Assessment of RANS and improved near-wall modeling for forced convection at low Prandtl numbers based on LES up to Reτ=2000

Most promising Generation IV nuclear reactor concepts are based on a liquid metal coolant. However, at low Prandtl (Pr) numbers such as those of liquid metal, classical approaches derived for unity, or close to unity, Pr fail to accurately predict the heat transfer. This paper assesses the RANS modeling of forced turbulent convection at low Pr and in channel flow. Reference results at high Reynolds (Re) number are required to ensure that the Peclet number is sufficiently high. Therefore, new reference results were obtained by performing a wall-resolved Large-Eddy Simulation of turbulent channel flows at a friction Reynolds number Reτ=2000 and at Pr=0.01 and 0.025 (this also corresponds to the highest Re Direct Numerical Simulation (DNS) available in the literature for the flow, but without heat transfer). The LES velocity statistics are in very good agreement with those of the DNS and, as validated by the authors in previous publications, the LES approach used here accurately predicts the temperature statistics at low Pr. The LES results are used to assess RANS heat transfer modeling based on the effective turbulent Prandtl number (Prt) concept. Among existing Prt correlations, the correlation by Kays (1994) [10] is shown to yield the best results. Since it is also shown that the near-wall temperature profile does not follow a log-law, a new “law of the wall for temperature” is here proposed, which does not use any blending function. Its use as a wall-function is also validated in actual RANS simulations.