An analytical approach for the closure equations of gas–solid flows with inter-particle collisions

• Published in: International journal of multiphase flow 2004-02, Vol.30 (2), p.159-180
• Main Authors: Kartushinsky, Alexander, Michaelides, Efstathios E.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fundamental areas of phenomenology (including applications); Inter-particle collisions; Multiphase and particle-laden flows; Nonhomogeneous flows; Particulate flow; Physics; Pipe flow; Pseudo-viscosity coefficients
• ISSN: 0301-9322; 1879-3533
• DOI: 10.1016/j.ijmultiphaseflow.2003.10.007

This work examines the effect of inter-particle collisions on the motion of solid particles in two-phase turbulent pipe and channel flows. Two mechanisms for the particle–particle collisions are considered, with and without friction sliding. Based on these collision mechanisms, the correlations of the various velocity components of colliding particles are obtained analytically by using an averaging procedure. This takes into account three collision coordinates, two angles and the distance between the centers of colliding particles. The various stress tensor components are obtained and then introduced in the mass, linear momentum and angular momentum equations of the dispersed phase. The current approach applies to particle–particle collisions that result from both the average velocity difference and the turbulent velocity fluctuations. In order to close the governing equations of the dispersed phase, the pseudo-viscosity coefficients are defined and determined by the time of duration of the inter-particle collision process. The model is general enough to apply to both polydisperse and monodisperse particulate systems and has been validated by comparisons with experimental data.