Large-eddy simulations of complex turbulent flows

大多数流体流动中都会出现湍流。它的复杂性是由于这样一个事实，即湍流传输主要是由于连贯的、螺旋状的运动(“旋涡”)，这些运动在性质上是确定性的，但出现在随机的时间和位置。例如，湍流传输在决定飞机阻力或热交换器内的热传递方面起着主要作用。由于流动分析的准确性和完备性较高，显式分解涡流的求解方法越来越流行，大涡模拟(LES)就是其中之一。这项建议首先将重点放在为大涡模拟开发改进的模型和方法，以减少其计算需求，并加速其向工业的过渡；第二，将大涡模拟应用于复杂的流动。我的团队最近开发了一种新的模型来对小涡进行参数化[Piomelli等人，J.Fluid Mech，766：499-527,2015]，在最初的测试中，它已经证明了自己比现有模型更准确，计算成本更低。我们建议对它进行修改，以更好地响应湍流的局部状态，并将其扩展到更现实的流动。此外，我们将致力于发展一种“最佳大涡模拟”，使计算网格适应流动，从而使网格大小与湍流特征长度尺度的比率是均匀的。这一改进有可能将模拟成本降低数量级，因为目前的应用程序使用的网格在某些区域过于精细，而在另一些区域则处于边缘。第二个主题是大涡模拟在与技术相关的问题上的应用，与其他技术相比，对大涡模拟所提供的流动物理有更详细的理解可以带来显著的好处。首先，我们建议研究粗糙度对热传递的影响，并探索决定能量传输的未知机制，为什么当存在粗糙度时动量传输的类比不成立，以及如何对其进行建模。其次，我们将研究河流沙丘上的流动，将我们之前的研究扩展到现实生活中的形态，包括沙子的运动和沙丘的动力学演变。最后，我们将应用大涡模拟来研究前缘突起如何影响机翼的性能，以及哪些形状可以改善机翼的气动性能和声音发射。总而言之，这项建议将采取双管齐下的方法，协调方法改进、基础研究和应用。模型开发的目的是显著降低计算成本，基础研究和应用将利用大涡模拟增强的能力来理解复杂的、以前无法接近的物理问题。这项提议还将导致培训至少四名总部基地干事。*****

Turbulence occurs in most fluid flows. Its complexity is due to the fact that turbulent transport is mostly due to coherent, whorl-like motions (“eddies”), which are deterministic in character, but appear at random times and locations. Turbulent transport plays the primary role in determining, for instance, the drag of an aircraft or the heat transfer in a heat exchanger. Solution methods in which the eddies are explicitly resolved are gaining popularity because of the higher accuracy and completeness with which the flow can be analyzed; among them is the large-eddy simulation (LES). This proposal will focus, first, on the development of improved models and methodologies for LES, to decrease its computational demands and accelerate its transition to industry; second, on the application of LES to complex flows. My group has recently developed a new model to parameterize the small eddies [Piomelli et al., J. Fluid Mech., 766:499-527, 2015], which, in initial tests, has shown itself to be accurate and computationally cheaper than existing models. We propose to modify it to respond better to the local state of the turbulence, and extend it to more realistic flows. Furthermore, we will work towards the development of an "optimal LES" in which the computational grid adapts to the flow so that the ratio of grid size to the characteristic length-scale of turbulence is uniform. This improvement has the potential of decreasing the cost of a simulation by orders of magnitude, since present applications use grids that are overly refined in some regions and marginal in others. The second theme is the application of LES to problems of technological relevance, in which the more detailed understanding of the flow physics that LES affords in comparison to other techniques can result in significant benefits. First, we propose to study the effect of roughness on heat transfer, and explore the unknown mechanisms that determine the transport of energy, why the analogy with the transport of momentum does not hold when roughness is present, and how to model it. Second, we will investigate the flow over river dunes, extending our previous research to real-life configurations, including the sand motion and the dynamical evolution of the dune. Finally, we will apply LES to study how leading-edge protuberances can affect the performance of wings, and which shapes can improve the aerodynamic behaviour and sound emission of the wing. In summary, this proposal will take a two-pronged approach that coordinates methodological improvements, fundamental studies and applications. The model development is designed to decrease significantly the cost of the calculations, and the fundamental studies and applications will use the increased capabilities of LES to understand the physics of complex, previously unapproachable, problems. This proposal will also result in the training of at least four HQP. *****