International Scientific Journal

Authors of this Paper

External Links


In this paper the three-dimensional model of gas-particle mixture turbulent flow in horizontal tubes and channels, as well as in complex pipes with bends was developed, in order to make a tool for analyzing processes in pneumatic conveying systems. Gas turbulence was modelled using k-ε model of turbulence. In getting the numerical solution for the gas phase a finite volume discretization scheme was used. Iterative procedure was based on SIMPLE algorithm. Numerical code CAST for single phase flow with colocated grid represented the basis for it. The presence of dispersed phase and its influence on gas phase was modelled by adding one additional source term in the equations of the gas phase (PSI-CELL method). Dispersed phase was treated by the Lagrangian approach. For particle motion LSD model was used [13]. The concept of parcel, the computational particle which represents the ensemble of real particles with the same performances was adopted. Particles were treated as ideal spheres. Beside the drag and the gravitational forces, the lift forces due to the particle rotation and the gradient of the gas velocity field were included in calculation. Special attention was devoted to the models of particle collision with the rough wall and mutual collisions of particles. On this way the use of the model on flows in which the particle-gas mass ratio is high was enabled. The stochastical approach was adopted, by which all the parameters with the stochastic nature in reality retain it in the model also. The modelling of roughness was performed by changing the wall surface with the 'virtual plane', whose position is detemined with the angle of inclination around horizontal axes (modelling of roughness height), and the angle of rotation around vertical axes (modelling of orientation of roughness in space). The first one was obeyed to the normal, and the second one to the uniform distribution. In the model of collisions between the particles the collision probability was calculated, and on this basis it was stochastically determined whether the collision of the particular particle with some other would happen or not. The calculation were made for particles of the mean diameter in the range 40-500 μm and for the particle-gas mass ratio 0-5. For the whole ensemble of particles in the flow: field the log-normal distribution of their diameters was adopted. The results of calculation were compared with the experimental results available in literature. For the profiles of gas velocity and pressure drop excellent agreement was achieved. The agreement of the concentration profiles of the dispersed phase was good, except for the regions of high particle concentration near the wall.
PAPER REVISED: 1998-06-29
PAPER ACCEPTED: 1999-02-02
CITATION EXPORT: view in browser or download as text file
  1. Patankar, S. V., Nunerical Heat Transfer and Fluid Flow, Hemisphere publ. Co., New York, 1980
  2. Hinze, J.O., Turbulence, 2nd Edition, Mc-Graw-Hill, New York, 1975
  3. Launder, B.E., Spalding, D.B., The Numerical Computation of Turbulent Flows, Computer Methods in Applied Mechanics and Engineering, 3, pp. 269-289, 1974
  4. Lee,S.L., Durst, F.,On the Motion of Particles in Turbulent Duct Flows, Int. J. Multiphase Flow, 8, (1982), 125-146
  5. Crowe, C. T., Sharma, M. P., Stock,D. E., The Particle-Source-in-Cell (PSI-CELL) Model for Gas-Droplet Flows, Journal of Fluids Engineering, June 1977
  6. Sommerfeld, M., Expansion of a Gas-Particle Mixture in a Supersonic Free Jet Flow, Z. für Flugwiss. und Weltraumforschung, /1 (1987), pp. 87-96
  7. Durst, F., Raszillier, H., Analysis of Particle-Wall Interaction, Chemical Engineering Science, 4 (1989), 12, pp. 2872-2879
  8. Durst, F., Milojević, D., Schonung, B., Eulerian and Lagrangian Predictions of Particulate Two-Phase Flows: a Numerical study, Applied Mathematical Modelling, 8, pp. 101-115, April, 1984
  9. Frank, T., Petrak, D., Computersimulation der feststoffbeladenen Gasströmung im horizontalen Kanal mit Hilfe des Lagrange-Modells unter Berücksichtigung von Wandrauhigkeiten, Institut für Mechanik der AdW der DDR Karl-Marx-Stadt
  10. Tsuji, Y., Shen, N. J., Morikawa, Y., Numerical Simulation of Gas-Solid Flows. I - Particle-to-Wall Collision, Technology Reports of the Osaka University, 39, No.197S, pp. 233-241, October 1989, Osaka, Japan
  11. Tsuji, Y., Shen, N. J., Morikawa, Y., Numerical Simulation of Gas-Solid Flows. I - Calculation of a Two-Dimensional Horizontal Channel Flow, Technology Reports of the Osaka University, 39, No.1976, pp. 243-254, October 1989, Osaka, Japan
  12. Matsumoto, S., Saito, S., Monte Carlo Simulation of Horizontal Pneumatic Conveying Based on the Rough Wall Model, Journal of Chemical Engineering of Japan,3 (1970), 2, pp. 223-230
  13. Milojević, D., Lagrangian Stochastic-Deterministic (LSD) Predictions of Particle Dispersion in Turbulence, Part. Part Syst. Charact., 7, pp. 181-190, 1990
  14. Oesterle, B., Petitjean, A., Simulation of Particle-to-Particle Interactions in Gas-Solid Flows, Int. J.Multiphase Flow, 19 (1993), 1, pp. 199-211
  15. Rubinow, S. I, J. Keller, B., The Transverse Force on a Spining Sphere Moving in a Viscous Fluid, Journal of Fluid Mechanics, 11(1961), pp. 447-459
  16. Saffman, P. G., The Lift on a Small Sphere in a Shear Flow, Journal of Fluid Mechanics, 22 (1965), Part 2, pp. 385-400
  17. Patankar, S.V., Spalding, D. B., A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flow, Int. Journal of Heat and Mass Transfer, 15 (1972), pp. 1787-1806
  18. Crowe, C. T., On the Relative Importance of Particle-Particle Collisions in Gas-Particle Flows, IMechE, C78, pp. 135-137, 1981
  19. Rowe, V. M., Some Secondary Flow Problems in Fluid Dynamics, Ph.D. thesis, Cambridge University, 1966.
  20. Ahmad, K., Goulas, A., A Numerical Study of the Motion of a Single Particle in a Duct Flow, Fifth International Conference on the Pneumatic Transport of Solids in Pipes, April 16-18, London 1980
  21. Ito, H., Friction Factors for Turbulent Flow in Curved Pipes, Trans. ASME, J. Basic Engineering, 82 (1959), pp. 123-132
  22. Sommerfeld, M., Živković, G., Recent Advances in the Numerical Simulation of Pneumatic Conveying Through Pipe Systems, Computational Methods in Applied Sciences, 1992, pp. 201-212
  23. Huber, N., Sommerfeld, M., Digital Image of Laser Sheet Visualizations; an Effective Method to Characterize the Nonuniformity of Two-Phase Flows, ICHMT Seminar on Imaging in Transport Processes, May 25-29, 1992, Athens
  24. Sommerfeld, M., Živković, G., Huber, N., Optimization of Pneumatic Conveying of Coal Dust in Pipe Systems with the Regard to an Efficient Combustion with Low Pollution, Technical Report about the Progress of the Investigations on Gas Solid Pipe Flows, Project No. 7220-Ed/105, 1991, Erlangen

© 2023 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence