Predictive Turbulence Models for Computational Fluid Dynamics

提案编号： CTS-0522089主要制造商：J. B。佩罗机构：当今工程设计中最大的瓶颈之一是湍流流体的计算预测。在各种各样的应用中：从空气污染，到发动机效率和排放，到全球气候预测，到潜艇性能，到银河系演化，湍流起着关键的物理作用。如果没有湍流模型，这些问题中的一些永远不会在计算上易于处理。 具有预测性的高效湍流模型可能会对如何在设计过程中使用计算流体动力学（CDF）产生深远的影响。虽然现有的工程湍流模型目前不提供预测精度，但在该资助下进行的工作通过对湍流结构以及波动速度幅度进行建模，涡动相互作用（EI）模型能够准确地预测平均流对湍流的影响。这种方法的计算成本是平均流计算的几倍，并且比大涡模拟（LES）或直接数值模拟（DNS）解决方案便宜许多数量级。这是一个区域的成本/性能参数空间，还没有被广泛探讨以前在湍流建模的背景下，这有很大的希望。工作的目的是探索广义的EI模型，利用其直接连接的精确（但未关闭）的两点速度相关输运方程和概率密度函数（PDF）输运方程的非均匀流。该模型的预测能力将被证明在各种各样的知名的基准湍流，其中一些不能准确地预测使用现有的建模方法。这项工作的更广泛的影响，超越其跨学科的性质，将产生新的兴趣，在这个困难的，但极其重要的问题。从数学的角度来看，它将阐明如何复杂的多尺度约束系统可以有效地近似（粗粒度）。从技术的角度来看，值得注意的是，液晶（用于现代电视和计算机）遵循与EI模型几乎相同的方程，并且可以直接从这些方法中受益。该项目将为应用数学和工程领域的研究生和本科生提供相互合作的机会，同时参与跨学科的前沿研究。

PROPOSAL NO.: CTS-0522089PRINCIPAL INVESTIGATOR: J. B. PEROTINSTITUTION: UNIVERSITY OF MASSACHUSETTS- AMHERSTOne of the greatest bottlenecks in Engineering Design today is the computational prediction of turbulent fluids. In a vast variety of applications: from air pollution, to engine efficiency and emissions, to global climate prediction, to submarine performance, to galactic evolution, turbulence plays a critical physical role. Some of these problems will never be computationally tractable without a turbulence model. Efficient turbulence models that are predictive could have a profound effect on how computational fluid dynamics (CDF) is used in the design process. While existing engineering turbulence models do not currently provide predictive accuracy, work performed under this grant by modeling the turbulence structure as well as the fluctuating velocity magnitudes the Eddy Interaction (EI) Model is able predict the influence of the mean flow on the turbulence exactly. The computational cost of this approach is a few times that of the mean flow calculation and many orders of magnitude less expensive than large eddy simulation (LES) or direct numerical simulation (DNS) solutions. This is a region of the cost/performance parameter space that has not been extensively explored previously in the context of turbulence modeling and which holds great promise. The objective of the work is to explore generalizations of the EI model to inhomogeneous flows by exploiting its direct connection with the exact (but unclosed) two-point velocity correlation transport equation and probability density function (PDF) transport equations. The model's predictive capabilities will be demonstrated on a wide variety of well-known benchmark turbulent flows, some of which cannot be accurately predicted using existing modeling approaches. The broader impact of this work, beyond its interdisciplinary nature, will be to generate renewed interest in this difficult but extremely important problem. From a mathematical standpoint it will elucidate how complex multi-scale constrained systems can be approximated (coarse grained) efficiently. From a technological standpoint, it is noted that nematic liquid crystals (used in modern televisions and computers) obey almost identical equations to the EI model and could benefit directly from these methods. This project will provide graduate and undergraduate students within applied mathematics and engineering the opportunity to collaborate with each other while participating in cutting edge research that spans between disciplines.