Flow through a rotating helical pipe with a wide range of the Dean number

Abstract

The incompressible viscous steady flow through a helical pipe of circular cross-section rotating at a constant angular velocity about the center of curvature is investigated numerically to examine the combined effects of rotation (Coriolis force), torsion and curvature (centrifugal force) on the flow. The flow depends on the Taylor number T r =[equation], the Dean number D n =[equation], the torsion parameter β 0 =[equation] and the dimensionless curvature of the duct δ , where a is the radius of the helical pipe, Ω T the angular velocity, μ the viscosity, v the kinematic viscosity, G the constant pressure gradient along the pipe axis and β 0 -a parameter related to the torsion τ and curvature δ . When Ω T >0, the rotation is in the direction in which the Coriolis force produces the curvature effect. When Ω T <0, the rotation is in the direction in which the Coriolis force exhibits an opposite effect to that of curvature. The calculations are carried out for -500 ≤ T r ≤ 500, 1500 ≤ D n ≤ 2000 (large Dean number), 0≤ β 0 ≤ 0.4 and 0 < δ ≤ 0.2. The total flux through the duct has a sharp peak at a negative T r .