Scaling relationships for rotating drums

Rotating drums are extensively used in the chemical and process industries as kilns, mixers, dryers and reactors. Despite challenges from the development of newer and more specialised technologies such as fluidised beds, rotating drums continue to find applications. This is mainly due to their ability to handle varying feed stocks, in particular granular materials with broad particle size distribution and significant difference in physical properties. However, the scale-up methodology for such devices is still largely empirical and no general and systematic method has been established. This work is therefore devoted to the development of a set of scaling relationships which can be used to properly design rotating drums. The scaling relationships are obtained by non-dimensionalising the differential equations governing the behaviour of solids motion in rotating drums. The derived dimensionless groups include Froude number, pseudo-Reynolds number. pseudo-Euler number. drum geometric ratios, drum inclination, drum fill percentage, size distribution of particles, and physical properties: of the particles and drum wall such as restitution coefficient and elasticity modulus. At relatively low pseudo-Reynolds numbers, the effect of velocity fluctuation and hence the granular temperature can be neglected, the granular flows are thus in the quasi-static regime. At relatively low pseudo-Euler numbers, the effect of the frictional contribution to the total stress tenser is negligible and the flow is in the rapid granular flow regime. The upper limit of the quasi-static regime is evaluated and the adequacy of the application of granular flow kinetic theory to rotating drums is discussed. It is shown that granular Rows in large drums operated at low to medium rotational speeds are often in the quasi-static regime, whereas those in small drums operated at medium rotational speeds may be in the transition flow regime. Preliminary experiments have been carried out with the aim of reducing the total number of controlling dimensionless groups. The dimensionless groups investigated include the drum length-to-diameter ratio, rotational Froude number, fill percentage, particle-to-drum diameter ratio. particle restitution coefficient, and the relative drum wall roughness. It is shown that the Froude number, particle-to-drum diameter ratio, drum fill percentage, and particle restitution coefficient can be combined to give a single dimensionless parameter if drums are operated in a rolling mode and the Froude number is greater than 0.003. (C) 2001 Elsevier Science Ltd. All rights reserved.