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There are many rocket engines for liquid propellants which use the fuel (rocket petrol or liquid hydrogen for instance) to cool the walls of the combustion chamber and the nozzle.

But are there any engines which use the oxidizer liquid oxygen for cooling?

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Yes, DLR tested a EADS/Astrium modified test chamber cooled by liquid oxygen as part of the "Phase 2 Technology Demonstration Programme" research work for Reaction Engines' SABRE engine, some time between 2009 and 2012.

As well as tests using liquid oxygen in the combustion chamber's cooling jacket while running on H2/LOX (shown in CCTV images in the linked document), separate tests at DLR used air in the cooling jacket with heavy hydrogen film cooling in a EADS/Astrium built combustion chamber, while the engine runs on compressed air and hydrogen (shown on the inset image) DLR tesing Astrium build oxidiser cooled rocket engine

Details from Hempsell, Mark (September 2013). Progress on SKYLON and SABRE (IAC-13.D2.4.6). 64th International Astronautical Congress. Beijing, China.

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    $\begingroup$ And it didn't run on engine-rich mix? :D $\endgroup$
    – SF.
    Mar 25, 2019 at 8:52
  • $\begingroup$ no @SF. it seems these rocket scientists know a thing or two. $\endgroup$
    – user20636
    Mar 25, 2019 at 8:58
  • $\begingroup$ (although that red tinge to the flame suggests something other than H and O, but I'm assuming an ablative throat/nozzle) $\endgroup$
    – user20636
    Mar 25, 2019 at 10:08
  • $\begingroup$ So there was liquid oxygen in the cooling jacket and hydrogen film cooling in the combustion chamber but not both during the same test? $\endgroup$
    – Uwe
    Mar 25, 2019 at 10:35
  • $\begingroup$ I've reread the summary, @Uwe The LOX test was actually a different test chamber -- as might have been inferred by a closer look at the two test setups. $\endgroup$
    – user20636
    Mar 25, 2019 at 10:51

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