对二维分离流涡黏性系数非线性分布的新认识

A NEW UNDERSTANDING OF THE NONLINEAR EDDY-VISCOSITY DISTRIBUTION FOR THE TWO-DIMENSIONAL SEPARATION FLOWS

以弱非线性涡黏性模型为出发点,对Delery分离流动实验结果进行分析并获得了非平衡态分离区涡黏性系数与形状因子J之间的非线性关系.该非线性关系显示在分离起始阶段,涡黏性系数较平衡态先减小,后增大;再附阶段,涡黏性系数较平衡态数值逐渐增大,并在再附点位置接近最大,而后又逐渐减小,恢复到平衡态水平.总结涡黏性系数的这种非线性发展数学关系式,并将它应用于BL模型,在不添加微分方程的情况下发展出一种适用于分离流动的改进代数湍流模型.对低速平板流动,跨声速,超声速以及高超声速分离流动的计算结果表明,该改进湍流模型可以较准确地模拟各类复杂分离流动,计算精度明显优于传统代数模型以及一些两方程模型,而计算工作量仍与BL模型相当.这表明所提出的涡黏性系数非线性发展规律是正确的,且应用在二维分离流动中具有一定的普适性.

A study of turbulence modeling of 2D separation flows is presented in the paper. First, experimental data analysis of Delery＇s transonic bump showed the nonlinear development, of the eddy viscosity in the separation zone. Second, it is found that the eddy-viscosity decreases in the separation part and then enlarges during reattachment and relaxation process. Third, a nonlinear correlation is extracted from the experiment data and then successfully applied into the Balwin-Lomax model to form a mathematically new and simple algebraic turbulence model. The proposed model was evaluated with several typical separation flows, including low speed flow over plate, transonic flow, supersonic flow and the hypersonic flow. The numerical results are compared with the experimental data and the results obtained from other models to show that the nonlinear characteristics of eddy-viscosity proposed in this paper is correct and suitable for 2D separation flows.