Accession Number : AD0705657

Title :   ON THE STABILITY OF NORMAL SHOCK WAVES WITH VISCOSITY AND HEAT CONDUCTION,

Corporate Author : POLYTECHNIC INST OF BROOKLYN FARMINGDALE N Y DEPT OF AEROSPACE ENGINEERING AND APPLIED MECHANICS

Personal Author(s) : Morduchow,Morris ; Paullay,Alvin J.

Report Date : JAN 1970

Pagination or Media Count : 34

Abstract : The stability problem, for small arbitrary one-dimensional disturbances of a normal shock wave with viscosity and heat conduction in a thermodynamically perfect gas with a Prandtl Number of 3/4 is treated, and is formulated explicitly as an eigenvalue problem involving ordinary linear differential equations with polynomial coefficients in a fixed finite domain whose end points are singular points of the differential equations. It is shown by a simple general type of mathematical argument that one possible mode shape for the perturbations is a translation of the shock-structure, and that such a disturbance is neutrally stable. For the limiting case of a weak-shock structure, the equations developed are shown to reduce systematically to a perturbed form of Burger's equation. The weak shock structure is shown to be stable for any Prandtl Number and general equation of state, and a complete solution for the disturbance eigenvalues and eigenfunctions in this case is derived and discussed. (Author)

Descriptors :   (*SHOCK WAVES, STABILITY), VISCOSITY, THERMAL CONDUCTIVITY, NAVIER STOKES EQUATIONS, PERTURBATION THEORY, PRANDTL NUMBER, ONE DIMENSIONAL FLOW

Subject Categories : Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE