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.

中文翻译：

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气水两相分散流中声速的直接数值研究

声速是多相流中可压缩性效应的关键参数。我们基于分层多相流模型 (Chang & Liou, JCP 2007)，提出了一种对可压缩两相流中的声速进行直接数值模拟的新方法。该方法通过重构体积分数将每个面分为气-气、气-液和液-液部分，并通过黎曼求解器计算出相应的通量。包括粘度和传热模型。研究了频率（低于气泡的固有频率）、体积分数、粘度和传热的影响。频率为1 kHz，在粘性和等温条件下，模拟结果很好地满足了实验结果。仿真结果表明，频率越高，气-水气泡两相流中的声速越大。在较低频率下，对于相速度，更能满足均匀条件。考虑到相温度，在波传播过程中观察到等温气泡行为。最后，将两相流中声学的色散关系与固有频率以下的分析结果进行比较。这项工作首次提出了一种直接数值模拟多相流中的声速和其他压缩性效应的方法，可以应用于研究更复杂的情况，特别是在难以进行实验研究的情况下。考虑到相温度，在波传播过程中观察到等温气泡行为。最后，将两相流中声学的色散关系与固有频率以下的分析结果进行比较。这项工作首次提出了一种直接数值模拟多相流中的声速和其他压缩性效应的方法，可以应用于研究更复杂的情况，特别是在难以进行实验研究的情况下。考虑到相温度，在波传播过程中观察到等温气泡行为。最后，将两相流中声学的色散关系与固有频率以下的分析结果进行比较。这项工作首次提出了一种直接数值模拟多相流中的声速和其他压缩性效应的方法，可以应用于研究更复杂的情况，特别是在难以进行实验研究的情况下。