TWO-PHASE FLOW OF HIGHLY CONCENTRATED SLURRY IN A PIPELINE

325Journal of Hydrodynamics, Ser. B,2004 ,16(3):325. - 331China Ocean Press, Beijing- Printed in ChinaTWO- PHASE FLOW OF HIGHLY CONCENTRATED SLURRY IN A PIPELINE .NI Fu-sheng, ZHAO LijuanFaculty of Mechanical and Electrical Engineering, Hohai University, Changzhou 213022，China,e- mail:f. ni@ hhuc. edu. cnMATOUSEK V.，VLASBLOM W. J. ，ZWARTBOL A.Section of Dredging Technology, Delft University of Technology，The Netherlands( Received Mar. 12, 2003)ABSTRACT: Hydraulic transport of sand is one of the key tics of pipeline flow. In order to detect the sand- wa-processes in river, lake, harbor and waterway dredging engi-ter two-phase flow phenomena with high solid con-neering. Understanding the flow resistance， solid distribu-centration, a number of intensive laboratory experi-tion, flow stratification, transport economy, etc.，in the two-ments were carried out at the Delft University ofphase flow of sand- water mixture through a pipeline is crucialTechnology, The Netherlands，from Sept. 1998 toto the design and operation of power drives of a dredger, andto the construction of a dredging project. This paper presentsMar.，1999. Three narrow-graded sand fractions ofthe intensive laboratory experimental data and physical and different sizes were respectively tested in a horizon-numerical analyses on the highly concentrated slurry flow un- tal 150 mm pipeline circuit. These were the fineder an extended large range of slurry mean velocities for three sand of the mass median diameterdso = 0. 123 mm,narrow graded sands of different sizes. The investigation indi-the medium sand ofd:o = 0. 372 mm and the coarsecates that the solids concentration and particle size strongly af-sand of dso = 1. 840 mm. The density of the dryfect the slurry flow characteristics.sand was 2650kg/m3. The tested slurry densityKEY WORDS: two phase flow, hydraulic transport, labora-ranged from 1160kg/mto 1710 kg/ m3 and the slurrytory experiment, modelingvelocity range was extended from 1. 0m/s to 9. 0m/s，which covered the possible operation conditions1. INTRODUCTIONin dredging engineering.In dredging engineering, the underwater mud,clay, sand or other materials cut by a soil-cutting 2. PARAMETER MEASUREMENTtool are usually transported through a long pipelineThe pressure difference over a pipeline sectionto a certain disposal spot by using centrifugal was measured as the pressure gradient by a Rose-pumps. Though slurry densities in the range of mount differential pressure transmitter Model 1151.1200kg/m3-1300 kg/ m' are usual, great efforts have The K rohne magnetic inductive flow meter Altome-been made to increase the densities for higher pro- ter TIV 50 was used to measure the mean slurry ve-ductivity and transport efficiency. With rapid devel-locity Vm in the circuit. The spatial solid concentra-opment of new techniques in dredging engineering， tion across the pipe cross section C。，which givesit is now possible to hydraulically transport sand- the fraction by volume of solids actually resident inwater slurries at increasingly higher solids concen- slurry, was detected by a radiation density metertrations in pipelines. Sand water mixture densities Berthold LB 367 with a Cs-137 source. In order toeven up to 1700kg/ m3-1800kg/m° can be reached in obtain the concentration distribution, a special sup-the pipeline connecting a Trailing Suction- Hopper- port f中国煤化工: horizontal pipeline toDredger ( TSHD) with an onshore deposit site'1l.set c|YHC N MH Gve source and the de-Despite some practical experience， there is still a tector at dlterent vertical positions across the pipe-lack of refined information on the effects of high sol- line cross section. For determining the solid produc-id concentration and particle sizes on the characteris- tion or the solids amount per hour transportedT2忘数据was supported by the Project Qing Lan 2001, Jiangsu provincial Governement.326through a pipeline, the so-called delivered volumet- slurry velocity. The solids-effect Im-Iw，where sub-ric concentration Cvd must be introduced, which scripts m and w stand for mixture flow and clear wa-gives the fraction by volume of solids delivered in ter flow respectively, increases gradually with theslurry, and is calculated as the ratio between solids increase of mean velocity and delivered concentra-flow rate and the slurry flow rate. An inverted， tion.vertically mounted, U-tube in the pipeline was usedas a counter- flow meter to determine the delivered0.67◆Water .concentration-2. For detailed description of the la-人14%- 15%boratory circuit and the data acquisition system， see0.4-Refs. [3,4]. During each experimental run, the to-▲26%-28%tal amount of sand in the circuit was constant but口34% -35% .0.2-the delivered concentration may increase slightlywith increasing mean slurry velocity. .024，68103. OBSERVED PHENOMENAK/ms:'3.1 Fine sand slurry flowThe most interesting phenomenon is the devel-1(a) Hydraulic gradient Imopment of the pressure gradient occurring in thepipeline. The pressure gradient is usually expressedx 14%-15%as the dimensionless hydraulic gradient Im which isdefined as the frictional head loss in meter-water-40十column over one meter pipeline. The curve of I,AA。34%-35%vorsus the increasing slurry velocity Vm shows the0tdevelopment of slurry flow resistance. While thehydraulic gradient was measured under each slurryvelocity, the local solids concentration near the pipe0246810bottom C。b was simultaneously measured at the ver-V, /ms'ical positiony/D= 0.1 to judge flow stratification, .where y denotes the vertical distance from pipe walland D the inner diameter of the pipe. Figs. l(a) and 1(b) Concentration near the pipe bottom Coa1(b) show the measured data of the fine sand slurryFig. 1 Flow of fine sand slurrywith the delivered concentration C。equal to 14%-15%，26%-28%，and 34 %-35% respectively. Gen-0.6-erally speaking, the fine sand slurry exhibits a pseu-●Waterdo-homogeneous pattern. Only at the velocities low-人11%-13%0.4.er than the deposition-limit threshold or，less accu-▲25%-26%rately, the critical velocity Va，does the flow be-0.24comeheterogeneous.The visualobservations。42%-43%through a plexiglass section indicated that deposi-tion-limit velocities of the three fine sand slurries re-spectively areVau = 1.8m/s，1. 67m/s and 1. 55m/s，0243 10decreasing with the increase of delivered concentra-K./ms*'tion，which shows that a slurry with higher density2(a)中国煤化工has stronger particle carrying capability to preventsand from depositing on the bed. At high velocities[HCNMHGof each slurry the local concentration near the bot-.2 Medium sand slurry flowCompared to the fine sand slurry, the heteroge-tom decreases slowly and converges towards the de-neous flow pattern prevails in the medium sand slur-livered concentration， which suggests that solidsry (see Figs. 2(a) and 2(b)). The local concentra-concentration, would approach a uniform distributiontion near the pipe bottom gradually decreases andacross the 万帮插ne cross- section with increasing327concentration. .70 1x11%-13%3.3 Coarse sand slurry flow&The coarse sand slurry behaves quite differently▲25%-26%and two peaks occur in each resistance curve ( see。34%-35%Fig. 3(a)). The solids- effect neither monotonously”30increases as in the case of fine sand slurry nor mo-。42%-43%notonously decreases as in the case of medium sand .slurry. The two peaks tend to be shifted to lowervelocities with the increase of slurry density and be-V, /ms'‘come more pronounced for middle and low deliveredconcentrations. The pipe bottom concentration C。remains much higher than the corresponding deliv-2(b) Concentration near the pipe bottom C。Fig.2 Flow of the medium sand slurryered concentration， indicating that the spatial con-keeps higher than the corresponding delivered con-centration distribution across the pipeline cross sec-centration，which indicates a non- uniform solids dis-tion must be non-uniform (see Fig. 3(b)). The de-tribution across the pipeline cross -section. The het-velopment of the bottom concentration shares theerogeneous flow is characterized by the gradual de-same variation trend as the hydraulic gradient. Thecrease，rather than increase， in the solids-effectvisual observation revealed that it is impossible toI-Iw with the increasing slurry mean velocity Vmdevelop a steady thin bed in the coarse sand slurryVery high concentration of the medium sand of ap-to determine the deposition- limit threshold. Veryproximately 42% (the slurry density Pm≈1700kg/strong instabilities occurred during the observationsin the slurries of all tested delivered concentrations.m3 ) considerably increases frictional head losses atWhen the slurry velocity was reduced to below 1.velocities not far above the deposition-limit thresh-0m/s, an very thick unsteady bed, which occupied aold. At high velocities ( approximately above 6. 0m/considerable area of the pipe，was developed， buts)，however, the frictional head loss of highly con- this observation might be risky and would easilycentrated medium. sand slurry seems to be lower block the pipeline near the bends or other criticalthan that in highly concentrated fine sand slurrycomponents. Laboratory tests showed that theflow (see Figs. 1(b) and 2(b)). Experiments alsomechanism governing the coarse sand slurry flowshowed that when Cod was below 35%，a very thinwould be rather complicated.stationary bed could be easily developed for the de-termination of the deposition-limit velocities, whichwere visually observed as Vu =2. 63 m/s，2. 57m/s0.6◆Waterand 2. 50m/s，respectively， again slightly decrea-sing with the increasing Cua。For the highest con-h 13%-16%0. 4centration Cva≈42%，however, a thin stationary心bed could not be developed even at very low veloci-0.2。40%-4!%ty. Instead， the bed regularly stopped, grew inthickness even up to approximate 0. 33D and thenwas flushed away. As a result， the flow velocityl0and pressure gradient in the pipeline fluctuatedK./ms^strongly. At a velocity of about 2. 6m/s-2. 8m/s the3(a) Hydraulic gradient Imfluctuations were considerably weaker and an un-中国煤化工steady sliding bed formed. The unsteady processfurther weakened with increasing the velocity. FigYHCNMHGures 2(a) and 2(b) also show that the deposition- 4.1 上 low StratificatonThe observed phenomena reveal that the char-limit velocity Vu does not coincide with the mini-mum velocity Vmin at the lowest point of the resist-acteristics of flow resistance and the local concentra-ance curve. The_ difference between the two specialtion near the pipe bottom have a strong relation withvelocities万友数据es with the increase of deliveredthe flow stratification. When sands are transported328◆K=1.66C.=35. 2%S, =0.97101x 13%-16%K,=2. 08.思Cs=35. 4%▲23%-24%号0.5s;1.010g50。32%-33%K.=4. 25Cw =34.8%。40%-41%s, =1.030+ V.=6.00Cw=34. 6%02468 10s,=1. 044K./ms^.201060C/%3(b) Concentration near the pipe bottom C。Fig.3 Flow of the coarse sand slurryin a pipeline, some degree of flow stratification oc-Fig.4 Solids distribution in fine sand slurrycurs. This is due to the tendency of solid particles1V.;=2.18settling in a carrying liquid. As a result， a particle-Cw =31. 6%rich zone in the lower region and a particle-lean zones, =0. 81:in the upper region are typically developed acrossK. =2.97the pipeline cross section. Figures 4-6 show the typ-Cu -=33.6%ical spatial concentration distributions across the“0.5-s, =0.947whole pipeline cross-section for slurries of the fine,V.=4.25medium and coarse sand fractions respectively. TheCu=34.0%S, =0.993fine sand particles almost uniformly distributer =6.00across the pipeline cross section, producing a pseu-Cui=34. 5%do-homogeneous slurry flow in which viscous fric-s, =I.029.tion and turbulence mainly contribute to the flow re-30 500sistance. Thus the solids-effect gradually increases:/%with the increase of slurry velocity (see Figs. 1(a)Fig. 5 Solids distribution in medium sand slurryand 4). The medium sand slurry experiences somedegree of flow stratification. Local concentrationsnear the bottom area remain high, which producesan additional friction， i. e.，the mechanical frictionbetween the sliding sand bed and the pipe wall. TheV. =1.64, Cw =25.5%mechanical friction prevails at low velocities. W henS.=0. 618, strongslurry velocity grows， more particles are erodedstratificationfrom the sliding bed and the solids distribution。V=2.24, CrF28. 0%S=0. 731tends to be more uniform, and thus the flow strati-兰 0.5+fication becomes weaker. Hence the solids-effect- o V.=3.01,Cw=29.8%gradually decreases with the increase of mean veloci-S=0.823 lessty (see Figs. 2(a) and 5).Vz4. 24, Cw=30. 1%4.2 Slip ratio between two phasesThe flow stratification originates from the den-40re- stratification'sity difference between the two phases. The less .Fig. '中国煤化工e sand slurrydense phase usually tends to flow at a higher veloci- velocMHCNMHGslipratioofthemeanty than the denser phase does, resulting in the ex-solids velocity to the mean mixture velocity, S, =istence of the“slip”between the two phases. The V,/Vm. Since CoQ./Qm = (A,V,)/(AV) =degreeof the“mean slip” between the two phases (A,/A)/(V,/V.) = C。/Cs,，the average slip ratiocan be expressed by the“slip velocity” between thecan be calculated with S, = V./Vm = Cua/C.i，average C开寡数居water velocity and the mean solidswhere Q, and Qm denote respectively the solids flow .329rate and the slurry flow rate, A, denotes the area oC- instead of a sharp interface (see Fig. 6). Because ofcupied by the solids andA the area of the pipe cross the existence of the concentration gradient betweensection, Cri = A,/A is the mean spatial concentra- the two zones，the transition zone may behave like ation calculated by integrating the measured distribu- shear layer. At low velocities not far above the dep-tion profile over the pipeline cross-section. Figs. 4- osition-limit threshold, a sliding sand bed was al6 also give the values of the slip ratio for each deliv- ready fully developed and most particles occupiedered concentration and explain well the relation be- the almost uniformly distributed bed. A gradual in-tween the flow stratification and the slip ratio. In crease of the slurry velocity started a gradual ero-fine sand slurry, the slip ratios approach unity even sion of sand from the bed by a shearing force fromat very low velocity，which indicates that the slip in the shear layer, resulting in the expansion of thethe pseudo-homogeneous slurry can be negliglected，shear layer and the decrease of the area of uniformand thus the slurry behaves like a single- phase liq- bed. The concentration distribution became more u-uid. Because of the inaccuracy of the measurement niform and the slip ratio became bigger. Fig. 6some slip ratio values are bigger than one. Fig. 5 shows that the slip ratio increases from 0. 618 to 0.shows that the medium sand slurry suffers flow 823 with the increase of slurry mean velocity. How-stratification under velocities lower than 4. 25m/s，ever, when the velocity exceeds a certain value, theabove which solids distribution gradually becomes thick shear layer gradually diminished, and the res-more uniform and produces even smaller flow resist- toration process of a uniform bed started. Thereforeance than the fine sand slurry under the same mean the behavior of the shear layer played an importantvelocities (see Figs. 1(b) and 2(b)).role in the development of the“two-peak”flow re-4.3 Flow re- strati ficationsistance curve and the re-stratification.It is generally accepted that increasing the slur-4.4 Economy of sand trans portry velocity can reduce the flow stratification. How-The economy of sand hydraulic transport can beever the monotonic trend was not observed in the evaluated by the specific energy consumption, SECcoarse slurry flow (see Figs. 3(a)， 3(b) and 6). in the units of[kW●h/ton ●km], which is definedThe resistance curves were shaped with two peaks as the required energy to transport a given amountand the measured spatial concentration profiles indi-of solids over a given distance. From the view pointcated that the coarse slurry was first gradually ho- of energy consumption，the solids should be trans-mogenized if the slurry velocity increased from the ported at high concentrations of Cud≈25% -30%，deposition-limit threshold, but then above a certain with the mean velocity Vm≈Vmin (see Figs. 7-9). Itvalue of Vm，which varied for different Cou，the seems to be more economical to transport the coarseslurry flow experienced a gradual re-stratification sand at the second minimum velocity, which couldwith the increase of mean velocity. Carefully loo-obtain a productitivity three times as high as that atking into Fig. 6，one can easily find that the varia- the first smaller minimum velocity， but the pumption in the shape of the solids distribution curves and the pipeline would undertake severe wear. Ourand in the values of the slip ratio does exhibit a laboratory tests showed that the slurry became veryprocess of strong stratification ( S,=0.618 ) to less warm when transporting highly concentrated coarsestratification ( S, =0.823 )，and further to re-strat- sand at high velocities.ification ( S,= 0.798 ) with increasing velocity. 4. 5Flow resistance prediction with a two-layerAfter re- stratification，the slurry was gradually ho-modelmogenized again if the slurry velocity increased fur-Due to the complexity of solid-liquid two phasether, and correspondingly the flow resistance curves flow, it is very difficult to model the interaction be-seemed to converge towards lines parallel to the re- tweer中国煤化土ly concentrated slurrysistance curve of clear water flow (see Fig. 3(a)). by coCics. Many researchersThe above phenomena can be explained as follows. haveTYHC N M H Gblishing empirical for-Due to a much greater weight difference between the mulae to predict the flow resistance in dredging andtwo phases， a particle-lean zone and particle- rich other solids hydraulic transport engineering4+6] .zone were obviously formed in the upper and lower These formulae are characterized by some uncertainregions in the. coarse sand slurry. Between the two coefficients which might differ greatly in differentzones，hoWe科there was actually a transition zone engineering fields under different conditions such as330coarse sand slurry, the calculated hydraulic gradienta 14%-15%金2▲26% 28%only shows a reasonable variation trend coincidingwith experimental data (see Fig. 11)，which indi-cates that further study should be eonducted to034%-35%model the mechanism governing the complicatedflow of coarse sand slurry characterized by re- strati-fication.00400600Cw =25%-26%P,/ ton. h"'十Calculation0.4。Exper imentWater:Fig. 7 SEC of the fine sand transport0.2十▲11%-13%246810▲25%-26%2HK. /ms'口34%-35%(a)i 1-。42%-43%Cw =34%-35%0+0.67200P, / ton. h-'0.4-。 Experinent .0.2+Fig.8 SEC of the medium sand transport020x 13%-16%。/ms^(b21▲23%-24%Fig.10 Flow resistance prediction for the medium sand0 32%-33%slurry。40%-41%Gw =13%- 16%0.6100300 400-Calculat ionP. / ton.h'0. 40 ExperimentwaterFig.9 SEC of the coarse sand transport0.2-the types of solids and their concentration, density，size, shape, pipeline diameter, characteristics of thecarrying liquid, etc. In this paper we use a two-lay-46er model to predict the flow resistance of stratifiedV./ms'slurry [7-8]. The model simplifies the stratified slur-ry as a particle-lean zone and a particle rich zone,Fig.中国煤化工ion for the carse sandeach having a uniform solids concentration. The hyMHCNMHGdraulic gradients are obtained by solving a set of e-quations expressing the conservation of mass andmomentum in the two layers. For the medium sandslurry，the model leads to a good agreement with 5. CONCLUSIONSthe measa (see Fig. 10)，while for theThe following conclusions can be reached by331the observations and physical and numerical analy- slurry， it can not simulate the re- stratificationses of the phenomena detected in our laboratory ex- mechanism which should be subject to further inves-periments:tigation in the future.(1) Particle size and solids concentration havestrong influences on the flow resistance, deposition-limit velocity, flow stratification, slip velocity be- REFERENCEStween the two phases, solids concentration profile ,transport economy, etc. in the two-phase flow of [1] BERG VAN DENC. 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