采用过滤广义Kolmogorov方程构建新型壁湍流亚格子模型

For the lack of information on the interactions between resolved and subgrid scales, actually the energy backscatter from the subgrid scales to resolved scales, there is no satisfied subgrid-scale (SGS) model of large-eddy simulation (LES) developed for wall-bounded turbulence, especially at high Reynolds numbers. Therefore, it is an obvious obstacle for LES to be used in practical engineering. The objective of this project is to acquire the required information and to develop new type of SGS models that can mostly reproduce the interactions between the resolved and subgrid scales. The generalized Kolmogorov equation (GKE) is an equation of second-order structure function (defined as scale energy) and can describe the energy transfer in scale and physical space, which is exactly the required tool. First, direct numerical simulation (DNS) data the filtered GKE will be employed to exhibit the energy-transfer mechanism between the resolved and subgrid scales in physical and scale space, when the filter widths are varied in streamwise and spanwise directions. The backscatter zones will be figured out. The relationship between the energy-transfer mechanism and the resolved coherent structures will be exploited. The key issues of the mechanism will be also figured out to develop the SGS models. Second, two types of new SGS models will be constructed based on the key energy-transfer mechanism and the velocity-reconstruction procedures, respectively. In the former type, the filtered energy-production and energy-transfer terms will be used. In the later type the whole velocity will be approximately reconstructed by two models. The first one is the predictive inner-outer model recently developed by Marusic (Marusic I.,et al., Science, 2010, 329 (5988), p193). The second one is originally promoted by the proposer based on the approximated deconvolutions in physical and scale space. The obtained SGS models will be analyzed a priori on DNS data and a posteriori in LES to know their capabilities in accounting for the energy backscatter between resolved and subgrid scales and in modeling of high Reynolds-number wall turbulence. The project can provide suitable SGS models in high Reynolds-number wall-turbulence simulation and the new tools for the SGS modeling.

能正确模拟亚格子尺度和可解尺度之间的相互作用是大涡模拟成功的关键。但目前使用的亚格子模型无法正确模拟能量从亚格子尺度向可解尺度输运的反级串机制，在近壁面区对网格密度的要求高，计算量大，使大涡模拟被限制在中等雷诺数壁湍流问题的模拟中。本项目采用过滤广义Kolmogorov方程研究槽道湍流亚格子尺度与可解尺度之间的能量输运特性及其随滤波尺度和空间位置的变化规律，获得能量从亚格子尺度向可解尺度输运的反级串机制，获得能量输运的主导物理机制与可解速度场相干结构的关系。分别采用多尺度能量输运机制和亚格子尺度速度重构模型，建立两类满足能量输运特性的亚格子模型，并对亚格子模型进行先/后验分析，以研究其模拟能量反级串的能力，最终获得可正确模拟壁湍流能量输运特性的亚格子模型和新型亚格子模型构建方法，为研究高雷诺数壁湍流和工程问题提供相应基础。

正确模拟亚格子尺度和可解尺度之间的相互作用是大涡模拟成功的关键。然而目前使用的亚格子模型无法正确模拟能量从亚格子尺度向可解尺度输运的反级串机制，在近壁面区对网格密度的要求高，计算量大，使大涡模拟被限制在中等雷诺数壁湍流问题的模拟中。本项目采用直接数值模拟方法和广义过滤Kolmogorov方程在理论上揭示了尺度能量输运特性，发现尺度能量的生成、输运和耗散与相干结构紧密相关。随着流动从层流向湍流转变，流动结构的变化也带来能量生成、反级串和耗散空间分布的变化。流动发展至完全湍流的情况下，生成项和反级串项均出现在近壁缓冲层内。在滤波尺度较小时，均为能量正级串，当滤波尺度较大时在缓冲层出现能量反级串，从而给壁湍流亚格子模型构建带来很大困难。对亚格子应力的几何结构和亚格子耗散的多尺度分解分析，发现滤波算子决定亚格子应力的特征，而可解应变率状态概率密度分布与滤波算子关系不大。亚格子应变率状态在近壁区以平面剪切为主，随壁面距离的增加逐渐向各向同性湍流的轴对称收缩状态转变。当进入对数区后，应变率状态的概率密度分布函数基本稳定。最大亚格子尺度在亚格子耗散中起主导作用，但随着滤波尺度的增大，关键的亚格子尺度比滤波尺度小，最大亚格子尺度的作用逐渐减小，而更小亚格子尺度的作用增大。.在理论与数值分析的基础上，构建了基于尺度空间速度重构和尺度能量输运的两类亚格子模型。采用第二代提升小波分析方法构建了小尺度速度重构亚格子模型。模型的后验分析表明该模型能正确预测湍动能谱和流动从层流向湍流变化的转捩过程，优于自适应局部近似反卷积模型。采用附面层对数区可解速度对近壁面内层统一速度的非线性模化和线性叠加机制，构建了内外层相互作用的近壁新型亚格子模型。该模型的后验分析结果表明，在近壁区能准确给出亚格子和可解尺度间的能量输运，减小近壁网格分辨要求，获得比传统涡粘模型更准确的结果。采用广义过滤Kolmogorov方程，构建了尺度能量输运新型亚格子模型。后验分析表明，该模型能较好地模拟可解尺度与亚格子尺度之间的能量反级串，获得了比动态Smagorinsky模型和WALE模型更准确的结果。本研究获得了适于高雷诺数壁湍流模拟的亚格子模型和构建亚格模型的方法。