Abstract A novel hybrid method combining direct numerical simulation (DNS) and the Reynolds-averaged Navier Stokes (RANS), denoted as a stress-blended method (SBM), has been developed. The SBM is targeted at simulating turbulent flows over arbitrary rough surfaces in which computational savings can be achieved by making the DNS domain as small as possible. Within the SBM framework, a RANS model is enforced above the roughness layer to prevent the momentum build-up which arises in simulations where the computational domain is too small to represent the largest eddies. The SBM is validated for turbulent channel flow, both for smooth wall turbulence and using a parametric forcing approach to mimic roughness effects, with a computational cost that scales linearly with Re τ . The method is then applied to selected subsets of a scanned grit-blasted surface. For the same subset, the roughness function is found to be within 1 % of available DNS. Comparisons of small and large subsets showed differences of over a factor of two in equivalent sand grain roughness, indicating the importance of choosing representative surface samples. Simulations in the fully rough regime are carried out using one to two orders of magnitude fewer points than in a typical DNS. Since no assumptions on the roughness properties or the flow structure (such as outer layer similarity) are made, we expect the SBM to be applicable to non-equilibrium turbulent boundary layer flows.

中文翻译：

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一种模拟粗糙壁湍流的 DNS/URANS 方法

摘要 开发了一种结合直接数值模拟 (DNS) 和雷诺平均纳维斯托克斯 (RANS) 的新型混合方法，称为应力混合方法 (SBM)。SBM 旨在模拟任意粗糙表面上的湍流，其中可以通过使 DNS 域尽可能小来节省计算量。在 SBM 框架内，RANS 模型在粗糙度层上方强制执行，以防止在计算域太小而无法表示最大涡流的模拟中产生动量积聚。SBM 针对湍流通道流进行了验证，包括平滑壁湍流和使用参数强迫方法来模拟粗糙度效应，计算成本与 Re τ 成线性比例。然后将该方法应用于扫描喷砂表面的选定子集。对于相同的子集，发现粗糙度函数在可用 DNS 的 1% 以内。小子集和大子集的比较显示等效砂粒粗糙度的差异超过两倍，表明选择具有代表性的表面样本的重要性。使用比典型 DNS 少一到两个数量级的点来进行完全粗糙的模拟。由于没有对粗糙度特性或流动结构（例如外层相似性）进行假设，我们预计 SBM 适用于非平衡湍流边界层流动。小子集和大子集的比较显示等效砂粒粗糙度的差异超过两倍，表明选择具有代表性的表面样本的重要性。使用比典型 DNS 少一到两个数量级的点来进行完全粗糙的模拟。由于没有对粗糙度特性或流动结构（例如外层相似性）进行假设，我们预计 SBM 适用于非平衡湍流边界层流动。小子集和大子集的比较显示等效砂粒粗糙度的差异超过两倍，表明选择具有代表性的表面样本的重要性。使用比典型 DNS 少一到两个数量级的点来进行完全粗糙的模拟。由于没有对粗糙度特性或流动结构（例如外层相似性）进行假设，我们预计 SBM 适用于非平衡湍流边界层流动。