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

本文提出了一种大涡模拟（LES）方法来模拟含空化的非定常湍流流动。特别注意的是，由于细尺度湍流涡的空化初生的建模。此外，还发展了弱可压缩流动的计算格式。主要研究结果如下：（1）大涡模拟的亚网格方法：结合湍流细尺度涡统计特性的最新研究成果，提出了一种基于压力脉动的空化初生预测方法。此外，本文还建立了适用于低马赫数流动的亚网格尺度动能输运方程的大涡模拟高阶有限差分方法。(2)直接数值模拟（DNS）数据库：DNS应用于分离湍流在相应的实验条件。结果表明，Burgers型的细尺度涡能引起空化，空化对涡结构有影响。然后，为了模拟湍流涡与空化现象之间的相互作用，我们将DNS应用于Burgers涡，它代表了湍流中涡的普遍性质。DNS数据库将用于次网格规模建模。(3)数值模拟方面：考虑到气液两相流中密度变化的重要性，提出了一种适用于低马赫数流动的基于椭圆型压力偏微分方程的计算方法。并将其应用于NACA0012翼型绕流和非稳定热分层的湍流流动，验证了该方法的有效性和准确性。另外，对运动方程中的对流项引入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.