Viscous Hypersonic Flows

In the first part of this chapter, inviscid hypersonic flows are discussed, starting with hypersonic similarity parameters. High Mach number flows over plates, wedges and cones are treated with hypersonic small disturbance theory as well as the Newtonian flow theory. Numerical methods to solve the blunt body problems are also covered.

To account for viscous effects, boundary layers and viscous/inviscid interaction procedures will be covered next. The main feature of hypersonic boundary layer is the high temperature effects and aerodynamic heating, while the main feature of the interaction problem is the vorticity and entropy in the inviscid layer.

Other important factors, including chemical nonequilibrium with dissociation and ionization as well as low density and rarefied gas dynamics will not be covered here and the reader is referred to more specialized references (see Park [12]).

The discussion is based on the continuum model, where the mean free path of the molecules A is much smaller than the characteristic length of the body, i. e. the Knudsen number is small (say less than 0.1), where

A

Kn =- (12.178)

From kinetic theory of gases, Kn = 1.26jYM0/Rel. For Kn > 10, free molec­ular regime exists and Boltzmann equations must be used.

For the continuum model, the flow is governed by the Navier-Stokes equations. At a solid surface, no penetration and no slip boundary conditions are imposed. Either the temperature or the heat flux are also specified (the effect of slip velocity and jump in temperature at the boundary will not be covered). Moreover, we will assume perfect gas. In general, real gas is governed by p = pRTZ, where Z is the compressibility factor and 7, the ratio of specific heat under constant pressure and constant volume (7 = Cp /Cv), is different before and after the shock.

Another important factor is the dependence of the viscosity coefficient on tem­perature, and we will assume in this discussion a power law, namely

Viscous Hypersonic Flows

and for simplicity, let w = 1. Also, radiation effects will not be considered.

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