基于卡门尺度和滤波方法的SST方程改进

IMPROVEMENT AND ASSESSMENT OF THE SST EQUATION BASED ON KARMAN SCALE AND FILETER METHOD

基于滤波方法和卡门尺度对原始剪切应力输运(shear stress transport,SST)湍流模型进行了改进,提出了一种卡门尺度修正的滤波SST方法.湍流多尺度效应必须在分离流场模拟中给予反映,该方法减弱了雷诺平均(Reynolds averaged Navier--Stokes,RANS)方法时间平均特性对于流场脉动量的压迫作用,在流场中引入了大涡模拟(large eddy simulation,LES)方法的亚格子模型,形成一种新型的脱体涡模拟方法(detached eddy simulation,DES)方法;同时,为了降低原始DES方法在网格加密过程中产生网格诱发的雷诺应力损耗,利用卡门尺度对滤波因子进行修正.平板边界层算例中,卡门尺度对于RANS方法的跟随性远远强于DES方法,在边界层内的速度型和RANS方法吻合很好,而DES方法在加密过程中速度型的鲁棒性较差,说明卡门尺度在有效地保护了边界层内使用RANS求解,降低速度型偏离对数率现象的产生;HGR-01翼型算例证明BY-SST方法可以有效的避免网格诱导分离现象的产生;证明BY-SST方法在分离流动中的精度高于DES方法.

A modified filter method of SST turbulence model based on Karman length scale correction has been proposed in this paper. With application of the sub-grid model in LES theory, a new DES method has been established, which could alleviate the restriction to flow fluctuation by the time averaging in RANS solver so that the multi-scale effect in separated flow could be simulated. Besides, the filter factor has been modified with the Karman scale to reduce the dissipation of Reynolds stress which would occur in the original DES cased by grid refinement o In the numerical study case of flat plate boundary layer, the velocity profile within the boundary layer would match well the result by RANS, compared to the low robustness and poor capability inside boundary layer of DES method with grid refinement, which shows that the Karman scale has guaranteed that the flow inside the boundary layer would be solved by RANS instead of LES. HGR-01 airfoil test case proves that BY-SST method can avoid the grid induced separation more robust than that of DES method.