A New Anisotropic Four-Parameter Turbulence Model for Low Prandtl Number Fluids

Abstract

Due to their interesting thermal properties, liquid metals are widely studied for heat transfer applications where large heat fluxes occur. In the framework of the Reynolds-Averaged Navier–Stokes (RANS) approach, the Simple Gradient Diffusion Hypothesis (SGDH) and the Reynolds Analogy are almost universally invoked for the closure of the turbulent heat flux. Even though these assumptions can represent a reasonable compromise in a wide range of applications, they are not reliable when considering low Prandtl number fluids and/or buoyant flows. More advanced closure models for the turbulent heat flux are required to improve the accuracy of the RANS models dealing with low Prandtl number fluids. In this work, we propose an anisotropic four-parameter turbulence model. The closure of the Reynolds stress tensor and turbulent heat flux is gained through nonlinear models. Particular attention is given to the modeling of dynamical and thermal time scales. Numerical simulations of low Prandtl number fluids have been performed over the plane channel and backward-facing step configurations.

CFD Investigations on Heavy Liquid Metal Alternative Target Design for the SPS Beam Dump Facility

“…When trying to model turbulent heat flows in liquid metals, standard models implemented in commercial codes such as Fluent and CFX are generally not accurate enough to reproduce the heat transfer in such regimes. The turbulent Prandtl number Pr t = α t /ν t is defined as the ratio between the diffusivity α t and the turbulent viscosity ν t , and it is commonly assumed to be constant: this is not the case for these fluids [16]. Commercial codes are, in fact, calibrated on materials such as water and air where the hypothesis of similarity between the dynamics of thermal and viscous turbulence holds and the calculation of turbulent diffusivity is set by taking Pr t ≈ 0.8 and therefore α t = Pr t ν t .…”

“…The CFD simulations performed with the CFX software v2021-R1 use the k − ω SST turbulence model. The k − ω and the k − ω SST turbulence model are considered the best approximations among RANS models for the simulation of heavy liquid metals, see references [5,16]. The boundary condition at the inlet is an imposed mass flow rate for the velocity and fixed temperature.…”

Challenge Problem 1: Preliminary Model Development and Assessment of Flexible Heat Transfer Modeling Approaches

“…To address some limitations of the Reynolds analogy including the statistical differences between turbulent momentum and heat transfer at non-unity Prandtl number, higher order methods such as algebraic heat flux modeling (AHFM) have been introduced to transport temperature variation [2]. Some complex models even transport the dissipation rate of the temperature variance, similar to the transport of turbulent kinetic energy dissipation [8]. However, these approaches require closures that are uncertain.…”

“…Future work could focus on applying higher order heat transfer models [8,2]. However, due to the limitations of these models, it may be more impactful to retain the Reynolds analogy and develop a universal framework for predicting model error across a range of flow conditions.…”

“…The last term is THF, which is estimated using the turbulent momentum diffusivity, 𝜈 𝜏 . When the Acton method is applied, the perturbations propagate in two ways: first, the velocity propagate through the second term in Equation (8). Second, the model perturbations propagate to the heat transfer through the Reynolds analogy in the last term.…”