THREE-DIMENSIONAL SHOCK SEPARATED FLOW CORRECTIONS OF k-ω SST MODEL
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摘要: “激波−边界层分离”是航空气动领域的典型湍流非平衡流动问题, 准确模拟激波分离对于跨声速飞行器气动性能评估和优化设计具有重要意义. 然而传统涡黏性湍流模式中涡黏性系数的定义方式并不适用于非平衡流动, k-ω SST湍流模式为此引入的Bradshaw假设在应用于三维强逆压梯度和较大分离流动时反而限制了雷诺应力的生成, 导致包括k-ω SST在内的常用涡黏性湍流模式均无法对此类流动进行准确模拟. 同时, 现有的非线性雷诺应力本构关系也并不能有效提高模拟精度. 为此, 针对k-ω SST模式分别提出了基于Bradshaw假设和基于长度尺度的两种激波分离流动修正方法. 前者通过提高Bradshaw常数的方式放宽了对雷诺应力生成的限制, 后者则从湍流长度尺度概念出发, 利用混合长度理论、湍动能生成/耗散之比和一种新定义的长度尺度之比构造了ω方程耗散项修正函数, 提高了模式在三维激波分离流动中的建模长度尺度. 两种方法对ONERA M6机翼跨声速大攻角流动均能得到较雷诺应力模式更好的模拟结果. 进一步的雷诺应力分析表明, 三维激波分离流动中“主雷诺应力分量”的概念不再成立, 各雷诺应力分量大小接近. 网格收敛性分析、对其他攻角状态的验证以及湍流平板边界层壁面律验证进一步确认了所提出的两种修正方法的合理性、有效性和通用性.Abstract: Shock/boundary-layer separation is a typical turbulence non-equilibrium flow in the field of aeronautical aerodynamics. Accurate simulation of shock separated flow is of great significance for aerodynamic performance evaluation and optimization of transonic aircraft. The definition of eddy viscosity coefficient in conventional eddy-viscosity turbulence models (EVM), however, is not suitable for non-equilibrium flow. The Bradshaw assumption introduced by k-ω SST turbulence model for this purpose instead restricts the generation of Reynolds stress when applied to three-dimensional flow with strong adverse pressure gradient and large separation, which results in the invalidity of k-ω SST model as well as other commonly used EVMs for this kind of flow. Moreover, the existing nonlinear constitutive relation of Reynolds stress cannot effectively improve the simulation accuracy. To this end, two shock separated flow correction methods respectively based on Bradshaw assumption and length scale are proposed for k-ω SST model. The former correction relaxes the limitation of Reynolds stress generation by increasing Bradshaw constant. While based on the concept of turbulence length scale, the latter correction constructs a modified function for the dissipation term of the ω equation by using the mixing length theory, the generation-dissipation ratio of turbulent kinetic energy and a newly defined ratio of length scale to improve the modeling length scale in three-dimensional shock separated flow. The two methods both get better simulation results for the transonic flow of ONERA M6 wing at high angle of attack than those of Reynolds stress model. Further Reynolds stress analysis reveals that the concept of "major Reynolds-stress component" in three-dimensional shock separated flow is no longer tenable since the magnitude of each Reynolds-stress component is close. The grid convergence analysis, and verifications on other angles of attack and the wall-function law of turbulent boundary layer on the flat plate further confirm the validity, applicability and universality of the proposed correction methods.
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图 1 计算压力系数和摩擦系数分布与实验的对比
Figure 1. Comparison of computed pressure and skin friction coefficients distribution with experiment
图 5 小攻角状态计算压力分布与实验的对比
Figure 5. Comparison of computed pressure distribution with experiment at small angles of attack
图 6 表面压力分布与极限流线对比
Figure 6. Comparison of surface pressure distribution and limited streamline pattern
图 7 α = 6.06°状态计算压力分布与实验的对比(非线性模式与RSM、SST和BSL模式)
Figure 7. Comparison of computed pressure distribution with experiment at α = 6.06° (nonlinear models with RSM, SST and BSL models)
9 α = 6.06°状态计算压力分布与实验的对比(修正方法与RSM、SST和BSL模式对比)
9. Comparison of computed pressure distribution with experiment at α = 6.06° (correction methods with RSM, SST and BSL models)
图 10 表面压力分布与极限流线对比(修正方法)
Figure 10. Comparison of surface pressure distribution and limited streamline pattern (correction methods)
图 11 采用FPD修正的压力分布与其他结果的对比
Figure 11. Comparison of FPD-fixed pressure distribution with other results
图 13 y/b = 90%截面前缘及分离前湍动能生成/耗散之比
Figure 13. Pk/Dk contour at leading edge and before separation of y/b = 90% section
14 对修正函数FPD进行限制前后的湍流量计算结果对比
14. Comparison of the computed turbulence variables before and after limiting the modified function FPD
图 15 α = 6.06°状态两种修正方法的网格收敛性对比
Figure 15. Grid convergence comparison of two corrections at α = 6.06°
16 两种修正方法应用于其他攻角状态的计算压力分布对比
16. Computed pressure distribution comparison of two corrections at other angles of attack
16 两种修正方法应用于其他攻角状态的计算压力分布对比(续)
16. Computed pressure distribution comparison of two corrections at other angles of attack (continued)
图 17 不同流动中雷诺应力分量的对比
Figure 17. Comparison of Reynolds-stress component for different flows
图 18 湍流平板边界层计算网格
Figure 18. Computational grid of turbulent boundary layer of flat plate
图 19 不同方法的壁面律曲线与实验数据和理论值的对比
Figure 19. Computational wall-function law by different methods comparing with experimental and theoretical data
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