Modeling fully developed laminar flow in a helical duct with rectangular cross section and finite pitch

The mass and momentum transport equations are written in an orthogonal coordinate system using Germano’s transformation to model a laminar flow in a helical duct with a rectangular cross section and finite pitch. The system of governing equations are discretized and solved by the finite-volume numerical method. The three dimensional domain is reduced to a two dimensional slab of cells, orthogonal to the main flow direction, enforcing the fully developed state for 2π/(τ · d_h) >> 1 where τ and d_h representing the duct’s centerline torsion and its hydraulic diameter. This approximation and the use of an orthogonal grid allow a great simplification on the numerical procedure. Comparisons of the numerical solution against experimental data are drawn to assess the accuracy of the approximation.