不同雷诺数下方柱绕流的数值模拟

Numerical simulation of flow around square cylinders at different Reynolds numbers

在不同雷诺数条件下,对流体绕经方形柱体的流动进行了数值模拟,计算雷诺数分别为100,1×103,1×104和2.2×104.当Re=100时,直接采用N-S方程进行计算;当Re=1×103,1×104和2.2×104时,则引入k-ε湍流模型进行计算.应用Galerkin有限元法对控制方程进行离散和求解,利用分离时间步长法处理控制方程中的非线性项.模拟计算得出了在不同雷诺数下的卡门涡街脱落形态.方柱后尾涡的形态会随雷诺数的变化而产生一定的变化.当雷诺数较低时,尾涡会拖得比较长,随着雷诺数的增加,尾涡长度会随之缩短.计算得到了方柱的受力系数和Strouhal数.将计算结果与文献上的实验和计算结果进行了比较,两者吻合较好.

Flow around a square cylinder is numerically simulated at different Reynolds numbers. The Reynolds numbers of computation are selected to be 100, 1 × 10^3 , 1 × 10^4 and 2.2 × 10^4. For the lower Reynolds number, Re = 100, N-S equations are directly used in the simulation. For the higher Reynolds numbers, Re = 1 × 10^3 , 1 × 10^4 and 2.2 × 10^4 , a κ-ε based model of turbulence is applied to solve the turbulent problem. Variational form of the numerical system is discretized with the Galerkin finite element method and non-linear coupling terms in the equations are treated separately at different fractional time steps, by an operator-splitting time-stepping method. The shedding modes of the Karman vortex streets after the cylinder at different Reynolds numbers were calculated out. When the Reynolds number is smaller, the forming length of the vortex in the near wake of the cylinder is longer. Increased Reynolds number results in shortened forming length. The force coefficients and the Strouhal number are calculated out and compared with the previous experimental and numerical data. These results are in good agreement.