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中文核心期刊

基于常微分边界层方程求解的笛卡尔网格湍流壁面模型RANS模拟方法

AN ODE-BASED WALL MODEL FOR RANS SIMULATIONS ON CARTESIAN GRIDS

  • 摘要: 在高雷诺数湍流模拟中, 应用笛卡尔网格精确解析近壁流动时, 巨大的网格量会显著降低数值求解的计算效率. 为解决这一问题, 本研究引入了双层壁模型方法将计算域分解为RANS主导的外层区域和壁面模型模化求解的近壁子网格区域. 在近壁子网格区域内, 采用二阶中心差分方法在虚拟子网格点阵上离散求解简化的边界层动量方程, 而后根据模型求解结果重构近壁模化单元的流动物理量使其严格满足壁面边界条件, 最终将双层壁模型方法植入笛卡尔网格浸没边界法(IB方法)框架内. 该策略在较高的壁面高度处借助壁面模型模化求解边界层, 极大放宽了近壁网格要求, 大幅减少网格量并提升计算效率. 在平板T3b、湍流凸包以及NACA0012翼型绕流算例中的验证结果表明: 所发展的双层壁模型方法能有效缓解笛卡尔网格湍流模拟面临的网格困境, 将壁面第一层网格尺度放宽1-2个量级, 在多种典型流动工况下保持关键流动特征模拟精度, 为解决笛卡尔网格高雷诺数湍流模拟效率瓶颈问题提供了切实有效的方案.

     

    Abstract: In the simulation of high-Reynolds-number turbulent flows, the use of Cartesian grids for accurately resolving near-wall regions often leads to a large number of grid points, which significantly reduces the computational efficiency of the numerical solver. To address this issue, this study introduces a two-layer wall-modeling approach. The computational domain is divided into an outer region dominated by the Reynolds-averaged Navier–Stokes (RANS) equations and a near-wall subgrid region modeled and solved using a wall model. Within the near-wall subgrid region, the simplified boundary layer momentum equation is discretized and solved on a set of virtual subgrid points using a second-order central difference scheme. Based on the model solution, the flow quantities in the near-wall modeled cells are reconstructed to strictly satisfy the wall boundary conditions. Finally, the two-layer wall model is integrated into the framework of the Cartesian-grid immersed boundary (IB) method. This strategy employs the wall model to simulate the boundary layer at a relatively large distance from the wall, greatly relaxing the grid resolution requirements in the near-wall region. As a result, the total number of grid points is significantly reduced, and computational efficiency is improved. Validation cases—including the flat-plate T3b, a turbulent bump, and flow around a NACA0012 airfoil—demonstrate that the developed two-layer wall-modeling method effectively alleviates grid-related challenges in Cartesian-grid-based turbulent flow simulations. It allows the size of the first grid layer near the wall to be increased by one to two orders of magnitude while maintaining simulation accuracy for key flow characteristics under various typical flow conditions. The proposed approach thus provides a practical and effective solution to the computational efficiency bottleneck in high-Reynolds-number turbulent flow simulations using Cartesian grids.

     

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