Find the total temperatures at the exit of the air intake and the compressor respectively.

A jet engine is operating at a Mach number of \(0.8\) at an altitude of \(10 \;km\).The efficiency of the air intake is \(0.8\) and that of the compressor is \(0.87\).What is the total temperature at the exit of the air intake and the compressor respectively ?(ambient pressure = \(26.5\; kPa\); ambient temperature =\(223.3\; K\); gas constant \(\gamma =1.4\) ;\(P_{rc}=8\))

Asked on 10th October 2019 in Propulsion.
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    Jet engine is operating at a Mach number of 0.8 at an altitude of 10 km.Efficiency of the air intake and that of compressor are 0.8 and 0.87.We need to find here total temperatures at the exits of air intake and compressor.

    Total temperature at the exit of the intake is given as \[T_{01}=T_{amb}\left [ 1+\frac{\gamma-1}{2}M^{2} \right ]
    \\=223.3\times \left [ 1+0.2\times(0.8)^{2} \right ]
    \\=251.88\;K\]

    Total temperature at the exit of the compressor will be given as \[T_{02}=T_{01}\times \left [ 1+\frac{1}{\eta _{c}}\left ( p_{rc}^{\frac{\gamma-1}{\gamma}}-1 \right ) \right ]
    \\\Rightarrow T_{02}=251.88\times\left [ 1+\frac{1}{0.87}\times\left ( 8^{\frac{0.4}{1.4}}-1 \right ) \right ]
    \\\Rightarrow T_{02}=486.80\;K\]

    Therefore total temperature at the exit of the intake and compressor are 251.88 K and 486.80 K.

    Answered on 10th October 2019.
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