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As we know that for the upper stages of the rocket, we need high propulsion efficiency thereby high specific impulse. For that we employ a nozzle with higher expansion ratios.

Now, if we conduct the static tests of such nozzles at sea-level, it will result into an over-expanded plume.

So, how so we get the details of upper-stage engines accurately?

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You need a massive facility that can maintain a near vacuum while dealing with the engine exhaust. There are (were) a couple in the US.

enter image description here

(picture from this informative paper)

These facilities typically use steam ejector systems to keep the test cell pumped down in the presence of huge amounts of exhaust entering it.

enter image description here

Note: these facilities typically don't claim to produce pure vacuum conditions. Commonly they advertise 100,000 ft (~30 km) altitude conditions (~ 0.2 psi or ~ 0.0014 MPa)

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    $\begingroup$ Wow, this is extreme. Are there any such sites in the former Soviet Union or in Europe? I guess there should be one in Europe, for the development of the Vinci engine. $\endgroup$
    – Everyday Astronaut
    Jul 29, 2019 at 10:53
  • $\begingroup$ Good question, I don't know. I would imagine the Soviets had one. They are expensive to maintain and not used a lot; reading between the lines it seems Plum Brook is falling into disrepair. $\endgroup$
    – Organic Marble
    Jul 29, 2019 at 10:56
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    $\begingroup$ @EverydayAstronaut I would conjecture that nowadays these facilities aren't as important anymore, since there are much better fluid-dynamics simulations available. They give pretty reliable predictions of how the flow in the engine bell will behave. Real tests are still indispendable for the nitty-gritty narrow pipes and certainly for turbopumps, but those operate at such high pressure that I'd expect sea-level vs. vacuum won't make much difference. So, I wouldn't be surprised if most of the development of the Vinci is done without vacuum nozzle, and only a few such tests outsourced to the US. $\endgroup$
    – leftaroundabout
    Jul 29, 2019 at 12:26
  • $\begingroup$ The Plum Brook station is limited to engines of 10,000 lbf thrust for a few seconds. The J-2 engine of Saturn V second and third stage had a vacuum thrust of 232,250 lbf. $\endgroup$
    – Uwe
    Jul 29, 2019 at 15:31
  • $\begingroup$ @Uwe when Plum Brook was fully working " Rocket engines producing up to 100,000 lbf thrust may be run for durations up to 270 seconds with the LOX/LH2 propellant combination. " As I stated in an earlier comment, I don't think the facility has been well maintained. $\endgroup$
    – Organic Marble
    Jul 29, 2019 at 15:54

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