How to Perform a Complete Engine Cycle Analysis for a Twin-Spool Turbojet?

[claire_hender]

A twin- spool turbojet powered aircraft flies at 600(ms-1) at an altitude where the temperature and pressure are 0.116bar and 216K. The air mass flow rate into the engine intake is 20kgs-1. The isentropic efficiences of the components are: intake (diffuser) 0.95; low pressure compressor: 0.92, high pressure compressor: 0.94. High pressure turbine: 0.96, low pressure turbine: 0.97; nozzle 0.98. There is power take-off from the low pressure spool of 250kW and 0.5kgs-1 of air is bled from the low pressure compressor. Compressor pressure ratios are 1.5 and 2 for the low and high pressure compressors respectively, and the combustion chamber operates a constant pressure. The combustion chamber exit temperature is 850 degreesC, and the nozzle expands the gas to the ambient pressure.

The question is: Perform a complete engine cycle analysis to determine the nozzle exhaust velocity and hence the engine thrust.I know the mass flow rate if the high pressure compressor = 19.5 kgs-1
And similarly through the high pressure turbine = 19.5 kgs-1
Also, my intake (diffuser) pressure ratio = p2/p1 = 7.614

Apart from that I am really stuck, I don't know how to actually start the question? If anyone could give me any guidelines or help, it'd be much appreciated.
Thank you ! xxx

 

[deepthishan]

i find that the best way to tackle these questions is to start with a schematic diagram of the twin spool engine then construct a t-s sketch.
im not about to do all that here! but anyway it's not as hard as it sounds. use the efficiency equations for the compressors, turbines and nozzles, don't forget to use the combustor pressure loss fact and the mechanical efficiency of each spool as well.
go step by step very gradually and ul end up with the answer
gluck

 

[Mene]

Hello, thank you for reaching out for help with your engine cycle analysis question. To start, let's review the information given in the problem. We know that the aircraft is flying at a speed of 600 meters per second at an altitude where the temperature is 216K and pressure is 0.116 bar. The air mass flow rate into the engine intake is 20 kgs-1. We are also given the isentropic efficiencies of the components, which are important for calculating the actual performance of the engine.

To begin the analysis, we need to use the equations for the Brayton cycle, which is the thermodynamic cycle that describes the operation of a gas turbine engine. The Brayton cycle consists of four main processes: isentropic compression, constant pressure heat addition, isentropic expansion, and constant pressure heat rejection.

First, we need to determine the pressure at the intake of the engine. We can use the given pressure ratio of the intake (diffuser) to calculate the intake pressure (p1). We know that p2/p1 = 0.95, so p1 = p2/0.95 = 0.116/0.95 = 0.122 bar.

Next, we can calculate the pressure at the exit of the low pressure compressor (p3) using the given pressure ratio of 1.5. So p3 = p2*1.5 = 0.116*1.5 = 0.174 bar.

Now, we can use the isentropic efficiency of the low pressure compressor (0.92) to calculate the actual pressure at the exit of the low pressure compressor (p3a). p3a = p3/0.92 = 0.174/0.92 = 0.189 bar.

Next, we can calculate the pressure at the exit of the high pressure compressor (p4) using the given pressure ratio of 2. So p4 = p3*2 = 0.174*2 = 0.348 bar.

Using the isentropic efficiency of the high pressure compressor (0.94), we can calculate the actual pressure at the exit of the high pressure compressor (p4a). p4a = p4/0.94 = 0.348/0.94 = 0.370 bar.

Now, we can calculate the temperature at the exit of the high pressure compressor (T4) using the