A common way to transport solids in large quantities is by using a carrier fluid to transport the solids as a concentrated solid/liquid mixture or slurry through a pipeline. Typical examples are found in dredging, mining and drilling applications. Dependent on the slurry properties and flow conditions, horizontal slurry pipe flow is either in the fixed-bed, sliding-bed or fully-suspended regime. In terms of non-dimensional numbers, the flow is fully characterized by the bulk liquid Reynolds number (Re), the Galileo number (Ga, a measure for the tendency of particles to settle under gravity), the solid bulk concentration (ϕ_b), the particle/fluid density ratio (ρ_p/ρ_f), the particle/pipe diameter ratio (D_p/D_pipe), and parameters related to direct particle interactions such as the Coulomb coefficient of sliding friction (μ_c). To further our fundamental understanding of the flow dynamics, we performed experiments and interface-resolved Direct Numerical Simulations (DNS) of slurry flow in a horizontal pipe. The experiments were performed in a transparent flow loop with D_pipe=4 cm. We measured the pressure drop along the pipeline, the spatial solid concentration distribution in the cross-flow plane through Electrical Resistance Tomography (ERT), and used a high-speed camera for flow visualization. The slurry consisted of polystyrene beads in water with D_p=2mm, ρ_p/ρ_f=1.02, Ga between 40–45 and ϕ_b between 0.26–0.33. The different flow regimes were studied by varying the flow rate, with Re varying from 3272 till 13830. The simulations were performed for the same flow parameters as in the experiments. Taking the experimental uncertainty into account, the results from the DNS and the experiments are in reasonably good agreement. The results for the pressure drop agree also fairly well with popular empirical models from literature. In addition, we performed a parametric DNS study in which we solely varied Re and Ga. In all flow regimes, a secondary flow of Prandtl's second kind is present, ascribed to the presence of internal flow corners and a ridge of densely packed particles at the pipe bottom during transition towards the fully-suspended regime. In the bulk of the turbulent flow above the bed, secondary flow transport of streamwise momentum dominates over turbulent diffusion in regions where the secondary flow is strong and vice versa where it is weak. The transition between flow regimes appears to be governed by the competition between the net gravity force on the particles and shear-induced particle migration from particle–particle interactions. This competition can be expressed by the Shields number, θ. For θ≲0.75, gravity is dominant and the flow is in the fixed-bed regime. For θ≳0.75, shear-induced migration becomes progressively more important for increasing θ. Low-concentration zones flanking the sliding bed start to form at the top corners of the bed, and gradually expand downwards along the pipe wall till the pipe bottom is reached. For θ≳1.5, shear-induced migration is responsible for lifting the particle bed away from the wall, associated with the onset of the suspended regime. For θ≫1, gravity is of minor importance and the mean flow eventually reaches axi-symmetry with a high-concentration particle core at the pipe center and negligible secondary flow.

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Path instabilities of a sphere rising or falling in a quiescent Newtonian fluid have been studied experimentally. The rich palette of possible instabilities is dependent upon two dimensionless quantities, namely the Galileo number (Ga) and the particle/fluid mass density ratio (ρ¯). In recent literature, several (Ga,ρ¯) regime maps have been proposed to characterize path instabilities, based on both numerical and experimental studies, with substantial disagreements among them. The present study attempts to shed light on path instabilities for which previous studies disagree. A detailed experimental investigation has been conducted for 219 different combinations of Ga and ρ¯, grouped around four values of ρ¯ (∼ 0.87, 1.12, 3.19 and 3.9) and Ga in the range of ∼ 100 to 700. Our results agree well with literature for the low Ga range in which a particle takes a steady vertical or steady oblique path and for which all previous studies agree with each other. For the higher and more controversial Ga range, we discuss consensus and disagreements with previous studies. Some regimes, which were only recently observed in numerical simulations, have been observed experimentally for the first time. Also, intriguing bi-stable regimes (i.e., coexistence of two stable asymptotic states) have been observed. For all four investigated density ratios, an update of the regime map is proposed. Finally, for both the rising and falling spheres, the drag coefficient as function of terminal settling Reynolds number has been determined, which for the investigated density ratios does not differ significantly from that of flow past a fixed sphere.

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Natural particles are frequently applied in drinking water treatment processes in fixed bed reactors, fluidised bed reactors, and sedimentation processes to clarify water and to concentrate solids. When particles settle, it has been found that, in terms of hydraulics, natural particles behave differently when compared to perfectly round spheres. To estimate the terminal settling velocity of single solid particles in a liquid system, a comprehensive collection of equations is available. For perfectly round spheres, the settling velocity can be calculated quite accurately. However, for naturally polydisperse non-spherical particles, experimentally measured settling velocities of individual particles show considerable spread from the calculated average values.

This work aims to analyse and explain the different causes of this spread. To this end, terminal settling experiments were conducted in a quiescent fluid with particles varying in density, size, and shape. For the settling experiments, opaque and transparent spherical polydisperse and monodisperse glass beads were selected. In this study, we also examined drinking-water-related particles, like calcite pellets and crushed calcite seeding material grains, which are both applied in drinking water softening. Polydisperse calcite pellets were sieved and separated to acquire more uniformly dispersed samples. In addition, a wide variety of grains with different densities, sizes, and shapes were investigated for their terminal settling velocity and behaviour. The derived drag coefficient was compared with well-known models such as the one of Brown and Lawler (2003).

A sensitivity analysis showed that the spread is caused, to a lesser extent, by variations in fluid properties, measurement errors, and wall effects. Natural variations in specific particle density, path trajectory instabilities, and distinctive multi-particle settling behaviour caused a slightly larger degree of the spread. In contrast, a greater spread is caused by variations in particle size, shape, and orientation.

In terms of robust process designs and adequate process optimisation for fluidisation and sedimentation of natural granules, it is therefore crucial to take into consideration the influence of the natural variations in the settling velocity when using predictive models of round spheres.@en