A Study of the Effects of Anisokinetic Sampling

Abstract

The results of a numerical investigation of sampling bias through cylindrical probes are presented for both iso-and anisokinetic conditions for thin- and thick-walled probes. Laminar flow fields are calculated using a finite-difference solution of the Navier-Stokes equations; particle trajectories are then calculated with a fourth-order Runge-Kutta method to integrate the particle equation of motion. An ultra-Stokesian drag law and particle interception are included in the calculation. Based on a dimensional analysis of the problem and on the assumptions of the physical model, five dimensionless groups, Re, [Ubar]/U₀, D/d, St, and ρ/(ρ _p C) are identified that specify the aspiration coefficient, A_i=[Cbar]/C_a . Systematic investigations show that the tube Reynolds number, Re, and the slip-modified density ratio, ρ/(ρ _p C), have only a minor influence in determining A_i . Calculations are made to determine the influence of the remaining groups—velocity ratio ([Ubar]/U_B), diameter ratio (D/ d), and Stokes number (St)—on the sampling process. For thin-walled probes, the present results are found to be in good agreement with reported experimental data, and with a semiempirical expression proposed by Belyaev and Levin. A least-squares curve-fitting method is used to determine a slightly more accurate correlation. Results for thick-walled probes are found to be in qualitative agreement with reported experimental findings: 1) even isokinetic sampling does not insure a representative sample; 2) probe thickness was found to play a minor role for superisokinetic sampling ([Ubar]/U₀ > 1); and 3) for subisokinetic sampling ([Ubar]/U₀ < 1), a thick-walled probe actually provides a sampling efficiency that is closer to unity than a thin-walled probe.