Impingement of particles on a transverse cylinder

Abstract

Abstract Symbols R The Reynolds number with respect to the cylinder. Re The Reynolds number with respect to the particle. Re0 The Reynolds number with respect to the particle when the latter is held at rest in the undisturbed air stream. ψ Drag coefficient of the particle. x', y', t' Spatial co-ordinates and time. x, y, t Dimensionless co-ordinates and time. q'(u', v') Particle velocity and resolutes. q(u, v) Dimensionless velocity and resolutes. Q'(U', V') Fluid velocity and resolutes. Q(U, V) Dimensionless velocity and resolutes. U0 Velocity of undisturbed flow stream. r, m Radius and mass of particle. σ, η, v Density, viscosity and kinematic viscosity of fluid. R Radius of cylinder. P Particle parameter, mU0/6πrηR, equal to the distance the particle will travel before coming to rest when launched with velocity U0 into stationary fluid. xi, yi Starting co-ordinates of a trajectory (dimensionless). y0 Ordinate of a trajectory a great distance upstream from the cylinder (dimensionless). rc Critical radius of particle which just touches the cylinder. E Collision efficiency. du/dx Retardation of a particle approaching the cylinder on thex-axis. (du/dx)8 The same at the instant of impact. u8 The impact velocity of a particle on the x-axis (dimensionless). θ Polar co-ordinate of point of contact. N Number of particles per unit volume of fluid at a great distance from the cylinder. ψ Stream function of flow field. γ Euler’s constant. K0, K1 Bessel functions. vs Rate of fall of particle under gravity. g Acceleration due to gravity.