Viscous Transonic Flow in Relaxing Gases.
MICHIGAN UNIV ANN ARBOR DEPT OF AEROSPACE ENGINEERING
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A general differential equation governing the flow of a viscous, relaxing gas valid in the transonic range is derived. Using this equation, the structure of a shock wave with relaxation is studied in detail in order to clarify the effect of viscosity in relaxing flows. Asymptotic solutions, valid in three different regimes of flow, depending on the order of magnitude of the free stream frozen Mach number with respect to unity, have been obtained. The results show that the viscous solutions successfully eliminate some of the difficulties encountered in inviscid theory. It is also shown that the inviscid relaxing flow equation is valid as long as the free stream frozen Mach number is much less than one. A bulk viscosity can be used to account for the relaxation when the equilibrium Mach number is close to one. The analytic results have been verified by the numerical solution of the general equation. Two dimensional versions of viscous transonic relaxing equations valid for frozen and equilibrium regimes have also been obtained.
- Fluid Mechanics