On the influence of gravitational and centrifugal buoyancy on laminar flow and heat transfer in curved pipes and coils

Abstract

The effects of gravitational and centrifugal buoyancy on laminar flow and heat transfer in curved and helical pipes were investigated by numerical simulation. Six dimensionless numbers characterizing the problem were identified, and an analysis was conducted on the possible combinations of signs of the gravitational and centrifugal buoyancy effects. Two distinct Richardson numbers were introduced in order to quantify the importance of the two types of buoyancy, and it was shown that, in the case of heating from the wall, a maximum realizable value of the centrifugal Richardson number exists which is a linear function of the curvature δ (ratio of pipe radius a to curvature radius c). Detailed results were obtained for δ = 0.9, torsion λ (ratio of reduced pitch H/(2π) to curvature radius c) = 0 (toroidal pipe) or 0.4 (helical pipe), Re = 100, Pr = 1 and gravitational and centrifugal Richardson numbers Rig, Ric each varying from −0.1 to +0.1. A complex interaction between the two forms of buoyancy was found to exist. In the helical geometry, provided |Rig| ≈ |Ric| they exhibited effects of the same order. The lowest values of both the friction coefficient and the mean Nusselt number were obtained in the presence of positive gravitational and centrifugal buoyancy, while the highest values were obtained when both forms of buoyancy were negative; the reason for this behavior was identified in the different degree of coupling between the distributions of axial velocity and temperature. In the toroidal geometry, a simpler behavior was predicted due to the presence of top–bottom symmetry; both the friction coefficient and the mean Nusselt number were found to decrease with the intensity of centrifugal buoyancy and to be little affected by gravitational buoyancy in the range of Rig investigated.