发表机构
Institute of Extreme Mechanics, School of Aeronautics, Northwestern Polytechnical University; National Key Laboratory of Aircraft Configuration Design, Key Laboratory for Extreme Mechanics of Aircraft of Ministry of Industry and Information Technology（西北工业大学航空学院极端力学研究所; 飞机总体设计全国重点实验室、工业和信息化部飞机极端力学重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出浮力修正的对数-二次壁面模型，用于不稳定分层湍流槽道流动的壁面模化大涡模拟，在高达Reτ≈6000和Ra=10^10下显著减少网格数量，并准确预测平均速度、温度及全局输运量。
AI 中文摘要
不稳定的热分层改变了近壁动量和热量输运，导致平均速度剖面偏离经典对数律，并使湍流混合对流的壁面模化复杂化。我们针对不可压缩泊肃叶-瑞利-贝纳德流动，开发了一种浮力修正的对数-二次壁面模型。该模型将近壁平均温度与平均流向速度之间的近似线性关系，与受混合长度标度启发的热修正平均梯度表示相结合。利用直接数值模拟（DNS）数据库中的壁面量进行的先验评估表明，标定后的壁面律能够重建近壁速度和等效于壁面函数的涡粘性剖面。我们在摩擦雷诺数高达$Re_\tau\approx6000$、瑞利数高达$Ra=10^{10}$的壁面模化大涡模拟（WMLES）中实现了该壁面模型。对于具有$Ra=10^8$和$10^9$的DNS参考剖面的案例，平均速度的最大逐点绝对相对误差为$3.6\\%$，平均温度的最大逐点绝对相对误差为$1.9\\%$。对于具有可用DNS全局输运数据的案例，努塞尔数$Nu$和壁面摩擦系数$C_f$的最大相对偏差分别为$11.7\\%$和$15.9\\%$。与相应的DNS网格相比，WMLES将网格数量减少了约$195$至$542$倍。对于$Ra=10^{10}$和$Ri_b=0.1$的案例，参考DNS分辨率策略的外推给出网格数量约为$10^{11}$量级，比当前WMLES网格数量大约三个数量级。我们还研究了剪切与浮力之间的平衡如何重组流动结构，并识别出与类似超大尺度运动的流向拉长运动和与浮力相关的流向滚转共存的标志性特征。
英文摘要
Unstable thermal stratification modifies near-wall momentum and heat transport, causing the mean velocity profile to depart from the classical logarithmic law and complicating wall modelling for turbulent mixed convection. We develop a buoyancy-modified logarithmic-quadratic wall model for incompressible Poiseuille--Rayleigh--Bénard flow. The model combines an approximately linear relation between the near-wall mean temperature and mean streamwise velocity with a thermally modified mean-gradient representation inspired by mixing-length scaling. A priori assessments using wall quantities from the direct numerical simulation (DNS) database show that the calibrated wall law reconstructs near-wall velocity and wall-function-equivalent eddy-viscosity profiles. We implement the wall model in wall-modelled large-eddy simulations (WMLES) at friction Reynolds numbers up to $Re_τ\approx6000$ and Rayleigh numbers up to $Ra=10^{10}$. For cases with DNS reference profiles at $Ra=10^8$ and $10^9$, the maximum pointwise absolute relative errors are $3.6\%$ for the mean velocity and $1.9\%$ for the mean temperature. For cases with available DNS global-transport data, the maximum relative deviations in the Nusselt number $Nu$ and skin-friction coefficient $C_f$ are $11.7\%$ and $15.9\%$, respectively. The WMLES reduces the mesh count by factors of approximately $195$--$542$ relative to the corresponding DNS meshes. For the $Ra=10^{10}$ and $Ri_b=0.1$ case, extrapolation of reference DNS resolution strategies gives a mesh count of order $10^{11}$, approximately three orders of magnitude larger than the present WMLES mesh count. We also examine how the balance between shear and buoyancy reorganises flow structure, and we identify signatures consistent with the coexistence of streamwise-elongated motions resembling very-large-scale motions and buoyancy-associated streamwise rolls.
Comments36 pages, 26 figures
