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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.

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

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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.

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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.

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