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 β₀=[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 β₀ - 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≤ β₀ ≤ 0.4 and 0 < δ ≤ 0.2. The total flux through the duct has a sharp peak at a negative T_r