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 2020-21 Energy Systems LM – written test of 08 February 2022 page 1 of 2 Written Exam of 08 February 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 data depend on your person code according to the following two variables: X = sum of the numbers of your person code Y = sum of the first 4 numbers * sum of the last 4 numbers of your person code So, for instance, if the person code is 12345678  X = 36  Y = 10*26 = 260 INDICATE ON THE FIRST PAGE THE VALUES OF X AND Y DERIVING FROM YOUR PERSON CODE THAT YOU WILL USE IN THE EXAM Problem 1 (16 points) A gas turbine is fed with natural gas with molar composition: 88% CH 4, 4% C 2H6, 8% N 2 and generates a net power of 2*X MW e with net electric efficiency 34%. Considering that: − losses due to thermal dissipations and incomplete oxidation account for 1% of fuel input; − mechanical and electric losses account for 5% of power output; − ambient temperature is 25°C; − turbine outlet temperature is 550°C − specific heat of exhaust flow is constant and equal to 1.15 kJ/kg°C calculate the following: 1) mass flow rate of fuel (2 points) 2) maximum thermal power that can be recovered from the turbine exhaust flow (2 points) 3) air flow rate (2 points) 4) oxygen concentration in the exhaust flow (3 points) 5) maximum power that could be generated by an ideal recovery cycle converting the thermal power in the exhaust flow into electricity (3 points) Now consider that the exhaust flow enters a single-pressure level HRSG which generates steam at 60 bar, 450°C from water entering the economizer at 60 bar, 80°C (for the sake of simplicity, assume that all pressure losses are zero). 6) Calculate the maximum steam flow that could (ideally) be generated in the HRSG (3 points) 7) For such maximum steam flow, calculate the gas temperature at the exit if the HRSG (1 point) Politecnico di Milano School of Industrial Engineering Course Energy Systems proff. S. Consonni, E. Martelli, M. Romano - Academic Year 2020-21 Energy Systems LM – written test of 08 February 2022 page 2 of 2 Fuel / air data: - CH 4: MM=16 kg/kmole, LHV=50 MJ/kg - C 2H6: MM=30 kg/kmole, LHV=47.6 MJ/kg - Air composition: 21% O 2, 79% N 2 (molar basis) Problem 2 (18 points) At design conditions, the turbine of a steam power plant discharges 400+Y tons/hr of two-phase flow at 0.07 bar with vapor fraction 88%. The flow is condensed into saturated liquid in an air- cooled condenser where ambient air at 15°C is heated to 27°C. Cooling air is forced through the condenser by fans with overall efficiency 75% (including mechanical and electric losses), undergoing an overall pressure drop of 1 kPa. The overall heat transfer coefficient (referred to the air-side heat transfer area) is 50 W/m 2 air- side °C. For such design conditions, calculate the following 1) Mass flow rate of cooling air (1 point); 2) Air-side heat transfer area of condenser (1 points) 3) Fan power (1 points) 4) Reversible power lost (i.e. exergy lost) due to heat transfer irreversibilities between condensing steam and cooling air and between the cooling air and the ambient (2 points) Now consider winter off-design conditions, when ambient air is at -5°C. For the sake of simplicity, assume that steam flow and thermal power exchanged in the condenser do not change. A) Assuming that fans are controlled to maintain the same air mass flow rate of the design case and the overall heat transfer coefficient stays at the design value: 5) calculate the off-design condensing temperature (2 points); 6) discuss possible variations of steam-side conditions and plant power output (2 points) 7) compare the on-design vs the off-design T-Q diagram (2 points) B) Now assume that fans are controlled to maintain steam-side conditions at their design value and that (i) overall heat transfer coefficient (referred to the air-side heat transfer area) and (ii) air-side pressure drop vary with air flow rate as follows: ������������������������������������������������ ������������������������������������ =� ������������̇������������������������������������ ������������������������������������ ������������̇������������������������������������ ������������������������������������������������������������������������ � 0.6 ������������������������������������������������ ������������������������������������������������������������������������ ∆������������ ������������������������������������ ������������������������������������ =� ������������̇������������������������������������ ������������������������������������ ������������̇������������������������������������ ������������������������������������������������������������������������ � 0.7 ∆������������ ������������������������������������ ������������������������������������������������������������������������ . For such control mode calculate: 8) exit air temperature (3 points); 9) fan power (2 points). Hint: In this case the solution procedure is iterative. As first guess you can assume that the air flow rate is 50% of its design value, and stop the computation after two iterations. 10) Compare / discuss off-design strategies A) and B) (2 points) Air data: - Air constant pressure heat capacity = 1.05 kJ/kgK - Air molecular weight = 28.84 kg/kmol Politecnico di Milano Department of Energy - School of Industrial Engineering Course Energy Systems proff. S. Consonni, E. Martelli, M. Romano - Academic Year 2020-21 Energy Systems – Theoretical Questions – 8 February 2022 page 1 Written Exam 8 February 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 (18 points) Consider a combined cycle with HRSG with two evaporation pressure levels and reheat. A. Draw the HRSG, indicating a name for each heat exchange section (3) B. Draw the T-Q diagram indicating the corresponding names of the different heat exchange sections (3) C. What are the main improvements with respect to a single evaporation pressure HRSG from the point of view of the exergy losses? (3) D. What would be the advantages and disadvantages of designing the HRSG with the LP evaporation level with lower, same or higher pressure than the RH pressure? What would be the best option from your point of view? (5) E. Consider the extraction of steam for cogeneration before the inlet of the LP turbine, like in the precept on repowering. Does the amount of steam extracted affect the pressure of the steam delivered for cogeneration ? If yes, how is it possible to ensure that steam is always delivered at the same pressure at any load? (4) Politecnico di Milano Department of Energy - School of Industrial Engineering Course Energy Systems proff. S. Consonni, E. Martelli, M. Romano - Academic Year 2020-21 Energy Systems – Theoretical Questions – 8 February 2022 page 2 Question 2 (16 points) Consider the combustion process of a generic solid fuel containing C, H, N, O, S, H 2O and ash. A. Write a generic expression to compute the stoichiometric amount of oxygen needed for the combustion. (3) B. Write the expression to calculate the equivalence ratio. (2) C. Write the generic expression to compute the adiabatic flame temperature. (2) D. Explain weather it would be preferable to preheat air or fuel to reduce the combustion exergy losses. (3) E. Discuss whether and why for a given fuel the adiabatic flame temperature changes if fuel humidity increases (e.g. after a rain wetting the fuel pile). (3) F. Show through a qualitative example, possibly supported by a T-Q chart, that adiabatic flame temperature and boiler efficiency are not necessarily connected (i.e. that higher flame temperature does not necessarily lead to a higher boiler efficiency, assuming that other sources of losses such as combustion or heat losses are not affected). (3) GIVE CONCISE ANSWERS CLEARLY SPECIFYING WHICH ANSWER YOU ARE ADDRESSING: A), B), C), …