Experimental and numerical investigation of three equispaced cylinders in cross-flow

Abstract

Flow around a cluster of three equally spaced cylinders with a spacing ratio of P/D = 1.35 was studied experimentally and numerically. The main focus of this investigation is the effect of cluster orientation on flow characteristics. Two Reynolds numbers were investigated: ReD = 100 and ReD = 2100. Experiments were conducted at the University of Waterloo water flume facility at ReD = 2100 for a range of cluster orientation angles 0◦ ≤ α ≤ 60◦ using hydrogen bubble technique, particle image velocimetry, and laser Doppler velocimetry. The flow was modeled numerically at ReD = 100 and ReD = 2100 for α = 0◦ and 60◦. A laminar model was used for ReD = 100 and a RANS model was used for ReD = 2100. For the RANS case, four turbulence models were evaluated: SST, k−ω, k−ε, and LRR-IP.

For all cluster orientations, the experimental results show large scale vortex shedding, similar to single bluff body flows, beyond x/D = 5. Wide and narrow wakes are produced downstream of the cluster due to jets, that form in the passages between the cylinders, exiting the cluster. Small scale vortices are shed from shear layers bounding the narrow wake(s). For α = 0◦, a bistable wake development is present, in which the jet exiting the cluster is directed towards either one of the two downstream cylinders. The asymmetry in the wake development about y = 0 decreases as α increases from 0◦ to 60◦. For α = 60◦, the wake development is symmetric, consisting of two narrow wakes behind the two upstream cylinders and a wide wake behind the downstream cylinder. For all orientations, interactions between the inner shear layer of the wide wake and small scale vortices shed from the shear layers bounding the narrow wake occur. As a results, each large scale structure forming on this side of the wake axis encompasses smaller scale vortices with opposite vorticity sense, which reduces the coherence of the large scale vortices compared to that of their counterparts on the opposite side of the wake for 0◦ ≤ α < 60◦. The small scale vortex shedding frequency increases with increasing α for 0◦ ≤ α ≤ 60◦. For all orientations, the large scale vortex shedding frequency, when scaled by the projected height of the cluster, is equal to that for a single cylinder at the same Reynolds number, suggesting that the cluster behaves like a single bluff body.

For ReD = 100, the numerical results show a symmetric wake development for α = 0◦ and 60◦. No bistable wake development is present for α = 0◦. Also, there is no presence of small scale shedding in the near wake of the cluster for both orientations. The Strouhal number based on the projected height of the cluster is equal for both cluster orientations and to that expected for a single cylinder at the same Reynolds number. The total drag on the cluster for α = 0◦ and 60◦ is CP ≈ 1.35 and CP ≈ 1.5, respectively. The maximum drag occurs on the two upstream cylinders for α = 60◦, and is approximately 10% larger than that on a single cylinder. The drag coefficient on all other cylinders is at least 25% lower than that on a single cylinder. Mean lift forces are produced on the two downstream cylinders for α = 0◦ and the two upstream cylinders for α = 60◦. The total RMS for the cluster for α = 0◦ and 60◦ is CL′ ≈ 0.3 and CL′ ≈ 0.5, respectively. The maximum lift RMS occurs on the downstream cylinder for α = 60◦ and is approximately 35% larger than that for a single cylinder.

Numerical results for ReD = 2100 show that, out of the four turbulence models tested, the SST and k−ω models perform the best overall when compared to experimental results. Based on the results of the SST model, for α = 0◦ (i.e., the bistable case), the maximum drag occurs on the cylinder producing the narrow wake. For α = 60◦, the maximum drag occurs on cylinders 1 and 3. For both orientations, the total drag coefficient for the cluster is approximately 15% smaller than that for a single cylinder case. Also, the mean lift forces are generated only on the two downstream cylinders for α = 0◦ and the two upstream cylinders for α = 60◦.