  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
multiphase flow model (Chang & Liou, JCP 2007). In this method, each face is
divided into gas-gas, gas-liquid, and liquid-liquid parts via reconstruction of
volume fraction, and the corresponding fluxes are calculated by Riemann
solvers. Viscosity and heat transfer models are included. The effects of
frequency (below the natural frequency of bubbles), volume fraction, viscosity
and heat transfer are investigated. With frequency 1 kHz, under viscous and
isothermal conditions, the simulation results satisfy the experimental ones
very well. 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, for the phasic velocities, the homogeneous condition is better
satisfied. Considering the phasic temperatures, during the wave propagation an
isothermal bubble behavior is observed. 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.
