Hybrid LES/DNS of turbulent forced and aided mixed convection to a liquid metal flowing in a vertical concentric annulus

In the present study fully-developed turbulent forced and mixed convection heat transfer to a liquid metal flowing upwards in a concentric annulus is numerically investigated by means of Large Eddy Simulation (LES). The inner-to-outer radius ratio is 0.5. The Reynolds number based on bulk velocity and hydraulic diameter is 8900, while the Prandtl number is set to a value of 0.026. A uniform and equal heat flux is applied on both walls. Three different buoyancy strengths are considered, corresponding to onset of turbulence reduction, maximum impairment and recovery condition on the inner wall while recovery and enhancement develop on the outer wall. Due to the difference between thermal and hydrodynamic turbulent scales in liquid metals it is shown that with the same grid resolution a LES is performed for the flow field and at the same time a "thermal" Direct Numerical Simulation (DNS) for the temperature field. From a detailed analysis of the two-point correlation functions of velocity and temperature fluctuations it emerges that a streamwise extent of 25d and 40d (being d the half gap width) is necessary for forced and mixed convection, respectively, while a quarter of circumference is enough in azimuthal direction for this radius ratio, Reynolds and Prandtl number. Comparison of the forced convection flow field with available DNS simulations shows very good agreement. Nusselt numbers evaluated from the few available literature correlations for liquid metals flowing in an annulus give unsatisfactory results, mainly on the inner wall. The mixed convection results are thoroughly analyzed and discussed in terms of friction factor, Nusselt number, first and second order statistics, budgets of turbulent kinetic energy and budgets of temperature variance. The obtained data are also useful for validating Reynolds-Averaged turbulence models. Moreover, simulations with two coarser grids at the condition of maximum turbulence reduction are also compared with the reference results of the fine LES. It results that when turbulence is impaired the grid resolution in circumferential direction can be strongly coarsened.