Erosion of Sediment Beds by Turbulent Wall Jets in Combined-Sewer-Overflow Reservoirs

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1 Esin f Sediment Beds by Tubulent Wall Jets in Cmbined-Sewe-Oveflw Resevis Octavi E. Sequeis a, Yak Niñ b, and Macel H. Gacia c a Ven Te Chw Hydsystems Laaty, Depatment f Civil and Envinmental Engineeing, Univesity f Illinis at Ubana-Champaign, 205 Nth Mathews Ave., Ubana, IL eseque@uiuc.edu b Assciate Pfess, Depatment f Civil Engineeing, Univesity f Chile, c Cheste and Helen Siess Pfess, and Diect, Ven Te Chw Hydsystems Laaty, Depatment f Civil and Envinmental Engineeing, Univesity f Illinis at Ubana-Champaign Abstact: Sediment management with the help f wate jets in cmbined-sewe-veflw (CSOs) esevis in the Chicag aea has mtivated this wk. Esin caused by single and multiple submeged cicula tubulent wall jets n a ganula (nn chesive) sediment bed f finite thickness laying n a fied unday was studied with the help f laaty epeiments. Plane tubulent wall jets wee als tested n sewe sediment in de t detemine its citical shea stess. Thugh nt stngly chesive this sewe sediment pesented sme flculatin. Regading cicula jets, diffeent cmbinatins f jet diamete, jet sepaatin, and ati between sediment thickness and jet diamete wee tested. F ganula sediments esults shw a elatin between dimensinless paametes chaacteizing the steady state bed pfile and the densimetic paticle Fude numbe F given by the velcity at the nzzle, and the effective diamete and submeged specific density f the sediment. Sewe sediment is bette chaacteized by the citical shea stess beynd which tanspt ccus. F th kinds f sediment, evlutin f scu with time cnfims pevius studies whee the esin was fund t initially gw with the lgaithm f time up t a cetain efeence time. This time, made dimensinless with a time scale t c invlving the vlume f sediment scued and the ate f esin, was als elated t the densimetic Fude numbe in the studies invlving ganula (nn chesive) sediment. Keywds: Submeged jets, Esin, Scu, Chesinless sediment, Sewe sediment.. INTRODUCTION The use f jets t pevent sedimentatin at the ttm f esevis and has is nt a ecent idea but it has nt been fequently implemented. Depending n the aea t be cleaned, an aay f jets can be set t emve the newly depsited sediments. Pevius laaty and field epeiments have shwn that the esive actin f a submeged wall jet is a functin f the jet diamete, velcity, and ientatin elative t the ttm [Van Dn et al. 975, Jenkins 98]. The limit f the scu patten can be cnsideed t be an isline f cnstant shea stess with a value equivalent t the theshld ttm stess. Hweve, estimating the theshld shea stess f a cetain mateial pesents uncetainties. An altenative appach t chaacteize the espnse f the sediment t jet flw, in the case f nn-chesive sediment, is t use the densimetic Fude numbe assciated with a epesentative diamete. The densimetic Fude numbe F is defined as U /(gd i ρ/ρ) /2, whee U is the jet velcity at the nzzle, g the acceleatin due t gavity, d i a epesentative size f the bed mateial, and ρ is the diffeence between the density f the bed mateial ρ s and the density f the fluid ρ. This appach was develped by seveal investigats studying a simila pblem als fund in hydaulic engineeing, namely, the esin f a semi-infinite laye f sediment due t submeged cicula wall jets [Rajaatnam & Bey 977]. The epesentative dimensins f the scued bed wee fund t be functin f F. The eseach epted in this pape fcused n: a) finding the chaacteistics f sediment typical f cmbined sewe veflw esevis, b) estimating the esin f a laye f sediment f finite thickness esting upn a fied unday, with the gal f applying this technlgy t the pjected McCk

2 esevi f cmbined sewe veflws in Chicag, Illinis. Being the ttm f the esevi f limestne ck, the use f a fied unday in the epeiments was thught t be apppiate. Cmpaed t the fast scu f the sediment bed, the esin f the ttm by jets peating f a sht peid f time is cnsideed t be negligible. This wk etends pevius eseach n jet scu fm single t multiple jets. Jet diamete and sepaatin wee vaied in de t test the validity f the dimensinless equatins deived. The dischages wee selected t cve a wide ange f F mainly unde highly tubulent cnditins. The evlutin f the scu with time is als addessed. 2. SEWER SEDIMENT EXPERIMENTS 2. Sewe Sediment Chaacteizatin The sewe sediment was pvided by the Metplitan Wate Reclamatin Distict f Geate Chicag, the samples wee taken fm O Hae esevi. A LISST-ST lase-diffactin instument was used t analyse its ppeties [Sequeis et al. 2005]. Tests with and withut disaggegated samples wee made in de t estimate the size f aggegate fmatin. The mean size f paticles belnging t the iginal samples (nt disaggegated) was aut 24 µm, while cespnding values f disaggegated samples wee 0.8 µm. The mean size f the aggegates fund in the iginal sediment samples was estimated t be aut 84 µm. Given the ange f paticles sizes fund in this study, the sediment may pesent sme chesivity. Nevetheless epeiments pefmed in an annula flume shwed that the sediment was easily eded by shea stesses as lw as 0.06 N/m 2. These facts indicate that this sewe sediment can neithe be classified as ganula due t the small size f its paticles and aggegates and the tendency t fm flcks, n as chesive, because it lacks the stng chesin that chaacteizes clay and the simila sediments. 2.2 Citical Shea Stess Deteminatin The deteminatin f the citical shea stess was based n the tests pefmed by Sequeis [2004] n the scu caused by plane wall jets upn a laye f finite thickness f sewe sediment (see Figue ). Fllwing Mazuek et al. [2003] the asympttic length f esin, m, can be epessed as: [( λ λc ) λc m = f ] () whee λ = ρu 2 is elated t the ttm shea stess, U is the velcity at the nzzle, b is the thickness f the nzzle, ρ is the density f the eding fluid, λ c is elated t τ c is the citical shea stess f the sil belw which n significant esin happens. The ttm shea stess τ b is elated t the velcity as τ b = C f ρu 2 /2 whee C f epesents the nndimensinal skin fictin cefficient. It is elated t the me cmmn Dacy Weisbach fictin fact f as f = 4C f. Q sluice gate U m sediment Figue : Plane wall jet tests n sewe sediment. Figue 2 shws the dependence f the final scu length n λ. The asympttic scu length m was aveaged at thee psitins alng the fnt. The citical value f λ can be estimated by etaplating the data t the cnditin m = 0. Clse bsevatin f Figue 2 indicates this etaplatin shuld be pefmed with cae. In the pimity f the abscisses ais the pints appea t fllw a cuve difting away fm the linea tendency cespnding t high Reynlds numbe tests. Applying the least squae methd the pwe law that yields the best fit is: [( λ λ )/ λ ] m b = 5.08 (2) c c whee λ c = 3.3 Pa. This is shwn in Figue 3. It shuld be mentined that because f the limited set f data available it may be bette t define a ange f λ c athe than a single value. In any case thee is n need t change the analysis hee pusued. m / λ [N/m2] Figue 2: Dimensinless scu length as vesus λ. m / Equatin (λ λc)/λc Figue 3: Asympttic scu length as a functin f (λ-λ c )/ λ c and pwe-law best fit (Eq. 2). Fm Myes et al. [963] the fictin cefficient C f = 0.0 f u ange f Reynlds numbes. This gives 2

3 a value f citical shea stess τ c = 0.02 Pa, which esults t be insignificant cmpaed t esults f chesive sil btained by Mazuek et al. [2003], but has the same de f magnitude as the esults btained in the annula flume. The evlutin f the scu with time was fund t be analgus t that f cicula jets and will be teated belw. 3. GRANULAR SEDIMENT EXPERIMENTS 3. Multiple Jet Studies The epeiments invlving sewe sediment wee nt etended t multiple jets mainly t avid its hazadus manipulatin in the laaty lage facilities. Fine ganula mitues wee emplyed instead as a fist appimatin t the pblem. Table displays the chaacteistic sizes and the dimensinless gemetic standad deviatin, defined as σ g = (d 84 /d 6 ) 0.5, f each mateial. The specific gavity f all mateials was Mateial d 50 d 95 d 84 d 6 σ g.3 d 50 σ g [µm] [µm] [µm] [µm] [µm] Table : Chaacteistic diametes f the sediments A linea aay f submeged tubulent cicula wall jets paallel t and esting n a fied unday was applied upn a laye f sediment esting n the same fied unday. The diamete f the jets and the distance between them wee tw f the vaiables studied. Single jet tests wee als caied ut t cmpae the scu pattens f jets acting alne and in paallel. The epeiments wee caied ut ve a steel plate 5.4 m lng and 2.6 m wide, lcated inside a wate tank 7.3 m lng, 2.7 m wide, and 2.3 m high. A pump cnveyed the wate fm a secnday tank placed neaby t the jet aay (see Figue 4). In mst cases the dischage Q was measued using a magnetic flwmete having a capacity f up t 20 l/s, lcated in the supply pipe. In the few epeiments f which the dischage was lwe than 0.0 l/s, the flw was btained by measuing the time equied t fill a cetain vlume f wate. A 50.8 mm manifld having banches sepaated 0.3 m cmpsed the jet system. The use f theaded jints facilitated the ceatin f diffeent aays, by mdifying jet diamete and spacing. The manifld was cmpised f up t 3 jets. The adjustable slpe f the ttm plate was set at.5%. A laye f sediment f cnstant thickness, b s, placed n the plate, set the initial cnditin. Figue 5 depicts a geneic sketch f single jet epeiment. The wate depth at the nzzle was fied at 0.35 m f all the epeiments. Once eleased, the jet dags the wate ave it, geneating entainment f ambient fluid int the main flw. In a elated study [Sequeis 2004] velcity pfiles wee measued using acustic Dpple velcimetes and shwed a gd fit t the wall jet empiical equatin ppsed by Vehff [963]. The epeiments wee un until a steady appimate asympttic state scu cnditin was eached. Once the jets wee stpped, measuements f final scu wee taken using a digital camea. A 3-mm definitin gid was placed at the ttm t impve the accuacy f the data cllectin pcess. Sme epeiments wee als ecded t study the evlutin f the scu with time. supply tank tp view f a single jet epeiment y z pump supply line 7.3 m jets 0.35 m veflw 2.6 m 2.7 m Figue 4: Set-up f the epeiments U φ φ m m y Initial Cnditin Final Cnditin ym 5.4 m 2.3 m h bs lngitudinal css sectins at the centeline Figue 5: Sketch f a single jet epeiment The thickness f the sediment laye was changed in diffeent epeiments t study the influence f the ati between jet diamete and bed sediment thickness. Diffeent dischages wee used in de t detemine the scu patten f a wide ange f densimetic Fude numbes. A detailed tabulated summay f the cnditins f all 58 epeiments can be fund at Sequeis et al. [in pess]. 3.2 Asympttic values analysis The scu patten ceated by a single jet can be chaacteized by measuing cetain paametes, e.g., the maimum scu length, m ; the maimum scu width, y m ; the distance fm the nzzle t the pint 3

4 whee the maimum width ccus, y ; the angle φ fmed by the jet dwnsteam f the nzzle. Stating fm the nzzle thee is a egin in the patten f esin whee the scu width gws linealy as twice the distance fm the nzzle times the tangent f φ/2. This ate f incease in scu width is maintained up t a cetain distance fm the nzzle, φ. Beynd this pint, due t lateal dissipatin f mmentum, the jet is n lnge able t keep the linea ate f lateal esin and the scu width gws at a lwe ate until it eaches its maimum value, y m, at y. Dwnsteam fm this pint the width deceases until it vanishes at the tip f the scu hle. All these paametes used t define the gemety and dimensins f the scu hle ceated by the jets can be seen in Figue 5. At the asympttic state the jet can n lnge tanspt sediment because its mmentum has been dissipated thugh fictin, and the scu undaies emain unmved. At this pint m, y m, φ, and y, becme m, y m, φ, and y, espectively. In case f multiple jets, the distance between jet nzzles is dented d j. The the paametes emain the same, nting that, depending n the distance between nzzles and the Fude numbe, the scu f diffeent jets may may nt be in supepsitin. The maimum length f esin f a single jet at the steady state, dented m, can be epessed as the fllwing functinal elatinship: m = f (U,b, ρ, µ,g ρ, d 95,b s,h) (3) Applying dimensinal analysis, it can be shwn that: m b = f 2 U gd 95 ρ U bs h,,,, (4) ρ ν b d 95 whee U is the velcity at the nzzle, b is the thickness f the nzzle, ρ and µ ae the density and dynamic viscsity f the eding fluid espectively, ρ is the diffeence between the density f the bed mateial and that f the fluid ρ, d 95 is the epesentative size f the bed mateial in this situatin, b s is the initial thickness the sediment laye, and h is the wate depth, F = U /(gd 95 ρ/ρ) /2, and R = U b /ν ae the densimetic paticle Fude numbe and the Reynlds numbe at the nzzle, espectively. The densimetic Fude numbe, was defined using, nt the median d 50 as the effective diamete, but d 95. Adeibigbe and Rajaatnam [998] shwed that n the esin f well-gaded mitues the mst significant gains ae the case nes and nt thse f sizes cmpaable t the median diamete that culd be used t chaacteize the gain size distibutin. Epsed t a cetain flw, the smalle gains ae me easily mved while the case gains emain in place. This is knwn as aming, because the tp laye f the bed will eventually becme a egin fmed mainly by case gains with just a few smalle gains. The size f the iginal sediment mitue that best celates with the scu length was fund t be d 95 by Adeibigbe and Rajaatnam [998], which accding t them is equivalent t the median size f the am cat. An altenative appach is t include the gemetic standad deviatin in the cmputatin f F, Adeibigbe and Rajaatnam [998] nted that using d 50 σ g.3 as a substitute f d 95 in the definitin f the densimetic Fude numbe yields an equivalent celatin f the epeimental data. Table shws the altenative vaiable d 50 σ g.3 that culd be used instead f d 95 t take accunt f the sediment gadatin in the pesent epeiments. Beuses and Raudkivi [99] set the limit f the gemetic standad deviatin beynd which a mitue can be cnsideed t be nn-unifm as.35. Mateials and 2 emplyed hee wee thus epected t am and that was cnfimed when building the dimensinless cuves. Mateial 3 was nt epected t am given its unifmity, and, indeed, n significant diffeences wee fund when chsing eithe d 95 d 50 as the effective diamete. Rajaatnam [976] shwed that the effect f the Reynlds numbe can be neglected if it is lage than a few thusands (R > ). Epeiments cnducted by Rajaatnam and Bey [977] pved that the effect f b /d 95 can be neglected f lage enugh values f this ati, such as, and even lwe than, thse in the pesent epeiments. Adeibigbe and Rajaatnam [998] fund that the effect f submegence is nt imptant when the mean velcity field in the flw is simila t that f a classical (infinitely submeged) wall jet [Rajaatnam, 976] and the flw depth, n aveage, is at least fu times the dune height. In the cuent study the effect f the submegence was neglected based n simila easns. The velcity field was simila t that f the classical wall jet as eplained peviusly. The flw depth h was at least 5.8 times the initial thickness f the sediment bed b s, 4.6 times the jet diamete b, and, in the epeiments whee lngitudinal pfiles wee measued, at least 4.6 times the idge height. Finally it was fund that the ati b s /b has n influence n the steady state pfiles as lng as it is kept at least belw 5. Unde these cnditins Equatin 4 can be educed t: ( ) m b = f 3 F (5) A simila analysis can be dne t find analgus dimensinless elatins f the the chaacteistic dimensins f the scu hle, y m, y, and φ. Mateials and 2 have cetain amunt f silt, which is pne t sme kind f chesive behavi, like esin f chunks athe than just paticles [Mazuek et al. 2003]. Duing the cuent epeiments nt such chesive behavi was bseved. As a esult chesive effects wee neglected. F chesin 4

5 dminated sils a dimensinal analysis using the citical shea stess f the sil athe than a chaacteistic gain size shuld be caied ut. In case f studying nt a single jet but an aay f them, the same analysis just pesented hlds, ecept that thee is anthe vaiable that must be incpated, i.e., the jet spacing, d j. It can be epessed in dimensinless fm as d j /b. Figue 6 shws the dimensinless maimum scu length vesus F cmputed with d 95 sted using the ati d j /b. Tests cespnding t diffeent effective diametes d 95 and diffeent jet nzzle diametes b cllapse faily well t a single cuve. This cnfims the validity f neglecting the effect f the dimensinless paamete b /d 95 n jet scu. 000 m / 00 0 Equatin 6 dj/ = single jet F Figue 6: Asympttic dimensinless value f maimum scu length as a functin f F. The tests with lw F whse cllapse is p cespnd t 3.5 < F < 9. and have a Reynlds numbe ange f 2900 < R < This ange is within that fund by Rajaatnam [976] f which the viscus effects ae still cnsideable, which culd help eplaining the p cllapse. Hence lw F tests wee ecluded fm the analysis. Equatin 6 fits the pesent data f F lage than 9. = (6) 0.75 m 3.5F The behavi f y m /b, y /b, and φ /b, is epesented by y m /b = 0.47F 0.96, y /b = 2.4F 0.74, φ /b =.87F 0.65 espectively. When me than ne jet is cmbined, a new vaiable entes the scene, the distance between utlets. Depending n hw clse the nzzles ae lcated t each the, the flw field might be alteed enugh t cause a significant incement in the esive capacity. The clse the jets ae t each the, the clse t the nzzle the single velcity fields will stat t be affected by neighing jets and, cnsequently, the clse the flw will tend t be 2D. Pani and Dash [983] epeimented with atis d j /b lwe than 3. F these lw atis the flw decays like that f the plane wall jet, pviding thee ae enugh jets t pevent the 2D flw fm speading lateally. Values f the dimensinless sepaatin length in the pesent epeiments (6.3<d j /b <37.) ae highe than thse f Pani and Dash (d j /b <3). This fact is imptant t undestand why, in the pesent tests, the maimum lngitudinal etent f the scu achieved by a single jet is, n aveage, n lnge than the maimum lngitudinal etent f the scu pduced by multiple jets unde the same cnditins (see Figue 6). If the utlets ae spaced beynd a cetain distance, the flw field f a single jet will be nly affected fa away fm the nzzle and in just a small amunt, nt enugh t incease the ttm shea stess beynd the theshld value. Tests invlving lwe jet spacing wee nt cnducted. Being the scpe f this study the feasibility f using wall jet aays t manage sediment depsits n esevis, the inteest was placed n hw fa the jets culd be lcated t efficiently clean a cetain aea with the lwest pssible dischage minimizing velapping between jet scus. 3.3 Evlutin f scu with time The develpment f scu with time was studied f sme tests. As Rajaatnam and Bey [977] nted the esin length inceases with the lgaithm f time befe the asympttic state is eached. The scu length, thus, is pptinal t the lgaithm f time up t a time t* beynd which the slpe f the scu-time cuve stats deceasing and finally becmes ze at the asympttic steady state. This same behavi was als bseved in the pesent study, even thugh the esin patten is diffeent. The length used t evaluate the fnt mvement alng time was m. T cllapse the individual pfiles t a geneal cuve, the scu scale was chsen as m. The time scale was taken as t*, the time whee the scu stps gwing pptinally t the lgaithmic f time. Figue 7 shws a plt f m / m vesus t/t* f the tests whee t* culd be btained. When t equals t*, m is appimately 0.95 m ; and m is m when t is appimately 5 times t* (t /t* 5). This means that it is pssible t pedict the asympttic time t by knwing t* withut the need t un the whle epeiment. Thus t* gives a measue f hw lng the scu pcess may last befe eaching the asympttic state. In de t make the t* dimensinless, a time scale is equied. The time it takes the jet t scu the asympttic pfile can be defined as t c = V/Q s, whee V is the ttal scued vlume and Q s is an aveage scu ate. An estimatin f the ecavated vlume pe unit width is b s m, whee b s is the initial thickness f the bed and m is the asympttic scu length. The chaacteistic time is then given by t c = b s m /q s whee q s is the aveage bedlad ate pe unit width. Sequeis et al. [in pess] ppsed the fllwing equatin f t c : t ( β ) 3/2 m b s m gr c = (7) 3 c f 8U 5

6 The paamete β depends n the natue f the jet. F cicula wall jets it can be taken as 2. [Jenkins, 98]. The fictin cefficient c f f smth undaies can be estitmated fm Myes et al. [963] as c f = m/m t/t* 0 Figue 7: Dimensinless evlutin f maimum scu length with dimensinless time. Because t * and t c wee fund t be in the same de f magnitude, it can be infeed that the chaacteistic time t c is a easnable time scale f the jet scuing pcess. This esult is elevant f design pupses, as the peatin time f the jet aay system t clean a given bed aea shuld be small enugh t keep assciated csts easnably lw, paticulaly in the case f lage bed aeas. 4. CONCLUSIONS The citical shea stess f typical sewe sediment was estimated studying the scu f plane wall jets. This mateial has special chaacteistic being neithe chesive n ganula. The esin caused by single and multiple cicula wall jets acting paallel t a fied ttm ve a ganula laye f sediment f finite thickness was studied etensively and fund t be a functin f the jet velcity, jet diamete, density f the eding fluid, and the ppeties f the sediment t be eded, in paticula its size and citical shea stess. Thee kinds f ganula sediment wee emplyed in the tests. In the asympttic state, the maimum scu length and the epesentative dimensins f the final scu hle seem t depend n F. A set f equatins was ppsed f these paametes t pedict the main dimensins f the scu given F and the diamete f the jet. Othe vaiables wee fund nt t affect the final dimensinless etent f the scu hle f the anges f gvening paametes emplyed in these epeiments. The scu was fund t initially gw with the lgaithm f time, until a efeence time dented t*, and then t tend slwly twads and asympttic value at a time t. An equatin f the time scale t c invlving the vlume f sediment scued and the ate f esin was als ppsed. 5. ACKNOWLEDGEMENTS This eseach was suppted by gants fm the Metplitan Wate Reclamatin Distict f Geate Chicag and the U.S. Amy Cps f Enginees (Chicag Distict). This suppt is gatefully acknwledged. 6. REFERENCES Adeibigbe, O. & Rajaatnam, N. (998). Effect f sediment gadatin n esin by plane tubulent wall jets. J. Hyd. Eng., ASCE, 24(0), Beuses, H.N.C. & Raudkivi, A.J. (99). Scuing. Hydaulic Stuctues Design Manual, n. 2, Int. Assc. Hyd. Res. (IAHR), A.A. Balkema, Rttedam. Nethelands. Jenkins, S.A., Inman, D.L. & Van Dn, W.G. (98). The evaluatin f sediment management pcedues. Phase IV-VI. Final Rept. SIO Refeence Seies N Scipps Institutin f Oceangaphy, La Jlla, Calif. Mazuek, K.A., Rajaatnam, N. & Seg, D.C. (2003) Scu f a chesive sil by submeged plane tubulent wall jets. J. Hyd. Res., 4(2), Myes, G.E., Schaue, J.J. & Eustis, R.H. (963). Plane tubulent wall jet flw develpment and fictin fact. Junal f Basic Engineeing, Tansactins f the ASME, 83, Pani, B.S. & Dash, R.N. (983). Thee-dimensinal wall jets fm multiple utlets. Pc. Instn Civ. Engs, Technical Nte 376, Pat 2, 75, Rajaatnam, N. (976). Tubulent Jets. Elsevie, Amstedam, The Nethelands. Rajaatnam, N. & Bey, B. (977). Esin by cicula tubulent wall jets. J. Hyd. Res., 5(3), Sequeis, O.E., (2004). Wate jet esin f a finite laye f sediment. Maste thesis, Dept f Civil and Env. Eng., Univesity f Illinis at Ubana-Champaign, Ubana, USA. Sequeis, O.E., Niñ, Y, & Gacia, M.H. (2005). Sedimentatin management in cmbined sewe veflw stage esevis using wate jets. Hyd. Eng. Seies N. 76, UILU-ENG Ven Te Chw Hydsystems Lab., Univesity f Illinis at Ubana-Champaign, Ubana, USA. Sequeis, O.E., Niñ, Y, & Gacia, M.H. Esin f finite thickness sediment beds by single and multiple cicula jets. J. Hyd. Eng., ASCE, HY2430, in pess. Van Dn, W.G., Inman, D. L. & Hais, R.W. (975). The evaluatin f sediment management pcedues. Phase I. Final Rept. SIO Refeence Seies N Scipps Institutin f Oceangaphy, La Jlla, Calif. Vehff, A. (963). The tw-dimensinal tubulent wall jet with and withut an etenal steam. Rept N. 626, Pincetn Univesity, Pincetn, USA. 6