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BRAYTON CYCLE – IDEAL GAS TURBINE CYCLE MET 401 POWER PLANT ENGINEERING DR. TAIB ISKANDAR MOHAMAD
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Objectives• Evaluate the performance of gas power cycles for which the working fluid remains a gas throughout the entire cycle.• Develop simplifying assumptions applicable to gas power cycles.• Analyze both closed and open gas power cycles.• Solve problems based on the Brayton cycle; the Brayton cycle with regeneration; and the Brayton cycle with intercooling, reheating, and regeneration.• Identify simplifying assumptions for second-law analysis of gas power cycles.• Perform second-law analysis of gas power cycles. 2
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BASIC CONSIDERATIONS IN THE ANALYSISOF POWER CYCLES Thermal efficiency of heat enginesMost power-producing devices operate on cycles.Ideal cycle: A cycle that resembles the actual cycleclosely but is made up totally of internally reversibleprocesses is called an.Reversible cycles such as Carnot cycle have thehighest thermal efficiency of all heat enginesoperating between the same temperature levels.Unlike ideal cycles, they are totally reversible, andunsuitable as a realistic model. Modeling is a powerful engineering tool that provides great The analysis of many insight and complex processes can be simplicity at the reduced to a manageable expense of some level by utilizing some loss in accuracy. idealizations. 3
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On a T-s diagram, the ratio of the The idealizations and simplifications in thearea enclosed by the cyclic curve to analysis of power cycles:the area under the heat-addition 1. The cycle does not involve any friction.process curve represents the thermal Therefore, the working fluid does notefficiency of the cycle. Any experience any pressure drop as it flows inmodification that increases the ratio pipes or devices such as heat exchangers.of these two areas will also increase 2. All expansion and compression processesthe thermal efficiency of the cycle. take place in a quasi-equilibrium manner. 3. The pipes connecting the various components of a system are well insulated, and heat transfer through them is negligible.Care should be exercised On both P-v and T-s diagrams, the area enclosedin the interpretation of the by the process curve represents the net work of theresults from ideal cycles. cycle. 4
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THE CARNOT CYCLE AND ITSVALUE IN ENGINEERINGThe Carnot cycle is composed of four totallyreversible processes: isothermal heat addition,isentropic expansion, isothermal heat rejection, andisentropic compression.For both ideal and actual cycles: Thermalefficiency increases with an increase in the averagetemperature at which heat is supplied to the systemor with a decrease in the average temperature atwhich heat is rejected from the system. P-v and T-s diagrams ofA steady-flow Carnot engine. a Carnot cycle. 5
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AIR-STANDARD ASSUMPTIONS Air-standard assumptions: 1. The working fluid is air, which continuously circulates in a closed loop and always behaves as an ideal gas. 2. All the processes that make up the cycle are internally reversible. 3. The combustion process is replaced by a heat-addition process from an external source. 4. The exhaust process is replaced by a heat-rejection process that restores the working fluid to its initial state.The combustion process is replaced bya heat-addition process in ideal cycles.Cold-air-standard assumptions: When the working fluid is considered tobe air with constant specific heats at room temperature (25°C).Air-standard cycle: A cycle for which the air-standard assumptions areapplicable. 6
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BRAYTON CYCLE: THE IDEAL CYCLE FORGAS-TURBINE ENGINESThe combustion process is replaced by a constant-pressure heat-additionprocess from an external source, and the exhaust process is replaced by aconstant-pressure heat-rejection process to the ambient air.1-2 Isentropic compression (in a compressor)2-3 Constant-pressure heat addition3-4 Isentropic expansion (in a turbine)4-1 Constant-pressure heat rejectionAn open-cycle gas-turbine engine. A closed-cycle gas-turbine engine. 7
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Pressure ratio Thermal efficiency of the ideal Brayton cycle as aT-s and P-v diagrams for function of thethe ideal Brayton cycle. pressure ratio. 8
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The two major application areas of gas- The highest temperature in the cycle isturbine engines are aircraft propulsion limited by the maximum temperature that the turbine blades can withstand. Thisand electric power generation. also limits the pressure ratios that can be used in the cycle. The air in gas turbines supplies the necessary oxidant for the combustion of the fuel, and it serves as a coolant to keep the temperature of various components within safe limits. An air–fuel ratio of 50 or above is not uncommon.For fixed values of Tmin and Tmax, the network of the Brayton cycle first increaseswith the pressure ratio, then reaches a The fraction of the turbine workmaximum at rp = (Tmax/Tmin)k/[2(k - 1)], and used to drive the compressor isfinally decreases. called the back work ratio. 9
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Example 1 10A gas-turbine power plant operating on an ideal Brayton cycle has a pressure ratio of 8. The gas temperature is 300 K at the compressor inlet and 1300 K at the turbine inlet. Utilizing the air-standard assumptions, determine (a) the gas temperature at the exits of the compressor and the turbine (b) the back work ratio (c) the thermal efficiency.
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Development of Gas Turbines1. Increasing the turbine inlet (or firing) temperatures2. Increasing the efficiencies of turbomachinery components (turbines, compressors):3. Adding modifications to the basic cycle (intercooling, regeneration or recuperation, and reheating).Deviation of Actual Gas-Turbine Cycles from IdealizedOnesReasons: Irreversibilities in turbine andcompressors, pressure drops, heat lossesIsentropic efficiencies of the compressorand turbine The deviation of an actual gas- turbine cycle from the ideal Brayton cycle as a result of irreversibilities. 11
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THE BRAYTON CYCLE WITHREGENERATIONIn gas-turbine engines, the temperature of the exhaustgas leaving the turbine is often considerably higher thanthe temperature of the air leaving the compressor.Therefore, the high-pressure air leaving the compressorcan be heated by the hot exhaust gases in a counter-flowheat exchanger (a regenerator or a recuperator).The thermal efficiency of the Brayton cycle increases as aresult of regeneration since less fuel is used for the samework output. T-s diagram of a Brayton cycle with regeneration.A gas-turbine engine with regenerator. 12
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Effectiveness of regenerator Effectiveness under cold- air standard assumptions Under cold-air standard assumptionsT-s diagram of a Braytoncycle with regeneration. Can regeneration be used at highThe thermal efficiency pressure ratios?depends on the ratio of theminimum to maximumtemperatures as well as the Thermalpressure ratio. efficiency of the idealRegeneration is mosteffective at lower pressure Brayton cycleratios and low minimum-to- with andmaximum temperature ratios. without regeneration. 13
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Example 2 14 A Brayton cycle with regeneration using air as the working fluid has a pressure ratio of 7. The minimum and maximum temperatures in the cycle are 310 and 1150 K. Assuming an isentropic efficiency of 75 percent for the compressor and 82 percent for the turbine and an effectiveness of 65 percent for the regenerator, determine (a) the air temperature at the turbine exit (b) the net work output (c) the thermal efficiency. Answers: (a) 783 K, (b) 108.1 kJ/kg, (c) 22.5 percent
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For minimizing work input toTHE BRAYTON CYCLE WITH compressor and maximizingINTERCOOLING, REHEATING, work output from turbine:AND REGENERATIONA gas-turbine engine with two-stage compression with intercooling, two-stageexpansion with reheating, and regeneration and its T-s diagram. 15
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Multistage compression with intercooling: The work required to compress a gasbetween two specified pressures can be decreased by carrying out the compressionprocess in stages and cooling the gas in between. This keeps the specific volume as lowas possible.Multistage expansion with reheating keeps the specific volume of the working fluid ashigh as possible during an expansion process, thus maximizing work output.Intercooling and reheating always decreases the thermal efficiency unless they areaccompanied by regeneration. Why? Comparison of work inputs to a single- stage compressor (1AC) and a two-stage compressor with intercooling (1ABD). As the number of compression and expansion stages increases, the gas-turbine cycle with intercooling, reheating, and regeneration approaches the Ericsson cycle. 16
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Example 3 17 An ideal gas-turbine cycle with two stages of compression and two stages of expansion has an overall pressure ratio of 8. Air enters each stage of the compressor at 300 K and each stage of the turbine at 1300 K. Determine the back work ratio and the thermal efficiency of this gas-turbine cycle, assuming (a) no regenerators (b) an ideal regenerator with 100 percent effectiveness.Compare the results with those obtained in Example 1.
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