How can I calculate turbofan efficiency as a function of turbine inlet temperature?

Question

I know that increasing the turbine inlet temperature (TIT) increases the overall efficiency of the jet engine. So I wanted to find the overall efficiency as a function of TIT. I used the equations from this website. But the efficiency seems to go down as I increase the TIT. I have attached the pictures of the functions I used to get the graph.

I assumed a compressor pressure ratio of 30, a fan pressure ratio of 1.5 and a bypass ratio of 8.

stages of the cycle the way I defined it as 1-2 is inlet 2-3 is compressor 3-4 is combustor 4-5 is a turbine 5-6 is afterburner(I didn't use it so 5 and 6 are same) 6-7 is the nozzle

I have also found another picture from this website that showed the similar result with efficiency going down as TIT is increased

Can someone please tell me what I did wrong? Or if you can provide a similar graph with similar assumptions that would be great.

Answer 1

First, you should state whether you are designing an engine (increasing the TIT) or if you are doing an off design calculation for an existing engine.

In the case of design we gas turbine performance engineers call this design point analysis, increasing the TIT indeed would increase the efficiency, but this would require an increase of the pressure (OPR, Overall Pressure Ratio) as the pressure ratio is a parameter in the thermodynamic efficiency equation. A rise in compressor exit temperature by the increased pressure ratio requires raising the TIT to be able to add power/heat to the cycle. See e.g. the following example:

When increasing the pressure, the exit temperature of the high spool speed compressor also increase and results in an even higher amount of cooling flow required to cool the turbine. Using simple formulae is possible, but not preferred, specific software exists to do this for you.

If you are doing an off design analysis, so basically you have a frozen design and want to see the effects of TIT on efficiency, this can only be done with a gas turbine simulation program. To do this you would require the off design characteristics of the turbomachinery components, which are highly classified data.

Looking at the formulae you posted, I assume that you are looking at various designs. Please download a free copy of a gas turbine performance simulation tool and it will tell you the answer in minutes. E.g. this tool or this tool are free to use. There are probably much more tools.