The Riemann Problem for the Flow Pattern in Deviated Pipes Carrying Isentropic Two-Phase Flows

Abstract

We study the Riemann problem for the one-dimensional two-phase isentropic flow in deviated pipes. The model under consideration is nonconservative and conditionally strictly hyperbolic. The generalized Rankine–Hugoniot conditions are established for the present system with nonconservative products to define weak solutions. Exact Riemann solutions are presented in fully explicit forms for the nonhomogeneous model, where the elementary waves are discussed along parabolic curves. Moreover, it is demonstrated that a delta shock wave appears in the Riemann solutions under specific conditions when the pressure vanishes.