Flow pattern analysis around a solid cylinder with both porous and water rings in porous media

The flow field around a solid cylinder with both porous and water rings embedded vertically in an infinite large porous media is analytically simulated. The Brinkman model are applied for both the internal porous ring and external infinite large porous media. The Stokes model is used for the open water ring. By coupling the mass and momentum conservations at the interfaces between different regions, a general set of stream function equations can be derived. The program code is firstly validated by comparing the results of a typical two layer case with those of the previous literature. Then, the flow patterns for this complicated multilayer coaxial structure is analytically simulated by giving different geometric parameters and different coefficients of permeability of the inner and outer porous media. The influences of the width of the water ring gap and the coefficients of permeability of the internal and external porous media on the flow patterns and the velocity distribution of vertical and horizontal profiles are also emphatically studied. The results show that the flow pattern in the external porous zone is mainly controlled by its permeability. The width of the water ring has a great influence on the peak value of the velocity profile in the vertical cross section. With the increasing coefficient of permeability of the internal porous zone to a critical value, the velocity profile in the cross section will change from a step-shaped pattern to a parabolic one, which is viewed as a penetration phenomenon. It is believed that these obtained results are helpful in guiding a design such as borehole heat exchanger, groundwater pollutant absorption device, groundwater velocity measurement device, etc., with similar geometrical configuration.