Viscous laminar flow in smooth coil tubes

Abstract

A mathematical model of incompressible viscous laminar flow in smooth coil tubes is proposed and the results of its numerical realization in a nonorthogonal helical coordinate system are presented. This coordinate system is free of singularities in the domain of definition of the unknown functions, that is, the pressure and the velocity components, which makes it possible to refine the existing distributions of the axial component and the secondary crossflows obtained using the well-known orthogonal coordinate system having a singularity at the center of the coil channel. The momentum transport equation is written in the projections on the axes of the natural basis of the coordinate system, which makes it possible to subdivide the system of equations into two alternately solved subsystems. The distributions of the axial and two transverse components show that at the center of coil tubes the transverse components are comparable with the axial velocity (the transverse components can be as high as half the mean-flow-rate velocity and one third of it at the center of the channel).