University Thermodynamics- Turbojet

[andymarra]

Hello, I am currently revising for a thermodynamics resit exam and I cannot get past a certain part in a turbojet question from a past paper. This is the past paper which I failed a few months ago and still can't understand it. Any help would be appreciated.

A single spool, axial flow turbojet propels an aircraft at a cruise Mach number of 1.8 at
an altitude where the ambient pressure and temperature are 0.116 bar and 216K. The air
mass flow rate through the gas turbine is 20kgs−1, the rate of fuel consumption is 0.2kgs−1
and auxiliary devices take 100kW of power from the turbine. The compressor pressure
ratio is 3.0. The turbojet has component isentropic efficiencies as follows: intake, 0.92;
compressor, 0.93; turbine, 0.94; nozzle, 0.97. Determine the following:
i) Flight speed in ms−1;
(answer Ua = 530ms−1)
ii) Compressor entry temperature and intake pressure ratio;
(answers T2 = 356K, p2/p1= 5.138)
iii) Compressor power;
(answer 2.83MW)
iv) Turbine inlet temperature, and the turbine pressure ratio;
(answers T4 = 923K, p4/p5= 1.915)

Its the turbine inlet temp that I can't work out, i can work out the first parts fine. Basically, I am unsure of how to work out T4 by using the information given in the question.
Any help appreciated!
Regards, Andy

 

[Valkarie]

To calculate the turbine inlet temperature, you will need to use the information from the question as well as the energy equation. The energy equation states that the change in enthalpy of the air flow is equal to the work done by the turbine plus the power taken away by the auxiliary devices. Assuming ideal isentropic efficiencies for all components and no losses, you can use the following equation to calculate the turbine inlet temperature (T4): T4 = T3 + (h5-h3)/CpWhere Cp is the specific heat capacity at constant pressure of the air. Using the information given in the question, you can then calculate T4. First, calculate T3 using the equation: T3 = T2 * (P3/P2)^((γ-1)/γ)Where γ is the ratio of specific heats. Then calculate h3 and h5 using the equation: h = cv * T + (γ/(γ-1)) * PWhere cv is the specific heat capacity at constant volume of the air. Finally, substitute all the values into the equation above and calculate T4.