# What turbine temp. would result from burning pure stoichiometrically?

I've heard that jet engine efficiency is limited by turbine temperatures---that is, the max temp. that the turbine blade alloy can withstand before weakening too much.

So jet engines are run fuel-lean. But they do achieve > 99% combustion of all fuel, so at least that's good. However, if we could burn stoichiometrically, then the engine could be smaller and lighter since it would need less air intake for the core.

So I want to know what is the max temperature that would result if you tried to burn pure stoichiometric?

BTW, to keep it simple, I'm asking about TIT (Turbine Inlet Temperature), which is the temperature of the gas right after combustion, right before it enters the first turbine stage. You can actually do complicated cooling on the blades to keep them less hot than that temperature somehow but I don't wanna get into that aspect.

Note, I'm interested in any typical large jet engine, like the PW6000, running at cruising conditions.

I found an example of actual TIT saying 1600 C: Mitsubishi site link. However, it was a gas turbine not jet engine, so I can't be sure if this is typical for jets too. What I want to know is the theoretical TIT if you could burn pure stoichiometric, to see what the difference is.

• A gold and silver dealer once lamented to me about how his little torch could not melt a larger piece. We then realized the silver was conducting the heat away faster than the torch was raising its temperature. Removing heat enables the metal to remain solid, even though the flame temperature is higher than than its melting point. He found a larger torch melted the silver well. Even in jets, the fuel burn quantity and stoichimetric ratio is important. This is why we cannot "lean" at full throttle. – Robert DiGiovanni Jan 11 at 11:38

So, the combustor (between the compressor discharge and turbine inlet) adds 600K. Let's assume this happens at $$\varphi=0.45%$$ fuel equivalence ratio, which is equivalent to about 3% of fuel by mass. Since that's so low, we may also assume that all energy is put into heating the air (both the air used for combustion and the excess air for cooling the flow before the turbine). We start with a $$\Delta T_c=1200K-600K = 600K$$. Since a combustor is approximately isobaric, we can use the $$c_p$$ heat capacity for the reaction products, which is (for an ideal gas) not a function of temperature. We can thus simply calculate the stoichiometric temperature increase $$\Delta T_{s} = \frac{\Delta T_c}{\varphi} = \frac{600K}{0.45} = 1333K.$$ So the turbine inlet temperature is then $$600K+1333K = 1933K.$$ In reality, fuel heating (especially fuel evaporation) will represent a more sizeable chunk near stoichiometry, but I think it's safe to assume it's around the $$1900K$$ range.
Note however that the theoretical efficiency (ignoring the inevitable viscous losses from handling such a large flow of air) is determined solely by the pressure ratio of the compressor: $$\eta = 1-\left(\frac{P_1}{P_2}\right)^\frac{\gamma-1}{\gamma}.$$ So if TIT were not an issue, by enriching the mixture closer to stoichiometric, we do reduce the mass flow required through the engine (at constant power), so we proportionally reduce the viscous losses in the engine. If on the other hand viscous losses did not exist, for the most efficient design we would increase the compression ratio and lean the mixture even further to the point where the compressor discharge and turbine inlet temperature would be almost equal.