Towards the accurate prediction of the turbulent flow and heat transfer in low-Prandtl fluids

Abstract

In the numerical simulation of turbulent heat transfer, a reliable representation of the turbulent flow field is a prerequisite in order to obtain an accurate prediction of the thermal field. In the framework of RANS modelling approach, classical two-equation eddy-viscosity models present intrinsic limitations for applications characterised by complex flow fields where significant turbulence anisotropy can be expected. In this respect, differential Reynolds stress models represent the natural choice for dealing with such highly anisotropic flows. On the other hand, the modelling of the turbulent heat flux term almost universally relies on the so-called Reynolds analogy, due to its simplicity and robustness. Nevertheless, this approach presents several well-known limitations, especially when dealing with low-Prandtl fluids. In this context, algebraic heat flux models are regarded as a promising approach to overcome the shortcomings of the Reynolds analogy. In particular, an implicit algebraic heat flux closure, called as AHFM-NRG, has been proposed for applications involving low-Prandtl fluids. In its original formulation, the algebraic turbulent heat flux closure was coupled with a low-Reynolds linear k-ε model for the closure of the Reynolds stress tensor. In the present work, the applicability of the AHFM-NRG model is extended to an advanced low-Reynolds differential Reynolds stress model. This new version of the model is validated against different planar channel flows at unity and low-Prandtl number; successively, the model is applied to two relatively complex flows, i.e. a planar impinging jet and a bare rod bundle configuration. It is shown that the coupling of the AHFM-NRG with an advanced closure for the Reynolds stresses gives encouraging results for these cases, where an accurate prediction of the anisotropy in the flow field results in a noticeable improvement in the prediction of the turbulent heat transfer.