GATE 2021 AE – Question 55
A twin-spool turbofan at sea level (1 bar,288 K) has separate cold and hot nozzles, total air flow 100 kg/s, cold exhaust temperature 288 K, fan pressure ratio 1.6, overall pressure ratio 20, bypass ratio 3, turbine entry temperature 1800 K, cp=1.005 kJ/(kg K), γ=1.4. Assuming ideal fan and ideal nozzle expansion, static cold-nozzle thrust is ___ kN (two decimals).
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Correct answer: 21.52 to 21.74
Explanation
**Fan exit stagnation temperature.** For an ideal fan the compression is isentropic:
$$T_{0,fan}=T_{01}\left(\frac{p_{02}}{p_{01}}\right)^{\frac{\gamma-1}{\gamma}}=288\times1.6^{0.2857}=288\times1.1437=329.4\text{ K}.$$
**Cold nozzle exit speed.** With ideal expansion to the ambient pressure, the exit static temperature is 288 K (given). The kinetic energy is the drop in enthalpy:
$$V_e=\sqrt{2c_p\,(T_{0,fan}-T_e)}=\sqrt{2\times1005\times(329.4-288)}=\sqrt{2010\times41.4}=288.4\text{ m/s}.$$
**Cold air mass flow.** Total flow is 100 kg/s with a bypass ratio of 3, so the cold (bypass) flow is
$$\dot m_c=\frac{3}{3+1}\times100=75\text{ kg/s}.$$
**Static thrust** from the cold nozzle ($V_0=0$, ideally expanded):
$$F_c=\dot m_cV_e=75\times288.4=21\,630\text{ N}=\mathbf{21.63\ kN}.$$