Development of curvature-dependent two-equation model for prediction of two-dimensional turbulent recirculating flows

Abstract

Problems of the numerical prediction by previous computational models on the recirculating flows are identified by comparing the various model predictions and experiments on the representative recirculating flows such as backward-facing step flow and the normal fence flow. It was found that previous modifications on the standard twoequation model are not adequate for the prediction on the recirculating flows with appreciable streamline curvature. It was also found that the higher-order turbulence models such as 3-equation model and algebraic stress model show a strong zonal dependency in prediction accuracy. By careful examination of experimental data on the third-order transport terms in a turbulent flow around a normal fence, it was shown that the streamline curvature has strong effects on the spatial transport of the second-order moments. Such streamline curvature effects on the third-order correlations are modeled by devising a curvature time scale for the third-order transport mechanism from the analogy between buoyancy and streamline curvature effects on turbulence. The proposed curvature dependent third-order correlation model is proved that it yields considerably better prediction than that of the simple gradient diffusion model. Incorporation of the new curvature dependent third-order model into the k- $\varepsilon$ equation method with a curvature dependent term in $\varepsilon$-equation is found to yield very good prediction accuracy for the turbulent recirculating flows. Particularly, the recovery of the mean velocity profile in the redeveloping region after the reattachment is correctly simulated by the present method.