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 2021-22 Energy Systems LM – written test of 6 September 2022 page 1 of 2 Written Exam of 6 September 2022 - 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 (15 points) An industrial furnace burns natural gas to heat up steel bars. The flue gases leave the combustor at 1500 °C and they exit the furnace at 400 °C transferring 10 MW of thermal power to the steel bars. At the outlet of the furnace, the flue gases enter an air preheater. The following data are known: • ambient air temperature is 15°C; • Air is pre-heated to 250 °C in the air-preheater • Thermal losses and unburned fuel losses account for 0.6% of the fuel thermal power, on LHV basis • The natural gas molar composition is: CH 4: 84%, C 3H8: 2.3%, C 4H10: 3.2%, CO 2: 6.5%, N 2: 4.0%; molar mass: 20.29 kg/kmo; LHV: 39.82 MJ/kg Requests: 1) draw the plant scheme (1 point) 2) determine the mass flow rate of air and natural gas (5 points) 3) determine the flue gas temperature at the outlet of the air-preheater (2 points) 4) determine the furnace thermal efficiency (2 points) 5) determine the effectiveness of the air-preheater (2 points) 6) determine the excess of air of the combustion process (3 points) Other data: • Cp of flue gases = 1.12 kJ/kg-K • Cp of air = 1.04 kJ/kg-K • O 2 concentration in air: 0.207 • air molar mass: 28.85 kg/kmol Politecnico di Milano School of Industrial Engineering Course Energy Systems proff. S. Consonni, E. Martelli, M. Romano - Academic Year 2021-22 Energy Systems LM – written test of 6 September 2022 page 2 of 2 Problem 2 (16 points) The industrial refrigeration cycle shown in the figure below operates with CO 2 as working fluid and features a two-level evaporation process to cool a stream of water-glycole mixture (assumed as a liquid with constant specific heat capacity) from +10 to -20°C. The two evaporators exchange the same thermal power. The following data are given: • Thermal power exchanged in each evaporator: 2 MW • Minimum temperature difference in the evaporators: 5°C • No superheating (i.e. saturated vapor) at evaporator outlet • Condensation temperature: 20°C • Open compressors (i.e. the heat generated by electric motors is dissipated to the environment), each one with isoentropic efficiency 75% and electric efficiency 94% 1) Indicate the cycle points on the p-h diagram provided (4 points) 2) Report on a table pressure, temperature, enthalpy and flow rate of each stream. (4 points) 3) Compute the COP of the cycle. (3 points) 4) Compute the expected evaporation temperatures in case the overall heat transfer coefficient in the evaporators is reduced by 10% due to fouling, considering that the exchanged thermal power and the water-glycole flow rate do not change. (5 points) 2 3 Condenser HT Evaporator 4 5 6 7 1 8 LT Evaporator Water/ glycole circuit Problem 1 Data Furnace power, MW10 Flue gas inlet temperature, °C1500 Flue gas outlet temperature, °C400 Preheated air temperature, °C250.00 air ambient temperature, °C15 Combustor total heat losses0.006 cP flue gases, kJ/kg-K1.12 cP air, kJ/kg-K1.04 O2 conc in air0.207 Molar mass of air28.85 NG molar compositionmolar MM, kg/kmol mass LHV, MJ/kg CH40.840160.662550.01 C2H60.000300.000047.48 C3H80.023440.049946.35 C4H100.032580.091547.88 CO20.065440.14100.00 N20.040280.05520.00 totale1.00020.291.000039.82 Results 2)flue gas flow rate, kg/s8.12 Air temperature at comb inlet, °C250.0 air/fuel mass ratio26.75 From combustor energy balance fuel flow rate, kg(s 0.293 air flow rate, kg/s 7.82 3)Thermal power exchanged in preheater, kW1912 Flue gas outlet temperature, °C 189.6 4) Furnace thermal efficiency 0.8585 5) Effectiveness of preheater 0.6104 6)Air molar flow rate, kmol/s0.271 O2 molar flow rate, kmol/s0.0561 fuel molar flow rate, kmol/s0.01442 O2 stoich flow rate, kmol/s0.0289 excess of air 94.4% Problem 2 DataValues from tables/Mollier charts Qeva,i = 2MW Twg,in = 10°C Twg,out = -20°C eta,is = 0.75 eta,me = 0.94 Tcond 20°C DTmin,eva = 5°C U,foul/U,base = 0.9 1)DTwg,tot =30 °CDTwg,i = 15°C Twg,int = -5°C Teva,HT = -10°C Teva,LT = -25°C Dhref 0.00 Dsref 0.000 2)Fluid nameHEOS::CO2 p1 = p8 = 16.83bar p2 = p3 = p4 = p7 = 26.49bar p5 = p6 = 57.29bar h6 = h7 = h8 = hls(T6) = 256kJ/kg h1 = hvs(T1) = 437kJ/kg s1 = svs(T1) = 1.97kJ/kgK h2,is = h(p2,s1) = 455kJ/kg h2 = h1 + (h2,is - h1) / eta,is = 461kJ/kg h3 = hvs(T3) = 435kJ/kg m3 = m7 = Qeva,i / (h3 - h7) = 11.16kg/s m1 = m8 = m2 = Qeva,i / (h1 - h8) = 11.04kg/s m4 = m1 + m3 = 22.19kg/s h4 = (m3*h3 + m2*h2) / (m2 + m3) = 448kJ/kg T4 = T(h4,p4) = -0.67°C s4 = s(h4,p4) = 1.95kJ/kgK h5,is = h(p5,s4) = 482kJ/kg h5 = h4 + (h5,is - h4) / eta,is = 493kJ/kg 3)Qeva,tot =4000kWPcomp,LP = m1 * (h2 - h1) / eta,me = 286kW Pcomp,HP = m4 * (h5 - h4) / eta,me = 1069kW COP = Qtot / (Pcomp,HP + Pcomp,LP) = 2.95 4)The two evaporators have the same LMTD and effectivenessEps, base = 0.75 DThe,eva = 20 DTce,eva = 5°C LMTD = 10.8°C UA,base = 184.84kW/K UA,foul = 166.36kW/K 1 3 8 5 4 7 6 2 Cmin = Qwg / DTwg = 133.33 kW/K NTU,base = 1.386 NTU,foul = 1.248 Eps,foul / Eps,NTU = (1 - e -NTU,foul ) / (1 - e -NTU,base ) = 0.950 Eps,foul = 0.713 DTmax,i,foul = DTwg,i / Eps,foul = 21.04 °C Teva,HT = -11.04 °C Teva,LT = -26.04 °C Politecnico di Milano Department of Energy - School of Industrial Engineering Course Energy Systems proff. S. Consonni, E. Martelli, M. Romano - Academic Year 2021-22 Energy Systems – Theoretical Questions – 06 September 2022 page 1 Written Exam 06 September 2022 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. FIRST NAME…………………………………….......……FAMILY NAME………………………………………………….. Question 1 (16 points) The water-cooled condenser of a steam power plant handles 100 ton/hr of two-phase mixture with 10% liquid (by mass) at a pressure of 0.05 bar. Cooling water enters at 12°C A. Depict a presumable schematic arrangement of the condenser and the T-Q diagram (3 points) B. In the design phase of the condenser, discuss the criteria to determine the optimal choice of the water flow rate (4 points) C. For fixed condenser heat transfer area and geometry, how would the condensation temperature change if the inlet temperature of water were 5°C instead of 12°C and the water flow rate is kept constant ? (4 points) NOTE: to answer this question, show the impact on the TQ diagram D. For fixed condenser heat transfer area and geometry, discuss the operation at part load when steam flow is reduced to 50 ton/hr, with water inlet temperature (12°C) and water flow rate at the same value of design conditions (5 points) Politecnico di Milano Department of Energy - School of Industrial Engineering Course Energy Systems proff. S. Consonni, E. Martelli, M. Romano - Academic Year 2021-22 Energy Systems – Theoretical Questions – 06 September 2022 page 2 Question 2 (17 points) Consider two Combined Cycles, one with a single and the other one with a double evaporation pressure heat recovery steam cycle. A. Draw the plants configuration (4 points) B. Draw the T-Q diagrams of the two HRSG (4 points) C. Discuss the choice of the evaporation pressures in the two HRSGs (5 points) D. Discuss the effect of adding a regenerator (feedwater preheater) to the steam cycle (4 points) GIVE CONCISE ANSWERS CLEARLY SPECIFYING WHICH ANSWER YOU ARE ADDRESSING: A), B), C), …