Effect of Torsion on the Friction Factor of Helical Pipe Flow

Three-dimensional direct numerical simulations of a viscous incompressible fluid flow through a helical pipe with a circular cross section were conducted for three Reynolds numbers, Re (= 80, 300, and 1000), and two nondimensional curvatures, δ (= 0.1 and 0.05), over a wide range of torsion parameters, β (= nondimensional torsion=2 √2δ), from 0.02 to 2.8. Well-developed axially invariant regions were obtained where the friction factors were calculated, in good agreement with the experimental data obtained by Yamamoto et al. [Fluid Dyn. Res. 16, 237 (1995)]. It was found that the friction factor sharply increases as β increases from zero, then decreases after taking a maximum, and finally slowly approaches that of a straight pipe when β tends to infinity. It is interesting that a peak of the friction factor exists in the region 0.2 ≤ β ≤ 0.3 for all the Reynolds numbers and curvatures studied in the present paper, which manifests the importance of the torsion parameter in helical pipe flow.