Calculation of particle concentration around aircraft-like geometries

Abstract

A computationally-efficient method is presented to calculate local particle concentration enhancements resulting from potential fluid flow around an idealized aircraft fuselage and wing. The geometries chosen for study are a 10:1 prolate ellipsoid at 0° angle of attack and a Joukowski airfoil at 0° and 5° angles of attack, for which potential flow analytic solutions are known. The collection efficiency of and surface concentration on a cylinder in potential flow are also considered for algorithm verification. Particle concentration is calculated along particle pathlines by a mixed Eulerian-Lagrangian technique developed by Fernandez de la Mora and Rosner (1981, Fernandez de la Mora, J. F. and Rosner, D. E., Physico Chem. Hydro. 2, 1). Ordinary differential equations for particle position, velocity, and concentration are integrated numerically by a variable order, backward difference algorithm. The calculations show the creation of regions of increased concentration near objects, and of particle-free shadow zones downstream. The magnitudes of the concentration disturbances are greatest at intermediate Stokes numbers (0.1–1.0) where inertia and drag are equally dominant. Samplers placed in these regions of enhanced particle concentration may not provide accurate concentration measurements. Ultimately, this approach could be included with detailed flow solutions about specific aircraft geometries to provide guidance in locating samplers in regions of acceptably small concentration deviations.