Transition to turbulence in serpentine pipes

The geometry considered in the present work (serpentine pipe) is a sequence of U-bends of alternate curvature. It is characterized by pipe diameter, d = 2a and bend diameter, D = 2c. The repeated curvature inversion forces the secondary flow pattern, typical of all flows in curved ducts, to switch between two mirror-like configurations. This causes (i) pressure drop and heat or mass transfer characteristics much different from those occurring either in a straight pipe or in a constant-curvature pipe, and (ii) an early loss of stability of the base steady-state flow. In the present work, four values of the curvature δ = a/c (0.2, 0.3, 0.4 and 0.5) were considered. For each value of δ, the friction velocity Reynolds number Reτ = uτa/ν was made to vary in steps between 10 and 50. Fully developed flow was simulated using a three-dimensional, time-dependent finite volume method and computational grids with a number of nodes ranging from ∼1.8 to ∼4.6 × 106, according to the curvature. The computational domain included two consecutive and opposite bends and thus coincided with the minimum spatially repetitive unit. Heat transfer was also simulated for uniform wall heat flux conditions and a Prandtl number of 1. A complex scenario of transitions was predicted, leading from the base steady-state, top-down symmetric flow to turbulence through intermediate regimes which included steady-state asymmetric and time-periodic flows. For all curvatures, at the highest value of Reτ investigated (50) the flow was turbulent and exhibited top-down symmetric time averages.