Thermal convection of liquid metal in a long inclined cylinder

The turbulent convection of low-Prandtl-number fluids (Pr = 0.0083) in a long cylindrical cell, heated at one end face and cooled at the other, inclined to the vertical at angle beta, 0 <= beta <= pi/2 with step pi/20, is studied numerically by solving the Oberbeck-Boussinesq equations with the large-eddy-simulation approach for small-scale turbulence. The cylinder length is L = 5D, where D is the diameter. The Rayleigh number, determined by the cylinder diameter, is of the order of 5 x 10(6). We show that the structure of the flow strongly depends on the inclination angle. A stable large-scale circulation (LSC) slightly disturbed by small-scale turbulence exists in the horizontal cylinder. The deviation from a horizontal position provides strong amplification of both LSC and small-scale turbulence. The energy of turbulent pulsations increases monotonically with decreasing inclination angle beta, matching the energy of the LSC at beta approximate to pi/5. The intensity of the LSC has a wide, almost flat, maximum for an inclined cylinder and slumps approaching the vertical position, in which the LSC vanishes. The dependence of the Nusselt number on the inclination angle has a maximum at beta approximate to 7 pi/20 and generally follows the dependence of the intensity of LSC on the inclination. This indicates that the total heat transport is highly determined by LSC. We examine the applicability of idealized thermal boundary conditions (BCs) for modeling a real experiment with liquid sodium flows. Therefore, the simulations are done with two types of temperature BCs: fixed face temperature and fixed heat flux. The intensity of the LSC is slightly higher in the latter case and leads to a corresponding increase of the Nusselt number and enhancement of temperature pulsations.