Written Exam 02 March Problems - Time: 2 hours PLEASE NOTICE

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1 Politecnico di Milano Department of Energy - School of Industrial Engineering Course Energy Systems LM prof. S. Consonni, E. Martelli, M. Romano - Academic Year 2014/15 Written Exam 02 March 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) The final grade is the sum of the points assigned to the solution of each problem plus a bonus of max 3 points. The bonus will be given based on whether the solution of each problem is complete, with clear details and explanations. FIRST NAME..... FAMILY NAME... Problem 1 (16 points) The steam cycle of a power plant features the following characteristics. Steam turbine is fed with 120 ton/hr of steam at 90 bar, 520 C (stream 3) Condensation pressure 0.08 bar (absolute) (stream 4 at condenser inlet, stream 1 at outlet) Steam bleed from turbine for feedwater heating at 6 bar (stream 6). After being condensed and subcooled to 80 C in the FeedWater Heater (FWH), the condensate exiting the FWH (stream 7) is throttled to the condensing pressure and discharged to the condenser (stream 8) Subcooled liquid at 34 C collected in the hot well at the bottom of the condenser (stream 1) is pumped to 130 bar (stream 2) by the feedwater pump and sent directy to the FeedWater Heater, where it is heated to 150 C (stream 5) The pre-heated liquid exiting the FeedWater Heater (stream 5) goes directly to the boiler The condenser is cooled with water at 12 C, which exits the condenser at 37 C 1) Draw configuration and T-s diagram of the cycle 2) Draw T-Q diagram of the feedwater heater 3) Draw T-Q diagram of the condenser Considering that: Isoentropic efficiency of high-pressure turbine (before the steam bleeding) is 85%; for low-pressure turbine (after the steam bleeding) 90% Hydraulic efficiency of feedwater pump is 88% Mechanical-electrical efficiency is 97% for the turbine, 95% for the pump All pressure drops are negligible except those in the boiler All thermal losses are negligible Determine the following: 4) Mass flow rate of steam bled from the turbine 5) Net power output 6) Mass flow rate of condenser cooling water 7) NTU of condenser (both condensing and subcooling sections) Written Exam Energy systems LM pag. 1 di 4

2 Politecnico di Milano Department of Energy - School of Industrial Engineering Course Energy Systems LM prof. S. Consonni, E. Martelli, M. Romano - Academic Year 2014/15 Problem 1 (16 points, continues) Answer to the following will give 3 extra-points 8) Discuss qualitatively if/how the cycle operating conditions would change in winter, when the same flow rate of cooling water evaluated at point 6) is available at 5 C rather than at 12 C. Consider that steam pressure and temperature at turbine inlet are kept constant. Properties of saturated liquid state p, bar T, C h, kj/kg sat liq 0,053 34,0 142,4 sat liq 0,080 41,5 173,9 sat liq 0,474 80,0 334,9 sat liq 4, ,0 632,1 sat liq 6, ,8 670,4 sat liq 120,0 324,6 1491,8 Written Exam Energy systems LM pag. 2 di 4

3 Problem 2 (16 points) Politecnico di Milano Department of Energy - School of Industrial Engineering Course Energy Systems LM prof. S. Consonni, E. Martelli, M. Romano - Academic Year 2014/15 A simple cycle gas turbine is equipped with an air filter at compressor inlet and a silencer at turbine outlet. The gas turbine features the following characteristics: Air flow rate 250 kg/s at 1 atm, 20 C Compressor pressure ratio = 15 Turbine Inlet Temperature C Pressure loss at compressor inlet (air filter) 1kPa Pressure loss in the combustor 2% of inlet pressure Pressure loss at turbine outlet (silencer + stack) 1.5 kpa Compressor with isoentropic efficiency 90%, mechanical efficiency 99% Combustion efficiency 99% (i.e., heat dissipation = 1%) Turbine with isoentropic efficiency 92%, mechanical efficiency 98% Generator electric efficiency 97% The gas turbine is fed with natural gas available at 30 bar, 20 C, with the following properties molar composition: CH 4 = 0.90, C 2 H 6 : = 0.05, N 2 = 0.05 molar mass: kg/kmol lower heating value: MJ/kg specific heat capacity at constant pressure c p = 2.34 kj/(kg K) For the sake of simplicity it can be assumed that: a) ambient air comprises just 21% molar O % molar N 2 (molecular weight = kg/kmol) b) gas turbine cooling flows can be neglected c) specific heat of air and combustion products is constant, equal to 1.04 and 1.14 kj/kgk, respectively d) molecular weight of combustion products is the same as air Recalling that the gas constant R = 8314 J / kmol- C, 1) Draw configuration and T-s diagram of the cycle 2) Determine fuel flow rate 3) Determine Turbine Outlet Temperature 4) Determine electric power output and electric efficiency Assume now that the gas turbine is installed in a Combined Cycle with supplementary firing, where supplementary firing is fed by the same natural gas used to feed the gas turbine. Combustion efficiency of the supplementary burner is 99% Combustion products exiting the supplementary burner at 750 C enter the Heat Recovery Steam generator, where they are cooled down to 100 C Net electric efficiency of bottoming steam cycle (net electric power / recovered thermal power) is 32% Determine: 5) Fuel flow rate of supplementary burner 6) Electric power output of steam cycle 7) Electric efficiency of Combined Cycle with supplementary firing Answer to the following will give 3 extra-points Determine oxygen concentration in combustion products discharged at the stack Written Exam Energy systems LM pag. 3 di 4

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5 Politecnico di Milano Department of Energy School of Industrial and Information Engineering Course Energy Systems LM proff. S. CONSONNI, E. MARTELLI, M. ROMANO - Academic Year 2014/15 Written Exam 02 March QUESTIONS - Time: 1 hour PLEASE NOTICE 1) This part of the exam is closed book. Computers and cell phones are NOT allowed. Talking with colleagues and/or copying will lead to the immediate cancellation of the exam. 2) 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 whether the answer to each question is complete, as well as the clarity and the details of the explanations. 3) Wherever possible, support your statements with clear drawings and/or graphical representations Question 1 (15 points) A) Illustrate and discuss reversible work losses associated to heat transfer. B) Give an expression for the reversible work loss in a generic heat exchanger. C) Give an expression for the reversible work loss in the regenerator of a steam cycle. D) Can these losses become zero by adopting an infinite heat transfer area? E) Given an example of an ideal system/process where heat transfer takes place with zero reversible work losses Question 2 (15 points) A) Discuss the choice of the condensation pressure for the steam cycle of a large-scale power plant. More specifically: 1) What are benefits/penalties of adopting a high or low condensation pressure? 2) What are the constraints that delimit the range of values that can be adopted? 3) Is there an optimum value? If yes, how would you determine it? B) Discuss whether the answers to point A) would change with the type of coolant (water vs air). If yes, what type of variations would you expect? Answer to the following will give 3 extra-points C) Assume now that, rather than adopting H 2 O as the working fluid, the Rankine Cycle of a power plant uses ammonia (NH 3 ) as the working fluid. Would you expect that one or more of the answers to questions A) would change? In particular, would you expect advantages of NH 3 vs H 2 O at particular geographic locations? Give examples. Energy Systems LM - written test of March 2nd, 2015 page 1 of 1

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