Analytical solution of a shock wave in gas sphere in lagrangian coordinates

Abstract eng:
An exact solution of the problem of a convergent shock wave and dynamic compression of the gas in a spherical vessel with an impermeable wall has been constructed in Lagrangian coordinates. At the initial time a negative velocity is set at the gas border; when t > t0 the shock wave spreads in the gas. The boundary of the ball will move under the certain law, which is agreed with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and the Lagrangian coordinate; the dependence of the entropy on the speed of the shock wave has been found too. In Lagrangian coordinates the problem is solved for the first time, and it is fundamentally different from previously known formulations of the problem of the self-convergence of the shock wave to the center of symmetry and its reflection from the center, in which there is no boundary of the gas.

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