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Brayton Cycle Brayton Cycle Reading Problems 9-8 → 9-10 9-78, 9-84, 9-108 Open Cycle Gas Turbine Engines • after compression, air enters a combustion chamber into which fuel is injected • the resulting products of combustion expand and drive the turbine • combustion products are discharged to the atmosphere • compressor power requirements vary from 40-80% of the power output of the turbine (re- mainder is net power output), i.e. back work ratio = 0.4 → 0.8 • high power requirement is typical when gas is compressed because of the large specific volume of gases in comparison to that of liquids Idealized Air Standard Brayton Cycle • closed loop • constant pressure heat addition and rejection • ideal gas with constant specific heats 1 Brayton Cycle Efficiency The Brayton cycle efficiency can be written as (1−k)/k η =1− (rp) wherewedefine the pressure ratio as: P2 P3 rp = = P1 P4 2 Maximum Pressure Ratio Given that the maximum and minimum temperature can be prescribed for the Brayton cycle, a change in the pressure ratio can result in a change in the work output from the cycle. The maximum temperature in the cycle (T3) is limited by metallurgical conditions because the turbine blades cannot sustain temperatures above 1300 K. Higher temperatures (up to 1600 K can be obtained with ceramic turbine blades). The minimum temperature is set by the air temperature at the inlet to the engine. 3 Brayton Cycle with Reheat • T3 is limited due to metallurgical constraints • excess air is extracted and fed into a second stage combustor and turbine • turbine outlet temperature is increased with reheat (T6 >T4), therefore potential for regen- eration is enhanced • when reheat and regeneration are used together the thermal efficiency can increase signifi- cantly 4 Compression with Intercooling • the work required to compress in a steady flow device can be reduced by compressing in stages • cooling the gas reduces the specific volume and in turn the work required for compression • by itself compression with intercooling does not provide a significant increase in the effi- ciency of a gas turbine because the temperature at the combustor inlet would require addi- tional heat transfer to achieve the desired turbine inlet temperature • but the lower temperature at the compressor exit enhances the potential for regeneration i.e. a larger ΔT across the heat exchanger 5 Brayton Cycle with Regeneration • a regenerator (heat exchanger) is used to reduce the fuel consumption to provide the required Q˙ H • the efficiency with a regenerator can be determined as: W˙ net Q˙ L η = =1− Q˙ H Q˙ H 6 cp(T6 − T1) =1− ⇒ (for a real regenerator) cp(T3 − T5) cp(T − T1) =1− 6 ⇒ (for an ideal regenerator) − cp(T3 T5) cp(T2 − T1) =1− cp(T3 − T4) and Tmin (k−1)/k η =1− (rp) Tmax • for a given Tmin/Tmax, the use of a regenerator above a certain rp will result in a reduction of η with an ideal regenerator without a regenerator better with a better without T/T=0.21 3 regenerator a regenerator T1 / T3 = 0.25 T/T=0.31 3 rp, cr rp 7 Regenerator Effectiveness Q˙ reg,actual h5 − h2 h5 − h2 T5 − T2 = = = = ˙ − − − Qreg,ideal h5 h2 h4 h2 T4 T2 Typical values of effectiveness are ≤ 0.7 Repeated intercooling, reheating and regeneration will provide a system that approximates the TL Ericsson Cycle which has Carnot efficiency η =1− . TH Brayton Cycle With Intercooling, Reheating and Regeneration 8 T Tmax QH, R QH 7s 9s Qreg Qreg 2s 4s Q Tmin L QL, I s Compressor and Turbine Efficiencies Isentropic Efficiencies h2,s − h1 cp(T2,s − T1) (1) ηcomp = = h2 − h1 cp(T2 − T1) h3 − h4 cp(T3 − T4) (2) ηturb = = h3 − h4,s cp(T3 − T4,s) Wnet QH − QL QL cp(T4 − T1) (3) ηcycle = = =1− =1− QH QH QH cp(T3 − T2) Given the turbine and compressor efficiencies and the maximum (T3) and the minimum (T1) tem- peratures in the process, find the cycle efficiency (ηcycle). (4) Calculate T2s from the isentropic relationship, (k−1)/k T2,s P2 = . T1 P1 Get T2 from (1). (5) Do the same for T4 using (2) and the isentropic relationship. (6) substitute T2 and T4 in (3) to find the cycle efficiency. 9.
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