Open Cycle mf dot fuel QH dot combustor 3 2 ma dot air compressor 4 turbine W dotnet Wt dot Wc dot 1 turbine Wc dot ma dot h 2 h 1 ma dot cp air T2 T1 power compressor mf dot Wt dot ma dot mf dot h 3 h 4 ma dot 1 T T4 c ma dot p prod 3 Jet engine as a side note if the net work were converted to velocity via a nozzle jet engine the relationships would be Wnet dot Wt dot Wc dot determines state 4 out of turbine at p 4 p1 atmosphere is state 5 wnet cp T3 T4 T 4 determined from equation for net work 1 could determine p 4 from nozzle anlysis First law Q W 0 p4 T3 p3 T4 1 determine T 5 from p5 T3 p3 T5 or 1 p5 T4 p4 T5 2 V h4 h5 2 determines V thrust from momentum change combustor 1 atmosphere 0 HR2 HP3 rewrite using LHV adiabatic combustion Q W 0 0 Enthaply of reactants at combustor inlet compressor outlet Enthalpy of products out of combustor first law 0 HR2 HR0 HP3 HP0 LHV rewrite using specifi enthalpy and mass flows on a per unit mass flow of fuel ma dot ma dot 0 h f2 h f0 h a2 h a0 1 h p3 h p0 LHV mf dot mf dot to account for incomplete combustion introduce combustion efficiency 12 19 2005 1 only obtain comb HV Given ma dot ma dot 0 h f2 h f0 h a2 h a0 1 h p3 h p0 comb LHV mf dot mf dot can solve for ma dot introduce average specific heat cp bar air h p3 h p0 h a2 h a0 h a2 h a0 cp bar prod T2 T0 h p3 h p0 T3 T0 cp bar fuel comb LHV cp bar fuel T2 T0 cp bar prod T3 T0 cp bar prod T3 T0 cp bar air T2 T0 mf dot or inverting ma dot comb LHV h f2 h f0 h p3 h p0 mf dot mf dot mf dot Find ma dot h f2 h f0 h p3 h p0 comb LHV h a2 h a0 h p3 h p0 ma dot mf dot ma dot T2 T0 cp bar prod T3 T0 cp bar air T2 T0 h f2 h f0 comb LHV cp bar fuel T2 T0 cp bar prod T3 T0 gas turbine efficiency efficiency dividing by m a dot mf dot 1 T T4 cp bar air T2 T1 c Wnet dot Wt dot Wc dot ma dot p bar prod 3 mf dot LHV mf dot LHV mf dot ma dot kg SFC hr power kW SFC 12 19 2005 fuel mf dot Wnet dot kg kW hr mf dot lb not equality hp hr LHV Wnet dot LHV 1 LHV 2 LHV Open cycles have similar alternatives to closed analysis would be similar as well so not repeated here Open Cycle Regenerative Recouperative 6 regenerator 3 combustor mf dot fuel mp dot products 2 5 4 ma dot air compressor turbine W dotnet Wt dot Wc dot 1 static data for plot T s diagram temperature 1000 irreversible cycle irreversible heat exchanger maximum regeneration inlet temperature irreversible 500 1 1 2 1 4 1 6 1 8 2 entropy N B cycle is drawn closed from state 6 to 1 but is taking place in atmosphere 12 19 2005 3 2 2 Intercooled Regenerative Recouperative Cycle stack Rolls Royce WR 21 is an example see links regenerator 8 5 combustor mf dot fuel 6 mp dot products QL dot 1 compressor 2 ma dot air 7 4 3 turbine compressor W dotnet Wt dot Wc dot static data for plot T s diagram 1200 irreversible cycle irreversible heat exchanger maximum regeneration inlet temperature irreversible temperature 1000 800 600 400 0 8 1 1 2 1 4 entropy 12 19 2005 4 1 6 1 8 2 thermodynamic models for combustion Various thermodynamic models can be used for analysis of products of combustion 1 Single gas model perfect gas constant cp 1 kJ kg K close enough 1 4 2 Two gas model a perfect gas air for compression c p 1 0035 kJ kg K a 1 4 b perfect gas combustion products c pp 1 13 kJ kg K p 1 3 3 Tabulated data e g Keenan Kaye Gas Tables property data for air Table 1 Air at low pressure T deg F abs t deg F h pr u v r Table 2 Air at low pressures T t c p cv k cp cv a Gmax pi Pr Table 3 R Log N for air Table 4 Products 400 Theoretical Air for One Pound Mole Table 5 Products 400 Theoretical Air for One Pound Mole fuel data Table 6 Products R bar Log e N 4 57263 n Table 7 Products 200 Theoretical Air for One Pound Mole etc data for oxygen hydrogen carbon monoxide dioxide etc T deg F abs t deg F h enthalpy per unit mass pr relative pressure c p specific heat at constant pressure c v specific heat at constant volume G flow per unit area or mass velocity k cp cv u internal energy per unit mass vr relative volume p pressure Pr Prandtl number cp R gas constant for air a velocity of sound thermal conductivity viscosity T cp T dT T0 Notes Appendix Sources and methods calculated for one particular composition of the hydrocarbon fuel it has been shown that it represents with high precision the properties of the productsof combustion of fuels of a wide range of composition all for 400 theoretical air page 205 bottom problems involving intermediate mixtures to Table B can be solved by interpolation based on theoretical air or extrapolated to 100 for products is valid except for effects of disassociation products reactants air and Table theor theor theor water vapor Number air fuel fuel mass water Table B 1 inf 0 0 0 4 400 25 14 6 7 200 50 28 7 12 19 2005 5 4 Polynomial equations example in combustion example c p f polytropic process compressor isentropic process dT dp ds cpo R T p 7 21 in gas relationships R dp dT pc cpo p T T dp p dT 1 c R po T T 1s p1 1 ln p2 R T p1 cp T p2 dT e 1s cp pc dT T R T 2 turbine 2 T p1 p2 e 1s c p 1 dT T R T T 1s c p dT T pt R T 1 p1 2 p2 e High Temperature Gas Turbines Advantages high efficiency low specific fuel consumption high specific horsepower small size and weight Disavantages materials strength problems Creep see separate notes re creep corrosion Solutions better materials blade and combustor cooling ceramic materials 12 19 2005 6 2 blade cooling mf dot fuel QH dot combustor 3 2 4 to blades ma dot air compressor turbine W dotnet Wt dot Wc dot 1 cooling flow compressed air ducted into stationary AND …