Abstract
In this paper, we make clear the performance of a magnetic filter in which the ferromagnetic wires are arranged perpendicular to the air flow (perpendicular stream type of magnetic filter). The perpendicular stream type of magnetic filter has been investigated by Watson, Luborsky et al. and the capture radius (i.e. single wire collection efficiency) was calculated based on the particle trajectory model. In their work the calculated capture radius was rather larger than the experimental results. The authors, in analytical and experimental estimation of the collection efficiency of air-borne particles, take into account the three points as follows. Firstly, in the previous models, as the flow pattern around a circular wire, were used the potential flow for high Reynolds numbers and the viscous flow due to Lamb for low Reynolds numbers. The actual flow for high Reynolds numbers, however, deviates very much from potential flow because of the dead water with eddies conditioned by the breaking away of the boundary layer. On the other hand, the viscous flow solution due to Lamb for low Reynolds numbers, exactly satisfies the boundary conditions at the cylinder, however, it doesn't pass over to the undisturbed parallel flow at infinity. Then in our model, as the flow field around a cylinder, is used the numerical solution of steady two-dimensional flow of an incompressible Newtonian fluid past the circular cylinder governed by the Navier-Stokes equations. Secondly, the inertia forces acting on a particle which could be usually neglected in slurry treatment by previous investigators, cannot be ignored for the magnetic filtration of aerosol particles. In the present model, the authors solve the differential equation of the trajectory of particles without neglecting the inertia terms. Thirdly, in the previous analyses of the magnetic filtration, the magnetic particle was assumed a sphere. The actual magnetic particle usually isn't spherical. So, in the comparison of the experimental collection efficiency with calculated results, on the analogy of the Stokes' diameter which is adopted in investigating the motion of particles in gravity, we choose the measured diameter based on the velocity of magnetic particles precipitating in the low gradient magnetic field near the polar of the permanent magnet.The inertia effect of fine particles on capture radius, which can be usually neglected in high gradient magnetic filtration for slurry treatment, cannot be ignored for removal of air-borne particles. Numerical calculation shows that the inertia effect makes a great difference between for the system with magnetic field parallel to air flow across the cylindrical wire and for that with magnetic field perpendicular to air flow. The capture radius calculated for the flow field in the intermediate Reynolds numbers region around a circular wire is smaller than that for potential flow field. Experimental data on model filters, which are made of a uniform parallel arrangement of wires oriented ar right angles with the flow direction, have shown good agreement with the calculated results.
