How can firing a Space Shuttle OMS engine below 21 km cause its nozzle to "collapse"?

This answer to Can the space shuttle use OMS engines during landing? says:

No

and quotes Section 3.7 of the Orbital Maneuvering System Workbook; OMS 21002 October 10, 2006, Final version, USA006500 Rev. A:

3.7 CONSTRAINTS AND LIMITATIONS

The following is a list of the constraints and limitations for the OMS that are relevant to crew operations.

The minimum altitude for an OMS engine burn is 70,000 feet. Below this altitude, the pressure difference between the inside and the outside of the OMS engine nozzle could cause it to collapse.

If a vacuum engine is operated with a significant ambient pressure then the exhaust will be under-expanded, and it might separate from the inside walls of the nozzle. I'd always assumed this was due to ambient pressure sneaking in from outside.

Is the phenomenon that could lead to nozzle collapse in this case due to "separation failure"? Though it's hard to imagine, is the pressure of the OMS rocket exhaust lower than ambient pressure significantly lower than 21 kilometers?

• Don't forget Bernoulli - en.wikipedia.org/wiki/Bernoulli%27s_principle Commented Jan 24, 2021 at 17:02
• It sounds like you're basically asking for clarification on an answer to a previous question. That's one of the things that comments are meant for. Is there some reason why you felt this needed to be a separate question instead? Commented Jan 24, 2021 at 19:34
• @IlmariKaronen: I disagree. Even though uhoh is referencing an answer, this is an entirely new and interesting question. The answer to that may be (and is hopefully) so complex that it cannot fit into another comment. Commented Jan 24, 2021 at 20:22
– user20636
Commented Jan 24, 2021 at 23:16
• Commented Jan 25, 2021 at 5:03

A thruster is overexpanded if the nozzle exhaust pressure is less than ambient pressure, ambient if the nozzle exhaust pressure equals ambient pressure, or underexpanded if the nozzle exhaust pressure is greater than ambient pressure. Since ambient pressure is essentially zero in vacuum, any thruster operating in vacuum is by definition an underexpanded nozzle.

A thruster that is designed to operate in vacuum will have an extremely low nozzle exit pressure when the thruster is operating. Operating a thruster designed for use in vacuum when ambient pressure is greater than the exhaust pressure results in that vacuum level underexpanded nozzle becoming an overexpanded nozzle. If the ambient pressure is much greater than the exit pressure the nozzle is danger of becoming a grossly overexpanded nozzle.

There are many serious problems associated with grossly overexpanded nozzles. The exhaust can separate from the nozzle, which can result shock damage to the nozzle. Even worse, the pressure difference between the outside of the nozzle (ambient pressure) and inside the nozzle can cause the nozzle to collapse in on itself. Think back to your childhood education when you put water in a tin can, heated it to boiling, and then inserted the can upside down in a container of cold water. Rocket nozzles can withstand being underexpanded. It's being overexpanded that is dangerous, grossly overexpanded in particular.

• A 1 gallon square "gas can" with a little boiling water in the bottom was dramatically crushed in my kitchen when I was 5 by cranking down a cap then removing the heat. I'll never forget it, It "buckled". (1 2) At 21 km pressure is 0.06 bar so this altitude limit may include some safety factor i.e. it's not guaranteed to buckle at 21 km, but that's when you'd better shut it down because you may be descending pretty quickly at that point.
– uhoh
Commented Jan 25, 2021 at 0:11
• It's still counterintuitive to me that low pressure exhaust can push itself into higher pressure ambient. I don't mean I don't believe it; it's just one of those things I can't quite feel settled with. Is the thrust divided by the nozzle area really the pressure here, or is the "sideways pressure" on the nozzle different due to some Bernoulli thing mentioned in comments below the question?
– uhoh
Commented Jan 25, 2021 at 0:11
• @uhoh pretty much all booster engines are overexpanded at liftoff; i.e. "low pressure exhaust pushing itself into higher pressure." Left engine in the graphic aerospaceweb.org/design/aerospike/figures/fig11a.jpg Commented Jan 25, 2021 at 1:48
• @OrganicMarble Continuing your train of thought, the reason a low pressure exhaust can push itself into a higher pressure atmosphere is that the exhaust exits the nozzle at velocity greater than the speed of sound. The exhaust doesn't quite know that the air is there. Commented Jan 25, 2021 at 4:49
• @uhoh You can easily see when an engine that is originally overexpanded at launch reaches the altitude at which the exhaust stream becomes underexpanded. That's when the exhaust plume suddenly blooms. There's a related question on this topic asked by you that has a correct answer that you have not yet accepted, What factors determine the altitude at which rocket exhaust plumes start blooming hugely? Commented Jan 25, 2021 at 4:56