Mechanical Engineering - Energy Systems LM

Full exam

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 (CH 4) 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 (=c P/cV)= 1.39, molar mass = 28.8 kg/kmol − Flue gases: γ (=c P/cV): 1.35, molar mass: 28.4 kg/kmol Assuming that the turbine cooling flows are negligible, for the full-load condition determine: 1) The pressures and temperatures at compressor outlet, combustor outlet and turbine outlet (5 points) 2) The air and fuel mass flow rates (5 points) 3) Net electric power and net electric efficiency of the gas turbine (3 points) At part-loads the gas turbine is controlled with the VIGV mode while keeping constant the turbine inlet temperature. Knowing that the exhaust gas mass flow rate is 60 kg/s, determine: 4) The pressure ratio of the compressor (4 points). Consider that the pressure drops of the air filter is reduced to 2 mbar, that of the stack is reduced to 6 mbar, while the percentage pressure drop of the combustor remains equal to 3%. The heat losses, mechanical/electrical losses, the isentropic efficiencies of turbine and compressor, and the fluid properties (molar mass and c p/cv) remain constant (same as full load). 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 2 of 2 Problem 2 (17 points) Consider a simple reversed (refrigeration) cycle using CO 2 as working fluid, with the following operating parameters: • Evaporation temperature: -20°C • No superheating at evaporator outlet (i.e. saturated vapor at compressor inlet) • Isentropic efficiency of the compressor: 80% • Electric and mechanical efficiency of the compressor (hermetic compressor): 90% • Negligible pressure drop in all the heat exchangers The condenser is air-cooled. In a winter condition, with ambient air temperature of -5 °C, the condensing temperature is 10 °C and saturated liquid is discharged from the condenser. In such operating condition, the refrigeration capacity is 500 kW. 1) Draw the cycle on the p-h diagram provided. (3 points) 2) Compute the COP of the cycle and the electric power consumed by the compressor (4 points) 3) Compute the area of the condenser, considering that the air temperature at the condenser outlet is 5 °C and the overall heat transfer coefficient of the condenser is 300 W/m 2K (4 points) In the peak summer hour, with ambient temperature of 30 °C, the condenser operates in supercritical condition, with condensing pressure of 90 bar and CO 2 temperature at condenser outlet of 40°C. Because of the increased pressure ratio, the volumetric efficiency of the compressor reduces by 10%. 4) Draw the cycle on the p-h diagram provided. (2 points) 5) Compute the COP of the cycle (2 points) 6) Compute the refrigeration capacity and the electric power consumed by the compressor (2 points) Politecnico di Milano Department of Energy - School of Industrial Engineering Course Energy Systems proff. S. Consonni, E. Martelli, M. Romano - Academic Year 2022-23 Energy Systems – Theoretical Questions – 7 February 2023 page 1 Written Exam 7 February 2023 Theoretical Questions - Time: 1.00 h PLEASE NOTICE 1) Books, lecture notes, cell phones are strictly forbidden. Using them or talking with colleagues and/or copying will lead to the immediate invalidation of the exam. 2) Answer clearly ONLY to the questions. Even if correct, additional considerations will NOT contribute to the final grade – and you have NOT enough time! 3) Fill this sheet with your name and return it with your answers. 4) MARK EACH SHEET OF YOUR ANSWERS with YOUR NAME AND PAGE/SHEET NUMBER. 5) WRITING AND SHEET/PAGE SEQUENCE MUST BE LEFT TO RIGHT AS USED IN WESTERN COUNTRIES. 6) Wherever possible, support your statements with clear drawings and/or graphical representation 7) ORGANIZE YOUR ANSWERS CLEARLY: ANSWER TO 1.a; ANSWER TO 1.b, ETC. 8) The final grade is the sum of the points assigned to the answer of each question plus a bonus of max 3 points. The bonus will be given based on completeness, clarity and details of the explanations. FIRST NAME…………………………………….......……FAMILY NAME………………………………………………….. Question 1 (16 points) The condenser of a steam cycle condenses 200 ton/hr of steam at 0.05 bar, 32°C. A) Represent the typical arrangement of the condenser for the case where the refrigerant is seawater at 15°C, discussing why such arrangement is adopted (2 points) B) Represent the typical arrangement of the condenser for the case where the refrigerant is ambient air at 10°C, discussing why such arrangement is adopted (2 points) C) Compare / discuss the cases illustrated at points A) and B). In particular, discuss differences in terms of: − auxiliary power consumption (2 points) − plant lay-out and investment cost (2 points) D) Discuss and estimate how the condensation pressure would change if the seawater temperature becomes 10 °C while the cooling water flow and the inlet steam flow rate remain constant (200 ton/hr) (4 points). E) Discuss how the condensation pressure would change if the cooling water flow rate is kept constant and the steam cycle operates at part-loads (e.g., the inlet steam flow rate is decreased to 120 ton/hr). (4 points) Explain and motivate your answers using the appropriate equations / balances / methodologies / approaches learned in the course. Politecnico di Milano Department of Energy - School of Industrial Engineering Course Energy Systems proff. S. Consonni, E. Martelli, M. Romano - Academic Year 2022-23 Energy Systems – Theoretical Questions – 7 February 2023 page 2 Question 2 (18 points) Consider a coal-fired steam plant with reheat, 2 low-pressure regenerators, deaerator, 2 high- pressure regenerators and Ljungstrom air pre-heater. A) Draw the scheme of the steam cycle (4 points) B) Draw the TQ diagram of the regenerators indicating the key temperature differences (2 points) C) Explain and motivate the effect of the regenerators on the efficiency, net power output (for a given steam flow rate from the boiler) and specific investment cost (€/kW) of the steam cycle (6 points) D) Depict the configuration of the steam generator and the T-Q diagram, motivating why that particular order of the tube banks (ECO, EVA; SH, RH, air preheater) is adopted (4 points) E) Which technical and economic criteria would you consider to determine the optimal preheating temperature of combustion air in the Ljungstrom preheater? (2 points) GIVE CONCISE ANSWERS CLEARLY SPECIFYING WHICH ANSWER YOU ARE ADDRESSING: A), B), C), …