(I understand it's a particularly deep and difficult engineering problem to solve this in space: in zero-gravity, liquid fuels turn into bubbles floating around in nearly-empty fuel tanks—all sorts of phenomena going on).
Common axes they care about in rocket design are weight, cost in money, reliability/complexity, and lately reusability.
You do not want extra weight on your rocket. Every bit of non-fuel weight you add means you have to add extra fuel, and the extra fuel to carry the extra fuel along with any extra tank needed for the extra fuel. It gets bad fast.
It just isn't worth it when you can just add that weight as fuel that normally doesn't get used. Ideally would dump in the ocean (which you cleared) so it didn't matter (much).
> I sort of imagine a board with a spring on the top end of the canister
You are better off doing it with gas pressure instead of a spring, but yeah absolutely. Very good thinking.
Perihelions says it absolutely right. (Fitting nick name :))
There is a beautifull footage of the phenomenon from spacex: https://youtu.be/mVAGoWJuDKk?si=AkjH5hAm-dHC0V87
From 34s onwards it shows an internal view of the liquid oxygen tank. Just to better understand the picture the camera is inside the cylindrical tank. The viewpoint is facing backwards, so the camera is at the bulkhead closer to the tip of the rocket and it is looking “down” towards the engines. The blue “magical portal” is the surface of the liquid oxygen draining away rapidly by the rocket engines. And then suddenly there is main engine cutoff and the rocket is no longer pushed forward by the engines. That is when you see that the “magical portal” sloshes to the side and then breaks up into many floating bubbles. They float because the whole rocket, including the liquid oxygen is in free fall.
Why is this a hard problem? It is absolutely not a problem… unless you want to re-ignite the engine. (Which you might want to do to conduct further maneuvers) If you do that and don’t do anything special to shepherd the fuel to the pumps of the rocket engine they might not suck in a propellant bubble. If they don’t your engine fails to reignite. If the engine ignited, but then the pumps suck in a gas bubble they will break apart. So you absolutely have to coax the fuel to the intake before you try to reignite.
How do you do that? There are multiple strategies. At smaller scales you can try to have a flexible bladder. But at large rockets your best bet is to accelerate the rocket forward so all the propellant sloshes to the back and then you can ignite. Once the engine(s) are ignited you don’t have to worry about it anymore (that much) because the acceleration will keep the propellants bunched up at the aft bulkhead.
But if you need the engines to be ignited to accelerate, and you need to accelerate to ignite them then you have a circular dependency. How do you in theory solve this? You have some other mean of temporary propulsion. Either a cold gas truster, or a monopropellant rocket with a flexible blader, or a solid propellant engine. It doesn’t have to be powerfull, and it doesn’t have to push you for long. Just enough to collect the propellant while the main engines are reignited. These auxilary motors are frequently called ullage rockets.[1]
Now of course how long is long enough, and how much push you need is the black magic with the whole thing.
(And of course this has nothing to do with the pictured rockets. I don’t think those are reignitable.)
There's some diagrams and discussion here: https://exrocketman.blogspot.com/2021/08/propellant-ullage-p...
Edit: The tank isn't at vacuum. It started full of liquid oxygen. I assume (without researching) that the oxygen would change phase and fill the void with gas as the liquid is pumped out.
Overall, it's less of a problem in pump fed rockets, since the gas only has to pressurize the propellant up to the inlet pressure of the pumps, not above the pressure of the rocket thrust chamber as it would in tank pressure fed rockets.
1: this is not easy at all, they lost a rocket due to the helium bottle breaking free once: https://sma.nasa.gov/SignificantIncidents/assets/spacex-falc...
> wouldn't pulling a vacuum in the tank on the way up make it a lot harder to pump the liquid
It would make it impossible to pump. But that is not the only reason you need a pressurant. The tank wall is relatively thin. It would implode in the lower atmosphere if you would have vacuum in it.