Numerical Simulation of Granular Particles Moving in Fluid Flow

A coupled method between discontinuum and continuum approaches has been developed to simulate granular particles moving in a flowing fluid. The movement of granular particles is modeled using the discrete element method, while the finite volume scheme is used to simulate the fluid flow. The existence of granules in the flow region is assumed to cause a reduction in the amount of fluid flow in that region. The flowing fluid is expected to induce drag forces on the granules which are computed based on the relative velocities between the fluid and the particles. Buoyant forces on a particle are equal to the weight of the fluid displaced by the particle. All forces acting on each individual particle are summed in determining the particle movement. An example is given to illustrate the possibility of the proposed method in simulating granular particles moving in a flowing fluid. The problem of modeling wet granular flow requires the solution of two major physical problems; granular material as discontinua and fluid as continua. The discrete element method or DEM, proposed by Cundall and Strack, conceives granular materials as the assemblage of distinct rigid particles. Particles can interact with each other or with a solid boundary only at contact points. By using the contact force-displacement law, the forces at the contact are related to the magnitude of the overlap between particles or between particle and a solid boundary. The displacements and velocities of each individual particle are calculated from the summation of all forces acting on the particle using Newton's Second Law of Motion. The movement histories of individual particles at each time-step are traced based on the force-displacement law and the Newton's Law. Various particle shapes can be used such as polygonal, elliptical, circular shape, etc. The circular shape is selected in this paper due to its simplicity. For the fluid computational part, fluid flow is modeled using a finite volume scheme. The flow field is divided into a finite number of subregions, called cell. The continuity and Navier-Stokes equations are both applied at each cell in the flow field. To couple the movement of particulate material into fluid flow, fluid/particle interactions must be taken into account. Cundall classified five types of fluid/particle interactions depending upon the situations. Babic' and Shen as well as Sun and Vinogradov considered drag forces as the interaction of fluid flow to solid particles. Chan simulated the wet granular flow by considering buoyant and drag forces as the interaction of fluid flow to particles; on the other hand, the interaction of particle to the fluid flow is represented by using the different permeability to control the flow volume. In this paper, drag and buoyant forces are included in the fluid/particle interaction. For interaction between granular particle and the flowing fluid, the existence of the solid particles will cause resistance to the flowing fluid, In essence, the discrete element method is used to track the particles movement and the location of the particles is taken into account in the continuum calculation of fluid flow by introducing local impedance. The continuum method obtains the position of granular particles, computes the flow velocity and pressure, and imposes a drag force on each particle for the DEM calculation.

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