Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Крайко А.Н.  

Shock waves in unsteady self-similar, supersonic axysimmetrical and conical-supersonic flows


The questions connected with the shock waves (SW) in unsteady self-similar flows, in stationary axisymmetric supersonic jets and in conical-supersonic flows arising when supersonic overflow of corner-typed configurations (for example, V-shaped wings) framed from crossed half-planes are discussed. For self-similar un-steady flows they are the SW, which propagate («reflect») from the center or axis of symmetry in a problem about an empty spherical cavity collapse or in the Guderley's problem. As against the classical statements the reduction of the perfect gas specific thermal capacities ratio («adiabatic ratio») on the reflected SW is supposed. The fea-tures of flows, caused by this assumption, are described.
The amplification of weak SW, going to an axis of symmetry in stationary axi-symmetric supersonic jets is investigated. According to «approach of nonlinear acoustics» in contradiction with the results of Euler equations numerical solution such amplification does not depend on the adiabatic ratio and the flow Mach number before SW. More accurate nonlinear theory, deprived of this defect, is designed. The amplification of SW in it is defined from the decision of Coshy's problem for two ordinary differential equations. The Bounds of applicability of the advanced approach are defined when their numerical integration.
It is shown, that along the two-dimentional conic flows parabolicity line (the trace of a Mach cone) the uniform conical-supersonic flow can be continuously adjoined by the both depression and compression flows. In a number of works the statement of such situation impossibility has formed the basis for so-called «hanging shocks» in-troduction, which end on a parabolicity line.

Abstracts file: Тезисы.doc
Full text file: ДокладЯненко2011Крайко.pdf

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