Exam 20240206 Eng

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ENERGY CONVERSION Exam 06/02/2024 Please, write your person code and surname-name on all sheets you hand in. Exercise 1 (10 points) A reverse closed Joule-Brayton cycle uses a 1 kg/s -flow of helium as working fluid to liquefy a flow of hydrogen, as in the following diagram. In particular, the inlet flow of hydrogen is 0.33 kg/s; moreover, the outlet liquid fraction of this hydrogen flow after the throttling valve is separated from the vapor fraction in a separator. The fluid properties are: • helium, critical temperature 5.2 K, critical pressure 0.22 MPa, and molar mass 4 kg/kmol; • hydrogen, critical temperature 32.9 K, critical pressure 1.29 MPa, molar mass 2 kg/kmol , ideal gas specific heat 14.5 kJ/(kg K), and enthalpy of vaporization at 0.1 MPa of 450 kJ/kg. Neglecting all pressure drops, please: i. motivate clearly the solution procedure and highlight neatly the assumptions (1 point); ii. sketch the T-s diagrams of both the hydrogen liquefaction and the helium process as well as sketch the T-Q diagram of the hydrogen-helium heat exchanger (3 points); iii. calculate the electrical power required by the helium intercooled compressor (1.5 point); iv. compute the mass flow rate of the hydrogen that is liquefied (3 points); v. propose one solution, among many, to improve the performances of the plant (1.5 points). Exercise 2 (12 points) A natural gas-fired steam Rankine cycle is designed to opera te as a combined heat and power plant. It is a reheated cycle with maximum pressure equal to 7.0 MPa. For cogeneration purposes, s team at 0.1 MPa is taken from the inlet of the low -pressure turbine to serve a thermal duty and is returned to the plant in saturated liquid conditions; this thermal duty is equal to 20 MW. The low-pressure steam turbine does not have any…