The dynamics of waves including shocks in two-phase flow

Abstract

In this work linear and non-linear wave propagation are investigated analytically for one-dimensional two-phase bubble flow with heat addition. Linear wave propagation results in weak shocks. The restriction to weak shock strengths leads to low velocities of sound with upper and lower limits in two-phase mixtures. Hence, the occurrence of shocks is probable in two-phase flows. The non-linear basic equations of two-phase bubble flow with heat addition are solved by the characteristics method. For stepwise calculation of the three dependent variables along the three characteristics a digital computer program was set up. The calculations showed that in compression waves the vapor is condensed almost completely under thermodynamic equilibrium. The pressure increase in the shock front then obviously leads to residual condensation. The existence of shocks is demonstrated for various boundary conditions. In two-phase one-component mixtures with small void fractions condensation in a compression wave causes a steep increase in the velocity of sound. For void fractions approaching zero the velocity of sound approaches the high velocity of sound of the saturated liquid. This greatly accelerates the convergence of characteristics in the case of compression waves. Hence, in two-phase flow a shock will always occur before complete condensation takes place in a compression wave.