A Comprehensive Evaluation of Turbulence Models for Predicting Heat Transfer in Turbulent Channel Flow across Various Prandtl Number Regimes

Abstract

Turbulent heat transfer in channel flows is an important area of research due to its simple geometry and diverse industrial applications. Reynolds-Averaged Navier–Stokes (RANS) models are the most-affordable simulation methodology and are often the only viable choice for investigating industrial flows. However, accurate modelling of wall-bounded flows is challenging in RANS, and the assessment of the performance of RANS models for heated turbulent channel flow has not been sufficiently investigated for a wide range of Reynolds and Prandtl numbers. In this study, five RANS models are assessed for their ability to predict heat transfer in channel flows across a wide range of Reynolds and Prandtl numbers (Pr) by comparing the RANS results with respect to the corresponding Direct Numerical Simulation data. The models include three Eddy Viscosity Models (EVMs): standard k−ϵ, low Reynolds number k−ϵLS, and k−ωSST, as well as two Reynolds Stress Models (RSMs): Launder–Reece–Rodi and Speziale–Sarkar–Gatski models. The study analyses the Reynolds number effects on turbulent heat transfer in a channel flow at a Pr of 0.71 for friction Reynolds number values of 180,395,640, and 1020. The results show that all models accurately predict velocity across all Reynolds numbers, but the accuracy of mean temperature prediction drops with increasing Reynolds number for all models, except for the k−ωSST model. The study also analyses the Pr effects on turbulent heat transfer in a channel flow with Pr values between 0.025 and 10.0. An error analysis is performed on the results obtained from different turbulence models, and it is shown that the k−ωSST model has the smallest error for the predictions of the mean temperature and Nusselt number for high-Prandtl-number flows, while the low Reynolds number k−ϵLS model shows the smallest errors for low-Prandtl-number flows at different Reynolds numbers. An analytical solution is utilised to identify Pr effects on forced convection in a channel flow into three different regimes: analytical region, transitional region, and turbulent diffusion-dominated region. These regimes are helpful to discuss the validity of the models in relation to the Pr. The findings of this paper provide insights into the performance of different RANS models for heat transfer predictions in a channel flow.