Finite element analysis of incompressible viscous flow in a helical pipe

This paper presents an accurate finite element procedure to deal with steady state, fully developed and incompressible viscous flow in helical pipes with arbitrary curvatures and torsions. The full Navier-Stokes equations and continuity equation have been explicitly derived using a non-orthogonal helical coordinate system. To obtain the final simultaneous non-linear algebraic equations, a pressure-velocity finite element formulation is formulated based on the Galerkin Method.The combined influence of finite curvature and finite torsion on the helical flow is studied. The secondary flow patterns and contours of axial velocity of helical flows show the significant distinction with those of toroidal flows. Further, the effect of torsion on flow rates can be neglected.Several numerical examples are presented. Excellent correlations between the computed results and available referenced solutions can be drawn.