Three-dimensional unsteady cavitating flow around a NACA0015 hydrofoil fixed between the sidewalls was simulated and the mechanism of U-shaped cloud cavity formation was clarified. A local homogeneous model was used for the modeling of the vaporliquid two-phase medium. The compressible two-phase Navier-Stokes equations as the governing equations were solved. To describe the phase change between water and vapor, the mass transfer model based on the theory of evaporation/condensation on a plane interface was introduced. The cell-centered finite volume method was employed to discretize the governing equations. Assuming turbulent flow, the turbulent eddy viscosity coefficient was computed by using the Baldwin-Lomax model with the Degani-Schiff modification. As a result, even in the case of cavitating flow without sidewalls, the shed cloud cavities has slightly 3D structure, which was not so much large as extending across the whole spanwise direction. On the other hand, in the case of cavitating flow with sidewalls, the end of sheet cavities bows in the spanwise direction because of the development of boundary layer near both sidewalls. After that, due to the occurring of the reentrant jet towards the mid-span region, the sheet cavities breaks off from mid-span region near the leading edge of the hydrofoil, and became the vortical cloud cavities, which have the large-scale U-shaped structure.
In numerical fluid dynamic simulations, adaptive mesh refinement (AMR) approaches have recently been growing in popularity, particularly when the target flow field includes complex turbulent shear flows such as jets, mixing layers, and shear layers in separated regions. In the AMR approach presented in this paper, for numerical simplicity and practicality we adopt a block-based method that uses a structured mesh in each block, a body-fitted coordinate system and a self-similar tree-based hierarchical data structure. We also implement measures that address memory/communication reduction and load balancing. As application examples we solve a separated flow around an airfoil, a transonic flow around a reentry capsule, and a coaxial jet flow. The examples demonstrate that the AMR approach is effective for capturing complex turbulent shear flows, although numerical issues such as scalability remain to be addressed for larger simulations.
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