Abstract
As proven in a recently published paper [Messa GV, Matoušek V (2020) Analysis and discussion of two fluid modelling of pipe flow of fully suspended slurry. Powder Technol 30:747-768.], the beta-sigma two-fluid model is capable of accurately reproducing the main features of turbulent, fully-suspended slurry flows in horizontal pipes provided that suitable values of the two parameters beta and sigma are chosen. At present, the case-specific nature of beta and sigma and their lack of a clear physical meaning are the main obstacles that must be overcome to give the beta-sigma two-fluid model value not only as interpretative tool, but also as a predictive one. An important preliminary step to achieve this goal is to disclose the mathematical essence of the beta-sigma two-fluid model, namely, to interpret the fluid-dynamic solution on the grounds of the structure of the differential and discretized equations. Such a methodological approach is applied here to the benchmark case of turbulent slurry flow between two infinite, horizontal, parallel plates, focusing, in particular, on the influence of the bulk-mean velocity of the slurry and the volumetric concentration of the solids in the flow. The study provides not only deeper insight into the beta-sigma model, but also indicates important implications for alternative two-fluid models.
Highlights
Computational Fluid Dynamics (CFD) exhibits great potential in the application to slurry flows in pipeline systems for a number of inter-related reasons, including the relatively low cost compared to experimental testing, the growing capability of computer technology and CFD codes, the detailed information on the flow that can be obtained from a CFD simulation, and the absence of constraints on the size and the geometrical complexity of the system under investigation
The case studies considered in the present work can be interpreted as the ‘‘channel-flow’’ analogous of the fine glass-bead slurry pipe flow experiments of Matousek et al [28], in the sense that the distance between the parallel plates, H, was equal to the pipe diameter in [28] and the other features of the flow were the same
This article focuses on the numerical simulation of turbulent slurry flow between two horizontal plates in the fully-suspended regime, performed using the b-r two-fluid model described in a previous publication [1]
Summary
Computational Fluid Dynamics (CFD) exhibits great potential in the application to slurry flows in pipeline systems for a number of inter-related reasons, including the relatively low cost compared to experimental testing, the growing capability of computer technology and CFD codes, the detailed information on the flow that can be obtained from a CFD simulation, and the absence of constraints on the size and the geometrical complexity of the system under investigation. In order to achieve these goals, it is of utmost importance to understand deeply the principles of the b-r model, going beyond its function of being a tool to predict engineeringrelevant features of slurry flows This requires going back to the fundamental conservation equations, trying to understand how the interplay of their different terms affect the fluid dynamic solution provided to the user. The Eulerian-Eulerian, two-fluid approach appears to be the preferred one, because models relying on the Lagrangian tracking of the solid particle trajectories require much higher computational capacity, especially when particle-particle interactions need to be accounted for in the model This explains why the number of studies in which slurry pipe flows were simulated using Eulerian-Lagrangian models is still rather limited [2,3,4], whereas there are a lot of published literature concerning the Eulerian-Eulerian modelling of these flows.
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