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ENGR5003 / Week 5
Week 5 Q1Exercise sheetCurrent spec2:125 min

ENGR5003 Week 5 workshop sheet Q1 (worked in Lecture 13, worked example 3) official answers

In a gas turbine plant, air is compressed from 1.01 bar and 15 ∘C15\ ^\circ\mathrm{C} through a pressure ratio of 4:1. It is then heated to 650 ∘C650\ ^\circ\mathrm{C} in a combustion chamber and expanded through a turbine back to atmospheric pressure of 1.01 bar.

Formulas you may need
  • Isentropic: T2sT1=rp(γ−1)/γ\dfrac{T_{2s}}{T_1} = r_p^{(\gamma-1)/\gamma} (on the formula sheet)
  • Isentropic efficiencies: ηC=T2s−T1T2−T1\eta_C = \dfrac{T_{2s} - T_1}{T_2 - T_1}, ηT=T3−T4T3−T4s\eta_T = \dfrac{T_3 - T_4}{T_3 - T_{4s}} (learn this, Lecture 13)
  • cp=γRgγ−1c_p = \dfrac{\gamma R_g}{\gamma - 1} (on the formula sheet)
  • SFEE for compressor/turbine: w=Δh=cpΔTw = \Delta h = c_p\Delta T (on the formula sheet)
  • Ideal (countercurrent) regenerator: T2′=T4T_2' = T_4 (learn this, Lecture 14)
  • Work ratio: rw=Wnet/Woutr_w = W_{net}/W_{out} (on the formula sheet)
  1. (a)
    Calculate the cycle efficiency and compare the efficiency when the system is with and without heat regeneration
  2. (b)
    and the ratio of the net work to positive work (work ratio) if an ideal regenerative heat exchanger is used. The isentropic efficiencies of the turbine and compressor are 0.85 and 0.8 respectively. For compression, γ=1.4\gamma = 1.4 and for expansion γ=1.33\gamma = 1.33. Assume that Rg=0.287 kJ/kg/KR_g = 0.287\ \mathrm{kJ/kg/K}