不可压缩湍流的色散模型

分析了广泛存在于湍流运动中的能量逆转现象,揭示了其产生的原因,提出了湍流的色散性质.在此基础上,修改了Boussinesq假设,建立了包含色散效应的新的雷诺应力封闭式和湍流色散系数,给出与不同模型相结合时,湍流色散系数所具有的不同形式,并阐述了湍流运动中能量的传递方向及条件.采用不可压缩平板边界层流动和平面后台阶流动验证了其可信性和优越性.平板摩擦阻力系数及边界层速度型与实验结果吻合良好,平面后台阶流动的流向再附长度、台阶边压力系数及湍流强度等参数均比标准k-ε模型更接近实验结果.结果表明:色散项的加入可以在不显著增加计算量的同时显著改善预测精度,模型具有一定的工程应用价值. 

Dispersion model for incompressible turbulent flows

The energy inversion phenomenon which widely exists in turbulent flows was analyzed. Its cause which was called dispersion effect in turbulent flows was revealed. On this basis, a modified Boussinesq hypothesis containing dispersion coefficient and a new kind of eddy viscosity model were presented. The dispersion coefficient had different forms when the modified Boussinesq hypothesis was coupled with different turbulence models. The condition and direction of energy transfer were also described. The credibility of the new model was verified in numerical simulation of wall boundary layer flow and back-facing step flow. The frictional resistance coefficient and the velocity profile for turbulent boundary layer were in good agreement with the experimental results; the reattachment length, the surface pressure coefficient on step-side wall and the turbulence intensity profile for backward-facing step flow were closer to the experimental results than the standard k-ε model. Results show that the introduction of dispersion term can improve the accuracy of the prediction significantly with very little expenses, so the model should be useful in engineering application.