Zdenek Chara

2D Numerical model of particle–bed collision in fluid-particle flows over bed

This paper deals with bed load transport and the movement of rotating spherical particles in an open channel flow is considered. A numerical model for the random process of the particle impact and rebound from the channel bed is developed. Stochastic methods of collision height and collision angle calculation are proposed. The velocity components of particle translational and angular movement of the particle immediately after collision are expressed as function of the particle translational and angular velocity components immediately before collision for two patterns of saltation process: impact with slip and impact without slip. The condition for the collision without slip is determined. Numerical simulation of particle saltation using this model of particle–bed collision is performed. It is shown that this model allows describing double collisions of the particle with a rough bed and that the mechanism of particle–rough bed collision supports sufficiently bed load transport in the form of saltation. In the case of smooth bed the particle jumps are quickly extinguished and after a few jumps the particle slides and rolls along smooth bed without jumps

Effect of Particle Size Distribution and Concentration on Flow Behavior of Dense Slurries

The flow behavior of concentrated slurry depends on particle size distribution, shape, density, and concentration. The slurry flow behavior can change from Newtonian to non-Newtonian depending on the concentration, slurry composition, and content of fine and especially colloidal particles, which evoke a complex rheological behavior of the slurry. The present article deals with experimental investigation of the flow behavior and pressure drop of dense complex slurries containing sand of different particle size distribution (five different monodispersed and polydispersed sands with mean diameters ranging from 0.20 to 1.40 mm), stony dust (mean diameters of 8 μm and 33 μm), or clay conveyed in water. The slurries were tested using experimental pipeline loops with inner diameters of 17.5 and 26.8 mm. The slurry concentrations range from 6% to 40% for sand slurries, from 26% to 48% for stony dust slurries, and from 45% to 51% for stony dust-sand slurries. The study revealed the time-independent yield pseudo-plastic behavior of the concentrated fine-grained stony dust slurries and the possibility of reducing their flow resistance by adding coarse-grained material. The flow behavior of the stony dust slurries can be approximated by the Herschel-Bulkley or the Bingham model in the laminar region and by the Wilson model in the turbulent region.

Flow Structure of Coarse-Grained Slurry in A Horizontal Pipe

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. Struktura Proudu Hrubozrnné Suspenze v Horizontálním Potrubí Tokové chování hrubozrnných suspenzí závisí na velikosti, tvaru a hustotě částic, koncentraci pevné fáze a hustotě a reologických vlastnostech nosné kapaliny. Článek popisuje výsledky experimentálního výzkumu a vizualizace proudění modelové hrubozrnné suspenze v experimentální potrubní lince s hladkým nerezovým potrubím s vnitřním průměrem 36 mm. Skleněné kuličky a praný oblý štěrk (kačírek) se středním zrnem d50 = 6 mm byly použity jako modelový materiál. Byl vyhodnocen vliv rychlosti proudění suspenze a koncentrace pevné fáze na chování a tlakové ztráty suspenze. Rozdělení částic v příčném průřezu potrubí a pohyb částic podél dna potrubí, jejich saltace a unášení v nosné kapalině byly zkoumány v transparentní části potrubí a byl popsán pohyb jednotlivých částic a pro vybrané případy byly stanoveny rychlostní profily nosné kapaliny a unášených částic.

Drag reduction of dense fine-grained slurries

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. Snižování tření zahušťěných jemnozrnných suspenzí Přitažlivé a odpudivé síly působící mezi částicemi v suspenzi v důsledku různých iontů absorbovaných povrchem jemných, zejména koloidních částic, silně ovlivňují tokové chování vysoce koncentrovaných jemnozrnných suspenzí. Přitažlivé síly mezi jemnými částicemi iniciují proces koagulace, umožňují vznik objemných agregátů, v nichž je vázáno značné množství vody. Změna fyzikálně-chemického prostředí suspenze přidáním peptizačního činidla podpoří vznik odpudivých sil mezi částicemi, které způsobí rozbití objemných agregátů a voda vázaná v agregátech se uvolní, vazké tření tak bude hrát v suspenzi významnější roli a dojde k ztekucení suspenze. Tento proces byl ověřen experimentálním výzkumem třech různých kaolinových suspenzí jednak na kapilárním přetlakovém viskozimetru, na rotačním viskozimetru a na experimentální potrubní trase. Byl ověřen účinek dvou peptizačních činidel a bylo ukázáno, že velmi nízká koncentrace peptizačního činidla vede k významné redukci zdánlivé viskozity a počátečního napětí.

Laminar and turbulent flow experiments with yield-power law slurries

Abstract Pipeline transport has been one of the progressive technologies for conveying a large quantity of bulk materials. The modern way of pipelining prefers the dense slurries, which can be in some cases directly processed without dewatering. The hydraulic transport of dense hydromixtures can bring several advantages. Compared to a mechanical transport, it is dust free, it demands substantially less space, makes possible full automatization and needs a minimum of operating staff. On the other hand, it brings higher operational pressures and considerable demands for a high quality of pumping equipment and control system. For the proper design of economical and operate safe pipelining, a good knowledge of the flow behaviour of highly concentrated slurries is necessary. The flow behaviour of highly concentrated fine-grained hydromixtures can be approximated by rheological models for laminar flow regime. These models seem to be suitable for slurry containing clay, kaolin, coal, ash, ash-gypsum, tailings, metallic ores and similar materials. The rheological parameters — yield stress τy, fluid consistency K and flow behaviour index n — have to be determined experimentally. The flow behaviour of dense fine-grained slurries was experimentally investigated on tube viscometer with three different pipe diameters varying from D=10.5 to 26.8 mm, for the kaolin and ash-gypsum slurry. For the turbulent regime, two models based on above mentioned rheological parameters [P. Slatter, in: Proc. 8th Conf. Transport and Sedimentation of Solid Particles, Prague, Czech Republic, 1995, p. A3; A.D. Thomas, K.C. Wilson, Can. J. Chem. Eng. 65 (1987) 335.] were analyzed.

Fully Stratified Particle-Laden Flow in Horizontal Circular Pipe

This article describes the results of an experimental measurement and visualization of coarse-grained fully stratified particle-water mixtures. This article focuses on the study of the carrier liquid velocity field and behavior and local velocities of conveyed particles. Glass balls and graded pebble gravel of 6 mm mean diameter were conveyed by water in a horizontal smooth pipe loop with a transparent pipe viewing section of inner diameter 40 mm. The measurements were performed in the smooth pipe and the pipe with rough stationary bed created by two layers of spherical particles of the same mean diameter as the conveyed particles. Particle movement along the pipe bottom was studied and the effect of the stationary bed on local velocity values of the carrier liquid and conveyed particles were evaluated. It was concluded that in the flow with stationary bed the maximum liquid velocity is markedly shifted from the pipe center to its top. The coarse-grained particles moved principally in a layer close to the pipe invert, for higher flow velocities particle saltation becomes the dominant mode of transport.

Drag Force, Drag Torque, and Magnus Force Coefficients of Rotating Spherical Particle Moving in Fluid

The mutual influence of translational and rotational spherical particle movements in calm water was studied using experimental data and numerical simulation. Spherical balls with a density close to that of water were speeded up in special devices, which ensured the required ball rotational and translational velocity in the given plane. A video system was used to record the ball trajectory in water. The values of the drag force, Magnus force, and drag torque coefficients were determined experimentally and compared with the results of the numerical simulation of the particle motion. The evaluation of the experiments focused on the effects of two dimensionless parameters of the particle motion: the translational Reynolds number (or Reynolds number) and rotational Reynolds number. The experiments were carried out for the relatively slow (the dimensionless angular velocity Γ < 3.5) and relatively fast (5 < Г < 10) particle rotation. Relationships describing the abovementioned coefficients were developed, taking into account the mutual influence of the translational and rotational particle movements. It was found that the drag force and drag torque coefficients can be expressed as the functions of both the translational and rotational Reynolds numbers.

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

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. Numerický model saltace kulovité částice v korytě s příčně skloněným drsným dnem Studie popisuje numerickou simulaci saltačního pohybu kulovité částice v korytě s příčně skloněným drsným dnem. Předložený numerický model je založen na autory vyvinutém 3D modelu saltačního pohybu kulovité částice, který počítá s translačním i rotačním pohybem částice. Pro výpočet trajektorie částice a její závislosti na příčném sklonu dna koryta, průměru částice a smykové rychlosti nosné kapaliny byla použita stochastická metoda a koncept kontaktní zóny. Vlivem příčného sklonu dna koryta dochází k odchylce trajektorie částice od směru proudu. Trajektorie částic začínajících svůj pohyb v jednom bodě byly vypočteny a bylo ukázáno, že trajektorie jsou náhodného charakteru a tvoří společně svazek trajektorií, jehož osa může být pro nízké a střední hodnoty příčného sklonu dna koryta aproximována přímkou. Vlivem příčného sklonu dna koryta může dojít k roztřídění částic podle velikosti. Bylo spočteno několik příkladů třídění, definováno kriterium třídění a určeny oblasti třídění podle velikosti částic a sklonu dna koryta.

Flow behaviour and local concentration of coarse particles-water mixture in inclined pipes

Abstract 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.

Influence of Inflow Conditions on Saltation Movement of Spherical Particles

The contribution deals with an influence of velocity profiles on trajectories of solid particles during a saltation process in a channel with rough bottom. The saltation is modeled with help of a numerical stochastic model. The collision height and contact point are defined as random variables.