On the wave interactions in the drift-flux equations of two-phase flows

Abstract

In the present work, we investigate the Riemann problem and interaction of weak shocks for the widely used isentropic drift-flux equations of two-phase flows. The complete structure of solution is analyzed and with the help of Rankine–Hugoniot jump condition and Lax entropy conditions we establish the existence and uniqueness condition for elementary waves. The explicit form of the shock waves, contact discontinuities and rarefaction waves are derived analytically. Within this respect, we develop an exact Riemann solver to present the complete solution structure. A necessary and sufficient condition for the existence of solution to the Riemann problem is derived and presented in terms of initial data. Furthermore, we present a necessary and sufficient condition on initial data which provides the information about the existence of a rarefaction wave or a shock wave for one or three family of waves. To validate the performance and the efficiency of the developed exact Riemann solver, a series of test problems selected from the open literature are presented and compared with independent numerical methods. Simulation results demonstrate that the present exact solver is capable of reproducing the complete wave propagation using the current drift-flux equations as the numerical resolution. The provided computations indicate that accurate results be accomplished efficiently and in a satisfactory agreement with the exact solution.