How Do I Make a Grossly Overexpanded Rocket Nozzle Exhaust Jet Stable?

[nitronewt]

I have a question regarding the design of rocket nozzles. I am not an engineer nor a physicist but I am involved in amateur experimental rocketry and I was curious regarding grossly overexpanded nozzles.

According to Wikipedia a grossly overexpanded rocket nozzle (very bottom of the above image) burns more efficiently but the exhaust jet is not stable. I would assume that is because in the case of a grossly overexpanded nozzle, the jet flows more freely but maintaining pressurization within the motor casing and thus creating an even burn rate becomes a problem. I might be fundamentally wrong on this assumption, but, assuming the above is correct, theoretically couldn't you make a nozzle that converges on the throat, diverges into gross overexpansion, and then releases into a sort of second nozzle. I guess I'm thinking like a two-stage nozzle that will capture the efficiency of gross overexpansion, but fix the problem of engine pressurization and unstable exhaust jet.

Please feel free to correct any and all misconceptions above.

 

[boneh3ad]

Where is the source that says that a grossly underexpanded nozzle is the most efficient? I have never heard of that and it seems quite counter-intuitive given that it means that the nozzle is unstarted and will likely have a subsonic exhaust.

 

[nitronewt]

According to the Wikipedia article, it cites this as the source

Huzel, D. K. and Huang, D. H. (1971). NASA SP-125, Design of Liquid Propellant Rocket Engines (2nd Edition ed.). NASA.Technical report

 

[nitronewt]

Found it - here it is http://ntrs.nasa.gov/search.jsp?R=19710019929

 

[boneh3ad]

Well I've browsed a bit but haven't found anywhere it would say that yet. Generally, though, if the nozzle is started, there is no information about the flow downstream of the throat that can propagate upstream to affect the combustion occurring in the combustion chamber. Basically, information in a fluid propagates as sound waves, and since the flow downstream of the throat is supersonic, whether the flow is underexpanded, overexpaned or operating at condition has no effect on anything upstream since disturbances emitted in that region can't move faster than the air is already moving downstream. So, in other words, I find it quite hard to believe that combustion efficiency would be higher for a grossly overexpanded nozzle.

Regarding stabilizing the jet, the problem is that the unstable jet results from unstead flow separation, and that would be extraordinarily difficult to control. It depends on so many parameters that you would need to find some way to fix the location, and the only way this is typically done for a turbulent flow such as this is through protrusions in the flow that create a local pressure gradient that separates the boundary layer (for example the spoiler on the Audi TT). The problem is that thin, sharp features in a flow like this would quickly ablate away.

 

[cjl]

I suspect that the author means that the grossly overexpanded nozzle is more efficient relative to the overexpanded nozzle that still has attached flow (since in effect, the flow detaching from the nozzle walls serves to decrease the effective expansion ratio). It definitely won't be more efficient than an ideally expanded nozzle though.

 

[boneh3ad]

Sure it will decrease the effective expansion ratio, but then you will end up with a slower exhaust jet, which would certainly seem counterproductive here since the overall mass flow is still staying the same.

 

[cjl]

Sure it will decrease the effective expansion ratio, but then you will end up with a slower exhaust jet, which would certainly seem counterproductive here since the overall mass flow is still staying the same.

Sure, but you'll also end up with a higher net thrust, since the slower exhaust jet will be more than offset by the fact that you don't have an enormously negative pressure thrust term (due to the extremely low pressure across the nozzle).