Two-layer model for non-suspension gas–solids flow in pipes

Abstract Dense-phase pneumatic conveying systems have been applied in many industrial situations. These systems offer the potential benefits of lower energy consumption and reduced particle degradation, or pipeline wear. In such systems, the particles that comprise the bulk material are transported in a non-suspension mode of flow. Many fine powders, such as cement and flour, which exhibit very low de-aeration rates, are suitable for dense-phase transport. Observation of the flow patterns, in horizontal pipes, when these powders are transported in dense phase reveals a stratified flow. A high concentration layer of fluidised material occupies the lower portion of the pipe. In the upper portion of the pipe, particles are suspended in the transport gas. The two-layer concept developed by Wilson [K.C. Wilson, A unified physically based analysis of solid–liquid pipeline flow, Proc. Hydrotransp. 4, BHRA, Paper A1 (1976) 1–16.] for a liquid–solids flow has been adapted to model dense-phase transport of powders in pneumatic conveying systems. In this new model, the flow in a horizontal pipe was modelled as two layers: a dilute gas–solids mixture flowing above a dense gas–solids mixture. For each layer, the conservation equations for mass and momentum were solved for both the gas and solids phases. In addition, mass and momentum transfers between the two layers were modelled. A parametric study was conducted to assess the influence of the boundary conditions on the overall behaviour of the model. The prediction of dense layer depth shows reasonable agreement with experimental observations. The predicted pressure gradient for fully developed flow was compared to experimental data of Mason et al. [D.J. Mason, A. Levy, P. Marjanovic, The influence of bends on the performance of pneumatic conveying systems. Adv. Powder Technol. 9 (3) (1998) 197–206.]. In general, the prediction of pressure gradient was reasonable.