Numerical Simulation of the Sedimentation Process in a Trailing Suction Hopper Dredge

Transcription

1 Numercal Smulaton of the Sedmentaton Proce n a Tralng Sucton Hopper Dredge C. van Rhee 1 Abtract: In the lat decade large area of land were reclamed ung tralng ucton hopper dredger, and large reclamaton project wll be executed n the near future, epecally n the Far Eat. Durng the overflow phae of the loadng tage of the dredgng cycle a part of the dredged volume of and wll not ettle n the hopper but tranported wth the overflow dcharge overboard. For producton, and qualty and envronmental reaon t mportant to predct the amount of th o-called overflow lo. Both the total volume of loe a the nfluence on the loaded (and lot) partcle ze dtrbuton (PSD) mportant. In 1997 a reearch program wa tarted to get more under-tandng of the edmentaton proce onboard a hopper dredge. The goal of the programme wa to develop a numercal model that can be ued to predct the nfluence of the relevant parameter a hopper geometry, and, dcharge and concentraton on the overflow loe (and whch fracton of the PSD wll be lot). The reearch programme cont of three part: laboratory experment, development of numercal model and full-cale valdaton of the model. In the paper the reult of the laboratory tet and the developed 1DV numercal model wll be preented. The 1DV-model one-dmenonal, but n contrary to mot extng model n the vertcal drecton. The nfluence of the PSD dtrbuton modelled ung a coupled ytem of tranport equaton (convecton-dffuon) for the dfferent gran ze. The numercal reult wll be compared wth the experment. Good agreement acheved n predcton of the overflow loe a functon of the loadng tme wth contant and varyng nflowng andflux. Keyword: Hopper Sedmentaton, Overflow lo, Fnte Dfference Method. Expemerment 1 Faculty of Mechancal Engneerng and Marne Technology, Delft Unverty of Technology, Mekelweg 2, 2628 CD Delft, The Netherland, Tel: , Fax: , c.vanrhee@wbmt.tudelft.nl, www-ocp.wbmt.tudelft.nl/dredgng/home.htm

2 1 INTRODUCTION Large volume of and are beng dredged and tranported nowaday by Tralng Sucton Hopper Dredger (TSHD). A TSHD a ea-gong veel that equpped wth one or two ucton ppe, whch are lowered to the bottom durng dredgng. From the bottom a and-water mxture ucked up and dcharged nto one large cargo hold, the o-called hopper. Sand ettle from th mxture and when the hopper flled wth and the hp al to the locatng where the and beng dumped or pumped ahore. Generally a part of the ncomng and wll not ettle durng loadng nto the hopper, but wll go overboard wth the overflow mxture. To acheve a good predcton of the producton and the qualty of and beng dredged knowledge of the amount and fracton of and lot mportant. For th reaon a reearch program wa ntated and fnanced by the Dutch dredgng ndutry. The ultmate goal of th reearch program to gan more nght n the edmentaton proce and to develop a model to decrbe th proce. The reearch program cont of three part: Expermental nvetgaton ung model tet. Numercal modellng ung an one-dmenonal (1DV) and two-dmenonal approach. Prototype verfcaton of the numercal model. In th paper the expermental arrangement and ome of the reult wll be preented and a bref outlne of the one-dmenonal numercal model wll be gven. Fnally the theory wll be compared wth the experment. 2 EXPERIMENTS In the pat model tet were carred out generally by the dredgng contractor. The dmenon of the tet were n mot cae rather mall and the meaurement were lmted to the nflow and outflow quantte. The procee nde the hopper were more or le regarded a a black box. To gan more nght n the phycal proce nde the hopper t wa decded to perform tet wth large dmenon (to mnme cale effect). Durng thee experment the nflow and outflow quantte were recorded but the attenton wa focued on the tuaton nde the hopper. A lot of ntrument were ntalled n the hopper to acheve the velocty and concentraton dtrbuton a functon of tme and pace. The next ecton wll decrbe the expermental etup, the tet program and the ntrumentaton. 2.1 Expermental et-up The experment were carred out n the dredgng flume of Delft Hydraulc. In Fg. 1 and Fg. 2 a chematc overvew of the arrangement gven. The et-up compoed of three ban: a and torage ban that contan 15 m 3 of and, the model hopper and a econdary ettlement ban n whch the and fracton from the overflow mxture wll ettle. Durng a tet a and water mxture n ucked from the torage ban and pumped to the mxng tank that buffer poble flow varaton and damp concentraton varaton of the ucton proce. From the mxng tank the mxture flow to the nflow contructon located n the model hopper. The dcharge to the hopper controlled ung a control valve. From the overflow mxture flow to a contaner n whch two ubmerble pump are placed. The two pump dcharge the overflow mxture to the econdary ettlement ban n whch the and fracton preent n th mxture can ettle. The exce water from the econdary ettlement ban water flow under gravty back to the torage ban. The econdary ettlement ban an eental component n the arrangement. Wthout th ban the overflow mxture, contanng the fner fracton, would flow drectly back to the torage ban leadng to a changng partcle ze dtrbuton durng the tet. The model hopper had a length of 12 m, a wdth of 3.8 m and a heght of 2.5 m. One of the de wall of the hopper contaned gla ecton whch made vual npecton of the proce poble. On the bottom of the torage ban fludaton ppe were ntalled. The fludaton ytem decreaed the effectve preure n the andbed whch made large ucton producton poble.

3 Fg. 1 Top vew of expermental et-up. Fg. 2 Sde vew of expermental et-up 2.2 Tet Program In total 19 experment were carred out. The followng parameter were vared: Dcharge m3/ Concentraton 6 3 % (11 15 kg/m3) Overflow level 2. and 2.25 m Inflow ytem Over total wdth of hopper ung a dffuer or a prayng ppe. Overflow ytem Edge over total wdth of hopper, round overflow a preent on many hopper Water level Level at tart of a tet. Vared between m (1 tet), 1 m (17 tet) and 2 m (1 tet) Sand. 15 mcron (15 tet) and 14 mcron (4 tet). After completon of a tet the model hopper wa flled wth and. The amount of (fne) and n the econdary ettlement ban wa dependent on the magntude of the overflow lo and could be ubtantal a well. Before the next experment could be commenced and had to be removed from the hopper and the econdary ettlement

4 ban and tranported to the and torage ban. Th actvty wa tme conumng therefore only one tet per day could be performed. 2.3 Intrumentaton The ntrumentaton can be dvded nto the general (bulk) meaurement of the nflow and outflow fluxe and the ntrument placed nde the hopper. The followng bulk meaurement were carred out (the meaurement prncple between bracket): Dcharge nto the hopper (Electromagnetc Flow meter) Inflow concentraton (Radoactve Denty meter) Outflow concentraton (Radoactve Denty meter) Concentraton n Mxture Tank (electrc conductvty) Concentraton n U-bend on the ucton carrage (Preure dfference) Water temperature (electrc conductvty) At regular nterval ample were taken from the nflow and outflow mxture. From thee ample the mxture denty and the partcle ze dtrbuton wa determned. The mxture denty wa ued to check and calbrate the radoactve concentraton meter. Inde the hopper the followng quantte were meaured: Concentraton profle On x locaton vertcal bar were placed each contanng 12 gauge for concentraton meaurement ung the electrc conductvty prncple. Th reulted n 72 meaurement locaton from whch 42 locaton were ampled durng an experment. Mxture velocty Durng a tet the mxture velocty wa meaured ung 15 Electromagnetc Velocty Meter (E-4 probe developed by Delft Hydraulc, ee Fg. 3). Th ntrument meaure the velocty n the plane of the dk. Mot ntrument were placed horzontally, hence velocty wa meaured n the upward (z) and longtudnal (x) drecton, other meaured the velocty n a horzontal plane (xy). Th reulted n 3 velocty gnal durng a tet. Fg. 3 E4-probe of Delft Hydraulc (Photo by Delft Hydraulc) Durng an experment the hopper wa flled wth and. Buryng of the ntrument had to be avoded for two reaon. Frt of all mxture velocte wll only be meaured above the and urface and econdly t wa very lkely that the gauge would be damaged durng and removal from the hopper. When the andbed reached a certan probe the ntrument wa moved n vertcal drecton by.2 to.4 m. The moment of relocaton and the new poton wa recorded for later proceng of the velocty gnal. 2.4 Data acquton The ntrument were ampled ung two PC. The bulk data were ampled wth a frequency of 2 Hz, the concentraton and velocty probe n the hopper were ampled at 1 Hz to preerve nformaton of the turbulence. After a tet wa fnhed the frt tage of pot proceng wa carred out to convert the gnal to phycal value and to convert all ampled velocty gnal u(t) to u(x,y,z,t). 3 ANALYSIS OF EXPERIMENTAL RESULTS 3.1 Proce Decrpton From the velocty and concentraton meaurement and vual obervaton through the gla dewall a flow pattern could be dtnguhed a ketched n Fg. 4. The nflow located at the left de and the overflow at the rght de of the hopper:

5 Fg. 4 Schematc overvew of flowfeld n hopper The hopper area can be dvded nto 5 dfferent ecton: 1. Inflow ecton 2. Settled and or tatonary and bed 3. Denty current over ettled bed 4. Horzontal flow at urface toward the overflow 5. Supenon n remanng area In the nflow ecton the ncomng mxture flow toward the bottom and form an eroon crater and denty current. From th current edmentaton wll take place whch lead to a rng and bed. The part of the ncomng edment whch doe not ettle wll move upward nto upenon. At the water urface the vertcal upply of water and edment creatng a trong horzontal flow toward the overflow ecton. Apart from the nflow ecton the flow n the upended part of the hopper bacally one-dmenonal. In horzontal drecton the (meaured) concentraton very unform (vertcally layered). 3.2 Overflow Loe A very mportant quantty durng the loadng proce the overflow lo. Two dfferent defnton of th quantty are ued. The lo can be defned a the rato of the outflow and nflow and flux at a certan moment, or a the rato of the total outflow and nflow volume. The overflow flux defned a: The (cumulatve) overflow lo defned a: () t C () t () t C () t Q o OVflux () t = ( 1 ) Q t () t C () t Q o o dt OV cum () t = t ( 2 ) Q dt () t C () t In whch Q the dcharge and C the volume concentraton. The ndexe and o relate to the nflow and outflow repectvely.

6 1 tet 5: Q=.1 m 3 /, C n =.21, d 5 =15 µm.9 OV flux OV cum.8.7 OV flux, OV cum [ ] Tme [] Fg. 5 Overflow lo a functon of tme durng tet 5 Fg. 5 how both meaured relaton for the overflow lo a functon of tme. Th relaton typcal for mot of the experment; the loe ncreae gradually durng tme. From th follow that the loadng tme not uffcent to acheve a tatonary tuaton n mot cae. 3.3 Overflow rate In the prevou chapter the overflow loe were hown a functon of tme. It wll now be nvetgated whch parameter wll nfluence thee loe. It known for a long tme that the ettlng effcency of a hopper largely nfluenced by the overflow rate or dcharge per unt of urface area of the ettlng zone (Camp, 1946). The overflow rate (or hopper load parameter) defned a: Q v = ( 3 ) BL A drect relaton between th quantty and loe cannot be expected for dfferent gran ze nce th nfluence not ncluded n th parameter. Th can be acheved when the overflow rate dvded by the ettlng velocty of the and gran. In that cae the dmenonle hopper load parameter found. v H * = ( 4 ) w The ettlng or fall velocty apart from the gran properte (ze, hape etc.) nfluenced by the concentraton due to hndered ettlement. If the relaton of Rchardon and Zak, (1954) ued, the hopper load parameter can be wrtten a: Q H* = ( 5 ) BL w ( 1 ) n c In th relaton w the fall velocty of a ngle gran, c the concentraton and the exponent n wll depend on the gran ze. Mot experment were performed on 15 mcron and. In th cae the exponent wll be between The meaured cumulatve overflow lo at the end of the tet, o wth a fully loaded hopper, wll now be plotted veru the hopper load parameter n Fg. 6.

7 OV cum [ ] mcron 15 mcron H* [ ] Fg. 6 Cumulatve overflow lo a functon of the hopper load parameter H* Th fgure how clearly that, a can be expected, the loe ncreae wth the hopper load parameter though a lot of catter preent and the reult of the 14 and 15 mcron do not ft entrely. Intead of comparng velocte a parameter can be derved baed on and fluxe. In that cae the andflux n the nflow can be compared wth the ettlng andflux. The maflow n the nflow equal: The ettlng maflux equal: ed n = ρ QC ( 6 ) n ( 1 n ) BLved = ρ ( 7 ) In th equaton n the poroty, ρ the denty of the gran and v ed the edmentaton velocty whch defned a the vertcal velocty of the andbed, the nterface between the ettled and and and the mxture above. The edmentaton velocty (ncludng hndered ettlng) follow from (when the eroon neglected): v ed ( 1 c ) b n w c b b = ( 8 ) 1 n c Now the hopper load parameter S* wll be defned a the rato between the nflowng and ettlng andflux : S* = n ed 1 n c = 1 n b Qcn BLc w b Problem that the concentraton at the bottom not known a pror. A a frt approxmaton c b =c n wll be ued to plot the reult from a functon of S* n Fg. 7. c = c n b 1 n 1 n c b H * ( 9 )

8 OV cum [ ] mcron 15 mcron S* [ ] Fg. 7 Cumulatve overflow lo a functon of the hopper load parameter H* It clear that a much better relaton acheved ung the hopper load parameter baed on the and fluxe. The bet ft through the data pont can be expreed a: OV cum ( S*.43) =.39 ( 1 ) Although th relaton gve a reaonable decrpton of the meaured cumulatve overflow loe, t not yet clear f the relaton vald on another cale. Furthermore the nfluence of the loadng and overflow ytem not ncluded n the defned hopper load parameter, though Fg. 7 how that, at leat for the experment, th nfluence n clearly of mnor mportance compared wth the hopper load parameter. The hape of the gran ze dtrbuton not ncluded ether and t wll be hown later that th ha an mportant nfluence on the loe. 4 NUMERICAL MODELLING 4.1 Overvew of extng model In the pat a number of model to decrbe the hopper edmentaton proce are publhed. Thee model were all baed on the deal ettlement ban theory of Camp (1946) and Dobbn (1944). In th theory the hopper dvded n three area: the nflow, outflow and ettlng ecton. From the nflow ecton the mxture flow over the total depth (lke n rver flow) n the ettlng ecton. Both the flowfeld a the dffuon coeffcent are baed on velocty (unform or logarthmc) over the total depth. Vlablom and Medema (1995) extended th theory wth the nfluence of hndered ettlng and the nfluence of the rng and bed. Due to the rng and bed, horzontal velocty ncreae durng loadng whch lead to ncreaed cour. The effect on the overflow loe however lmted nce t aumed that velocty unform over depth and therefor apart from the very lat moment wll reman at a low value. More recently Ojen (1999) extended th model by addng dynamc to the ytem. In the Vlablom and Medema model the concentraton n the hopper alway equal to the nflow concentraton and outflow concentraton react ntantaneouly on the calculated ettlng effcency. Ojen add the tme effect by regardng the hopper a an deal mxng veel. The calculated concentraton n the hopper ued for the ettlng effcency calculaton. The extenon an evdent mprovement, nce t enable for ntance the nfluence of overflow level varaton on the calculaton. The ba of the method however tll the Camp theory that baed on a flowfeld and turbulence dtrbuton not accordng to realty a wa hown n par Introducng the new model In par. 3.1 wa mentoned that apart from the nflow ecton, near the bottom and near the water urface, the flow n the upended part of the hopper bacally one-dmenonal. In horzontal drecton the (meaured)

9 concentraton very unform (vertcally layered). Baed on th oberved flow feld a one-dmenonal model n the vertcal drecton (1DV) wa developed. In Fg. 8 the chemated flowfeld n the hopper ketched. We can dtnguh four dfferent area n th fgure From bottom to top: 1. Settled and 2. Area where and uppled to the model (mplfcaton of the denty current) 3. Supenon 4. Overflow ecton (the overflow ecton normally preent at one or two locaton unformly dtrbuted over the total urface) In the area 2 above the bottom the nflowng andflux precrbed. A part (dependng on gran ze and local concentraton) wll ettle nto zone 1. The remander wll be tranported nto zone 3. At the top (area 4) the and can ecape nto the overflow. The concentraton development n zone 3 decrbed wth the advecton-dffuon equaton for all fracton. The theory wll be outlned n the next paragraph. Lke all model th model mplfe realty: The (poble) eroon or decreaed edmentaton due to the bottom hear tre from the denty current not taken nto account. The upenon layer uppled wth a and-water mxture wth a concentraton and dcharge (pont B n Fg. 4). It aumed that thee quantte at th locaton are the ame a at the nflow locaton n the hopper (pont A n Fg. 4). In realty th wll not be the cae nce due to entranment between pont A and B mxng wll take place between the nflow ecton and the upended ecton. Reducton of the effectve hopper area due to the preence of an eroon crater not taken nto account. The and unformly dtrbuted over the total urface of the hopper, o n fact an deal nflow ytem created (an nfnte number of nflow pont equally dvded over the total hopper area). In realty the nflow only located n a fnte number of locaton (n practce only at one locaton) and horzontal edment tranport mut dtrbute the and over the hopper urface. Th horzontal tranport accompaned by a horzontal mxture velocty whch, when above a certan threhold value, can reduce the edmentaton velocty. Due to cale effect th mechanm wll not play an mportant role at the model hopper edmentaton. Intead of the horzontal one-dmenonal approach of the Camp-lke model wth a horzontal upply of and on one de and overflow on the other, th model upple and from the bottom (fed by the denty current) Fg. 8 Defnton 1DV Model and the overflow wll be located at the top. It wll be hown that th wll mplement the nfluence of the hopper load parameter and the mutual nteracton of the dfferent gran ze of the partcle ze dtrbuton n a relatve mple way. The latter effect totally abent n the Camp model; every fracton calculated ndependently. 4.3 Bac equaton of the 1DV model The vertcal tranport of edment zone 3 decrbed wth the one-dmenonal advecton-dffuon equaton. Ung the gran-ze dtrbuton the ncomng and flux can be dtrbuted over the dfferent fracton. The cumulatve partcle ze dtrbuton (PSD) ued n the model to take the dfferent granze nto account. If the PSD preented wth N+1 pont N fracton are ued. The advecton-dffuon equaton for one fracton can be wrtten a: c t = z c ( c v z, ) + ε z + q z In th equaton c the concentraton and v z, the vertcal velocty of a certan fracton. The vertcal dffuon coeffcent repreented wth ε z. The equaton nclude a ource term q, whch ued to nert the edment nflux nto the ytem. If the equaton olved for a mono-zed upenon (only one gran dameter preent), the fall velocty for that gran ze can be ubttuted for v z. The fall velocty of a gran a functon the gran properte and the z ( 11 )

10 concentraton. In general th relaton wrtten a the product of the fall velocty of a ngle gran w and a functon of the concentraton. One of the earlet and mot frequently ued relaton the well-known Rchardon and Zak (1954) formulaton: w = w( 1 c) n ( 12 ) When a mult-zed mxture mulated, the tuaton become more complcated nce the dfferent fracton wll have a mutual nfluence. The mplet approach, often ued n numercal model ued to compute upended edment tranport, to ue the total concentraton n the reducton functon. The vertcal velocty of a certan fracton n that cae calculated wth eq. ( 13 ). (N the number of fracton, and n the exponent vald for that fracton). The exponent n a functon of the Reynold number defned a Re=w D/ν, ee (Rchardon and Zak (1954) and (Selm et al., 1983). n N v = w (1 c) ; c = c ( 13 ) z,, Th approach however not correct becaue the effect of the return flow of large partcle on the mall partcle not ncluded. Wth th mple relaton all partcle wll move n the ame drecton, whle n realty t poble that mall partcle move n oppote drecton due to the return flow of the large partcle. When the effect of the gran ze to be modelled correctly a more ophtcated approach needed. A better approach to aume that every gran ettle wth a certan lp velocty relatve to the flud velocty v w (Mrza and Rchardon,1979), : The lp velocty calculated accordng to Mrza and Rchardon (1979) wth: v z, w, = 1 = v w ( 14 ) w,, n 1 ( 1 c) = w ( 15 ) Th reult follow drectly from the hndered ettlng equaton nce the ettlng partcle create a return flow that ha to flow through an area 1 c. In th approach the nfluence between two or more dfferent fracton preent wth the total concentraton and the return flow of all partcle. The partcle-partcle nteracton between dfferent fracton are however not ncluded and a a reult th approach doe not gve good agreement wth expermental data for partcle wth large dfference n ze (or denty). A relatve mple method to nclude the nterpartcle nfluence for dfferent fracton wa propoed by Selm, et al (1983). In the fall velocty w the effect of the preence of the maller gran on the fall velocty of the larger gran taken nto account by a correcton of the pecfc denty for thee gran. In general the fall velocty of a gran d k follow from: The pecfc denty follow n that cae from: k ρ ρ = ρ up up w = f (d,, ) ( 16 ),k k k k 1 k 1 ; ρ up = ρ c + ρ w 1 c ( 17 ) = 1 = 1 In other word: It aumed that a gran wth a certan ze ettle n a upenon formed by the gran wth a maller ze. To olve the advecton-dffuon equaton for all gran ze the combned acton of all gran ze mut be quantfed. Th can be done ung the volume balance n vertcal drecton for both and and water: N N Q + n v c 1 c = = v w w ( 18 ) A z, = 1 = 1 Pleae note that the vertcal bulk or mxture velocty w baed on the dcharge nto the hopper and the total hopper area a a reult from the mplfcaton of par Together wth ( 14 ) th lat relaton form a ytem of N+1 equaton wth N+1 unknown (v w and v z, ). Wth ome mathematc the followng mple relaton can be derved form th ytem:

11 Subttuton n ( 14 ) lead to the followng reult: N v = w + c w ( 19 ) w j= 1 j, j v z, N = w + c j= 1 j w, j w, ( 2 ) Apart from the vertcal bulk velocty w th reult wa already publhed by (Smth, 1966). When at a certan tme the concentraton of all fracton known, the rght-hand de of th equaton known a well and the gran velocty can be calculated. Ung the gran velocte on tme t the advecton-dffuon equaton can be olved for the next tme tep. 4.4 Numercal Procedure For every fracton the partal dfferental equaton ( 11 ) olved ung a fnte dfference cheme. A emmplct approach ued. The frt term n of the rght hand de (advecton) treated explctly wth a frt order upwnd cheme or wth central dfference, the econd term (dffuon) treated mplctly wth central dfference. Th lead to a tr-dagonal ytem of equaton. The numercal procedure a follow: 1. At the begnnng of loadng the concentraton dtrbuton known for all fracton. In mot cae c= over total heght (but can be arbtrarly choen). 2. Ung ( 2 ) the vertcal velocte of the gran can be calculated. 3. Subequently ung the fnte dfference method all fracton are olved ndependently for one tme-tep. Th lead to a new concentraton dtrbuton on tme t+ t. 4. Step 2 and 3 are repeated untl the hopper flled to certan level or for a certan total mulaton tme. The ytem can be olved when the followng parameter and condton are known: 1. The ntal condton (value of all quantte at t=) 2. The boundary condton.. 3. The value of the dffuon coeffcent ε z. a a functon of heght z and tme t. 4. The value of the vertcal bulk velocty, needed to calculate the gran velocty v z,, ee equaton ( 2 ). 5. The gran ze dtrbuton. 6. The value of q, the ncomng andflux per fracton. A detaled decrpton of the numercal procedure (Fnte Dfference Method) beyond the cope of th paper. Reference made to Ferzger & Perć (1999). The boundary condton and dffuon coeffcent deerve however ome extra attenton. 4.5 Boundary Condton At the bottom the net edmentaton flux (dependng on the concentraton at the bottom) wll be calculated, and th amount wll be tored n the bed. At the water urface normally the andflux wll be put to zero. In th cae at the urface the andflux wll be precrbed to mulate the overflow. ( v > Q ) = v z,c z, n > ( 21 ) The two condton mut be ncluded, nce overflow wll only take place when mxture dcharged n the hopper, and to prevent the urface pont from actng a a ource term n cae the vertcal and velocty drected downward. 4.6 Turbulent Dffuon Coeffcent It common to relate the dffuon coeffcent to the turbulent eddy vcoty ung the Schmdt number σ t : ν t ε z = ( 22 ) σ Unlke the eddy vcoty, whch not a real flud property nce t depend trongly on the flow feld, the Schmdt number only vare lttle acro any flow and alo lttle from flow to flow (Rod, 1993). Ung the above relaton we have hfted the problem toward the determnaton of the eddy vcoty. When we focu on the tuaton near the bottom n the denty current the order of magntude of th parameter durng the tet can be etmated ung the mxng length theory of Prandtl: t

12 2 u ν t = m ( 23 ) z The mxng length ncreae wth dtance from the bottom. When δ the thckne of the denty current the mxng length can be etmated a.9 δ (Rod, 1993). Typcal value meaured from the experment are: δ =.25 m and u/ z = Th lead to an eddy vcoty of.13 m 2 /. 4.7 Comparon between 1DV model and experment Model reult wll be compared wth two experment: Tet 5 and Tet 6. For both tet 15 mcron and wa ued. The PSD chemated to 7 fracton. The followng table how the value ued n the calculaton:. Operatonal parameter: Tet 5 Tet 6 Dcharge m 3 / Average Denty kg/m3 Overflow level m Waterlevel at tart tet m Durng the calculaton the turbulent dffuon coeffcent wa contant over the heght and equal to.1 m 2 /. In Fg. 9 and Dameter µm Cum. Percentage Fg. 1 the meaured nflow concentraton and the meaured and calculated outflow concentraton plotted a functon of tme. The reult of two calculaton are hown. Computaton wth the 7 fracton hown above and a calculaton wth one partcle ze equal to the d 5 of the PSD. The reult from the mono-zed mxture underetmate the overflow concentraton durng the larget part of the loadng tme (whch lead to a lower cumulatve overflow lo). The fnal outflow concentraton agree however wth the meaurement. Tet 6 tet wa performed at maxmum (for the ntallaton) ncomng and flux. Due to the hgh andflux the meaured concentraton n the overflow reman almot contant durng ome tme. The model very well reproduce th phenomenon (whch only occur at very hgh or low andflux). At the end of the tet the ncomng and flux decreae due to a lack of and n the torage tank (the overflow loe durng the tet were hgh, o a lot of and wa needed). A a reult of the decreang ncomng andflux, the overflow concentraton decreae a well. The model predct thee phenomena very well. Fg. 9 Comparon between 1DV model and experment for tet 5

13 Fg. 1 Comparon between 1DV model and experment for tet 6 5 CONCLUSION Large-cale experment have been performed to tudy the phycal proce nde the hopper. Concentraton and velocty dtrbuton were meaured and provded a good mpreon of the flowfeld n the hopper. When a hopper load parameter defned a the rato between the nflowng and ettlng andflux (S* parameter) a good relaton found wth the meaured cumulatve overflow loe. The oberved flow feld formed the ba of the one-dmenonal model that developed. In th model the nfluence of the hopper load parameter and gran ze dtrbuton mplemented. The agreement of the model and the experment good. The nfluence of the velocty n the denty current on the edmentaton velocty not ncluded n the model. Addtonal nvetgaton wll be carred out n the future (experment and two-dmenonal numercal modellng) to determne the poble nfluence. ACKNOWLEDGEMENT The fnancal upport of the VBKO (Verengng van Waterbouwer n Bagger-, Kut en Oeverwerken) gratefully acknowledged. REFERENCES Camp, T.R. (1946), Sedmentaton and the degn of ettlng tank, ASCE tran, paper 2285, pp Dobbn, W.E. (1944), Effect of Turbulence on Sedmentaton, ASCE Tran, 19443, paper no Ferzger, J.H., Perć, (1999),Computatonal Method for Flud Dynamc, Sprnger Verlag. Mrza, S, Rchardon, J.F., (1979), Sedmentaton of Supenon of Partcle of two or more ze, Chemcal Engneerng Scence, Vol. 34, pp , Oojen, S.C.,(1999), Addng dynamc to the Camp model for calculaton of overflow loe, Terra et Aqua, no 76. Rchardon, J.F., Zak, W.N (1954), Sedmentaton and Fludzaton: I,Tran. Int. Chem. Eng, 32, 35. Selm, M.S., Kothar, A.C., Turan R.M,(1983), Sedmentaton of Multzed Partcle n Concentrated Supenon, AIChE J,m 29, 129. Rod,W.,(1993),Turbulence Model and ther Applcaton n Hydraulc, A tate of the art revew, IAHR, Thrd Edton. Smth, T.N.,(1966), The edmentaton of partcle havng a dperon of ze, Tran. Int. Chem. Eng., 44, T153. Vlablom, W.J.,Medema, S.A., (1995), A theory for determnng edmentaton and overflow loe n hopper, Proc. of the 14th World Dredgng Congre, Amterdam 1995.