Study of Large-Eddy Simulation Method for Turbulent-Vortex Cavitating Flow

提出了一种适用于含空化非定常湍流的大涡模拟方法。特别关注了由于细尺度的湍流涡旋而产生的空化起始的模型。此外，还给出了弱可压缩流动的计算格式。主要研究成果如下：(1)大涡模拟的亚格子尺度模拟：考虑到湍流细尺度涡统计特性的最新知识，提出了一种基于压力脉动的空化起始预报方法。建立了低马赫数流动的大涡模拟高阶有限差分方法。(2)直接数值模拟数据库：在与实验相对应的条件下，将直接数值模拟应用于分离湍流。结果发现，Burgers型细尺度涡可以引起空化，并且空化对涡旋结构有影响。然后，为了模拟湍流涡旋和空化现象之间的相互作用，我们对Burgers涡进行了数值模拟，它代表了涡旋在湍流中的普遍性质。(3)算法开发：由于密度变化在气液两相流体中是重要的，我们提出了一种基于椭圆型偏微分方程组的压力计算方案，适用于低马赫数流动。然后将其应用于NACA0012翼型绕流和不稳定热层结中的湍流流动，验证了该方法的有效性和准确性。此外，在运动方程中引入对流项的TVD格式，得到了二维叶栅非定常空化流动的改进结果。

We proposed a Large-Eddy Simulation (LES) method for unsteady turbulent flows including cavitation. Particular attention was focused on the modeling of cavitation inception due to the fine-scale turbulent eddies. In addition, the computational scheme for weakly-compressible flows was developed. Major results are as follows:(1) Subgrid scale modeling for LES :We proposed a method to improve the accuracy in the prediction of cavitation inception based on the pressure fluctuation, taking into account the recent knowledge of statistical property of turbulent fine-scale vortices. In addition, high-order finite-difference method for LES with transport equation of subgrid scale kinetic energy in generalized coordinate system for low Mach number flows was constructed.(2) Database by direct numerical simulation (DNS):DNS was applied to a separated turbulent flow in the condition corresponding to an experiment. As a result, we found that fine-scale vortices of Burgers type could cause the cavitation and that the cavitation affects the vortex structure. Then, to model the interaction between turbulent vortices and cavitation phenomena, we applied DNS to a Burgers vortex, which represents the universal property-of vortex in turbulence. DNS database are to be used for the subgrid scale modeling.(3) Algorithmic development :Since the density variation is important in gas-liquid two-phase fluids, we proposed a computational scheme based on the elliptic-type partial-differential equation for pressure, which is suitable for low Mach number flows. Then the efficiency and accuracy were confirmed by applying it to the flow around NACA0012 airfoil and turbulent flow in unstable thermal stratification. In addition, introducing TVD scheme for convective term in the equation of motion, we obtained an improved results for unsteady cavitating flow through two-dimensional cascade.