Blade Exit Angle Effects on Performance of a Standard Industrial Centrifugal Oil Pump

Transcription

1 Journal of Applied Fluid Mecanic, Vol., No., Iue, pp. -9,. Available online at ISSN 7-7, EISSN 7-6. Blade Exit Angle Effect on Performance of a Standard Indutrial Centrifugal Oil Pump W.G. Li Department of Fluid Macinery, Lanzou Univerity of Tecnology 7 Langongping Road, 7 Lanzou, P R Cina Correponding Autor Liwg@yaoo.com.cn (Received November, 9; accepted January, ) ABSTRACT Te effect of blade dicarge angle on te performance of a tandard indutrial centrifugal oil pump of type 6Y6 were invetigated experimentally a te pump andled bot water and vicou oil. A one-dimenional ydraulic lo model wa etablied to identify uc effect matematically. Te effect ave been etimated analytically by uing te model at variou vicoitie. Te reult owed tat te blade dicarge angle a ignificant but equal influence on te ead, aft power and efficiency of te centrifugal oil pump at variou vicoity condition. For any vicoity, te total ydraulic lo in te impeller and volute rie wit increaing blade exit angle. Te diffuion lo in and beind te impeller a well a te friction lo in te volute are noticed in te pump, epecially for igly vicou liquid. Te ydraulic lo in te impeller i about.-.6 time te lo in te volute. In order to improve te pump performance, te ydraulic lo in te volute mut be kept a mall a poible. Keyword: Centrifugal pump, Centrifugal oil pump, Performance, Blade angle, Hydraulic lo, Dik friction lo NOMENCLATURE b b b widt of blade inlet widt of blade outlet widt of volute C M torque coefficient due to dic friction diameter of blade inlet D D D D diameter of blade outlet diameter of circle tangential to volute tongue tip equivalent diameter of volute troat D 9 mean diameter of D and D9 D 9 D D w diameter of dicarge nozzle ydraulic diameter diameter of wear-ring dh dq lope of ead-flow rate curve F cro-ectional area of ection - exit area of impeller F F F9 troat area of volute cro-ectional area of nozzle exit F m mean area of F and F Q t teoretical flow rate troug impeller Q W flow rate of water Re Reynold number Re impeller dic Reynold number Re Reynold number in nozzle R w d radiu of wear-ring on impeller S u tangential blade tickne at outlet t ditance between caing and impeller roud or ub T temperature of fluid u impeller tip peed V 9 mean velocity in volute D 9 V mean velocity troug area of V 9 mean velocity troug nozzle exit V m meridian velocity at outlet V u tangential abolute velocity at outlet W mean relative velocity of W and W W relative velocity at entrance of impeller W relative velocity at exit of impeller W relative velocity at te exit of impeller wit

2 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. f geo g l id ie impeller ape factor for dik friction lo acceleration due to gravity total ydraulic lo expanion lo in impeller mixing lo beind impeller if kin friction lo in impeller V total ydraulic lo in volute Vde expanion lo in nozzle Vdf kin friction lo in nozzle Vf kin friction lo in piral body of volute H pump ead H teoretical ead of impeller t H ead of duty point for water W K Q k L i LK L V n n P P d P Q correction factor of flow rate to vicoity rougne of wetted wall blade lengt lengt of dicarge nozzle lengt of piral body of volute pump rotating peed pecific peed of pump n =.6n Q / H (r/min, m /, m) aft-power of pump power due to dic friction of impeller ydraulic power of pump pump flow rate. INTRODUCTION Te effect of blade dicarge angle of impeller on te performance of centrifugal pump ave been invetigated ince 9. Kamimoto and Matuoka (96) experimentally invetigated variou model centrifugal pump impeller wit ix logaritmic piral blade wit te contant angle of º, º, 7º and 9º repectively by uing water a working fluid. Te impeller wa cloed type and ubject to a rotting peed of 7r/min. It wa made clear tat te impeller wit º dicarge angle acieved bet performance. Te maximum variation of impeller ydraulic efficiency wa a ig a %. Varley (96) conducted te experimental invetigation into te effect of te blade dicarge angle on te performance of a double uction centrifugal pump wit pecific peed of 6 wen andling water. Te pump rotating peed wa r/min. Te impeller of te pump wa cloed type and tere were five blade in it. Te blade pattern wa a ingle arc. Te inlet angle of te blade wa 6º, te dicarge angle were º, 7º, º, 9º, 7º and º, repectively. Te reult demontrated tat te ead increaed wit increaing dicarge angle and te larger te flow rate, te more te increae in ead. Wen te blade dicarge angle wa between º and 9º, te maximum variation of efficiency of te pump wa only about.6%. Toyokuro et al (979) made experiment on te influence of te dicarge angle on te infinite number of blade equivalent expanion angle of dicarge nozzle blade inlet angle blade dicarge angle tickne of ub-laminar layer lip velocity at impeller outlet V u pump efficiency pump ydraulic efficiency V pump volumetric efficiency m pump mecanical efficiency equivalent diffuion angle of impeller paage kin friction coefficient kinematic vicoity of fluid expanion lo coefficient expanion lo coefficient wen Re denity of fluid lip factor number of blade circumferential angle of tongue of volute blockage factor of blade at outlet angular peed of impeller Abbreviation BEP bet efficiency point of pump Subcription i impeller V volute performance of a ingle-tage, end-uction and cantilevered centrifugal pump wit pecific peed 7 at rotating peed r/min wen andling water and vicou oil. Te impeller wa alo cloed type wit ix blade and te blade pattern wa ingle arc too. Te dicarge angle were º and 6º repectively. Te fluid vicoity wa up to 9mm / (Reynold number Re wa between and.9 6 ) in te experiment. Te reult revealed tat te ead wa improved a te dicarge angle increaed, te larger te flow rate wa, and te more te ead wa improved. However, te efficiency of te pump for te dicarge angle of 6º wa jut about % le tan tat of º wen pumping water. Not only did te ead increae wit increaing dicarge angle, but te efficiency wa improved alo by % wile andling vicou oil. Te iger te oil vicoity, te larger te improvement in efficiency. Tanaka and Oai (9) made experiment on a erie of emi-open, end-uction centrifugal pump impeller wile tranporting igly vicou oil wit vicoity of -mm / (Reynold number Re wa in te range of -. 6 ). Te radial blade (9º) could acieve bet performance for ig vicoity liquid. Aoki et al (9) and Ota et al (99, 996) experimentally tudied te influence of te dicarge angle on te performance of a ingle-tage, end-uction and cantilevered centrifugal pump wit te pecific peed of 7 wen andling water and vicou oil. Te fluid vicoity wa in te range of -6mm / 6

3 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. (Reynold number Re wa in ). Te impeller wa cloed or emi-open type wit ix blade. Te two-arc-aped blade exit angle were º, º, º, 6º, 7º, repectively. Te experimental reult were imilar to toe of Toyokuro et al (979). In ummary o far, wen te centrifugal pump andle water, one experiment ow te pump ydraulic efficiency can be improved by % wit a variable blade exit angle (Kamimoto et al, 96), but te oter experiment indicate te pump efficiency jut i improved by.6% (Varley, 96). Obviouly, ti dipute need to be confirmed experimentally. A a pump andling vicou oil, owever, a conitent reult eem to be acieved, i.e., te blade exit angle a ubtantial influence on bot ead and efficiency for model impeller. Te reult ugget large dicarge angle i elpful to improve bot ead and efficiency for a liquid wit iger vicoity tan water. Te centrifugal oil pump wit low pecific peed a found ignificant application in oilfield and refinerie in Cina. Wat will appen in te performance for uc a kind of pump wen pumping variou vicou oil for variou blade dicarge angle i intereting ince ti will reult into an improved pump performance to ave energy. clean crude oil and oter liquid petroleum product at - C~+C in Cina (Fig. ). Te pump duty pecification are a follow: te flow rate Q m /, ead H 6 m, rotating peed n 9 r/min, pecific peed n. 6. Te impeller wa cloed type wit five twited tree-dimenional blade (ee Fig. c). Te cro-ectional drawing of te pump and impeller ave been own in Fig. and. Te main dimenion of te impeller are: D =mm, b =7.mm, D =6mm, b =6mm, =, = o, S u =mm. Te major dimenion of te volute are a follow: D =mm, b =6mm, D 9 =6mm, F =mm, L k =mm, =6 o. dicarge nozzle uction nozzle entry impeller volute In ti paper, a tandard indutrial centrifugal oil pump of type 6Y6 wit low pecific peed of.6 wa employed a a tet model and te effect of it blade dicarge angle on te performance were invetigated experimentally a te pump andled bot water and vicou oil wit variou vicoitie, repectively. Te reult owed tat te influence of te angle on te ead wa dominated at all vicoity condition. Te impeller wit te dicarge angle of º illutrated a bet efficiency a te vicoity of liquid wa le tan mm /; owever, a te vicoity wa more tan ti value, te impeller wit te dicarge angle of 6º demontrated iget efficiency. Moreover, a onedimenional ydraulic model wa propoed to invetigate te effect of blade dicarge angle at variou vicoitie analytically. = o = o = o (c). EXPERIMENTAL SETUP. Tet Rig Te ketc of te tet rig for meauring te performance of centrifugal oil pump wile andling water or vicou oil a been own by Li (). Te detail of te tet rig can be found out in tat reference. An oil temperature control ytem wa intalled in te tank of te rig in order to eat te oil and reduce it vicoity. Te meaurement uncertaintie of flow rate, ead, aft power and efficiency were.77%,.%,.% and.9%, repectively (Li, ).. Pump and Blade Pattern Te tet pump wa a tandard indutrial centrifugal oil pump of type 6Y6 wit ide-uction entry and ingletage, wic a been extenively applied to tranport =6 o Fig.. Pump cro-ectional view, impeller tyle and blade pattern (c) Te tree impeller wit dicarge angle,, º, º and 6º, were prepared to illutrate teir influence on te performance of te pump. Te blade lengt, blade warp angle and Su were different from to of te original impeller wit a dicarge angle of º, but te ret geometrical dimenion remained uncanged. Te number of blade of toe impeller wa five and te blade pattern were NURBS curve. Te comparion of te four blade pattern a been demontrated in Fig. (c). 7

4 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. 7 6 mm / (oil), were coen in te experiment. Te performance tet were conducted in uc a way tat te oil temperature wa raied from low to ig in order to control it vicoity conveniently. H(m) H(m) H(m) =mm / = o = o = o =6 o Q(m /) 7 6 =9mm / = o = o = o =6 o Q(m /) 7 6 =mm / = o = o = o =6 o (c) Q(m /) Fig.. Head curve in term of flow rate at tree vicoity value. Working Liquid Te working liquid were bot water and Cina # macine oil in te performance experiment, repectively. It wa made clear tat bot liquid are Newtonian fluid by uing a rotating dynamic vicoity meter. Te denity and kinematical vicoity of water are kg/m, mm / at C, repectively. However, te denity and dynamic a well a kinematical vicoitie of te oil demontrated a variation wit temperature in te experiment wen te temperature wa varied in te range of C-6C. Subequently, baed on te tet data, te formula for calculating te denity and kinematical vicoity of te oil wa got and read a T -. T -. T. 6 () Te value of te kinematical vicoity of working liquid, namely (water), 9,, 7, 9,, and Te oil temperature wa monitored bot in te oil tank and in te pump uction nozzle. Uually, te oil temperature rie le tan during a performance tet. In toe experiment, Reynold number Re wa in te range of EXPERIMENTAL RESULTS. Performance Curve Figure ow te variation of ead curve veru flow rate wen te vicoitie of working liquid are, 9 and mm /, repectively. A larger dicarge angle caue te pump to develop a iger ead tan a maller one doe. A te vicoity i mm /, te peak ead a occurred at a flow rate of Q =m /; rater tan at zero flow rate. P(kW) P(kW) P(kW) =mm / = o = o = o =6 o Q(m /) =9mm / = o = o = o =6 o Q(m /) (c) =mm / = o = o = o =6 o Q(m /) Fig. Saft-power curve in term of flow rate at tree vicoity value

5 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. Ti i o-called untable or ooked ape ead curve effect. Fortunately, uc an untable curve diappear gradually wit increaing vicoity. No matter watever value te vicoity i, te maximal cange of te ead curve due to te dicarge angle variation almot maintain te ame amount, i.e., te effect of dicarge angle on te ead curve eem to be independent upon te vicoity of te working liquid. Hence, canging dicarge angle ould be an effective way for altering te ead of centrifugal oil pump. Figure illutrate te variation of aft power curve in term of flow rate a te vicoitie of working liquid are, 9 and mm /. Like te ead curve, te effect of te dicarge angle on te aft-power curve appear to be independent on te vicoity of te working liquid. Furter, a larger dicarge angle definitely conume more power tan a maller one doe. Figure demontrate te variation of te efficiency curve againt flow rate wile te vicoitie of working liquid are, 9 and mm /. Firt of all, te efficiency reduce continuouly wit increae in vicoity. Unlike toe in te ead curve, te effect of te dicarge angle on te efficiency curve i dependent on te vicoity of te working liquid. A te vicoity i le tan mm /, te efficiency of te pump wit a dicarge angle of º i iger tan tat wit an angle of 6º. However, for te vicoity more tan mm /, te ituation i revered.. Hydraulic Parameter at BEP In order to illutrate te effect of vicoity on te performance of te centrifugal oil pump wit variou dicarge angle more clearly, Fig. i applied to ow te ydraulic parameter, uc a ead, ydraulic power and efficiency at te bet efficiency point (BEP) againt vicoity. Te impeller wit a dicarge angle of 6º alway develop a iger ead tan te oter at te BEP. A te vicoity i iger tan mm /, te ead i improved by %; a te vicoity i up to mm /, te efficiency i increaed by % compared to te original impeller wit º exit angle. However, at te ig flow rate, te efficiency i improved by 6%. Te reaon for ti i tat te ydraulic power of te impeller wit 6º dicarge angle drop off very lowly tan te oter wit increaing vicoity. A imilar beavior wa oberved in te perviou tudie (Toyokuro et al, 979; Tanaka and Oai, 9; Ota and Aoki, 99). Ti fact eem to reveal tat te blade exit angle effect on te pump ead and efficiency i nearly equal. Wen a pump pumping water, it wa own experimentally tat te blade exit angle effect wa dominated on te pump efficiency (Kamimoto and Matuoka, 96) rater tan on te ead. However, te reult wa dicovered tat te effect on te ead not efficiency wa ubtantial (Varley, 96). Our current reult don t agree wit tem. (%) (%) (%) 6 =mm / = o = o = o =6 o Q(m /) 6 =9mm / = o = o = o =6 o Q(m /) 6 =mm / = o = o = o =6 o Q(m /) Fig. Efficiency curve againt flow rate at tree vicoity value From te point of view of efficiency, wile te vicoity of liquid i lower tan mm /, te performance of te original impeller wit a dicarge angle of º, i bet. However, wile te vicoity i iger tan ti value, te performance of te newly deigned impeller wit a dicarge angle of 6º i bet. Te impeller wit an exit angle le tan º a a very poor performance.. Slip Factor Te lip factor i ued to pecify te flow lip effect at te exit of a centrifugal pump impeller and i a key parameter to etabli a teoretical ead developed by te impeller. Tere are everal verion of definition for te lip factor (Qiu, Mallikaracci and Anderon, 7). (c) 9

6 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. H(m) 7 6 = o = o = o =6 o (mm /) 6 = o = o = o =6 o in () Z Tee equation do not involve te effect of bot fluid vicoity and flow rate. V u u-vu u V u It i intereting to note tat a lip factor of centrifugal pump impeller can be calculated baed on te pump experimental performance curve and impeller geometry (Li, ). Te following equation i ued to etimate te lip factor at te BEP W W Fig. 6 Velocity triangle at impeller exit P (kw) g dh u H Q u dq g F tan V () (%) (mm /) 6 (c) = o = o = o =6 o (mm /) Fig. Head, ydraulic power and efficiency (c) at BEP in term of vicoity However, te following definition (Brennen, 99) i adopted in ti paper u V u u () u V u were te lip velocity of fluid (Fig. 6) depend on te impeller geometry and flow rate a well a fluid vicoity etc. Traditionally, te lip factor of a centrifugal pump impeller i frequently etimated by mean of te Weiner or Stodola formula. Te Weiner expreion i read a (Brennen, 99) in (). 7 Z and te Stodola relation i written a (Brennen, 99) were te volumetric efficiency, V wa calculated by uing Stepanoff metod for te geometrical parameter of bot te wear-ring intalled in te impeller roud and ub, ring radial clearance a well a te preure differential acro te ring (Stepanoff, 9). Te detail of te calculation are available in Li (). Figure 7 illutrate te lip factor at te BEP a a function of blade dicarge angle at te vicoitie of, 9 and mm /. From Fig. 7, it wa learnt tat no matter watever value te vicoity i, te lip factor calculated by uing te experimental ead-flow rate relation decreae wit increaing blade dicarge angle. Te fluid vicoity doe affect te lip factor, but te effect i not ubtantial. Tee finding are conitent wit toe illutrated by Toyokuro et al (979) and Ota (999) regreion =mm / =9mm /. =mm / Wiener Stodola. 6 Fig. 7 Slip factor a a function of blade exit angle at tree vicoity value at BEP If regardle of te vicoity effect, te cattered point of te lip factor etimated via te experimental data can be repreented by te following linear equation wit repect to te blade dicarge angle

7 W.G. Li / JAFM, Vol., No., Iue, pp. -9, (6) Moreover, te lip factor etablied by te Weiner and Stodola formulae ow extremely large difference from toe determined by te experimental data. Ti ugget tat if toe expreion are applied to etimate te lip factor for igly vicou oil, ignificant error will be caued.. MODEL EXIT ANGLE EFFECT Te centrifugal pump performance prediction wa traditionally baed on te ydraulic lo analyi in a pump (Aientein, 97; Pigott, 9; Ratod & Donovan, 9; Takagi et al, 9; Stirling, 9; Aly & Al-Zubaidy, 99; Yoon et al, 99; O & Cung, 999; Zaer, ). In toe prediction, te fluid vicoity remain uncanged. More recently, te effect of fluid vicoity on centrifugal pump efficiency wa own analytically wit te caling law related to te pump mecanical, volumetric and ydraulic efficiencie (Gulic, 999a; 999b; ). Te performance of tree centrifugal pump wa evaluated by conidering blade loading lo and impeller and volute friction lo baed on pipe flow at a variety of fluid vicoity (Hamkin and Hergt, 97). Unfortunately, any ueful equation for etimating toe loe were not preented by tem at all. Te ydraulic loe in centrifugal oil pump were calculated by uing te boundary layer teory in fluid mecanic at different vicoitie of liquid pumped to explore te caue for te uddenriing ead effect in te pump (Li, ). However, in te calculation te diffuion lo in te impeller wa ignored. friction coefficient for uc pipe are applied to determine te friction lo in te actual flow paage. Te experimental centrifugal oil pump i a low pecific peed pump becaue te pecific peed of it impeller i jut around. In te impeller of uc a pump, te expanion of te cro-ectional area of flow cannel i muc large in te radial direction even a ligt contraction in te axial direction. Conequently, te impeller are ubject to a diffuion lo, wic mut be taken into account in te ydraulic lo model.. Hydraulic Lo in Impeller Te major dimenion of te impeller and volute were ketced in Fig.. Te ydraulic loe in te impeller conit of te kin friction and diffuion loe. volute roud mean tream urface wear-ring balancing ole t b b b t caing ub wear-ring In ti ection, it i intended to teoretically invetigate te effect of exit blade angle on te pump performance at different vicoitie of fluid at te pump duty point and to compare wit te experimental obervation. In fact, uc an invetigation i equivalent to ow to exactly etimate ydraulic loe inide te pump, eventually cauing precie prediction of te performance parameter at toe vicoitie. Dw piral body D D D dicarge nozzle. Hydraulic Lo Model It i aumed te flow in te pump i one-dimenional, teady, laminar or turbulent. Since te fluid velocity in te ide-entry of te pump own in Fig. i muc lower tan toe in te impeller and volute, te ydraulic loe can be ignored in te entry. Jut te loe acro te impeller and volute are conidered ere. It i believed tat te angle of attack to te entrance of blade i o mall tat te ock lo tere alo can be neglected. Terefore, a flow jut uffer from kin friction and diffuion loe in an impeller. For te volute, a flow i ubject to te kin friction lo in te piral body a well a kin friction lo and diffuion in te dicarge nozzle. A mixing lo occur at te boundary between te impeller exit and volute inlet. For convenience, te complicated flow paage in te impeller and volute are converted into traigt circular pipe by uing ydraulic diameter properly; te kin Fig. Major dimenion of impeller and volute Te following expreion i employed to figure out te friction lo if Li W (7) D g i D L i tongue L K

8 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. were te blade lengt L i on te mean tream-urface wa correlated to te blade exit angle of four experimental impeller by te following equation L i (). Te mean relative velocity of fluid troug te impeller paage W i equal to alf um of toe at te blade inlet and outlet, repectively W W W (9) Te ydraulic diameter Db D b Z Z D D b b Z Z D i D i etimated by te formula i Furter, te equation can be implified a follow () D i () Zb D D b D b Zb D Te kin friction coefficient,, depend on te flow regime in te paage and Reynold number Rei ( Rei W Di v ) and te rougne of wetted urface, k. Te diffuion lo in te impeller can be calculated by uing te following equation W id () g Te diffuion coefficient i dependent on te equivalent expanion angle of te impeller flow paage, wic i determined by D D tan () ZL i For te perviou experimental impeller, te equivalent expanion angle can be expreed in term of blade dicarge angle ().. Hydraulic Lo in Volute Tere are tree kind of ydraulic lo in te volute. One i te kin friction lo in te piral body, one i te friction and diffuion loe in te dicarge nozzle and one i te mixing lo beind te impeller. Te friction lo along te wall of te piral body can be calculated by uing te following equation Vf LV V () D g V Te ydraulic diameter D V i related to te mean cro-ection area of te volute a follow D V F (6) b b m Fm Te mean cro-ection area i decided by te area of te cro-ection -, F, and -, F a follow F m F F (7) F. D D b and F a Note tat te area included te area of D D b.. Te mean velocity of fluid, V, in te volute i imply etimated via V Q 6 F () Te lengt of te piral body, uing te expreion L V, i determined by L V D 6 (9) Likewie, te kin friction coefficient,, alo depend on te flow regime in te volute and Reynold number Re ( Re V D v ) and te rougne of wet urface V, k. V V Te kin friction lo in te dicarge nozzle i etimated by mean of te following expreion Vdf L V k 9 () D g 9 Te mean diameter of te dicarge nozzle can be determined by D 9 D D9 () Te equivalent diameter of te ection - i given by F D () Te velocity of fluid troug te pipe wit a diameter D i calculated by te equation of 9 V9 Q F 9 () were te mean area F. Te kin friction 9 D 9 coefficient,, i in term of te Reynold number Re ( d Re V D v ) and te rougne of wet urface, k. d 9 9 Te diffuion lo in te dicarge nozzle i determined by te following equation V Vde () g Te diffuion lo coefficient depend on te equivalent expanion angle of te dicarge nozzle,, i written a D tan D 9 L K () Te mixing lo beind an impeller i conidered to be te lo due to a udden expanion of te meridian flow and te lo due to turbulent or laminar earing effect

9 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. in te tangential direction between flow exiting te impeller and tat in te volute. Te mixing lo beind te impeller i calculated by te equation b b V V V m u ie (6) g Te firt term i Eq. (6) i according to te udden expanion lo in Wite (99), but te econd term i propoed by te autor of ti paper.. Hydraulic Parameter Etimate For te volumetric efficiency of a pump, V, i ligtly increaed by a iger vicoity of liquid pumped (Kurokawa, 99). Since it variation i very mall, it i imply be etimated by uing te Lomakin empirical equation (Kurokawa, 99) V. 7 (7) 6n. Note tat te econd term i added into Eq. (7) by te autor of ti paper to approximately account for te effect of te wear-ring and balancing ole in te experimental impeller ub on te volumetric efficiency. Te ydraulic efficiency of te pump, can be determined according to te teoretical ead and total ydraulic loe in te impeller and volute. It i expreed by l () H t Te total ydraulic lo, l, i te um of all te loe in te impeller and volute, it i read a (9) l if id ie Vf Te teoretical ead generate by te impeller, H t, depend on te flow rate and impeller geometry a well a rotating peed. It i pecified by te Euler equation for turbomacine u Q H t u () g VDb tan Te lip factor a been decided wit Eq. (6). Te blade blockage coefficient at te outlet,, i calculated via te expreion ZS u () D Te mecanical efficiency of te pump i etimated by uing te mecanical lo and aft-power a follow. Pd m () P It wa found tat te meaured dik friction loe in te actual impeller uually were iger tan toe etimated wit empirical equation (Nemdili and Hellmann, 7). Te factor. in Eq. () i ued to take ti effect into account. Te dik friction power lo of te impeller, P, i calculated by te following equation (Gulic, 999a) d Vdf Vde P d CM f geo R Rw () were f i te ape factor for cloed type impeller geo of centrifugal pump, f geo =. (Gulic,999a). Te torque coefficient due to dik friction on te impeller roud and ub, C i written a (Sclicting, 96) C M M R t Re.. 67 Re. 6 Re. Re Re Re () Te dik Reynold number baed on te impeller radiu i defined by Re D. Te aft-power tat a pump conumed i expreed by P gq H. P () t t d Te teoretical flow rate troug an impeller i Q Q. Te gro efficiency of te pump can be t V etimated by mean of te volumetric, ydraulic and mecanical efficiencie available via (6) V m At te ame time, te actual ead generated by te pump and te flow rare troug te pump can be predicted by uing te following equation accordingly. Te ead i read a H H t l (7) And te flow rate Q K Q Q W () Te flow rate of pumped water at te deign duty Q W i pecified. However, it will get mall wit increaing vicoity of fluid becaue of vicou effect. Te correction factor for uc an effect i correlated to te vicoity by an equation Friction and Diffuion Lo Coefficient K Q Wen te Reynold number Re, te flow in a traigt duct wit circular cro-ection i in te laminar regime, and te kin friction coefficient i determined by te following formula (Sclicting, 96) 6 (9) Re For te impeller, Re Rei ; for te volute, Re ReV ; but for te dicarge nozzle, Re Red. Wen Re >, te flow in te impeller or volute i turbulent. If k, ten te flow i in te turbulent moot regime. In ti cae, te friction coefficient i independent of te relative rougne k D ( k Di or k D V or k D9 ), but correlated to te Reynold number Re ( Re i or Re V or Re d ). Te correponding friction lo coefficient i written a (Sclicting, 96)

10 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. Re.. lg Te rougne of wet urface i () k 6Ra for cat wall. For te cat impeller and volute in te paper, te rougne eigt, wic i rated a te aritmetic average deviation of te urface valley and peak, i Ra m. Te tickne of te ub-laminar layer i expreed by. D Re. If k, ten te flow i in te turbulence tranition zone. Conequently, te friction lo coefficient depend on bot Re and k D, and i read a (Sclicting, 96) k. 7 lg D. Re 7 () However, if k, ten te flow i in te complete turbulence roug zone, cauing te coefficient jut related to k D and own a follow (Sclicting, 96) () k 7. lg D Te impeller and volute dicarge nozzle are ubject to a diffuion lo. A coefficient related to uc a diffuion lo i conidered to be equal to tat in conical diffuer approximately. Troug fitting te curve of diffuion lo coefficient in a conical diffuer wit fully developed inlet flow, an empirical relation i obtained to etimate uc a coefficient for any diffuion angle (Wite, 99) Re (). ln( Re) Re were Te lat term in te econd expreion in Eq. () i propoed by te autor of ti paper to involve low Reynold number effect on te diffuion lo coefficient baed on te experimental data preented in Fried and Idelcik (99). For te volute dicarge nozzle, angle ould be replaced wit te nozzle equivalent expanion angle..6 Computed Reult Te computation were conducted at te duty point Q =m / for te denity =(water), 9.96, W 9.,.,.,.9, 77.6, 7.(oil) kg/m and =(water), 9,, 7, 9,, and mm / (oil), repectively. Te blade dicarge angle wa varied between o and 6 o. Te reult for jut te vicoitie of,, and mm / are own to get tidy plot. Te ead and aft-power and total efficiency in term of blade exit angle are illutrated in Fig. 9 for different vicoitie at te duty point. Tey can be compared wit te experimental data in Fig.. Te ead etimated rie wit increaing blade exit angle but reduce teadily wit increaing vicoity. Note tat a more cange of ead appen wen te exit angle i between o and o. Suc variation trend eem to agree wit experiment. H(m) P(kW) (%) 6 6 =mm / =mm / =9mm / =mm / =mm / =mm / =mm / =9mm / =mm / =mm / (c) =mm / =mm / =9mm / =mm / =mm / peak Fig. 9 Computed ead, aft-power and efficiency (c) at duty point in term of blade exit angle Te computed aft-power get large wit increaing vicoity and blade dicarge angle imultaneouly. However, it really a a maller riing lope tan te experimental curve. Te reaon for ti migt be Eq. () i unable exactly to account for te dik friction over te actual impeller wit complicated roud and ub geometry. Ti problem need to be confirmed wit experiment or CFD imulation.

11 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. H(m) P(kW) (%) 6 6 =mm / =mm / =9mm / =mm / =mm / =mm / =mm / 6 =9mm / =mm / =mm / (c) =mm / =mm / =9mm / =mm / =mm / Fig. Experimental ead, aft power and efficiency (c) at duty point in term of blade exit angle Like te experimental pump efficiency, te etimated one i igly vicoity-dependent. Moreover, te optimal blade exit angle for bet efficiency occur at around o at le vicoity, but wit increaing of vicoity it prefer to be large one. Ti feature a been demontrated in Fig. 9 clearly by uing te peak efficiency curve. Note tat for te experimental pump efficiency in Fig., maximum efficiency i obtained at =º for mm / and for mm / te peak efficiency i acieved at =6º. Te ydraulic efficiency i own in Fig. for variou vicoitie in term of blade dicarge angle at te duty point. Te effect of vicoity on te ydraulic efficiency muc reemble to tat on te pump total efficiency. Te ydraulic efficiency i reduced ubtantially by te increaing vicoity. However, at a low vicoity, a relative mall blade angle allow te pump to ave bet ydraulic efficiency; contrarily, a relative large blade angle enure te pump to acieve bet performance at a iger vicoity. It i uc a variation of ydraulic efficiency againt blade exit angle tat reult into te pump total efficiency to preent te profile own in Fig. 9 (c). (%) m (%) 7 6 =mm / =mm / =9mm / =mm / =mm / =mm / =mm / =9mm / =mm / =mm / 6 7 Fig. Etimated ydraulic and mecanical efficiencie at duty point in term of blade exit angle Te mecanical efficiency i given in Fig. a a function of blade dicarge angle a well. It i noted tat te mecanical efficiency i ignificantly affected by vicoity, but it i jut ligtly increaed wit increaing dicarge angle. It i te dramatic reduction in te ydraulic and mecanical efficiencie tat contribute to te degraded performance of a centrifugal oil pump wit increaing vicoity. Te kin friction lo in te impeller a been demontrated in Fig. in term of blade exit angle for different vicoitie. Ti lo i very dominated in te impeller wit a maller dicarge angle rater tan wit a larger angle at a iger vicoity. It ugget tat for pumping igly vicou liquid an impeller aving a larger blade angle ould be more efficient compared to tat wit a maller one. Te friction lo in te volute i preented in Fig.. Wit increaing blade exit angle, a teady but low increae lo i oberved. Ti indicate an impeller

12 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. wit a larger blade angle a a negative effect on te performance of volute. if (m) =mm / =mm / =9mm / =mm / =mm / Moreover, for laminar flow, te lo wan t canged ignificantly until Reynold number le tan (Olveira and Pino, 997; Oliveira, Pino and Sculte, 99). In our cae, ince te Reynold number i more tan (impeller) or 9 (volute), te udden expanion lo can be conidered to be vicoityindependent. Te mixing lo may be affected by Reynold number, but no relevant evident i found in literature, tu, it a to be treated regardle of vicoity of fluid i mm / Vf (m) 6 =mm / =mm / =9mm / =mm / =mm / 6 7 Fig. Hydraulic loe in impeller and volute at duty point in term of blade dicarge angle v Rei mm / Te friction lo in te impeller ow a little variation wen 9mm /. Te mall friction lo coefficient, own in Fig., are reponible for ti effect. Te friction lo in te volute alo i ligtly increaed wen mm /. Likewie, in tat cae, te mall friction lo factor are een in Fig.. Te diffuion loe in te impeller and beind te impeller ave been plotted in Fig. and, repectively, at variou vicoitie. Te diffuion lo i ligtly vicoity-dependent and get ignificantly large wit increaing blade exit angle. Compared to te friction lo in te impeller in Fig., te diffuion lo i quit ubtantial, o tat te expanion of croectional area of impeller paage ould be carefully controlled to make te diffuion lo a mall a poible. Te expanion lo beind te impeller grow quickly wen º, but lowly wen º. Ti lo magnitude i comparable to te kin friction lo in te impeller but muc maller tan tat in te volute. Te expanion lo beind te impeller conit of a udden expanion lo in meridian plane and a mixing lo in te tangential direction. It wa own experimentally tat te udden expanion lo wa independent wen Reynold number i in a range of (- 6) for turbulent flow (Iguci and Omi, 96).. 6 Rev Fig. Friction lo factor in term of Reynold number in impeller wit =º and volute, figure in plot ow vicoitie of fluid Te total ead lo and ratio of total ydraulic lo in te impeller to tat in te volute ave been own in Fig. and. Te total ead lo grow teadily wit increaing blade exit angle and vicoity of fluid, epecially wen te vicoity i more tan mm /. Te ratio of ead lo i in te range of.6-.9 and depend on bot blade exit angle and vicoity of fluid. Ti ugget tat for a maller blade exit angle te ydraulic loe in te impeller are comparable to toe in te volute; owever, a te blade angle increaing, te loe in te impeller are around 6% of te loe in te volute, epecially wen vicoity i iger tan 9mm /. Ti implie te volute may play an important role in te pump performance, o tat it ould be deigned a perfectly a poible, epecially for igly vicou liquid. Note tat tee finding are conitent wit te reult preented in Li () by uing te boundary layer teory. 6

13 W.G. Li / JAFM, Vol., No., Iue, pp. -9, mm / mm / id (m) 6 =mm / =mm / =9mm / =mm / =mm / 6 7 H(m) 6 6 mm / mm / 9mm / =mm / ie (m) =mm / =mm / =9mm / =mm / =mm / 6 7 Fig. Etimated diffuion and udden expanion a well a mixing loe at BEP in term of blade exit angle i + V (m) i / V =mm / =mm / =9mm / =mm / =mm / =mm / =mm / =9mm / =mm / =mm /. 6 7 Fig. Total ead lo and ratio of ydraulic loe in impeller to toe in volute at BEP in term of blade dicarge angle (%) mm / 9mm / mm/ mm / 6 7 Fig. 6 Comparion of ead and efficiency between original and redeigned cae, olid line i for redeigned cae and daed line i for original cae At te vicoity of mm /, te ratio of ydraulic lo i iger tan tat at mm /. Te reaon underlying ti effect i tat te diffuion lo in te impeller i increaed remarked at mm / own in Fig.. Te experiment on te model pump wit two impeller of º and 6º dicarge blade angle and 7 pecific peed (Toyokura, Kurokawa and Kanemoto, 979), te pump wit te impeller of 6º exit angle owed a better efficiency tan tat of º angle at a vicoity of mm / ( Re =. ) yet. However, in our cae, te pump wit te impeller of 6º dicarge angle demontrated a iger efficiency compared to tat of º angle at a vicoity a ig a mm / ( Re =.7 ). Te effect of blade dicarge angle on te pump performance in our cae doen t eem to be tronger at variou vicoitie. Te reaon for ti may be te pecific peed of te indutrial pump ued in te experiment i jut.6, le tan alf of te pecific peed of te model pump. Te pecific peed effect need to be invetigated in future. Since te friction lo in te volute i primary a own in Fig., te volute cro-ection area i enlarged by % (widt and eigt are increaed by %, repectively) to reduce uc a lo. In order to keep te ratio b b uncanged, te widt of blade exit b alo i increaed by %. Fig. 6 illutrate te comparion of ead and efficiency between te original and redeigned 7

14 W.G. Li / JAFM, Vol., No., Iue, pp. -9,. cae. It i clear tat te pump wit increaed volute cro-ection and enlarged blade exit widt doe get a better performance, epecially at mall blade exit angle ( º). Te ydraulic diameter of te volute and impeller are increaed to.mm and 9.mm from.6mm and.mm, repectively. A a reult, te peak pump efficiency i improved by % and te ead i increaed by.7% wen =º.. CONCLUSION Te effect of blade dicarge angle on te performance of a centrifugal oil pump ave been invetigated experimentally and analytically wile te pump andle water and oter vicou oil. Te ydraulic lo in te impeller and volute a been calculated in term of bot vicoity and blade exit angle by uing a model on te fluid mecanic bae. Te following concluion can be drawn: () te blade dicarge angle a a trong but equal influence on te ead, aft power and efficiency of te centrifugal oil pump at variou vicoitie of liquid pumped; () Te rapid reduction in te ydraulic and mecanical efficiencie i reponible for te pump performance degradation wit increaing vicoity of liquid; () at all te vicoity value, te volute ow ignificant effect on te performance, it ould be deigned a perfectly a we can; () te teoretical ydraulic lo model i able to get broadly imilar beaviour to te experimental curve; () for te ydraulic lo model i ubject to limitation, it a been planned tat te effect of blade exit angle will be invetigated numerically by uing CFD code, uc a Fluent. It i opeful te reult will be available oon. ACKNOWLEDGEMENTS Te reearc wa conducted under a grant awarded troug te Key Reearc and Development Program for te Quality Reearc Group at Lanzou Univerity of Tecnology. Te univerity wa acknowledged indeed; additionally te previou potgraduate tudent FYL and tecnician FZS and CX were alo appreciated very muc for teir fantatic contribution in laboratory. REFERENCES Aientein, M.D. (97). A new metod of eparating te ydraulic loe in a centrifugal pump. ASME Tranaction 9, -7. Aly, S. and S. Al-Zubaidy (99). Performance prediction metod for centrifugal pump. SAE paper 97. Aoki, K., H. Ota, and Y. Nakayama (97). Study on centrifugal pump for ig vicoity liquid (te t report, effect of impeller output angle and number of blade on te pump performance of cloed type impeller). Proceeding of te Scool of Engineering, Tokai Univerity 7(), -. Aoki, K., T. Yamamoto, H. Ota and Y. Nakayama (9). Study on centrifugal pump for ig vicoity liquid. Tran JSME, Serie B (6), 7-7. Brennen, C.E. (99). Hydrodynamic of Pump. Oxford, UK, Oxford Univerity Pre, -. Fried, E. and I.E. Idelcik (99). Flow Reitance: a Deign Guide for Engineer. New York, USA: Hemipere Publiing Corporation, -. Gulic, J.F. (999a). Pumping igly vicou fluid wit centrifugal pump-part. World Pump 9, -. Gulic. J.F. (999b). Pumping igly vicou fluid wit centrifugal pump-part. World Pump, 96, 9-. Gulic. J.F. (). Effect of Reynold number and urface rougne on te efficiency of centrifugal pump. ASME Journal of Fluid Engineering, Hamkin, C. P. and P.H. Hergt (97, May). Prediction of vicoity effect in centrifugal pump by conideration of individual loe. In Proceeding of te Tird European Congre on Fluid Macinery for te Oil, Petrocemical and Related Indutrie, Hague, Neterland, pp Iguci. M. and M. Omi (96). Lo coefficient foe flow troug a udden expanion and a udden contraction cloely placed. Tran JSME, Serie B (), -. Kamimoto, G. and Y. Matuoka (96). On te flow in te impeller of centrifugal type ydraulic macinery (te nd report). Tran JSME, Serie (), -9. Kurokawa, J. (99, April). Simple formulae for volumetric efficiency and mecanical efficiency of ydraulic macinery. In Proceeding of te rd Japan-Cina Joint Conference on Fluid Macinery, Oaka, Japan, pp. -. Li, W.G. (). Te udden-riing ead effect in centrifugal oil pump. World Pump 9, -6. Li, W.G. (). Te Influence of number of blade on te performance of centrifugal oil pump. World Pump 7, -. Li, W.G. (). A metod analyzing te performance of centrifugal oil pump. ASME Journal of Fluid Engineering 6(), -. Ota, H (999). Effect of Reynold number of lip factor of centrifugal pump for ig vicoity liquid. Tran JSME, Serie B 6(69), Nemdili, A. and D.H. Hellmann (7). Invetigation on fluid friction of rotational dik wit and witout modified outlet ection in real centrifugal pump caing. Forc Ingenieurwe 7, O, H.W. and M.K. Cung (999). Optimum value of

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