Control of flow separation around bluff obstacles by superimposed thermal buoyancy

We analyze through numerical simulation the phenomena of suppression of flow separation around bluff obstacles by superimposed thermal buoyancy. For that purpose, we consider an unconfined flow of a Newtonian fluid around heated cylinders of circular and square cross-sections in a buoyancy-aided vertical flow configuration. The Reynolds numbers of the flow are kept intentionally low such that the flow remains steady and separated without imposition of the thermal buoyancy. When the buoyancy is added, it is observed that the flow separation diminishes gradually and at some critical value of the buoyancy parameter it completely disappears resulting a creeping flow like phenomena. Additionally, it is observed that the square cylinder requires more heating in comparison to its circular counterpart of equal linear dimension for complete suppression of flow separation. Although the phenomena is known, the exact quantification of the buoyancy parameter for which the flow separation around various types of bluff obstacles completely vanishes is unknown which is of tremendous fundamental importance. The major contribution is the determination of the critical Richardson numbers for the complete suppression of the flow separation around circular and square cylinders for the steady flow in the low Reynolds number laminar regime. Furthermore, the effect of Prandtl number on suppression of flow separation is also investigated and it is found that the high Prandtl number fluid requires less heating for suppression. The recirculation lengths and skin friction coefficients are computed to substantiate the above findings. Additionally, the Nusselt numbers are computed to predict the heat transfer rates from the obstacles under the superimposed thermal buoyancy condition.