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ENGR5003 / Week 2
Week 2 Q2Exercise sheetCurrent spec2:125 min

ENGR5003 Week 2 workshop sheet Q2

Consider the Brayton cycle. Given that the pressure ratio, rp=p2p1=p3p4=16r_p = \dfrac{p_2}{p_1} = \dfrac{p_3}{p_4} = 16, p1=101 kPap_1 = 101\ \mathrm{kPa}, V1=4.5 m3V_1 = 4.5\ \mathrm{m^3} and V3=4.2 m3V_3 = 4.2\ \mathrm{m^3}. Assume we have 10 kg of an ideal gas with Rg=0.287 kJ/kg/KR_g = 0.287\ \mathrm{kJ/kg/K} and γ=1.4\gamma = 1.4.

Formulas you may need
  • Ideal gas: pV=mRgTpV = mR_gT (on the formula sheet)
  • Isentropic: pVγ=constpV^\gamma = \text{const}, T2T1=(p2p1)(γ−1)/γ\dfrac{T_2}{T_1} = \left(\dfrac{p_2}{p_1}\right)^{(\gamma-1)/\gamma} (on the formula sheet)
  • cp=γRgγ−1c_p = \dfrac{\gamma R_g}{\gamma - 1} (on the formula sheet)
  • Brayton efficiency: ηth=1−1rp(γ−1)/γ\eta_{th} = 1 - \dfrac{1}{r_p^{(\gamma-1)/\gamma}} (on the formula sheet; the derivation is in Lecture 4)
  • Work ratio: rw=WnetWout=1−T1T3rp(γ−1)/γr_w = \dfrac{W_{net}}{W_{out}} = 1 - \dfrac{T_1}{T_3}r_p^{(\gamma-1)/\gamma} (on the formula sheet)
  • Heat exchanger: heat gained by the compressed air = heat lost by the exhaust (learn this, Lecture 14)
  1. (a)
    Determine the pressure, temperature and volume at all 4 states.
  2. (b)
    Derive and calculate the thermal efficiency of the cycle.
  3. (c)
    What is the work ratio of the process and explain why the work ratio affects the practical efficiency of the cycle.
  4. (d)
    A heat exchanger is used to increase T2T_2 up to 1000 K and T4=1000 KT_4 = 1000\ \mathrm{K}. How does this affect the thermal efficiency?
    First