Fully developed laminar flow and heat transfer in serpentine pipes

Abstract

A serpentine pipe is a sequence of parallel straight pipe segments connected by U-bends. Its geometry is fully characterized by pipe radius, a, bend curvature radius, c and length of the straight segments, l. The repeated curvature inversion forces the recirculation (secondary flow) pattern to switch between two specular configurations, which may enhance mixing and heat or mass transfer with respect to a constant-curvature pipe at the cost of an increase in pressure drop. In the present work, fully developed laminar flow and heat transfer in serpentine pipes were investigated by numerical simulation. The curvature d = a/c was made to vary between 0.1 and 0.5 while the parameter g = l/c was made to vary between 0 and 8; for each geometry, the friction velocity Reynolds number Ret = uta/n was made to vary between a very low value (5), yielding almost creeping flow, and the highest value Re∗t still yielding steady laminar flow (~35e40 in most cases). For Ret Re∗t results were obtained for values of the Prandtl number between 1 and 100; predicted values of the friction coefficient and of the Nusselt number were compared with experimental results and correlations proposed in the literature. For Ret Re∗t convergence to steady flow was not achieved and an oscillatory behaviour of the solution was observed, indicating a transition to unsteady regimes which deserves a more focused study.