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An extended stereoscopic method, which identifies, and tracks particles based on their colour in solid-liquid flow, is tested for its capability to separately measure velocity distributions of particles of two fractions transported as bimodal sediment mixture in water flow through a laboratory flume. The principle of the tested method extension is a use of colour-based processing of images collected by two high-speed cameras which enables to filter out particles of one fraction from the image and leave particles of the other fraction in the image based on a selected colour hue range. The modified images are then processed by the original stereoscopic method to produce velocity distribution of particles of the individual fraction in the flow. The method extension is first tested in simple vertical flow carrying neutrally buoyant spherical particles of two distinct colours in a recirculation cell. In the next step, lightweight plastic particles of two fractions of different properties (size, shape, density) and colours are introduced to flow through a laboratory flume and velocity distributions of the two fractions are measured separately at flow conditions which mimic intense transport of bimodal combined-load in an open channel. Results exhibit a very good agreement with previous measurements with unimodal sediment in hydraulically similar flow.

A relation between the discharge and the flow depth in an open channel is quite sensitive to resistance (expressed by the friction coefficient) of the channel bottom. This relation is straightforward if the bottom is a fixed boundary, and the discharge is a result of one-phase (water) flow. The relation is considerably more complex if the channel bottom is an eroded mobile bed and the flow is solid-liquid flow. Sediment-transport experiments with various model lightweight sediments in a tilting flume of the Water Engineering Laboratory at Czech Technical University in Prague produced information suitable for an evaluation of the eroded bed resistance at conditions of intense bed load and intense combined load in the upper plane bed regime. An evaluation of the bed load condition has been published recently. This paper discusses a description and quantification of the bed resistance in the case of transported combined load, i.e., at the condition where a certain portion of the sediment is transported as bed load and the rest is transported as suspended load. The results show that the presence of transported sediment tends to increase the bed resistance and hence increases a flow depth for a certain discharge of water in an open channel with an eroded bed.

Very coarse basalt-water slurry forming fully stratified flow with a sliding bed and producing considerable friction loss was tested in a laboratory pipe. A considerably finer fraction of sand was added in steps to gradually increase the concentration of this fraction in the flowing slurry. The frictional pressure drop was measured together with the slurry discharge and slurry density. Furthermore, solid particles and their motion were observed at the bottom of the pipe. This observation indicated that finer particles in basalt-based bimodal slurry flows positioned themselves below the coarse particles at the pipe wall. The experimental results show that a quite small amount of fines is sufficient to produce a considerable friction reduction in settling slurry flow. Furthermore, the results indicate that there is a certain optimum quantity of fines at which the maximum reduction is reached and further addition of the fines does not bring any further improvement.

Vertical concentration distributions of solids conveyed in Newtonian fluids can be modelled using Rouse-Schmidt type distributions. Observations of solids conveyed in turbulent low Reynolds number visco-plastic carriers, suggest that solids are more readily suspended than their Newtonian counterparts, producing higher concentrations in the centre of the pipe. A Newtonian concentration profile model was adapted to include typical turbulent viscosity distributions within the pipe and particle motion calculated using non-Newtonian sheared settling. Predictions from this and the unmodified model, using the same wall viscosity, are compared with the chord averaged profile extracted from tomographic data obtained using a 50 mm horizontal pipe.

Intense collisional transport of bimodal sediment mixture in open-channel turbulent flow with water as carrying liquid is studied. The study focusses on steep inclined flows transporting solids of spherical shape and differing in either size or mass. A process of vertical sorting (segregation) of the two different solids fractions during the transport is analyzed and modelled. A segregation model is presented which is based on the kinetic theory of granular flows and builds on the Larcher-Jenkins segregation model for dry bimodal mixtures. Main modifications of the original model are the carrying medium (water instead of air) and a presence of a non-uniform distribution of sediment across the flow depth. Testing of the modified model reveals that the model is applicable to flow inclination slopes from 20 to 30 degrees approximately, making it appropriate for debris flow conditions. Changing the slope outside the specified range leads to numerical instability of the solution. A use of the bimodal mixture model is restricted to the grain size ratio 1.4 and no restriction is found for the grain mass ratio in a realistic range applicable to natural conditions. The model reveals trends in the vertical sorting under variable conditions showing that the sorting is more intense if flow is steeper and/or the difference in size or mass is bigger between the two sediment fractions in a bimodal mixture.

In an open channel with a mobile bed, intense transport of bed load is associated with high-concentrated sediment-laden flow over a plane surface of the eroded bed due to high bed shear. Typically, the flow exhibits a layered internal structure in which virtually all sediment grains are transported through a collisional layer above the bed. Our investigation focuses on steady uniform turbulent open-channel flow with a developed collisional transport layer and combines modelling and experiment to relate integral quantities, as the discharge of solids, discharge of mixture, and flow depth with the longitudinal slope of the bed and the internal structure of the flow above the bed.

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.

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.

The contribution deals with the determination of the ratio of volumes of particles of individual fractions in flows transporting bimodal granular mixtures. The spatial distribution of the ratio is obtained by analyzing images collected by video recording. The measuring method and post-processing analysis are demonstrated on experiments in our new recirculating fluidization cell. The tested bimodal mixture is composed of two granular fractions of different colors – black and white. The analysis is based on a local identification of particles and their background in the collected images. More precisely, the identification of individual particles is based on the grayscale screening of the images. The method allows to identify both the instantaneous and time-averaged spacious distribution of the grain volume ratio. The experimental results reveal that the measuring method is successful if constant light condition is secured and the medium carrying particles is sufficiently transparent. The method is applicable to laboratory flows with sediment transport no matter whether sediment particles are transported as bed load or as suspended load.

Collisional interactions in a sheared granular body are typical for intense bed load transport and they significantly affect behavior of flow carrying bed load grains. Collisional mechanisms are poorly understood and modelling approaches seldom accurately describe reality. One of the used approaches is the kinetic theory of granular flows. It offers constitutive relations for local shear-induced collision-based granular quantities - normal stress, shear stress and fluctuation energy - and relates them with local grain concentration and velocity. Depth distributions of the local granular quantities produced by these constitutive relations have not been sufficiently verified by experiment for the condition of intense bed load transport in open channels and pressurized pipes. In this paper, results from a tilting-flume facility including measured velocity distribution and deduced concentration distribution (approximated as linear profiles) are used to calculate distributions of the collision-based quantities by the constitutive relations and hence to test the ability of the kinetic-theory constitutive relations to predict conditions observed in these collision-dominated flows. This test indicates that the constitutive relations can be successfully applied to model the local collisional transport of solids at positions where the local concentration is not lower than approximately 0.18 and not higher than approximately 0.47.

Gravity-driven open-channel flows carrying coarse sediment over an erodible granular deposit are studied. Results of laboratory experiments with artificial sediments in a rectangular tilting flume are described and analyzed. Besides integral quantities such as flow rate of mixture, transport concentration of sediment and hydraulic gradient, the experiments include measurements of the one-dimensional velocity distribution across the flow. A vertical profile of the longitudinal component of local velocity is measured across the vertical axis of symmetry of a flume cross section using three independent measuring methods. Due to strong flow stratification, the velocity profile covers regions of very different local concentrations of sediment from virtually zero concentration to the maximum concentration of bed packing. The layered character of the flow results in a velocity distribution which tends to be different in the transport layer above the bed and in the sediment-free region between the top of the transport layer and the water surface. Velocity profiles and integral flow quantities are analyzed with the aim of evaluating the layered structure of the flow and identifying interfaces in the flow with a developed transport layer above the upper plane bed.

Principles of gamma-ray-based measurement are summarized and their application is demonstrated on an operation of the radiometric facility installed in the test loop for slurry flows at the Institute of Hydrodynamics. The facility is able to measure vertical profiles of chord-averaged concentrations and concentration maps in the pipe cross section. A methodology of measurement is proposed including detection and quantification of random and systematic errors. Experimental results are discussed in the light of the proposed methodology. Experimentally determined vertical profiles of concentration are presented for slurry flows of four different fractions of glass beads. The tomographic application of the radiometric device is demonstrated on a measured concentration map and a suitable image reconstruction method is tested. High reliability of measured concentration distributions is proved except for regions near the pipe wall. The radiometric method is shown to be a useful tool for measurement of concentration distribution in slurry flow through a pipe.

Intense bed load transport in open channel flow is typically associated with a layered structure of the flow, in which individual layers exhibit different mechanisms of support and friction of transported sediment grains. In the lowermost layer adjacent to the channel bed, the grains slide over each other and maintain virtually permanent contact. In the uppermost layer below the water surface, typically no grains are transported. In the central layer, the grains collide with each other producing typical distributions of granular concentration and velocity across the collisional layer. Mathematical models describing the layered flow with intense bed load (as models based on kinetic theory of granular flows) consider flow conditions at interfaces of the individual layers in their flow predictions. Usually, experimental verification of interfacial predictions is lacking. We exploit results of our new experiments with plastic cylindrical sediment to identify a variation of the conditions at the interfaces (local interfacial granular concentrations and velocities) with varying flow discharge, depth and slope in a laboratory tilting flume. The experimental results include local granular concentration using an improved laser stripe method. The experiments are compared with predictions using our kinetic-theory based transport model with the aim to evaluate a match for experimentally-determined and model-predicted interfacial parameters.

Pipe flow of sand-water slurry (settling slurry) is sensitive to pipe inclination. The effect of the angle to which the partially stratified flow is inclined from the horizontal has been subject to investigation in numerous studies. However, almost all of them focus on ascending flows, i.e. flows inclined to positive angles of inclination. It is well known that settling slurry flows inclined to negative slopes (descending flows) differ from those inclined to positive slopes, particularly at velocities near the deposition limit. The deposition limit velocity is the flow velocity at which stationary deposit starts to be formed at the bottom of the pipe. We investigate the effect of the negative slope on pipe flow near deposition limit velocity in the broad range of inclination angles. Besides the deposition limit, we focus on the distribution of solids across the pipe cross section. We combine experimental approach with mathematical modelling. Our new experiments with medium-to-coarse sand (mass-medium grain size 0.87 mm) in a 100-mm pipe inclined from 0 to -45 degree provide suitable data for a validation of predictions of our layered model for partially stratified flows in inclined pipes.

The paper describes results of validation of authors' recently proposed formulae for sediment transport and bed friction in the upper plane bed regime using laboratory experiments in a pressurized pipe. Flows of mixture of water and fine to medium ballotini (d50 = 0.18 mm) were observed in a rectangular pipe (51 x 51 mm) with a deposit at the bottom of the pipe. A comparison of test results with transport-formula predictions shows a satisfactory match confirming a good prediction ability of the proposed transport formula at high bed shear. A prediction ability of the friction formulae appears to be less convincing but still reasonable. A joint use of the formulae for transport and friction predicts the delivered concentration of transported sediment within the accuracy range of ± 40 per cent for flows in which transported sediments strongly affect the bed friction, i.e. for flows with delivered concentration of sediment higher than say 3 per cent.

Intense transport of bed load is associated with highconcentrated sediment-laden flow over a plane mobile bed at high bed shear. Typically, the flow exhibits a layered internal structure in which a vast majority of sediment grains is transported through a collisional layer above the bed. Our investigation focuses on steady uniform open-channel flow with a developed collisional transport layer and combines modelling and experiment to relate integral quantities, as the discharge of solids, discharge of mixture, and flow depth with the longitudinal slope of the bed and the internal structure of the flow above the bed. In the paper, flow with the internal structure described by linear vertical distributions of granular velocity and concentration across the collisional layer is analyzed by a model based on the classical kinetic theory of granular flows. The model predicts the total discharge, the discharge of sediment, and the flow depth for given (experimentally determined) bed slope and thickness of collisional layer. The model also predicts whether the intefacial dense layer develops between the bed and the collisional layer and how thick it is. Model predictions are compared with results of intense bed-load experiment carried out for lightweight sediment in our laboratory tilting flume.

The deposition velocity is an important operation parameter in hydraulic transport of solid particles in pipelines. It represents flow velocity at which transported particles start to settle out at the bottom of the pipe and are no longer transported. A number of predictive models has been developed to determine this threshold velocity for slurry flows of different solids fractions (fractions of different grain size and density). Most of the models consider flow in a horizontal pipe only, modelling approaches for inclined flows are extremely scarce due partially to a lack of experimental information about the effect of pipe inclination on the slurry flow pattern and behaviour. We survey different approaches to modelling of particle deposition in flowing slurry and discuss mechanisms on which deposition-limit models are based. Furthermore, we analyse possibilities to incorporate the effect of flow inclination into the predictive models and select the most appropriate ones based on their ability to modify the modelled deposition mechanisms to conditions associated with the flow inclination. A usefulness of the selected modelling approaches and their modifications are demonstrated by comparing model predictions with experimental results for inclined slurry flows from our own laboratory and from the literature.

A series of laboratory experiments on turbulent open-channel two-phase flow in a form of intense bed load transport is reported. Measurements in a laboratory tilting flume included camera based imaging techniques to identify the structure of the flow at the local level. Obtained experimental distributions of two-phase flow related parameters - granular velocity, concentration, and temperature - across a collisional transport layer are discussed. The results are analysed together with additional measured quantities (discharges of mixture and grains, flow depth, bed slope etc). Our major goal is to evaluate the distribution of granular stresses across the transport layer with a special attention paid to the interface between the transport layer and the bed. Furthermore, comparisons are discussed between the experimental results and predictions produced by suitable kinetic-theory based models.

Lack of experimentally determined information on inner structure of flows carrying large amount of coarse sediment is an important limitation for development and validation of appropriate mathematical models. Measurement of local flow properties is particularly difficult in case of coarse sediment due to specific features associated with high ratio of the sediment size to the flow depth. This paper focusses on two methods of evaluation of vertical concentration profiles in the flow of a mixture of plastic grains and water in a laboratory flume. The first one was proposed by B. Spinewine et al. in 2011 and it is based on the relation between concentration of solids and the depth of penetration of a laser stripe to the flow, which is evaluated from a high speed camera record. The second method is based on well-known relation between the concentration and electrical conductivity of a mixture sensed by immersed probe. A sensitivity analysis of both the methods is performed to show the most crucial parameters affecting accuracy of the results. The methods are validated on data measured in fluidization cell with controlled particle concentration. Presented results on flow show limitations and potential of the methods for laboratory studies on liquid-granular flow.

Open-channel two-phase flow above a granular mobile bed is studied experimentally and theoretically. In the two-phase flow, water serves as a carrying liquid for plastic grains transported as collisional contact load in the upper-stage plane bed regime. The investigation evaluates friction- and transport characteristics of the flow under the condition of intense collisional transport of grains and links them with the internal structure of the two-phase flow. The paper focusses on the effect of bimodal solids (mixed two fractions of grains of similar density and different size and shape) on the flow characteristics and internal structure. Hence, experimental results obtained for the bimodal mixture are compared with results for individual grain fractions. The experiments show that the bimodal character of the transported solids affects the layered internal structure of the flow as a result of fraction segregation due primarily to gravity (kinetic) sieving during transport. The segregation also affects the friction- and transport characteristics of intense bed load. In the paper, the effects are described and quantified.

The paper deals with a flow behaviour of mixture composed of coarse glass-bead particles and non-Newtonian carrying liquid of Herschel-Bulkley type in a pressurized pipe. Essentially, there are two mechanisms governing support of particles in the flowing carrier: mutual inter-particle collisions and interaction of particles with carrier turbulent eddies. The turbulent support is quantified by a turbulent-diffusion model, which predicts a distribution of concentration of particles in the flow. In the model, the particle turbulent diffusivity is an important parameter dependent on a number of flow quantities, e.g. the carrier rheological parameters. In case of Newtonian carrier, the viscosity is the only rheological parameter and it is constant throughout the flow. In the non-Newtonian carrier, however, local values of the viscosity vary with the shear strain and so affect the particle diffusivity. The paper discusses experimental and analytical results for non-Newtonian mixture flows of measured rheological parameters and flow characteristics. Based on measured concentration profiles, a suitable method is used to determine the local particle diffusivity experimentally.

Extreme conditions as flash floods in steep mobile-bed streams induce flows which carry a huge amount of sediment. Typically, the flow with the intense transport of sediment is stratified with a layered structure above an erodible plane bed. The paper deals with local flow characteristics in the layered structure of the two-phase flow composed of water and sediment. We present experimental data and results for two different fractions of plastic particles obtained using two acoustic Doppler methods and a Prandtl probe. The results contain vertical profiles of longitudinal velocity component and local turbulent characteristics of the flow as the Reynolds stress and turbulent intensity. The effect of the layered character of the flow on the flow characteristics is discussed. Special attention is paid to the distribution of Reynolds stress in the sediment-rich transport layer above the bed and to the evaluation of ability of carrier turbulent eddies to support sediment grains in and above the transport layer.

The paper deals with laboratory experiments in open-channel flows with intense transport of model sediment (coarse plastic particles) in our new tilting flume. The major objectives of the paper are: 1. to discuss applied measuring methods, 2. to analyze measured velocity profiles. Ad 1. A profile of the longitudinal component of local velocity was measured across the vertical axis of symmetry of a flume cross section using three independent measuring methods (Prandtl tube, Ultrasonic Velocity Profiler, Acoustic Doppler Velocity Profiler). Due to strong stratification of the flow in the flume, parts of the profile are measured in regions of very different local concentrations of sediment (from virtually zero concentration to the maximum concentration of bed packing). This makes measurements complicated, particularly for ultrasonic measuring techniques. Profiles measured using the different techniques are evaluated and mutually compared. Ad 2. The layered character of the flow causes that shapes of velocity profiles tend to be different in the transport layer (rich on transported particles) above the bed and in the solids-free region between the top of the transport layer and the water surface. Shapes of the profiles are analyzed. Particular attention is paid to the logarithmic profile in the solids-free region of the flow cross section. The profile can be handled using the law of the hydraulically-rough wall. In the law, the eroded top of the bed with the transport layer is supposed to be the rough boundary and appropriate values are sought for its variables.

Solid–liquid flows are encountered in various industrial and natural environments. The internal structure of such flows is highly sensitive to the grading of the solid particles present. In this experimental study, an extended stereometric method is employed to assess the distributions of velocity of particles of different fractions, distinguished by different colors, in vertical and nearly horizontal granular flows. In the vertical flow experiments, mixtures comprising three fractions of lightweight particles, characterized by a very similar density, size, and shape, were tested. The results affirmed the method's ability to discern particle velocity differences on the order of millimeters per second, establishing its suitability for characterizing nearly horizontal open-channel flows with bimodal mixtures that are stratified and exhibit more complex velocity distributions. Tilting flume experiments, incorporating additional measurements of water velocity distribution, allowed for the evaluation of local slip between water and particles, as well as between particles of the two fractions in the flow. The results indicated that, although the local slip velocity was relatively small, the average slip velocity between the carrying water and transported particles was significantly larger. This factor must be taken into consideration when evaluating bed friction or bed erosion for granular flow in a channel with an erodible bed. [ABSTRACT FROM AUTHOR]

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