Effect of Blockage Ratio on Drag and Heat Transfer from a Centrally Located Sphere in Pipe Flow

Abstract

Hydrodynamic and heat transfer analyses were carried out for laminar fluid flow past a heated sphere placed centrally in a pipe using Computational Fluid Dynamics (CFD) simulations. Fully developed parabolic velocity profile characteristic of laminar flow was specified at the pipe inlet. The effects of blockage ratio, defined as the ratio of the sphere diameter to the pipe diameter, on the drag coefficient and Nusselt number are reported. The particle Reynolds numbers were varied up to a maximum of 500 while the Prandtl number for the water system studied was fixed at 5.12. At lower blockage ratios (<0.3), transient and three-dimensional simulations were required for particle Reynolds numbers exceeding 270. The effect of blockage was more significant at lower particle Reynolds numbers and influenced the drag coefficient more than the Nusselt number for this system. At high particle Reynolds numbers, reasonable predictions of the drag coefficient could be obtained even at high blockage ratios, by using the standard correlations available for a sphere immersed in an unbounded domain and the fluid approaching the sphere with a uniform velocity profile. Conversely, at low blockage ratios and low Reynolds numbers, considerable deviation from the standard drag correlation predictions was observed. Higher blockage ratios delayed boundary layer separation. The local Nusselt number distribution trends along the sphere are also reported. Correlations were developed for the drag coefficient, boundary layer separation angle and the average Nusselt number as a function of the blockage ratio and particle Reynolds number.