thermodynamic modeling and performance optimization for

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

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oned the coole gas turbinacteristic perine plant cone key charactwith respect ing method w

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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


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


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


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

AIAA Paper No.7narayana B., Fchinery, Wiley, J.H., The basion of the ASME1, pp.583-592.

J.H., Watson Derformance impSME J. Eng. G487-494.

a predictive mwith respect considering

e gas, and inveof the plant.with the design

turbine develis reasonabl

s turbine cycby taking t

plant as theaximum poweponding coolioptimal total

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

S ank the revieuggestions, w

Gas Turbine C.

ance of combin72-8, 1972.

Fluid DynamicsNew York, 199c thermodynam

E: Journal of T

.T., and Jones mposed by largeGas Turbines &

model of the aito simple-cyc the thermestigates the p Some charn performanceloped by Ukre and can pr

cle effectivelythe power oue objectives br output, the ming air percenpressure ratiohe models est

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

Cycles, London

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

chamber, maximum vely. The the total

ding total while the erature of efficiency while the ase as the es.

ir careful, his revised

n: Elsevier

with film

Transfer of

ne cooling, y, Vol.123,

ons on gas ing flows, 123, No.3,


896

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