Notes%2011.24.10

Notes%2011.24.10 - Happy Thanksgiving! Please note you are...

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1 Happy Thanksgiving!! Please note you are responsible for this material. Work any examples noted Have a safe holiday! See you all on Monday.
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2 Brayton Cycle Proposed by George Brayton in 1870!
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3 Other applications of Brayton cycle Power generation - use gas turbines to generate electricity…very efficient Marine applications in large ships Automobile racing - late 1960s Indy 500 STP sponsored cars
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4 Schematic of simple cycle
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5 TEAMPLAY What expression of the first law applies? ∆ ∆ u or h? Why?
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6 Idealized Brayton Cycle
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7 Brayton Cycle
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8 Brayton Cycle 1 to 2--isentropic compression 2 to 3--constant pressure heat addition (replaces combustion process) 3 to 4--isentropic expansion in the turbine 4 to 1--constant pressure heat rejection to return air to original state
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9 Brayton Cycle Because the Brayton cycle operates between two constant pressure lines, or isobars, the pressure ratio is important. The pressure ratio is not a compression ratio.
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10 Brayton cycle analysis in net q w = η As with any cycle, we’re going to concern ourselves with the efficiency and net work output: comp turb net w w w - = Efficiency: Net work:
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11 1 2 comp h h w - = - w h h comp = - 2 1 1 to 2 (isentropic compression in compressor), apply first law: When analyzing the cycle, we know that the compressor work is in (negative). It is standard convention to just drop the negative sign and deal with it later: Brayton cycle analysis
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12 2 3 23 in h h q q - = = 2 to 3 (constant pressure heat addition - treated as a heat exchanger) Brayton cycle analysis
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13 or , h h w 3 4 turb - = - 4 3 turb h h w - = 3 to 4 (isentropic expansion in turbine) Brayton cycle analysis
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14 , h h q 4 1 out - = 1 4 out h h q - = 4 to 1 (constant pressure heat rejection) We know this is heat transfer out of the system and therefore negative. In book, they’ll give it a positive sign and then subtract it when necessary. Brayton cycle analysis
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15 Brayton cycle analysis Or, substituting: comp turb net w w w - = The net work is: ) h (h ) h (h w 1 2 4 3 net - - - =
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16 Let’s get the efficiency: Brayton cycle analysis in net q w = η ) h (h ) h (h ) h (h 2 3 1 2 4 3 - - - - = ) h (h ) h (h 1 2 3 1 4 - - - = η
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17 Brayton cycle analysis Let’s assume cold air conditions and manipulate the efficiency expression: ) T (T c ) T (T c 1 2 3 p 1 4 p - - - = η ( 29 ( 29 1 T T 1 T T T T 1 2 3 1 4 2 1 - - - = η
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T T p p k k 2 1 2 1 1 = - ; T T p p p p k k k k 4 3 4 3 1 1 2 1 = = -
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Notes%2011.24.10 - Happy Thanksgiving! Please note you are...

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