Simulations of reflected-shock waves in shock tubes taking account of side-wall boundary-layer effects.

Abstract

Numerical simulations are conducted for behaviors of reflected-shock waves interacting with side-wall boundary-layers in shock tubes. A finite-difference procedure is developed as a solver of the thin-layer Navier-Stokes equations. This procedure, which combines the Lax-Wendroff-FCT scheme with the Crank-Nicolson scheme, is applied to initial and boundary conditions in which effects of shock-tube side-wall boundary-layers. are taken account of by use of the Pohlhausen polynomials. Computations are carried out for reflected-shock waves in nitrogen and in argon gas, respectively. Bifurcated reflected-shock waves, observed experimentally in polyatomic gases in shock tubes, are reproduced in simulations for nitrogen gas and compared with semiempirical theory for bifurcated reflected-shock waves. Good agreements between them lead us to conclude that the present procedure can simulate essential parts of interactions between reflected-shock waves and side-wall boundary-layers.