Torsion effect on the flow in a helical pipe

The effect of curvature and torsion on the flow in a helical pipe of circular cross-section is studied numerically by the spectral method. The calculations are carried out for 0 ⩽ δ ⩽ 0.6, 0 ⩽ β 0 ⩽ 1.4 and 500 ⩽ D n ⩽ 2000, where δ is the non-dimensional curvature, β 0 the ratio of torsion to square root of curvature, and D n the Dean number. The results obtained indicate large effects of torsion on the flow: The conventional two-vortex secondary flow is distorted to become almost one single recirculating cell when β 0 ≳ 0.8. The flux through the pipe at the given Dean number and curvature first decreases from that of the toroidally curved pipe as β 0 increases from zero, reaches a minimum at β 0 ≈ 0.8, and then increases to values larger than that of the toroidally curved pipe. The minimum value decreases as δ increases.