The current study evaluates the effect of taking into account the second order term of the Rayleigh–Plesset equation for the numerical simulation of cavitation with homogeneous mixture models. For that, the corrected expression for the condensation mass transfer rate has been mathematically derived and implemented in the original Zwart and Singhal cavitation models. Two tests cases of steady sheet cavitation around a NACA 0009 hydrofoil and a hemi-spherical body at different cavitation coefficients have been simulated with both the original and the corrected models. The results demonstrate that the pressure distribution at the closure region of the attached cavity is better predicted and a stronger pressure gradient is obtained. Consequently, the cavity length is slightly shortened and it gets closer to the experimental observations. Another test case of cloud cavitation around a NACA 0009 hydrofoil has confirmed that the prediction of the shedding frequency is also improved with the corrected Zwart model because the maximum cavity length is significantly reduced. In conclusion, the proposed modification of the Zwart and Singhal cavitation models helps to ameliorate the numerical simulation of both steady and unsteady cavitation flows.

当前的研究评估了将Rayleigh–Plesset方程的二阶项用于均质混合模型的空化数值模拟的效果。为此，已经通过数学推导并在原始的Zwart和Singhal空化模型中实现了冷凝物传质速率的校正表达式。使用原始模型和校正模型，都模拟了两个不同的空化系数下，NACA 0009水翼和半球形体周围的稳定片状空化的测试案例。结果表明，可以更好地预测附着腔封闭区域的压力分布，并获得更强的压力梯度。因此，腔体长度略微缩短，并且更接近于实验观察值。另一个围绕NACA 0009水翼的气蚀现象的测试案例已经证实，校正后的Zwart模型还可以改善脱落频率的预测，因为最大空腔长度明显减小了。总之，对Zwart和Singhal空化模型的拟议修改有助于改善稳态和非稳态空化流的数值模拟。