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Rocket engines typically employ a cooling jacket of sorts, usually dual-purposing the fuel as a liquid coolant before it flows into the injectors.

Here is an example turbojet using a bypass. As you can see, the bypass air is far cooler in temperature than the air combustion chamber:

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Why are there no designs that use an air bypass (similar to a turbojet) to cool the engine/nozzle? Obviously once the rocket has escaped the atmosphere, a bypass would be of little use. However usually by that stage in a rocket, thrust has been greatly reduced and therefore generated heat as well.

Wouldn't a bypass cooling system make a rocket engine a tad less complex (especially for the first stage)?

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    $\begingroup$ On a rocket, where is this bypass air going to come from? Also, fuel has a much higher heat capacity than air. $\endgroup$ – fooot Oct 16 '15 at 20:31
  • $\begingroup$ @fooot I imagine vents near/around the nose cone to open the bypass. Since the rocket is traveling very fast, it would ram air through the bypass without a fan being necessary. $\endgroup$ – SnakeDoc Oct 16 '15 at 20:32
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    $\begingroup$ @SnakeDoc Heating fuel isn't as dangerous as you might think, as long as you don't combine it with an oxidizer. Even aircraft that fly in air frequently make use of the high heat capacity of their fuel. It's orders of magnitude higher than what you'll get from air, especially at high altitudes, and its effectiveness will be more or less constant, rather than decreasing rapidly with altitude. Furthermore, rocket engines used in a space launch will generally be releasing orders of magnitude more energy than a turbofan jet engine would be. $\endgroup$ – reirab Oct 17 '15 at 0:48
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    $\begingroup$ This is not really air cooling, but some engines use curtain cooling where relatively cool exhaust gases from the turbopumps are fed to part of the nozzle. See en.wikipedia.org/wiki/Rocket_engine#Cooling . $\endgroup$ – Andy Oct 19 '15 at 14:44
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    $\begingroup$ @SnakeDoc In the presence of oxidizer, perhaps. Nothing combusts without oxidizer, though, regardless of temperature. (The 'burning' in the sun slebetman mentioned is not combustion; it's nuclear fusion.) Combustion is a chemical reaction (specifically, a redox reaction.) A chemical reaction can't take place without all of the reactants being present. $\endgroup$ – reirab Oct 19 '15 at 15:37
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Air cooling is not going to contribute much here.

The Shuttle engines were cooled by liquid hydrogen (-253°C) from the fuel supply being pumped up cooling ducts inside the nozzle. Typical nozzle temperature in operation was around 54°C. Yes, fifty-four Celsius. (BBC Engineering Connections - see this Youtube clip)

The top speed of the SR-71 (about Mach 3.2) was limited by the temperature of the air arriving at the engines which, after being compressed in the inlet ducts, reached temperatures around 400°C. (Wikipedia: SR-71)

The shuttle passes Mach 4 about 2 minutes after launch.

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    $\begingroup$ A spacecraft also climbs above the atmosphere to minimize drag as quickly as possible, so for big part of the engine operation there is no air around. $\endgroup$ – Jan Hudec Oct 17 '15 at 17:36
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    $\begingroup$ Great point about the air being effectively too hot for cooling so soon after launch--that's something I didn't consider in my answer. $\endgroup$ – Alec Martin Jul 27 '18 at 17:36
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Virtually all jet engines use a technique very similar to the technique you're proposing: the inside of the combustion chamber, turbines, and exhaust, (and afterburner, if the engine has one) as well as the turbine blades and stators, are covered with small holes. Cooling air is forced through these holes, forming a boundary layer between the metal and the super-hot gases.

The temperature of burning fuel/air in a jet engine is well above the melting point of the metals used to build these components, which is why this is necessary. In fact, the temperature of the gases exceeds the vaporization temperature of a number of metals.

Where does this cooling air come from? It comes from the engine's compressor. The reason bypass air isn't used is because it is at a lower pressure than the inside of the core of the engine, so the hot gases would move out through the holes toward the bypass duct. In this case, the boundary layer is made of hot gas instead of cool gas, which destroys the engine.

To get air of adequate pressure, air is "bled" out of the compressor at points where the pressure is high enough to provide adequate flow (in the right direction!) to the parts of the engine that need it. This method of cooling is so effective that the components in a jet engine that need to withstand the most heat are actually the highest pressure parts of the compressor, because (a) air heats up when you compress it, and (b) you can't use the same cool boundary layer technique in the compressor because you need higher pressure air than the hot air from which you're trying to protect the component, and the component is part of the highest-pressure part of the compressor.

Here's a picture of a jet exhaust guide vane, with cooling holes clearly visible:

Laser-drilled holes permit film cooling in this first-stage V2500 nozzle guide vane

On a rocket engine, you could potentially cool it with compressed atmospheric air, but doing would add weight and complexity, and would only work in the lower layers of the atmosphere where there's enough air density to provide an adequate mass flow rate to absorb the heat. Since, as you mentioned, fuel (or potentially oxidizer) can be used to effectively cool the engine for a much lower penalty in weight and greater freedom in operating environment, that's been the obvious choice for most high-performance liquid fueled rockets.

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The air augmented rocket uses air from the freestream to provide extra thrust (and potentially) cool the motor. Two of the main issues with trying to add 'extra' air into the rocket stream are: drag over the rocket body (pretty much the main one) and disruption of the high-temperature flow (especially if you are trying to introduce air somewhere around the nozzle).

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    $\begingroup$ Ah, somebody has tried this before - NASA even. I didn't think disrupting the high-temperature flow would be an issue, since the thrust is being generated inside the nozzle. $\endgroup$ – SnakeDoc Oct 16 '15 at 20:41
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    $\begingroup$ Disrupting the jet flow is mostly a concern if you are trying to incorporate the freestream air into the nozzle $\endgroup$ – costrom Oct 16 '15 at 20:42
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Two main reasons: Firstly rockets operate at a preposterous level of power - the fuel and oxidiser pumps alone on a space shuttle have a combined shaft power greater than a GE90 turbofan - so you'd really struggle to get enough airflow, liquid hydrogen is a far better heatsink especially in the quantities they use.

Secondly, most rockets are built with the intention of going to space, where there in no cooling air at all, so as you got higher and the air got thinner your air-cooled rocket would rapidly overheat.

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