A Numerical Simulation of Swirling Gas-solid Flow in a Vertical Pipeline

A numerical prediction for axial and swirling gas-solid flows in a vertical pipe was carried out with an Eulerian approach for the gas and a stochastic Lagrangian approach for particles, where particle-particle and particle-wall collisions were taken into consideration. The kε turbulence model was used to characterize the time and length scales of the gas-phase turbulence. Models predicting the particle source and additional pressure loss were proposed. The numerical results were presented for polyethylene pellets of 3.2mm diameter conveyed through a pipeline of 12m in height with an inner diameter of 80mm, solid mass flow rate of 0.03kg/s and 0.084kg/s, and gas velocity varying from 11m/s to 17m/s. The axial and radial distribution of particles, the particle concentration, the particle velocity, gas velocity, turbulent kinetic energy and turbulent energy dissipation were obtained. The numerical results agreed with the experimental data. INTRODUCTION Pneumatic conveying is an important operation in a significant number of industrial processes, such as in the transportation of materials from storage areas, in catalytic cracking in the petroleum industry, and in the production of synthetic fuels from coal in energy conversion systems. Conventional vertical pneumatic conveying, that is axial flow pneumatic conveying (AFPC), is frequently operated in the dilute-phase regime in the high air velocity region. Power consumption, pipe erosion, and particle degradation considerations dictate that the conveying velocity be held to a minimum. In the last thirty-five years, there has been increasing interest in dense-phase pneumatic conveying, and several commercial systems have been developed. Unfortunately, these systems require high pressure drops and have high initial costs. Furthermore, dense-phase pneumatic conveying may lead to unstable flows at low conveying velocities. These unstable flows often cause blockage and pipe vibration. To reduce power consumption, blockage, particle degradation, and pipe wear, this new swirling flow technique, called swirling flow pneumatic conveying (SFPC), was applied to horizontal and vertical pneumatic conveying by Li and Tomita (1996, 1998). In the low velocity conveying range, SFPC was determined to be effective. However, in order to investigate the characteristics of SFPC, it is important to predicate the particle behaviors. The present paper concerns three-dimensional numerical predictions of the swirling gas-solid flow in a vertical pipe based on the Euler/Lagrangian approach including two-way coupling, turbulence, turbulent particle dispersion, particle interactions with rough walls, and collisions between particles. The main objective was the prediction of the evolution of the particle velocity, concentration, gas velocity, swirl number, turbulent kinetic energy, turbulent energy dissipation, and additional pressure loss. NUMERICAL METHOD AND MODELS Assumptions In the present study the assumptions were as follows. (1) The particle phase is dilute and comprised of spherical particles of uniform of size. (2) The mean fluid flow is steady, three-dimensional, incompressible and isothermal. Effect of molecular diffusion and Brownian motion on the particle phase is negligible as compared with the turbulent dispersion. (3) The particle rotation, the pressure gradient force, the virtual mass force, the Basset force, the Magnus effect and the Saffman force are neglected. 1 Copyright © 1998 by ASME Equations for the Carrier Phase The numerical calculations were performed by the Euler/ Lagrangian approach for the fluid and particle phases. The cylindrical ( ) x r , ,θ coordinate system was used for the fluid motion, and the Cartesian (x, y, z) coordinate system was adopted for the particle motion. The x-axis was taken as the direction of the vertical main stream, the y-z plane was perpendicular to the x-axis. The fluid motion calculations were based on the time-averaged Navier-Stokes equations in connection the two equation multiphase k − ε turbulent model (Adeniji-Fashola and Chen, 1990) taking into account the source terms resulting from the momentum exchange with the dispersed phase. The non-dimensional elliptic differential equations governing a three-dimensional incompressible turbulent flow can be written as follows: Continuity equation ( ) 0 1 1 = + + x u w r v r r r ∂ ∂ ∂θ ∂ ∂ ∂ ; (1)