Predictive Turbulence Models for Computational Fluid Dynamics

建议没有。当前工程设计的最大瓶颈之一是紊流的计算预测。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，到星系演化，湍流起着至关重要的物理作用。如果没有湍流模型，其中一些问题将永远无法在计算上处理。高效的湍流预测模型可以对计算流体动力学（CDF）在设计过程中的应用产生深远的影响。虽然现有的工程湍流模型目前还不能提供预测精度，但在这项资助下进行的工作通过对湍流结构和波动速度大小进行建模，涡流相互作用（EI）模型能够准确地预测平均流量对湍流的影响。该方法的计算成本是平均流计算的几倍，比大涡模拟（LES）或直接数值模拟（DNS）解决方案便宜许多个数量级。这是成本/性能参数空间的一个区域，以前在湍流建模的背景下没有被广泛探索，但前景广阔。这项工作的目的是通过利用EI模型与精确（但不封闭）两点速度相关输运方程和概率密度函数（PDF）输运方程的直接联系，探索EI模型在非均匀流动中的推广。该模型的预测能力将在各种众所周知的基准湍流中得到证明，其中一些湍流无法使用现有的建模方法进行准确预测。这项工作的更广泛的影响，超出其跨学科的性质，将产生新的兴趣，这一困难，但极其重要的问题。从数学的角度来看，它将阐明如何有效地近似复杂的多尺度约束系统（粗粒度）。从技术的角度来看，向列液晶（用于现代电视和计算机）几乎遵循与EI模型相同的方程，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专业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.