小攻角下三维细长体定常空化形态研究

基于边界元方法, 使空泡表面和细长体表面分别满足Dirichlet 边界条件和Neumann边界条件, 数值迭代获得小攻角下三维细长体的定常空化形态. 采用线性三角形单元, 将控制点布置在网格节点上, 应用局部正交坐标系并采用迭代方法获得空泡表面的速度势, 进而通过边界积分方程确定空泡厚度的分布. 采用拉格朗日插值方法得到空泡末端的厚度, 避免了迭代过程中网格的重新划分. 数值结果与实验值符合良好, 验证了该方法的合理性. 系统研究了空化数、攻角以及锥角对于三维细长体空化形态的影响规律. 数值结果表明: 攻角使得细长体的空化形态呈现不对称性, 出现空泡向背流面“堆积”的现象; 而空化数越小或锥角越大, 空泡形态的不对称性将越严重. 关键词： 边界元方法 三维细长体 局部空化 攻角

Cavitation shape of the three-dimensional slender at a small attack angle in a steady flow

In this paper, based on the boundary element method, the cavitation shape of the three-dimensional slender at a small attack angle in a steady flow is simulated through the iterative method, while Dirichlet boundary conditions and Neumann boundary conditions are satisfied in cavitation and slender respectively. The linear triangular elements are adopted and the control points are arranged in grid nodes. The velocity potential for cavity surface is determined through an iterative method in a local orthogonal coordinate system, and then the distribution of cavitation thickness can be determined by the boundary integral equation. To prevent the remeshing operation in the iterative process, the Lagrange interpolation method is used to determine the thickness at the end of cavity. The numerical results are in good agreement with the experimental data. The influence of those on cavitation shape of the three-dimensional slender are investigated, such as cavitation number, attack angle and cone angle. Numerical results show that the cavitation shape of the three-dimensional slender is asymmetric at an attack angle and is analogous to the cavitation stacking in the lee side. While with the decrease in the cavity number or the increase in cone angle, the asymmetry for the cavity shape will be more serious.
Keywords： boundary element method three-dimensional slender partial cavitation attack angle