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

In this paper a numerical method to compute time-dependent flows in helical ly coiled pipes with circular cross-section and constant curvature rc and t orsion tau is presented. The incompressible Navier-Stokes equations, explic itly derived in an orthogonal helical co-ordinate system, are integrated nu merically. The results show for example, the influence of curvature and tor sion on the axial velocity profile. Good agreement with experiment is found . The numerical simulations also allow a detailed study of the secondary mo tion in the cross-section of the pipe by considering vector plots and conto ur lines of the streamfunction. Furthermore, the formation of a pressure di stribution perpendicular to the pipe axis is shown. Besides the Reynolds nu mber, other characteristic flow parameters, like the Dean numer De, and the Germane number Gn, are used to compare the flow through different pipe con figurations. Copyright (C) 1999 John Wiley & Sons, Ltd.