DEVELOPMENT TECHNOLOGY UNIT Working Paper No. 41 Algebraic Modelling of the Behaviour of Hydraulic Ram-Putops TH Thomas Developnicnt Technology Usit Teparicaeut ai Bngineering. Cniversity of Warwick Cosenlry UVF VAL UK, Tel: 444 (0; 1203 523121 Fass (0) 1203 418922. eriall: du@eng warwick acak Working Paper No. 41 Algebraic Modelling of the Behaviour of Hydraulic Ram-Pumps by Dr. T.H, Thomas January 1994 Abstract: ‘The matherratica! ana ysis of hydrant aun-puorgs egan soon efter thew invention in the Jore Lith century However simple models 0° adegrate wtciescy for use ay system designers, pomp onanufaceurers.inscallers and opera il net aveileble. This paper deserihes algebraze srodels ot varying complenity for vce hy systcim acd pump eesigners and Ly ‘hose valved in aainia, iusiless aud uses. Ttsagses thats pure pls drivenipe, eather thar pomp wore ig the natural ara for mocet‘ing and for charactensing pestermerce in aprtivasions Lteraure. Retavioer is shown +0 opend nvimarity uooa theee parameters, The tinst ig A, the ratic of peak drive Mow ¢whiet, depends por tuning) 0 che aump's ouaxieum flow ‘sith is impulse weve loaced open. ‘The seucod is, the tatio of peas drive flow 70 che “Toukowski’ uw just sutficieat (9 actieve the system de'ivery ead ‘The thd is A, tie rasio of delivery head wy Onive head. The asalysis shows some of zhe trade-offs entailed in tuning, izdicawes che optimum choice ef deivepipe and exs/aics vertain Zorme of rmalfarction observable tt the tield. Several ‘rales of rhemb’ are derived, ‘The edper aso indicates reas whee: the greserorecision of veropucer simclation over syebraic modelling is desirable CONTENTS 4. Ingoduction 2 Representing System Perfor 3. Models 3.1 Algebraic und Sireclation Mausts Compared 32 Sieple Models 3s Acce‘eratian Phase Maafels 3S elivery Fhase Medel As ern Phrse Vode 26 Combining Acceieration. Delivery and Recon Phase Models 4. The Application of Algebraio Madels 4.1 Explsitsng Paenomers and Improving Pamp De 42 Ceenleing Pomp Characteristics 43 System Design 44° Tunicg 5. Conclusion A. Biklfogaphy A INTROPUCTION They paper clescribes 4 To'nber of analyte mede!s, of varying degiees of ccmaplendty, for representing Tyckaulic sam amps. Ie exes how such imadsls van bo used © aptinise ryning, expsain ansrins ehavinue, kl systern design aed Melp in he design af betict pumps ‘The hydraulic ram pump, 1 wutespomerad aserithag device, is of some wntiguity. Saving heen ‘oped oy Wliicturst, Mumegslies cul ochors arin the righizerah cencury, Although £ heyday was ¢he lave 1925 eure over oxen mamufectnrars wosklwKle sill procueang machines, “The ree pump pettoras the sane cole as 2 kow-heaul highsiliw lurbire drivirg a high-head lov-slow pump: iis however auch sumplee thay: tarbine-pimap xe 3 epeting arly 8 eng parE, eel spoof valor ‘The raat pump <awaly dyed 16 Tf ceinhings waler Zeon small ersaens 1a ineadions ‘where elwriaty is not nvilable snd engine driven pun ps woul be eostly Io operace. The: rar pamnp aiDy 3209 tes te sperates continvousty bet usually sf a law pwr level ay purapiny: Sein sore estly hieved by ather meats, NG wauis}, h gher-powersd ‘hese 9s eurretly aiT strnaiutes. tslhowing, privinisiion « revive of interest in in Sump an Ge counties anil fue «s canging orto anplics) it some iadustislised swanties 100. fone back usually aecennparied by design taneling, Rat purus, wo) why heir simple constesetion. fume aie undeigene some design es ges effezting thew ott sail performance. “More emportan: 10 their wider use hive heer o-ganisitiony! charges Gedicing the eommusicabon diftialues Serwecn warlisiuvets, ieselless and potential users). In develo vuncries popolacion growth a8 oaising espirsion 4 nucal sel nnn kx tel higher than song Jes ra ictensificution wf zh ies polis, Both of these ineresse the demand Fre water powered pumping. The rviel af nigrest has Boen veflzeied i several new publierrions (SKAT Teilery 1992, Kavi 19921 yal sare uansfer OF marescave 40 8. fimeriee and Alviso from ether Recewable energy davives in general ars asporienci fugrovements resuling Svea neo neti so new on “he modeling of rsct jump behowisur also has & conskdorahle hisiouy te. Eytan eros T91G, OBrien d Costing 1932. Krol 1981, Keane & Bune 181, Clover & Boldy 1990), lshowgh Uren Ts Htle evidence at wh imgroveme rs sh undersiod.ng allecting pump design oe ins! taen > fuciliuted the devising of beter madels~ easier te observe the vermplex movement oF shox k prsetice iv he jase, To Gary cent ceveiopinenns ha Imprevenscass In instr menialor iuve nse waves in setial syseees and the Uran’s dnp ie eoenp samulision models using shoe ime Steps (ex. 1.1 sans cams tee peemitied the use ef ‘This paper arisus can the werk of he Developniess Teshenlogy Unit at Warwick University over nearly en yous Cat she ilentiicaiuar yP social ane echnical vonetisines co vam pura se, eM the dlevslopment of low-cost guaypy “to Inese maTeacTERe 39 Peas oF ese and an Fas Urarser OF system instalsuon sKiUhs inte teu eve pping eotmaries, Out oF that work tae aved Ten, ane che Tiications of srede“ing have 2 REPRESENTING SYSTEM PERFORMANCE, The key cnmmponents nfs ram-purap ststem are shown in Eigse Ail of these kane propartios die af ee. There ane se Trsle meimning, that vn be altace is the * pe system perform) jenmmplss amraractians eu Cisse Components, 6 that lomaance” oF he pump in isolation. Wher ancysing the IH mnotoctest PUM ALS possible ¥9 chortcteise the parm and the 12s unt sepucatety re ks Gen eomANe rerisatigns, ‘The behsviews af snn-pamp 30 sttong!y inlnenee I ube ears eb seve pine th hs soot af alte separa pF sytem pans is Hor Rell overatisn cf a mere vanven Uf ty hyraaie 1 Conny ls of Femepamp system fe eempenents of the system ure Une Co Kassin gsneral chargeterisiies shat iniluenee overall performance ws tad the mean How sel ipe ns has reat fs ickependeat upon its length, linmaten en Q.) wheh can be rewlly caloulared unlepoiuertly ol alee system ctsnrnen, thee ig brs nogtighe effet en system Drive rank. his: wswally of stfViciely Linge sunt expat and Goes sized can be fell es eC ay Gee ail ysis, Dive pie. is Is ye G0) cha ve primacily determines che wh mers se even the enlest of proms: seveleratiow during the ageeleranea phuse a pumpéng. an ‘ur olaing trevor wel Tow co insunkvegus wake Movies and an arta {A th salutes velaety to Hoserare. Paes {His eas a anon romiet “ se valve once iniiates! and ‘leratica phe, inertia when apering and closing help deterrine pumping eltieionay nd Enally 4 flar-vmuoniing sesiee (e.g, presse vense.) whi if adequately Sized hes fee effect on systera pertorrmanee, eit doermenes the riveree Qa Cav om closure, 2% injpifae save ostose inesia wad Bia caw dluemines speed of cles Aperture shen open determi Ii etices al Kinet: ererpy tneers rag th slelvery vatve wha fhe iohes open ane sos Delivery... his comprises a dette i readily andl seqtitely & keelahle for £2 hours store get hos Tile oe ew ats system aertoeware, Ue every Bedghe (oF couse Jserrines rhe guile pressure ie pun stectly Tow: fat venose ficult is g stand “outa, and a sory a: which onve sed Ce.p Wee we corne te eharacie“Ise Ce peeteuma swe netslly trea ine FL 0 Wo Aieay Tow a Fish anean eivelow Q,, chew a se average verona eyes sf a ssstem baving output iclepouenth sae.thles, ven site, purnp. ceive pne ex (i eure ie) efficiency . of the pein alone inet sn easily deéined emlty o€ the pump. pis delve pine or of the whole sysiom. Eelticioney is ised 94 a Knew 2H ss a tendesc variable x miore elaborate models lence} &, rng sveles per sevand iat Gidependent waruble ia erude ‘The norcsaity determmmabie indopendene vanshles are ij delivery head ot a higher head 8a eiuces feeton hes ky if te delivers pipe iy seive seid HF usually weisueed var the écive lank ad hence already allowang for Fesdpipe Feicsion hss “oss ills acive aipe effective slope S. detized as drive hed AF vk somewhat mere dvect influence on zefernvnice thie 3 tlle fw at hich Cie iempaise waive hes been tuned t9 commence clasins this Sv earshot ith other virinhles dstermines Pre pak rsectlaw G, arewerrg devin by vine pipe “engi & LY bas & sie} porn sewing 2, bach cycle (a Key variable in mir analytic meds} (2) deive pips oe a cel dive pipe aype. seal hee Hetty us fection eneiviont and secondly is wall sifeness chat deverinizes the velocity of scund inthe woner within i Cri) gusnp tyne, and Rene fs irerna figtors. extant wsioeny lov a given drive leer: spent We fave thus a plethors of independent varstbles whose uirter is goleable for eauy wo a Computerised model ba + eatleraitly h gh: we intend to prepare graphs Or tables 2 be Used by system designer 1c the tld, (Caer! for a designer eves the hess AF and fave atsrative variables sunce system design inches selecting hermes Merri ‘water sources and pumphouse sic) The Jist of variables ubove dows aut include Teed pps or delivery pipe ekaretorisnes snd forthe tho pager these wll bs asauwncd Ue be vellected in the vases axad foe ceive head (P aad effecrive delivery had #. Ta practice chase pipes will be su taking into :eecumt Uheér probaly Lage eanatbution wy system ett, 9 give hystraic‘erielencies of around 959 er even OOS Far oko: thas Hi might only be 8% oF the dep Framr source wp punnphowS 096. La 28 eur models we will be epresenting aly thar pat af the sym xtc the entey Wo the erie wipe and Jie easy Ke the deivary pipe OF the soves iadepe wien! variables Inte’ warhgr, we waight eupMbine Ure last Ihre Fer purpases of display output characreristies, prslucing graphs or tib.cs Tor 4 Rarieular so bisitan at ouep il dove pine tepe te gum XYZ owhon ised with & 110 men OD. LD has. PWC drive nine. ‘Pais leaves for independent variables, wn Pure shan ca he hinds ay « seigle #adlily readable geaph tal pf ibost Hapa sales upun the nsdn euput oid Ths wsetul aheraFore to i ify the degree of inf vieubles Table | shows such an infizenee chan. ‘The erties ie shirt ie ocd! Ou Sap estimates of ie War elas oF sensitively [EL levsasl saa as the depencens wuvilile To emphasise Fie sensitivities dativecy ead & and oad ravi P~ AFH ane ased rather tang and AE Sensicvines 1 outpat varie t» cae input virahh Mocsted 2139 Four acting aloes 2 ceegoiies = high seusitiviey ISO ove: anus ot bow variables’ rang Ms inecaumnsensiivity — O8-& [Ei 0.8, Ls dow sens tvits Hs (ets VL ality les 0.1 i unps Vorahe | Dewey low | Devetow | Baraw | Pacioney q a b a Input variable eo Pump setae Q,, H H B M Meedratio | vw L L Delivery nend A M L | VL M vrveopesiope S| vi | i ML OF these: outst varivalss, beatrate bi of se Sineamentel importance but aay be Used A€ a taxing indicator by operators. Mean drive‘low Q, any be corstiained by the availabre source flow Q. and Irense should be kacwt. Delivery flow is of pismaty inteuest 30 the wysceea desigaer an! kaw efficieacy ts useful when choosing between models of puings. OF the indepeedes: vaciiles, purse setting Q, and head ratio & are the main ceterninests of betaviour, with delivery head A Raving a song lofluence near tle tap af its reage. Figure 2 illusmaces the form of the selationsbip between inpets Q.and & and the outputs gaaé @. ts A et-very flow 044 4a, 25 4a, ¥Nrive Few R20 Fig. 2. Churacteristic for pump type MB with $0 mm drive pipe when tuning ¢Q.,)is varied (qetivery head of k= 80m, drive plpe Sage S$ O41, drive head H'= 2, 4or 8a) 3. MODELS 4.1 Algchraie and Simlacion Madels Compared Algebraic models, invariable entailing the use of approximations «i» keep tham snanageable, wre suited ation by nana! or By smal ecapuler to rege OF activities - eduction, systaen 36°F. PUIG go. Bevae ii ciZicul 0 soles sore nf Me eens, sth models Ere often employed iceratively & indiceze che pertovmaace, ov exanigle as puesserbad system: deste. ae: haw Je might be improved by a ohange inp ar eleven and pan desi Users of vam Some jnst‘Ders have I na ps ave WoL. ger evally specialist engin le educaron aad cumet understand any dleebsaie vewtion. A wajer use of mes therefore iat orepars desige le! ermulexity can infounations 2vee at the level of “ules of dauab", in Beat these cevels uf sefuily be ok Simple malets ere these cperabie by (some? water tech ieia aT or syviem design engineers, by marwfaccarers 49 propase chants al fens. Researvin ruaels are priwanly fer pare dessgsers. ‘The hiss ould bis a saneyaimp usage wicks i qaticulary <Tt el ws comemmnivas and ppm anders in Ins form of computes suttcnre sed wise bees devel fr “an Time-step (orsevers-sept mulatior modes. asus en thy anetes! of characteristics 3 represent irnsoent Lows m she dave pipe, imps «Chovers. The powerlul but sa costly of computes paiwes chal they are pill asefub for eating purep design ov explaining system phewomena reher than Gulouliing routine partinunce graphs Likes -M swensrisa techniques, tose slia ato deal sith Uae paticular «the inllusnoe af a particular veriable enn only he explared by rap eat las of that varigale are used With scrall cempuners, sven wath 4h processors. daacsiep slmulisions 62 reps systenns ner at Only serall faetioe fe. 169 rel fe simnliion “ies ie shicl dil his nape sestiens asl single gad naan tere ¢ models and these use a2 aple Models ‘The simplest sel a 4 zam-furp employs the concen ef poser bakies axl eTicieney to give: carpi pe inp paar ettirsoney pyr 203,401 NOIR ores hendaran R Syit iu Tin ellistney 10 selina varies wie!y with operating Conditions fling wo sang FQ, foe smal or Ris to Large. Manuticaners tbies ane howezer gaily hse on ar asked cose ane users are often vised of eonsrains ousics which they shinald an sray repKesens the higheal hovel af muchsasuties vampiceny ene C28 expect any cia te hic A model thst eu be empl in de fauching of tld caw is the angselesystem one wheredy He pump eycie is awoken into two phases. Duriag an accaleraicn phase the wer an the drive pise seculecates uiler the drive beng tian ist sate = g8HF- = gS. During the det heigl wT En Hee = aS Ry wiley decelesutes enviar reglests fect oF Gie Kivete en invompressible snd ken ste wer in th lof-eyese rshound sk are falls pre the aygabice pressures dit mpottint Soe pump apereuan Blgsever tes limpocesystom randel has & no seriously affected by he ror Beas porno liste cloeay profile chat the nidel zeneriges is shaynin sn Figure 3 superimposed open a more velocity (v} in drivepipe at purpent:y Fig. 3 Velocity pratite predicted by Ivivtiontess humped-system mudel ‘AenuaT profile shown dleshedy peosinetions cecil w zdictions ot sevelrsation plese tne #3 ite Sorter that FEBIRY fe a delivery phase of about the rigkt dursuon (4, = 44) a3d na woound tine fr, = 25. However it nonnal operative the deisepige friction eversing &, to sored +, will he Feisly srual und the sebouncs Fase may he sagct. Within thout 10% severaey this macel scrrectly indica the Fellows, Fi The yet rime i lonimaeal by the teem phi ge Fil) Por high head ratios. (R> 1059. 4s peak velocty miss drive Mowrnte 9, 05 4 1 inp Phe shape of sho drivellow cersas one plo, Fig. wil he roughly a sawtooth csiace Q a sy uth seswtet ehaw fon a sttne 2, bu Hower steadily drive flowrate Area equois drivetiow volume per cycle Area equals delivery flow volurne per cycle time Fig. 4 Flowrate versus time predicted by frictionless lumped-system model ‘hax drive pipe and oxhacst kinetic enargy losses can be lis! calou‘ated ess ming Q, Alews eoeatently and then dovb.ed 10 allow for the seavefors1. Derived ftom ‘his and the assumption that acithes vive Irivtiua loss nor wateftow Ninotc cnetgy should exceed, sy, 12% of input ensrgy gives so rules ‘ram: ROT. "Drive pipe size senuld be such that is eadices when exrryiog steady flow Gy does not exceed 5% of ROT] “The main height 1 whack extasess water sprays above the impulse valve (gust before the ater closes} should not exceed 20% of H" (Height assured proportional tw KE, mavinuen flow rate Q, assumed to be sviee Od For any specifie tuning, the purip =tanutacturer could deere the pump's friction aid kinetic fosses by epesigving an equivstent leagih ot fsteucaud diesete) Urive pipe C. Drivepipe plas pum ca he replaced by 3 smxate ‘i: Longer drivepipe (Iengih € + £3, enabling a designer with access to pipe Friction tables wo apply ROTI "The headloss tereugh 3 exceed 10% of H” rwepine and pump together wher carrying steady flaw Q, shoud not 3.3. Acceleration Phase Mudels ‘The acceleration phase -nodel shove neglee:s vatioss nipesteal effects. mot reivebly fkcters which FeUIE the giavitGtovsl acceleralin, Mure avcanate models were developed long ago bu: ate not tua ly of 2 teem enavenient fora system: doi The acceleration ahase cin be deemed io start when che water in the érive pige sarts 20 move downwards agaia (following ie cowards recall movement ut the exd of the atevious eyele). Aldhough shock waves tnay sell be travelling up and dows she waste i the drive gine, eheie amined shacld be smal! enough that the whole water colzma cen be tsated ax having 4 sing’esnstally z270, veloc.