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\ ME 200 L34 Self Study Assignment 9.6 Todays Class 9.11 Material not picked up this week may be recycled! \ ME 200 L34 Gas Turbine Power Generation and Aircraft Propulsion Self Study Assignment 9.6 Todays Class 9.11 Kim Sees Office ME Gatewood Wing Room 2172 Examination 3 grades, Quiz 5 grades are available Blackboard and Examinations and Quizzes can be picked up all of this week from Gatewood Room 2172 Material not picked up this week may be recycled! https://engineering.purdue.edu/ME200/ ThermoMentor © Program Spring 2014 MWF 1030-1120 AM J. P. Gore gore@purdue.edu Gatewood Wing 3166, 765 494 0061 Office Hours: MWF 1130-1230 TAs: Robert Kapaku rkapaku@purdue.edu Dong Han han193@purdue.edurkapaku@purdue.eduhan193@purdue.edu

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2 Outline Brayton Cycle (with Improved Performance) –Brayton Cycle for land based power generation and for aircraft propulsion (9.6; 9.11) –Reheating- land based power generation: will mention but leave for you to explore (9.7) –Regeneration - will mention but leave for you to explore (9.8) –Combined Regeneration and Reheating, Cogeneration - will mention but leave for you to self-study (9.9, 9.10) –Aircraft Propulsion (9.11) Will cover today including using Quiz 6.

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3 Inlet State Component aDiffuser 1Compressor 2Combustor 3Turbine 4Nozzle Aircraft Propulsion (9.11) : Quiz 6.

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Air Standard Brayton Cycle 1 23 4 1 2 3 4 Thermal Efficiency back work ratio

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Compressor Pressure Ratio and Brayton Cycle Performance The Brayton cycle thermal efficiency increases as the compressor pressure ratio increases 60 th (%) 246810 Compressor Pressure Ratio See Figure 9.12

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6 Gas Turbine Example Problem Given: Heat supplied by the boiler = 5.2x10 8 Btu/h, Pressure ratio = P2/P1=P3/P4=12, Tmin = T1 = 520 o R, Tmax = T3= 2800 o R 1 2 3 4 Find: Thermal efficiency: Eta Th, m dot air (lb/hr), w dot cycle (Btu/hr) If the turbine and the compressor are not isentropic but operate with T, C find the impact on the work of the cycle, heat input and thermal efficiency C = 0.86 (Chosen in class based on student input); T =0.91 chosen to be higher than Compressor efficiency since turbine efficiency matters more and companies must improve it sooner. Steps: (1) Identify and number all states and start a table of properties for the states. (2) Recognize that compressor efficiency and turbine efficiency lead to additional state definitions (2s, 2a in place of 2 and 4s and 4a in place of 4).

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Steps: (1) Identify and number all states and start a table of properties for the states. (2) Recognize that compressor efficiency and turbine efficiency lead to additional state definitions (2s, 2a in place of 2 and 4s and 4a in place of 4). (3) Table A 22 E is to be referenced with the known states and knowledge of process definitions to find all properties necessary to calculate the work of compressor, work of Turbine, heat added, heat rejected and resulting Eta Th, m dot air (lb/hr), w dot cycle (Btu/hr) StateT, o Rh, Btu/lbmPrP, atm 1520124.271.21471 2s1040250.951.2147*12= 14.5764 or ~14.1812 2a1120271.57 ~ 271.03Pr not relevant12 32800732.3370212 4s1520374.47702/12=58.5 ~ 58.781 4a1650406.67~409.13Pr not relevant1

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Answers

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Gas Turbine Power Plants 3. Compressor, combustion chamber, and turbine are treated as control volumes and mass, energy, and entropy balances are applied to each. 4. The heat rejection process substitutes exhaust and fresh air admission. 1.Compression, heat addition and expansion are followed by exhaust of products and induction of fresh air. 2. The last two steps represent heat rejection. 1 23 4 1 2 3 4

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Gas Turbine Power Plants 1 23 c4 1 2 3 4

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Gas Turbine Power Plants 1 23 4 1 2 3 4 Thermal Efficiency back work ratio

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Compressor Pressure Ratio and Brayton Cycle Performance Consider compressor pressure ratios p 2 /p 1 and p 2 /p 1 yielding cycles: 1-2-3-4-1 to 1-2 -3 -4-1. T H greater in cycle 1-2 -3 -4-1, and both cycles have the same heat rejection, hence cycle 1-2 -3 -4-1 has inherently greater thermal efficiency. The Brayton cycle thermal efficiency increases as the compressor pressure ratio increases 60 th (%) 246810 Compressor Pressure Ratio

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13 Gas Turbine Example Problem Given: Heat supplied by the boiler = 5.2x10 8 Btu/h, Pressure ratio = P2/P1=P3/P4=12, Tmin = T1 = 520 o R, Tmax = T3= 2800 o R 1 2 3 4 StateT, Rh, Btu/lbPr 1520124.271.2147 21047.5252.8414.5764Pr2=Pr1*P2/P1 32800732.33702 41518373.9558.5Pr4=Pr3/12 Find: Thermal efficiency: Eta Th, m dot air (lb/hr), w dot cycle (Btu/hr)

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ME 200 L23: Clausius Inequality and Control Volume Example Problems Kim See’s Office ME Gatewood Wing Room 2172 Please check your HW Grades on Blackboard.

ME 200 L23: Clausius Inequality and Control Volume Example Problems Kim See’s Office ME Gatewood Wing Room 2172 Please check your HW Grades on Blackboard.

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