Direct numerical study of speed of sound in dispersed air–water two-phase flow

Abstract

Speed of sound is a key parameter for the compressibility effects in multiphase flow. We present a new approach to do direct numerical simulations on the speed of sound in compressible two-phase flow, based on the stratified flow model (Chang and Liou, 2007). In this method, each face is divided into gas–gas, gas–liquid, and liquid–liquid parts via reconstruction of volume fraction. The numerical fluxes of both liquid and gas flows are calculated by AUSM+-up scheme, and the flux due to interactions between different phases is solved by the exact Riemann solver. The effects of frequency (below the natural frequency of bubbles), volume fraction, viscosity and heat transfer are investigated. With frequency f=1 kHz, under viscous and isothermal bubble conditions, the simulation results agree with the experimental results. The simulation results show that the speed of sound in air–water bubbly two-phase flow is larger when the frequency is higher. At lower frequency, the homogeneous condition is better satisfied for the phase velocity. Considering the phasic temperatures, an isothermal bubble behavior is observed during the pressure wave propagation. Finally, the dispersion relation of acoustics in two-phase flow is compared with analytical results below the natural frequency. This work for the first time presents an approach to the direct numerical simulations of speed of sound and other compressibility effects in multiphase flow, which can be applied to study more complex situations, especially when it is hard to do experimental study.