# Is there an equation for jet engine efficiency as a function of turbine inlet temperature?

I know that there is a relation between the turbine inlet temperature and the engine's efficiency. But, can anyone provide an equation or efficiency as a function of just the turbine inlet temperature?

I am looking for something like this: If the turbine inlet temperature goes up by 200K, efficiency goes up by 10%. Any numbers like this are appreciated.

Also, let's say that if GE invents a material that does not melt at all(just imagine), what is the highest temperature that can be produced by burning the fuel assuming nothing can melt.

• This answer by Peter Kämpf should explain it. If you are asking about something else, please clarify. Nov 10, 2019 at 19:05

## 1 Answer

The jet engine efficiency is unfortunately more complicated than just a one-to-one function between static Turbine Inlet Temperature and efficiency. Thermodynamic efficiency of a turbine engine is defined as the useful generated power extracted from the chemical energy added by the fuel.

The following is extracted from a paper format uni book on aircraft gas turbines.

Station 0 is for the engine inlet, the other station numbers are:

1. Compressor inlet.
2. Combustion chamber inlet.
3. Turbine inlet.
4. Turbine outlet.
5. Engine exhaust.

Energy IN

The heat flow $$\dot{Q}$$ added to the engine is:

$$\dot{Q} = \dot{m} \cdot c_{pg} \cdot (T_{3t} - T_{2t}) \tag{1}$$ With $$\dot{m}$$ = mass flow through engine, $$c_{pg}$$ = gas constant, $$T_{3t}$$ = total temperature at turbine inlet. Total temperature is the temperature reached when a gas flow is compressed isentropically, measured in the stagnation point, and defined as $$T_t = T + v^2/(2 * C_p) \tag{2}$$

So energy IN is a function of:

• Static Turbine Inlet Temperature
• total mass flow
• gas flow velocity at the turbine inlet.

Useful power OUT

The power delivered by the gas generator is:

$$P_{gg} = \dot{}m \cdot c_{pg} \cdot T_{4t} \left[ 1 - {\left(\frac{p_0}{p_{4t}} \right)}^{\frac{\kappa_g - 1}{\kappa_g}} \right] \tag{3}$$

with

• $$T_{4t}$$ = stagnation temperature at the turbine outlet.
• $$p_0$$ = static pressure at engine inlet, a function of air density and airspeed.
• $$p_{4t}$$ = stagnation pressure at the turbine outlet, which depends on how much energy the turbine has extracted from the gas flow.

Efficiency

If we could vary the $$T_{3t}$$ only and keep the other variables constant, we could indeed get to the sort of function sought after - but we cannot. Increasing T.I.T creates more thrust, accelerates the aircraft, increases inlet pressure, increases turbine outlet pressure etc.

From Gas Turbine Theory by Saravanamuttoo/Rogers/Cohen, page 81:

The large number of variables involved make it impracticable to derive algebraic expressions for the specific output and efficiency of real cycles.