Question

Consider a turbojet engine on an aircraft flying at M=0.9 at an altitude of 38,000 ft where ambient pressure = 20 kPa and ambient temperature = 220 K. The diffuser, compressor, and turbine adiabatic efficiencies are 0.95, 0.85, and 0.9, respectively. The compressor pressure ratio = 30 and the stagnation temperature at the combustor exit is 1600K. You may assume γ = 1.4, R = 287 J kg-1K-1, QR = 44 MJ/kg, Cp = 1 kJ kg -1K -1 in general. Assume any missing parameter if required, but clearly state the assumption. a. Sketch the thermodynamic cycle in a T-s diagram. b. Where are the maximum stagnation pressure and stagnation temperature encountered in the flow within this engine? What are those values? c. What are the stagnation temperature and stagnation pressure at the exit of the turbine?

Answer 1

The thermodynamic cycle in a T-s diagram for a turbojet engine at M=0.9 is described. The maximum stagnation pressure and temperature are encountered at points 3 and 4 respectively. The stagnation temperature and pressure at the exit of the turbine can be calculated using the turbine adiabatic efficiency, initial stagnation temperature, and ambient conditions.

Step-by-step explanation:

To sketch the thermodynamic cycle in a T-s diagram, we need to understand the different processes involved in the turbojet engine. The cycle starts at point 1, where the ambient conditions are given. The diffuser process is represented by a horizontal line from point 1 to point 2. The compressor process is represented by an upward diagonal line from point 2 to point 3. The combustion process is represented by a constant pressure line from point 3 to point 4. The turbine process is represented by a downward diagonal line from point 4 to point 5. And finally, the nozzle process is represented by a horizontal line from point 5 to point 1.

The maximum stagnation pressure is encountered at the end of the compressor process, at point 3. The value can be found using the compressor pressure ratio and the ambient pressure. The maximum stagnation temperature is encountered at the end of the combustion process, at point 4. The value is given as 1600 K.

At the exit of the turbine, the stagnation temperature and stagnation pressure can be found using the turbine adiabatic efficiency, the initial stagnation temperature, and ambient temperature. The stagnation temperature is calculated by multiplying the initial stagnation temperature by the efficiency, and the stagnation pressure is calculated by multiplying the ambient pressure by the pressure ratio across the turbine.