Question

2. A gas turbine power plant operating at a steady state consists of a compressor, a heat exchanger, and a turbine. Air enters the compressor with a mass flow rate of 3.8 kg/s at 0.95 bar, 27 °C and exists the turbine at 0.95 bar, 452 °C. Heat transfer to the fluid at the heat exchanger occurs at an average of 537 °C. Other parameters are To = 300 K, po = 0.95 bar, and Wnet = 0.8 MW. The compressor and the turbine operate adiabatically. Using the ideal gas model and neglecting the kinetic and potential energy effects, determine the followings: a) The rate of exergy transfer accompanying heat transfer to the air flowing through the heat exchanger. b) The net rate of exergy carried out at the turbine exit. c) The rate of exergy destruction. d) The exergetic efficiency of the turbine considering 90% thermal efficiency and a use temperature of 200 °C. (20 points)

Answer 1

0.95 bar Given :- Mass flow rate of air (Ⓡ) = 3.8 kg/s compressor inlet pressure CĐ): compressor Inget temperature CTO) = 27 °C Turbine exit pressure (P2) 0.95 bar Turbine exit temperature (T2) 452°c =725K Average temperature (Tb) = 537°C = 810 K Ambient temperature (To) = 300 k Ambient pressure CPol=0.95 bar Rate of exergy transfer accompanying heat is Ėq = (1-To) AC Qcv. = 300 (1 :-) x 2472.11. 810 ) 556.51 KW Answer. by Net rate 0.15 exergy carried out at the turbine exit Éfa - Efi = m [ Cha-hu) – To CS2 - 31).] w [Cha-hu)- To [S: -si - Ren ("%12)]] [1940.22- ..)] 3.8 300.19) – 300 (2.6J061 – 1.70203 Éfa - Éşi 636. 33 28 KW C] Rate of exergy destruction. By using steady state energy rate balance Net work output (Wnet) 0.8 mW From ideal gal properties At T = 27 c. of air hi si = 300.19 kJ/kg 1.70203 kJ/kg. K At T2 725k. from ideal gas...properties of air ha S2 740.22 KJ/kg 2.61061 kJ/kg-s Rate of exergy transfer Les accompanying heat transfer to the airo flowing through the heat exchanger.. balance By using the energy Qcv + mihi Wert n ha acv Wcv tim Chachi) 800 + 3.8 x (740.22 - 300:19) QCV = 2472.11 kW Ėq - Wcv + Efi Efa 11 & = 1556.51-800 + (-636-3328) 120.1772 KW 0:1201772 "w