Heat transfer and wake-induced vibrations of heated tandem cylinders with two degrees of freedom: Effect of spacing ratio

Abstract

The heat transfer and wake-induced vibrations of a cylinder of circular cross section in the wake of another identical cylinder are numerically studied in this work at a Reynolds number ( Re) = 100. The reduced velocities ( Ur) are varied in the range of 2–14. The downstream cylinder is allowed to oscillate in two degrees of freedom, i.e., in the transverse as well as in the streamwise direction. The mass ratio ( m*) is taken as 10, while the structural damping is ignored to get the maximum amplitude of vibration. The spacing ratio ( L/D) between the cylinders is varied from 1.5 to 6, covering the major regimes, i.e., single body, reattachment, and co-shedding. The coefficients of lift ( CL) and drag ( CD), vibrational amplitudes of the cylinder, the Nusselt number ( Nu), the Strouhal number ( St), and vortex shedding patterns are studied. The results are discussed with the help of lift-displacement phase plots, cylinder trajectory plots, and vorticity and temperature contours. The lock-in condition at Ur = 8 is observed for all values of L/D, whereas the lock-in zone is the widest for the co-shedding regime at L/D = 6. By increasing L/D from 1.5 to 2.5 at Ur = 8, the CL of the downstream cylinder increases by 43%, whereas the CL of the upstream cylinder decreases by 61%. The downstream cylinder experiences lower drag as compared to the upstream cylinder and stationary isolated cylinder. A maximum decrease in the average drag coefficient of 107%, as compared to the stationary isolated cylinder, was observed for the downstream cylinder at L/D = 1.5 and Ur = 2, leading to the negative drag. Mostly, the 2S and C(2S) vortex shedding pattern is observed, whereas a steady flow and chaotic pattern emerged in a few cases. The results reveal that with increasing L/D, the average Nu for both the upstream and downstream cylinders increases as the effect of each cylinder on the other diminishes.