A numerical technique for laminar swirling flow at the interface between porous and homogenous fluid domains

Abstract

SUMMARYThere have been a few recent numerical implementations of the stress-jump condition at the interface of conjugate flows, which couple the governing equations for flows in the porous and homogenous fluid domains. These previous demonstration cases were for two-dimensional, planar flows with simple geometries, for example, flow over a porous layer or flow through a porous plug. The present study implements the interfacial stress-jump condition for a non-planar flow with three velocity components, which is more realistic in terms of practical flow applications. The steady, laminar, Newtonian flow in a stirred micro-bioreactor with a porous scaffold inside was investigated. It is shown how to implement the interfacial jump condition on the radial, axial, and swirling velocity components. To avoid a full threedimensional simulation, the flow is assumed to be independent of the azimuthal direction, which makes it an axisymmetric flow with a swirling velocity. The present interface treatment is suitable for non-flat surfaces, which is achieved by applying the finite volume method based on body-fitted and multi-block grids. The numerical simulations show that a vortex breakdown bubble, attached to the free surface, occurs above a certain Reynolds number. The presence of the porous scaffold delays the onset of vortex breakdown and confines it to a region above the scaffold.

A three‐dimensional hybrid meshfree‐Cartesian scheme for fluid–body interaction

“…They explained that the detached recirculating regions are caused by the stagnation of the fluid on the axis downstream of the ring resulting from an adverse pressure gradient induced by the divergence of fluid radially outward around the leeward surface of the ring. To further confirm this flow phenomenon, an axisymmetric simulation of flow past a stationary ring with Ar = 2 and Re = 50 was conducted by using an FVM code 48, 49. The axisymmetric flow field shown in Figure 10 is consistent with that demonstrated in Figure 9(b).…”

Numerical simulation on steady flow around and through a porous sphere

“…The generalized model is thus introduced to include all the non-Darcy flow behaviour. In recent years, this generalized model has been applied by many researchers (Vafai, 1984;Lage, 1992;Nithiarasu et al, 2002;Yu et al, 2009b). It is very difficult to evaluate the accuracy of this model at various flow scenarios.…”

“…The porous medium is considered to be rigid, homogeneous and isotropic; and saturated with the same single-phase fluid as that in the homogenous fluid region. Considering viscous and inertial effects, the governing equations for the flow in the porous region, based on Darcy-Brinkman-Forchheimer extended model, can be expressed as (Yu et al, 2009b):…”