The Role of Particle Shape in Pneumatic Conveying

Pneumatic conveying, in which granular materials are transported using a gas phase, is an important industrial process for bulk particulate transport. This is usually carried out in either a dilute phase, in which the particles are effectively suspended in the gas phase, or a dense phase, in which the particles move in a bulk flow. Dense phase conveying is becoming increasingly popular as it reduces collisional and abrasional forces on both the particles and the walls, reducing breakage and wear in the system. The motion of the particles is difficult to capture experimentally making computational simulation of such systems invaluable for understanding their dynamics. Previous experimental and computational studies have investigated both horizontal and vertical dense conveying and the effect of gas flow velocity and pressure on the bulk particle flow rate. It has also been found that the formation and movement of slugs of particles in a wave-like motion in the direction of the flow accounts for the majority of the bulk flow in the system. However, most simulations have modelled the particles as spheres, which is a considerable approximation as many particles in industrial applications are non-spherical. We explore the role of shape in horizontal dense phase pneumatic conveying by investigating how cubical and elliptical particles change the dynamics of the system. We compare both slug formation and the movement of slugs to the spherical case and show the bulk flow is highly sensitive to particle shape. NOMENCLATURE A⊥ particle flow projected area cls shear lift coefficient clm rotational lift coefficient cd drag coefficient C particle damping coefficient D duct equivalent diameter D rate of deformation tensor Fci particle collisional force F particle force k particle spring stiffness m particle mass p pressure q super-quadric exponent r characteristic particle radius Re particle Reynolds number T particle torque u gas velocity ur relative particle velocity v particle velocity δx particle overlap ε voidage fraction ρ gas density ρp particle density ρb bulk particle density = (1-ε)ρp μ particle friction coefficient η gas viscosity χ drag correction coefficient Φ particle sphericity Φ⊥ particle crosswise sphericity ωf fluid vorticity ωp particle spin ωr relative particle spin INTRODUCTION The rapid transportation of large volumes of granular matter is a prime concern in industry. A popular method is the use of pneumatic conveying, in which the granular matter is driven along pipes using air flow. The bulk grain motion in pneumatic conveying can occur in several regimes depending on parameters such as grain inflow rate, imposed gas flow rate, grain density and diameter (Molerus, 1996). The motion is usually classified into two phases; dilute phase, where the grains move as a suspension in the conveying gas, and dense phase, where the grains are subject to long lasting collisions and move in bulk along the pipe (Jones and Williams, 2008). Large particles with high density, categorised as type D in the Geldart scheme (Geldart, 1973), typically move as a sequence of solid plugs within the pipe. This is known as slug flow and is a dense phase flow mode. In this mode particles initially sediment in a layer over the bottom of the pipe. The particle bed then rises to fill the bore of the pipe and the pressure builds up behind this blockage, pushing a slug out from the front of the particle bed. If the pipe in front of the slug is empty then the slug collapses into a layer of particles and the sequence repeats. A steady sequence of slugs only occurs if particles have already been deposited over the length of the pipe (Tomita et al., 1981). Due to low power consumption and particle attrition (Pan and Wypych, 1997), this plug flow mode has received a large amount of attention computationally and experimentally. Experimentally, plug flow regimes can be determined from visual inspection of the flow using a transparent tube for the granular transport (Wen and Simons, 1959, Woods et al., 2008, Tomita et al., 2008). The presence of slugs can also be inferred using pressure measurements (Li et al., 2002) from a series of pressure transducers attached along the transporting pipe. Plugs have also been experimentally measured using capacitance computed tomography in which radial electrodes measure the electric field around a pipe during conveying. By measuring the capacitance between each electrode the permittivity, and hence particle concentration, can be computationally determined (Takei et al., 2004).