Flow pattern and heat transfer of swirling flows in cylindrical container with rotating top and stable temperature gradient

摘要

The flow pattern and the heat transfer characteristics of confined swirling flows of viscous incompressible fluid in an cylindrical container are numerically investigated in the axisymmetric flow regime under the Boussinesq assumption. The flows are driven by rotating the top cover at a constant angular speed and stable temperature difference is imposed between the top and bottom discs with the side walls thermally insulated. Steady state solutions are obtained for ranges of governing parameters, the Reynolds number Re, the Richardson number Ri in 10~2 ≤ Re ≤ 3 x 10~3 and 0 ≤ Ri ≤ 1.0 at fixed values of the Prandtl number P_r = 1.0 and the cylinder aspect ratio h = 1.0. For the flows with small Ri, meridional main circulation resides in the entire container convecting the heat from top to bottom disc. When Ri is increased to O(10~0), horizontally layered structure appears with quiescent lower half and vertically linear distribution of the temperature prevailing in much of the balk. At intermediate values of Ri, i.e. Ri ～ O(10~(-1)), flow separation occurs on the bottom disc depending on the values of Re and Ri. The flow patterns are classified into several different types on the (Ri,Re) plane. The average Nusselt number Nu which reflects the change of the flow structure, is a monotonically decreasing function of Ri and an increasing function of Re. The torque coefficient C_T is also computed and found to be a mildly decreasing function of Ri for the parameters considered.