Oblique wave interactions in 2D steady supersonic flows of Bethe-Zel'dovich-Thompson fluids

Abstract

This paper studies steady supersonic flow in a 2D semi-infinite divergent duct. We assume that the flow satisfies the slip boundary condition on the walls of the duct, and the state of the flow is given at the inlet of the divergent duct. When the fluid is a polytropic ideal gas, the problem can be reduced to some interactions of rarefaction simple waves, and the existence of a global classical solution inside the divergent duct can be established using the method of characteristics. In this paper we assume that the fluid is a nonconvex Bethe-Zel'dovich-Thompson (BZT) fluid. This type of fluid may significantly differ from polytropic ideal gases. For instance, physically admissible rarefaction shocks can occur. Depending on the oncoming flow state and the flare angles of the divergent duct, thirteen distinct types of oblique wave interactions may occur, including oblique composite waves consisting of shocks and centered simple waves. This paper systematically studies these oblique wave interactions and constructs global, piecewise smooth, supersonic solutions within the divergent duct using characteristic decomposition and hodograph transformation methods. We also obtain the detailed structures of these solutions in addition to their existence. The results and methods of this paper are also applicable to some 2D Riemann problems for gases with nonconvex equations of state.