Characteristics of slurry transport regimes: Insights from experiments and interface-resolved Direct Numerical Simulations

Abstract

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 (${\varphi }_b$), the particle/fluid density ratio (${\rho }_p/{\rho }_f$), the particle/pipe diameter ratio ($D_p/D_{pipe}$), and parameters related to direct particle interactions such as the Coulomb coefficient of sliding friction (${\mu }_c$). 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 $D_p=2\mathrm{mm}$, ${\rho }_p/{\rho }_f=1.02$, $Ga$ between 40–45 and ${\varphi }_b$ 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, $\theta$. For $\theta \lesssim 0.75$, gravity is dominant and the flow is in the fixed-bed regime. For $\theta \gtrsim 0.75$, shear-induced migration becomes progressively more important for increasing $\theta$. 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 $\theta \gtrsim 1.5$, shear-induced migration is responsible for lifting the particle bed away from the wall, associated with the onset of the suspended regime. For $\theta \gg 1$, 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.