This numerical study investigated the flow-induced vibration (FIV) on non-heated and heated cylinders with different normalized corner radii (r*) at different Reynolds numbers (Re). Four different values of r* were considered (i.e., 0 (square cylinder), 0.5, 0.75, and 1.0 (circular cylinder)) at three different Re: 100, 150, and 200 within the laminar regime. The cylinder constrained in the axial direction and oscillated transversally was considered for a fixed nondimensional cylinder mass $\left(m^{*}\right)$ of 10 and a reduced velocity (Ur) of 4.92. The effect of r* and Re could be seen in the vibration modes of cylinders. The two-dimensional incompressible Navier–Stokes and energy equations were solved together with Newton’s Second Law governing the motion of the cylinder with the help of a computational solver. Four different modes were observed in this study: Mode-I characterized by exceptionally low amplitude; Mode-II characterized by fluctuating amplitude known as hysteresis (beating); Mode-III characterized by high amplitude due to synchronization or lock-in; and Mode-IV characterized by the monotonic oscillation of fixed amplitude. For r* = 1, synchronization phenomenon/lock-in was observed. For the heated cylinder cases, due to the change in the normalized corner radius, a notable change in nondimensional vibrational amplitude $A/D$ and the average Nusselt number $N{u}_{avg}$ was seen. It was observed that A/D was higher when lock-in occurred (at Re = 100 and r* = 1), leading to a rise in $N{u}_{avg}$ by 47.9% compared to Re = 100 and r* = 0. Due to the change in r*, a shifting phenomenon was observed at Re = 150, r* = 0.75 and Re = 200, r* = 1. A major change in $N{u}_{avg}$ was observed from the circular cylinder to square cylinder at different Re. The beating phenomenon was observed at Re = 100 for r* = 0.75, which was similar to that occurring at Re = 150 and r* = 0.5, and those at Re = 200 and r* = 0. Heat transfer and wake structure parameters were found to be dependent on r* and Re.

Flow-induced vibration (FIV) on two tandem cylinders with forced convection is investigated numerically 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 1.0 (circular cylinder) with two spacing ratio (L/D)=4 and 2 are 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. Both cylinder's 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 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 impingement of vortex shedding from the upstream cylinder (U_c). 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. Average Nusselt number strongly depends on flow topology, corner radius, and vibrational amplitude.

Flow induced vibration (FIV) and forced convection heat transfer from staggered cylinders are numerically investigated with Re = 150 and Pr = 0.7. Cylinders are arranged in a staggered manner with three different stagger angles (α) = 15°, 30°, and 45°. The upstream cylinder (UC) is kept fixed while the downstream cylinder (DC) is mounted. The cross section of the bluff body is altered by parameter (r*) = 0 (square cylinder), 0.5, 0.75, and 1 (circular cylinder). For every stagger angle and r*, the reduced velocity is varied from 2 to 10. The mass ratio (m*) of the DC is kept at 10 and damping constant set to zero for maximum vibrational amplitude. The incompressible Navier–Stokes equations are coupled with Newton's equation for the mass-damper system of the vibrating cylinder. Flow induced vibration was studied with the help of frequency characteristics, dynamics response of cylinders, and instantaneous phase plots of lift and amplitude. Generally, in the case of square cylinders a delayed response can be observed as compared to other configurations. For α=15°, the DC is fully submerged into the wake of static UC. P + S (P: pair; S: singlet)-type vortices can be observed for r* = 0. For other configurations of filleted cylinders, such as r* = 0.5, 0.75, and 1 at Ur=4, 2 parallel row formation is formed due to negative sign vortices while the other one was a combination of positive and negative vortices in pseudo-P formation. At higher Ur=6 and 8, coalesced and irregular wakes can be noticed. As the stagger angle is increased to higher than 30°, the wake of both cylinders becomes more pronounced. Due to the change in stagger angle, fs (vortex shedding frequency) of UC and DC forces decouples. 2P-type vortex shedding can be observed at Ur=4 for r* = 0.75 and 1. Pairs of vortices are coupled from each cylinder in a row where negative vortices coalesce while losing energy. For lower r* = 0 and 0.5, there is a tendency for three row formation. Further increase in angle pushed the DC completely out of the wake of the UC although vortices from both cylinders are still found to interact and exhibit three row formation and 2P-type vortex shedding. Heat transfer from the DC is highly dependent on the stagger angle. For r* = 1 and 0.5 at Ur=2, the change in Nuavg is 15% and 14.7%, respectively, when the angle changed from 15° to 45°. Heat transfer from any FIV system can be directly influenced by dynamic response, position, shape, and flow topology. The generated results are provide insight for understanding the vibrational modes and heat transfer from two bluff bodies involving fluid–structure interactions.