-
5/19/2018 Compressors Design T11105-112
1/8
FFIIY H I P F I PF
byDavd Japkse
d I IN Vm
avd ]apks s sdnt of Concs, owch, Vont, and pblsof th Tuboacny sn
stHs wok clds consltn pblshnth st nd t sn nna and t ppaaton nd
psntatono advancd toacny coss fodsy woldw H svd as psdnt of th Fl
achn vson ata Incpoatd fo to an pously wokd at at & ht
ny cat fo to cv nnn fo th as Instto Tchnoloy hs and hdegrees
from the Department of Mechanical Engineering,d Unvsty H sd
postdoctoal wok at thTchnsch Hocschl n acn Gany as a Flbhtschlar
and NSF Fellow .
Japs's pncpl as o wok ncl th dsn anddvlopnt of vaos cntal opsso
d adaltbn stas ncln th dvlopnt of dsn tools Hsconsltn an sn wok has
covd a dvs an opcss chny tbochas, as tbns and cy oncans H has ca ot
basc sach on both toachny coponnts and systs H has psntd o plaons
and pad appoatly opos covn th dsn, dvlopnt an toblshootnof
tboachny
BCare attenton is given to the most common tr
bmachiner perforance probems which res o an inadeate
nderstanding o component and mahne eiencExampes o severa cassica
probems are presentd and thebsic denition ad princies invoved are
carefl reviewd Comn erors in measrng machine ecienc arediscssed
with exampes and sgetions as appropriate thogh machine eienc eent
pas a seconar roecompared with estions of drabiit it is pointed ot
thateven sma errors in rated ecienc can case signicantstabiit
probems, power/speed mismatch and even contribte to noise and
vibation probems Three dierent eves o
design anases are discssed at which new machines can edesigned
and their ecienc predicted Tpica advantagesand disadvntages of each
approach are presented The inormation presented herein is an
experience based smmar togide engineers in their review o machine
performance
DMachine ecienc is a popar topic of discssion
whenever the cost of es and eedstocks is high bt enthsiasm ick
wanes whenever costs drop, even momentari As recent as ve ears ago,
concern with the ecienc of
105
indstria trbomachiner was comparative sight otside ofte hdrac
trine ed In recent ars concern as become comparative intense e to e
high cost of f bevn this recent concern s comparative mid when
ntrasted with the intense concern fet or machine reiabit
andmaitainaiit which has been foremos in most ds ofinstria
trbomachiner dsin and saes One co reaistica as the rhetoria estion
wo cares abot achineecienc? Even wit the recent psrge in concrn at
eprices machine ecinc is a weak partnr whn contratdith aintinabiit
and is ick pshed asid wn stions of mechanica perrmanc arise Ther
are everman reasons wh machine ecien mst aas kpt
cose to the ont o an enginers concern r machin prormance There
is a direct eationship between the ad rise(or pressre ratio)
estabished b a achin and coponenteienies imiar noise and vibration
probems an oftnbe traced to iddnamic procsss which rt poormachine
esign rom a gas dnamic or termodnamic ecinc vieoint Ths the
ojective of this paper is to providesome o the ndaton isses pon
wich a reaistic appreciation or machine ecienc can b based
The rst ecienc isse is the power reire or deivered r a iven head
or prese ratio and a givn w ratethrog a compression or expansion
sstem If ecin of one
o more important sctions of a machie is xceded r missedin the
deign or devepment o a machine ten ess oradditioa powr wi be reired
to operate the nit troghot its itime If we consider the denition of
ecienc on acomonnt basis then we recognize e power transfrred
isgiven accoring to the foowing eations
aaJ n n \' C ; n 2
To be sre, most indtria machies are comprised f mtistage
machines for whih we mst cosider the eciies ofvarios stages as an
aggregate \hat e are particar concerned with is redicting the fccs
for an givn compression or expansion process e know that we i
notachieve the idea (isentropic) ve of ork extraction from
anexpansion process nor wi we achiev a desired pressre risefor a
compression stage with st th isentropic rk Thedierences between the
isentropic proess and t actaprocess wi amont from 1% to 25% of the
idea ork eveimping eciencies anwhere from 75% to 9% pndingon the
tpe of expansion or ompression process e are,
-
5/19/2018 Compressors Design T11105-112
2/8
106 PROCEEDINGS OF THE ELEVENTH TURBOMACHINERY SYMPOSIM
thereore rightlly ephasizing or ability to predict theieciency
(or loss of a stage accrately to one or two pointsot o 1 or 25,
which wold seem to be a airly straightorwardprocess oweer or
reasons presented in the next sectionthis eqently can be a ery
diclt process indeed
The pressre ratio achieed or reqired by a gien com-pression or
expansion process is directly related to the ecien-cy o the
stage
can see this in the ollowing eqation whichis obtained by
manipating eqations 1 and
2aboe:
_, k/k_ kk
pr - [1 + T \ aol (C,T)] - [1 + (T.c;t - T_)IT]3
.
kk klk [1 -Wdoali
T C, T] [1 - T - T T)
pr k/(k1 prlk (To,exit - Too)
6'T
er k/(k-1)
1
2k j _ -o _o_ _ _xi_t 6'
T '
4
5
6
If we dierentiate these expressions as shown by eqations 5and 6
we can nd that an increment of one point of stageeciency will
typically mean approximately to 3% on pres-sre ratio for a typical
compression or expansion process or apr (or er 2 per stage for
example sing air as a workingmedim Ths the hed rise or pressre
ratio of gien stageis inenced by or ability to predict the eciency
or theineciency of a stae
The preceding two principles might appear to be
obiosapplications of the most basic principles om a rst corse
intrbomachinery; bt they gain signicant importance when
we begi to combine them r a mltistage machine Considerfor
example a compressor characteristic shown in Figres aand b The
conditions or stage 1 are the parameters which setthe inlet
conditions for stage 2. A mltistage machine is madep of any nmber
(reqently on the order of 6 or 7 stageswhich mst be matched by
carel consideration of the charac-teristics o each indiidal stage
and how they feed om onestage to the ext Conside the conditions o
Figre a as theyfeed Figre b and imagine that the perormance o the
stage
bT T
:
i/;
m T/ m T/tt t x
Figure 1 Stage Maps Shoing Match Conditions at DesignPoint and
When a Stage Delivers Excess Efciency and/orHead
n Figre a might actally hae been three poits higher tharated in
the origial design itent This chanes the atcconditions or Figre b
to the alternate match point as showin the gre In short one has oed
or exaple abot 2%toward the srge line This does not appear to be
too great change bt it is magnied throgh an additioal e or
sisbseqent stages It reslts n the oerall reatching of astages o the
le ths iplyin a potentially signcant reduction in table operating
range; tat is the range rom the matc
point to the srge point (for denition o srge and range sepikse
[1] Ths een a sall change o a ew percent oeciency when taken in the
st stage or two o f a mltistagmachine can lead to signicant hanges
in the oerall perormance characteristics o the mahine as a whole
One simpcannot take eiciency or grated little extra eciency nice
for power saings bt the iplications st be carellconsidered
An additional characteristi o machine perormance is thtradeo
between stage eciecy and stable operating rangeAn example of
perrmance data or a wide rane o centrigcompressors inclding both
common process stages ansophisticated high performance gas trbine
stages is shown iFigre 2 and Figre 3 Figre illstrates the decay in
desigpoint eciency as machines o greater and greater operatin
range are reqiredIn addition to reqiring good stable operating
range thslope o a gien operating line (on a head s ow coecien
9
'ts
6
Ntes:
:ri; ;cato flw rt, /Se dt biy ccte fm TT t SN tp cence cctn
uAdbtc cnin gey nt cnfr
5
0
t
Figure State-of-the-Art Single Stage Centrugal Compressor
Efciencies on an Isentropi Basis
85
0
'ts,%7
70
,. pr=1.5,1975
_ -
-
-pr=s.o6. 1975
/ ?5-19 .
pr=7.0-.o pr=9.o-q.o - 197-195
1960-1965
65 -
Rage,(lmsurge/chke)x10
Figure 3 State-of-the-Art Singl Stage Centrifugal Compressor
Isentropic Efciency versus Range
-
5/19/2018 Compressors Design T11105-112
3/8
ICINCY: THE SILENT ARTNER OF MACHINE RFORMANC 107
characteristic plot may frequently be specied to meet
apredetermined system requireent. One can appreciate thedesign
requirements for the slope characteristic by consideringthe
following equation, which is deduced om the essentialvelocity
triangles:
k/k1pr= [1 + T(U2 Cm2tan2h -
-
5/19/2018 Compressors Design T11105-112
4/8
108 PROCEEDINGS OF THE ELEVEN URBOMACHINERY SYMPOSIUM
ic scaling is used according to the resultant scale factor,
thenone will obtain an extreely high degree of precision in
theresultat machine characteristics The only corrections whichmust
be de ar fr a scond orde eect wih is notincue in he basic goups
given abve, an that s due o teReyls umer eect Vaios Reynols number
correctiosare recommnde in AS T1 ] and the AI [5]odes An example of
thi tpe of ata is shwn in Fure 4 fo a
varit of centrigal compressors
In cases whee we are scaig from very large to very sallsie,
oweer, it may not pssile t aintain a preciseeoric scaling e we may
very well introuce someimortnt deiatios from coret scalin which
could causeerrors in predictig the machine erformance For exameblae
tickesses miht not scale, fillt radii mght not scaleges may be
modied slih, and operating clearances aycange oticeably. ese ecs
coud cause signicant deia-tios wih should be wathe closely.
However, the biggesproblem would robaly exit i he machine was scled
fromone operating id to aother. hile tis could be one wihrelative
impunity for ideal gase, it coul also be the source ofconsiderable
diculty for real gases
At the second level of design analysis, a mnucturer canconsider
the use of a wide variety of dirent components in amix and match
mode This approach gives a manucturermaximum exibility in meeting
design requirements whilemaintaining a very high degree of condence
in the resultantstage permance. The central element of such a stag
is therotor se Figure 5. An example of correlations of
rotorperrmance are shown in Figures 6 and 7 r the rotors
'
E
B;-f
t=
REYNOLDS NO
Uy O laJ
1
0
NAA IN OIA. COMP 0 HO, ARGON0 G Uy ROTOR TIP D fP OTR IP DIATfR
FO!r > m!NL TNTION DNSIY $US/3
J"VIITY UG/f C
" - _1
9 NA 8RU 4 IN , OIA COMP, 1 SPD ARONl N 3. IN OIA COMP. 100':
SPD AIRI N A IN OM 90 SPEED AIR0 N IN. DIA OMP PD AIR" N 2 IN DI
CMP 0 PD AIRn > 05 lN IA OP SO AIR S IN IA MP 0% D R
.
,,''
,
-',,
'"'
REYNLD NUMB( A X 0 6
Figue 4 Compilation of Centrgal Compressor EfciencyDecrement as
a Function of Reynolds Numberfrom Pampreen(11).
D ()
E2 272 A 27
Figure 5 olar Centrifuga Compressor Impelers WhichFo a aily for
Various Design equirements. Rodgers ( 6
Figure 6. Solar Centrugal Copressor Impeller iecieRodgers
(6)
9
9
03 0 05 10
h 032 o2 0.25
Mu0
AVEAGE DESIY SPECIFIC SPEED LOG SCALEpecc peed c ( = 77
oh 0
Mu:1
0N EGE ESY SPEIFI SPEED LOG SALE
ii pd c = 4
20
20
Figure 7. olar Centrifugal ressor Impeller Efcienias a Function
of Impo en Variables. odger (6)
-
5/19/2018 Compressors Design T11105-112
5/8
EICIENCY THE SILENT PARTNER OF MCHINE PERFOMANCE 109
dslayed n Fgure 5 Ths artcular exale s o olnodgers 6] a dslays a
ses o Solar oressor rotos.Around t rotor an derent nlt onguratns
and df-sr conuratons can be loyd. Adtonl downstreaelents, u as
return chanel cascades r volutes, can alsoe use. ach f these adtnal
eleens ust saly eaed n tes of ts basc erfoane aracterstcs orcoted
fro rst rncles level 3 aroach. By cobn-ng thee arous elents, an
verall stage charatrst canbe eaed.
oweer, a ts leel the roble bes te a btore colcated. The actal
perfance o the rotor llepend on the ype f nlt ow whch t receves. If
the w slean as n th case of Fgures 5 - 7 then coaratvely
hgherforance wl resl owever, the nlet ow s dstotd,then the
perforance of he rotor ust be downgraded sgn-cantly. Slarly, the
erforance of an eleent after therotor, such as a duser ad
subsequent eleents lke a voluteor return channel, wll deend on te
detaled structur of theoweld enterng those eleents. For exale, the
tye ofvelocty gradent enterng a vaneless dser has been shonto have
sgncant nuence on the exected errance ofthe duser tself An exale s
shown n Fgure 8 whh staken fro fundaental research by rossor Senoo
n an
t shows that the nu anle ertted nto the vanelessdser deends
sgncantly n the level of nlet veloctyprole dstorton. Angls lower
than ths level are ssetbleto rtatng stall. Many other exales of
dser errancesubject to nlet velocty role varatons can be
resented.Most process achnes are prepared by usng a varety ofdrent
stages and stage eeents whch are ether saled bythe Level I aroch or
rexed/atched accordng to a LevelII aproach. No anufacturer has yet
reorted sucentlydetaled nraton on whch ths x and atch rocesscan be
carred ot wth colete recson. To do so woldrequre corehensve and
sophstcated traversng of thenlet and otlet condtons of each eleent
used n the stageatchng rocess and a corehensv data base of
correlateddata fro whch to choose for nw desgns. Ths has not
been
done and would be rohbtvel expensve. Instead, suchrobles st be
dealt wth fro a ore general and overall
)
>i
,, Z
Figure 8. Example of Velocity Prole Eects on a CriticalDfuser
Peormance Parameter !rr and ! areProle Distortios in Meridional ad
Tangential Velocity Etering a V aneless Dfuser n is the Critical
Dfuser InletFlo Angle Belo Which Rotating Stall and Possibly
SurgeCould Be Initiated From Senoo 7)
exerence base o the anufcturers ror d anddeveloent hstory. The
sle fact tat the vast ty fprocess turboachnery anufactures acheve t
dsredseccaons n ost cases, s a stron credt to t ll anexperenc whch
they brng to bear n the desgn ad devel-oent rbles. To be sure,
nteorthy excet exstwere the desred perfoance ha nt been achevd.
henths occurs, t s ost oen due to te unusual plng fderent eleents
whch could nt b sucentl revedbefore the achne was onstructd.
At the thrd level of desgn anlys, one oves aay froeprc data
bases and attets to predct the rancef a roposed stage by usng basc,
ccetual o des fthe derent henoena nvolved n the stage acdng
tondaental herodynac and ud dyna rnples athand. A certan aount of
erl nforaton s dd forts rocess but t s ercal nfoaton wch debes
theessental ow rocesses and not coelatons of pnenterforance er se.
In any cass t s ossble t ttack adesgn probe wth approxately te sae
level veralluncertanty wth ether a Level II r a evel II technque
for atycal process stage. However, te vel II has tadtnallybeen
referred snce one can at least take ofrt usngnforaton whch coes fro
cpnents very lar to
those whch wll be used n the nal desgn Howver, f acoletey ne
oeratng ud s to be sed or f sncantdepartures fro revous geoetc
onatons a to beconsdere, then the corehnse evel II I dl ng aybe
prerred. Detals of Level I II odelng are prsnted byapkse [8].
V Much of the hstorcal conon surrondng a roer
understandng of achne ececy can be trace to thetechnqes r denng
and cotng eeny, fr testngahnes to deterne ecency, and the ethds usd
toreort both coted and easurd ecency levels. ach ofthese ssus wll
receve attentn n ts secton
The basc sentroc ecency a dened n equatons 1
and 2, whch sly relate the ctual work nut r workextacton for a
rocess to the deal wrk transfer wh couldbe obtaned n an sentroc
rocs. hs ecency s a veryclear denton whch can be used ay abguous
ways. Inorder o hav a eanngful coason between the dealedsentroc
rocess and any actual procss of work exchange, ts necessary that we
antan an stoales carson.
The ost coon error whch s trduced n turbachn-ery testng s to
easure the actual wk nut wth a tea-ture change, wthout beng care as
to whether r nt heatay have been lost or added to te syste through
nvron-ental heat transfer. Thus, n rde for any ecency values tobe
vald, t s necessary to thoouly nslate the tst facltywhen easurng
actual work transr aordg to teperaturechange. Ths ncludes all aths
of osble heat transfer, not
only through casngs, but throug adacent ol bts, and soforth. Of
course, f the ower s en easured drctly byeans of shaft torque
easureents adjacent t the tur-boachnery rotors, thn thse robles can
be aoded.However, suh easureents ar coparatvely rar due tother
olexty and exense. Te adabatc sentrc e-cency s erhas the ost conly
eloyed denton ofecency for the turboachnry el as a whole.
Hwever,for procs coressors, t ay be rerable n any cases touse a
olytropc ecency.
Fgure 9a. shows the essnt aracterstc of t sen-tropc ecency
calculaton for a coesson rocess, heras
-
5/19/2018 Compressors Design T11105-112
6/8
110 PROCEEDINGS OF THE ELEENTH TURBOMACHINERY SYMPOSIUM
Figre 9b. shows the equivaent parameters for an
expansionprocess. We observe that if any given compression or
expan-sion process is broken into a series of smaller processes,
thatthe method of bookkeping will become ite important
fordetermining actal levels of the eivalent isentropic
worktransfer. Taking the copression process as an example, wecan
observe that the summation of seeral smaller, sbse-qent,
compression processes has an isentropic work which isgreater than
the reference isentropic work taken from theinitial entropy level.
We an dene an eciency with eitherdenition and observe that the
overall isentropic eciency isless than the stage eiency which wold
be obtained bysmming p the arios segments of the compression
process.The drence boils down to one important fact: as a
compres-sion or epansion process proceeds, the temperare of the
gashanges. For a compressor this means that the inlet tempera-tre
to a sbseqent compression process is higher, thsmaking the sbseqent
compression eort more diclt. Bybreaking the process into a seuence
of individal steps, thischange in temperatre is correctly recognie
and each sbse-ent step is rated realistically acoring to the
conditions atthe beginning of its process This ect has oen been
called apreheat eet for compression or a reheat ect for an
expan-sion process.
If an eort is made to consider a compression process as aseence
of innitesimal isentropic processes, ten we are ledto the denition
of polytropic eciency. Tis result is obtainedby integrating the
following euation:
W
_ prk/(k1)
-
1w
-
-
- tr-
1aal(16)
1
dp k k1+ 1) 1
T dpp+ ) 1 (7)=dT + 1
)1 dT
p
T
so as to obtain the following relationship for polytropic
ecien-cy (after expanding the power term with a series
expression):
k/(k1) n (p/p)ln (T/T)
(18)
(19)
To evaluate this epression, i t is neessary to know the
temper-atre T which can be obtained om the conventional deni-tion
of isentropic ecieny (equation 1) ths giving:
s
k/(k)
J( _ (2)
Ths we have seen that there are several ways of ratingeciency
which will ive, in fact, derent numerical values
g 9a
6Tctul
Enropy, nop
Figure 9 Examples of Overall Isentropi iieny andyle or Proess
Efiieny for a ompressor 9a) andTurbine (9b). the Proess is Broken
into a Series of Initesimal Steps a Poly tropi Proess is
esribed
depending on the choie whic as been ae. he polytropeciency is
perhaps the most commonly use in the proceeld and it is clear that
one must always uestand when isentropi or polytropic eiency denitio
is being employed This distintion can be emphasized by replotting
tdata shown previosly in Figre 2 (now as iure 1 in termof
polytropic eciency. It may be observed tat some (aboal of the
eiciency dcay wit increasing pessure atio (forgiven ow) has been
eliminated, which is a oseence of tbasic idea of the polytropic
eciency deitio.
A second important issue in nderstandig machine ecieny is the
reiremnt of proper testing. aspect of thproblem was indicated
previously if repeatale tests are to perrmed on any trbomachinery
where the ork transferdetermined by a temperatre change, then he
rig mst thoroghly inslated. This single proble is perhaps the
moprevalent sorce of error in trbomachinery test data anhence, in
reported ecencies In some cases the amountheat rejeted into the
atmosphere is omparatively negigib
in other cases, it can inence the reported eiiency by 5, or 15
points of stage eciency. The proble is circumventby thoroghly
inslating he test rig whe access can obtained. owever, it is very
common to d situations wheaccess is not possible. In this case, it
is neessay to repeat tewith varios environmental fators in order to
permit a corretion to be made to the reported data This approach
has workwell in a nmber of instances, bt does requie increased
tecommitments. owever, this is only one of a nuber of serioproblems
which can occr in turbomachiey testing.
100.
90
80
60
.4
.54 z
8
1 0
-t
6
J .68
,
_
mr&=0.25
0
' kgsec mrf" ks
6 7 8 9 0STAG U RTIOTOTL TO TTC
Figure 10 Reomputation of the Figure 1 sentropi ataTerms of
Polytropi ieny. Note that the Slope of tm=ost. ures has ereased by
a ator of Two. TRemaining Slope s ue to Sale ets.
-
5/19/2018 Compressors Design T11105-112
7/8
EFFICIENCY: TE SILENT RTNER OF tCINE ERFORNCE lll
Aitinal prblems inlue the fllwing:
1 Instrumentation alibratin inluing trquemetersthermuples an
pressure transuers);
2 Crretin fr reery tr eets stem ntineets an raiati eets n
thermuples;
The use f rret thermynami prperty ata
Examples f seeral f these eets are gien with mre
mplete infrmatin aailable in etaile leture ntesapikse [9])
Reery fatr is ne f the mst ften omitte rretins frm thermuple
mesurements Een shiele thermuples reqire a reery fatr rretin fr ws
withMah numbers er apprximately 0 Fr example if atemperature f 600R
is measure 140F) in a stream f Mah0 then a typial reery fatr rretin
f 06 is require This rretion may or may nt be signiant but inmany
tests it is imprtant If there is a temperature hange f0 thrugh the
stage then we are ealing with 06 pints fstage eieny as an
unertainty If the Mah number was 06then the errr wl be about 2
pints Unshiele thermples hae mh larger errrs Inee many mpressoran
trbine tests require measurement f inlet an tlet
temperatures in this Mah number range In aitin t thisoen rgtten
orretin it is neessary t allow r stemnutin an raiatin in ertain
installatins rerablyne hses th thermuple installtin s as t minimize
reliminate sh rretin trs
Basi alibratin f eqipment is essntial bt nt alwaysarrie t
arately ressure transuers mst be properlyalibrate s as to hae a
traeable rerene with an aeptable egree f preisin In atual usage
instruments an riftan lse alibratin an test preres mst allw r
theseariatins Usaly pressure errors are less sigiant in etermining
stage eieny than temperature measrement errrsbt they still an be
imprtant Fining a realisti inlet antlet pressre an be a sre f
trle
quit apart mbasi alibratin errrs If an inapprpriate measurement
la
ti is selete it is pssible t inen reprte einiesby ne r tw pints
of stage eienyFinally the issue f apprpriate thermoynami
prperty
ata is imprtant The best way t mpte an isentrpieieny is t use
gas table ata iretly an wrk withenthalpies an entrpy This gives a
preise allatin whihis traeable t the basi thermoynami ata weer if
asemiperfet gas law relatinship is emplye it is pssible tbtain
ierent leels f eiieny fr exatly the samepress Errrs f ne r w pints
f stage eieny anour Thus if a semiperfet gas relatinship is emplye
thenit is imprtant t state this preferene an t rer the leel fgas
onstant emplye Similarly when a plytropi press isuse the mputatinal
proeure an the eients emplye must be rere
Finally the isse f reprting eieny ata is imprtantThe preeing
setins shl make it lear that experimentally etermine eiieny
infrmatin requires an auratestatement f the mputatinal meth employe
the instrumentatin use fr measuring eah f the essential parameters
speiatins fr eah instrment emplye in btainingthe measre ata
unertainty statements fr the ierentparameters sre f thermoynami
infrmation emplyean nally an nertainty alulatin The nertainty
alulatin is freqenty base n a rot mean square statistialpproah as
set forth by Kline an MClintk [10] In thisproah one mst itemize the
unertainty f eah measurepraeter an intrue this int the erall
alulatin An
example is shwn in Table ; the pei unertaities areintre int the
basi equatin a fllws
2)
WR = nertainty f reslt Rw = nertainty ue t eah ariable
e see that this allatin then implies an nertainty fapprximately
045 pints f eieny fr a sigma ertainty r 0 pints of eieny for 2 sima
nertainty an frthe ase shwn in Table Althgh mst labratry sientiwrk
is arrie t with a 2 sigma unertainty ba 20s) it is the authors
experiene that mst inustrial work isnt arrie t at this leel Instea
it is the pn f thisauthr that mst wrk tens t be arrie t with
pprximately a sigma nertainty ban
TABLE SAMLE ALUES F RIL RBINEUNCERTAINTY CALCLAIN
arameter w araeter) w araeter)Name lue 20 s 1 os
P0 psia) 36 00 05T R) 6620 05 0Pout psia) 1 00 05Tout (0R 54600
00 5atm psia) 46 001 5
ResulsET 0007 045
CLOSUE
Attention has been gin t both esign alulatio meths fr stage eien
an experiental preures as employe wiely in the turbmahinery instry
Three irentleels f esign analysis are pssible an are se i
variusappliatins epening on the problem at han No oe leelf esign
analysis is more apprpriate than the other in thegeneral sense bt
the leel f esign analysis emplye shulbe hsen base n the requiremets
f the gie esignprblem Frequently the saling of n existing stage to
a newappliatin is the most reliable approah pssible egarlessf the
leel f esign analysis selete it is pssile t intre signiant errrs in
the preitin f a me eieny These errrs an be minimize by arel
attentin tothe infrmatin emplye an the termynami elatinships use
for the eieny alulations Similar are ust be
taken when an experimental measueent is mae of stageeiieny Eieny
measrements hae numeros opprtunities fr signifiant errr The ost
frequent soes oferrr are heat transr t r frm the test faility an
theoerlking f signiant temperature orretion fatos weer ther errrs
an be mae as etaile in this sey Aninetigatr an fus these
experimetal prblems qikly if aoprehensie unertainty analysis s mae
of the eporteperfrmane ata
NOMENCLATEA area
-
5/19/2018 Compressors Design T11105-112
8/8
112 OCEEDIGS OF HE ELEVENTH TRBMHIRY SYMPOSIM
a speed of sondb passage widthC absolte veloci (rlative to a
Newtonian frame, eg
ompessr casingc specc heat at constnt pressre diameterer turbine
expansin ratio, PoofPexit
h static enthalpy/nit mass; also, annls heighth stanation
ehaly/nit massk raio of specic heatsM Mach nmberm mass ow rateN
shaft speedNs specic speed: N = NQ/(h),
where N =Q
N = NQ/(h
rotational speed in rpminlet ow = m/ in ft/sec,(Note: for
trbines se exit Q)stage enthalpy change in ftlb/lbstae isentropic
enthalpy change
in ftlb/lbpowerstatic pressre
pp
prQ
stagnation pressrepressre ratio: pr = p/pvolmetrc ow rate
gas constantr radiso degrees ankine
entrop/nit massT static temperatreT stagnation temperatreU
impeller (metal velocityV, slipvelocity: V, = Cmz tan 1b2 + WzW,
total shaft wor per nit mass of id absolte ow agle
ecincy c = h h> =w
w
(measring stations mst be specically deneddynamic viscosity
dimensioness gropingsdensitystagnation densityslip factor: = 1
Vow coecient:
ncertainty in a specied parameter
Substs
b ld propertyc cmressorm merdionalo stagnatio, also inlet
stationp olytropicref rference state or station (mst be speciclly
dened
indicats that process folows an isentroic pahtrbie
ts totaltostatictt otaltototale tangential2 impeler tip
1 Japise, Stall, Stage Stll, and Srge, Proceedings o
the th Annal Trboachinery Syosim, Trbomachinery aboratories,
Dept of Mec Eng, TexaA&M University, Dec 13, 1981
2 Shepherd, D G, Principes of rboachinery Ne
York City, The Macmillan o, 19563 orloc, J , Axia Fo rbines
Hntington, New
York, Krieger Pblishing o, 1963
4 ASME Paper PTC1, Prrmance Tet Coe, Compressors and Exhasters,"
merican Society of MechanicaEngineers, 345 East 47th St, New Yor, Y
117
5 API Paper AI Standard 617, Forth Edtion, Novembe1979,
Centrifgal Compresors for General enery Services," American
Petrolem nstitte, 11 StreeNorthwest, Washington, DC 237
6 odgers, C, Eciency of entrifgal Coressor Impellers, AGA
Conference Proceeings No 282 Centrigal Compressors, Flow Penomena
and Performance,page 221, Brssels, May 79, 198
7 Senoo, Y, Kinoshita, Y, Inence of Inlet Flow Conditons and
Geometries of Cetrigal Vaneless Disers oCritical Flow Angle r
everse Flow, Jrnl of FlidEngr, P 9813, Vol 99, eries 1, No 1, arch,
1977
8 Japikse, D, Centrifgal ompressor Deign," ConceptCorse #2,
Second Editio, May, 1982
9 Japikse, D, Experimental Technies and Data Acisition for
Trbomachinery valation," Concepts Cors#7, Febrary, 1982
1 Kline, S J, and McClintoc, F A, Describing Uncerainties in
SingleSample Eeriments," echanical Engineering, Janary, 1953
11 Pampreen, C, Small Trbomachinery opressor an
Fan Aerodynamics; ASME Pblication, 73T6
