The Best Turbulence Models for Engineers

Abstract

“The best turbulence model” is obviously the Navier-Stokes equations, which are almost universally accepted as an accurate description of turbulence in simple fluids. Solving them to obtain converged statistics (DNS) requires computer work proportional to the cube of the Reynolds number, approximately, so there will always be a limit to the attainable Reynolds number, At present this limit is of the order of the Reynolds number attained in small-scale laboratory experiments. Thus “The best turbulence model for aeronautical engineers” is — again obviously — not the Navier-Stokes (NS) equations. (DNS is and always will be a valuable research tool for developing and testing models based on simplifications of the NS equations: see Moin and Mahesh (1998).) The less-obvious point of this Abstract is that “best”, in the title, is a time-dependent word and that it is short for “most cost-effective”. This paper is a review of options, a brief history, and an assessment of current ideas and future possibilities. It seems likely that Reynolds-averaged models will continue to advance modestly, somewhat less likely that engineers will routinely use the highest-level models, and almost certain that large-eddy simulation will start to replace or assist Reynolds-averaged models in the next decade or so.