Numerical study of curvature correction to reynolds stress model for computation of turbulent recirculating flows

Abstract

A curvature dependent Reynolds stress model is developed by including streamline curvature corrections to the conventional Reynolds stress model for computation of turbulent recirculating flows. The time scale of third order diffusive transport term in Reynolds stress equation and the rate of turbulent kinetic energy dissipation equation is modified by using a curvature time scale. Also, a model coefficient of the destruction term in the dissipation rate equation is modified for including the curvature effect on the decay rate of turbulent kinetic energy. Two sets of velocity field measurements in the recirculating flow around a backward facing step in which the streamlines are highly curved, are used to resolve the dispute about necessity of streamline curvature correction to the conventional Reynolds stress model. The predictions by three variations of conventional Reynolds stress model showed a zonal dependency and did not agree well with the experimental data. The results by curvature dependent Reynolds stress model showed better prediction than conventional model and confirmed that the Reynolds stress model does need appropriate curvature correction to its model coefficients. Such curvature corrections improve the predictions of Reynolds shear stress and streamwise normal stress. The improvements of the computations were significantly in the recirculating region. Consequently, the mean velocity profiles, the reattachment length and the skin friction are better predicted by the curvature Reynolds stress model. In order to calculate recirculating flows economically as compared to full curvature dependent Reynolds stress model, a curvature dependent hybrid simple algebraic/Reynolds stress model is proposed. In this scheme, by using tensor transformation, the normal stresses can be calculated from simple algebraic equations. This model has also been tested against the backward-facing step flow. It was found that the curvature dependent hybrid simple algebr...