Mathematical modelling of two‐phase non‐Newtonian flow in a helical pipe

Governing equations for a two-phase 3D helical pipe flow of a non-Newtonian fluid with large particles are derived in an orthogonal helical coordinate system. The Lagrangian approach is utilized to model solid particle trajectories. The interaction between solid particles and the fluid that carries them is accounted for by a source term in the momentum equation for the fluid. The force-coupling method (FCM), developed by M.R. Maxey and his group, is adopted; in this method the momentum source term is no longer a Dirac delta function but is spread on a numerical mesh by using a finite-sized envelop with a spherical Gaussian distribution. The influence of inter-particle and particle–wall collisions is also taken into account. Copyright © 2005 John Wiley & Sons, Ltd.

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