正交曲线坐标在湍流计算中的应用

Application of Orthogonal Curvilinear Coordinates in Turbulent-Flow Predictions

选用直角座标系来计算流场的几何边界为曲线或曲面的这样一些有实际意义的流动,通常导致误差较大,边界处理很不方便,并且很不经济。在本文的计算中,我们采用贴体的正交曲线网格来处理曲线边界。正交曲线网格通过用迭代和有限差分形式求解Possion方程,并运用Visbal ＆Knight的二步网格生成法获得。在流场计算中,我们用k-ε二方程形式的Boussinesq粘度模式(BVM)封闭时均流动方程中的雷诺应力,同时,时均流和湍流的控制方程都写成与它们在直角座标系中相同的形式,从而使一般的直角座标形式的计算软件可以继续使用。通过计算并与实验数据比较,显示本文的组合方法基本有效可靠。

Numerical simulations of steady, incompressible turbulent flows with complex boundaries are presented in this article. The complex boundary geometries are accurately represented via a boundary-fitted orthogonal coordinate system which is generated by solving a set of elliptic partial-differential equations (PDEs). Thus, an irregular physical space can be mapped into a rectangular computational domain.The turbulent flow is described by time-averaging technique in which theκ-∈ two-equation-type Boussinesq-viscosity model (BVM) is employed to represent the resulted turbulence quantities, Reynolds stresses u uj. Numerical solution is then obtained by solving the transport equations in their physical-component forms which are derived through the coordinate transformation from Cartesian coordinates to the orthogonal ones. Solution algorithm employes finite-volume method, with SIMPLE procedure to determine pressure field.The combined procedures are tested in a single-sides, sudden-expansion flow situation. Computational results show favourable agreement with experiment data, indicating that curvilinear-orthogonal coordinate system can be incorporated into turbulent flow with computations. A further computation of a pipe flow with rapid converging/diverging wall provides confirming results.