Gas Turbine Cycle Analysis

Transcription

1 Gas Turbine Cycle Analysis Session delivered by: Prof. Q.H. Nagurwala 1

2 Session Objectives This session is intended to introduce the delegates to: Analysis of shaft ower gas turbine cycles Analysis of aeroroulsion gas turbine cycles 2

3 Analysis of Shaft Power Cycles Design Parameters Comressor Pressure Ratio Turbine Inlet Temerature Comressor, Combustor, Turbine and other comonent efficiencies Pressure Losses Performance Calculations Secific work outut Secific Fuel Consumtion Cycle efficiency 3

4 Thermodynamic Cycle Analysis The task of thermodynamic cycle analysis is imortant, as it constitutes the base where the knowledge of how to model a gas turbine is acquired and is a rerequisite for erforming all other tasks Gas Turbine works on Brayton Cycle as we have seen earlier Here we analyse gas turbine cycle adoted for ower gas turbine and roulsion gas turbine with the hel of simle numerical examles 4

5 Nomenclature C c f h ΔH m M n Velocity Secific heat at constant ressure Fuel/air ratio by weight Secific enthaly Enthaly of reaction Mass flow Molecular weight, Mach number Polytroic index r s T t W γ η ρ Pressure ratio Secific entroy Absolute temerature Temerature ratio Secific work (ower) outut Ratio of secific heats Efficiency density Absolute ressure Q Heat transfer er unit mass flow Q net, Net calorific value at constant R ~ R Gas constant molar (universal) gas constant 5

6 Nomenclature Suffixes 0 stagnation value 1,2,3 reference lanes olytroic a ambient,air b combustion chamber c comressor f fuel g gas h heat-exchanger i intake, mixture constituent m mechanical N net s stage t turbine 6

7 Examle-2 (Simle cycle with Free Turbine) Determine the secific work outut,secific fuel consumtion and cycle efficiency for a simle cycle gas turbine with a free ower turbine (see figure) given the following secification: Comressor ressure ratio 12.0 Turbine inlet temerature 1350 K Isentroic efficiency of comressor, η c 0.86 Isentroic efficiency of each turbine, η t 0.89 Mechanical efficiency of each shaft, η m 0.99 Combustion efficiency 0.99 Combustion chamber ressure loss Exhaust ressure loss Ambient conditions, a,t a 6 % comressor delivery ressure 0.03 bar 1 bar, 288 K 7

8 Examle-2 ( contd.) Proceeding as in the revious examle, T 02 T [ 12 1] K W tc 1.005* kJ / kg (1 0.06) 11.28bar The intermediate ressure between the two turbines, 04, is unknown, but can be determined from the fact that the comressor turbine roduces just sufficient work to drive the comressor. The temerature equivalent of the comressor turbine work is, therefore, Wtc T03 T K c g 8

9 Examle-2 ( contd.) The corresonding ressure ratio can be found using the relation T T T * η T t K γ 1 γ The ressure at entry to the ower turbine, 04, is then found to be 11.28/ bar and the ower turbine ressure ratio is /(1+0.03)

10 Examle-2 ( contd.) The temerature dro in the ower turbine can now be obtained T * T K and the secific work outut, i.e. ower turbine work er unit air mass flow, is W W t t c g ( T T ) η m ( ) kj/kg (or kw/kg) The comressor delivery temerature is K and the combustion temerature rise is K The theoretical fuel/air ratio required is (from available chart) giving an actual fuel/air ratio of /

11 Theoretical Fuel-Air Ratio Combustion temerature rise vs theoretical fuel-air ratio 11

12 Examle-2 ( contd.) The SFC and cycle efficiency, η, are then given by SFC η f W t * * kg/kWh 12

13 Examle-2 ( contd.) It should be noted that the cycle calculations have been carried out as above to determine the overall erformance. It is imortant to realize, however, that they also rovide information that is needed by other grous such as the aerodynamic and control design grous. The temerature at entry to the ower turbine, T 04, for examle, may be required as a control arameter to revent oeration above the metallurgical limiting temerature of the comressor turbine. The exhaust gas temerature (EGT), T 05, would be imortant if the gas turbine were to be considered for combined cycle or cogeneration lant. In this Examle, T K or 527 C, which is suitable for use with a waste heat boiler. When thinking of combined cycle lant, a higher T I T might be desirable because there would be a consequential increase in EGT, ermitting the use of a higher steam temerature and a more efficient steam cycle. If the cycle ressure ratio were increased to increase the efficiency of the gas cycle, however, the EGT would be decreased resulting in a lower steam cycle efficiency. 13

14 Proulsion Gas Turbine Cycles Design Parameters Comressor Pressure Ratio Turbine Inlet Temerature Comressor, Combustor, Turbine and other comonent efficiencies Pressure Losses Performance Calculations Secific Thrust Secific Fuel Consumtion Proulsive Efficiency 14

15 a A sonic velocity cross-sectional area B byass ratio (m c /m h ) F F s K F M net thrust secific thrust secific thrust coefficient Mach number Nomenclature Suffixes c h j m critical condition,cold stream hot stream jet mixed η e η i η j η m ηo η η r η efficiency of energy conversion intake efficiency nozzle efficiency mechanical efficiency overall efficiency roulsion (Froude)efficiency ram efficiency olytroic efficiency 15

16 Proulsion Gas Turbine Cycle In Aircraft Gas Turbines the useful ower outut is in the form of thrust. In Turbojet and Turbofan engines the whole of thrust is generated in roelling nozzles In turboro engines most of the thrust is generated in the roeller with relatively small thrust in the exhaust nozzle The forward seed and altitude affect the erformance of an Aircraft Gas Turbine From designer s oint of view, there may be differing requirements for take off, climb, cruise and maneuverings. Further, these requirements may also be different for civil and military aircrafts; and for long- and short-haul aircrafts. 16

17 Proulsion Gas Turbine Cycle Examles in the resent session will show design oint calculations for take off and cruise conditions. The net Thrust due to change of momentum is: F m(c j - C a ) mc j : gross momentum thrust mc a : intake momentum drag If the exhaust gases are not exanded comletely to a in the roulsive duct, then F m(c j - C a ) + A j ( j - a ) Momentum Thrust + Pressure Thrust 17

18 Schematic of a Turbojet 18

19 Proulsion Efficiency Proulsion efficiency, η : It is defined as the ratio of the useful roulsive energy or thrust ower (F.C a ) to the sum of that energy and the unused kinetic energy of the jet. The latter is the kinetic energy of the jet relative to the earth, namely m(c j - C a ) 2 /2 η m[ C a ( C j mc a C ( C a j C ) + ( C j a ) C a ) 2 / 2] 2 C 1+ C j a This is also known as Froude Efficiency. Efficiency of Energy Conversion η e m( C C m 2 j f Q 2 a net, ) / 2 Useful kinetic energy for roulsion Rate of energy sulied by fuel 19

20 Efficiency and Thrust Overall efficiency, η o, is the ratio of the useful work done in overcoming drag to the energy in the fuel sulied. mc ( C C FC a j a a η o η m f Qnet, m f Qnet, ) Secific Thrust, F s, is the thrust er unit mass flow of air. SFC f/f s Well designed intakes are used for uniform and non- distorted fluid flow. Ram Pressure 01 - a Pressure rise in the intake η e 20

21 Examle-1(Turbojet Engine) Determination of the secific thrust and SFC for a simle turbojet engine, having the following comonent erformance at the design oint at which the cruise seed and altitude are M 0.8 and m. Comressor ressure ratio 8.0 Turbine inlet temerature Isentroic efficiency: 1200 K of comressor, 0.87 of turbine, 0.90 η t of intake, 0.93 η i η c of roelling nozzle, 0.95 Mech. transmission efficiency, 0.99 Combustion efficiency, 0.98 η b Combustion ressure loss, η j b η m 4% of comressor delivery ressure 21

22 Examle-1( contd.) Turbojet cycle with losses 22

23 Examle-1( contd.) From the ISA table, at m a bar, T a K and a m/s The stagnation conditions after the intake may be obtained as follows: Ca 2C T a 2 01 T a ( 0.8* 299.5) 28.6K 2*1.005*1000 Ca + 2C 2 C a 1 + ηi 2c T * K 2 a 2 γ ( γ 1) bar 0.93*

24 Examle-1( contd.) At outlet from the comressor, * bar 01 ( γ 1) T T T γ K c η T K Ca( T 02 T 01) 1.005x234.9 W t W c / η m and hence T T04 Cgηm 1.148x0.99 T K b (1 0.04) 3.018bar T 0.90 ' 04 T03 ( T03 T04) K ηt γ ' T ( γ 1) bar T K 24

25 Examle-1( contd.) The nozzle ressure ratio is, therefore a The critical ressure ratio is 04 c 1 1 η j 1 γ 1 γ + 1 γ ( γ 1)

26 Examle-1( contd.) Since 04 / a > 04 / c, the nozzle is choking. 2 2*992.3 T 5 T c T K γ c c 1.284/ bar ρ C 5 5 A5 m R c T c ( γrt ) 1 ρ C 5 c 5 100* * (1.333*0.287*850.7*1000) * kg / m m s / kg 570.5m / s 26

27 Examle-1( contd.) The secific thrust is A 5 F s (C 5 -C a ) + ( c a ) m ( ) ( ) Ns/kg For T K and T 03 - T K, we find that the theoretical fuel/air ratio required is Thus the actual fuel/air ratio is f The secific fuel consumtion is therefore f *3600 SFC kg/h N F S 27

28 Examle-1( contd.) For cycle otimisation, calculations would normally be done on the basis of secific thrust and SFC. A common roblem, however, is the determination of actual engine erformance to meet a articular aircraft thrust requirement. The engine designer needs to know the airflow, fuel flow and nozzle area ; the airflow and nozzle area are also imortant to the aircraft designer who must determine the installation dimensions. If, for examle, the cycle conditions in the examle were selected to meet a thrust requirement of 6000 N, then F m F s kg/s the fuel flow is given by m f f m * * kg/h (it should be noted that fuel flow is normally measured and indicated in kg/h rather than kg/s) The nozzle area follows from the continuity equation : A * m 2 28

29 Session Summary This session has covered the following: Cycle analysis of shaft ower gas turbines Cycle analysis of roulsion system gas turbines Aroriate examles have been resented for both these cases. 29

30 Thank you 30