Flows through helical pipes with elliptic cross-sections

Abstract

Flows through helical pipes are important in many applications, such as blood flow through the coiled veins and arteries of an umbilical cord, and flow through industrial heat exchangers and reactors. This research examines flows through helical pipes with elliptic cross-section. The incompressible Navier-Stokes equations are solved for steady and unsteady flows through these geometries at low Reynolds numbers using the finite-element method library oomph-lib. The effect of changes in the various non-dimensional parameters such as the aspect ratio of the ellipse, curvature and torsion of the helix and the Reynolds number on the flow dynamics are explored. The computed results are compared with theoretical solutions, previous computations and experimental results to verify and validate the solver. Trends for elliptical cross-sections are usually similar to those of circular cross-sections. However for a geometry of very high torsion and low aspect ratio, the flow develops a persistent oscillation with streamwise distance along the pipe. This behaviour is not present for circular cross-sections. The aspect ratio controls the period of the oscillation and the Reynolds number controls the magnitude of the oscillation. At low Reynolds and Strouhal number, steady results can be used to predict time-averaged pressure values of unsteady flows. This is important for umbilical cords as it allows for simple predictions of pressure drops using empirical data.