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When the Saturn V launch vehicles reached high altitudes and speeds, the exhaust plume looks drastically different compared to how it did at launch (it is much larger, and has a cone about halfway down the plume). Also, the flames seem to be creeping up the bottom of the S-IC stage. What causes these observations?

enter image description here

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The contained shape of the exhaust you see at sea level is being constrained by the atmosphere. It is expanding as much as it can, as it moves downwards.

As the rocket goes higher, the air pressure decreases and the exhaust plume expands. Watch a SpaceX Falcon 9 launch and it is really obvious. Actually, watch any sea level launch from a good camera position and it is really obvious. SpaceX just happens to be flying cameras and posting videos.

That is why the nozzles on upper stage engines are longer to prevent expansion as long as possible to maximize performance. An aerospike engine is designed to expand as per atmospheric pressure. I.e. Use the atmosphere as your nozzle, and it adjusts itself as the pressure changes.

Not sure why the exhaust appears to creep up the stage, but probably same reason.

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    $\begingroup$ What about the extra cone down in the plume? (i.e., do you know why it's there?) $\endgroup$ – user2822 Dec 12 '14 at 4:25
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    $\begingroup$ @RickyDemer My guess is a form of shock diamond. $\endgroup$ – Thomas Dec 12 '14 at 8:17
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    $\begingroup$ Maybe the "creeping flames" are not flames at all but atmospheric moisture condensing in a shock wave, and bright yellow due to illumination from the rocket exhaust? $\endgroup$ – Anthony X Dec 13 '14 at 16:56
  • $\begingroup$ creeping flames - exhaust from turbopump gas generator? $\endgroup$ – Daniel Chisholm Dec 14 '14 at 13:46
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    $\begingroup$ The gas generator on the F-1 dumps its exhaust into the nozzle, creating a relatively cool gas film to protect the lower part of the nozzle from the primary exhaust. $\endgroup$ – Russell Borogove Jan 28 '16 at 4:19
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To answer the creeping of the exhaust plume up the side of the first stage, it's called Plume Induced Flow Separation (PIFS). This paper (PDF) explains and simulates the computational fluid dynamics (CFD) of the PIFS phenomenon on the Saturn V. It's pretty heady but it explains the physics behind it.

USM3D Simulations of Saturn V Plume Induced Flow Separation

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