Tuesday, May 22, 2007
HW #9, P1 - Brayton Cycle with Variable Heat Capacities - 6 pts
A gas turbine power plant operates on the basic Brayton Cycle. Air is the working fluid and the cycle delivers 15 MW of power. The minimum and maximum temperatures in the cycle are 310 K and 900 K, respectively. The air pressure at the compressor outlet is 8 times the pressure at the compressor inlet. Assuming an isentropic efficiency of 80% for the compressor and 86% for the turbine, determine the mass flow rate of air through the cycle. Assume that air behaves as an ideal gas, but do not assume that the heat capacities of the air are constants.
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6 comments:
I cant seem to get the correct mass flow rate. I keep getting 120kg/s. I am hoping somebody can tell me if these values are wrong. For Hhat actual out of the compressor I got 329.53kJ/kg and for Hhat actual out of the turbine I got 369.19kJ/kg. Also, I am wondering if it is correct to think that the net power of the cycle if 15MW, not that the cycle delivers/puts out 15MW and uses an unknown amount, in which case the 15 MW would have been produced soley by the turbine. Thanks!
ello! :
The mass flow rate is not 120 kg/s.
H2 is wrong, but H4 is correct (using the numbering scheme for Brayton Cycles in the book).
I strongly suspect you inverted the equation for isentropic efficiency of a compressor. It should be Wisen/Wact.
Dr. B, H2 and H4 are both coming out of devices according to the diagram on page 210. So did you mean that ello! got H3 correct (H out of the turbine)?
Will someone please confirm that H1 (out of the compressor) is ~412 and that H3 (out of the turbine) is ~369.
I'm then using the first law for turbines and saying that mdot = -W/(H3 - H2) where W = 15000 kJ, H3 is given above, and H2 was looked up in the I.G. tables for air at T = 900K.
I must be doing something wrong because my answer is no where near 360 kg/s...
Nevermind, I got the right answer with the help of ello!
So...I just straight up forgot a number in one of my equations. I have the answer now, but I got the answer by assuming that the net work of the cycle was 15MW. Using the word "delivers" power really makes it sound like that is the actual output of the cycle. What's the deal with the wording, will deliver always mean net?
Cary & ello :
I messed up my stream numbers. I apologize. My reply to ello was correct though. Cary, ello's H3 is correct and your H1 is correct, 412 kJ/kg.
The problem was that the net work output for the cycle is 15 MW, not just the Wturb. What we should notice from your result is that the amount of work consumed by the compressor in a gas cycle is VERY significant ! Remember that Wsh = INT{Vhat dP} and Vhat for gases is large. So, compressing gases takes a lot of work !
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