The other method involves the use of Eulerian/ Lagrangian method in which the particles are treated individually or as a group tracked by the Lagrangian frame of reference. Cundall and Starck developed the discrete element method in 1979 and has been widely used for the study of parcticles in the solid state. Studies conducted using DEM coupled with CFD showed that particles move in plugs along the conveying pipes.
According to Kuang et al (2008), one of the most important technologies in the industry is dense phase pneumatic transportation of bulk material in the slug form. In his research paper, Kuang et al (2008) focuses on the numerical study of the slug flow in horizontal pneumatic conveyor by means of discrete particle simulation. Low velocity and dense gas system are common in industries such as mineral processing, agricultural industries and chemical industries. Slug flow is used in the industry to transport materials from one location to another. The slug flow is particularly considered in industries because of its ability to reduce the degradation of plant and also reduce wear. The power utilization of the system is also superior as compared to other flows. The study and simulation of the slug flow therefore brings into light the nature of flow with the aim of understanding the system and improving it.
According to the research done by Kuang (2008), the particles used were spherical in shape, made of polythene material with a diameter (dp) of the particle density (pp) was 922 Kgm-3.air was used for the gas phase. The viscosity was taken to be and a density of .The underlying equations for particle flow were the rotational and translation motion determined by the Newton's laws of motion given as;
Where mi is the mass, Ii is the momentum or rotation inertia, is the rotational velocity while is the translational velocity of the particles (Kuang et al, 2008). For the gas phase, the gas flow was considered as a continuous phase and the governing equations are as shown below.
The coupling method used in Kuang (2008) simulations was both DEM and CFD. At an individual particle scale, modeling of the flow was done using DEM while the gas flow modeling was done using CFD. At each step, DEM gave information of the velocity and position of the particles. The data given by DEM was used by CFD to determine the gas flow field; this then yielded the particle fluid forces acting on individual particles. The resulting forces were then incorporated into DEM to yield the next time phase. The simulation test lasted for 15 seconds, numerical flow during the first 2 seconds was not considered in the analysis as only the macroscopically stable slug flow was considered during the simulation. Property mapping due to the many particles that reside in a given cell was done; the mapping technique was used to aid in the correct calculation of particle fluid force acting on the particle. The least square interpolation was used. Based on this interpolation the particle position was given by;
Where is the gas properties at the cell center and Is the particle position at the cell center. is The vector denoting the distance from the cell center