Solution to Propagation of Shock Wave Based on Continuum Hypothesis

Abstract

Based on the continuum hypothesis, problem of compressing wave was studied analytically. By exploring the temperature distribution, the propagation velocity, and the thickness of the transition region, the developing process of compressing wave turning into shock wave was revealed, and the following conclusions were reached: (1) the governing equations of compressing wave can be turned into two autonomous equations, and the phase diagram can be used as an effective tool for the analysis of the compressing wave; (2) the solution of compressing wave was composed of two parts: the inner solution and the outer solution; when Pr = 3/4, the analytical inner solution can be obtained; (3) as the disturbance velocity increases, the thickness of compressing wave will decrease, and the propagation velocity of the compressing wave will increase, and the compressing wave will become shock wave when the disturbance velocity is large enough; (4) velocity and temperature across compressing wave change monotonically and continuously, but the entropy generation changing tendency is closely related to Pr; therefore, the inner solution reveals the mechanism of irreversibility happening in compressing waves.

Shock waves in gas flows with nanoparticles

“…Among the analytical methods for modeling the shock waves, the most widely used is the one that assumes that the shock wave is a plane orthogonal to the main flow and separating the flow parameters before and after the plane [7]. One can also obtain the classical Prandtl relation and the Rankine-Hugoniot relations [8].…”