Details at each station of an ideal turbojet

[roldy]

I'm working on a project of which involves the analysis of a fixed area ideal turbojet. I'm calculating all the parameters at each station. I'm having a problem with stations 3, 4, 5 (end of compressor, end of burner, end of turbine). What happens to the mach number, pressure, and temperature (not total pressure and temperature) at each of these stations. I've calculated the parameters for all other stations but I can't find information on what happens to P and T.

 

[minger]

Why don't you start with what you think happens.

You should know what happens through the compressor (the name kind of gives it away). Through the burner, the gas turbine is modeled as a Brayton cycle, or a constant [what] combustion. You should know what happens to temperature.

After that, what happens in the turbine? Why is it there?

 

[roldy]

Here is what I know:

Inlet to compressor:
Pressure and Temperature increase
Total Pressure and Total Temperature remain constant

Compressor to burner:
Pressure=?
Total Temperature, Total Pressure, and Temperature increase

Burner to turbine
Pressure=?
Total Temperature and Temperature increases
Total Pressure remains constant

Turbine to end of turbine
Pressure=?
Temperature remains constant
Total Pressure and Total Temperature decrease

end of turbine to nozzle
I have a value for the Pressure but I'm not sure if it increased or decreased
Temperature decreased
Total Temperature and Total Pressure remained constant

nozzle to end of nozzle
Pressure is equal to Pressure at inlet
Temperature has decreased
Total Temperature and Total Pressure still remain constant

At station 5, would the flow be choked too? Meaning, would the Mach number be 1.0?
Attached is a table of calculations I have thus far done.

 

[minger]

At Station 3, at the end of compression, we essentially have our maximum pressure in the engine (commonly called CDP or PCD compressor discharge pressure).

Across the burner, it you look at the general cycle diagrams
http://en.wikipedia.org/wiki/File:Brayton_cycle.svg
you'll see that we have essentially constant pressure combustion. That's what defines the cycle.

Across the turbine, the flow is expanded, or pressure decreases to ambient at the exhaust. Static enthalpy is extracted and turned to usable work. This causes a reduction in static temperature.

You're just about there.

 

[roldy]

Yes, I understand that after the compressor we have maximum pressure. What I don't know, is how to calculate the static pressure when I know all parameters except for the density and area.

 

[minger]

Often times the compressor pressure ratio is a design parameter. From your workbook you have both temperatures and total pressure. Can you use an isentropic relation?

 

[roldy]

I think I solved for the pressures correctly according to the formula below.
$$\frac{P}{P_{t}}=\left(\frac{T}{T_{t}}\right)^\frac{\gamma}{\gamma-1}$$

Solving for P I can now find $$\rho$$ and the area at each station.
Below is the new table. I looked over the values and they all seem correct to me. Do you see any errors?