Steady Developing Laminar Flow in Helical Pipes with Finite Pitch

Abstract

Steady developing laminar flow of incompressible Newtonian fluids in helical pipes having a constant circular cross-section and a finite pitch was numerically studied. The governing equations were fully parabolized and were written in the orthogonal helical coordinate system. A loose coiling analysis was employed to obtain the axial length scale and the parabolic behavior of the developing flow. The numerical simulations were carried out without invoking the loose coiling approximation. The results for the axial wall shear rate and axial velocity agree with published data for the developing flow in a torus. The flow was found to be oscillatory in the developing region. The hydrodynamic developing length was correlated with the flow Dean number (Dn = Reγ½). Here Re is the flow Reynolds number and γ is the dimensionless curvature ratio. When torsion is small, its effect is more pronounced in the developing flow region. This is specially true for 0.1 < γ < 0.3. Here γ ( = η γ−½ Dn −½) is the flow pattern transition parameter for high Dean number flows and η is the dimensionless torsion. When the torsion is large, the friction factor and the developing length approach the limits corresponding to a straight pipe flow as torsion is increased.