Unsteady flow and heat transfer for cylinder pairs in a channel

Abstract

The incompressible, two-dimensional, unsteady flow past a pair of cylinders of square cross-section, placed in tandem normal to the flow in a channel, has been investigated by dye visualization and direct numerical simulation. The objective has been to evaluate the effect of cylinder separation distance, λ, on the flow behavior and heat transfer, for cylinder diameter ratios, D d , of 1 and 2 over a range of Reynolds numbers 200 ⩽ Re ⩽ 1600, based on the larger (downstream) cylinder diameter. A comparison between the experimental and numerical results for cylinders of equal cross-section dimensions shows very good agreement. The results for D d = 1 reveal three distinct flow patterns as a function of λ and Re which, apparently, have not been previously reported: (1) For 0.25 ⩽ λ ⩽ 4 with Re ⩽ 200, the inter-cylinder flow consists of a pair of steady counter-rotating eddies which do not exchange fluid with the surrounding flow and eddy shedding is observed only for the downstream cylinder. (2) For 0.25 ⩽ λ ⩽ 1.0 with 400 ⩽ Re ⩽ 1600, vertical flow oscillations arise in the inter-cylinder space, and the periodic ingestion of backward-jetting fluid from the top and bottom walls of the downstream cylinder into the inter-cylinder space is observed. For fixed λ the unsteadiness increases with Re but only the downstream cylinder sheds large eddies. (3) At a critical inter-cylinder spacing related to Re according to λ c ∼ Re − 2 3 , the shedding of large eddies also occurs at the upstream cylinder and this results in a highly mixed inter-cylinder flow. For a cylinder diameter ratio of D d = 2 , with the smaller cylinder located upstream of the larger heated cylinder, it is shown that for Re fixed an optimal location exists for the upstream cylinder such that the heat transfer from the downstream cylinder is maximized. The optimal location corresponds to a spacing smaller than the critical inter-cylinder spacing.