Use of a Generalized Stokes Number to Determine the Aerodynamic Capture Efficiency of Non-Stokesian Particles from a Compressible Gas Flow

Abstract

The aerodynamic capture efficiency of small but non-diffusing particles suspended in a high-speed stream flowing past a target is known to be influenced by parameters governing (a) small particle inertia, (b) departures from the Stokes drag law (associated with local particle Reynolds numbers greater than unity), and (c) carrier fluid compressibility (at nonnegligible free-stream Mach numbers). By defining an effective Stokes number in terms of the actual (prevailing) particle stopping distance, local fluid viscosity, and inviscid fluid velocity gradient at the target nose, we show that these effects are well correlated in terms of a “standard” (cylindrical collector, Stokes drag, incompressible flow, Re^½ ≫ 1) capture efficiency curve. We are thus led to a correlation that (a) simplifies aerosol capture calculations in the parameter range already included in previous numerical solutions, (b) allows rational engineering predictions of deposition in situations not previously specifically calculated, (c) should facilitate the presentation of performance data for gas cleaning equipment and aerosol instruments.