Fluid Dynamical Analysis of a Particle with Large Vapor Transport in Poiseuille Flow

Abstract

The fluid dynamics of a particle with vapor transport in the presence of gaseous Poiseuille flow is examined in detail for low translational Reynolds number. Poiseuille flow is used to represent an undisturbed steady flow in a cylindrical tube. The particle has a dominant radial field of condensation, evaporation, sublimation, or other form of gasification, with a corresponding radial Reynolds number of order unity. An analysis is carried out by using the perturbation method in which the purely radial flow is used as the leading order, and Poiseuille flow together with particle translation is a perturbation of higher order. Whereas the leading order motion may be described by potential flow, the higher order involves nonlinear interaction of viscous and inertial forces. With the perturbation process bringing about linearization of this interaction, an Oseen-like solution is obtained. However, with the dominant radial flow being strongly diminishing in the far field, a regular perturbation (instead of singular) is sufficient for the perturbed flow description. Presently, the axisymmetric case of a particle along the centerline of the cylinder is considered. The asymmetric case of the off-center particle is also under examination. The results show that the drag components decrease as the radial Reynolds number increases. The influence of the paraboloidal component of Poiseuille flow is a slight increase in the pressure drag as the ratio of the particle size and the tube radius (a/R(0)) increases for moderate values of the radial Reynolds number (Re(R) < 5). For higher values of Re(R), the pressure drag decreases with increasing (a/R(0)). The viscous drag, on the other hand, consistently decreases as the ratio (a/R(0)) increases.