Large-eddy simulation of smooth and rough-wall turbulent boundary-layer flows at arbitrary Reynolds numbers

湍流流体动力学现象的大规模计算模拟将继续对许多不同的科学和工程领域产生巨大影响，从地球气候模型到环境流体动力学，再到大雷诺数的工业和工程应用。理想的方法是直接数值模拟，其中所有相关的物理过程都得到了恰当的描述，所有长度尺度都在数值模拟中得到了解决。然而，在许多工程应用所需的极端雷诺数下，在可预见的未来，完全的域名系统不太可能是可行的。标准的工程预测工具是雷诺平均建模(RANS)。虽然RAN仍将用于许多应用，但在工程开发工作中，对更详细但易于计算的数值模拟能力的需求越来越大。例如内部管道流动和外部流线型和钝体流动，其中需要对包括转折、曲率、分离和雷诺数效应在内的湍流边界层动力学进行物理上真实的模拟，以实现准确的预测。大涡模拟(LES)介于RANS和DNS之间，在计算网格上对大尺度的湍流运动进行分辨，同时模拟小的、未分辨的涡旋的影响。大涡模拟在各种不同的环境下，对于自由剪切和混合湍流都非常成功。在无界流动中，大涡携带了大部分的湍流动能，主导着动量输运，并决定了小尺度湍流动力学的长度和时间尺度。这幅图是在光滑或粗糙的墙壁附近反转的，在那里，能量最大的涡流必然是小范围运动的一部分。因此，尽管经过了几十年的努力，但对壁面边界湍流的准确数值预测仍然是计算流体力学的一个具有挑战性的领域。本研究的主要目的是建立一个适用于实际工程中典型雷诺数的壁面湍流大涡模拟能力。该项目将致力于发展一种亚网格尺度的壁面湍流大涡模拟方法，重点应用于在存在有利和不利压力梯度、壁曲率、层流-湍流转变和实质上任意大雷诺数的流动分离的情况下空间演化的光滑或粗糙壁湍流边界层流动。该单元是一种基于流动量方程的壁法向积分的亚格子尺度壁面模型，可以在不需要近壁尺度分辨率的情况下动态计算壁面剪应力，但考虑了局部表面粗糙度、壁面法向动量输运和压力梯度效应。由这项工作产生的大涡模拟将可用于纳入通用计算流体动力学程序。预计这将大大提高我们在非常大的雷诺数下数值模拟复杂湍流流动的能力。这项研究将成为研究生个人教育和培训的重要组成部分。此外，这项工作将通过参加K-12外联方案，支持传播现代计算工程技术的概念和应用。

The large-scale, computational simulation of turbulent fluid-dynamical phenomena will continue to have an enormous impact on many diverse areas of science and engineering ranging from climate modeling of planet earth, to environmental fluid dynamics and to industrial and engineering applications at large Reynolds numbers. The ideal is direct-numerical simulation (DNS) in which all relevant physical processes are properly represented and all length scales are resolved within numerical simulation. At the extreme Reynolds numbers required for many engineering applications, however, full DNS is unlikely to be practicable within the foreseeable future. The standard engineering prediction tool has been Reynolds-averaged modeling (RANS). Whilst RANS will remain useful for many applications, there exists a growing need for a more detailed but computationally tractable numerical simulation capability in engineering development work. Examples include internal pipe flows and external streamlined and bluff-body flows where physically realistic modeling of turbulent boundary-layer dynamics including transition, curvature, separation and Reynolds-number effects is required for accurate prediction. Large-eddy simulation (LES), where the large scales of turbulent motion are resolved on the computational grid while the effects of small, unresolved eddies are modeled, is intermediate between RANS and DNS. LES has been very successful for free-shear and mixing turbulence in a wide variety of settings. In unbounded flows, the large eddies carry most of the turbulent kinetic energy, dominate momentum transport and set the length and time scales that condition the small-scale turbulence dynamics. This picture is reversed near a smooth or rough wall, where the most energetically productive eddies are necessarily part of the small-scale motion. Hence despite decades of effort, the accurate numerical prediction of wall-bounded turbulent flows remains a challenging area for computational fluid dynamics. The broad objective of the present research is to construct a robust LES capability for wall-bounded flows at Reynolds-numbers typical of practical engineering interest.The project will aim to develop a subgrid-scale methodology for LES of wall-bounded turbulence with emphasis on application to spatially evolving smooth or rough-wall turbulent boundary-layer flows in the presence of favorable and adverse pressure gradients, wall curvature, laminar-turbulent transition and flow separation at essentially arbitrarily large Reynolds numbers. The novel element is a subgrid-scale wall model, based on a wall-normal integration of the stream-wise momentum equation, which enables dynamical calculation of the wall shear stress without requiring near-wall scale resolution, but which incorporates local surface roughness, wall-normal momentum transport and pressure-gradient effects. The LES modeling resulting from this work will be available for incorporation into general computational fluid-dynamics codes. It is expected that this will provide a significant advance in our capability for the numerical simulation of complex turbulent flows at very large Reynolds numbers. The research will form an important part of the education and training of individual graduate students. Additionally the work will support dissemination of the concepts and applications of modern computational engineering technology through participation in K-12 outreach programs.