Effects of Prandtl number on the laminar cross flow past a heated cylinder

Abstract

Flow past a heated cylinder at constant surface temperature is computationally simulated and analyzed in the laminar regime at moderate buoyancy. The parameters governing the flow dynamics are the Reynolds number, Re, the Richardson number, Ri, and the Prandtl number, Pr. We perform our computations in the range 10 ≤ Re ≤ 35, for which the flow past an unheated cylinder results in a steady separation bubble, and vary the other two parameters in the range 0 ≤ Ri ≤ 2, 0.25 ≤ Pr ≤ 100. The heat transfer from the entire cylinder surface, quantified by the average Nusselt number Nuavg, is shown to obey Nuavg = 0.7435Re0.44Pr0.346 in the mixed convection regime we investigate. For a fixed Re and Pr, the flow downstream of the cylinder becomes asymmetric as Ri is increased from zero, followed by a complete disappearance of the vortices in the recirculation bubble beyond a threshold value of Ri. For a fixed Re and Ri, the vortices in the recirculation bubble are again observed to disappear beyond a threshold Pr, but with the reappearance of both the vortices above a larger threshold of Pr. In the limit of large Pr, the time-averaged flow outside the thermal boundary layer but within the near-wake region regains symmetry about the centerline and ultimately converges to a flow field similar to that of Ri = 0; in the far-wake region, however, we observe asymmetric vortex shedding for moderate Pr. The thermal plume structure in the cylinder wake is then discussed, and the plume generation is identified at points on the cylinder where the Nusselt number is a local minimum. The difference between the plume generation and the flow separation locations on the cylinder is shown to converge to zero in the limit of large Pr. We conclude by plotting the lift and drag coefficients as a function of Ri and Pr, observing that CD decreases with Ri for Pr < Prt (and vice versa for Pr > Prt), where Prt ≈ 7.5.