автомодельные течения

Modification for the Chisnell’s Method of Approximate Analytic Solution of the Converging Shock Wave Problem

Authors: Kozhanov V. S., Chernov I. A.

The self-similar problem about a convergence to the centre of a strong shock wave is discussed. The approximate analytical solution which has the same form as the Chisnell’s solution is proposed. The simple expressions for definition of self-similar representers of the velocity, density and square of the sound speed are written down. The self similar exponent is determined by solving the algebraic equation. The achived results correlate better with the exact solution of the classical numerical method.

Homentropic Model of Spherical Shock Wave Reflection from the Center of Convergence

Authors: Chernov I. A.

An implosive shock wave on a based gas the particular case of motion with zero pressure, but with variable density is discussed. The density is described by degree relation to distance up to a point of focusing of a shock wave. Such selection of an exponent in this relation that the entropy in all area of flow after passage of a shock wave was a constant (homentropic case) is offered. Thus qualitatively different behaviour of temperature in comparison with classical case Guderley – Landau – Stanjukovich is obtained.

Calculation of Outgoing Shock Waves in The Empty Cavity Collapse Problem

Authors: Kozhanov V. S.

The self-similar problem about a collapse of an empty cylindrical or spherical cavity in compressible fluid with adiabatic exponent γ is considered. Two possible variants of the flow after collapse are discussed. The variants are connected with the entropy behavior through the outgoing shock. The calculations show that the main difference in the flow quantities behavior at reflection stage have a quantitative character. Outgoing shock compression ratio, characterized by relation ρ2/ρ1, decreases for both variants of the reflection when γ is increase.