Performance of low-Reynolds-number URANS closures in the computation of vertical heater vertical cooler natural circulation loops

Here we present 3-D simulations of the flow dynamics and thermal behaviour in Natural Circulation Loop (NCL) systems relevant to the passive cooling of current and next generation nuclear reactors. The heating and cooling arrangements consist of a vertical heater and cooler on opposite side legs of the loop at operating conditions for a fully turbulent flow, relevant to the primary circuit of Pressurized Water Reactors. The thermal resistance of the solid material to the conduction heat transfer mode is considered, using conjugate heat transfer analysis, and the working fluid is water in single-phase. This study extends the investigations of this type of natural convection loop to heating rates, and consequently Grashof number levels, over an order of magnitude higher than those of earlier studies. More specifically, we produce simulations of a vertically heated and vertically cooled natural convection loop at heating rates of 1 kW, 5 kW and 25 kW, with the cooler at a uniform temperature of 34 o C . For the lower heating rate case of 1 kW, which had been extensively looked at in earlier studies, only the low-Reynolds-number Launder-Sharma model has been employed. At the medium heating rate of 5 kW, which has not been examined before, three turbulence models are employed: the Launder-Sharma k − ε , the k − ω SST and the Elliptic-Blending Reynolds stress model (EBRSM). This allows us to extend the model assessment of earlier studies to this higher Grashof number. For the highest heating rate of 25 kW, the Launder-Sharma k - ε , validated at the lower heating rate, has been used. Comparisons with the same model's predictions at the two lower heating rates provide this unique opportunity to assess the Grashof number effect on natural convection loops, to levels relevant to reactor conditions. The validity of the Launder-Sharma k - ε -ε is confirmed through detailed local flow and thermal comparisons with LES predictions for the heating rate of 1 kW and through global parameter comparisons with experimental data and empirical correlations for all heating rates. Comparisons of the simulations of the three models at the heating rate of 5 kW agree with the findings of similar earlier comparisons at the lower heating rate of 1 kW, with the Launder-Sharma and EBRSM returning similar results to each other. The most important original contribution is the information generated on the flow and thermal evolutions as the Grashof number is progressively raised by over an order of magnitude, to levels that approach reactor operating conditions. As the heating rate increases, it takes longer for steady-state conditions to be established, instabilities during the transient stage become stronger, and the rate of turbulence enhancement goes up. This has strong consequences on the hydrodynamic and thermal performance of the loop. The rate of increase of the loop mean dimensionless temperature with the Grashof number becomes weaker at higher Grashof numbers, while the dimensionless mass flow rate shows the reverse trend. Finally, at all heating rates, the centreline temperature variation around the loop suggests that the use of an overall energy balance to deduce the loop mass flow rate from local temperature measurements at the heater inlet and outlet is susceptible to significant error. • Widely used low- Re and advanced Reynolds stress transport models have been assessed in capturing the flow features of natural circulation loops and validated against recent LES data. • Dean vortices were captured by the RANS models due to the interaction between the centrifugal pressure gradient and the boundary layer fluid, and their effect on the flow development has been demonstrated. • Heating power, conjugate heat transfer and the geometric parameters influence the near-wall heat transfer and the development of 3-D structures within the loops. • The low- Re k-ε LS and EBRSM laminarised the flow compared to the k-ω SST, though all models agreed overall with the experimental data, consistent with the trend of the turbulent correlation.