List of top Propulsion Questions on Turbofan Engines

In an ideal turbofan engine shown in the figure below, the compressor is driven by the high pressure turbine, and the fan is driven by the low pressure turbine. The stations 0, 2, 3, 4, 4.5, and 5 refer to free-stream, compressor inlet, compressor outlet, combustor exit, high pressure turbine exit, and low pressure turbine exit, respectively, and the subscript 't' refers to the total condition. Also, \(\tau_r = T_{t0}/T_0\), \(\tau_c = T_{t3}/T_{t2}\) and \(\tau_\lambda = T_{t4}/T_0\). The total temperature ratio of the high pressure turbine \((T_{t4.5}/T_{t4})\) is given by ______.

For a given air-standard power, the propulsive efficiency of a turbofan engine is more than that of a turbojet engine. Which of the following is/are the reason(s) for this?

A twin-spool turbofan engine at sea level (\(P_a = 1\ \text{bar},\ T_a = 288\ \text{K}\)) has separate cold and hot nozzles. During static thrust test, the total air mass flow rate is 100 kg/s and the cold exhaust temperature is 288 K. Given:
Fan pressure ratio = 1.6
Overall pressure ratio = 20
Bypass ratio = 3.0
Turbine entry temperature = 1800 K
\(C_p = 1.005\ \text{kJ/kg-K}\), \(\gamma = 1.4\).
Find the static thrust from the cold nozzle (ideal fan and ideal expansion), in kN (round to two decimals).