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The question is explained pretty well in the title itself: Does the injector plate experience the same combustion temperature and pressure as the rest of the chamber? If so, how is it cooled?

However, the how is it cooled aspect of the question was for if the the propellants were both room temperature. If the injection plate does experience the combustion temperatures, how would it cool in the situation that both propellants are room temperature.

Thank you

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How would it cool in the situation that both propellants are room temperature?

Considering that combustion is happening at 3000K or more, whether the coolant is at 90K or 300K hardly makes a difference. It's only a change of ~7% of the temperature difference. This toaster in a freezer thought experiment outlines the basic concept. As long as you keep flowing enough propellant through it fast enough (so that the heat capacity per second is sufficiently high), there shouldn't be much change.

To get a grasp on the numbers: this is how much energy it takes to increase the temperature of one mole of molecular Oxygen ($O_2$):

  • Vaporise it from liquid to gas: $6.7kJ$
  • From 90K (cyrogenic storage) to 300 K: $6kJ$
  • From 300K (room temperature) to 3000K (engine temperature): $100kJ$

So the vaporisation matters as much as the next 200 degrees of heating, but even both effects put together only adds up to $11\%$ of the energy required to heat it all the way to that of the combustion chamber. Results will vary by propellent and the exact conditions (not least of which is that you don't want the injector plate to get as hot as 3000K) but the broad results should hold.

Compared to the combustion temperature, everything looks about as cold as each other.

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    $\begingroup$ If the propellant changes from liquid to gas then the energy difference between room temperature and cryogenic temperatures will be more significant $\endgroup$
    – Alan Birtles
    Commented Aug 3 at 18:03
  • $\begingroup$ I looked at some injectors for storable propellant engines like Titan 2 and shuttle OMS. I couldn't find enough detail to write an answer, but they didn't look any differently cooled than cryo engines. So, I agree with your answer. $\endgroup$
    – Organic Marble
    Commented Aug 3 at 18:17
  • $\begingroup$ @AlanBirtles fair, the latent heat can be important, so I amended my answer. $\endgroup$
    – user53400
    Commented Aug 3 at 19:26
  • $\begingroup$ So the injector plate does experience the same combustion temperature and pressure as the rest of the chamber, and it is cooled by the high flow of the propellants through the injector plate. $\endgroup$
    – Anish Kommireddy
    Commented Aug 3 at 19:27
  • $\begingroup$ @AnishKommireddy well yes, but the effect of the cooling is presumably to stop it getting as hot as the combustion itself. It ought to reach an equilibrium where the heating from the combustion and the cooling from the propellants cancel each other out - and that's hopefully far below the combustion temperature so the injector plate does melt or vaporise. $\endgroup$
    – user53400
    Commented Aug 3 at 19:36

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