双方程k-ωSST湍流模型的显式耦合求解及其在叶轮机械中的应用

Explicit Coupled Solution of Two-equation k-ωSST Turbulence Model and Its Application in Turbomachinery Flow Simulation

双方程k-ω剪切应力输运(SST)湍流模型通常以隐式耦合方式或者显式半耦合/解耦的方式来求解。本文提出了该模型的一种显式耦合应用方法,即通过点隐的方式来处理湍流源项的刚性,并与混合Runge-Kutta时间推进以及当地时间步长、隐式残差光顺等加速收敛技术相结合,从而使得湍流方程可以与流动方程同时求解。为了增强计算的鲁棒性,进一步对湍流变量进行了限制。将所发展的方法用于DLR平面叶栅算例,确认了求解结果的正确性以及刚性的来源。通过对三维NASA Rotor 67的模拟,验证了SST模型的精度;进一步将其与Badwin-Lomax(BL)模型、Spalart-Allmaras(SA)模型对比,发现三者都能正确地捕捉出口参数分布,且SST与SA模型的模拟结果比较一致;对于该算例,SST模型在总温模拟上更具优势,而BL模型在总压分布上与试验值更加接近。

The two-equation κ-ω shear stress transport （SST） turbulence model is commonly integrated in an implicit cou-pled way, or in an explicit loosely coupled/decoupled way, An explicit coupled implementation is proposed in the paper. In the present application, a point-implicit method is adopted to treat the stiffness of the turbulence source terms. Combined with hybrid Runge-Kutta time marching and popular accelerating techniques, such as local time stepping, implicit residual smoothing, etc., the turbulence equations can be solved simultaneously with the flow equations. In order to strengthen the robustness of the solver, the turbulent variables are limited. The proposed method is first validated against a DLR 2D cas- cade test case, which demonstrates the physical validity of the results, and determines the origin of the stiffness. Further, an NASA Rotor 67 test case is used to verify the accuracy of the SST model. The Baldwin-Lomax （BL） algebraic model and the Spalart-Allmaras （SA） one-equation model are also used for comparison. Final results indicate that the SA model and SST model achieve consistently better results, and the SST model has the best accuracy among the three models.