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ENGR5003 / Week 2
Lecture 4 Exercise 1 - ideal Brayton cycleTutorialCurrent specThird10 min

ENGR5003 Lecture 4 Exercise 1 (slides 20-21)

Consider an ideal Brayton cycle (isentropic compression and isentropic expansion). Air may be treated as an ideal gas with γ=1.4\gamma = 1.4 and cp=1005 J/(kg K)c_p = 1005\ \mathrm{J/(kg\,K)}. The inlet state is T1=300 KT_1 = 300\ \mathrm{K}. The compressor pressure ratio is rp=8r_p = 8. The maximum (turbine inlet) temperature after combustion is T3=1200 KT_3 = 1200\ \mathrm{K}. States are numbered as in Figure 1.

Figure 1: ideal Brayton cycle on a T-s diagram: 1-2 isentropic compression, 2-3 heat addition at constant p, 3-4 isentropic expansion, 4-1 heat rejection at constant p.
Figure 1: ideal Brayton cycle on a T-s diagram: 1-2 isentropic compression, 2-3 heat addition at constant p, 3-4 isentropic expansion, 4-1 heat rejection at constant p.
Formulas you may need
  • Adiabatic (isentropic) ideal gas: T2T1=(p2p1)(γ−1)/γ\dfrac{T_2}{T_1} = \left(\dfrac{p_2}{p_1}\right)^{(\gamma-1)/\gamma} (on the formula sheet)
  • SFEE with negligible KE and PE: q−w=Δh=cpΔTq - w = \Delta h = c_p\Delta T (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)
  • Thermal efficiency: ηth=wnetqin\eta_{th} = \dfrac{w_{net}}{q_{in}} (on the formula sheet)
  1. (a)
    Calculate T2T_2 and T4T_4 (isentropic).
  2. (b)
    Calculate the net work per kg of air (J/kg).
  3. (c)
    Calculate the thermal efficiency ηth\eta_{th}.