Three-Dimensional Simulation of Pulsatile Flow Through a Porous Bulge

Abstract

The present research deals with simulation of pulsatile flow through a tubular bulge filled with homogeneous, isotropic, saturated porous medium. For comparison, flow fields are also computed for the flow through clear medium in the same geometry. Both cases involve three-dimensional, unsteady, laminar, incompressible flow of Newtonian fluid. Flow through the porous medium is modeled via Forchheimer–Brinkman-extended Darcy model. While semi-analytical solutions are presented for the asymptotic cases, numerical techniques are used for the general solutions of the conservation equations. The governing equations, in both porous and clear media, are discretized by an implicit finite volume technique over an unstructured tetrahedral mesh. The resulting algebraic equations are solved using stabilized biconjugate gradient technique. Simulations include Darcy numbers of $$10^{-4}$$ and $$10^{-2}$$ at Reynolds numbers of 500 and 2000 based on the peak incoming average velocity and main tube diameter. The Womersley number is chosen to be 11.3 to mimic biomedical application. Results show that the porous medium naturalizes the recirculations and secondary flows while experiencing higher-pressure drop and wall shear compared to that of the clear medium.