exam 07 02 2023

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Politecnico di Milano School of Industrial Engineering Course Energy Systems proff. S. Consonni, E. Martelli, M. Romano - Academic Year 2022-23 Energy Systems LM – written test of 7 February 2023 page 1 of 2 Written Exam of 7 February 2023 - Problems - Time: 2 hours PLEASE NOTICE 1) Exam is open book, but computers and cell phones are NOT allowed. Talking with colleagues and/or copying will lead to the immediate cancellation of the exam. 2) Answer clearly ONLY to the questions posed by the problem sets. Even if correct, additional considerations and/or calculations will NOT be considered. 3) Fill this sheet with your name and return it together with your solutions. 4) Mark each sheet of the solution with your name and page number. 5) In addition to the points obtained for the solution of each problem, a bonus of max 1 point may be given based on whether the solution of each problem is complete, with clear details and explanations. Problem 1 (17 points) Consider a heavy-duty single-shaft gas turbine with the following full-load data: − Ambient design conditions: T = 15 °C, p = 1.01325 bar − Pressure drop of air filter = 5 mbar − Compressor pressure ratio = 15 − Isentropic efficiency of the compressor = 85% − Combustor pressure drop = 3% of the inlet pressure − Combustor heat loss = 0.5% of the fuel thermal power (LHV basis) − Fuel = pure methane (CH4) with LHV of 50 MJ/kg − Combustor outlet temperature = 1200°C − Flue gases mass flow rate at combustor outlet =100 kg/s − Isentropic turbine efficiency = 92% − Pressure drop of the stack at turbine outlet = 15 mbar − Mechanical efficiency of the shaft and gear box = 98.5% − Electrical efficiency of the alternator = 99% − Air properties: γ (=cP/cV)= 1.39, molar mass = 28.8 kg/kmol − Flue gases: γ (=cP/cV): 1.35, molar mass:…