Effect of corner radius on flow topology and heat transfer from free oscillating tandem cylinders at low Reynolds number

Abstract

Flow-induced vibration (FIV) on two tandem cylinders with forced convection is numerically investigated at a constant Re = 150. Elastically mounted cylinder with four different values of corner radii (r* = r/R: r = radius of fillet; R = radius of circle) = 0 (square cylinder), 0.25, 0.75, and 1 (circular cylinder) with two spacing ratio (L/D) = 4 and 2 is studied. Transverse oscillations are generated from the cylinder having non-dimensional mass (m*) = 10. The structural damping coefficient is assigned a zero value with varying reduced velocity Ur=2−10. The two-dimensional incompressible Navier–Stokes and energy equations are solved together with Newton's second law governing the motion of the cylinders. Both cylinders' surfaces are maintained at a higher constant temperature of T*=1, and incoming flow is set to be at T*=0 with Prandtl number (Pr) = 0.7. The effect of r* and L/D is observed on the flow structure and FIV parameters. Flow characteristics at L/D=4 such as steady flow, reattachment, and unsteady flow are examined. A “shift” in vibrational amplitude is noted from r* = 1 and 0.75 to r* = 0 and 0.5, respectively. The downstream cylinder (DC) experiences a hike in vibration amplitude due to the impingement of vortex shedding from the upstream cylinder (UC). r* = 1 has 18.1% higher vibrational amplitude than r* = 0 at their respective lock-in regimes for DC. For L/D=2, vortices from upstream and downstream cylinders interact to form C(2S) and 2S types of vortex shedding. Different regimes, such as single body, reattachment, and co-shedding, have been observed while changing L/D. r* = 0.75 results in 13.3% higher oscillation amplitude as compared to r* = 0.5 for DC. The average Nusselt number (Nuavg) strongly depends on flow topology, corner radius, and vibrational amplitude A/D. At low L/D, heat transfer from the downstream cylinder is plummeted due to rolling of shear layers over the cylinder. There is a significant change in Nuavg due to higher vibration; for example, increase in 10.71% change is observed from Ur=2 to Ur=6 for r*=1 and L/D=4. Corner radii also alter the Nuavg as a decrease in 27.39% from r* = 1 to r* = 0 at Ur=10 and L/D=4 (UC).