An improved k–ω–φ–α turbulence model applied to near-wall, separated and impinging jet flows and heat transfer

Abstract

A turbulence model based on elliptic blending concept, referred to as improved k–ω–φ–α model compared against the original k–ω–φ–α model developed previously, is developed and verified. This model consists of four governing equations. Among them the k and ω equations are based on the Wilcox's k–ω model with some modifications and improvements according to the original k–ω–φ–α model, and the φ and α equations are extracted from the original k–ω–φ–α model directly without any change. The improved k–ω–φ–α model is applied to near-wall, separated and impinging jet flows and convective heat transfer, i.e. the 2D fully developed channel flow, the 2D backward-facing step flow, the 2D impinging jet flow, and the convective heat transfer in the 2D fully developed channel flow and the 2D impinging jet flow. The computational results are compared with available DNS and experimental data and also to those computed using the original k–ω–φ–α model and the popular Menter's SST k–ω model. It is shown that the improved k–ω–φ–α model has better numerical stability, higher computational efficiency and more concise form than the original k–ω–φ–α model. In addition, compared with the original k–ω–φ–α model, the improved k–ω–φ–α model can yield similar velocity profiles in the fully developed channel flow and step flow and friction and pressure coefficients in the step flow and very close temperature profiles in the fully developed channel flow. Moreover, it shows significant improvements on the predictions for the fluid flow and heat transfer in the impinging jet flow. As a whole, the improved k–ω–φ–α model predicts better results than both of the original k–ω–φ–α model and the SST k–ω model.