Abstract
In the simple gradient diffusion hypothesis, the turbulent Prandtl number (Prt) with a constant of 0.85 is difficult to accurately predict for liquid metals having low Prandtl numbers (Pr), while a four-equation model can improve this solution by introducing the turbulence time-scale into the calculation of turbulent thermal diffusivity. However, the four-equation model’s transport form and numerical stability are so complex that suitable commercial code is lacking. Therefore, an isotropic four-equation model with simple Dirichlet wall boundary conditions is built in the present work. Based on the open-source computational fluid dynamics program OpenFOAM, the fully developed velocity, temperature, Reynolds stress, and heat flux of low Pr fluids (Pr = 0.01–0.05) in the parallel plane are obtained by numerical simulation. The results show that the time-average statistics predicted using the present four-equation model are in good agreement with the direct numerical simulation data. Then, the isotropic four-equation model is used to analyze the flow and heat of liquid metal (Pr = 0.01) in a quadrilateral infinite rod bundle. The numerical results are compared with the various and available experimental relationships. The Nusselt numbers calculated using the isotropic four-equation model are betweenness the available correlations, while the turbulent Prandtl number model using a constant of 0.85 over predicts heat transfer. More detailed local heat transfer phenomena and distribution of low Pr fluids are obtained using the present isotropic four-equation model.
Highlights
Liquid metals are widely considered coolants with good thermal-hydraulic characteristics for many energy systems, such as fast reactors and subcritical reactors (Gu and su, 2021; Wang et al, 2021)
In computational fluid dynamics (CFD), the computing cost required by the direct numerical simulation (DNS) method and the large eddy simulations (LES) method is too high to rely on this technique for a quick and economic calculation of heat transfer in complex geometries (Kawamura et al, 1999), while the Reynolds Averaged Navier–Stokes (RANS) method can be promoted
The turbulent heat transfer process of Prandtl numbers (Pr) = 0.01 ~ 0.05 fluid in the uniformly heated plane is numerically studied on the open-source program OpenFOAM
Summary
Liquid metals are widely considered coolants with good thermal-hydraulic characteristics for many energy systems, such as fast reactors and subcritical reactors (Gu and su, 2021; Wang et al, 2021). The velocity boundary layer and the temperature layer of traditional fluid (Pr ≈ 1) are generally considered to be similar in the RANS framework In this way, one can obtain a constant turbulent Prandtl number Prt to simplify the calculation of the energy equation after using the simple gradient diffusion hypothesis (SGDH) (Groetzbach, 2013). Assessment and calibration results of D/AHFM models for low Pr fluids completed in some simple geometries show that the heat transport of second-moment closure is very sensitive to the model coefficients and functions (Lai and So, 1990; Shikazono and Kasagi, 1996; Choi and Kim, 2007; Shams et al, 2019) Another popular model in the SGDH work, called the fourequation k-ε-kθ-εθ turbulent heat transfer model, is introduced into turbulent and thermal time-scales for the simulation of the explicit first-order turbulent heat diffusivity. The local distributions of dimensionless temperature, temperature fluctuation, turbulent heat diffusivity, and turbulent Prandtl numbers are analyzed
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