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The oxygen turbopump in the RL10 upper stage engine has been openly discussed by NASA for some decades now, in publications like SP-8107. On page 8 of this document is a drawing of this turbopump. The lower end of the oxygen pump shaft seems to be splined.

In the back of my head, I seem to remember reading somewhere that it has something to do with a possible usage of the engine in an ICBM, but that doesn't make much sense, considering it uses liquid hydrogen as fuel.

Can anyone tell me if it is indeed splined, and what is supposed to be connected there, if anything?

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Yes, at least in some Centaur applications, the LOX pump shaft is splined, and in fact has a gear drive attached to it. This drive provides mechanical power to a hydraulic pump which in turn supplies hydraulic fluid to the Centaur's Thrust Vector Control (TVC) actuators.

Source is this document, I quote the relevant paragraph (emphasis mine):

During steady state, the vehicle Propellant Utilization (PU) system provides commands to the OFCV to modulate mixture ratio. The chamber pressure is held nearly constant when the mixture ratio is increased or decreased by the TCV. The LO2 pump accessory drive pad supplies power to the vehicle hydraulic power unit pump which provides 1100 psia to vehicle thrust vector control servo actuators. The solenoid valves are closed at shutdown, closing both inlet valves and the MFSOV. The cooldown valves are opened, bleeding off system pressure.

Here's the schematic referenced in the question: enter image description here

And here is a picture of a very similar RL10 from the museum at MSFC. enter image description here

You can't see the drive gear in the above picture, but the accompanying label shows it: enter image description here

MSFC museum pictures taken from this reddit thread.

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