Advances in Water Treatment and Enviromental Management

COLLECTION EFFICIENCY OF LIQUID/LIQUID HYDROCYCLONES 169chamber, that is, for each cross section, It is independant of the velocity at the wall. Thus,this maximum value follows a classical vortex law only at the end of the chamber where it canbe written:(1)– The separation chamber can be separated in two regions: Region I is defined by 0 < r < RO/2. In this region, the velocity follows a vortex law and is thus characterized by a high accelerationfield.The other region, Region II, is defined by RO/2 < r < RO. In this region the velocity variesslowly between VO at the wall and V(r=RO/2), that is, according to (1), V=1.6Vs. Region IIrepresents 75% of the cross section of the separation chamber and can be considered as thedominant region for the separation process in the cyclone.4 COLLECTION EFFICIENCY4–1 Basic principleThe basic principle of the modelling which is proposed here has been given by DIETZ (Ref.3)as used for the evaluation of collection efficiency of dust cyclones. Where due to turbulence,the radial concentration C of the dispersion is uniform at any cross section while along theseparation chamber the axial concentration decreases due to the migration of droplets towardthe axis.Here, the separation chamber is divided in two regions, I and II, defined above. In anarbitrary cross section, droplets are uniformly spread in region II and, in a given time, someof them reach region I. In this region, the acceleration field is so high that these droplets areconsidered to be separated from the main flow and collected along the axis of the cyclone. Atime increment later, the cross section is located farther in the separation chamber and theremaining droplets are uniformly redistributed by the effects of turbulence. The abovemechanism is repeated until the cross section has reached the end of the separation chamber.4–2 Swirl decayThe modelling of the separation process described above needs a definition of the swirl decay.For this, we can write the conservation of angular momentum between two arbitrary crosssections of the separation chamber separated by a distance dx, which gives:(2)where to is the unitary stress at the wall. We can write tC as(3)where f is the friction factor. Putting (3) into (2) gives the differential equationIntegration for x=0 to a given section gives(4)Fig.6 shows that for a classical value of the friction factor for smooth walls f =.0055, the aboveexpression Eq.(4) gives satisfactory agreement with measured values.