Brayton-72-73 - The compression is reversible and adiabatic...

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11.72 A Brayton cycle produces 14 MW with an inlet state of 17 o C, 100 kPa, and a compression ratio of 16:1. The heat added in the combustion is 960 kJ/kg. What are the highest temperature and the mass flow rate of air, assuming cold air properties? Solution: Efficiency is from Eq.11.8 η = W . net Q . H = w net q H = 1 - r -(k-1)/k p = 1 - 16 -0.4/1.4 = 0.547 from the required power we can find the needed heat transfer Q . H = W . net / η = 14 000 0.547 = 25 594 kW m . = Q . H / q H = 25 594 kW/ 960 kJ/kg = 26.66 kg/s Temperature after compression is T 2 = T 1 r (k-1)/k p = 290 × 16 0.4/1.4 = 640.35 K The highest temperature is after combustion T 3 = T 2 + q H /C p = 640.35 + 960 1.004 = 1596.5 K 11.73 Do the previous problem with properties from table A.7.1 instead of cold air properties. Solution: With the variable specific heat we must go through the processes one by one to get net work and the highest temperature T 3 . From A.7.1: h 1 = 290.43 kJ/kg, s o T1 = 6.83521 kJ/kg K
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Unformatted text preview: The compression is reversible and adiabatic so constant s. From Eq.8.28 s 2 = s 1 s o T2 = s o T1 + Rln ( P 2 /P 1 ) = 6.83521 + 0.287 ln16 = 7.63094 T 2 = 631.9 K, h 2 = 641 kJ/kg Energy equation with compressor work in w C = -1 w 2 = h 2- h 1 = 641 - 290.43 = 350.57 kJ/kg Energy Eq. combustor: h 3 = h 2 + q H = 641 + 960 = 1601 kJ/kg State 3: (P, h): T 3 = 1471 K , s o T3 = 8.58811 kJ/kg K The expansion is reversible and adiabatic so constant s. From Eq.8.28 s 4 = s 3 s o T4 = s o T3 + Rln ( P 4 /P 3 ) = 8.58811 + 0.287ln(1/16) = 7.79238 T 4 = 734.8 K, h 4 = 751.11 kJ/kg Energy equation with turbine work out w T = h 3- h 4 = 1601 - 751.11 = 849.89 kJ/kg Now the net work is w net = w T- w C = 849.89 350.57 = 499.32 kJ/kg The total required power requires a mass flow rate as m . = W . net w net = 14 000 499.32 kW kJ/kg = 28.04 kg/s...
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This note was uploaded on 10/20/2009 for the course MECHENG MEecheng 3 taught by Professor Borgnakke during the Fall '09 term at University of Michigan.

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Brayton-72-73 - The compression is reversible and adiabatic...

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