2010Brayton Cycle HW Q and A

2010Brayton Cycle HW Q and A - Gas Turbine Problem Set...

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Center for Advanced Energy Systems Michael R. Muller, Director 640 Bartholomew Road, Piscataway NJ 08854 (732) 445-3655 FAX: (732) 445-0730 muller@caes.rutgers.edu http://caes.rutgers.edu Gas Turbine Problem Set Problem 1: The back-work ratio for a gas turbine is defined as the ratio of the work used to power the compressor to the work produced by the turbine. Consider a simple Brayton cycle using air as the working fluid, has a pressure ratio of 12, has a maximum cycle temperature of 600 ° C, and operates the compressor inlet at 90 kPa, 15 ° C. Which will have the greatest impact on the back-work ratio, a compressor efficiency of 90% or a turbine efficiency of 90%? Solution: Using the isentropic process relations for an ideal gas gives ( ) K P P T T k k s 586 90 1080 288 4 . 1 / 4 . 0 / 1 1 2 1 2 = = = Correcting this for the efficiency of the compressor gives K T T T T s 619 1 2 1 2 = + = η Similarly, K T s 429 1080 90 873 4 . 1 / 4 . 0 4 = = Correcting this for the turbine efficiency ( ) K T T T T s t 473 4 3 3 4 = = Applying the first law to the two work interaction processes gives () ( ) () kg kJ w kg kJ T T c w s p s / 0 . 299 586 288 0035 . 1 / 6 . 445 429 873 0035 . 1 2 1 4 3 4 3 = = = = = With a reversible compressor and turbine, the back-work ratio is answer r bw = = 6710 . 0 6 . 445 0 . 299
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Center for Advanced Energy Systems Michael R. Muller, Director When the compressor is not reversible, () ( ) kg kJ T T c w p / 2 . 332 619 288 0035 . 1 2 1 2 1 = = = and the back-work ratio becomes
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2010Brayton Cycle HW Q and A - Gas Turbine Problem Set...

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