How does the efficiency of the rocket engine using liquid propellants depend on the throttling setting? (Is it more or less efficient while working on eg.: 85% of its maximum thrust?). The rocket engine is in vacuum.
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$\begingroup$ I don't quite understand your question. Are you asking whether the throttle setting on a rocket engine (i.e. whether it's operating at 100%, 90%, 80% of its maximum thrust) affects the engine's efficiency? Also, keep in mind that most large rocket engines can be throttled very little (if at all). $\endgroup$– LightsiderSep 29, 2015 at 7:29
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1$\begingroup$ Are you asking about rockets being launched from earth or already in space? $\endgroup$– GdDSep 29, 2015 at 8:19
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$\begingroup$ ".. for rocket engines to work for a long time with very low power?" Perhaps you are thinking of Ion drives and similar. They produce only a small push, but for the mass of fuel, provide a greater end speed. They are good for objects already in orbit, but useless for escaping from the surface of any body that has a higher rate of surface gravitation than the drive can lift against (the craft never rises off the ground). $\endgroup$– Andrew ThompsonSep 29, 2015 at 10:42
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$\begingroup$ Re your edit, you'll still have to specify what type of engine do you have in mind. Otherwise, I'm afraid your question is still too broad / unclear. Cheers! $\endgroup$– TildalWaveSep 29, 2015 at 14:01
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1$\begingroup$ wedelfach, I re-edited your question and voted to re-open it. Now it doesn't depend on ballistics. $\endgroup$– Deer HunterSep 30, 2015 at 8:33
2 Answers
Corroborating Russell Borogove's answer, some Stennis test data I have from 1987 on three different SSMEs shows a small drop in Isp with power level. From 109% to 100% the Isp dropped about 0.08%. I can't find data at lower power levels but my recollection is that the trend continued, with a small degradation in Isp as you throttled down.
For reference, the original SSME could throttle from 109% to 65% of Reference Power Level. A "bi-stable turbopump anomaly" limited the lower end of the throttle range to 67% in the latter part of the program. The throttle range actually experienced in flight was from 65% to 104.5%.
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1$\begingroup$ "Historically, some of the issues experienced by the SSME during throttled conditions include nozzle flow separation, side loads and heat loads; preburner boost pump bistability (around 50% RPL); HPOTP preburner vane diffuser stall (prior to Block II upgrade); and HPFTP boilout (stall) at very low (dwell) mixture ratios. The SSME did not exhibit unstable combustion characteristics even at power levels as low as 17%." ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20100033271.pdf $\endgroup$ Sep 30, 2015 at 16:17
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$\begingroup$ I forget the details, but there was a crazy test stand anomaly where an SSME got down to around 30%. I never heard of the 17%, wow. $\endgroup$ Sep 30, 2015 at 16:19
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$\begingroup$ Yeah, sounds like a lot of different things outside of the injector and chamber would need to change to make it reliably throttle that low, though. $\endgroup$ Sep 30, 2015 at 16:21
It's surprisingly difficult to find a good answer to this question.
Generally, the rated full power level is where the engine is going to be most efficient.
According to Sutton's "Rocket Propulsion Elements", typical deep-throttling engines suffer between 1.5% and 9% reduction in specific impulse (fuel efficiency) at low power levels. It mentions an outlier, the engine in the Lance missile, which has an extraordinary 357:1 throttle range with 15% loss at the low end.
I found a poorly labeled and confusing graph that suggests that the CECE upper stage engine suffers about 5% when throttled far down.
The Apollo Lunar Module Descent Engine is upwards of 97% efficient at 30% throttle.
If you cared to, you could design an "afterburning" rocket engine, dumping extra fuel or oxidizer (or any other working fluid, for that matter) into the nozzle; this would give you a big thrust boost, cooler (and possibly dirtier) exhaust, and a large loss in efficiency. Thus power could be increased beyond the point of peak efficiency.
(Apparently AJR has patented a variation on this, injecting both fuel and oxidizer into the nozzle -- effectively using the upper part of the nozzle as combustion chamber, for a more appropriate expansion ratio at sea level, apparently?)
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$\begingroup$ Does it explains where does the loss of efficiency comes from ? For exemple with a cryogenic rocket, one must exacerbate fuel evaporation if he don't use it quickly enough $\endgroup$– AntziSep 30, 2015 at 15:59
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$\begingroup$ Lower chamber pressure and unsteady combustion, mainly. Cryogenic boil off doesn't factor in; ascent engines need moderate throttling at most and finish their work in minutes; descent engines need to hold their fuel for days or weeks depending on where they're descending to. $\endgroup$ Sep 30, 2015 at 16:05