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ENGR5003 / Week 5
ENGR217 2022 Q A2Past paperOld spec ENGR217First25 marks30 min

ENGR217 Summer 2022 Q A2[VALID] official answers

Answer ALL parts (a) - (d).

A gas power plant operates a gas turbine, which is modelled as an ideal Brayton cycle. At the compressor inlet, a mixture of natural gas and air is drawn in at a pressure of 5 bar at 32∘C32^\circ\mathrm{C}. After combustion, the temperature of the gas reaches 2800∘C2800^\circ\mathrm{C}. You may assume that the working fluid is an ideal gas, with Rg=0.301 kJ/kg/KR_g = 0.301\ \mathrm{kJ/kg/K} and γ=1.42\gamma = 1.42.

Formulas you may need
  • cp=γRgγ−1c_p = \dfrac{\gamma R_g}{\gamma - 1}; isobaric heat addition q=cp(T3−T2)q = c_p(T_3 - T_2) (on the formula sheet)
  • Adiabatic process: p2p1=(T2T1)γ/(γ−1)\dfrac{p_2}{p_1} = \left(\dfrac{T_2}{T_1}\right)^{\gamma/(\gamma-1)} (on the formula sheet)
  • Brayton efficiency: ηth=1−T1T2=1−rp−(γ−1)/γ\eta_{th} = 1 - \dfrac{T_1}{T_2} = 1 - r_p^{-(\gamma-1)/\gamma} (on the formula sheet)
  • Work ratio: rw=wout−winwout=1−T1T3rp(γ−1)/γr_w = \dfrac{w_{out} - w_{in}}{w_{out}} = 1 - \dfrac{T_1}{T_3}r_p^{(\gamma-1)/\gamma} (on the formula sheet)
  • Wnet=Qin−QoutW_{net} = Q_{in} - Q_{out}, ηth=Wnet/Qin\eta_{th} = W_{net}/Q_{in} (on the formula sheet)
  • Mass flow (continuity): m˙=ρAC=ACv\dot m = \rho A C = \dfrac{AC}{v}, with pv=RgTpv = R_gT (learn this; pv=RgTpv = R_gT is on the sheet)
  • SFEE for the heat exchanger: Q˙=m˙(hout−hin)=m˙cpΔT\dot Q = \dot m(h_{out} - h_{in}) = \dot m c_p \Delta T (on the formula sheet)
  1. (a)
    Determine the required pressure ratio if the specific heat addition is 1800 kJ/kg. What is the resulting thermal efficiency and work ratio?
    [7]2:2
  2. (b)
    The gas inlet duct has a cross-sectional area of 3.5 m23.5\ \mathrm{m^2}, determine the mass flow and flow velocity of the gas mixture in the inlet duct, given that the turbine provides a net power output of 10 MW.
    [4]2:2
  3. (c)
    A regenerative heat exchanger is added to increase the thermal efficiency of the turbine. 10% of the excess heat from the exhaust is lost to the surroundings before the heat exchanger and after the heat exchanger, the compressed gas and exhaust are at thermal equilibrium (T2′=T4′T_2' = T_4'). Determine this equilibrium temperature, T2′T_2', the specific heat exchanged as well as the new thermal efficiency and work ratio.
    [10]
  4. (d)
    Explain under what conditions a regenerative heat exchanger wouldn't be able to increase the thermal efficiency of the turbine. At what is the pressure ratio and thermal efficiency when a regenerative heat exchanger stops improving efficiency? You may assume that the specific heat addition does not change and neglect any heat loss for the exhaust gases prior to the heat exchanger.
    [4]