I know that there's a difference between SpaceX's Falcon 9 1st stage engines and the 2nd stage engine, since that stage is specifically tuned for vacuum. Wikipedia also says that the Merlin Vacuum Engine is larger than the standard Merlin 1D. That got me thinking... are there more differences?
What are the differences between the first stage Merlin engines and the second stage Merlin vacuum engine? (I'm especially interested in size comparison, efficiency, thrust, etc.)
The biggest difference is the nozzle. For optimal performance in vacuum, you want a much larger one.
According to Spaceflight 101, the chamber pressure is the same, but the expansion ratio (throat area to end-of-nozzle area) is 7 times larger in the vacuum variant, which (if correct) implies about 2.7 times the nozzle diameter if the throat is unchanged.
The Wikipedia description of the 1C-vacuum says the expansion nozzle length is 2.7 meters, while the overall length of the first-stage 1C is only 2.9 meters long - roughly half of that being nozzle. So the nozzle length is basically doubled. Presumably the relationship between the 1D and 1D vacuum is analogous.
This pic is said to be, left to right: Falcon 1 Merlin 1C, Falcon 9 1C (different mounting), and Falcon 9 2nd stage 1C vacuum -- without the extension nozzle, so it's a shorter, fatter nozzle than the others.
And here's what the extension nozzle looks like by itself:
Since the Falcon 9 second stage mounts a single engine, in the same diameter body as the first stage (with its cluster of 9), there's plenty of room for the large nozzle.
This reddit thread includes some inconclusive debate about how much different the vacuum engines actually are. There are certainly differences in mounting and layout (most obviously the gas generator exhaust nozzle is canted further out to avoid impinging on the nozzle extension), but the turbopumps etc. are apparently the same.
According to the October 2015 revision of the Falcon 9 user's guide, the 1D Vacuum has a much deeper throttling capability than the first-stage engine, down to about 40% of maximum thrust (360kN-934kN). It's unclear what the reason for the throttling difference is; it could be that the engine is susceptible to exhaust flow separation at low thrust settings into high ambient air pressure.
There are several reasons for having deep throttling in the vacuum engine but not the first stage engine.
(1) The first stage cannot use a large expansion bell, and couldn't even if the mechanicals allowed it, because the exhaust flow would separate from the bell. This would cause flow instability/backflow/... that would likely destroy or damage the bell, or worse. Any rocket bell's outflow pressure should match the ambient atmospheric pressure for maximum efficiency. (This does mean that any traditional rocket nozzle with best efficiency at sea level is less efficient at all higher altitudes.)
(2) The first stage only needs to throttle down slightly near the end of its burn to limit payload acceleration to five or six g (I forget... 6 I think). Even without throttling, this could be accomplished by shutting down engines.
(3) The second stage needs to throttle down much more and earlier (percentage-wise; the burn is considerably longer) to limit payload g forces. For lighter payloads, it has to throttle down even more and earlier. Because the engine is firing in empty space, there's no limit to the size of the nozzle or concern about flow separation.
The main object of any rocket engine is to give the highest impulse to the rocket. mv(rocket)=mv(fuel) so for a given mass of fuel you want the maximum velocity possible. The larger nozzle divergence bell makes the better use of the vacuum to reach the highest possible velocity.
