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中文核心期刊

SST湍流模型在逆压梯度流动中的改进

IMPROVEMENT OF SST TURBULENCE MODEL IN ADVERSE PRESSURE GRADIENT FLOW

  • 摘要: 逆压梯度和流动分离的正确预测在飞行器设计、发动机设计和机械工程等行业中至关重要. 然而, 目前在工程界中广泛使用的RANS模型如SA湍流模型等对于逆压梯度的预测往往不尽人意. SST湍流模型在构造时引入了Bradshaw假设, 提高了模型对压力梯度的敏感性. 但是在逆压梯度下其结果往往也存在一定偏差, 在实际使用中出现分离预测提前和再附滞后的问题. 本文从 SST 湍流模型的构造机理和控制方程入手, 结合壁面摩擦分解公式, 分析模型在逆压梯度下预测分离失准的原因, 并指出失准的原因和Bradshaw假设有关, 具体表现为 Bradshaw假设强制认为湍动能的生成项和耗散项平衡, 导致了雷诺应力和湍动能的生成受到限制, 降低流动抵抗分离的能力. 文章最后通过局部区域的动能的生成项和耗散项之比对结构参数 a_1 进行一定程度的放缩, 提出一种改进的 SST 湍流模型 SST-m 模型. 改进模型的效果在高斯鼓包、吹吸平板和二维驼峰等逆压梯度案例中进行了数值验证. 结果表明, 针对逆压梯度下的流动分离问题, 改进模型有效地提高了SST 模型对于流动分离、再附位置的计算精度, 同时雷诺应力和湍动能计算精度也有不同程度的提高.

     

    Abstract: Accurate prediction of adverse pressure gradients and flow separation is critically important in numerous high-performance engineering industries such as aircraft design, engine design, and mechanical engineering. However, widely used Reynolds-Averaged Navier-Stokes (RANS) models within the engineering community, such as the Spalart-Allmaras (SA) turbulence model, often exhibit unsatisfactory performance in predicting adverse pressure gradients. Although the Shear Stress Transport (SST) k-ω turbulence model incorporates the Bradshaw’s assumption which improves the sensitivity of the model to adverse pressure gradient influence, its predictions under adverse pressure gradients still exhibit deviations, manifesting in practical applications as premature separation prediction and delayed reattachment. This paper investigates the underlying causes of the SST model's inaccuracy in predicting separation under adverse pressure gradients by analyzing its construction mechanism and governing equations, integrated with a wall friction decomposition formula. The analysis of this paper identifies the Bradshaw’s assumption as a key contributor to the inaccuracy. Specifically, the assumption imposes a forced equilibrium between the turbulent kinetic energy production terms and dissipation terms. This constraint artificially limits the generation of Reynolds stress and turbulent kinetic energy, consequently diminishing the flow's ability to resist separation. To address this limitation, an improved SST turbulence model is proposed, namely SST-m turbulence model. The modification involves dynamically scaling the structural parameter a_1 based on the local ratio of turbulent kinetic energy production to dissipation terms within critical flow regions. The enhanced model was rigorously validated using benchmark cases including flow over a Gaussian bump, a two-dimensional turbulence separation bubble, and a two-dimensional hump. The results demonstrate that, for flow separation induced by adverse pressure gradients, the modified model achieves superior predictive capabilities for both separation onset and reattachment locations compared to the original SST model. Furthermore, calculations of Reynolds stress and turbulent kinetic energy distributions show varying degrees of enhancement, confirming the model's improved physical fidelity.

     

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