Application of a New Algebraic Structure-Based Model to Rotating Turbulent Flows

Abstract

This chapter discusses application of a new algebraic structure-based model to rotating turbulent flows. A primary goal of Reynolds averaged Navier-Stokes (RANS-based modeling is to determine the Reynolds stress tensor in order to close the turbulence problem at the mean velocity level. However, the Reynolds stresses alone do not characterize adequately the turbulence, especially in presence of rotation

the structure of the turbulence is also important. Hypothetical turbulent eddies are used to bring awareness of turbulence structure into the turbulence model. Averaging over an ensemble of eddies produces a set of one-point statistics, representative of the eddy field, and a set of equations of state relating the Reynolds stresses to these statistics. An algebraic model for the eddy statistics is constructed in terms of the local mean deformation and two turbulence scales

the turbulent kinetic energy and the large-scale enstrophy (LSE). Contrary to existing ad-hoc definitions of the second scale equation, the LSE equation has a fundamental background

it is derived from the large-scale vorticity equation. The algebraic model is further sensitized to the presence of walls, ensuring proper asymptotic behavior. The complete model is found to produce good results for a set of channel flows in fixed frames and in spanwise-rotating frames of reference. © 2005 Elsevier B.V. All rights reserved.