A New Method to Calculate Centrifugal Pump Performance Parameters for Industrial Oils

Transcription

1 Journal of Appled Flud Mechancs, Vol. 8, No. 4, pp , Avalable onlne at.jafmonlne.net, ISSN , EISSN DOI: /acadpub.jafm A Ne Method to Calculate Centrfugal ump erformance arameters for Industral Ols M.. Shojaeefard 1, B. Salman Rz 1, A. Khalkhal 2 and M. Tahan 3 1 School of Mechancal Engneerng, Iran Unversty of Scence and Technology, Tehran,16844, Iran. 2 School of Automotve Engneerng, Iran Unversty of Scence and Technology, Tehran,16844, Iran. 3 School of Ne Scences and Technologes, Unversty of Tehran, , Iran Correspondng Author Emal: behzad7038@gmal.com (Receved June 28, 2013; accepted August 16, 2014) ABSTRACT umpng of ol nstead of ater usng centrfugal pumps causes rapd ncrease n the hydraulc losses hch results sgnfcant reducton n head and effcency. Therefore, dervng analytcal methods to calculate varaton of pump performance parameters versus orkng flud vscosty s very mportant. In the present study, a novel method s proposed to calculate the head (), effcency ( ) and nput poer ( ) based on n the loss analyss for pumps usng ndustral ols. A computer code s developed based on represented method and the results of ths method are compared th expermental results for a centrfugal pump of type KW K- Bloc The results sho good agreement beteen analytcal and expermental methods. Fnally, usng such computer code, dagrams of head, effcency and nput poer versus orkng flud vscosty are plotted. The results sho an nterestng pont knon as sudden rsng head hch s observed expermentally and numercally n lteratures. Keyords: Centrfugal pump; Loss analyss; Analytcal method; Industral ol. NOMENCLATURE A Area ( 2 b dth of channel n merdonal secton (m) c absolute velocty ( ms) C eq roughness equvalence factor C f frcton coeffcent d dameter ( m ) db arthmetc average of dameters at mpeller (m) dm geomet rc average of dameters at mpeller (m) e vane thckness (m) f geo geometrcal factor f correcton factor for head f q mpeller eyes per mpeller f correcton factor for flo rate f R roughness nfluence on dsk frcton f η correcton factor for effcency f ηh correcton factor for hydraulc effcency g acceleraton of gravty ( ms 2 ) head (m) m ) * q flo rate referred to flo rate at BE r radus (m) Re Reynolds number S ax axal dstance beteen mpeller shrouds and casng u crcumferental velocty ( ms) equvalent sand roughness (m) slp factor effcency h hydraulc effcency vol volumetrc effcency head coeffcent densty ( kg m 3 ) sp leakage flo rate through seal at mpeller nlet knematc vscosty ( m 3 s ) blade blockage factor angular rotor velocty ( 1s)

2 M.. Shojaeefard et al. / JAFM, Vol. 8, No. 4, pp , K RR dsk frcton coeffcent k nfluence of mpeller nlet dameter on slp factor n rotatonal speed (rpm) n specfc speed q n m nput poer () mechancal poer losses () RR dsk frcton poer () u useful poer transferred to flud flo rate m 3 s E flo rate through axal thrust balancng devce unversal specfc speed s β B blade angle Abbrevatons, subscrpts, superscrpts 1 mpeller blade leadng edge 2 mpeller blade tralng edge BE best effcency pont CLA center lne average crt crtcal number step number mp mpeller Lam lamnar flo m merdonal component mod modfy Tu turbulent level turb turbulent flo ater ol 1. INTRODUCTION ydraulc losses n all components of pump are made up by frcton and turbulent dsspaton losses. Frcton losses are depended on orkng flud vscosty and therefore pump performance parameters are hghly affected by ths parameter. It should be noted that ths s because the flo regme of hghly vscous fluds tends to be lamnar, roughness of mpeller sde alls and roughness of hydraulc channels s of lttle mportance for operaton th vscous fluds. Due to mportance of orkng flud vscosty, there have been great researches done to study vscous flud pumpng (Nemdl and ellmann 2007; L 1999, 2000, 2002, 2004, 2008, 2010; Gulch 2003). Most of these studes are based on expermental orks hch are tme-consumng and costly. L et al. (L and u 1997) studed effect of vscosty of flud on performance of centrfugal pumps, expermentally. In ther studes, ol th dfferent knematc vscostes as used. Results of such studes sho that by ncreasng vscosty, head and effcency n dfferent operatonal condtons decrease and nput poer ncreases. They also represented correcton factors for calculatng pump performance parameters such as head, effcency and volumetrc flo rate hen the pump orks th vscous flud nstead of ater. Correcton factors are obtaned usng expermental data as: K, K, K, here, and are volumetrc flo rate, head and effcency, respectvely and subscrpts ν and represent vscous and ater fluds. Smlar orks have been performed by Gulch et al. (Gulch 1999, 2003) to nvestgate flud vscosty effects on the centrfugal pump performance. Shojaeefard et al. (Shojaeefard et al 2006, 2007, 2012) dd vast researches to optmze centrfugal pump geometry for vscous flud pumpng. These researches nclude expermental and numercal studes of mpeller roughness, number of mpeller blades, passage dth, blade outlet angle and type of mpeller (closed or sem open). They studed centrfugal pumps performance usng ater and ol th dfferent vscostes and evaluated role of flud vscosty n operaton of centrfugal pump. Most of prevous researches ere done expermentally or numercally. In ths paper, unlke prevous researches, analytcal method based on loss analyss s represented for calculatng centrfugal pump performance parameters hen the pump orks th vscous fluds. In ths ay, mechancal, volumetrc and dsk frcton losses are consdered n calculatng hydraulc effcency. A computer program as developed for computng the pump performance parameters such as head, effcency and nput poer for vscous flud pumpng. Results of ths ne method ere verfed by comparng th the expermental results. Dagram of head versus flud vscosty are also derved usng such computer program. The nterestng pont knon prevously as "sudden rsng head" can be seen on such dagram. 2. CALCULATION OF UM ERFORMANCE ARAMETERS FOR VISCOUS FLUID UMING In ths secton, performance parameters of centrfugal pump such as head (), effcency () and nput poer ( ), for vscous flud pumpng n ll be derved usng ne method based on loss analyss. Geometres of the typcal centrfugal pump mpeller have been shon n Fg. 1. ydraulc, mechancal, volumetrc and dsk frcton losses are consdered n ths loss analyss, separately. Frcton coeffcent s the most mportant parameter n hydraulc losses. The frcton coeffcent s depended on flo regme and relatve roughness. Transton from lamnar to turbulent flo occurs at the crtcal Reynolds number Re crt hch can be calculated as follo 674

3 M.. Shojaeefard et al. / JAFM, Vol. 8, No. 4, pp , (a) (b) Fg. 1. a) A ve of the modeled mpeller b) Merdan plane of the mpeller Recrt (1) Tu here Tu s turbulence ntensty and n the present study s consdered as 0.1 (Ladouan and Nemdl 2009). Accordng to the value of Re crt flo regme ll be determned. Reynolds number can be calculated from u2. d Re 2b (2) 2v here d, u and ν are mpeller outlet dameter, 2b 2 crcumferental velocty n mpeller outlet and vscosty of flud, respectvely. Frcton coeffcent of the centrfugal pumps can be rtten as c f, turb Re Re 12.5 crt (3) 2.15 ( log(0.2 )) r Re 2b c f, lam Re Re Re Re 0.01 Re Re crt (4) here denotes the equvalent sand roughness and s defned as 6. CLA (5) C eq here C and represent the equvalence factor eq CLA and center lne average roughness, respectvely. C eq s consdered as 2.6 (Gulch 2008) and CLA s also consdered as 100 µm accordng to the expermental results(shojaeefard et al 2012). The best method to acheve mechancal losses s to use documentaton of the manufacturer of the mechancal equpment. If more accurate nformaton s not avalable the mechancal losses n ts BE can be estmated usng equaton belo ref.( ) 0.4 n m ref.( ) 0.3 (6) u n In ths equaton ref and n ref are consdered as 1 m 3 s and 1450 rpm, respectvely. The mechancal effcency of large pumps s around 99.5% or even above (Gulch 2008). Dsk frcton losses are caused by shear stresses n boundary layers on sold structures. These are depended on Reynolds number and surface roughness hch have sgnfcant effects on the thn boundary layers and attached flo n comparson th decelerated or separated flo. Snce Reynolds number decreases, dsk frcton losses ll be ncreased. Dsk frcton effect on effcency s mportant especally n lo rotatonal speed. The dsk frcton losses equaton can be rtten as S 1 ax. r r K b RR. fr (7) 2Re. Sax Re S 1 ax 2 r2 b here S s geometrc parameter hch s ax consdered as 0.05 d2b. Also, f R ndcates roughness nfluence on dsk frcton hch has been extracted n (Gulch 2008). Usng expermental data such as head and volumetrc flo rate of ater at the BE for each mpeller geometry, head coeffcent and specfc speed for ater can be determned (Gulch 2008). 2 g. BE BE (8) 2 ( r2 b. ) n BE fq nq (9) 0.75 BE f denotes mpeller eyes per mpeller. For mpellers q th one entrance f s equal to one (Gulch 2008). q 675

4 M.. Shojaeefard et al. / JAFM, Vol. 8, No. 4, pp , Dsk frcton poer s rtten as 3 5 KRR... r2. RR b fgeo (10) u nq. BE. fq here geometrc factor f geo for radal mpellers s consdered as 1.22 (Gulch 2008). Densty of ater Kg ( ) s also consdered as 1000 m at 3 250c. Volumetrc effcency can be evaluated by follong formula vol (11) S E here ndcates volumetrc flo rate, s S leakage through the annular seal at the mpeller nlet and s the volumetrc flo through a devce for E axal thrust balancng flo. Accordng to the reference (Gulch 2008), and S can be E consdered equal, approxmately. ydraulc losses consst of mxng and frcton losses n all components beteen sucton and dscharge nozzles affect hydraulc effcency. Mxng losses are the result of non-unform dstrbuton of velocty. These losses are mostly depended on Reynolds number. Flo deceleraton causes a thck boundary layer hch makes non-unform velocty dstrbuton. In non-unform flo, momentum exchange beteen streamlnes ll be ncreased because of dfferent eddes th varous scales. Water hydraulc effcency at BE can be calculated as follong equaton. h, (12), 1 ( RR ) m vol u u ydraulc correcton factor s defned as follong equaton hch ndcates rato of vscous flud hydraulc effcency to ater h, R, W c f, f h 1 1 (13) h, BE c f, RW, BE can be found accordng to equaton stated n reference (Gulch 2008). Multplyng hydraulc effcency correcton factor by ater hydraulc effcency at BE, vscous flud effcency n ths pont s acheved n the form of: h, fh. h, (14) ead of centrfugal pump at BE for vscous flud can be rtten as 2 h. u2 c. 2 g u2.tan (15) 2B here h,, and 2B are the hydraulc effcency, slp factor, blade blockage factor and the blade outlet angle, respectvely. u and 2 C stand for crcumferental and merdan components of absolute velocty at mpellers outlet. Blade blockage and slp factors can be calculated from equatons (16) and (17). z. 1 2 (1 la e ) (16). d2b.sn2b f here sn 2B zla k (17) k denotes the nfluence of mpellers nlet dameter on slp factor. Value of coeffcent f 1 for radal mpeller s consdered as 0.98(Gulch 2008). The absolute velocty ll be calculated from equaton (18), cm (18) db b To calculate C at BE, t s necessary to calculate volumetrc flo rate of vscous flud n ths pont hch vary by varaton of knematc vscosty. To calculate volumetrc flo rate of vscous flud accordng to the knematc vscosty dvergence, a ne method s proposed and employed n the s calculated from present study. At the frst step, head correcton factor f, BE BE, BE, (19) here BE, and BE, are the head of the centrfugal pump at BE for vscous flud and ater, respectvely and superscrpt denotes the step number. It s needed to obtan the value of BE, for each pump th specfc mpeller, expermentally. BE, s the value calculated at the step (4), but t s requred to assume an ntal value for ths parameter. In ths ay, ntal estmaton of 0 the BE, s consdered equal to value of the ater volumetrc flo rate at BE. The value of c 0 s then calculated from equaton (18). Usng obtaned 0 values for BE, and 0 0 c the value of BE, can no be extracted by equaton (15). At the 2nd step, volumetrc flo rate for vscous flud pumpng s calculated by BE, BE, BE,., BE f (20) here f, BE as obtaned from step (1). s BE, value of the ater volumetrc flo rate of the pump at BE hch s obtaned expermentally. It should be noted that to derve equaton (20) t s supposed that f, BE fq, BE (Gulch 2008). At the 3rd step, merdan component of the outlet absolute velocty C s obtaned from equaton (18) 676

5 M.. Shojaeefard et al. / JAFM, Vol. 8, No. 4, pp , as BE, c2 m (21). b2. d2b here as calculated at the step (2). BE, At the 4th step, ne value for vscous flud head s calculated from equaton (15) as 2 1 h. u 2 c BE, 2 g u2.tan 2B here c as obtaned at step (3). (22) At the last step, the error value of the vscous flud head s examned usng follong crtera here s the user defned reference value consdered as 0.01 n ths paper. If the value of 1 s bgger than, then a return to the step (1) and consderaton ( ) ll be 1 (23) ne 1 occurred, else the algorthm ll be fnshed and value of vscous flud head, volumetrc flo rate, head correcton factor and volumetrc flo rate correcton factor at BE can be obtaned from BE, 1 (24) BE, (25) BE,, BE (26) BE, f f BE, BE, (27) After computng and BE, f, t s possble, BE no to calculate head of the pump for vscous flud pumpng at other orkng condtons (part load and over load). In ths ay, the follong equaton can be used. f (28) here s head of centrfugal pump based on ater volumetrc flo rate acheved expermentally. f s the head correcton factor hch s obtaned from (Gulch 2008) 0.75 f 1 (1 f, BE) ( q ) (29) here q s BE,. volumetrc flo rate of vscous flud n any orkng condton can be obtaned by f. (30) here f stands for flo rate correcton factor that ll be ndependent from ater volumetrc flo rate. ump effcency for vscous flud pumpng s obtaned usng equaton f (31) here s pump effcency for ater handlng hch s obtaned expermentally. f stands for effcency correcton factor that can be rtten as 19 y Re f (Re mod mod ) (32) here y s consdered as 0.7. Re mod s represented n reference(gulch 2008). Equaton (32) s based on the loss analyss and f s ndependent of pump performance condton. Useful poer transferred to the vscous flud can be rtten as u... g (33) here g s acceleraton of gravty and,, stand for densty, head and volumetrc flo rate of vscous flud, respectvely. Densty of each orkng flud can be obtaned from ASTM D7042 accordng to the flud knematc vscosty at 25 oc. Input poer as an mportant parameter can be acheved by dvdng useful poer transferred to flud by pump effcency, hch ll be defned as: u n (34) The procedure of proposed method s summarzed n Fg EXERIMENTAL ROCEDURE In order to evaluate the ne method represented n secton (2) some expermental tests are carred out by the authors. Tests programs and comprehensve explanatons can be found n reference (Shojaeefard et al 2012). The ppe of the rg as made of stanless steel th nner dameter of 80 mm. The tank net volume as 2400 lters. The operaton condton as controlled by a gate valve on the dscharge ppe. A dgtal pressure transmtter gage as used at the pump nlet and outlet ppes to measure the nlet and outlet pressures accurately. Baffle plates ere used for dampng the dsturbance of dscharged flud. Test setup schematc s shon n Fg. 2. KW K-Bloc pump made by umpran Company s used for expermental tests. Ths centrfugal pump has sngle axal sucton and vane less volute casng. The pump test s drven by a three-phase AC electrc motor, hch ts rated poer s 5.5 KW and speed s 1450 rpm. The performance parameter of centrfugal pump for ater and ol th vscosty of 1 and 43 CSt for three dfferent geometres of mpeller (A, B and C) under steady condtons ere measured. Specfcatons of mpellers A, B and C are depcted n table (1). The expermental results for sx experments at best effcency pont are ndcated n table (2). 677

6 M.. Shojaeefard et al. / JAFM, Vol. 8, No. 4, pp , Fg. 2. Centrfugal pump test setup. Fg. 3. Flo chart of computer code. 678

7 M.. Shojaeefard et al. / JAFM, Vol. 8, No. 4, pp , Impeller Type Test number Table 1 Specfcaton of the tested mpellers A, B and C parameters β 1B β 2B b 1 b 2 d 1b d 2b e 1 e 2 e ε CLA Z la Dmensons Degree Degree mm mm mm mm mm mm mm μm -- A (Orgnal mpeller) B C Table 2 Expermental and analytcal results acheved n three dfferent mpeller geometres for varous vscostes Geometry hyscal ead oer consumpton Total effcency Impeller Type β 2B b 2 ρ ν Expermental Analytcal 1 A A B B C C Error (%) Expermental Analytcal Error (%) Expermental Analytcal Error (%) 4. RESULTS AND DISCUSSIONS A computer program has been developed for performng the ne method presented n secton (2). The code has been developed usng MATLAB R2009a. To verfy the proposed method, the results of ths ork are compared th the expermental results. Analytcal results for to vscostes of 1 and 43 CSt for three dfferent mpeller (A, B and C) are shon n table (2). Comparng expermental and analytcal results shos that these results are n agreement th each other. Fgures. 4, 5 and 6 sho the performance curves (-, -, n -) of centrfugal pump for pumpng fluds th vscostes of 1, 35, 86, 119 and 228 centstokes for three dfferent mpeller geometres A, B and C, respectvely, extracted by the ne method presented n ths paper. When the hghly vscous flud s pumped by centrfugal pump, the head and effcency of the pump decrease and smultaneously nput poer ncreases th ncrease n flud vscosty due to ncrease n hydraulc losses and skn frcton. Fg. 5. The performance curve of centrfugal ol pump th dfferent vscostes for mpeller "B". Fg. 6. The performance curve of centrfugal ol pump th dfferent vscostes for mpeller. Fg. 4. The performance curve of centrfugal ol pump th dfferent vscostes for mpeller "A". Fgure 7 llustrates pumps head varaton versus orkng flud vscostes for three dfferent mpeller geometres at BE. It can be seen n ths fgure that decreasng trend of the curve s changed and a sudden rse n head occurs at vscosty of 115 centstokes. For ν 115 centstokes, Reynolds number (see equaton (2)) ll be smaller than crtcal Reynolds number (see equaton (1)) and thus flo regme changes to lamnar. It s obvous from equaton (4) that, n lamnar regme, roughness of 679

8 M.. Shojaeefard et al. / JAFM, Vol. 8, No. 4, pp , mpeller alls and hydraulc channels has no sgnfcant effects on the frcton coeffcent. Moreover, n ths case, ncrease n Reynolds number results n frcton coeffcent reducton. Furthermore, for ν 115 CSt the flo of the boundary layers on the mpeller alls and hydraulc channels s n the hydraulcally smooth regon hch causes reducton n frcton coeffcent, too. It s evdent that reducton n c f results n ncreasng of f h and (see equatons (13) and (15)). Ths phenomenon namely sudden-rsng head has been observed n reference (L 2000, 2008) prevously. Sudden-rsng head also can be seen n - curves (Fgs. 4, 5 and 6) beteen ν=86 CSt and ν=119 CSt. Fg. 7. -ν curve of centrfugal pump for three dfferent geometres at BE. Fgs. 8 and 9 represents the varaton of maxmum effcency and nput poer th flud vscosty for three dfferent geometres, respectvely. It s clear from fg. 8 that, the slope of curve decreases th ncrease n vscosty of flud. It s because that, accordng to equaton (32) a sharp fall n effcency correcton factor occurs hen vscosty s changed from 1 to 35 centstokes, otherse for ν 35 CSt ncreasng n vscosty causes less fall n ths factor. Furthermore, as shon n fg. 9 a steep slope s seen n the range of 100 CSt to 120 CSt. The steep slope of n can be justfed usng the sudden ncrease n the head that s shon n fg. 7. Accordng to equaton (33), as the head ncreases suddenly, shos a sgnfcant groth. u Fg. 9. curve of centrfugal pump for three dfferent geometres at BEB. 5. CONCLUSION In ths paper an analytcal nvestgaton nto the performance of centrfugal pumps for vscous flud pumpng has been carred out. Consderng the comparson beteen the performance of centrfugal pump th dfferent mpeller durng pumpng ater and ol, the follong conclusons can be made: The results obtaned from expermental and analytcal methods have satsfactory agreement hch shos accuracy and relablty of ne proposed method based on loss analyss. Accordng to fgure for three dfferent mpellers, the best effcency pont shfts to loer flo rates at hgher hydraulc losses. Comparng the performance curve of centrfugal pump for three dfferent mpeller geometres accordng to Fgs. 4, 5 and 6 llustrates that geometry B have got a prorty over to other geometres of A and C for pumpng vscous flud. Ths s because of ncreasng the mpeller passage dth from 17 to 21 mm hch ncreases the head and hydraulc effcency due to reducton of the frcton losses. Also the centrfugal pump performance th the mpeller passage dth equal to 21 mm, at outlet blade angle of 30 o s mproved n comparson th 27.5 o and 32.5 o. Ths s due to reducton of the dsspaton arsng by vortex formaton n mpeller passage hen the pump handles vscous lqud. Fgure shos that n vscosty of 115 centstokes the sudden rsng head s occurred. Accordng to fgure n, the slope of ncrease of n th the groth of n geometry B s smaller than other geometres due to the reducton of the hydraulc loss n ths geometry. REFERENCES Fg. 8. curve of centrfugal pump for three dfferent geometres at BE. Gulch, JF. (2003). Dsk frcton losses of closed turbomachne mpellers. Forsch Ingeneures, 68, Gulch, J. F. (1999). umpng ghly Vscous Fluds th Centrfugal umps-art 1. World pumps. Gulch, J. F. (1999). umpng ghly Vscous Fluds 680

9 M.. Shojaeefard et al. / JAFM, Vol. 8, No. 4, pp , th Centrfugal umps-art 2. World pumps. Gulch, J. F. (2003). Effect of Reynolds number and surface roughness on the effcency of centrfugal pumps. ASME Journal of Flud Engneerng 125(4), Gulch, J. F. (2008). Centrfugal pumps. Sprnger- Verlag, Berln edelberg, ISBN 978(3), Ladouan A. and A. Nemdl (2009). Influence of Reynolds number on net postve sucton head of centrfugal pumps n relaton to dsk frcton losses, Forsch Ingeneures 73, L, W. G. (1999). Effects of vscosty of fluds on centrfugal pump performance and flo pattern n the mpeller. Internatonal Journal of eat and Flud Flo 21, L, W. G. (2000). The Sudden-Rsng ead Effect n Centrfugal Ol umps. World umps. L, W. G. (2002). Expermental nvestgatons nto the performance of a commercal centrfugal ol pump. World umps L, W. G. (2004). A Method for Analyzng the erformance of Centrfugal Ol umps. ASME Journal of Flud Engneerng 126, L, W. G. (2008). erformance computatons of centrfugal pump handlng vscous ols. Dra Irr Mach. L, W. G. (2010). Blade Ext Angle Effects on erformance of a Standard Industral Centrfugal Ol ump. Journa l of Appled Flud Mechancs 4: L, W. G., Z. M. u (1997). An Expermental Study on erformance of Centrfugal Ol ump. Fluds Mach 25(2), 3-7. Nemdl, A. and D.. ellmann (2007). Investgatons on flud frcton of rotatonal dsks th and thout modfed outlet sectons n real centrfugal pump casngs. Forsch Ingeneures 71, Shojaeefard, M.., M. B. Ehghagh and F. A. Boyaghch (2006). Expermental study and three dmensonal numercal flo smulaton n a centrfugal pump hen handlng vscous fluds. IUST Int J Eng Sc 17(3-4), Shojaeefard, M.. and F. A. Boyaghch (2007). Studes on the nfluence of varous blade outlet angles n a centrfugal pump hen handlng vscous fluds. Amercan Journal of Appled Scence 4(9), Shojaeefard, M., M. Tahan, M. B. Ehghagh, M. A. Fallahan and M. Beglar (2012). Numercal study of the effects of some geometrc characterstcs of a centrfugal pump mpeller that pumps a vscous flud. Computers&Fluds 60,