Abstract
A forced convective and a buoyancy-aided turbulent liquid sodium flow over a backward-facing step with a constant heat flux applied on the indented wall is simulated. Linear eddy viscosity models are used for the Reynolds stresses. Turbulent heat fluxes are modelled with a single gradient diffusion hypotheses with two different approaches to evaluate the turbulent Prandtl number. Moreover, the influence of turbulence on heat transfer to sodium is also assessed through simulations with zero turbulent thermal diffusivity. The results are compared with DNS data from literature. The velocity and turbulent kinetic energy profiles predicted by all models are in good agreement with the DNS data. The local Nusselt number trend is qualitatively well captured, however, its magnitude is underestimated by all models for the mixed convection case. For forced convection, the heat transfer is overestimated by all heat flux models. The simulation with neglected turbulent heat transfer shows the best overall agreement for the forced convection case. For the mixed convection best agreement is obtained using a correlation to locally evaluate the turbulent thermal diffusivity.
Highlights
The influence of buoyancy on the heat transfer for very low Prandtl number, Pr, fluids like liquid metals - especially liquid sodium - differs from that in the case of fluids with a Prandtl number around unity or higher
The choice of the turbulence models for the Reynolds stresses is based on previous studies of Cotton and Jackson [1], who used the model of Launder and Sharma [3], including an additional source term from Yap [4] in the equation of the dissipation rate of turbulent kinetic energy
Two linear k − models in combination with two heat flux models have been compared with DNS data [2] for the forced and buoyancy-aided mixed convection of a turbulent liquid sodium flow over a backward-facing step
Summary
The influence of buoyancy on the heat transfer for very low Prandtl number, Pr, fluids like liquid metals - especially liquid sodium - differs from that in the case of fluids with a Prandtl number around unity or higher. Experiments of mixed convection with liquid sodium in a vertical pipe show an increase of heat transfer for buoyancy-aided mixed convection due to the increased advection of heat [1]. The same trend has been found by Niemann and Frohlich [2] in a numerical investigation of a turbulent flow over a backward-facing step under buoyancy-aided mixed convection conditions. The present contribution investigates the influence of buoyancy on the flow structure and the heat transfer characteristic for liquid sodium by means of steady state RANS simulations. Simulations are performed with different approaches to evaluate the turbulent thermal diffusivity, αt, including the case of αt = 0.
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