Predictive Turbulence Models for Computational Fluid Dynamics

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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.