Theoretical derivation of tangential velocity profiles in a flat vortex chamber-influence of turbulence and wall friction

As part of a study on the hydrodynamics of a cyclone separator, a theoretical investigation of the flow pattern in a flat box cyclone (vortex chamber) has been carried out. Expressions have been derived for the tangential velocity profile as influenced by internal friction (eddy viscosity) and wall friction. The most important parameter controlling the tangential velocity profile is ? = - u 0 R /( v + e), where u 0 is the radial velocity at the outer radius R of the cyclone, ? the kinematic liquid viscosity and e is the kinematic eddy viscosity. For values of ? greater than about 10 the tangential velocity profile is nearly hyperbolic, for ? smaller than 1 the tangential velocity even decreases towards the centre. It is shown how ? and also the wall friction coefficient may be obtained from experimental velocity profiles with the aid of suitable graphs. Because of the close relation between eddy viscosity and eddy diffusion, measurements of velocity profiles in flat box cyclones will also provide information on the eddy motion of particles in a cyclone, a motion reducing its separation efficiency.