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
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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
n2
,(2)
To
T=no
n2
,(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.
ηη
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
LρΔp( )+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].
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)"+'
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 .
ηη
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
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