Multiple-Scale Turbulence Model for Wall and Free Turbulent Flows.

Abstract

It is well known that turbulence models based on the eddy viscosity assumption have been quite successful in the numerical predictions of various kinds of turbulent flows. In particular, the k-εmodel is the most popular and has been proven to be effective in predicting wall shear layer turbulence. The k-ε models, however, show poor performance in the prediction of free shear flows. Such inconsistency is not caused by the crudeness of the eddy viscosity approximation, but by the inappropriate estimation of the relevant time scale of turbulence. Thus, in order to settle this problem, we propose a low-Reynolds-number-type "multiple-scale" turbulence model on the basis of the original model of Hanjalic et al. (Turbulent Shear Flows 2, 1980, Springer), in which multiple scales characterizing a turbulent flow are introduced by dividing the turbulence energy spectrum into two wave-number regions. In the present study, much emphasis is put on making a proposed model applicable to the prediction of near-wall turbulent flows without the controversial wall functions and reproduce the wall-limiting behavior of turbulence quantities. The proposed model has been tested in canonical wall and free shear flows and are found to work quite well regardless of the flow regimes.