Evaluation of pump characteristic from measurement of fast deceleration

E alua ion o pump cha ac e is ic om measu emen o as decele a ion Daniel Him 1,aand Vladim´ ı Hab´ an2 1Vˇ SB – Technical Uni e si y o Os a a, Facul y o Mechanical Enginee ing, Depa men o Hyd odynamics and Hy- d aulic Equipmen , 17. lis opadu 15, 708 33, Os a a, Czech Republic 2B no Uni e si y o Technology, Facul y o Mechanical Enginee ing, Ene gy Ins i u e, Vic o Kaplan Depa men o Fluid Enginee ing, Technick´ a 2, 616 69, B no, Czech Republic Abs ac . A icle desc ibes an expe imen whe e a pump connec ed o he simple hyd aulic ci cui is decel- e a ed. Since he decele a ion is as enough he ope a ing poin o he machine mo es om he ini ial s eady posi ion o he b eaking zone, u bine zone and back o he new s eady posi ion. A dependence o he specific ene gy and he o que on he flow a e was e alua ed om he measu emen o he inpu and ou pu p essu e, o que and o a ional speed eco ded du ing he decele a ion. Ob ained cha ac e is ic is much wide han cu es ob ained om egula measu emen o s eady s a e. 1 In oduc ion Pipeline ansien s a e o en connec ed wi h pump an- sien s when he machine is s a ing o s opping. Pump does no ope a e unde s eady condi ion du ing hese e en s and ope a ing poin can go ou o he pumping egime. When one designs a pumping sys em i is necessa y o conside such ansien s and sugges app op ia e p o ec ion o pipe- line sys em. A sudden pump ip is a ypical example o po en ially dange ous e en [1]. Ene gy, which pump supplies o a hy- d aulic sys em, is gi en by pump cha ac e is ic. I depends on he flow a e and o a ional speed. When pump loses in- pu powe i s speed goes down acco ding o cu en flow a e and o que cha ac e is ic. Ene gy supplied by pump goes down as well as speed and can each a high nega i e alue which b ings a isk o ca i a ion. To p edic he pump beha iou du ing he s opping pe- iod o he black ou , i is necessa y o know he ex ended pump cha ac e is ic. P oduce usually does no p o ide his cha ac e is ic because i is difficul and expensi e o ob- ain i . This pape desc ibes a p ocedu e how o ge he ex- ended cha ac e is ic om measu emen o as pump de- cele a ion in a simple hyd aulic ci cui . The e is a lo o a icles dealing wi h he p oblem o pump decele a ion [2], [3] o accele a ion [4], [5], [6], bu au ho s ound only li - le in o ma ion abou econs uc ion o pump cha ac e is ic om measu emen o his ansien s. 2 Theo y The simples ci cui o measu emen o pump cha ac e is- ic is shown in he figu e 1. I consis s o a ank, measu ed pump and a al e, which se es o flow a e egula ion. Fo e alua ion o he cha ac e is ic, one has o measu e in- pu p essu e p2, ou pu p essu e p3, flow a e Q, speed n and o que T. The las wo i ems a e gained by dynamome- e . ae-mail: [email p o ec ed]             Fig. 1. Expe imen al se -up P ocedu e o he measu emen is ollowing: To s a he pump, o se cons an speed and o open he al e as much as possible. When flow a e s abilizes, all measu ed quan- i ies can be w i e. Then, educ ion o he flow a e wi h he al e ollows and measu emen o he new alues o measu ed quan i ies can be done. These s eps a e epea ed ill he flow a e is ze o. Only sho pa o he whole pump cha ac e is ic can be ob ained by his p ocedu e. I is plo - ed by solid lines in he figu e 2. Maximal flow a e in he                             Fig. 2. Ope a ing poin o he sys em, when he al e is ully open [7] sys em is limi ed by minimal possible pipeline esis ance. DOI: 10.1051/ C Owned by he au ho s, published by EDP Sciences, 2015 / 02022 (2015) 201epjcon EPJ Web o Con e ences , 02022 59 92 2                       ! A icle a ailable a h p://www.epj-con e ences.o g o h p://dx.doi.o g/10.1051/epjcon /20159202022 Bu he pump cha ac e is ic con inues o e his poin and o que cu e changes significan ly in his zone. The knowl- edge o i is impo an when one needs o simula e pump ip in he sys em wi h g ea ine ia and low head [8]. The es ing ci cui should con ain ano he pump o ge o e he limi Qmax and o ob ain accu a e measu emen o he ex ended cha ac e is ic. The e is ano he possibili y, which does no in ol e wo pumps in he ci cui : When es ed pump gi es max- imal flow a e and i s sha is suddenly slowed down, he pump cha ac e is ic changes acco ding o affini y law, bu he ine ia o he wa e column keeps flow a e he same a he fi s momen . Ope a ing poin mo es o he new cha - ac e is ic and, a e ce ain ime, finds a new s eady po- si ion gi en by in e sec ion o he new pump cha ac e is ic and pipeline cha ac e is ic. The p ocess is shown in he fig- u e 3.                                 Fig. 3. Mo emen o he ope a ing poin while he pump is dece- le a ing Equa ions (1) o (4) desc ibe he affini y law. Subsc ip omeans o iginal alue. Qo Q=no n,(1) Yo Y=no n2 ,(2) To T=no n2 ,(3) ηo η=1.(4) The measu emen o his uns eady p ocess and ollow- ing e alua ion diffe om measu emen o he s eady s a e. 3 Measu emen Pa ame e s o es ed pump a e lis ed in he able 1. I is a cen i ugal pump made o s eel (impelle ) and cas i on (spi al case), which was connec ed o he ci cui acco ding o figu e 1. The p essu e was measu ed wi h p essu e ans- duce s ( ange 0 – 160 kPa abs. o suc ion and 0 – 400 kPa abs. o discha ge, accu acy 0.25% o he ange) in ou places ma ked in he figu e. Elec omagne ic flow me e was used jus o s eady flow ( ange 0 – 500 l/s, accu acy Table 1. Pump specifica ions En y Value Uni Suc ion diame e 0.39 m Discha ge diame e 0.352 m Impelle diame e 0.41 m Numbe o anes 6 - Specific speed 310 pm 0.2% o measu ed alue), dynamome e con olled speed, measu ed o que ( ange 0 – 1000 Nm, accu acy 0.5% o measu ed alue) and e olu ions ( ange 0 – 4500 pm, 1000 pulses pe e olu ion). As he sampling equency o e - olu ion measu emen was 10 Hz all o he quan i ies we e measu ed wi h he same equency. Measu emen o s eady cha ac e is ic was he fi s s ep. Figu e 4 is alid o speed n0=1000 pm, which was cho- sen as a e e ence alue. The cha ac e is ic ends almos immedia ely behind he bes efficiency poin due o high esis ance o he hyd aulic ci cui . All pa ame e s wi h subsc ip op mean he bes effi- ciency poin o speed 1000 pm.               ηη    Fig. 4. Cha ac e is ic o he pump 3.1 Momen o ine ia To ob ain cha ac e is ic om pump decele a ion, he ine - ia momen o he pump is necessa y. I was ound om decele a ion when he discha ge was closed. I means ha o que was known om s a ic cha ac e is ic (Q=0) and equa ion (3). Ini ial speed 1140 pm was educed o 10 pm in 5.65 s, i is decele a ion 200 pm pe second. G aph in he figu e 5 was plo ed using equa ion 5, whe e measu ed o que Tmis educed by he alue T(Q=0,n). The speed changed linea ly be ween alues 1000 pm and 100 pm, so he ine ia (9.5 kg·m2) was e alua ed om his ange. The esul was he same o any decele a ion. I=(Tm−T)Δ 2·π·Δn.(5) Po en ially, he same p ocess can be applied when pump is accele a ed, bu he esul s a e no unambiguous. 3.2 Flow a e Uns eady flow a e canno be measu ed wi h he elec o- magne ic flowme e , because his de ice has a g ea in e- EPJ Web o Con e ences 02022-p.2             !"#$% &$'#($% )!' *!' Fig. 5. Momen o ine ia om pump accele a ion and decele a- ion Table 2. Nume ical model pa ame e s En y Suc ion Discha ge Uni Leng h 1.65 8 m Diame e 0.39 0.352 m Roughness 0.5 0.5 mm Viscosi y 10−610−6m2/s Densi y 1000 1000 kg/m3 Wa e speed 1000 1000 m Leng h s ep 0.55 0.5 m Cou an numbe 1 1 - g a ing cons an so i is no sui able o uns eady e en s. To ge o e his complica ion, i is possible o compu e flow a e as a unc ion o ime om p essu e measu ed in wo places. In ou case, inle flow a e was compu ed om p es- su es p1and p2and ou le flow a e was e alua ed om p essu es p3and p4, see figu e 1. The flow a e was ob ained as a solu ion o equa ions (6, 7) wi h known p essu e bounda y condi ions p1and p2 o inflow and p3and p4 o ou flow. ∂Q ∂ +S ρ ∂p ∂x+λ 2DS |Q|Q=0,(6) ∂p ∂ +K S ∂Q ∂x=0.(7) The Lax-Wend offnume ical scheme was used he e. Basic pa ame e s o he nume ical model a e lis ed in he able 2, whe e leng h means dis ance be ween co esponding p es- su e ansduce s. Coefficien o ic ion loss was ob ained by Chu chill’s ela ionship. Figu e 6 shows an example o compu ed flow a e. One can see ha suc ion flow a e and discha ge flow a e a e almos iden ical. Simple me hod how o find flow a e om p essu e diffe ence is known as Gibson’s me hod. I can be de i ed by in eg a ion o equa ion (6), see ela ionship (8). Q( +Δ )=Q( )−Δ S LρΔp( )+R|Q( )|Q( ),(8) whe e Lis a dis ance be ween p essu e ansduce s and Δp is hei p essu e diffe ence. This equa ion is subjec o nu- me ical i e a ion as he esis ance Ris a unc ion o ini ial flow a e. Compa e he esul in he figu e 7 wi h he fig- u e 6. I only sligh ly diffe s, g aphs a e compa able. This app oach is possible, when he p essu e does no go oo deep unde a mosphe ic p essu e, hus he fluid densi y is cons an [9].             $#"%  )"+'  Fig. 6. Flow a e when pump decele a ed om speed 1140 pm o 10 pm. Decele a ion a e: 266.67 pm pe second             $#"%  )"+'  Fig. 7. Flow a e when pump decele a ed om speed 1140 pm o 10 pm. Decele a ion a e: 266.67 pm pe second. (Gibson me hod) 4 Pump cha ac e is ic We e alua ed pump cha ac e is ic om se en diffe en de- cele a ions. Ini ial speed was always 1140 pm (maximal possible speed wi h espec o inpu powe ) and he fi- nal speed was 10 pm ( he lowes possible speed o dy- namome e measu emen ). Co esponding ini ial flow a e was 1.175 ·Qop and ou decele a ion a es we e mea- su ed: 266.67; 400.00; 571.42 and 800.00 pm pe second. We also measu ed h ee cases wi h ini ial flow a e equal Qop (bu he ini ial speed was s ill 1140 pm) and h ee decele a ion a es 266.67; 400.00 and 800.00 pm pe sec- ond. The las h ee cases se ed o check i he cha ac e - is ic ob ained om uns eady e en would co e he s eady cha ac e is ic. All se en cases a e plo ed in he figu e 8 (some o hem we e measu ed wice). The figu e shows one qua e o Ka man-Knapp cha ac e is ic. Places, whe e he specific ene gy equals ze o, should be on he same hal line. The same s a emen is alid also o places, whe e he o que is ze o ( unaway). Bo h hal lines a e plo ed in he g aph as well. They we e ound by leas squa e me hod (LSM). The ins an specific ene gy was compu ed by equa ion (9) and ins an o que by equa ion (10). Y= x3  x2 dQ Sd dx+p3−p2 ρ+8Q2 π2·D−4 3−D−4 2+ +g·(H3−H2),(9) T=Tm−2π·I·Δn Δ .(10) EFM 2014 02022-p.3               Fig. 8. Measu ed cases o pump decele a ion (solid line), mea- su ed ze o specific ene gy (spo s), ze o specific ene gy by LSM (dashed line), measu ed ze o o que (squa es) and ze o o que by LSM (b oken line) In eg al limi s x2and x3delimi pipe om p essu e ansduce p2 o he impelle inle and om impelle ou - le o p essu e ansduce p3. Spi al case is included. The equa ions do no conside a iable speed. The specific en- e gy is plo ed in he figu e 9, whe e one can see ha he p ocess was s ongly uns eady. Specific ene gy s a ed om          Fig. 9. Specific ene gy du ing decele a ion (solid lines) compa ed wi h he s a ic cha ac e is ic (spo s) he s a ic pump cha ac e is ic line and eached a nega i e alue in all cases. The o que is plo ed in he figu e 10. Again, he ini- ial alue was on he s a ic cha ac e is ic line and d opped down o he nega i e alue. Only da a, whe e speed was          Fig. 10. To que du ing decele a ion (solid lines) compa ed wi h he s a ic cha ac e is ic (spo s) g ea e han 100 pm, we e e alua ed. Thus all solid lines in he figu es 9 and 10 a e no comple e, because speed unde 100 pm b ough oo big e o . When he esul s is co ec ed by affini y law, see equa- ions (1 – 3), he ex ended pump cha ac e is ic can be plo - ed. I is shown in figu es 11 and 12.     , , , ,                  Fig. 11. E alua ed specific ene gy o he pump o speed 1000 pm. S a ic cha ac e is ic (spo s) is ex ended by dynamic measu emen (c osses). Bo om g aph is a de ail     , , , ,                  Fig. 12. E alua ed o que o he pump o speed 1000 pm. S a ic cha ac e is ic (spo s) is ex ended by dynamic measu emen (c osses). Bo om g aph is a de ail EPJ Web o Con e ences 02022-p.4 I is ob ious ha pa o cha ac e is ic ob ained om decele a ion is easonable despi e he ac ha i is mo e sca e ed han pa ob ained om measu emen o s eady s a e. I means ha desc ibed p ocedu e is good when an app oxima e cha ac e is ic o he pump is needed. Typi- cally, o nume ical simula ion o ansien e en s in pi- peline sys ems, whe e he e o o se e al pe cen is, usu- ally, accep able. Bu his p ocedu e canno eplace exac measu emen o he cha ac e is ic needed o calcula ion o ope a ional expenses. The figu e 13 shows he efficiency compu ed om he eg ession analysis o he specific ene gy and he o que o speed 1000 pm. The e o in he bes efficiency poin is abou 5%, because he in e pola ing polynomial o he o que sligh ly o e es ima es he cha ac e is ic in he icin- i y o he bes efficiency poin .            ηη Fig. 13. Measu ed efficiency om s eady s a e (spo s) and eg es- sion unc ion om measu emen o s eady s a e and decele a ion (solid line) The da a, whe e Y>0, we e in e pola ed by polyno- mial unc ion o ge unc ion o specific ene gy (11) and o ge unc ion o o que (12). Bo h se s o da a (ob ained by measu emen o s eady and uns eady s a e) we e used as he inpu . The figu e 13 is plo ed acco ding o (13). Y Yop =−1.0689 ·Q Qop 2 +1.1081 ·Q Qop + +0.9448,(11) T Top =−0.2786 ·Q Qop 3 +0.0647 ·Q Qop 2 + +0.5856 ·Q Qop +0.6502,(12) η ηop =Q Qop ·Y Yop ·Top T.(13) Finally, he flow a e, whe e he specific ene gy equals ze o, was ound as 1.59 ·Qop wi h he app oxima e e - o ±5%. The flow a e, whe e he o que equals ze o, was ound as 1.93 ·Qop wi h he app oxima e e o ±3%. The e o is defined om s anda d de ia ion. 5 Conclusion The pape desc ibes e alua ion o pump cha ac e is ic om da a ob ained du ing measu emen o pump decele a ion. The p ocess allows measu ing he pump cha ac e is ic o e he poin o maximal flow a e in he hyd aulic ci cui ha is defined by in e sec ion o pump cha ac e is ic and pipe- line cha ac e is ic, hus he e is no need o ins all ano he pump o he ci cui . The esul is no as accu a e as cha ac e is ic gained by measu emen o s eady s a e, bu i eaches b aking and u bine zones o he machine. This is e y use ul, because p oduce s, usually, does no p o ide his pa s o cha ac- e is ic. The esul is accu a e enough o use i as an in- pu when nume ical simula ion o pump ansien is being done. Acknowledgemen This pape was elabo a ed in he amewo k o he p ojec Oppo uni y o young esea che s, eg. no. CZ.1.07/2.3.00/ 30.0016, suppo ed by Ope a ional P og amme Educa ion o Compe i i eness and co-financed by he Eu opean So- cial Fund and he s a e budge o he Czech Republic. This pape is also ou pu o NETME Cen e, egional R&D cen e buil wi h he financial suppo om he Op- e a ional P og amme Resea ch and De elopmen o Inno- a ions wi hin he p ojec NETME Cen e (New Technolo- gies o Mechanical Enginee ing), Reg. no. CZ.1.05/2.1.00/ 01.0002 and, in he ollow-up sus ainabili y s age, suppo - ed h ough NETME CENTRE PLUS (LO1202) by finan- cial means om he Minis y o Educa ion, You h and Spo s unde he ”Na ional Sus ainabili y P og amme I.” Nomencla u e D(m) Diame e g(m·s−2) G a i a ional accele a ion H(m) Ele a ion I(kg·m2) Momen o ine ia K(Pa) Bulk modulus L(m) Leng h n( ps) Ro a ional speed p(Pa) P essu e Q(m3·s−1) Discha ge R(kg·m−7) Resis ance S(m2) Pipe c oss-sec ion T(N·m) To que (s) Time x(m) Longi udinal coo dina e Y(J·kg−1) Specific ene gy Δn( ps) Speed change Δp(Pa) P essu e diffe ence ΔQ(m3·s−1) Discha ge change Δ (s) Time s ep η(-) Efficiency λ(-) Coefficien o ic ion loss ρ(kg·m−3) Densi y Subsc ip s: m Measu ed alue o O iginal ( e e ence) alue op Value a he bes efficiency poin ( o 1000 pm) EFM 2014 02022-p.5 Re e ences 1. S. Pejo ic, A. P. Boldy, Guidlines o Hyd aulic T an- sien Analysis o Pumping Sys ems (P & B P ess, Bel- g ade; Co en y 1992), pp. 181 2. H. Tsukamo o, S. Ma sunaga, H. Yoneda, S. Ha a, Jou - nal o Fluids Enginee ing 108 (1986), pp. 392 – 398 3. J. Liu, Z. Li, L. Wang, L. Jiao, Jou nal o Fluids Engi- nee ing 133 (2011), pp.1–7 4. H. Tsukamo o, S. Ohashi, Jou nal o Fluids Enginee - ing 104 (1982), pp.6–13 5. K. Fa hadi, A. Bousbia-salah, F. D’Au ia, P og ess in Nuclea Ene gy 49 (2007), pp. 499 – 510 6. F. F. Hu, X. D. Ma, D. Z. Wu, L. Q. Wang, IOP Con e - ence Se ies: Ea h En i on al Science 15 042016 (2012), pp. 8, DOI: 10.1088/1755-1315/15/4/042016 7. D. Him , V. Hab´ an, The 22nd In e na ional Con e ence on Hyd aulics and Pneuma ics (P ague 2013), pp. 91 – 97), ISBN 978-80-248-3136-7 8. D. Him , EPJ Web o Con e ences 67 02035 (2014), pp. 6, DOI: 10.1051/epjcon /20146702035 9. J. Jablonsk´ a, EPJ Web o Con e ences 67 02048 (2014), DOI: 10.1051/epjcon /20146702048 EPJ Web o Con e ences 02022-p.6