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ENGR5003 / Week 5
ENGR217 2019 Q A3Past paperOld spec ENGR2172:125 marks30 min

ENGR217 Summer 2019 Q A3[VALID]

Answer ALL parts (a) - (c)

Formulas you may need
  • 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 per unit mass for each component: q−w=hout−hinq - w = h_{out} - h_{in}, dh=cp dTdh = c_p\,dT (on the formula sheet)
  • Brayton: η=1−rp−(γ−1)/γ\eta = 1 - r_p^{-(\gamma-1)/\gamma}, 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)
  • ηth=Wnet/Qin\eta_{th} = W_{net}/Q_{in} (on the formula sheet)
  • Isentropic efficiencies: ηC=T2s−T1T2a−T1\eta_C = \dfrac{T_{2s} - T_1}{T_{2a} - T_1}, ηT=T3−T4aT3−T4s\eta_T = \dfrac{T_3 - T_{4a}}{T_3 - T_{4s}} (learn this)
  1. (a)
    A gas turbine operating on the air standard Brayton cycle has a pressure ratio of 9, a compressor inlet temperature of 300 K and a turbine inlet temperature of 1400 K. Calculate the compressor and turbine outlet temperatures, the heat added, the work ratio (i.e. (WT−WC)/WT(W_T - W_C)/W_T) and the thermal efficiency. (For the air standard cycle take cp=1.005 kJ kg−1 K−1c_p = 1.005\ \mathrm{kJ\,kg^{-1}\,K^{-1}} and γ=1.4\gamma = 1.4)
    [14]2:2
  2. (b)
    In practice the high temperatures during heating and in the turbine give a significant change to the specific heats and also the turbine and compressor are not perfectly efficient. Making the following assumptions:-
    • during heating and in the turbine cp=1.157 kJ kg−1 K−1c_p = 1.157\ \mathrm{kJ\,kg^{-1}\,K^{-1}}
    • during expansion the ratio of specific heats becomes γ=1.33\gamma = 1.33
    • isentropic turbine efficiency is 0.85
    • isentropic compressor efficiency is 0.80
    • heat input increases to maintain the turbine inlet temperature of 1400 K
    • air standard cycle parameters still apply to compression
    calculate the heat input, the cycle efficiency and the work ratio.
    [8]
  3. (c)
    How might re-generation be used to enhance efficiency.
    [3]Third