Three-dimensional simulations of flow past two circular cylinders in side-by-side arrangements at right and oblique attacks

The flow past two identical circular cylinders in side-by-side arrangements at right and oblique attack angles is numerically investigated by solving the three-dimensional Navier-Stokes equations using the Petrov-Galerkin finite element method. The study is focused on the effect of flow attack angle and gap ratio between the two cylinders on the vortex shedding flow and the hydrodynamic forces of the cylinders. For an oblique flow attack angle, the Reynolds number based on the velocity component perpendicular to the cylinder span is defined as the normal Reynolds number ReN and that based on the total velocity is defined as the total Reynolds number ReT. Simulations are conducted for two Reynolds numbers of ReN=500 and ReT=500, two flow attack angles of α-0ᵒ and 45ᵒ and four gap ratios of G/D=0.5, 1, 3 and 5. The biased gap flow for G/D=0.5 and 1 and the flip-flopping bistable gap flow for G/D=1 are observed for both α=0ᵒ and 45ᵒ. For a constant normal Reynolds number of ReN=500, the mean drag and lift coefficients at α-0ᵒ are very close to those at α=45ᵒ. The difference between the root mean square (RMS) lift coefficient at α-0ᵒ and that at α=45ᵒ is about 20% for large gap ratios of 3 and 5. From small gap ratios of 0.5 and 1, the RMS lift coefficients at α=0ᵒ and 45ᵒ are similar to each other. The present simulations show that the agreement in the force coefficients between the 0ᵒ and 45ᵒ flow attack angles for a constant normal Reynolds number is better than that for a constant total Reynolds number. This indicates that the normal Reynolds number should be used in the implementation of the independence principle (i.e., the independence of the force coefficients on the flow attack angle). The effect of Reynolds number on the bistable gap flow is investigated by simulating the flow for ReN=100-600, α=0ᵒ and 45ᵒ and G/D=1. Flow for G/D=1 is found to be two-dimensional at ReN=100 and weak three-dimensional at ReN =200. While well defined biased flow can be identified for ReN=300-600, the gap flow for ReN=100 and 200 changes its biased direction too frequently to allow stable biased flow to develop.