An ideal Brayton cycle has a pressure ratio of 12.4. Air enters the compressor a

Question

An ideal Brayton cycle has a pressure ratio of 12.4. Air enters the compressor at 90 kPa, 280K.The combustion chamber raises the temperature to 1750K at the turbine inlet. Analyze usingvariable specific heats and air-standard assumptions. a) Determine the thermal efficiency of the cycle. b) Determine the required effectivenessof a regenerator added to this cycle, if it mustincrease the thermal efficiency by 5 percentage (%) points.

Explanation / Answer

The thermal efficiency of a Carnot cycle provides a maximum estimate of the efficiency of an engine and power plant design. "Thermal-Fluid Sciences" by Stephen R. Turns states that for a Carnot cycle, "its usefulness (is) in establishing theoretical performance limits for real devices ... such as the closed-loop steam power plant". Friction and other factors encountered in reality can reduce the thermal efficiency estimated from a Carnot cycl efficiency: ? = 1 - To/T = 1 - (P/Po)^(1-?)/? = 1 - 10^-(0.4/1.4) = 1 - 0.518 = 0.48 ? = Wnet/Qin Wnet = Wout - Win To = 300k, => Pr1 = 1.386 atm, h1 = 300.2 kJ/kg Pr2 = (P/Po) Pr1 = 10*1.386 = 11.386 atm, T = 545 K, h2 = 544 kJ/kg Win = h2 - h1 = 544 - 300 = 244 kJ/kg Process 3-4 is also an isentropic process: (Vo/V')^(?-1) = (P'/Po)^[(?-1)/?] V' = Vo/(P'/Po)^? = 2/(10)^(1/1.4) = 0.386 m³ Now. look-up corresponding values of h3 and h4 in steam tables: Wo = h3 - h4 = ? = Wnet/Qin

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