SENSITIVITY ANALYSIS OF GAS TURBINE FUEL CONSUMPTION WITH RESPECT TO TURBINE STAGE EFFICIENCY. K. MAZAHERI Aerospace Engineering Department,

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1 Proceedings o the AME 22 International Mechanical Engineering Congress & Exosition IMECE22 ovember 9-5, 22, Houston, exas, UA IMECE EIIVIY AALYI OF GA URBIE FUEL COUMPIO WIH REPEC O URBIE AGE EFFICIECY M. ZEIALPOUR K. MAZAHERI Aerosace Engineering Deartment, Aerosace Engineering Deartment, hari University o echnology, ehran, Iran hari University o echnology, ehran, Iran m_zeinalour@ae.shari.ir mazaheri@shari.ir A. IRAEJAD Mechanical Engineering Deartment, Michigan tate University, East Lansing, Michigan 48824, UA irannea@msu.edu ABRAC In this aer, the eect o turbine stage eiciency on uel consumtion o both gas turbines and aerial engines is assessed quantitatively. At the beginning o the gas generator otimization to decrease the uel consumtion, it is necessary to analyze the sensitivity o uel consumtion to its main comonents eiciencies. his will guide us which comonent is more imortant to be otimized. Here a zero-dimensional analysis has been done to determine the eect o turbine stage eiciency on the uel consumtion. Results o this analysis are evaluated in the context o thermodynamic cycle o a gas turbine generator and an aerial engine. As an examle, it is shown that i the eiciency o irst stage o the turbine is increased rom 82% to 84%, the uel consumtion o an aerial engine is comuted to be decreased by %. he cycle analysis erormed imlies that the sensitivity o uel consumtion to turbine stage eiciency varies or dierent values o stage eiciency. IRODUCIO Because o imortance o energy, otimization o ower generation systems has been the main subect o many researchers in recent decades. In order to achieve higher eiciencies, all comonents o a gas generator must oerate with ossible maximum erormance. Beore each otimization eort or a comlicated system, it is necessary to recognize the imortance o each comonent o system by seciying its erormance eect on the overall erormance. In many cases a qualitative comarison is used based on exerimental trials. But i we derive a direct exression to comute the sensitivities, we can determine exactly all aecting arameters. here are some works which their ocus is on the evaluation o the erormance sensitivity [, 2]. Higher eiciency o a gas generator means less uel consumtion to obtain same ower. he urose o the resent aer is the quantitative evaluation o uel consumtion change in terms o turbine stage eiciency. In other words, an analytic exression will be derived or gradient o required uel rate with resect to each turbine stage's eiciency. OMECLAURE η t urbine isentroic eiciency η s, i Isentroic eiciency o stage i W Real turbine work outut W Ideal turbine work outut h otal enthaly otal temerature otal ressure m& Fuel mass low rate m& a Air mass low rate Fuel/Air ratio ensitivity o uel consumtion with resect to stage Q Fuel enthaly o reaction emerature dro in stage i,i Coyright 22 by AME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /5/24 erms o Use: htt://asme.org/terms

2 HEORY he eiciency o any machine is normally exressed in terms o the ratio o actual and ideal work transers. Because turbomachines are basically adiabatic, the ideal rocess is isentroic and the eiciency is called an isentroic eiciency. Using the concet o stagnation enthaly to take into account any changes in kinetic energy o the luid between inlet and outlet or a turbine we have [3], W h ηt () W h Assuming that the luid is erect gas and the mean c changes through the turbine is negligible; the isentroic eiciency is deined in terms o temerature as, ηt where indexes and 2 reer to inut and outut o turbine as indicated in ig.. Making use o the isentroic relations and the above deinition, the ollowing relation can be ound, γ /( γ ) (3) ηt Fig. : Axial low turbine For the stage i o turbine, the above relation is also valid between inut and outut o the stage (ig. ), i 2 i η, i, i s, i, i γ /( γ ) Pressure ratio between inut and outut o the turbine can be exressed as,, i i, i (5) Where is the number o turbine stages. Combining relations (4) and (5) and using relation (3), we have, 2i (2) (4) η (6) t i ηs, i, i By some maniulations, one can write, η t η i si,, i In a mathematical oint o view, sensitivity () is deined as the derivative o uel consumtion with resect to stage eiciency, m& m& a (8) s, s, Derivative o in the above relation can be exanded as, t s, t s, Assuming that the turbine outut ower is ixed and the low temerature entering the combustion chamber is constant, we have, Q const. () c hereore, c Q (), t he second term in relation (9) can be comuted using equation (3), ( γ )/ γ t (7) (9) (2) And the third term in relation (9) can be comuted using relation (7), η i ηsi,, i t, i, i si,, i 2 2 s,, η s, (3) 2 Coyright 22 by AME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /5/24 erms o Use: htt://asme.org/terms

3 ensitivity ( ) relation is derived by substituting the above derivatives in relations (9) and (8), a designer imroves it to 84%, uel consumtion reduction will be %. cm& a, i, i ηsi,, i 2 Q, η s, i ηsi,, i (4) Using the above relation, now we can calculate the uel consumtion reduction or an increase in stage eiciency, m& η (5) s, Fuel consumtion reduction (%) AERIAL EGIE AALYI he data shown in ab. reer to a twin-sool turboan engine, with the an driven by the LP turbine and the comressor by the HP turbine. he urose is to ind the sensitivity() variation versus stage eiciency or both LP and HP stages o the turbine. hrust o this engine is about 39k. It is assumed that the eiciency o all stages excet the stage in analysis is the same and equal to reerence stage eiciency. Parameter Value Inlet turbine temerature (K) 3 Outlet turbine temerature (K) umber o turbine stages 2 emerature dro in irst stage (K) 35.3 emerature dro in 2nd stage (K) 76 Air mass low rate (kg/s) Fuel mass low rate (kg/s) 69 Fuel enthaly o reaction (kj/kg) 43 Reerence stage eiciency.85 ab.: Engine cycle seciications Using ormula (4) and the data given in the table, curves o sensitivity () versus stage eiciency or both o turbine stages are lotted in ig. 2. hese curves show also the ercentage o uel consumtion reduction or % imrovement in the stage eiciency (right y-axis). It can be seen that the sensitivity o uel consumtion decreases as the stage eiciency increases. It means that attemts to otimize the turbine stage or high eiciency stages result in less imrovement in the uel consumtion. As an examle, i the irst stage eiciency is 7% and a new design increases it to 72%, using the curve in ig. 2, the sensitivity will be o the uel mass low rate reduction can be comuted using relation (5): m&.586 which is corresonding to.25% reduction in uel consumtion. I the initial eiciency o stage is 82% and Fig. 2: Variation o sensitivity with stage eiciency or both stages o turboan engine's turbine Fig. 2 shows that the uel consumtion is more sensitive to irst stage eiciency in comarison with second stage. his can be understood rom ormula (4), according to which, sensitivity o a stage is directly related to temerature dro through it. ensitivity o two stages or dierent stage eiciency is deicted in ig Fig. 3: ensitivity o each stage or dierent stage eiciencies GA URBIE AALYI In this section, a heavy duty 4MWgas turbine is analyzed. he gas turbine cycle seciications are given in ab. 2. his turbine is analyzed in two modes. In the irst mode, all stages are identical with the same total temerature dro. 3 Coyright 22 by AME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /5/24 erms o Use: htt://asme.org/terms

4 Parameter Value Inlet turbine temerature (K) 4 Outlet turbine temerature (K) 544 umber o turbine stages 4 emerature dro in each stage (K) 49 Air mass low rate (kg/s) 45.8 Fuel mass low rate (kg/s).6 Fuel enthaly o reaction (kj/kg) 43 Reerence stage eiciency.85 ab. 2: Gas turbine cycle seciications Curves o sensitivity versus stage eiciency or this state are shown in ig. 4. However, as deicted in ig. s 4 and 5, the total temerature dro in all stages is the same; the irst stage o the turbine has the minimum eect on the uel consumtion and sensitivity increases or the next stages. hereore it can be realized that in addition to total temerature dro, the osition o the stage is aecting the sensitivity. imilar to the revious engine, sensitivity decreases as the stage eiciency increases Fuel consumtion reduction (%) In the second mode, total temerature dro in each stage is dierent. ab. 3 gives the temerature dro or all stages. no. (K) ab. 3: emrature dro in each stage As shown in ig. s 6 and 7, the sensitivity o all stages has been close to each other. A comarison between ig. 4 and ig. 6 indicates that the range o uel consumtion reduction or the irst mode is rom.2% to.% whereas this range or the second mode is rom.35% to.73% Fig. 6: Variation o sensitivity with stage eiciency or all stages o gas turbine (second mode).7.5 Fuel consumtion reduction (%) Fig. 4: Variation o sensitivity with stage eiciency or all stages o gas turbine (irst mode) Fig. 5: ensitivity o each stage or dierent stage eiciency (irst mode) Fig. 7: ersitivity o each stage or dierent stage eiciency (second mode) 4 Coyright 22 by AME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /5/24 erms o Use: htt://asme.org/terms

5 COCLUIO In this study, using the zero-dimensional gas turbine relations, an exlicit exression or calculation o uel consumtion gradient with resect to the eiciency o an individual turbine stage was derived. he inal ormula obtained was demonstrated by some diagrams in the context o two dierent gas generators. he results show that the uel consumtion is more sensitive to earlier stages eiciencies and Also imrovement o stages with larger temerature dro has more imact on the uel consumtion. hereore it can be concluded that the osition o stage and its temerature dro will determine the extent o its imact on uel consumtion. Another imortant oint that can be concluded rom this study is that the sensitivity o uel consumtion with resect to stage eiciency reduces as the stage eiciency increases. It means that reduction o uel consumtion is more diicult or turbines with higher eiciency stages. REFERECE [] G. egri di Montenegro, A. Peretto, ensitivity Analysis on Brayton Cycle Gas urbine Perormance, AME J. Engg. Gas urbines Power, 9 (997) [2] Ho-Young Kwak, Ki-Moon Kang, ensitivity analysis o comonent eiciencies on erormance o a gas turbine cogeneration system, Int. J. Exergy, 9 (2) [3] H. Cohen, G. F. C. Rogers, H. I. H. aravanamuttoo, Gas urbine heory, 4 th edition 998: Longman eries. 5 Coyright 22 by AME Downloaded From: htt://roceedings.asmedigitalcollection.asme.org/ on /5/24 erms o Use: htt://asme.org/terms