Abstract
The rotation and an axial gradient of temperature drive the meridional circulation of a fluid filling a sealed cylindrical container. This numerical study explains why the flow remains stable up to the Grashof number Gr around 1011; Gr characterizes the circulation strength. The shear-layer instability, occurring in a rotating pipe for small values of the Prandtl number Pr [M. A. Herrada and V. N. Shtern, “Stability of centrifugal convection in a rotating pipe,” Phys. Fluids 27, 064106 (2015)], is suppressed here even for the cylinder length-to-radius ratio being ten. The cold end disk enhances the fluid circulation near the sidewall and diminishes it near the axis. The inflection point in the radial profile of axial velocity shifts to the sidewall vicinity where the stable centrifugal stratification and the no-slip condition prevent the disturbance growth. The cases Pr = 0, 0.015 (mercury), 0.7 (air), and 5.8 (water) are particularly analyzed. At Pr > 0, the stable density stratification develops and helps to suppress the disturbances. The obtained results are of fundamental interest and might be important for the development of efficient heat exchangers.
Published Version
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