A HEAD LOSS MODEL FOR SLURRY TRANSPORT BASED ON ENERGY CONSIDERATIONS

摘要

In the last decades many head loss models for slurry transport have been developed. Not just for the dredging industry but also for coal and phosphate transport and in the chemical industries. Some models are based on the phenomena occurring combined with dimensionless parameters, resulting in semi-empirical equations (Durand, Condolios, Gibert, Worster, Jufin Lopatin, Zandi & Govatos, Fuhrboter), while others are based on physics with 2 and 3 layer models (Newitt, Doron, Wilson, Matousek). The physical models are based on stationary transport in time and space, while the semi-empirical models may incorporate non-stationary processes. An analysis of these models and of data collected from numerous publications for particles with densities ranging from 1.24 ton/m~3 to 3.65 ton/m~3, diameters ranging from 0.08 mm up to 22.5 mm, concentrations up to 45% and pipe diameters from 0.0254 m up to 0.9 m has led to an overall model of head losses in slurry transport. The model is based on a set of characteristic velocities determining the source of energy losses. One can distinguish viscous friction losses, dry friction losses, potential energy losses, kinetic energy losses, Magnus lift work, turbulent lift work and turbulent eddy work. The losses do not have to occur at the same time. Usually one or two will be dominant depending on the flow regime. Most well-known head loss equations for heterogeneous transport, Durand & Condolios (1952), Fuhrboter (1961), Newitt et al. (1955), Jufin & Lopatin (1966) and Wilson et al. (1992) are based on a single excess pressure term. This term is based on curve fitting, some physics or dimensionless numbers. The main question is, can the excess pressure accurately be described by just one term and if so, does this term depend on the hydraulic resistance of the carrier fluid or is it independent. The model as derived here is based on the assumption that the excess pressure is the result of energy losses. These energy losses are identified as potential energy losses and kinetic energy losses. One could distinguish more types of energy losses and maybe come with a more accurate equation, but the current approach already gives a good correlation with the data of many researchers. The potential energy losses are dominated by the terminal settling velocity of the particles, including hindered settling. The kinetic energy losses are dominated by the ratio between the slip velocity of the particles and the terminal settling velocity of the particles (without hindered settling). The slip velocity cannot be derived fundamentally (yet), but is approximated by a function with the dimension of velocity. The final result is an equation with 3 independent terms. The viscous friction losses according to Darcy Weisbach, using the Moody diagram for the friction coefficient, the potential energy losses, using an approach similar to Newitt et al. (1955) and the kinetic energy losses as has been derived here. The paper describes the overall model and a verification of the different regimes is given based on data from the literature. The overall model correlates very well with the data measured.