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  • Author: Pavel Vlasak x
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In numerical models of fluid flow with particles moving close to solid boundaries, the Basset force is usually calculated for the particle motion between particle-boundary collisions. The present study shows that the history force must also be taken into account regarding particle collisions with boundaries or with other particles. For saltation - the main mode of bed load transport - it is shown using calculations that two parts of the history force due to both particle motion in the fluid and to particle-bed collisions are comparable and substantially compensate one another. The calculations and comparison of the Basset force with other forces acting on a sand particle saltating in water flow are carried out for the different values of the transport stage. The conditions under which the Basset force can be neglected in numerical models of saltation are studied.

Drag reduction of dense fine-grained slurries

Attractive and repulsive forces acting in the slurry due to different ions absorbed on surface of fine particles, especially colloidal ones, strongly affect the flow behaviour of highly concentrated fine-grained slurries. The attractive forces between the fine-grained solid particles initiate the coagulation process, which gives rise to voluminous aggregates where a large amount of water is fixed. A modification of the physical-chemical environment of the slurry by addition of a peptizing agent produces repulsive forces between particles. They result in destruction of the aggregates, water originally fixed in the aggregates is liberated, the viscous friction can play a larger role in the slurry, which is liquefied. To prove these process three different kaolin-water mixtures were tested with an overpressure capillary viscometer, rotational viscometer, and experimental pipeline loop. The effect of two peptizing agents and their concentration was investigated. It was demonstrated that even very low concentration of peptizing agent results in a significant reduction in the apparent viscosity and in the yield stress.

Flow Structure of Coarse-Grained Slurry in A Horizontal Pipe

The flow behaviour of coarse-grained slurry depends on particle size, shape, density and concentration, and on the density and rheological properties of the carrier liquid. The present paper describes the results of an experimental investigation and flow visualisation of model coarse-grained particle-water mixtures in a closed pipe loop with smooth stainless steel pipes of inner diameter 36 mm. Glass balls and washed graded pebble gravel of mean diameter d50= 6 mm were used as model coarse-grained material. The effect of slurry velocity and particle concentration on the slurry flow behaviour and pressure drop in the turbulent regime was evaluated. Particle distribution in the pipe cross-section and motion of particles along the pipe invert, particle saltation and particle conveying in the carrier liquid were investigated in a transparent pipe viewing section and motion of individual particles was described. Velocity profiles of the carrier liquid and conveyed particles were determined.

3D Numerical Model of the Spherical Particle Saltation in a Channel with a Rough Fixed Bed

The paper describes a 3D numerical model of the spherical particle saltation. Two stages of particle saltation were distinguished — the particle free motion in water and the particle-bed collision. The particle motion consists of the translational and rotational particle motion. A stochastic method of calculation of the particle-bed collision was developed. The collision height and the contact point were defined as random variables. Impulse equations were used and the translational and angular velocity components of the moving particle immediately after the collision were expressed as functions of the velocity components just before the collision. The dimensionless coefficients of the drag force and drag torque were determined as functions of both translational and rotational Reynolds numbers. The model is in good agreement with known experimental data. Examples of calculation of the particles' lateral dispersion and the mean absolute values of the deviation angle of the particle trajectory are presented.


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°.


Sand-water slurry was investigated on an experimental pipe loop of inner diameter D = 100 mm with the horizontal, inclined, and vertical smooth pipe sections. A narrow particle size distribution silica sand of mean diameter 0.87 mm was used. The experimental investigation focused on the effects of pipe inclination, overall slurry concentration, and mean velocity on concentration distribution and deposition limit velocity. The measured concentration profiles showed different degrees of stratification for the positive and negative pipe inclinations. The degree of stratification depended on the pipe inclination and on overall slurry concentration and velocity. The ascending flow was less stratified than the corresponding descending flow, the difference increasing from horizontal flow up to an inclination angle of about +30°. The deposition limit velocity was sensitive to the pipe inclination, reaching higher values in the ascending than in the horizontal pipe. The maximum deposition limit value was reached for an inclination angle of about +25°, and the limit remained practically constant in value, about 1.25 times higher than that in the horizontal pipe. Conversely, in the descending pipe, the deposition limit decreased significantly with the negative slopes and tended to be zero for an inclination angle of about −30°, where no stationary bed was observed.

Numerical model of spherical particle saltation in a channel with a transversely tilted rough bed

This paper deals with the numerical simulation of spherical particle saltation in a channel with a rough transversely tilted bed. The numerical model presented is based on the 3D model of spherical particle saltation developed by the authors, which takes into account the translational and rotational particle motion. The stochastic method and the concept of a contact zone were used for the calculation of a particle trajectory and its dependence on the bed lateral slope, particle diameter, and shear velocity. The effect of the bed lateral slope results in a deviation of the particle trajectory from the downstream direction. Some examples of the calculation are presented. The trajectories of the saltating particles starting their movements from one point were calculated and it was shown that they are of random character and together create a bundle or fascicle of trajectories. It was found that the centrelines of the bundles can be approximated by the straight lines for low and moderate values of the bed transverse slope, i.e. slopes less than 20°. The angle of deviation of the centreline from the downstream direction increases when the bed lateral slope and/or the particle diameters increase. However, with increasing shear velocity, the deviation angle decreases. Due to the lateral bed slope the particles are sorted according to their size, and the criteria for sorting particles were defined. An example of the particle sorting was calculated and the separable and non-separable regions were determined.


Narrow particle size distribution basalt pebbles of mean particle size 11.5 mm conveyed by water in the pipe sections of different inclination were investigated on an experimental pipe loop, consisting of smooth stainless steel pipes of inner diameter D = 100 mm. Mixture flow-behaviour and particles motion along the pipe invert were studied in a pipe viewing section, the concentration distribution in pipe cross-section was studied with the application of a gamma-ray densitometer. The study refers to the effect of mixture velocity, overall concentration, and angle of pipe inclination on chord-averaged concentration profiles and local concentration maps, and flow behaviour of the coarse particle-water mixtures. The study revealed that the coarse particle-water mixtures in the inclined pipe sections were significantly stratified, the solid particles moved principally close to the pipe invert, and for higher and moderate flow velocities particle saltation becomes the dominant mode of particle conveying.


A three-dimensional numerical simulation of particle motion in a pipe with a rough bed is presented. The simulation based on the Lattice Boltzmann Method (LBM) employs the hybrid diffuse bounce-back approach to model moving boundaries. The bed of the pipe is formed by stationary spherical particles of the same size as the moving particles. Particle movements are induced by gravitational and hydrodynamic forces. To evaluate the hydrodynamic forces, the Momentum Exchange Algorithm is used. The LBM unified computational frame makes it possible to simulate both the particle motion and the fluid flow and to study mutual interactions of the carrier liquid flow and particles and the particle–bed and particle–particle collisions. The trajectories of simulated and experimental particles are compared. The Particle Tracking method is used to track particle motion. The correctness of the applied approach is assessed.


For the safe and economical design and operation of freight pipelines it is necessary to know slurry flow behaviour in inclined pipe sections, which often form significant part of pipelines transporting solids. Fine-grained settling slurry was investigated on an experimental pipe loop of inner diameter D = 100 mm with the horizontal and inclined pipe sections for pipe slopes ranging from −45° to +45°. The slurry consisted of water and glass beads with a narrow particle size distribution and mean diameter d50 = 180 µm. The effect of pipe inclination, mean transport volumetric concentration, and slurry velocity on flow behaviour, pressure drops, deposition limit velocity, and concentration distribution was studied. The study revealed a stratified flow pattern of the studied slurry in inclined pipe sections. Frictional pressure drops in the ascending pipe were higher than that in the descending pipe, the difference decreased with increasing velocity and inclination. For inclination less than about 25° the effect of pipe inclinations on deposition limit velocity and local concentration distribution was not significant. For descending pipe section with inclinations over −25° no bed deposit was observed.