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In a paper by Sippel et al. [1] the following statement is made on page 2: "Consequently the LE-5B turbine drive gas temperature has been successfully reduced [w.r.t. the LE-5A engine]."

However, I was under the impression that you'd want your turbine drive gasses to be as hot as allowed by the turbine. Since every kilogram of fuel you route to the turbine instead of the chamber contributes little to the thrust, you'd want to get the most out of each kilogram. And higher turbine temperatures give more power per kilogram looking at the following formula for turbine power:

$$P_{output} = \eta\ \dot{m}\ T_{in}\ c_p \bigg(1- \Big(\frac{p_{out}}{p_{in}}\Big)^{\frac{\gamma-1}{\gamma}} \bigg)$$ With $P_{output}$ the output power of the turbine, $\eta$ the turbine efficiency, $\dot{m}$ the mass flow through the turbine, $c_p$ the specific heat capacity of the turbine drive gas, $T_{in}$ the inlet temperature of the turbine drive gas, $p_{out}$ the turbine outlet pressure, $p_{in}$ in the inlet pressure and $\gamma$ the heat capacity ratio.

So the question is: is my understanding correct? And if so, why would they be happy about a reduced turbine temperature?

I guess it would be good for the turbine and allow for more restarts, but I wouldn't say that is enough of a reason to use the fuel less efficiently

[1] Sippel et al. 2003, Studies on Expander Bleed Cycle Engines for Launchers

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    $\begingroup$ The turbines in the paper are expected to be reused as part of the LFBB's. Citation from page 1: "Lower cost and higher reliability of the turbines are to be expected due to lower turbine inlet temperatures [4]." $\endgroup$
    – Cornelis
    Jul 19, 2022 at 10:10

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As a general principle, turbine efficiency decreases with increasing inlet temperature (or ambient temperature, if ambient gas is used as the inlet), and this drives power input down. In the equation the efficiency factor outweighs the explicit temperature factor. See, for instance, https://adgefficiency.com/energy-basics-ambient-temperature-impact-on-gas-turbine-performance/. (That link is the source of the chart below; the link unfortunately does not cite its reference fully.)

enter image description here

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    $\begingroup$ The effort is much appreciated, but inline air breathing gas turbines are quite something different from the turbine in the turbopump of an expander bleed cycle rocket engine. There is combustion in the former, while there is no combustion in the loop of the latter. $\endgroup$
    – Ruben
    Jul 18, 2022 at 10:33
  • $\begingroup$ @Ruben On page 2: "At the same time, the fuel injection temperature of the LE-5B is much lower than that of the LE-5A." Couldn't that fuel injection gas be compared with the inlet gas of a gas turbine ? $\endgroup$
    – Cornelis
    Jul 21, 2022 at 13:26
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    $\begingroup$ Thanks for the point @cornelis. $\endgroup$
    – Oscar Lanzi
    Jul 21, 2022 at 13:40
  • $\begingroup$ @Ruben But your question is about the turbine inlet temperature, not the rocket engine inlet temperature. And indeed that turbine cannot be compared with a gas turbine ( en.wikipedia.org/wiki/Gas_turbine ), but it should be compared with a steam turbine ( en.wikipedia.org/wiki/Steam_turbine ). $\endgroup$
    – Cornelis
    Jul 22, 2022 at 7:12

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