Navier-Stokes solutions of laminar flows based on orthogonal helical co-ordinates

• Published in: International journal for numerical methods in fluids Vol. 29; no. 7; pp. 749 - 763
• Main Authors: Hüttl, T.J., Wagner, C., Friedrich, R.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 15.04.1999; Wiley
• Subjects: Computational methods in fluid dynamics; Computer simulation; curvature; Exact sciences and technology; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); helical pipe; Incompressible flow; Integration; laminar; Laminar flow; Laminar flows; Low-reynolds-number (creeping) flows; Physics; Pipe; Pipe flow; Pressure distribution; Reynolds number; secondary flow; torsion; Torsional stress; Pipe flow; Computational fluid dynamics; Digital simulation; Pressure distribution; Finite volume method; Helical pipe; Velocity distribution; Coil tube; Laminar flow; Curved pipe; Secondary flow; Curvature; Numerical convergence; Navier-Stokes equations
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/(SICI)1097-0363(19990415)29:7<749::AID-FLD815>3.0.CO;2-4

In this paper a numerical method to compute time‐dependent flows in helically coiled pipes with circular cross‐section and constant curvature κ and torsion τ is presented. The incompressible Navier–Stokes equations, explicitly derived in an orthogonal helical co‐ordinate system, are integrated numerically. The results show for example, the influence of curvature and torsion on the axial velocity profile. Good agreement with experiment is found. The numerical simulations also allow a detailed study of the secondary motion in the cross‐section of the pipe by considering vector plots and contour lines of the streamfunction. Furthermore, the formation of a pressure distribution perpendicular to the pipe axis is shown. Besides the Reynolds number, other characteristic flow parameters, like the Dean numer De, and the Germano number Gn, are used to compare the flow through different pipe configurations. Copyright © 1999 John Wiley & Sons, Ltd.