Far field perturbations caused by a roughness element to the three dimensional hypersonic plate flow boundary layer


For the three dimensional hypersonic viscous compressible flat plate flow, when there is only small roughness on the wall, its effect can be considered as perturbation to two dimensional roughness-free plate flow. To study such a flow problem, we will assume there is only a single roughness element on the plate, of which the equation is in the self-similar form η = eY0 (E), where E =zx -¾ and e << 1, and thus the perturbed flow boundary layer equations will also have self-similar solutions. When solving the boundary layer equations, we use the Dorodnitsyn Transformation and write the solutions in coordinate asymptotic expansions. In these expansions, the leading order terms are the solutions to the two dimensional flat plate flow boundary layer equations, and the expression of these terms will be treated as already known since they can be obtained from the Blasius Equation. The solutions for the perturbation terms show that the perturbations produced by the roughness are capable of propagating against the flow in the boundary layer. This is despite the fact that in the flow regime analysed in this thesis the longitudinal boundary-layer equation does not involve the pressure gradient, and this equation can be thought of as parabolic.Open Acces

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