Self-cleansing velocity in upward three-phase steady pipe-flow

Abstract

The solids transport and the conditions required to begin the transport of granular particles, or to avoid their deposition, in three-phase turbulent flows of mixtures of gas–liquid–solids, in upward inclined pipes, are complex phenomena whose governing equations and corresponding solutions can be approximated via experimental investigation and numerical computation. An experimental installation for establishing steady flow conditions of air–water-solids in an upward transparent acrylic pipe of 84 mm was built and prepared to allow the measurement of the transported flow rates of air, water, sand and fine gravel, with particle diameters between 0.425 and 7.20 mm. Two full set of experiments with water-solids, and air–water-solids, under comparable conditions, were performed in Laboratory, in order to analyse the influence of the gas phase. Three pipe angles between 30° and 58°, and four solid particle ranges with intermediate sizes forming a bed were tested. The average water superficial velocity demonstrates to be the most relevant variable for the solids transport beginning, and the presence of air has a positive influence, even without the mobilisation of the water flow rate increase due to air-lift pumping. A model relating a modified Shields parameter (Shmixc) with a modified Reynolds number of the particles (Remixc), both defined for the critical average flow rates of three-phase mixtures under steady flow, for which a residual mass of solid particles begins to be transported, is proposed. The resulting equation follows a power law of the generic type Shmixc = a Remixc−b, where a and b are positive constants experimentally obtained for the different angles of inclination of the upward pipe, with coefficients of determination well above 90%. The mathematical model proposed in this work allows the explicit computation of the self-cleansing velocity required for two-phase flows. The critical average air superficial velocity and subsequent average velocity of the mixture required for the solids transport in steady three-phase flows, when the average water superficial velocity is below the two-phase self-cleansing velocity, are computed using the proposed model by numerical iterative processes.