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Self-conditioned fields for large-eddy simulations of turbulent flows

Published online by Cambridge University Press:  13 April 2010

STEPHEN B. POPE
STEPHEN B. POPE*
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: s.b.pope@cornell.edu
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Abstract

An alternative foundation is developed for the large-eddy simulation (LES) of turbulent flows. It is based on ‘self-conditioned fields’, for example, the mean velocity field conditional on a discrete representation of the filtered velocity field. It is shown that the self-conditioned velocity field minimizes the residual kinetic energy, and that, with the ideal model, the method yields the correct one-time behaviour as determined by the Navier–Stokes equations. The approach is extended to the self-conditioned probability density function (PDF) of compositions. Compared to LES formulations based on the filtered velocity and the filtered density function, the self-conditioned field approach has several advantages: for laminar flow, and in the direct-numerical-simulation limit, the residual fluctuations are zero or exponentially small; full account is taken of the probability distribution of turbulent fields; there are no commutation issues; and there are no issues with filtering at walls, where the self-conditioned velocity is zero. The exact evolution equations for the self-conditioned velocity and composition PDF are derived. Basic models are presented, and the development of improved models is discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 652 , 10 June 2010 , pp. 139 - 169
Copyright
Copyright © Cambridge University Press 2010

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