THERMODYNAMIC MODELING AND PERFORMANCE OPTIMIZATION FOR SIMPLE-CYCLE GAS TURBINE WITH AIR COOLING
Wenhua Wang, Lingen Chen* and Zemin Ding *Author for correspondence
Institute of Thermal Science and Power Engineering, Naval University of Engineering,
Wuhan, 430033, P. R. China
E-mail: [email protected] and [email protected]
NOMENCLATURE A = Surface area (m2) c = Specific heat (kJ/kg.K); Blade chord length (m) I = Enthalpy (J) L = Blade height (m) m = Mass flow rate (kg/s) P = Power (kJ/kg) p = Pressure (kPa) s = Blade pitch (m) T = Temperature (K) V = Velocity (m/s)
Greek symbol η = Efficiency α = flow outlet angle л = Pressure ratio ρ = Mass density (kg/m3) σ = Pressure loss coefficient ξ = Cooling air percentage
superscript 0 = Relative - = Mean
subscripts a =air; fitting coefficient b = fitting coefficient c = Cooling air;
CC =Combustion chamber f = Fuel g = Gas
HC = High-pressure compressor i = Inlet
HT = High-pressure turbine LC = Low-pressure compressor LT = Low-pressure turbine
max = Maximum o = Outlet
PT = Power turbine 1,2,21, 3… = State points
ABSTRACT A predicting model of cooling air percentage for turbine
blades with respect to simple-cycle triple-shaft gas turbine plant considering the thermophysical properties of the air and the gas
is established. The thermodynamic performance of the cycle is investigated. The calculation flow chart of the power output and the efficiency is exhibited, and the verification computation is performed based on the design performance data for ДН80Л-type industrial gas turbine plant developed by Ukraine. The results indicate the model is reasonable and can predict the design performance of gas turbine cycle effectively. The maximum power output, the maximum efficiency and their corresponding cooling air percentages are obtained by optimizing the pressure ratio of the low-pressure compressor and the total pressure ratio, respectively. The results also indicate that the outlet temperature of combustor chamber or the inlet temperature of turbine affects the thermodynamic performance of the cycle evidently.
INTRODUCTION
One of the most effective technological innovations to enhance specific power output and efficiency of gas turbine cycle is to enhance outlet temperature of the combustion chamber or the inlet temperature of the turbine. To prevent the turbine blades from hot corrosion, part of compressed air in the compressor must be bled to cooling the front blade stages of the turbine [1, 2]. In general, the cooling air should be so sufficient that it will cool the blades effectively, but bleeding too much compressed air will decrease the mass flow rate of main working fluid in the later flow path and then decrease the power output and efficiency of the gas turbine cycle [3]. How to determine the optimal cooling air percentages with respect to different cooling measures is very difficult. To solve this problem, many scholars have performed lots of research work. Ref.[2] presented a predicting model of cooling air percentage without involving the thermodynamic modelling of gas turbine cycle. Based on Ref.[2], Horlock et al [4, 5] and Jordal [6] pursued further studies with considering ideal air as working fluid [4, 5], and estimating the cooling air percentage with convection cooling and air film cooling [6]. Yong and Wilcock [7, 8] studied the thermodynamic performance of single-shaft ideal gas turbine cycle by considering the air cooling and the specific heat ratio of the air changes with temperature only, and the established thermodynamic model couldn't reflect the real operation process as the mass flow rate ratio of the fuel and the air was taken as perfect. Refs.[9-11] built the thermodynamic model of gas turbine cycle with the help of ASPEN soft, and
13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
892
reckocyclecharaturbicycleetc. coolivanethermturbiefficparamrespeturbi
Infor dshaftpropthermThe efficwill ДН80The correoptimand t
CYCF
plantmassthe chigh(CC)burnresidcombpressrespeConscomptemp
Fig B
the abello
oned the coole gas turbinacteristic perine plant cone key charactwith respect ing method w
e cooling withmal load at thine vane. Mciency of thmeters of coectively. Sanjine cycle withn this paper,
different turbit gas turbin
perties of themodynamic p
calculation ciency will be
be performed0Л-type indusmaximum poesponding comizing the prthe total press
CLE MODELFig.1 shows at considering s flow rate of cooling air ma-pressure com), the fuel (mf
ned with the aidual air and pbustion chamsure turbine ectively. The sidering the tpressors and perature and c
gure 1 The sim
Based on Ref.air/pure gas ow
ling air percenne. Refs.[12-rformance ba
nsidering air cteristic paramto the cycles
which integrath the aim to she trailing edg
Moskalenko ethe first stageooling mediujay [21] studi
h air film bladea predicting mine blades witne plant coe air and theerformance oflow chart o
e exhibited, ad based on thstrial gas turbwer output, th
ooling air perressure ratio osure ratio, resp
LLING a simple-cyclair cooling. Inthe low pressu
ass flow rate tmpressor (HC
mf denotes fueir and the prodpure gas) mas
mber is mg. LC(LT) and thpower turbin
thermophysicagas in GT hoomponents as
mple gas turbin
[22], the enthcan be obtai
ntage for a si-18] estimatedased on the cooling but deters such as . Shi et al [1tes steam and olve the probge region of at al [20] stue turbine blums of air ied the therme cooling. model of coolth respect to sonsidering the gas will beof the cycle wof the powe
and the verifiche design perine plant devehe maximum ercentages wiof the low-prpectively.
le triple-shaftn the figure, mure compressothat is bled froC). In the col mass flow rduct (gas, viass flow rate a
C and HC are he high-pressne (PT) driveal properties
ot section) is cs it passes alon
ne plant consi
halpy and the rined by the f
ingle-shaft, sid or analyze
simple-cycledidn't optimiz
the pressure 9] proposes aair for gas tu
blem of a verya steam-cooleudied the colade for difand water v
moeconomics o
ling air percensimple-cycle the thermophe established
will be investiger output andcation compurformance daeloped by Ukefficiency andll be obtaineressure compr
t gas turbine ma denotes inor (LC), mc deom the outlet ombustion charate) is ignite. the mixture at the outlet odriven by the
sure turbine es the load sof the fluid (changeable wng the flow pa
idering air coo
relative pressufitting formul
imple-ed the e gas ze the
ratio, a new urbine y high ed gas ooling fferent vapor, of gas
ntages triple-
hysical . The gated. d the
utation ata for kraine. d their ed by ressor
(GT) nlet air enotes of the amber
ed and of the of the e low-(HT),
solely. (air in
with its ath.
oling
ure of las as
wrlor
pe
wpi
I
wpi
woIrpdinlo
we(
C
c
bbthsI
rr
I a=0lgπ
where ai and respectively, aocal pressure
reference condConsiderin
process, the enthalpy 2I at
02π
where 01π , 1I ,
pressure ratiosentropic outl
Also, the a
3I at HC outle03sπ
where 01π , 21I
pressure ratiosentropic outl
According g am m m= −
HT gm m=
LT Hm m=where 31I , 4Ioutlet enthalpy
5sI denote therate, efficiencpressure turbidenote the manlet enthalpy,ow-pressure t
The powerPTP m η=
where PTm , efficiency and(PT). Obvious
COOLING BThere are
cooling procesFor conve
blades (Fig.2)blades throughhe turbine b
surface of turbIn Fig.2, gVrespectively. Trespectively.
20 1 2a a T a T+ +
00 1b bT b= + +
bi (i=0, 1, 2and the relatie p and thedition. ng an adiabatair isentropict LC outlet can0 02 1s LCπ π= , 2I
, LCη , LCπ ao, inlet enthalet enthalpy ofair isentropicet can be writt
021 HCπ π= , 3I
, HCη , HCπo, inlet enthalet enthalpy ofto mass and e
c fm m+ , fm H
g cHTm+ , HTm η
HT cLTm+ , LTm ηand CCη deno
y and efficiene main gas macy and isentrine (HT); an
ain gas mass fl, efficiency anturbine (LT).r output and th
6 7( ) /PT sI I mη −
PTη and sI7
d isentropic ously, PT LTm m=
LADE MODtwo major b
ss and film coction cooling
), the coolingh inner passagblades, decrebine blade, and and cV are
giT and goT ar
ciT and coT
2 33 4a T a T+ +
2 32 3b T b T b+ +
2……5) are tive pressure e standard pr
tic and irrevec relative prn be written a
1 2( sI I I= + −
and 2sI denotalpy, efficiencf the LC. relative presten as
21 3( sI I I= + −
and sI3 denotalpy, efficiencf the HC. energy conser
4u CC gH m Iη =
4 5( )HT sI Iη − =
5 6( )T LT sI Iη − =ote the workincy of the CC;ass flow rate,ropic outlet ed LTm , cLTm
flow rate, coolnd isentropic
he efficiency oam , /aPmη =
s denote the utlet enthalpy
T .
ELLING blade cooling oling process.
g process per air flows int
ges, takes awayases workingd then blends gas and c
re gas inlet an are cooling
4 55T a T+
4 54 5b T b T+ the fitting co
0π is the ratressure 0p u
ersible thermoressure ratioas
1) / LCI η
te the air inlecy, pressure r
ssure 03sπ and
21) / HCI η
te the air inlecy, pressure r
vation, one ha31( )a cm m I− −
3 21( )am I I= −
2 1( )am I I= − ng fluid inlet ; HTm , cHTm , cooling air menthalpy of t
T , 5I , HTηling air mass outlet enthal
of the cycle ar/ ( )f u CCm H η
gas mass fy of the powe
processes: co. rformed in thto and out thy quantity of hg temperaturinto the main
cooling air v
nd outlet tempair inlet an
(1)
(2) oefficients tio of the under the
odynamic 02sπ and
(3)
et relative ratio and
enthalpy
(4)
et relative ratio and
as 1 (5)
(6) (7) enthalpy,
HTη and mass flow the high-
and 6sI flow rate, py of the
re (8)
flow rate, er turbine
onvection
he turbine he hollow heat from e of the
n gas flow. velocities,
peratures, nd outlet
13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
893
temp
and blade
Fig In
fromthe l
neQ
wherblade
Dcomb
ξ
wherand respeturbi[5];
DEq.(
wherF
(Fig.innerand denomixi
blT .
A
netQ
peratures, resp
temperature, e inner passag
gure 2 Convec
n order to anm the compres
aw of conserv(co
ci
T
et c pcTm c= ∫
re gα denotese surface and
Defining coobining it with
/c gm m λ= =
re /sgA Aλ =α denote the bectively. Genine blades co
/ (g g pgSt cα=
Defining 0ε =10) gives
re / cooK C η=For film cooli.3), as the coor passages it covers the b
otes the air fing condition
Figure 3 Film
According to t(sg fg awA Tα=
pectively. sgArespectively.
ge.
ction cooling t
nalyse problemsor outlet to c
vation of energ( ) g
go
T
g TT dT m= ∫s the heat exthe gas [4, 5]ling efficien
g g g gm A Vρ=
( / )(g pg pcSt c cλ
2 / (gA Lc Ls=blades heighterally, s/c=0.8
ooling air per)g g gVρ ; and ρ
( ) / (gi blT T T= −
Kζ ε=
ol and C Sλ=ing process poling air flowforms a film
blades surfacefilm temperatuof hot gas an
m cooling ther
the law of con) co
ci
T
bl c TT m− = ∫
g and blT are
gA is the ef
thermal mode
m convenientlcool CC is igngy, one has
( )gi
opgc T dT α=
xchange coeff.
ncy (cool cTη =
g and Eq.(9) g
( ) / [gi bl coT T η−
cos ) 2 / (cα =, chord, pitch8 and α=75°rcentage’s num
gρ denotes th)gi ciT T− and
0 0/ (1 )ε ε− /g pg pcSt c c .
performed in ws out the holl
in the high-pe like fire wure which is
nd cooling air
rmal model fo
nservation of e( )o
pcc T dT m=
blade surface
ffective area o
el for turbine b
ly, the air blenored. Accord
(g sg gi blA T Tα −
ficient betwee
) / (co ci blT T− −
gives
( )]ool bl ciT T− ( cos )s α ; L,
h, flow outlet a are designa
merical calcuhe gas mass de
combining it
the turbine blow blades thpressure gas swall. In Fig.3
resulted fromand different
or turbine blad
energy, one ha( )c pc co cim c T T−
e area
of the
blade
eeding ding to
)l (9)
en the
)ciT− ,
(10)
c, s angle, ted in
ulation ensity.
t with
(11)
blades hrough stream , awT m the t from
de
as ) (12)
wa
Eξ
w
ce
F
wthth
M
thmthcДT
LoPtLcmPCoCo
aob
where fgα deair film and bl
Defining εEq.(12) gives
/c gm mξ = =
where C Sλ=The total
cooling air aefficiency of th
Figure 4 The The total p
tpΔ
where /cVχ =he angle betwhe gas.
MODEL VER
Using thhermodynami
mentioned abohermodynami
compare the ДН80Л-type inThe results are
Tab.1 the cal
Name,
Low-pressure outlet temperaPower turbinetemperature TLow-pressure compressor inmass flow ratePlant’s efficieCooling air peof high-pressuCooling air peof low-pressur
It shows th
air mass flow of the coolingbe relatively la
enotes the heaade surface.
( )f gi awT Tε = −
0[ (1 coC ε η− −
/g pg pcSt c c . pressure loss
and the gas he simple-cyc
mixture mode
pressure loss c/ 0.5tp kξ= −
/ gV , gM Mg iween the veloc
RIFICATIONhe simple-cic model andove, one makeic performancresult with d
ndustrial gas e listed in Tab
lculation value
unit
turbine ature T6, K outlet
T7, K
nlet air e ma, kg/s ency η ercentage ure ture ξHTercentage re ture ξLT
he relative errorate are less
g air flow ratearge as compa
at exchange co
) / ( )gi coT T− a
0)ool f f cε ε ε η−
s resulted frostream (Fig.
cle gas turbine
el for cooling
oefficient is d2 / (1 /g ckM T T+
is the gas maccity directions
cycle tripled turbine blaes approximatce and coolindesign perforturbine devel
b.1.
es and design Design value
Ca
1070
773
85
34.25%
15.12%
3.61%
ors of the temthan 3%, but s and the planaring those to
oefficient betw
and combinin
] / [ (1cool coolη η −
om the mixtu.4) will decre plant.
air and the ga
determined as2 cos )gT χ φ−
ch number andof the cooling
-shaft gas ade air coolinte calculation ng air informarmance publioped by Ukra
value of ДН8alculation
value R
1083.5
754.8
83.4
36.81%
13.40%
2.95%
mperatures andthe calculatio
nt’s efficiencythe design va
ween the
ng it with
0 )]ε− (13)
ure of the rease the
as stream
[5] (14)
d φ is g air and
turbine ng model about the ation and c-data of aine [23].
80Л plant Relative
error
1.26%
2.35%
1.88%
7.47%
11.38%
18.28%
d the inlet on results y seem to alues. The
13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
894
reasoaccuActuincreturbiThe guid
CYC
Tturbi(1) necetotal streaoutp
Cdisplthe turbibladestatioturbibladedecrefrom
Intempp0=1
LCηcalorcoefftemp
Fbadeobtaibladecan oand shou
Hη
wherstatiorespe
5gsI enthacooliaccothe mfurthcompderivbase
ons maybe: urate that moreually, the deease the cooliine’s safety a
mathematicaelines in cooli
CLE PERFORThe thermodyine plant consestimate the
essarily in eachpressure loss
am and coolinut and efficien
Considering layed in Fig.1high-pressure
ine (single-staes of the fronary blade roine stationary e rows needeases markedl
m the high-presn the calculat
perature is .013bar, each=0.88, HCη =rific value of
fficient of coperature of comFirst, assumine row A blT =1in 0ε and Aξe row B inletobtain Bξ . Herotor blades
uld rewritten a( )HTg g cHTgm m+
re HTgη andonary blade ectively, cHTmand 5gI are ralpy, respectiing the HT. L
ording to Eq.(mixture proc
her, power ouponent, of theved. The corrd on Matlab i
(1) The mae realities are signers and ing air mass fs it operates al model buing system de
RMANCE OPynamic perfosidering blade
quantity ofh blade row; s resulted fromng air and mixncy calculatiothe simple-c
1, one can dive turbine (sage) and the pfront three roow A and rotoblade row C)
dn’t as wherly. It is assumssure comprestion, some in
T0=300.15Kh GT compon=0.88, and ηfuel is Hu=42mbustion chambustion cham
ng the surface1073K, coolη =. Then, takin
t gas stream teere, as the airof the HT ar
as 4 5( )gs HTI I η− +
d HTbη are row A and r
Tg is working
row A outletively, and mLike Aξ and ξ(13) one can ess and effic
utput and effice simple-cycleresponding cs displayed in
athematical mshould be takthe manufac
flow rate to win the most auilt above
esign of turbin
PTIMIZATIONrmance calcu air cooling in
f the cooling(2) estimate thm the heat traxture, et al; (
on based on stecycle triple-svide the turbinsingle-stage), power turbineow (the higor blade row B) need air coolre the gas s
med that the cossor outlet.
nitial values ar, the stand
nent’s isentropHTη = LTη = η
2700kJ/kg, theamber is Bσmber is T4=17e temperature
=0.7 and fε =ng it for granemperature gTr cooling procre considered
5 5( )Tb HT g sm I I−
isentropic efrotor blade rfluid mass fl
t gas stream
cHTm is the a
Bξ , Cξ can beobtain the totciency loss ociency, even ee triple-shaft gomputer calc
n Fig.5.
models are nken into accouctures intentiowell ensure thatrocious condcan give h
ne blade.
N FLOW CHAulation of thncludes three g air that nhe total energansfer betwee(3) the plant peps (1) and (2shaft gas tune into three
the low-pree (multi-stage)gh-pressure tuB, the low-preling while thestream tempeooling air is al
re set: the amdard pressurpic efficienciePTη =0.96, the
e total pressurB =0.02, and 700K. e of the stati0.4 [4, 5], onnted that the
gBT =( 4T + 5T )/2cesses of statid separately, E
3 21) ( )am I I= −
fficiencies orow B of thelow rate in ro
isentropic andair mass flowe obtained. Fital pressure lo
of each turbinexergy loss ingas turbine placulation flow
not so unt; (2) onally he gas dition.
helpful
ART e gas steps:
needed gy and en gas power
2). urbine parts:
essure ). The urbine essure
e latter erature ll bled
mbient re is es are e low re loss outlet
ionary ne can
rotor 2, one ionary Eq.(6)
(15)
f the e HP, ow A,
d real w rate inally, oss in ne, in n each ant are
chart
O
πincc
thth
in
w
T
cCto
Figure 5 Th
OPTIMIZATIOFig.6 illust
LCπ . It showsncrease in π
chamber T4 iscooling measu
Figure 6 Th Fig.7 illust
he total presshat P and
ncreases with
which leads t
There also ex
correspondingConsideration otal pressure r
he thermodynam
ON RESULTtrates the chas that P and
LCπ as the s given and thure.
he characteris
trates the cha
sure ration πη increase
h increase in πto maxP with
xists an optim
g max
Pη and ηξboth plant po
ratio should ra
mic performance
TS AND ANAaracteristics ofη decrease woutlet tempehe turbine bl
stics of P , η
aracteristics of
witha selectefirst and the
π . There exi
the correspon
mum maxηπ l
maxη . It is evidower and its eange from
mPπ
e calculation flo
ALYSES f P , η and while ξ increrature of coades are appo
and ξ versu
f P , η and ξ
ed LCπ π= .en decrease
ists an optimu
nding maxPη a
eads to maxη
dent that maPπ
efficiency, the
maxP to maxηπ .
ow chart
ξ versus eases with ombustion ointed air
s LCπ
ξ versus
It shows while ξ
um maxPπ
and maxPξ .
with the
ax<
maxηπ . e suitable
13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
895
F F
maxPπ
cham
maxPη
Fi
F
maxηπ
maxPη
Fi
Figure 7 The
Fig.8 illustrate
versus the
mber. It show
decreases wi
igure 8 The ch
Fig.9 illustrate
x versus T4.
and maxηξ de
igure 9 The ch
characteristic
es the charact
outlet temp
ws that maxP ,
ith increase in
haracteristics vers
es the charact
It shows tha
creases as T4 i
haracteristics vers
cs of P , η an
teristics of mP
perature T4 o
, maxPξ and π
n T4.
of maxP , maxPη
sus T4 teristics of mη
at maxη and ηπ
increases.
of maxη , max
Pηsus T4
nd ξ versus π
max , maxPη ,
maPξ
of the combu
maxPπ increase
x
, maxPξ and Pπ
max , max
Pη , maηξ
maxηπ increase
x
, maxηξ and ηπ
π
ax and
ustion
while
maxP
ax and
while
maxη
C
fspepДrdoeneooaca
cbdin
thpcp
pcthaco
A
um
R
[
[
[
[
[
CONCLUSIOThis paper
for different tushaft gas tuproperties of thefficiency peparameters areДН80Л-type inresults indicatdesign performoptimization iefficiency of numerical examefficiency andobtained by seoptimal pressuand the effecchamber on analysed.
The results (1) giving
chamber and tblades are coodecrease whilncrease in the
(2) giving here exist dif
power output cooling air ppressure ratio;
(3) the mpressure ratio correspondinghe combustio
and its correscorrespondingoutlet tempera
ACKNOWLEThe author
unbiased and cmanuscript.
REFERENCE
1] Horlock JScience Pu
2] Raymond cooling, A
3] LakshminTurbomac
4] Horlock JTransactioNo.3, 200
5] Horlock Jturbine peTrans. AS2001, pp.4
ON r establishes aurbine blades urbine plant he air and the
erformance oe compared wndustrial gas te the model mance of gasis performed gas turbine
mple. The mad their correspearching the ure ratio of thct of the outl
the thermod
s and the analyg the outletthe total pressuoled by air, thle the coolin
e pressure ratiothe outlet te
fferent total pand the max
percentage inc
maximum poand cooling
g efficiency deon chamber insponding totalg power and coature of the co
EDGEMENTSrs wish to thaconstructive su
ES
J.H, Advance Gublishers, 2003S.C., Importa
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s turbine cycby taking t
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he LC using tlet temperatu
dynamic perf
yses indicate: t temperatureure ratio and che power outng air perceo of the LC;
emperature of ressure ratios
ximum efficiecreases with
wer and theg air percentaecreases as thncreases. Thel pressure ratooling air permbustion cham
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ance of combin72-8, 1972.
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.T., and Jones mposed by largeGas Turbines &
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ure of the coformance of
e of the coconsidering thtput and the eentage increa
f combustion s lead to the mncy, respectivincrease in
e correspondage increase we outlet tempee maximum etio decrease wcentage increamber increase
ewers for theiwhich led to th
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ng convection
s and Heat T95. mics of turbin
Turbomachinery
T.V., Limitatioe turbine cool
& Power, Vol.1
ir cooling cle triple-
mophysical power and racteristic e data for aine. The redict the y. Further utput and based on maximum ntages are o and the tablished,
ombustion plant is
ombustion he turbine efficiency ases with
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ding total while the erature of efficiency while the ase as the es.
ir careful, his revised
n: Elsevier
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13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
896
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“Софиевская”. ГазотурбинныеМехнологии, Vol.4, No.4, 2002, pp. 6-10.
13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
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