Asymptotic analysis of hypersonic boundary layers over an adiabatic wall with deformations
Following the achievement of a man made vehicle attaining hypersonic speeds in the late 1940's, hypersonic flow quickly became a field great interest. Early on, in the 50's and 60's, analytic methods for hypersonic flow were developed by early pioneers of the field, but by the late 60's and into the 70's these methods began to be overshadowed by CFD methods. By this time CFD had become sufficiently powerful and commercially available such that they became the more attractive option and have since become the dominate method of study for high mach flows. Though the power and effectiveness of CFD has only grown with time the demand for computer resources has grown even more so and flow phenomena of interest has become increasingly computationally expensive.
Herein is presented a reduced order model of hypersonic flow that can aid in determining approximate affects of high mach flow over a variety of wall geometries. A steady, 2D laminar, hypersonic flow is analyzed over a variety of wall geometries (flat plate, compression ramp, semicircle and sinusoidal protrusions) for a range of hypersonic interaction parameter values, assuming a perfect gas with no real or high-temperature gas effects. Though it is assumed that an attached shock is formed at the leading edge, only the boundary layer edge and underlying viscous layer are considered as the tangent wedge approximation is used to determine the prescribed pressure on the boundary layer, rather than determining the full inviscid layer between the shock wave and boundary layer edge. The flow within this viscous boundary layer is computed via a downstream marching method with multiple sweeps in order to achieve convergence of the pressure and boundary layer thickness. Assuming a Prandtl number of unity and an insulated wall, the flow is held to be adiabatic in all cases. Results are compared to CFD solutions of the parabolized Navier-Stokes equations. The behavior of wall pressure, boundary layer, and other flow variables are analyzed. Additionally, the shear stress and pressure gradient on the various geometries are examined to determined the accuracy of areas where flow separation is predicted.