Investigation on complete characteristics and hydraulic transient of centrifugal pump

Transcription

1 Journal of Mecancal Scence and Tecnology 5 (1) (11) 58~59 DOI 1.17/s Investgaton on complete caracterstcs and ydraulc transent of centrfugal pump Wuy Wan 1,,* and Wenru Huang, 1 College of Cvl Engneerng and Arctecture, Zejang Unversty, Hangzou 158, Cna Department of Cvl and Envronmental Engneerng, Florda State Unversty, Tallaassee, FL 1, USA Department of Hydraulc Engneerng, Tongj Unversty, Sanga 9, Cna (Manuscrpt eceved November 14, 1; evsed May 6, 11; Accepted June 1, 11) Abstract An mproved metod was developed to obtan te complete caracterstc of centrfugal pump. Te converson formula of complete caracterstcs s establsed based on te normal performance curve. An example was presented to llumnate te new metod, and te complete caracterstc curves of 14SA-1 centrfugal pump were obtaned by te new metod. Te ydraulc transent of te centrfugal pump falure and start-up was smulated by metod of caracterstcs (MOC), wc quote te complete caracterstcs data. Te results sow tat te nverson metod s avalable to obtan te complete pump caracterstc curves provded te normal performance curve. For ydraulc transent smulaton, more accurate numercal result can be obtaned, f te new model s adopted to convert te expermental normal performance curve to complete caracterstcs curve of centrfugal pump. Keywords: Centrfugal pump; Hydraulc transent; Complete caracterstcs; Performance curve Introducton Hydraulc transent usually appen durng te pump falure and start-up. Te smulaton and control of ydraulc pressure s sgnfcant to te stablty and safety of te ppelne system. Tere are some metods to smulate te ydraulc transent of pump falure and start-up, ncludng grapc metod, analytc metod and metod of caracterstcs. Metod of caracterstcs s used wdely to compute te ydraulc transent of pump falure and start-up [1, ]. Many cases of pump ydraulc transent were smulated by suc numercal metod. Spence [] computed te ydraulc oscllaton n te ppelne wt pump. Cen [4] smulated te ydraulc transent of pump start-up. ao [5] smulated te ydraulc transent of pump falure. Srdaran [6] researced te ydraulc transent of nterlnked pumpng mans. zwan [7] researced te steady caracterstc of pump by te transent numercal model. Tese studes ave sown tat te MOC s convenent to compute te ydraulc transent of pump falure or start-up. However, te complete caracterstcs of te pump are necessary wen te MOC s appled to te ydraulc transent smulaton. Accordng to te dmensonal smlarty prncple, Marcal, Fles and Ts paper was recommended for publcaton n revsed form by Assocate Edtor Byeong og Sn * Correspondng autor. Tel.: , Fax.: E-mal address: wanwuy@zju.edu.cn KSME & Sprnger 11 Suter [8] developed te complete caracterstc curves of pump, wc ncludes only two curves and can represent te pump s complete caracterstcs at varous rotate speed. However, complex experments are usually requred to gan te complete caracterstc curves [9, 1]. In fact, manufactory can only supply normal performance curve wc can also be predcted by some numercal metods [11, 1]. However, t s dffcult to gan te complete caracterstc curves by experments or numercal smulatons. In order to avod te expensve experments, researcers developed many fttng metods to gan te complete caracterstc curves. Zang [1] developed te complete caracterstc curves by B-spne nterpolaton. Sao [14] ganed te curves by surface fttng and least square metod. Lu [15] developed te neural network model to compute te complete caracterstc curves. Berndt [16] nvestgates te complete caracterstc curves of large scroll pumps. Tese lteratures present metods to get complete caracterstc curves based on te specfc speed. However, tese metods strongly depend on oter known complete caracterstc curves, and can gan te approxmate data. Te fttng curves may gve some naccurate results wen tey are appled to te flud transent smulatons. A new nverson metod was presented n ts paper, based on te expermental normal performance curve from te manufactory. Te metod gves a formula to transform te normal performance curve nto te complete caracterstc curves. An example s pre-

2 584 W. Wan and W. Huang / Journal of Mecancal Scence and Tecnology 5 (1) (11) 58~59 sented to llustrate te metod. Consderng te avalable expermental data was lmted, an extenson metod was also establsed to obtan te wole complete caracterstc curves data. nd zone 1 (,) π 1st zone. Operaton zones analyss ( π,) Wb (,).1 Complete caracterstc curves and normal performance curve W Pump s complete caracterstc curves represents te unstable caracterstcs of pump, wc nclude te complex relatonsp among te flow rate, pumpng ead and torque at te varyng rotaton speeds. It s te foundaton of pump s ydraulc transent smulaton. Te performance curve of pump represents only te stable caracterstc of pump at te rated rotaton speed. It conssts of flow-ead curve Q H, flowenergy curve Q P and flow-effcency curve Q η. Because performance curves are te caracterstcs at te constant speed, t can t be drectly appled to smulaton of pump s ydraulc transents.. Operaton zones and dgtal complete caracterstc curves Pump caracterstcs consst manly of pump ead H, flow rate Q, speed N and torque T. Tere are only two ndependent varables and oter two varables are correlatve wt tem. In dmensonless sceme, all tese varables can be expressed as: N Q, v, N Q H, H T β T were s te dmensonless speed; v s te dmensonless flow rate; s te dmensonless pumpng ead; β s te dmensonless torque; Q s te rated flow; N s te rated speed; H s te rated ead and T s te rated torque. Gven, v and represent te pump ead curve, as well as v and β represent te torque curve of pump. In fact, tere are dfferent curve for dfferent speed. Te complete caracterstcs of pump can be expressed only by curves system. It s dffcult to apply drectly tese curves to ydraulc transent numercal smulaton, snce tese relatonsps consst of many curves. In order to apply tese curves to smulaton of ydraulc transents, Marcal et al. [8] used only two curves to represent te complete caracterstcs of pump. Te Suter s sceme can be wrtten as: W( x) + v β Wb( x). + v v x π + arctan (1) rd zone (,) π Fg. 1. Operaton zones n polar coordnate system. Turbne zone (1st zone) π/ Dsspatve zone (nd zone) W(x) Wb(x) Normal pump zone (rd zone) π x π + arctan v π / 4t zone Converse dsspatve zone (4t zone) Fg.. Operaton zones n rectangular coordnate system. In ts equaton, W( x ) s te ead curve; Wb( x ) s te torque curve. x π + arctan v s te ndependent varable n te doman (, π ). Te two curves establsed by ts equaton represent all unstable caracterstcs of pump, so t named complete caracterstc curves of pump. Accordng to te and v, pump s operaton s dvded nto four pattern zones [1]. As sown n Fg. 1, te area < x < π ( <, v ) s te turbne zone (1st zone); te area π < x < π (, v < ) s te dsspatve zone (nd zone); te area π < x < π (, v ) s te normal zone ( rd zone); te area π < x < π ( <, v > ) s te converse dsspatve zone (4 t zone). Tese zones can be also expressed n rectangular coordnate system. As sown n Fg., te rd zone (sadow area) s te pump normal operaton area, wc s te focus of te researc. Pump s complete caracterstcs consst of ead curve W and torque curve Wb, bot of wc can t be represented by contnuous regular functons for computer use. In order to use te curves for te computer, te curves wll be stored as data arrays n computer. Te complete caracterstc curves are equally dvded nto 88 segments and 89 data ponts. Te segment between two adjacent ponts s used to substtute for te correlatve practcal curve sown n Fg.. Snce reverse speed and flow s possble, te ndependent varables v and nclude te real number feld. It s dffcult to get te complete caracterstc curves by experments. In order to gan te complete caracterstc curves based on te manufactory s expermental normal performance curve, te nverson model of te complete caracterstc curves was establsed. π

3 W. Wan and W. Huang / Journal of Mecancal Scence and Tecnology 5 (1) (11) 58~ y data pont Approcxmate segment (W or Wb) data pont Practcal curves (W or Wb) 1 +1 x Fg.. Approxmate substtute for complete caracterstc curves. Normal performance curve Dmensonless curve Complete caracterstc curve η η β ( ) W x H Arbtrary pont H Q ated pont Q v Wb( x ) x vq Q, H H, bv QvQ, HH, v b β x π + arctan v, W( x), Wb( x ) 1+ v 1+ v 1. v tan( x π), (1 + v ) W( x), β (1 + v ) Wb( x) 1. Fg. 4. Te flow cart and basc prncple of nverse metod.. Inverse model for complete caracterstc curves.1 Mappng analyss of caracterstcs curve Complete caracterstc curves stand for te unstable flow caracterstcs and performance curve stand for stable flow caracterstcs of pump. Te normal performance curve can be consdered as te curve W and Wb at te rated speed ( 1. ). Te W( x ) and te Wb( x ) are only dependent on te x, toug x s dependent on and v. For any and v, wc meet te equaton π + arctan( v ) x, te W and Wb can just be obtaned. If tere are a known con dton pont, v, and β, te W( x) and te + v β Wb( x) can be obtaned, n ts formula x x + v π + arctan( v ). As sown, for (, v) (, v) arctan v π + x n te normal performance curve, te condton pont can gve te β value of W( x) and Wb( x). In oter + v + v words, any pont at te normal performance curve can always deduce a pont n complete caracterstc curves. For x ( π, π ), (, v) n te performance curve can meet π + arctan v x. Te complete caracterstc curves at te rd zone can be obtaned, snce pont x can be establsed accordng to te performance curve. Te speed 1. s specfc constant wen pump work at te stable condtons.. Inverson model Above analyss sown tat te rd zone complete caracterstc curves can be obtaned based on te performance curve of pump. Te nverson prncple and te solutons process of te curve can be llustrated by Fg. 4. Te performance curves often nclude te pump ead curve and effcent curve at te rated speed. However, te torque curve sn t drectly ncluded n te performance curves, wc needs to be computed by oter varables. After all varables s transformed nto dmensonless varables, te complete caracterstc curves W and Wb can be obtaned by te dmensonless varables. Accordng to te dependent relatonsp, te dmensonless torque can be expressed as: T QHγηω β vη η. () T Q H γ η ω In ts equaton, ω s te speed, ω s te rated speed, η s te effcency; η s te rated effcency at te best effcency pont (BEP). As sown n Fg. 4, te dmensonless performance curves

4 586 W. Wan and W. Huang / Journal of Mecancal Scence and Tecnology 5 (1) (11) 58~59 can be obtaned accordng to tese orgn varables of performance curves, wc nclude te ead curve and torque curve. Provded 1., te ( v,, β) n te curve can gve te pont ( x, W( x )) and ( x, Wb( x )) of te complete caracterstc curves. Te rd zone complete caracterstc curves W can be expressed as H(m) q ~ q ~ η η % x π + arctan v W( x) 1+ v v [, ), x [ π, π ]. () 5 5 Analogously, te rd zone complete caracterstc curves Wb can be expressed as: x π + arctan v β Wb( x) 1+ v v [, ), x [ π, π ]. (4) Accordng to te equatons, provded 1., te W( x ) and Wb( x ) can be computed by applyng te v, and β to te Eqs. () and (4). Above analyss sow tat every expermental data pont of normal performance curve can be used to deduce a data pont of complete caracterstc curves. For a wole normal performance curve, te rd zone s complete caracterstc curves can be ganed by te nverson metod. As sown n ts paper, te nverson metod was establsed wtout any approxmate assumptons. Its relablty s dependent on te performance curve wc s te observed data from te experment. Because te approxmate error s avoded n ts computaton, te metod as more teoretcal foundaton tan te tradtonal fttng metod. However, consderng te condton v [, ), only rd zone s curve can be obtaned by te metod. 4. Te applcaton procedure and dscusson 4.1 Applcaton procedure of nverson metod A case was presented followng to llustrate te applcaton procedure of nverson metod. Fg. 5 sows te normal performance curve of 14SA-1 centrfugal pump, n wc only ead curve and effcency curve are sown. Te pump caracterstc curve can be suppled by manufactory. All rated varables can be ganed accordng to te BEP, Q. m /s, H 66 m, P 4 Kw, η 89%. Te flow rate, ead and effcency can be expressed as dmensonless number accordng to te performance curve. Te dmensonless torque can be establsed by te Eq. (). Fg. 6 sowed te dmensonless performance curve. Te area ( π, π ) ncludes data ponts accordng to Suter s dgtal sceme. In order to meet te storage sceme, π te sequence was defned as v tan( ),,1,,L, π 44 x π + arctan v π +. Te W( x ) and v Q(m /s) Fg. 5. Centrfugal pump performance curve β Wb( x ) can be obtaned accordng to te correla v tve (,, β ). Te value was full n te 5-6 column of Table 1 and te correlatve curve was drawn accordng to tese data. Fg. 7 sowed te complete caracterstc curves W and Wb. Specally, only 17 of data ponts were predcted by te nverson metod because te expermental data was lmted. However tese data ponts can represent almost all complete caracterstc curves of rd zone. In order to compare te proposed metod wt tradtonal metod, te tradtonal fttng metod s presented ere. Te specfc speed of te centrfugal pump s computed as: 4 N N Q H 5.4. (5) s v ~ v ~ β Fg. 6. Dmensonless performance curve. v Accordng to Hollander s expermental data [1] for N s 5, 147 and 61, te fttng data was sown n column 7-8 of Table 1. Fg. 7 sowed te complete caracterstc curves based on te tradtonal fttng metod. Fg. 7 ncludes 17 data ponts n rd zone by dfferent metods. Comparng wt te fttng model, te nverson metod gave te same trend n te complete caracterstc curves. Te fgure sows tat complete caracterstc curves can be predcted by reverse trackng te pump s performance curve. Te β.8.6

5 W. Wan and W. Huang / Journal of Mecancal Scence and Tecnology 5 (1) (11) 58~ Table 1. complete caracterstc data. v x β Inverson Fttng W( x ) Wb( x ) W( x ) Wb( x ) W(x), Wb(x) W( x) a + v Wb( x) β + v W from nverson metod Wb from nverson metod W from tradonal fttng Wb from tradonal fttng. 1.π 1.1π 1.π 1.π x π + arctan v Fg. 7. Comparson of dfferent metod (17 data ponts n rd zone). predctons from nverson metod and te tradtonal fttng ave smlar tendency, but tere are dfferent value between two results. Te relablty comparson wll be presented n next secton. 4. Model verfcaton and dscussons of model lmtatons In fact, no assumpton was made durng te dervaton process, so te nverse model as good teoretc foundaton and avods unnecessary errors from approxmate assumptons. In order to corroborate te model, te comparson of experment and computaton wll be presented. Head curve of pump s avalable from manufactory, wc was obtaned from expermental observaton n te stable condtons. Snce complete caracterstc curves represent all unstable condtons as well as stable condtons, ead curve can be ganed by numercal metod accordng to te known complete caracterstc curves. Two knds of complete caracterstc curves data Pump Zu Fg. 8. Pump ppelne system. H (m) D1.m were appled to te MOC numercal model to compute te gradually unsteady process n rd zone wt dfferent ydraulc pressure. Te computaton s completed by transent smulaton wt two dfferent complete caracterstc curves data, one of tem s nverson data and te oter s tradtonal fttng data. Te pump system sown n Fg. 8 was computed by dfferent complete caracterstc data. Fg. 9 nclude results from two transent smulaton and experment data from manufactory, te example prove te nverson curve based on te performance curve s more close to te experment data. In ts fgure, dfferent ponts wt symbols ( and ) are te predctons of complete caracterstc curves obtaned separately from tradtonal fttng metod and nverson metod, and te lne s te expermental result. As sown n te fgure, te results obtaned by te nverson metod are more close to te expermental curve tan tose by te fttng metod. Comparson between smulatons and expermental curve sowed tat te nverson complete caracterstc curves are more reasonable. Snce t was establsed based on te expermental data, te nverson metod can gve more reasonable results n pump s transent smulatons. In fact, te fttng complete caracterstcs curve brngs on some approxmate error. As demonstrated n Fg. 9, te result based on nverson metod matc well wt te expermental curve. Especally, te process also proved tat normal performance curve can be computed by numercal smulaton based complete caracterstcs curve. In order to analyze te applcaton scope of nverson Zd Expermental curve Fttng metod result Inverson metod result Q (m /s) Fg. 9. Comparson of numercal result. H

6 588 W. Wan and W. Huang / Journal of Mecancal Scence and Tecnology 5 (1) (11) 58~59 v,, a v from fttng curve a from fttng curve. from fttng curve v from nverson curve a from nverson curve from nverson curve T (s) Fg SA-1 pump start-up transent. 1.4π 1.π 1.π.8π.6π.4π Start-up wt one way valve Pump falure wt one way valve Pump falure wtout valve.π 1 4 T (s) Fg. 1. Te tracked data process durng te transent process. v,, a 1..5 v from fttng curve a from fttng curve from fttng curve v from nverson curve a from nverson curve from nverson curve 1.5π ) was used n te smulaton. Moreover, all data used are located n te sadow area, wc s wtn te range covered by te complete caracterstc data from nverson metod based on te performance curve. Te result sowed tat te complete caracterstc data of nverson model s capable of smulatng te common pump falure and start-up transent process. 4. Extenson of te curve to oter zones T (s) Fg. 11. Pump falure transent wt one way valve. metod, dfferent condtons were dscussed n ts secton. Te nstantaneous caracterstcs ( x π + arctan v ) were traled durng te transent smulaton process. Te scope of applcaton was analyzed by comparng te tracked caracterstc data wt te nverson data. For te example, te pump system sown n te Fg. 8 s te 14SA-1 centrfugal pump. Te ppe s m n lengt and 1. m n dameter. Consderng te one way valve, te common start-up and falure process were smulated by MOC wt dfferent complete caracterstc curves data. Fg. 1 sowed te course of speed, flow and ead durng te start-up. It sowed tere are no reverse speed or flow n te transent process. Te complete caracterstc data ave some nfluence on te transent process, toug te trend was smlar. Fg. 11 sows te tral of varables durng te pump falure process. It ndcates tat te complete caracterstc data as nsgnfcant nfluence on te course of te transent process. Bot of complete caracterstc data were used n te example and te results ave some dfference. Fg. 1 s mportant to llustrate te scope of applcaton, wc sowed te tracked data x π + arctan v durng te transent process. In fact, only part rd zone s data ( 1 π, Only n rd zone, te complete caracterstc curves can be obtaned by te nverson model. It s avalable for te condton wtout reverse speed and flow. However, reverse speed and flow wll also appen n some specal condtons, suc as pump s runaway speed wtout one way valve. Pump s runaway transent process needs to be smulated f tere s no one way valve to prevent reverse speed or flow. Oter zones complete caracterstc data may be necessary, because te reverse speed and flow may appen n ts knd of specal transent process. However, because only te rd zone s complete caracterstc data can be obtaned by te nverson model, t s dffcult to smulate te runaway transent process of pump. Te extenson metod was presented below to extend te lmted data area of te nverson model. For te pump falure transent process wtout one way valve, te tral n te Fg. 1 sows te tracked data x π + arctan v durng te transent process. As sown n te fgure, te tracked pont falls nto te nd zone at te tme t 1. It sows tat te nverson data (sadow area) can t cover te wole transent process. In order to meet te need, te nverson curves need to be extended to oter zones. A metod s presented, and te oter zone s data s substtuted by te correlatve data of fttng metod. Fg. 1 sowed te extended curve by substtutng te fttng data for te necessary data n oter zones. Fg. 14 sowed te pattern varables process durng te pump falure transent process. Te result sowed tat te ydraulc varables s slgt dfferent n te rd zone n wc dfferent complete caracterstc data was adopted. Tere s almost same varables process n 1st and nd

7 W. Wan and W. Huang / Journal of Mecancal Scence and Tecnology 5 (1) (11) 58~ W, Wb 1-1 Fttng curve W Fttng curve Wb Inverson curve W Inverson curve Wb -. π.5 π 1. π 1.5. x π + arctan v π π Fg. 1. Te extended complete caracterstc curves. v,, a rd zone nd zone T (s) zones because only te same fttng complete caracterstc data s avalable n tese zones (turbne zone and reverse zone). Te results also sow tat te valves preventng reverse flow and speed ave great nfluence on te transent process. For pump system wt one way valve, nverson model s capable of smulatng te transent process. For te computaton of runway speed, te extenson of complete caracterstc curves s needed to smulate te pump falure transent process. Te extenson metod s to substtute te fttng data for te undetermned n te 1 st, nd and 4t zones data. Ten te fnal complete caracterstc curves are avalable to all knds of pump transent processes. 5. Conclusons Tere are some nevtable relatonsp between complete caracterstc curves and normal performance curve of centrfugal pump. By analyzng te caracterstc of tese curves, te nverson model of pump s complete caracterstc curves was establsed n ts paper. It sets up te transformaton formula from normal performance curve to complete caracterstc curves of pump. Te nverson model can be used as an effectve tool to obtan te complete caracterstc curves 1 st zone Fg. 14. Te transent smulaton wtout valve. v from fttng curve a from fttng curve from fttng curve v from nverson curve a from nverson curve from nverson curve based on te expermental data of normal performance curve for centrfugal pump. Wt more teoretcal foundaton and expermental data, te nverson metod can gve more reasonable results to descrbe te pump s transent process. As sown n te comparson fgure, te results from te nverson metod can mat well wt expermental result. Based on te performance curve, only rd zone s data can be obtaned, wc s te lmtaton of ts metod. However, te metod s good enoug to smulate common pump falure and start-up transent process wtout reverse speed and flow. For te smulaton of runaway transent process wt reverse speed and flow, te extenson metod was presented to extend te nverson complete caracterstc data. By substtutng te fttng data for te nverson curve n oter zones, te wole complete caracterstc curves of pump can be obtaned. Ts metod s convenent for applcatons to all knd of pump s transent process. Usng te performance curve suppled by te manufactory, te nverson metod can be used to derve te complete curve. Acknowledgment Ts work s supported by te Natonal Natural Scence Foundaton of Cna (Grant No. 5799, Cna) and te Fundamental esearc Funds for te Central Unverstes, Cna. Te autors tank Zejang Unversty and Cna Scolarsp Councl for supportng te Vstng Scolar Program n Florda State Unversty. Nomenclature Q : Instantaneous dscarge of pump (m /s) H : Pezometrc ead, dynamc ead (m) P : Power produced by a turbne (w) η : Pump effcency N : otatonal speed of pump (rpm) T : Instantaneous torque of pump (Nm) N : ated rotatonal speed of pump (rpm) Q : ated dscarge of pump (m /s) H : ated pressure ead (m) T : ated torque of pump (Nm) η : ated effcency : Dmensonless speed rato v : Dmensonless velocty : Dmensonless pressure ead β : Dmensonless torque rato W : Dmensonless ead caracterstcs of pump Wb : Dmensonless torque caracterstcs of pump x : Instantaneous poston of pump operaton x : Known pont of pump operaton a : Known dmensonless speed v : Known dmensonless velocty H : Known dmensonless pressure ead β : Known dmensonless torque rato : Subscrpt for an operaton pont

8 59 W. Wan and W. Huang / Journal of Mecancal Scence and Tecnology 5 (1) (11) 58~59 γ : Unt wegt of water (N/m ) ω : Angular velocty of turbne (rad/s) ω : ated angular velocty (rad/s) Z u : Upstream water level (m) Z d : Downstream water level (m) D : Dameter of ppe (m) eferences [1] E. B. Wyle and V. L. Streeter, Flud transents, McGraw- Hll Internatonal Book Company, New York, USA (1978). [] P. Tanapand and. Prasad, Centrfugal pump transent caracterstcs and analyss usng te metod of caracterstcs, Internatonal Journal of Mecancal Scences, 7 (1) (1995) []. Spence and J. A. Texera, Investgaton nto pressure pulsatons n a centrfugal pump usng numercal metods supported by ndustral tests, Computers & Fluds, 7 (6) (8) [4] S. Y. Cen, C. F. L and Y. P. Qu et al., Transent ydraulc performance of a centrfugal pump durng rapd startng perod, Kung Ceng Je Wu L Hsue Pao/Journal of Engneerng Termopyscs, 7 (5) (6) [5] S. S. ao, S. amasesan and D. K. Sng, Hydraulc transents n pumpng mans due to power falure, Journal of te Insttuton of Engneers (Inda) Part CV: Cvl Engneerng Dvson, 7 (5) (199) 181. [6] K. Srdaran, A. Gulam and B. amakrsna et al., Case study of ydraulc transents n nterlnked pumpng mans. Journal of te Insttuton of Engneers (Inda), Part CI: Cvl Engneerng Dvson, 66 () (1986) [7] zwan-uddn, Steady-state caracterstcs based model for centrfugal pump transent analyss, Annals of Nuclear Energy, 1 (5) (1994) 1-4. [8] M. Marcal, G. Fles and P. Suter, Te Calculaton of Water-ammer Problems by Means of te Dgtal Computer, Proc. Int. Symp. Water amamer Pumped Storage Projects, ASME, Ccago, USA (1965). [9] S. Deraksan and A. Nourbaks, Expermental study of caracterstc curves of centrfugal pumps workng as turbnes n dfferent specfc speeds, Expermental Termal and Flud Scence, (8) (8) [1] S. Deraksan and A. Nourbaks, Teoretcal, numercal and expermental nvestgaton of centrfugal pumps n reverse operaton, Expermental Termal and Flud Scence, (8) (8) [11] W. L. Ammnger and H. M. Bernbaum, Centrfugal pump performance predcton usng computer ad. Computers & Fluds, (8) (1974) [1] J. S. Anagnostopoulos, A fast numercal metod for flow analyss and blade desgn n centrfugal pump mpellers, Computers & Fluds, 8 () (9) [1] L. Zang, H. Xu and Y. H. Yu, Fttng metod for pump complex caracterstc curve based on B-splne, Dranage and Irrgaton Macnery, 5 (1) (7) 5-5. [14] W. Y. Sao and X. Zang, A new smulaton metod of complete caracterstc curves of reversble pump turbnemovng least square approxmaton, Journal of Hydroelectrc Engneerng, (5) (4) [15] G. L. Lu, J. Jang and X. Q. Fu, Predctng complete caracterstcs of pumps by usng BP neural network, Wuan Sul Danl Daxue Xuebao/Journal of Wuan Unversty of Hydraulc and Electrc Engneerng, () () 7-9. [16] U. Berndt, E. Krste and T. Le, Performance caracterstcs of large scroll pumps, Fuson Engneerng and Desgn, 18 (1) (1991) Wuy Wan currently s an assocate professor of Zejang Unversty n Cna. He receved s B.S. degree from X an Unversty of Tecnology n 1999, ten e receved s P.D degree form Tanjn Unversty n Cna n 4. He worked n Tsngua Unversty as a postdoctor n 4-6. He worked n Florda State Unversty as a vstng scolar n 8-9. Hs researc nterests nclude ydraulc smulaton and transent flow analyss of ppelne and pump. Wenru Huang currently s a professor n Department of cvl and envronmental engneerng, Florda State Unversty, USA. He receved s P.D degree from Unversty of ode Island n USA. Hs researc nterests nclude coastal ydrodynamcs, computatonal flud dynamcs and turbulence modelng.