A numerical formulation for the modeling of turbulent cavitating flows is presented. The flow field is governed by the 3D, time-dependent Navier–Stokes equations for a compressible isothermal mixture. The Arbitrary Lagrangian–Eulerian Variational Multiscale (ALE-VMS) formulation is adopted to model the turbulent flow on moving domains with no-slip boundary conditions imposed weakly. The formulation is first tested on the cavitating flow over a 2D NACA0012 airfoil and compared to published numerical results. Next, the framework is applied to the benchmark problem for the flow over a hemispherical fore-body. The numerical results are compared to the reported experimental data, showing a good agreement over the range of cavitation numbers. Finally, the simulation of a hydrokinetic turbine in cavitating flow at a low cavitation number is presented in order to test the stability of the formulation and the capability to handle real engineering problems involving turbulent cavitating flows on moving domains.

中文翻译：

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空化流的变分多尺度框架

提出了用于模拟湍流空化流的数值公式。流场由可压缩等温混合物的 3D 时间相关 Navier-Stokes 方程控制。采用任意拉格朗日-欧拉变分多尺度 (ALE-VMS) 公式来模拟运动域上的湍流，其中无滑移边界条件施加较弱。该公式首先在二维 NACA0012 翼型上的空化流上进行测试，并与已发表的数值结果进行比较。接下来，该框架被应用于半球形前体上流动的基准问题。将数值结果与报告的实验数据进行比较，显示出在空化数范围内的良好一致性。最后，