ratio provide maximal damping of second mode wave. Specifically, high porosity is associated with strong attenuation effect. Relatively high aspect ratio corresponds to relatively shallow pores, which results in a cancellation effect.