Experimental and theoretical study of fluid flow in porous tube systems using magnetic resonance imaging and two-dimensional finite element methods

Fluid flow in porous tube membrane systems was investigated using a 2-D finite element method (FEM) and magnetic resonance velocity imaging (MRVI). Qualitative flow experiments were performed on a multitube system while flow in a single tube and shell system was investigated quantitatively. The quantitative study was evaluated by comparing results from the MRVI experiments to the predictions of the FEM model.; The 2-D FEM used the Navier-Stokes equations to describe the flow phenomena in the tube and shell space while the continuum theory of Brinkman was used to describe flow in the porous tube wall. The solution method, based on the Galerkin finite element and Newton iteration techniques, provided velocities and pressures for a wide range of Reynolds numbers and operational modes. The approach was justified by a comparison to previous experimental, numerical and analytical results for flow in porous wall tubes.; The MRI experiments utilized a spin echo, time of flight technique to measure axial velocities in nonpermeable tubes and in the porous tube and shell modules. Results from the nonpermeable tubes were compared to MRI theory, while the porous tube and shell module results were compared to the FEM predictions.; The favorable comparison obtained between the MRI experiments and FEM predictions demonstrated that MRI may be used to measure axial velocities in porous tube and shell modules. Additionally, the FEM model may be used to predict pressures and velocities for steady, incompressible, laminar flow in axisymmetric porous tube and shell systems.