Muddy points Since n=1-=_looking at the P-V graph, does that mean the farther apart the T1,T2 isotherms are, the greater efficiency? And that if they were very close, it would be very nefficient?(MP 1A.1 In the Carnot cycle, why are we only dealing with volume changes and not pressure therms?(MP 1A.2) Is there a physical application for the carnot cycle? can we design a carnot engine for a propulsion device?(MP 1A.3 How do we know which cycles to use as models for real processes?(MP 1A. 4 1.A Brayton Cycles (or oule cycles): The power Cycle for a Gas Turbine et engine engine and the corresponding cycle are given in Figure A-g stant pressure legs. Sketches of an For a Brayton cycle there are two adiabatic legs and two cor Combustor Combustor citb Inlet Nozzle Turbine and nozzle P Compressor Turbine compressor a Heat rejectio Figure A-4: Sketch of the jet engine components and corresponding thermodynamic states Gas turbines are also used for power generation and for closed cycle operation(for example for space power generation). a depiction of the cycle in this case is shown in Figure A-5
1A-5 Muddy points Since η = −1 T T 1 2 ,looking at the P-V graph, does that mean the farther apart the T1, T2 isotherms are, the greater efficiency? And that if they were very close, it would be very inefficient? (MP 1A.1) In the Carnot cycle, why are we only dealing with volume changes and not pressure changes on the adiabats and isotherms? (MP 1A.2) Is there a physical application for the Carnot cycle? Can we design a Carnot engine for a propulsion device? (MP 1A.3) How do we know which cycles to use as models for real processes? (MP 1A.4) 1.A.3 Brayton Cycles (or Joule Cycles): The Power Cycle for a Gas Turbine Jet Engine For a Brayton cycle there are two adiabatic legs and two constant pressure legs. Sketches of an engine and the corresponding cycle are given in Figure A-4. Turbine and nozzle Heat rejection to atmosphere Inlet and compressor Combustor q2 PCompressor exit Patm q1 a d P V b c Combustor Compressor Turbine Inlet Nozzle Figure A-4: Sketch of the jet engine components and corresponding thermodynamic states Gas turbines are also used for power generation and for closed cycle operation (for example for space power generation). A depiction of the cycle in this case is shown in Figure A-5
Equivalent heat transfer at constant pressure Compressor Turbine Equivalent heat transfer at constant pressure Figure A-5: Thermodynamic model of gas turbine engine cycle for power generation The objective now is to find the work done, the heat absorbed, and the thermal efficiency of the cycle. Tracing the path shown around the cycle from a-b-c-d and back to a, the first law gives (writing the equation in terms of a unit mass) Aua-b-c-d-a =0=92+91-w The net work done is where qu q2 are defined as heat received by the system( q, is negative). We thus need to evaluate the heat transferred in processes b-c and d-a. For a constant pressure process the heat exchange per unit mass is dh=CpdT=dq, or [dq]onstant p=dh The heat exchange can be expressed in terms of enthalpy differences between the relevant states Treating the working fluid as an ideal gas, for the heat addition from the combustor, he-hb=Cp(T-T The heat rejected is, similarly, q1=ha-ha=Cp(Ta-Ta) The net work per unit mass is given by Net work per unit mass=q1+q2=CpI(T-b)+(Ta-Ta)] The thermal efficiency of the Brayton cycle can now be expressed in terms of the temperatures 1A-6
1A-6 Wnet 2 3 1 4 Equivalent heat transfer at constant pressure Equivalent heat transfer at constant pressure Turbine Compressor ⋅ Wcomp ⋅ Q ⋅ Q ⋅ Figure A-5: Thermodynamic model of gas turbine engine cycle for power generation The objective now is to find the work done, the heat absorbed, and the thermal efficiency of the cycle. Tracing the path shown around the cycle from a-b-c-d and back to a, the first law gives (writing the equation in terms of a unit mass), ∆u qqw abcda −−− − == + − 0 2 1 . The net work done is wq q = +2 1, where q q 1 2 , are defined as heat received by the system ( q1 is negative). We thus need to evaluate the heat transferred in processes b-c and d-a. For a constant pressure process the heat exchange per unit mass is dh c dT dq = = p , or dq dh cons t P [ ] = tan . The heat exchange can be expressed in terms of enthalpy differences between the relevant states. Treating the working fluid as an ideal gas, for the heat addition from the combustor, q h h cT T 2 =−= − c b pc b ( ). The heat rejected is, similarly, q h h cT T 1 =−= − a d p a ( ) d . The net work per unit mass is given by Net work per unit mass = qq cTT T T 1 2 += − pc b a [ ] ( ) + − ( ) d . The thermal efficiency of the Brayton cycle can now be expressed in terms of the temperatures:
Net work_cp(T-TD)-(Ta-Ta). Heat in (7- (-0)1、(T4-1) T(T/7-1) (A3.1) To proceed further, we need to examine the relationships between the different temperatures. We know that points a and d are on a constant pressure process as are points b and c, and Pa=Pd; P=P. The other two legs of the cycle are adiabatic and reversible, so Pa P /)- y P T T Therefore -=-,or, finally,=. Using this relation in the expression for thermal T efficiency, Eq (A1.3) yields an expression for the thermal efficiency of a Brayton cycle Ideal Brayton cycle efficiency: nB=1-A (A3.2) Th pressor exit The temperature ratio across the compressor, Tb/Ta=TR. In terms of compressor temperature ratio, and using the relation for an adiabatic reversible process we can write the efficiency in terms of the compressor(and cycle) pressure ratio, which is the parameter commonly used y-1)/y (A.33) R Figure A-6 shows pressures and temperatures through a gas turbine engine(the afterburning J57 which powers the F-8 and the F-101) AFTERBURNING MILITARY TURBOJET TYPICAL SEA LEVEL STATIC INTERNAL PRESSURES AND TEMPERATURES DATA FOR PRATT WHITNEY J57"B" SERIES AXIMUM AFTERBURNERJ ITITTTT STATION 2 pt(psia)14.7 540167.0158036.0 °F)59 330660 15701013 2540 Figure A-6: Gas turbine engine pressures and temperatures
1A-7 η = = [ ] ( ) − − − ( ) [ ] − Net work Heat in cTT T T cT T pc b d a pc b = − ( ) − ( ) − = − ( ) − ( ) − 1 1 1 1 T T T T TT T TT T d a c b a d a bc b / / . (A.3.1) To proceed further, we need to examine the relationships between the different temperatures. We know that points a and d are on a constant pressure process as are points b and c, and PPPP a = = d b c ; . The other two legs of the cycle are adiabatic and reversible, so P P P P T T T T d c a b d c a b = == = ( ) − ( ) − > γ γ / 1 γ γ / 1 . Therefore T T T T d c a b = , or, finally, T T T T d a c b = . Using this relation in the expression for thermal efficiency, Eq. (A.1.3) yields an expression for the thermal efficiency of a Brayton cycle: Ideal Brayton cycle efficiency:η B a b T T = −1 (A.3.2) = −1 T T atmospheric compressor exit . The temperature ratio across the compressor, T T TR b a / = . In terms of compressor temperature ratio, and using the relation for an adiabatic reversible process we can write the efficiency in terms of the compressor (and cycle) pressure ratio, which is the parameter commonly used: η B γ γ TR PR =− =− ( )( ) − 1 1 1 1 1 / . (A.3.3) Figure A-6 shows pressures and temperatures through a gas turbine engine (the afterburning J57, which powers the F-8 and the F-101). Figure A-6: Gas turbine engine pressures and temperatures
Equation(A3.3)says that for a high cycle efficiency, the pressure ratio of the cycle should be increased. Figure A-7 shows the history of aircraft engine pressure ratio versus entry into service and it can be seen that there has been a large increase in cycle pressure ratio. The thermodynamic concepts apply to the behavior of real aerospace devices Trent 890 Trent 77 cF6-80c2A8 CF6-80E1A4 CF6-80C2A8 M565c RB211524D4 CF6-50A RB211-22 CFM56-5B TF39-1 CF6-6d JT9D-70 CFM56-3C JT9D-3A Spey 512Spey 512-14 JT8D-219 BD- Spey 505- JT8D-17 Tay 611 Tay 651 占10 0 2000 Year of certification Figure A-7: Gas turbine engine pressure ratio trends (Janes Aeroengines, 1998) Muddy points When flow is accelerated in a nozzle, doesn t that reduce the internal energy of the flow and therefore the enthalpy? (MP 1A.5 Why do we say the combustion in a gas turbine engine is constant pressure?(MP 1A.6 Why is the Brayton cycle less efficient than the Carnot cycle? (MP 1A.7) still within the system boundary?(MP 1Af'g in the exhaust outside tsg-that Does it matter what labels we put on the corners of the cycle or not?(MP 1A.9) u the work done in the compressor always equal to the work done in the turbine plus Is vork out(for a Brayton cyle)?(MP 1A.10) L.A. 4 Gas Turbine Technology and Thermodynamics The turbine entry temperature, T, is fixed by materials technology and cost. (If the temperature is too high, the blades fail. )Figures A-8 and A-9 show the progression of the turbine entry temperatures in aeroengines. Figure A-8 is from Rolls royce and Figure A-9 is from Pratt whitney. Note the relation between the gas temperature coming into the turbine blades and the blade melting temperature
1A-8 Equation (A.3.3) says that for a high cycle efficiency, the pressure ratio of the cycle should be increased. Figure A-7 shows the history of aircraft engine pressure ratio versus entry into service, and it can be seen that there has been a large increase in cycle pressure ratio. The thermodynamic concepts apply to the behavior of real aerospace devices! Figure A-7: Gas turbine engine pressure ratio trends (Jane’s Aeroengines, 1998) Muddy points When flow is accelerated in a nozzle, doesn’t that reduce the internal energy of the flow and therefore the enthalpy? (MP 1A.5) Why do we say the combustion in a gas turbine engine is constant pressure? (MP 1A.6) Why is the Brayton cycle less efficient than the Carnot cycle? (MP 1A.7) If the gas undergoes constant pressure cooling in the exhaust outside the engine, is that still within the system boundary ? (MP 1A.8) Does it matter what labels we put on the corners of the cycle or not? (MP 1A.9) Is the work done in the compressor always equal to the work done in the turbine plus work out (for a Brayton cyle) ? (MP 1A.10) 1.A.4 Gas Turbine Technology and Thermodynamics The turbine entry temperature, Tc , is fixed by materials technology and cost. (If the temperature is too high, the blades fail.) Figures A-8 and A-9 show the progression of the turbine entry temperatures in aeroengines. Figure A-8 is from Rolls Royce and Figure A-9 is from Pratt&Whitney. Note the relation between the gas temperature coming into the turbine blades and the blade melting temperature. 1960 0 10 20 JT3D Conway 508 Conway 550 JT8D-17 JT8D-219 CFM56-3C PW4084 PW4168 CFM56-5B CFM56-5C4 CFM56-2 JT8D-1 Tay 611 Spey 555 Spey 512 JT9D-3A JT9D-70 TF39-1 RB211-22 RB211-524D4 CF6-50E PW4052 CF6-80C2A8 CF6-50A CF6-6 JT9D-7R4G Spey 512-14 Spey 505 Tay 651 GE90 Trent 890 Trent 775 30 40 1970 1980 Year of Certification Overall Pressure Ratio (OPR), Sea Level, T-O 1990 2000 CF6-80C2A8 CF6-80E1A4