Three-dimensional transition in the wake of two tandem rotating cylinders

Abstract

Three-dimensional (3-D) transition in the wake of two tandem co-rotating cylinders is studied numerically for Reynolds numbers $180\le Re\le 500$ . Infinite cylinders of equal diameter ( $D$ ) and span ( $8D$ ) are placed at streamwise gaps $Lx=2.5D$ and $7.5D$ , and rotated at rotation rates $\alpha =0$ , $0.5$ , $1$ and $2$ . For $\alpha =0$ and $Lx=7.5D$ , 3-D transition in the wake of the upstream cylinder resembles that for an isolated cylinder with the formation of Mode-A and Mode-B instabilities, whereas for the downstream cylinder, only Mode-A instability occurs in both the $Lx=2.5D$ and $7.5D$ cases with $\alpha =0$ . When the cylinders rotate at $\alpha =1$ for $Lx=7.5D$ , staggered transition takes place with the appearance of only Mode-B and only Mode-A instabilities in the near-wake regions of the upstream and downstream bodies, respectively. In the case $Lx=2.5D$ , the wake of the rotating cylinders transitions via Mode-C and Mode-D instabilities for $\alpha =0.5$ , Mode-D and Mode-D $^\prime$ for $\alpha =1$ , and Mode-C and Mode-A for $\alpha =2$ . A sudden decrease in near-wake fluctuations, accompanied by a downward jump in the force coefficients, is observed as the 3-D instability shifts from one mode to another, for $\alpha \ge 1$ and $Lx=2.5D$ . This discontinuity is caused by the formation of a pair of opposite-signed recirculation zones that mitigate each other's effects in the near-wake region.