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I uploaded a picture below explaining over-expanded flow/nozzle condition with regards to thrust.

This aviation source tells that “extra nozzle walls don’t generate any additional thrust because flow detaches from inner walls of nozzle (in other words, flow losses contact to inner walls of nozzle)”.

Does it mean that velocity of flow when flow pressure matches ambient pressure a distance back from nozzle exit must be taken for thrust equation? In general, we calculate thrust based on exit velocity but here why don’t we do it?

I asked Artifical Intelligence this question and it says: “Even after flow pressure matches ambient pressure, flow velocity still increases resulting in thrust increase. So, we should still take exit velocity, not velocity when flow pressure matches ambient pressure”.

I’m confused. What is your answer?

enter image description here

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  • $\begingroup$ It may be (with further studies) things will become more clear. Remember, that flow acceleration from the combustion chamber is greatest at the "throat" of the exit from the chamber, not the end of the nozzle. The "bell" is a pressure recovery device. Your rocket will still have thrust without one, but Isp will be lower. $\endgroup$ May 14, 2023 at 9:46
  • $\begingroup$ Quite sure you'll get a better answer on Space Stackexchange $\endgroup$
    – sophit
    May 14, 2023 at 12:14
  • $\begingroup$ Yea, and i wonder if there may be a second (aerodynamic) "throat" , so maybe (theoretically) the flow could expand until it is subsonic. All that balanced against weight. $\endgroup$ May 14, 2023 at 15:19

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The flow exerts force on the engine by pressurizing the walls. If the flow detaches from the wall, it cannot exert force on the engine bell. Instead the atmosphere exerts pressure on this section, resulting in net 0 forrward force. The extra nozzle wall is unnecessary weight, therefore decreasing efficiency.

Does it mean that velocity of flow when flow pressure matches ambient pressure a distance back from nozzle exit must be taken for thrust equation?

Yes, as it does not accelerate anymore.

Is contact between flow and inner walls of nozzle required for thrust generation?

In this sense, yes.

However note that the reason for the detachment is overextension of the flow.

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On a direct physical level, thrust is produced in the nozzle through higher-than-ambient pressure acting on nozzle walls from the inside. Ambient pressure acts on both sides of the surface equally.

Separated flow produces no or little thrust or lift. This is how airplanes stall - when flow separates from their wings.

In rocketry, it's common to describe propulsive efficiency through exhaust gas velocity. It works, but Newtons' third law only applies to the interacting parts of the system. Eventually, any rocket's exhaust will slow down to zero - that doesn't make their Isp zero!

This is also confirmed by practice. Nozzles designed for vacuum are larger than atmospheric nozzles. The same rocket always produces more thrust in vacuum than in the atmosphere.

P.S.: Do NOT ask Large Language Models questions that require deep technical knowledge. They don't have it. It's like a young kid that has read a lot of books - they can occasionally cite true facts, but as easily cite or invent fiction, and lack the wisdom to tell one from the other.

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  • $\begingroup$ So do you mean that thrust is generated until flow pressure matches ambient pressure a distance back from nozzle exit, and there is no thrust produced after flow detaches from nozzle walls resulting in loss of contact? $\endgroup$
    – Jawel7
    May 13, 2023 at 20:55
  • $\begingroup$ It depends on how you model things. But the physical interaction that produces the thrust force depends on a pressure difference between the inside and the outside of the nozzle. $\endgroup$
    – Therac
    May 13, 2023 at 21:06
  • $\begingroup$ Essentially, thrust comes from above-ambient pressure, and flow separation occurs when the exhaust gas is below ambient. Incidentally, this is something to avoid as it tends to result in severe vibration and can damage the bell. From a thrust point of view though, separation can be seen as a good thing because the lower-than-ambient gas pressure would actually reduce thrust. $\endgroup$
    – Frog
    May 13, 2023 at 21:18
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There is one obvious fact about rockets. They are generally (but not always) made for vertical flight. In other words, they launch at ground level pressure and fly to space.

with a vertical flight path, if flow is overexpanded at launch, it won't be for long.

Rockets are heaviest at launch. Best to have maximum nozzle efficiency here, and underexpand when the rocket is lighter.

staging can allow for more suitable "vacuum nozzles" at higher altitudes

Remember, a nozzle is designed to improve propulsive efficiency. This must be balanced with the weight penalty of a larger bell.

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