How do I calculate lines of constant pressure in a Brayton cycle diagram?

[ingmarvandijk]

Hey guys (and girls?)

I'm new here, just registered, because I have a problem that my textbooks or google can't help me with:

I am making "Brayton cycle diagrams" for a study in jet engine efficiency. It's basically a Temperature - Entropy diagram for those of you who are unfamiliar with it. I know how to calculate the temperature increase with a pressure increase (basic isentropic relationships), and the entropy increase with fuel addition (delta S = q * LN( delta T)).

The problem I'm having is calculating lines of constant pressure in this diagram. Every source talks about them, but no source tells me how to calculate them. I know they are supposed to be increasing curves (the temperature difference for a pressure ratio is higher at higher entropy).

Does anyone have a clue to calculate these isobars?

Any help is greatly appreciated!

 

[ingmarvandijk]

Some extra insight:

There are 2 important processes.
The first one is compression, where the pressure increases, the temperature as a result, and the entropy remains constant.
The second process is heat addition (or subtraction) where the temperature changes and the entropy follows

Also, in the formula for fuel addition it should of course be LN(T2/T1) instead of Delta T.

 

[charng]

To calculate lines of constant pressure in a Brayton cycle diagram, you can use the ideal gas law and the definition of enthalpy. The ideal gas law states that pressure (P) and temperature (T) are directly proportional, so as pressure increases, temperature also increases. This can be represented by a straight line on a Temperature-Entropy diagram.

To calculate the slope of this line, you can use the definition of enthalpy (H = U + PV) and the first law of thermodynamics (dH = dQ + dW). This will give you the equation dH = dQ + PdV. Since the process in a Brayton cycle is isentropic (constant entropy), dQ = 0. Therefore, dH = PdV. This means that the slope of the line of constant pressure is equal to the change in enthalpy divided by the change in volume.

To determine the exact values for the lines of constant pressure, you will need to use the specific heat ratio (γ) of the gas in the cycle. This can be found in your textbook or through online sources. The equation for the specific heat ratio is γ = C_p / C_v, where C_p is the specific heat at constant pressure and C_v is the specific heat at constant volume.

Once you have the value for γ, you can use the equation P = ρRT to calculate the pressure at any given point on the diagram, where ρ is the density of the gas and R is the gas constant. Then, using the equation for the slope of the line (dH = PdV), you can calculate the enthalpy values for each pressure point.

In summary, to calculate lines of constant pressure in a Brayton cycle diagram, you will need to use the ideal gas law, the definition of enthalpy, and the specific heat ratio of the gas. With these equations, you can determine the slope and exact values for each line of constant pressure. I hope this helps and good luck with your study on jet engine efficiency!