Simple formulae for the components of the added-mass coefficient tensor of a sphere moving near a wall with variable velocity in an ideal fluid bounded by a solid surface are derived. The added mass is calculated numerically as a function of the dimensionless distance between the sphere and the wall for both perpendicular and parallel motions. The calculation is performed by the method of successive images. The velocity field is computed as the sum of the velocity fields of sequences of dipoles located along the axis. The obtained dependences of the added-mass tensor components are fitted by simple continuous functions with high accuracy.
Abstract:The effect of solid concentration and mixture velocity on the flow behaviour, pressure drops, and concentration distribution of coarse particle-water mixtures in horizontal, vertical, and inclined smooth stainless steel pipes of inner diameter D = 100 mm was experimentally investigated. Graded basalt pebbles were used as solid particles. The study revealed that the coarse-grained particle-water mixtures in the horizontal and inclined pipes were significantly stratified. The solid particles moved principally in a layer close to the pipe invert; however for higher and moderate flow velocities, particle saltation became the dominant mode of particle conveyance. Frictional pressure drops in the horizontal pipe were found to be markedly higher than in the vertical pipe, while the frictional pressure drops in the ascending pipe increased with inclination angle up to about 30°.
LDA measurements were made of mean velocity and of turbulence intensity in a 39.4mm diameter tube, the first measurements in three directions on drag reducing surfactant solutions (0.05 % and 0.1% Habon G). Drag reduction exceeded the predictions of the Virk maximum drag reduction asymptote and elastic sublayer mean velocity profiles are steeper than the profile proposed by Virk for maximum drag reducing asymptote solutions. Axial turbulence intensities for Habon G solutions are higher than those for water near the wall, lower in most of the outer region and about the same at the center. Tangential and radial turbulence intensities are lower than those for water.
Slurry pipe transport has directed the efforts of researchers for decades, not only for the practical impact of this problem, but also for the challenges in understanding and modelling the complex phenomena involved. The increase in computer power and the diffusion of multipurpose codes based on Computational Fluid Dynamics (CFD) have opened up the opportunity to gather information on slurry pipe flows at the local level, in contrast with the traditional approaches of simplified theoretical modelling which are mainly based on a macroscopic description of the flow. This review paper discusses the potential of CFD for simulating slurry pipe flows. A comprehensive description of the modelling methods will be presented, followed by an overview of significant publications on the topic. However, the main focus will be the assessment of the potential and the challenges of the CFD approach, underlying the essential interplay between CFD simulations and experiments, discussing the main sources of uncertainty of CFD models, and evaluating existing models based on their interpretative or predictive capacity. This work aims at providing a solid ground for students, academics, and professional engineers dealing with slurry pipe transport, but it will also provide a methodological approach that goes beyond the specific application.
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