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Highlights • An extension of the AFHM-NRG model to an advanced low-Reynolds differential Reynolds stress model is proposed. • This new version of the model is validated against different planar channel flows at unity and low-Prandtl number. • The model is then applied to two relatively complex flows, i.e. a planar impinging jet and a bare rod bundle configuration. • The AHFM-NRG model with an advanced closure for the Reynolds stresses gives encouraging results. 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. [ABSTRACT FROM AUTHOR]

Turbulent heat transfer represents a considerably challenging phenomenon from the modelling point of view. In the RANS framework, the classical Reynolds analogy provides a simple and robust approach which is widely employed for the closure of the turbulent heat flux term in a broad range of applications. At the same time, there is an ever growing interest in the development and assessment of advanced models which would allow, at least to some extent, for the relaxation of the simplifying assumptions underlying the Reynolds analogy. In this respect, the use of algebraic closures for the turbulent heat flux has been proposed in the literature by different authors as a viable approach. One of these algebraic closures has been extended for its application to low Prandtl number fluids in various flow regimes, by means of calibration and assessment of the model against some basic test cases, in what is known as the AHFM-NRG+ model. In the present work the AHFM-NRG+ is applied for the first time to a relatively complex configuration, i.e. a backward facing step in both forced and mixed convection regimes with a low Prandtl working fluid, and assessed against reference DNS data. The obtained results suggest that the AHFM-NRG+ is able to provide more accurate predictions for the thermal field within the domain and for the heat transfer at the wall in comparison to the Reynolds analogy assumption. These encouraging results indicate that the AHFM-NRG+ can be considered as a promising model to improve the accuracy in the simulation of the turbulent heat transfer in industrial applications involving low Prandtl fluids. [ABSTRACT FROM AUTHOR]

• Liquid Metal thermal-hydraulics in forced and mixed circulation conditions is considered. • The capabilities of some selected turbulence models are assessed against DNS data. • The AHFM-SC model is found to represent a solid approach for the calculation of Turbulent Heat Flux. The present paper investigates the capabilities of some selected Reynolds-Averaged Navier Stokes (RANS) based turbulence models in reproducing liquid metals thermal hydraulics Direct Numerical Simulation (DNS) data. For this purpose, forced and mixed convection conditions, both addressing buoyancy-aided and buoyancy-opposed flow, are considered. The paper mainly focuses on velocity and temperature fields estimation, providing a comparison between the RANS and DNS computations. The capabilities of the turbulence models are discussed with the aim to highlight which ones provide the best predictions. In particular, attention is paid to the approach adopted for the calculation of the turbulent heat flux contributions. Together with models assuming the commonly adopted Simple Gradient Diffusion Hypothesis (SGDH) approach and the Reynolds analogy, a model including the Algebraic Heat Flux Model (AHFM) approach is considered. While being a practical and robust approach to deal with turbulent heat fluxes, the SGDH approach shows intrinsic limitation in dealing with liquid metal thermal hydraulics, mainly because of their low-Prandtl number. The adoption of a more advanced AHFM method may instead relevantly improve the quality of the obtained predictions. The obtained results show that the selected model adopting the AHFM method provides definitively better predictions of the addressed phenomena with respect to the ones considering the SGDH approach. While some discrepancies are still observed for the velocity fields, the temperature fields are captured very well, suggesting a clear superiority of the AHFM model. The present paper thus provides further validation and supports the use of AHFM as a valuable tool to predict turbulent heat fluxes. [ABSTRACT FROM AUTHOR]

• The calibration and optimization procedure is adopted to design a numerical experiment for a closely-spaced bare rod bundle in order to perform a DNS. • Reference database (DNS) is generated for Re = 9800 and three different Pr number fluids (Pr = 0.025, 1 & 2) combined with two thermal boundary conditions: constant temperature and constant heat flux. • DNS will serve as a reference for validation purposes. • An overview of 6 pragmatic RANS model results is given in order to assess the prediction capabilities of a linear and non-liner models. The understanding of flow behaviour and temperature distribution in rod bundles during operation is of great importance for the safety and economical design of existing nuclear reactors and as well as new nuclear technologies. In order to study the thermal-hydraulics phenomena in the fuel assembly geometries, researchers all over the world are increasingly using Computational Fluid Dynamics (CFD) as a reliable research tool. Nevertheless, the prediction capabilities of the most commonly used Reynolds Average Navier-Stokes (RANS) models must be assessed. In this regard, in the present research work, an extensive effort has been put forward and is described in three main steps. As a first step, a wide range of RANS and unsteady RANS computations have been performed to design a numerical experiment for a closely-spaced bare rod bundle in order to perform a direct numerical simulation (DNS), which will serve as a reference for the validation purpose. As a second step, the DNS of this bare rod bundle has been performed for three different Prandtl number (Pr) fluids, i.e. Pr = 2, 1 and 0.025. This DNS has been performed using a higher-order spectral element code and consists of 660 million grid points. Accordingly, an extensive database has been generated for validation purposes. Finally, this database is used to assess the prediction capabilities of different linear and non-linear RANS models. This article will provide a good overview of all three steps and will also highlight the main lessons learned from this research. [ABSTRACT FROM AUTHOR]

Liquid metal cooled reactors are envisaged to play an important role in the future of nuclear energy production because of their possibility to use natural resources efficiently and to reduce the volume and lifetime of nuclear waste. Typically, sodium and lead(-alloys) are envisaged as coolants for such reactors. Obviously, in the development of these reactors, thermal-hydraulics is recognized as a key (safety) challenge. A fundamental issue to this respect is the modelling of turbulent heat flux over the complete range from natural, mixed and convection to forced convection regimes. Current engineering tools apply statistical turbulence closures and adopt the concept of the turbulent Prandtl number based on the Reynolds analogy. This analogy is valid mainly for forced convective flows with Prandtl number of order of unity. In the particular case of liquid metal, where the Prandtl number is less than 1, the turbulent Prandtl number concept is not applicable and robust engineering turbulence models are needed. Thus, a model is required which can deal with all flow regimes simultaneously in liquid metal flows. In the framework of the European project THINS (thermal-hydraulics for innovative nuclear systems), some promising routes for improvements have been identified and are currently under evaluation. [ABSTRACT FROM AUTHOR]

• An overview of the AHFM-NRG formulations has been presented. • These formulations are based on an implicit algebraic heat flux model. • The AHFM-NRG formulations are well calibrated to predict flow and heat transfer in low-Prandtl flows. Turbulent heat transfer is a complex phenomenon, which is ubiquitous in engineering applications and has challenged turbulence modellers for several decades. In an attempt to simplify the problem it is often assumed that turbulent heat transfer can be inferred from the knowledge of the turbulent momentum transport, in what is known as the Reynolds analogy. This approach presents well-known drawbacks that limit its applicability to low-Prandtl fluids such as liquid metals. In an effort to overcome such limitations, an implicit Algebraic Heat Flux Model named AHFM-NRG has been recently proposed by the Nuclear Research and Consultancy Group (NRG). In the framework of the EU THINS project, this model was initially tested for a limited number of academic test cases in all three flow regimes (i.e.: natural, mixed and forced convection) and showed encouraging results. Further assessment and development of this or any other turbulent heat flux model with low-Prandtl fluids was hampered by the lack of accurate and reliable reference data. Thanks to the extensive reference database generated within the subsequent EU SESAME and MYRTE projects, the AHFM-NRG formulation has been further tested and developed. This article reports the development of the AHFM-NRG approach and its assessment against some representative test cases in all three flow regimes. It is shown that the AHFM-NRG formulations result in significant improvement with respect to the classical Reynolds analogy in all considered flow configurations. [ABSTRACT FROM AUTHOR]

Highlights • The turbulent flow field is better predicted with a non-isotropic RSM closure. • The Reynolds analogy assumption is reasonable at unity Prandtl number. • More advanced turbulent heat flux models are needed at low Prandtl number. • Algebraic heat flux models are identified as a promising approach. Abstract The numerical simulation of turbulent heat transfer in complex industrial flows represents a major challenge for RANS models. The impinging jet configuration is a popular test case for turbulence models, due to both the challenging nature of the flow field for the RANS approach and its widespread use in industrial applications. As a consequence, a large number of studies in the literature is dedicated to the assessment of a broad variety of turbulence models in this configuration. In particular, a significant effort has been put into the assessment of different closures for the turbulent momentum flux. In contrast, relatively little attention has been paid to the modelling of the turbulent heat flux term, and the classical Reynolds analogy is almost universally employed for this purpose despite its well-known limitations. Nevertheless, recently there has been a growing interest towards the development and assessment of more advanced closures for the turbulent heat flux. In this context, in the present work six turbulence models relying on different closures for both the turbulent momentum and heat fluxes have been used to simulate a planar impinging jet at unity, moderate and low Prandtl number and thoroughly assessed against a recently published reference DNS database. It is shown that the use of an advanced differential closure for the Reynolds stresses can result in an improvement in the prediction of the flow field. This, in turn, directly results in a more accurate prediction of the mean temperature at unity Prandtl number when the Reynolds analogy is employed for the closure of the turbulent heat flux. On the other hand, the inadequacy of the latter approach appears evident at low Prandtl values, and the necessity to account at least for the variability of the turbulent Prandtl number is demonstrated. It is then inferred that the most promising approach for such complex cases is represented by the combined use of anisotropic models for both the turbulent flow and the thermal fields. [ABSTRACT FROM AUTHOR]