Turbulent Convection of Liquid Sodium in an Inclined Cylinder of Unit Aspect Ratio

Abstract

Turbulent convection of liquid sodium (Prandtl number Pr = 0.0093) in a cylinder of unit aspect ratio, heated at one end face and cooled at the other, is studied numerically. The flow regimes with inclination angles β = 0°, 20°, 40°, 70° with respect to the vertical are considered. The Rayleigh number is 1.5 × 107 . Three-dimensional nonstationary simulations allow one to get instant and average characteristics of the process and to study temperature pulsation fields. A mathematical model is based on the Boussinesq equations for thermogravitational convection with use of the LES (large-eddy simulations) approach for small-scale turbulence modeling. Simulations were carried out with a nonuniform numerical grid consisting of 2.9 × 106 nodes. It is shown that the flow structure strongly depends on β. The large-scale circulation (LSC) exists in the cylinder at any β. Under moderate inclination (β = 20°), the strong oscillations of the LSC orientation angle with dominant frequency are observed. Increasing the inclination up to 40° leads to stabilization of the large-scale flow and there is no dominant frequency of oscillations in this case. It is shown that more intensive temperature pulsations occur at small cylinder inclinations. At any β the regions with intensive pulsations are concentrated in the areas along low and upper cylinder faces. The maximum values of pulsations occur in the area close to lateral walls, where hot and cold fluid flows collide. The intensity of temperature pulsations decreases with increasing distance from the lateral walls. The Reynolds number which characterizes the total energy of the flow reaches its maximum value at β = 20° and then decreases with increasing β. The mean flow has maximum intensity at β = 40°. Turbulent velocity pulsation energy decreases monotonically with increasing inclination angle. It is shown that the inclination leads to an increase in heat transfer along the cylinder axis. The Nusselt number at β = 40° is 26% higher than that in the vertical cylinder.