Towards Optimum Formulations of Large Eddy Simulaton of Turbulence

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ABSTRACT Proposal Number: CTS- 9616219 Principal Investigator: Moser This is a grant to initiate a focused project to develop reliable LES methods, with well defined bounds on their accuracy, that can be used in complex fluid dynamic applications. Several fundamental questions regarding the detailed derivation of the LES equations, the definition of optimal filters, and the development of subgrid models will be addressed. The work will focus on the challenges that need to be met in the treatment of near-wall regions and embedded small-scale laminar sub-regions that have hindered the wide spread applicability of LES in complex problems of practical interest. The outstanding issues of LES will be addressed using a new LES formalism based on the fact that without knowledge of the small scales, the large scale evolution is essentially stochastic. The formalism provides a technique to precisely measure the predictability of the evolution of the large scales, and the performance of any particular LES model. Furthermore, interpretation of LES in the light of dynamical systems theory, suggests that past time information can greatly increase the predictability of the large scales. It is expected that this research will lead to several advances in the practice of LES. The necessary data for this research will be obtained from direct numerical simulation (DNS) and/or particle image velocimetry (PIV) measurements in experiments. These techniques will be applied to three specific test flows: plane channel, cylinder in cross flow, and a sudden expansion. Both DNS and PIV are necessary because higher Reynolds numbers are accessible through PIV experiments and more detailed three-dimensional data are available from DNS. The three test flows were selected because they are the simplest flows that exhibit features that have caused difficulties in LES. The optimizations performed and the models developed in the context of these flows will be applicable to LES in a wide variety of flows. The work will be jointly sponsored by NSF and the AFOSR.