Proceedigs of the Iteratioal Gas Turbie ogress 3 Tokyo November -7, 3 IGT3Tokyo TS-86 A omparative Ivestigatio of Reheat I Gas Turbie ycles K. Sarabchi Departmet of Mechaical egieerig Uiversity of Tabriz Tabriz Ira Phoe: +98-4-339346, Fax: +98-4-334487, E-mail: sarabchi@tabrizu.ac.ir ABSTRAT The role of gas turbie power plats i electrical eergy productio has bee cosiderably icreased i the last -3 decades. Various methods have bee proposed to improve the performace of gas turbie cycles. I this reseah two methods: reheat cycle (R ad cycle with reheat ad heat exchager (RH were ivestigated. Today to achieve a higher efficiecy ad capacity i gas turbies, higher turbie ilet temperatures like 3 ad eve more are used. Basically applicatio of such temperatures without turbie blade coolig is impossible. Therefore aalysis of gas turbie cycles without cosiderig blade coolig i modelig will ot certaily lead to a valid ad correct results. The mai object of this paper is to study the performace of R ad RH uder actual coditios. I this regard all processes treated as actual ad particularly a relatively simple approach was used to predict the amout of coolig air. The obtaied results show that reheatig i the cotext of a realistic study has o positive effect o gas turbie performace ad of course this coclusio is ot i agreemet with some relevat published documets. INTRODUTION Gas turbie cycle is very flexible so that its performace i.e. efficiecy ad specific et work ca be improved by addig extra compoets to a simple cycle (S. I recet years may reseahes carried out regardig advaced gas turbie cycles like steam ijected gas turbie cycle [], humid air turbie [], heat exchager cycle [3], etc. Geerally the mai aim of theses reseahes are to achieve a higher efficiecies i gas turbie based cycles. A reheat combustio chamber is a compoet that ca be added to a gas turbie cycle to improve its performace [4]. I this method the expasio process i turbie is divided ito two processes ad a additioal combustio chamber is placed betwee high pressure ad low-pressure turbies. The exhaust gas -------------------------------------------------------------------- opyright 3 by GTSI Mauscript Received o Mah 8, 3 from high-pressure turbie that cotais sufficiet oxyge eters a reheat combustio chamber ad the temperature of gases ca be icreased as the result of supplemetary combustio. Previous reseahes o ideal R show that reheatig icreases specific et work but decreases efficiecy comparig to S [4, 5]. Also, these ivestigatios show that the maximum specific et work i R is obtaied if the pressure ratios for high ad low - pressure turbies are assumed equal. rae [5] has show that although equal pressure ratios lead to a maximum specific et work but uder this coditio the efficiecy is ot maximum ad the lower pressure ratio for high-pressure turbie icreases the efficiecy but this leads to the reductio of work output. May ivestigatios cocerig reheatig i gas turbie were carried out assumig some simplificatios icludig: costat specific heat, heat additio to workig fluid istead of combustio process, ad more importatly cosiderig ucooled turbie model [5] istead of cooled turbie model. These assumptios i particular the last oe leads to urealistic results because almost all turbies today are usually cooled by air ad eglectig the amout of coolig air fractio gives icorrect results. I this work it is attempted to model S, R, ad RH cosiderig all actual factors that affect the performace of real cycles. I this regard, amog the others, specific heat assumed to be fuctio of both temperature ad combustio product compositio [6] ad coolig air fractio were calculated usig a relatively simple approach [7]. I this paper i additio to actual R the RH were also aalysed ad compared to oe aother as well as to S. I the ext sectios it is show that the iclusio of the cooled turbie model i modelig of gas turbie based cycles gives results that are far differet from ucooled turbie model. Therefore by this approach the performace of reheat cycles ca be predicted correctly. THERMODYNAMIS ANALYSIS Geeral Descriptio Figure illustrates the R arragemet. The hot gas after leavig the first combustio chamber eters HP turbie where expads partially. The gases which cotais sufficiet uused oxyge eters reheat
combustio chamber where fuel is ijected ad supplemetary firig occurs. The hot gases ow havig higher temperature (equal to first turbie ilet temperature eters secod or LP turbie where expads to atmospheric pressure. Figure shows RH i which a heat exchager is used to icrease the air temperature before it eters to first combustio chamber by recoverig heat from LP turbie exhaust gases. ompressor Aalysis Followig equatios ca be writte assumig air as a ideal gas ad usig polytropic efficiecy [4] to model compressor actual behaviour. dp RT dhs p c ( dh.. dt T T dt T p p R c dp p ( I above relatios costat-pressure specific heat is fuctio of temperature ad relevat fuctios for various gases are give i [6]. The oly ukow parameter i Equatio is compressor outlet temperature which ca be foud usig umerical methods. ompressor specific work i terms of KJ/Kg is calculated from followig equatio: w comp T T M. dt a (3 ombustio hamber Aalysis Followig chemical reactio ca be writte by assumig a geeral formula of H m for a hydrocarbo fuel ad a theoretical air coefficiet of A: H m ( O + A ( + m / 4 + ( m / H [ 3.76 A ( + m / 4 ] N [ O + 3.76 N ] + [( A ( + m / 4 ] O O (4 The first law of thermodyamics for a adiabatic combustio process is: + i ( h i i reac ta ts ( ihi products i T (5 (6 o h h +. dt f 98 p Theoretical air ad the fuel air ratio ca be calculated from above equatio for ay turbie ilet temperature. High-Pressure Turbie Aalysis Actual behaviour of turbie ca be modeled by followig equatios. I this model, combustio products is assumed as ideal gas ad polytropic efficiecy is used for turbie [4]. dh pg. dt ht (7 dh dp s RT ( p p4 p3 ht where: T 4 dp dt R( pg( p T i pg ( i i T3 i pi ( products products (9 (8 Equatio 8 ca be used to evaluate HP turbie outlet temperature. Followig equatio gives turbie specific work (KJ/Kg. T4 pg. dt T3 whp M g ( Similar relatios ca also be writte for LP turbie. Reheat ombustio hamber Aalysis The equatio of combustio reactio for reheat combustio chamber ca be writte as:
x H m ( A ( + m / 4 O ( x + o + o + ( m / H o + 3.76A( + m / 4 N [( + m / 4( A x] O + 3.67A( + m / 4 N + (x + m / H o + + ( I the above equatio, x deotes cosumed fuel i reheat combustio chamber for oe mole of cosumed fuel i primary combustio chamber. x ca be foud by applyig the eergy balace equatio to the reheat combustio chamber. Heat Exchager Aalysis I heat exchager the exhaust gas from LP turbie is used to heat air before it eters to first combustio chamber ad therefore fuel cosumptio is reduced i the combustio chamber. Heat exchager effectiveess is defied as Equatio osiderig that the air is a miimum fluid [8]. Ta. dt q T ε ( T6 qmax. dt T T T Also, the eergy balace for this compoet is: T6. dt ( + f + f. dt (3 As T ad T 6 ca be obtaied respectively from compressor ad LPT models, therefore, combustio chamber ilet temperature (T a ad heat exchager exit temperature (T b ca be foud from above equatios. oolig Air Evaluatio. Aalysig the performace of moder gas-turbie egies without predictio of coolig air flows leads to iaccurate results as coolig air is a large fractio of ilet air flow i these machies. O the other had, to accurately model coolig airflow is a complex task. oolig flows are a complex fuctio of turbie operatig ad desig parameters such as compressor efficiecies, bleed pressures, turbie gas temperatures, ad allowable metal temperatures [9]. A large umber of detailed gas turbie desig iformatio is therefore required to accurately model the performace of moder gas turbies. A simple model based o figure 3 was also developed for estimatio of coolig air [7]. I this model compressor ad turbie are modelled as sigle stage Tb pg compressio ad expasio devices respectively. oolig air is assumed to be totally extracted from the compressor outlet, whilst the remaiig air flows to the combustio chamber. It is further assumed that half of the coolig air is mixed with combustor outlet gas i the first ozzle sectio. The temperature after this mix is called rotor ilet temperature. The rest of the coolig air is mixed after the gas expaded i the ozzle. Figure 4 represets existig relatioship betwee turbie ad rotor ilet temperatures for various gas turbies. Based o this figure, a simple correlatio ca be established betwee turbie ilet temperature (combustor outlet temperature ad turbie rotor ilet temperature. It was foud that this relatioship could be expressed with good approximatio by equatio: T r.845 T 3 + 36. (4 I this equatio temperature is i terms of. Eergy balace for ozzle sectio (for Kg of air at compressor ilet is give by: caf caf -caf+ f h 3 +.h ( - +f h (5 ( r This equatio ca also be simplified as : h3 - hr caf h3 - h - caf + f (6 Evetually coolig air for Kg of ilet air ca be estimated usig above equatios. Evaluatio of ycle Performace Parameters After calculatig compressor specific work, turbie specific work, fuel air ratio i both combustio chambers, ad air coolig ratio, the specific et work of the cycle ca be estimated usig Equatio 7. Gas turbie specific et work is defied as the work output of the cycle for oe Kg of compressor ilet airflow. w et w + w w (7 pt hpt Where we have: comp caf w hpt ( + f ( h3 h4 caf + ( h h3 (8 caf w lpt ( + f + f ( h5 h6 + ( h h5 (9
Kowig specific et work ad heatig value of the fuel,thermal efficiecy ca also be calculated usig followig equatio: w et th LHV ( f ( + f RESULTS AND DISUSSION Based o models preseted above, a computer code costructed for performace predictio ad parametric aalysis of S, R, ad RH. I this ivestigatio followig assumptios were made: Atmospheric air coditios are: T 5, P.3 bar, ad relative humidity 6%. As calculatios have bee performed over a rage of pressure ratio, polytropic efficiecy, for compressor ad turbie aalysis, have bee used istead isetropic efficiecy [4]. A typical value of.9 has bee assumed for both compressor ad turbie polytropic efficiecies. 3 Although a geeral formula of H m has bee used for the fuel i the model, for calculatio purposes, the fuel has bee assumed to be methae with lower heatig value of 5 KJ/Kg [6] throughout this work. It is also assumed that the fuel is available at atmospheric temperature ad the combustor ilet pressure P, so there is o eed for gas compressio work. 4 No pressure losses were assumed for either compressor ilet or turbie outlet (i.e. p p 4 p. 5 All iteral pressure losses are assumed to be cocetrated i the combustio chamber ad equates to 3% (p 3.97p. 6 ombustio efficiecy [4] has bee assumed to be 99%. 7 A overall % power loss has bee assumed. This icludes turbie-drive auxiliaries. 8 The effectiveess of heat exchager is assumed as.9. 9 The equal pressure ratios are assumed for high ad low pressure turbies i reheat cycles. HP ad LP turbie ilet temperatures are assumed the same. I this reseah all results are obtaied assumig ilet temperature of. The results of this aalysis are show as diagrams which are discussed below. Figures 5 ad 6 shows respectively specific et work ad thermal efficiecy for three cycles versus pressure ratio. These curves have bee plotted based o ucooled turbie model. It is observed that reheatig icreases specific et work of R comparig to S. The maximum value of specific et work for the former is about 36% higher tha that for the the latter. I cotrast, reheatig by itself reduces thermal efficiecy. ombied usage of reheatig ad heat exchager leads to a cosiderable icrease i thermal efficiecy because the combustio chamber ilet air is heated by recoverig heat from exhaust gases i heat exchager. Of course the work output for RH is slightly lower tha that for R ad S because of pressure drop i heat exchager. This results are qualitatively i agreemet with give results i [5]. Figures 7 ad 8 demostrate the differeces betwee air cooled ad ucooled turbie models to predict the performace parameters of S. Examiatio of these curves show that ucooled turbie model predicts specific et work ad efficiecy respectively by % ad 4% more tha cooled turbie model. Aother iterestig poit is that pressure ratios correspodig to maximum specific et work ad efficiecy are higher for ucooled turbie model rather tha cooled turbie model. These results clearly show that the performace criteria of gas turbie based cycles icludig reheat cycles ca ot be predicted accurately by igorig the amout of coolig air which is required for turbie blade coolig. Figures 9 compares the variatio of specific et work with compressor pressure ratio for S, R, ad RH usig cooled turbie model. It is see that R has higher w et tha S for pressure ratios of higher tha, but for pressure ratios of lower tha the w et of S is higher. I additio, the importat poit is that the maximum value of w et are almost equal for both cycles. Therefore it ca be said that the mai advatage of reheatig which is the icreamet of w et vaishes cosiderably if we cosider turbie air coolig i our aalysis. Of course this result is i cotrast to the result that obtaied from ucooled turbie model [5, ]. Figure depicts the efficiecy variatio of S, R, ad RH with pressure ratio usig cooled turbie model. As expected, the efficiecy of R is lower tha that for S. I this case the differece betwee this two is higher tha that for ucooled turbie model (Figure 6. A importat result is that the efficiecy of RH although is higher tha R, but it is slightly lower tha that for S. This result is i cotrast to the result obtaied from ucooled turbie model which gives the efficiecy of RH much higher tha S (Figure 6. The above results ca be justified kowig that the amout of coolig air for reheat cycles are much higher tha that for S ad this destroys the positive effect of reheatig o gas turbie performace. Fially it should be oted that i this paper coolig air is assumed to be totally extracted from the compressor outlet. Actually coolig air for the LPT does ot eed to have the pressure of the compressor outlet. It ca be extracted from the itermediate stages of the compressor where the pressure is slightly higher tha LPT ilet pressure. By this way the performace of R ad RH may be improved due to reductio of both compressor iput work ad coolig air for LPT. Therefore it is recommeded that a further ivestigatio should be carried out cosiderig this poit.
ONLUSION Followig results are obtaied from this ivestigatio: I the cotext of ucooled turbie model, reheatig icreases specific et work but reduces thermal efficiecy comparig to simple cycle. Also combied use of reheat ad heat exchager icreases thermal efficiecy too. I the cotext of cooled turbie model the mai advatages of R which is higher specific et work disappears ad its specific et work does ot differ cosiderably from simple cycle work output. Also i this case combiatio of reheat ad heat exchager does ot icrease efficiecy comparig to simple cycle. Pressure ratios correspod to maximum specific et work ad maximum efficiecy for a give turbie ilet temperature i cooled turbie model are smaller tha those for ucooled turbie model for R, RH, ad S. I both models, pressure ratio correspods to maximum specific et work for simple cycle is smaller tha those for R ad RH, whereas, pressure ratio correspods to maximum efficiecy for RH is much smaller tha those for simple cycle ad R. Fially it should be oted that the cooled turbie model should be improved, ad the detailed examiatio o the ifluece of coolig air o performace parameters of each cycles should be examied i the future. REFERENES - De Paepe, M., Dick, E., ycle Improvemets To Steam Ijected Gas Turbies, Iteratioal Joural of Eergy Reseah,. - S. S. Stecco, et al, Humid Air Gas Turbies ycle: A Possible Optimizatio, ASME Paper, No: 93-GT-78. 3- B. Facchii, New Prospects For Use of Regeeratio I Gas Turbie ycles, IGTI-Vol. 8,, ASME OGEN TURBO, 993. 4- ohe, H. et al., Gas turbie theory, 4rd ed., Lodo, Logma, 996. 8- Frak Kreith, Priciples of Heat Trasfer, 3rd Editio, Itext Educatioal Publishers, 973. 9- Erbes M. R., Gay R.R., oh A., "Gate: A Simulatio ode for Aalysis of Gas-Turbie Power Plats", ASME Paper, No : 89-GT-39 - Haris. F. R. Reheat i early gas turbies proc. Isth Mech. Egrs. Part A. Joural of power ad eergy, vol 8, No A, 994, pp.45-47. NOMENLATURE A excess air coefficiet p costat-pressure specific heat [KJ/Kg-K] caf coolig air fractio f fuel air ratio h ethalpy [KJ/Kg] LHV lower heatig value [KJ/Kg] M molecular weight N deotes spices P pressure [bar] R uiversal costat of gases [KJ/Kmole-K] T temperature [] w specific work [KJ/Kg] x fuel ratio for reheat combustio chamber polytropic efficiecy ε heat exchager effectiveess Subscripts a air c compressor f formatrio g gas Acroyms HPT high pressure turbie LPT low pressure turbie R reheat cycle RH reheat heat exchager cycle S simple cycle 5- rae. R. I, A critical aalysis of the thermodyamic advatages of reheat i gas turbies, Proc. Ist Mech. Egrs. Part A. Joural of power ad Eergy, Vol, No A, 998, pp8-87. 6- Sotag, R. E., Borgakke,., VaWyle, G.J., Fudametals of Thermodyamics, 5th Editio, New York, JohWiley & Sos, 998. 7- Sarabchi, K., A simple approach to gas turbies modelig, Proceedigs of Al Azhar. Egieerig Sixth Iteratioal oferecs, September, airo, Egypt.
Figures ad Diagrams: Fuel Fuel 3 4 5 omp HPT LPT Wet Air 6 Figure : Flow diagram of reheat cycle (R b 4 a 3 5 Fuel Fuel omp HPT LPT 6 Wet Air Figure : Flow diagram of reheat heat exchager cycle (RH Figure 3: Flow diagram for cooled turbie model Figure 4: Rotor ilet temperature agaist turbie ilet temperature for various gas turbies
6 5 Wet[kj/kg] 4 3 S R RH 5 5 5 3 35 4 45 Figure 5: Specific et work versus pressure ratio usig ucooled turbie model S R RH efficiecy 5 45 4 35 3 5 5 5 5 5 5 3 35 4 45 Figure 6: Efficiecy versus pressure ratio usig ucooled turbie model Wet[kj/kg] 5 45 4 35 3 5 5 5 5 5 5 3 35 4 45 ucooled cooled Figure 7: ompariso of variatio of S specific et work agaist pressure ratio usig both cooled ad ucooled turbie models
efficiecy 5 45 4 35 3 5 5 5 ucoole d cooled 5 5 5 3 35 4 45 Figure 8: ompariso of variatio of S efficiecy agaist pressure ratio usig both cooled ad ucooled turbie models Wet [kj/kg] 35 3 5 5 5 S R RH 5 5 5 3 35 4 45 Figure 9: Specific et work versus pressure ratio usig cooled turbie model efficiecy 5 4 45 3 35 5 5 5 S R RH 5 5 5 3 35 4 45 Figure : Efficiecy versus pressure ratio usig cooled turbie model