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. A transport model is presented which considers flow with the internal structure described by linear vertical distributions of granular velocity and concentration across the collisional layer. The model employs constitutive relations based on the classical kinetic theory of granular flows selected by our previous experimental testing as appropriate for the flow and transport conditions under consideration. For given slope and depth of the flow, the model predicts the total discharge and the discharge of sediment. The model also predicts the layered structure of the flow, giving the thickness of the dense layer, collisional layer, and water layer. Model predictions are compared with results of intense bed-load experiment carried out for lightweight sediment in our laboratory tilting flume.
If the Shields number of a flow above an erodible bed is higher than one, then the current exerts so high shear stress at the top of a granular bed that the upper part of the bed is eroded and the top of the non-eroded rest of the bed is flat (no bed forms occur). This flow regime is typical for flows over a stationary bed in pipes but it can occur also in open-channel flows, particularly under flood conditions when both the depth and velocity of the flow are high. The current picks up particles from the eroded part of the bed and transports them within the flow. The total load of transported particles is composed of particles transported either as the contact load or as the suspended load, depending on the dispersive mechanism that keeps the particles inside the flow. Solids distribution (i.e. the shape of the concentration profile) of the transported particles across the flow helps to identify an acting dispersive mechanism and hence a mechanism through which the transported particles contribute to flow friction. The paper analyzes the concentration-profile measurements in a medium-sand-slurry current above an erodible stationary bed in a 150-mm pipe. The experiments revealed interesting effects of high shear stress on the shapes of concentration profiles across the flow above the bed. The analysis suggests that carrier turbulence is a prevailing dispersion mechanism within the upper part of the discharge area above the bed for flow conditions characterized by values of the ratio u*b/vt higher than say 4.5. It seems that the shearing action as an exclusive particle dispersion mechanism is confined to the region not far above the top of the bed. Apparently, the high shear stress at the top of the stationary bed is capable of producing turbulent suspension that transports a considerable amount of medium-sand particles (average delivered volumetric concentrations of transported particles up to 0.26) through the 150-mm pipe. and Při proudění vody nad pohyblivým dnem za podmínek vysokého smykového napětí na povrchu dna (Shieldsovo číslo větší než 1) je horní vrstva dna erodována proudem vody a na povrchu neerodované části dna nevznikají dnové útvary. Takové proudění se vyskytuje například v potrubí dopravujícím směs nad sedlinou na dně potrubí, ale může se vyskytnout i v otevřeném korytě, zvláště za povodňové situace, kdy jsou pro proudění typické velká rychlost a velká hloubka vody. Proud unáší částice z erodované vrstvy dna. Mechanismy, které mohou udržovat částice v proudu, jsou v principu dva: turbulentní suspenze a mezičásticový kontakt. Každý z těchto mechanismů způsobuje jiné rozdělení částic, tj. jiný koncentrační profil, po svislici proudu. Měřením koncentračních profilů by tedy mělo být možné odhadnout, jaký mechanismus převažuje v proudění za určitých sledovaných podmínek. Příspěvek analyzuje koncentrační profily měřené v potrubí průměru 150 mm při proudění vodní směsi střednězrnného písku nad pískovou sedlinou. Analýza výsledků měření ukázala, že turbulence v proudu vody je převažujícím mechanismem podpory částic přinejmenším v horní polovině výšky průtočné části potrubí při podmínkách charakterizovaných hodnotou poměru třecí rychlosti ve dně a usazovací rychlosti unášené částice (u*b/vt) větší než přibližně 4,5. Na rozdíl od dřívějších závěrů v literatuře se zdá, že mezičásticové kolize se jako výhradní mechanismus disperze částic uplatňují jen v poměrně omezené oblasti proudu nad povrchem dna. Vysoké smykové napětí ve dně tak přispívá nejen ke vzniku mezičásticových kolizí, ale i k turbulentní podpoře částic. Turbulentní podpora umožňuje dosažení vysokých hodnot (až do 0,26) dopravní koncentrace částic střednězrnného písku ve směsi proudící potrubím průměru 150 mm.
If a sand slurry current flows over a plane bed the thickness of the bed remains constant providing that equilibrium is established between the vertical fluxes that govern the exchange of particles between the slurry current and the sand bed. These solids fluxes are the settling flux and the erosion (pick-up) flux through the top of the bed. In the literature, relations to quantify the erosion flux from a sand bed consider the water current above an erodible bed. The effect of the presence of solid particles in the current is not taken into account. However, it has been observed that the presence of solid particles tends to suppress pick-up. This phenomenon is called hindered erosion. At present, the knowledge of the process of hindered pick-up is very limited although it is suspected that the hindered pick-up plays an important role in many practical situations. The paper discusses the results of the plane-bed test recently carried out in a 150-mm pipe of the Laboratory of Dredging Engineering of Delft University of Technology. Measurements of the thickness of the bed, the concentration profiles in the pipe cross section, the mean velocity, and the pressure drop allowed us to evaluate the conditions governing the vertical exchange of solids at the top of the stationary bed for currents of different solids concentrations. and Při proudění písčité hydrosměsi nad nepohyblivým ložem v tlakovém potrubí dochází k výměně pískových částic mezi proudem a ložem. Tloušťka lože zůstává neměnná, pokud při výměně existuje rovnováha mezi vertikálním proudem částic ze suspenze do sedliny (sedimentační proud) a opačně (erozní proud). V literatuře existující modely pro erozní proud jsou navrženy pro situace, kdy eroze je způsobena prouděním vody nad ložem, vliv přítomnosti unášených částic v proudu tedy není uvažován. V minulosti však již bylo pozorováno, že přítomnost suspendovaných částic může vést k zmenšení schopnosti proudu sbírat částice ze dna. Tento jev se nazývá rušená eroze. V současnosti jsou ještě poznatky o rušené erozi velmi omezené, přestože se dá předpokládat, že rušená eroze hraje významnou roli v mnoha situacích vyskytujících se v praxi. Tento příspěvek pojednává o výsledcích nedávných měření proudění písčité směsi nad nepohyblivým ložem v kruhovém potrubí průměru 150 mm v Laboratoři Dredging Engineering Technické univerzity v Delftu. Měřeny byly tloušťky lože, koncentrační profily nad ložem, střední rychlosti a tlakové ztráty v potrubí. Tato měření umožnila vyhodnocení vertikálního erozního proudu částic z povrchu lože pro různé koncentrace unášených částic ve směsi proudící nad ložem a vlivu koncentrací na erozi.
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.
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.
The friction conditions at the top of a mobile bed are discussed for flows in the upper-plane-bed regime, i.e. for the flows with values of the bed Shields parameter larger than approximately 0.6. A special attention is devoted to flows of the bed Shields parameter bigger than 2. Experimental data for flows at high bed shear are collected from literature and new data are added from own measurements of flows of a 1.36-mm sand slurry in the 100-mm pipe loop of the Institute of Hydrodynamics. The database represents flows of very different solids and covers friction conditions within a broad range of Shields parameters up to the maximum value of about 23. The paper analyses the data in order to evaluate a relationship among the equivalent roughness of the top of the bed and other relevant parameters. A semi-empirical formula is proposed that relates the equivalent roughness to the bed Shields parameter, the ratio of flow velocity and particle settling velocity, and the ratio of flow hydraulic radius and particle diameter. The formula is applicable primarily to flows of combined load (contact- and suspended loads together). and Příspěvek se zabývá mechanismem tření na povrchu erodovatelného dna za podmínek horního režimu pohybu splavenin nad plochým dnem, to jest při hodnotách Shieldsova parametru větších než přibližně 0,6. Zvláštní pozornost je věnována proudění při Shieldsově parametru větším než 2. Z literatury byla sebrána experimentální data pro proudění za vysokých smykových napětí, ke kterým byla přidána nová data z vlastních měření s pískem velikosti středního zrna 1,36 mm v potrubí průměru 100 mm trubního okruhu Ústavu pro hydrodynamiku AV ČR. Databáze obsahuje výsledky měření pro částice různých vlastností v širokém rozsahu hodnot Shieldsova parametru až do hodnoty okolo 23. Příspěvek analyzuje data za účelem stanovení závislosti hydraulické drsnosti povrchu sedliny na ostatních parametrech proudění. Je navržen semiempirický vztah, který předpokládá závislost hydraulické drsnosti na Shieldsově parametru, poměru rychlosti proudění k usazovací rychlosti částic a poměru hydraulického poloměru průtočného profilu k velikosti částic. Tento vztah se doporučuje především pro proudění nesoucí jak dnové splaveniny, tak suspendované částice.
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 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.