Theory and Design Guidelines - Chapter 4

"4.1 IntroductionIn previous chapters impactors have been described as useful instruments for classifying particles by their aerodynamic diameters and for measuring particle size distributions. These impactors can be used most reliably if the user has some understanding as to how the impactor classifies particles and what parameters are important in this classification process. This understanding can best be obtained by a theoretical inspection of inertial principles.This chapter reviews the most recent theoretical impactor work and the latest theoretical efficiency curves. Procedures are then given for using these efficiency curves in the design and evaluation of cascade impactors. Finally, several examples are given comparing theoretical and experimental efficiency curves, pointing out when the theory can be used with great confidence and when the theory should be used only as a guideline.Due to the rather simple principle of operation of an inertial impactor (i.e., the impingement of a jet of particle-laden air on a flat plate) the impactor readily lends itself to theoretical analysis. Three notable works in the early 1950,s were those of Davies and Aylward (1951), Davies et al. (1951), and Ranz and Wong (1952).Davies and Aylward (1951) used a method of conformal mapping to obtain an analytical solution to Euler's equation for the flow of a frictionless fluid through a rectangular impactor. Numerical calculations were then carried out whereby the equations of motion of the particles were solved in a stepwise manner, leading to a determination of the efficiency curves. Since this theory assumed potential flow, the effect of Reynolds numbers on the characteristics of the impactor could not be determined.Ranz and Wong (1952) used an approximate flow field to calculate the efficiency of both round and rectangular nozzle impactors. In the vicinity of the stagnation point, the flow field was assumed to be that of frictionless stagnation flow. Here, the resulting equation of motion for the particles was found to be in a form similar to equations for free vibration with viscous damping. Therefore, the known solutions of the vibration equations were applied directly to the problem and the efficiency curves calculated. This solution technique, however, could not take into account the various geometric variations such as the jet-to-plate distance in the determination of the efficiency curves.The work of Ranz and Wong (1952) was later modified by Mercer and Chow (1968) and Mercer and Stafford (1969) so that the rather simple flow fields of Ranz and Wong (1952) could be used to account for various jet-to-plate distances. The same techniques, however, were used to determine the impactor collection efficiency curves."