Nonlinear Spatial Evolution Of Inviscid Instabilities On Hypersonic Boundary Layers

Nonlinear Spatial Evolution of Inviscid Instabilities on Hypersonic Boundary Layers

The spatial development of an initially linear vorticity-mode instability on a compressible flat-plate boundary layer is considered. The analysis is done in the framework of the hypersonic limit where the free-stream Mach number M approaches infinity. Nonlinearity is shown to become important locally, in a thin critical layer, when sigma, the deviation of the phase speed from unity, becomes o(M(exp -8/7)) and the magnitude of the pressure fluctuations becomes 0(sigma(exp 5/2)M(exp 2)). The unsteady flow outside the critical layer takes the form of a linear instability wave but with its amplitude completely determined by the nonlinear flow within the critical layer. The coupled set of equations which govern the critical-layer dynamics reflect a balance between spatial-evolution, (linear and nonlinear) convection and nonlinear vorticity-generation terms. The numerical solution to these equations shows that nonlinear effects produce a dramatic reduction in the instability-wave amplitude. Wundrow, David W. Glenn Research Center...

Nonlinear Spatial Evolution of Inviscid Instabilities on Hypersonic Boundary Layers

Spatial Evolution of Nonlinear Acoustic Mode Instabilities on Hypersonic Boundary Layers