Development of numerical schemes for the fluid flows with accurate boundary condition

开发具有精确边界条件的流体流动数值方案

• 批准号: 10440028
• 负责人: ISHII Katsuya
• 金额: $ 5.44万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10440028/
• 关键词: 3-dimensional free boundary condition; Two phase fluid; Level set method; no reflective boundary condition; vortex motion; acoustic wave; combined compact scheme; high resolution; 気泡; 自由境界条件

The Purpose of this study is to develop high accurate numerical schemes for the fluid flow by using the accurate boundary conditions. For the simulation of the fluid flow, the adequate choice of numerical boundaries and/or interfaces is needed. We considered three numerical problems : (A) the fluid flow with three dimensional free surface or interface, (B) the boundary conditions of the vortical flow field interacting with acoustic waves, and (c) the boundary conditions of the vortical flow field interacting with acoustic waves. and (c) the boundary conditions for the scheme with accuracy and high resolutions. The results of the study are as follows :(1) The level set formulation for the interface of two-phase fluids is developed in the three-dimensional incompressible flow calculations, including large density and viscosity ratio as well as surface tension effects. Numerical simulations carried out for two rising gas bubbles, the interaction of buoyant drops with a fluid-fluid interfa … More ce, and the propagation of surface waves. The results agree with previous experiment data, and make it possible to analyze the physical quantities near the boundaries.(2) Improving the boundary conditions for the vector velocity potential, we get the accurate numerical method for the localized vorticity fields. Using this method, the vortex sounds can be evaluated in the various flow fields, and the sound generation mechanism can be analyzed.(3) Using the no reflective boundary conditions, the acoustic control of flow separation at low Reynolds numbers are studied. We reproduced the phenomena that the tendency toward the separation on an airfoil is reduced by an acoustic excitation, and analyze the detailed flow field near the point of separation.(4) The combined compact scheme with high accuracy and high resolution is developed in the generalized grid system with concentrated points near the boundary. This scheme gives more accurate numerical results compared with the other finite difference methods. Less

本研究的目的是利用精确的边界条件建立流体流动的高精度数值格式。为了模拟流体流动，需要适当选择数值边界和/或界面。我们考虑了三个数值问题：(A)具有三维自由表面或界面的流体流动，(B)与声波相互作用的涡流场边界条件，(c)与声波相互作用的涡流场边界条件。(c)高精度高分辨率方案的边界条件。研究结果如下：(1)在三维不可压缩流动计算中，建立了两相流体界面的水平集公式，考虑了大密度、大粘度比以及表面张力的影响。数值模拟了两个上升气泡，浮力滴与流体-流体界面的相互作用，以及表面波的传播。结果与以往的实验数据吻合，使边界附近物理量的分析成为可能。(2)改进了矢量速度势的边界条件，得到了局部涡度场的精确数值计算方法。利用该方法可以对不同流场下的涡声进行评价，并分析其产生机理。(3)在无反射边界条件下，研究了低雷诺数流动分离的声学控制。我们再现了在声场激励下翼型的分离倾向减小的现象，并详细分析了分离点附近的流场。(4)在边界附近点集中的广义网格系统中，提出了高精度、高分辨率的组合压缩方案。与其它有限差分方法相比，该格式的数值结果更为精确。少

项目成果

Ishii, K.: "Sound Generation in Oblique Collision of Two Vortex Rings"J. Phys. Soc. Japan. 67. 2306-2314 (1998)

Ishii, K.：“两个涡环倾斜碰撞中的声音产生”J。

Suzuki, S.: "Numerical Analysis of the Separation on a 2-D Airfoil by Acoustic Excitation"to appear in Computational Fluid Dynamics J.. (2000)

Suzuki, S.：“通过声学激励对二维翼型件进行分离的数值分析”出现在《Computational Fluid Dynamics J.》（2000 年）中

Ishii, K.: "Sound Generation by Interactions of Two Vortex Rings""Dynamics of Slender Vortices", eds. E.Krause and K., Gersten, Kluwer. 347-361 (1998)

Ishii, K.：“两个涡环相互作用产生声音”“细长涡旋动力学”，编辑。

Kaneda, Y.: "Taylor Expansions in Power of Time of Lagrangian and Eulerian Two-Point Two-Time Velocity Correlations in Turbulence"Phys. Fluids. 11. 2154-2166 (1999)

Kaneda, Y.：“湍流中拉格朗日和欧拉两点两次速度相关性的时间幂的泰勒展开式”物理学。

Oka, H.: "Numerical Analysis on the Motion of Gas Bubbles"J. Phys. Soc. Japan. 68. 823-832 (1999)

Oka, H.：“气泡运动的数值分析”J。