The GATE Grind

GATE 2026 AE – Question 38

Propulsion · Engine performance: ramjet, turbojet, turbofan, turboprop, turboshaft and after-burners · 2 marks · Multiple choice

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 ______.

Engine layout with stations 0, 2 (compressor inlet), 3 (compressor outlet), 4 (turbine inlet), 4.5 (between the high and low pressure turbines) and 5 (nozzle). The fan is driven by the low pressure turbine.
  1. $1 - \frac{\tau_r}{\tau_\lambda}(\tau_c - 1)$
  2. $1 + \frac{\tau_r}{\tau_\lambda}(\tau_c + 1)$
  3. $1 - \frac{\tau_r}{\tau_\lambda}(\tau_c + 1)$
  4. $1 + \frac{\tau_r}{\tau_\lambda}(\tau_c - 1)$

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Correct answer: (A) $1 - \frac{\tau_r}{\tau_\lambda}(\tau_c - 1)$

Explanation

The high pressure turbine drives only the compressor, so with constant $c_p$ and no inlet loss $T_{t4} - T_{t4.5} = T_{t3} - T_{t2} = T_{t2}(\tau_c - 1)$. Then $\frac{T_{t4.5}}{T_{t4}} = 1 - \frac{T_{t2}}{T_{t4}}(\tau_c - 1)$, and with $T_{t2} = T_{t0}$ this gives $\frac{T_{t2}}{T_{t4}} = \frac{\tau_r T_0}{\tau_\lambda T_0} = \frac{\tau_r}{\tau_\lambda}$.