Numerical analysis on the distribution features of velocity circulation of axial-flow pump

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1 Numercal analss on he dsrbuon feaures of veloc crculaon of aal-flow pump ZHU Honggeng a and ZHANG Renan a, b a School of Hdraulc, Energ and Power Engneerng, Yanghou Unvers, Yanghou, Jangsu 4009, P. R. Chna; b Jangsu Surveng & Desgn Insue of Waer Resources Co. Ld., Yanghou, Jangsu 517, P. R. Chna Absrac: Aal-flow pumps are wdel used n man secors of naonal econom, and he mprovemen of her pumpng cenc means he savng of remendous energ and grea conrbuon o envronmen proecon. The veloc crculaon s an mporan parameer n he desgn of aal-flow pumps and s dsrbuon feaures wll drecl affec he shape of blades and performances. The urbulence modelκ-εs seleced o close he me-averaged ncompressble hree dmensonal Naver-Sorks equaons, and numercal smulaon s conduced o anale he nernal flow felds and dsrbuon feaures of veloc crculaon of aal-flow pumps. The smulaed resuls ndcae ha here ess crculaon n enrance secon of mpeller and a desgned flow rae he value of crculaon reaches mnmum. The crculaon n he dscharge secon of aal-flow mpeller vares wh he flow rae and radus. The smaller he flow rae and he larger he radus s, he greaer he value of veloc crculaon. There s resdual crculaon n he e secon of dffuser, and negave angenal veloc and crculaon are found near he hub of dffuser, leavng a bg space of opmaon desgn of mpeller and gude vanes. Ke words: veloc crculaon; dsrbuon feaures; aal-flow pump; numercal analss 1. INTRODUCTION Aal-flow pumps are characersc of large dscharge, low head and hgh cenc, whch are wdel used n feld rrgaon, muncpal dranage, flood conrol, ner-basn waer dverson, waer-e propulson, and waer crculaon n elecrc power plan. Takng he frs sage Easern Roue Proec of Souh-o-Norh Waer Dverson as an eample, here are more han 40 large pumpng saons n 13 cascades, of whch abou nne percen adop aal-flow pumps and he power of machng moors reaches kw. The annual operaon me s around 5000h, and s esmaed ha up o kwh of elecrc energ can be saved f he average pumpng ssem cenc s rased b 1%. Generall speakng, he operaon cenc of a pumpng saon depends on he desgn of pumps and scenfc managemen of pumpng ssems. The mpeller and gude vanes are ke pars of an aal-flow pump, of whch he mpeller are val n converng mechancal energ from he drvng machne o pressure energ and knec energ of flowng waer, and he gude vanes pla he role of reganng angenal veloc energ and dffusng waer. The bgges problem encounered n desgnng an aal-flow pump s he mahemacs model of crculaon dsrbuon n he oule of mpeller blades. A presen, here are wo heores. One s free vore mode, and he oher s forced vore model (Guan Xngfan,009). Each of hem has s dsncve desgn mehod, bu also reveals some shorcomngs a he same me. Beng lack of perfec heorec desgn mehod and check he ecs of dfferen dsrbuon of crculaon, phscal model ess are becomng necesses, and onl a few researchers and manufacurers can have successfull developed hgh performance aal-flow pump models (Lu Nng e al., 006). In hs paper, numercal smulaon of an aal-flow pump s carred ou o sud he dsrbuon model of crculaon and predc he pump performances. Based on he smulaon and b revsng he mahemacs model of crculaon dsrbuon, hdraulc opmaon desgns of aal-flow pump can be proceeded o acheve beer performances and cu down developmen coss. 14

a shaf, a 60 ben and a dscharge sragh ppe. The dameer of he mpeller s 300mm and he oule dameer of he dffuser s 350mm.

2 NUMERICAL SIMULATION OBJECT AND METHOD.1 Numercal smulaon obec The numercal smulaon obec s an aal-flow pump as shown n Fgure 1(a) wh 3 blades and 6 fed gude vanes, conssng of an enrance sragh ppe, a conracng reach, an mpeller, a dffuser, a shaf, a 60 ben and a dscharge sragh ppe. The dameer of he mpeller s 300mm and he oule dameer of he dffuser s 350mm. The specfc speed of he pump a he bes cen cenc pon s abou 1000, and he raed roaonal speed s 1450 r/mn. The compued doman s he same as arranged n a es-bed, so ha he compued resuls can be compared wh each oher o verf he vald of he smulaon. (a) Compued doman (b) 3D modelng of mpeller and gude vanes (c) Meshng of compued doman Fg. 1 Compued doman, modelng and meshng of an aal-flow pump. Modelng and meshng of compued doman The commercal code Gamb and Pro/E are seleced o reale he hree dmensonal modelng of mpeller and gude vanes (Fgure 1(b)), and he p clearance beween he pump casng and mpeller s no consdered. In order o mprove mesh qual and compuaon precson, unsrucured four-face and srucured s-face bod meshes are generaed wh he help of se funcon o accommodae comple srucure of he compued doman (Fgure 1(c)), and he checkng of ndependence of mesh se s done before he formal compuaon commenced. Famous compuaonal flud dnamcs code FLUENT s appled o smulae he nernal flow of he aal-flow pump. The mul-reference frame s used o rea he nerference beween he roaonal mpeller and he sac dffuser. The algorhm SIMPLEC s adoped o couple he calculaon of veloc and pressure o mprove compuaon cenc and accelerae convergence..3 Mahemacs model for numercal smulaon.3.1 Governng equaons Durng normal operaons of an aal-flow pump, he nernal flow veloc s relavel low and he change of waer dens can be negleced. The 3D me-averaged N-S equaons can be adoped o descrbe he nernal sead and ncompressble flow felds of aal-flow pump. The mass conservaon equaon and momenum equaon can be wren as Equaons (1) and () (Tao Wenquan, 001., Yan Chao, e al, 011., Verseeg e al.,1995). E F G S (1) u u 1 p f u [( )( u )] () where,, are relave Caresan coordnaes fed on he mpeller whch roaes around he as a angular speed ; E, F, G and S are column vecors, epressed as followngs. 15

3 E u uu u uv v uw w F v vu u vv v vw w G w wu u wv v ww w S 0 ( u ( u ) ) ( u ) ( v ) ( v ) ( v ) ( w ) ( w ) ( w ) P wv * P wu P * * n whch P * denoes oal pressure equalng o sac pressure plus cenrfugal force; s ecve vscos equalng o molecule vscos plus urbulen vscos..3. Turbulence model sandard Equaons (1) and () canno be solved because he varables are more han he number of equaons, and he urbulence model s seleced o close he me-averaged N-S equaons (Launder e al.,197., Chen e al.,1987), so ha he urbulence vscous cocen urbulence dsspaon rae. uk s conneced wh he urbulen knec energ and k [( )( )] pr (3) k u c1 pr c [( )( )] k where p s urbulen energ producv; r consans. p r u u u ) s funcons of and ; c, c 1, c, k (4) and are defned as ( (5) c k 3 INTERNAL FLOW AND VELOCITY CIRCULATIONS OF AXIAL-FLOW PUMPS 3.1 Inernal flow of aal-flow pump The nernal flow of an aal-flow pump s a resulan one of relave moon w from he nle o he oule of blades and crcular moon u along wh he mpeller. The veloc rangles of aal-flow pump n he nle and oule of blade can be drawn ou as shown n Fgure, where subscrp 1 refers o he nle, subscrp o he oule. Tangenal componens of absolue veloces v proeced on he drecon of u are gven anoher subscrp, u. Componens of he absolue veloc normal o he perpheral veloc are desgnaed as v m1 and v m, respecvel. (6) 16

4 Fg. Veloc rangles of aal-flow pump Fg. 3 Crculaons acng on a blade Accordng o he energ conservaon law and whou consderng he frcon loss beween blades, he dfferenal equaon for he oule veloces of mpeller can be derved (Guan Xngfan, 1995). v dv dvu vu ( )( r v ) (7) dr r m m u dr Based on Equaon (7) as long as he relaonshp beween vm and u solved and he profle of blades can be desgned. 3. Veloc crculaons of aal-flow pumps In mahemacs, veloc crculaon s lnear negraon of veloc smbolcall epressed b Γ. Γ V d s L L V cos( V ds) ds v s deermned, hen Equaon (7) can be V along a closed curve L of flow felds, For he compued doman as shown n Fgure 1(a) he crculaons along he enrance or dscharge crcumferences of he aal-flow mpeller can be calculaed b Equaon (9), n whch L πr. ud vd L 3.3 Epresson of head n erms of veloc crculaons As shown n fgure 3, veloc crculaons n he nle and oule crcumfluence of a sngle aal-flow blade s Γ 1 and Γ, respecvel. Accordng o he veloc rangles n Fgure and based on such assumpons as sead, aal-smmercal and unform nernal flow, nfne number of blades and deal flud, he heorecal head H T of an aal-flow pump can be epressed n erms of veloc crculaons as gven n Equaon (10) (Lu Chao,009). I saes ha he heorecal head H T of an aal-flow pump s deermned b he angular speed ω of he mpeller, he number of blades, he veloc crculaon dfference of Γ and he gravaon acceleraon g. H u vu u1v u1 u 1 ( vu vu 1 g g ) g g T (10) The phscal meanng of head s he energ ncremen of per un wegh of flud flowng hrough he pump. From Equaon (7) o Equaon (10) can be seen ha he dsrbuon of v u wll affec he shape of blades and he value of crculaon Γ and fnall affec he head H as well as he performances of he pump. (8) (9) 4 NUMERICAL SIMULATION RESULTS AND DISCUSSIONS 4.1 Flow paerns n he enrance and dscharge secon of aal-flow mpeller Flow paerns n he enrance secon of aal-flow mpeller 17

5 The flow enerng no he enrance secon (A-A secon n Fgure 1(a)) of aal-flow mpeller s desgned o be n aal drecon hrough a long sragh ppe. Due o he roaon of mpeller and he vscos of waer, he flow s wsed no he enrance secon of pump casng and he angenal componen v u1 ess obvousl, and does no equal o ero even a he desgned flow rae (Q=0.40m 3 /s) hough he value of v u1 s comparavel small (Fgure 4). (a) Q=0.3m 3 /s (b) Q=0.40m 3 /s (c) Q=0.48m 3 /s Fg. 4 Flow paerns n he enrance secon of aal-flow mpeller 4.1. Flow paerns n he dscharge secon of aal-flow mpeller When waer s sucked no he mpeller energ ransmed from he drvng machne wll be convered from mechancal energ o knec energ and poenal energ. Flow paerns n he dscharge secon of aal-flow mpeller (B-B secon n Fgure 1(a)) a dfferen flow raes are shown n Fgure 5, from whch can be clearl seen ha he waer flowng ou of he mpeller possesses srong crculaon and roaes around he as whle dscharged from he pump casng no he dffuser. (a) Q=0.3m 3 /s (b) Q=0.40m 3 /s (c) Q=0.48m 3 /s Fg. 5 Flow paerns n he dscharge secon of aal-flow mpeller 4. Tangenal veloc crculaon n he enrance and dscharge secon of aal-flow mpeller 4..1 Tangenal veloc and crculaon n he enrance secon of aal-flow mpeller The dsrbuon of angenal veloc v u1 along he radus n he enrance secon of aal-flow mpeller s shown n Fgure 6(a), from whch can be seen ha v u1 vares wh flow raes and he rad. A he desgned flow rae (Q=0.40m 3 /s) he magnude of v u1 s no larger han 0.01m/s n he whole enrance secon no maer he radus s smaller or larger. When he aal-flow pump operaes a off-desgn flow raes, v u1 s obvousl larger han ha a desgned flow rae, and ends o become larger wh he ncrease of radus. And also correspondng o smaller and larger flow raes here are larger angenal veloces, whch are parl caused b so called second flow nsde he mpeller. Fgure 6(b) gves he dsrbuon of veloc crculaon n he enrance secon of aal-flow mpeller. I ndcaes ha he crculaon vares wh he radus. The larger he radus s he sronger he crculaon. A he desgned flow rae (Q=0.40m 3 /s) he pre-swrl n he enrance secon of aal-flow mpeller s weak and whle operang a off-desgn flow raes he crculaon becomes sronger, whch wll reduce he nle aack angle of blades and change he flow condons of he pump and affec s energ and cavaon performances. 18

6 (a) Tangenal veloc (b) Veloc crculaon Fg. 6 Tangenal veloc and crculaon n he enrance secon of aal-flow mpeller 4.. Tangenal veloc and crculaon n he dscharge secon of aal-flow mpeller The dsrbuon of angenal veloc v u n he dscharge secon of aal-flow mpeller s shown n Fgure 7(a), from whch can be seen ha v u vares wh flow raes. The smaller he flow rae s he larger he angenal veloc. The dsrbuon of v u along he radus akes he form of a concave curve when he flow rae s consan. The waer bod near he hub obans larger angenal veloc v u and smaller crcumference veloc u. If he produc of u and v u can be kep unchanged, hen he heads a dfferen rad wll be a consan and no second flow should appear nsde he mpeller. Acuall, hs deal condon can rarel be acheved even under desgned condons. (a) Tangenal veloc (b) Veloc crculaon Fg. 7 Tangenal veloc and crculaon n he dscharge secon of aal-flow mpeller Fgure 7(b) shows he dsrbuon of veloc crculaon a he dscharge secon of aal-flow mpeller, whch s smlar wh he dsrbuon of angenal veloc. The smaller he flow rae s he hgher he crculaon and he head, whch s n accordance wh he characerscs of aal-flow pump. When he pump runs a he desgned flow rae he veloc crculaon s bascall a lnear dsrbuon, ncreasng wh he radus. The flow feld near he pump casng obans larger crculaon, whch s good for enhancng he mpeller s abl o do work, and n oher hand o offse he nfluence of leakage of p clearance. 4.3 Resdual crculaon n he e secon of dffuser Flowng waer from he dscharge secon of an aal-flow mpeller possesses srong crculaon and hgh veloc. Dffusers conss of fed gude vanes, whch are desgned o elmnae veloc crculaons from he dscharge secon of mpeller and conver he knec energ of waer o pressure energ hrough dffusng waer. Theorecall, he nflow angle of gude vanes s se o be equal o he ouflow angle of roang blades, and hrough he acon of gude vanes he flow ou of he dffuser s epeced o be free of veloc crculaon. However, due o he complcac of flowng waer and oher nfluencng facors veloc n he e secon of dffuser (C-C secon n Fgure 1(a)) canno compleel elmnaed, here remans resdual crculaons. 19

7 (a) Tangenal veloc (b) Veloc crculaon Fg. 8 Tangenal veloc and resdual crculaon n he e secon of dffuser Comparng Fgure 7 wh Fgure 8 s found ha afer flowng round he gude vanes he angenal veloc of waer n he e secon of dffuser has been reduced b 70% o 90%, wh respec o dfferen flow raes. The smaller he flow rae s he larger angenal veloc and resdual crculaon. Affeced b he conracon of gude hub cap and gude vanes he flow felds s ver urbulen. The appearng of negave angenal veloc and crculaon near he hub of dffuser ndcae ha he desgn of gude vanes does no oall mach he ouflow from he mpeller and here s bg space of opmaon desgn of mpellers and gude vanes (Tang Fang-png e al.,006., Sun e al.,001., Durmus Kaa,003). 5 CONCLUSIONS Veloc crculaon, negraon of veloc along a closed curve, s a ver mporan parameer n desgn of aal-flow pumps. The shape of blades and performance of pump s closel relaed wh he dsrbuon feaures of veloc crculaon. Wh he help of numercal smulaon and nernal flow analses he followng conclusons can be reached. (a) Numercal smulaon resuls ndcae ha here ess veloc crculaon n he enrance secon of aal-flow mpeller, resuled from he roaon of blades and waer vscos. The veloc crculaon vares wh he flow raes, and ges larger values when he pump runs a off-desgn flow rae. (b) There s srong crculaon n he dscharge secon of aal-flow pump, whch s nversel proporonal o he flow rae. When he pump operaes a he desgned flow rae he veloc crculaon bascall ncreases lnearl wh he ncrease of radus. (c) Resdual crculaon ess n he e secon of aal-flow pump, and leaves a bg space n opmaon desgn of mpellers and gude vanes. (d) The nfluence of p clearance on he dsrbuon feaure of veloc crculaon of aal-flow pumps needs o be nvesgaed and compared n he fuure. 0

8 ACKNOWLEDGEMENT Ths paper s fnancall suppored b he 11h Fve Year Ke Proec of Chna s Naonal Scenfc Suppor Scheme (Gran No.006BAB04A03); and he open proec from Jangsu Provnce Ke Lab of Hdraulc & Power Engneerng (Gran No.K100016). References Chen Y. S., Km S. W Compuaon of urbulen flows usng an eended k-e urbulence closure model, NASA CR Durmus Kaa Epermenal sud on reganng he angenal veloc energ of aal flow pump. Energ Converson and Managemen 44: Guan Xngfan. Handbook of modern pump echnques. Beng: Chna Asronauc Publshng House, Guan Xngfan. Aal-flow pump and dagonal pump. Beng: Chna Asronauc Publshng House, 009. Launder B. E., Spaldng D. B Mahemacal models of urbulence, New York: Academc Press. Lu Chao Pump and pump saons [M]. Beng: Chna WaerPower Press. (n Chnese) Lu Nng, Wang Ysen, Zhang Gang, e al Tes of pump models n he same es sand for Souh-o-Norh Waer dverson Proec. Beng: Chna WaerPower Press. Sun J., Tsukamoo H Off-desgn performance predcon for dffuser pumps. Proceedngs of Insuuon of Mechancal Engneerng, 15: Tang Fang-png, Wang Guo-qang Influence of oule gude vanes upon performances of waere aal- flow pump. Journal of Shp Mechancs, 10(6): Tao Wenquan Numercal hea ransfer ( nd Edon). X an: X an Jaoong Unvers Press. Verseeg H. K., Malasekera W An nroducon o compuaonal flud dnamcs [M]. New York:Longman Group Ld. Yan Chao, Yu Jan Xu Jngle, e al On he achevemens and prospecs for he mehods of compuaonal flud dnamcs advances n mechancs, 41 (5):

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