Reynolds-averaged Navier-Stokes simulations of opposing flow turbulent mixed convection heat transfer in a vertical tube

This study performed Reynolds-Averaged Navier-Stokes (RANS) simulations of a single-phase turbulent opposing flow mixed convection in a heated vertical circular tube. Previous research has reported that the Launder-Sharma $k-\epsilon$ model (hereafter the LS model), one of the most popular RANS turbulence models, sometimes overestimates experimental data of heat transfer coefficients for opposing flows. Although the RANS models have been widely applied to opposing flows in various engineering problems, the conditions under which the anomaly in the LS model occurs and the underlying mechanisms remain unclear. This study aimed to understand the model characteristics and their applicability under various mixed convection conditions. This study investigated the LS model, the LS model with the Yap correction, and the $v^2-f$ model, comparing them with existing experimental data of the Nusselt number and the friction coefficient in fully developed regions. The LS model remarkably over-predicted the Nusselt number and the friction coefficient under highly buoyant conditions. The error for the Nusselt number was >90 % for $N_{B,JF}\approx 3\times {10}^{-3}$, where $N_{B,JF}$ is a controlling parameter characterizing the strength of buoyancy influence. The conditions under which the prediction of the LS model failed were linked to those under which reverse flow occurred near the heated wall. We obtained $N_{B,JF}\approx 1.25\times {10}^{-3}$ for the reverse flow condition. This condition could be used where the LS model could not be applied. The LS model with Yap correction and $v^2-f$ model could predict experimental data successfully from forced convection to mixed convection conditions ${10}^{-6}<N_{B,JF}<{10}^{-2}$. For natural convection-dominant conditions $N_{B,JF}>{10}^{-2}$, the LS model with the Yap correction was numerically unstable and could not obtain a converged numerical solution; however, the $v^2-f$ model stably reproduced the experimental data. By optimizing the model constants included in the Yap correction, the stability and accuracy of the calculations could be improved under highly buoyant opposing flow conditions.