Interaction of jump-fan composite waves in a two-dimensional jet for van der Waals gases

Abstract

We consider a two-dimensional (2D) jet by van der Waals gas streaming in parallel supersonic flow out of a duct into the atmosphere. We assume that the pressure p0 of the oncoming uniform parallel flow is greater than the atmospheric pressure pA and belongs to (p1e,p2i). Then at the corners at exit the oncoming flow expands in two symmetric jump-fan (jf) composite waves to the atmospheric pressure. These two jf composite waves interact and emerge as simple waves from their zone of penetration. We present a mathematical analysis of the interaction of the jf composite waves. To construct the flow in the interaction region, we consider a discontinuous Goursat problem for the 2D isentropic irrotational steady Euler equations. The existence of global piecewise C1 solution to the discontinuous Goursat problem is obtained constructively.