三维小空化数空泡流数值方法

采用均质平衡流空泡模型,引入基于求解液体质量份数输运方程的空泡流模型,提出新的压力密度耦合的压缩性方法和控制气液两相转换的源项,求解汽水混合介质的RANS方程和带低雷诺数修正的k-ε模型,实现了小空化数(σ=0.2~0.01)下水下航行体的空泡流数值模拟.得到清晰的空泡形态特征与内部结构,以及空泡长度和最大直径随空化数的变化规律,给出航行体运动阻力系数与空化数之间的变化关系.将计算结果与解析结果及实验数据进行比较表明,该方法保证了极小空化数下自然空泡流计算的稳定性与收敛性,提高了空泡形态特性的预报精度.

Numerical Method for Three-dimensional Cavitation Flows at Small Cavitation Numbers

In a homogeneous equilibrum cavity model with solution of transport equations of liquid mass fraction, source terms controlling the transformation between gas and liquid and a compression method for pressure-density coupling are introduced. The RANS equations in a k-ε model with modified low Re of gas-liquid mixture are solved. Cavitation flows around an underwater vehicle at extremely small cavity numbers (σ=0.2~0.01) are simulated successfully. Clear cavity shape and inner structure are obtained. The variation of cavity length and maximal cavity diameter with cavity numbers is simulated and relation between drag force coefficients of the vehicle and cavitation number is shown. The method shows good convergence and stability in simulation of natural cavity at extremely small cavitation numbers, and shows high accuracy in predication of cavity shapes.