Starship On-orbit refueling - Options and Discussion

[TheRadicalModerate]

I'm not sure where you propose to mount the thrusters on Depot and/or Tanker. On HLS, they are at the waist, which means you need to compute the cosine loss. This affects the computation of the thrust needed at the Moon, and may also affect the system fuel efficiency for the transfer. I would also guess that there are 24 of them (or some other even number), not 27, because balancing the thrust is simpler if you use opposing pairs.

Fair points, both of them.  And both of them increase the thrust needed per engine, which is bad for settling.  Too lazy to recompute.  Also, I was thinking you could mount a separate engine in the engine bay, but it would be off-axis.  You probably need pairs of them firing to get the thrust to go through the combined center of mass, so that makes things even worse (by at least a factor of 2).

This is really a pretty gnarly problem.

[TheRadicalModerate]

Conditions change throughout a transfer campaign. Geysering is more of a problem with the first propellant to enter a tank. Calls for low transfer rate or a high settling acceleration. At the end of the last topoff geysering shouldn't be an issue. A high transfer rate or low settling thrust, albeit with a heavy load, works well.

After thinking about it, geysering only happens on the receiving end.  That still makes it a problem for managing propellant blobs slamming into things and causing transient acceleration, but it shouldn't be a major cause of ullage farts.  (Team Pump notes that ullage farts aren't a problem, as long as your pumps are self-priming.)

The initial settling thrust needed to get all the props to the bottom end of the tank can be extremely low. The lower it is, the less slosh. Once the fluids are in the bottom higher acceleration will settle out bubbles and residual slosh faster.

But that's worse.  Long-term high acceleration is what chews up prop for settling.  If my numbers just up-thread are correct (and Dan points out that they're probably optimistic), then we have a real problem:  There's not enough ullage for cold-gas settling, and the amount of combusting-gas methalox you'd need pretty much dictates that you have to draw the prop straight from the mains, which limits the thrusters' chamber pressure to something like 4bar.  The Isp is still probably quite a bit better than cold gas, and you have more-or-less unlimited prop, unlike driving things off ullage cold gas, but your prop losses for settling are going to be substantial.

Once everything is where it needs to be and is settled down, the question of geysering and acceleration tradeoffs becomes prominent. There may also an issue of outlet vortex leading to pump cavitation in the delivering craft - if pumps are used. Settling and geysering will change for each transfer.

We're not talking huge amounts of power here, so I doubt that cavitation is going to be a problem.

Elon may not like another thruster design but it's too handy a tool to ignore. He may find a workaround today but chances are that someday a small thruster will save another workaround or even keep him from dropping a handy idea because it would take more development than it warrants.

I suspect that all designs whose justifications have the word "someday" in them are discarded--or at least filed until someday arrives.  However, I think that "someday" may be now.

Things would be a lot better if we had net transfer rates of about 500kg/s and we could settle at 0.1mm/sē.  But that almost certainly requires a smaller combusting gas thruster than the one used for lunar landings.

Edit to add: I think we have been ignoring something. We're dealing with two systems that can run in parallel - fuel and propellant oxidizer [FTFY]. Probably not a good idea if there's crew on board, but safe enough for routine ops?

Well, they're loading fuel and oxidizer simultaneously on the pad right now, and if they change that sequence for (eventual) crewed launches, the prop loaded first isn't going to be fully subcooled.

We've mostly been assuming that everything uses the same QD in space at is uses on the ground.  I don't see why the risk is much higher in space, but it's an area where failures of imagination are possible.

[InterestedEngineer]

the 100N to 1KN range is a really odd place for a methalox thruster.

let's pick the middle, say 500N.   For a cold gas thruster with Ve of 1000m/sec:  The mass flow rate is 0.5kg/sec and the kinetic energy rate is 250kW.  Typical efficiencies for all sorts of thrusters are 60% so that's 420kW input power.  That's outside the range of reasonable electrical supply for something that lasts more than a few minutes, so electrical evaporators to renew ullage, electrically heated gas thrusters, etc. are out of the question.   Something is going to have to burn.

The energy of combustion for methane is about 10MJ/kg, so the the methalox mass flow rate to get 420kW is .04kg/sec.  10x energy density by batteries, btw.

But 40 grams / second is a really small flow rate.  A landing thruster for a low grav body is going to have a mass flow rate of 100x that, nothing has that kind of throttling range.

I keep wondering if there's some sort of general need for a high amount of electrical power, and whether that can be done with a methalox generator at very low mass.  If one could generate a megawatt with a mass flow rate of 166 grams/sec and you could keep the ullage up without fuel contamination, or heat the exhaust for lower mass flow rate (or both), and generally keep all the batteries charged all the time. 

It's easier and more reliable to run electrical cables than pipes.  You don't have to worry about leaks mixing methane and lox together (but you do have to detect shorts and arcs, as one Starship found out on the test stand)

[Twark_Main]

Dozens of tonnes of wasted propellant?  In a real SpaceX engineering discussion, this would be the point where Elon Musk chimes in, "so why aren't we doing spin gravity again?"

The problems with linear thrust gravity are mathematically unavoidable. The problems with spin gravity are 'just' engineering. SpaceX never shied away from a challenge, especially if there's a big efficiency payoff at the other end (FFSC, chopstick landing, etc).

It seems the big concerns are rotational instability (solved by rotating about the primary axis), and maybe mass imbalance between ships (this could be solved by docking nose-to-nose or interstage-to-interstage, but I wonder if there's a more clever way    ).


What's that old saying that IE is always reminding us of...  "The requirements are probably wrong?" 

[rsdavis9]

Dozens of tonnes of wasted propellant?  In a real SpaceX engineering discussion, this would be the point where Elon Musk chimes in, "so why aren't we doing spin gravity again?"

The problems with linear thrust gravity are mathematically unavoidable. The problems with spin gravity are 'just' engineering. SpaceX never shied away from a challenge, especially if there's a big efficiency payoff at the other end (FFSC, chopstick landing, etc).

It seems the big concerns are rotational instability (solved by rotating about the primary axis), and maybe mass imbalance between ships (this could be solved by docking nose-to-nose or interstage-to-interstage, but I wonder if there's a more clever way    ).


What's that old saying that IE is always reminding us of...  "The requirements are probably wrong?" 

A hub that 3 or more ships "dock" to nose first. Always rotating "slowly". If you keep 3 ships always docked then it would be stable. Docking while rotating shouldn't be too hard.

I get 23 min per revolution for a 50m starship and .001m/s^2 at the bottom
2pi / sqrt(.001m/s^2 * 50m) = 1404s

[Narnianknight]

In a real SpaceX engineering discussion, this would be the point where Elon Musk chimes in, "so why aren't we doing spin gravity again?"

Apparently not...

During these upcoming Starship test flights, engineers will measure the slosh of propellants inside the ship, along with tank pressures, and observe how the fluids respond to impulses from small thrusters. In microgravity, these small rocket jets provide "settling thrust" to guide the ship's liquid toward the outflow needed for refueling.

[Twark_Main]

A hub that 3 or more ships "dock" to nose first. Always rotating "slowly". If you keep 3 ships always docked then it would be stable. Docking while rotating shouldn't be too hard.

As I said, you only need to rotate about the primary axis in order to achieve stability. There's no need for >2 ships to dock at once, or for rotation during docking.

I get 23 min per revolution for a 50m starship and .001m/s^2 at the bottom
2pi / sqrt(.001m/s^2 * 50m) = 1404s

I get similar numbers.

In a real SpaceX engineering discussion, this would be the point where Elon Musk chimes in, "so why aren't we doing spin gravity again?"

Apparently not...

During these upcoming Starship test flights, engineers will measure the slosh of propellants inside the ship, along with tank pressures, and observe how the fluids respond to impulses from small thrusters. In microgravity, these small rocket jets provide "settling thrust" to guide the ship's liquid toward the outflow needed for refueling.

"End of history" bias. Who says SpaceX is done making iterative changes as they learn? Certainly SpaceX doesn't ever say that, that's for sure... 

Who says SpaceX doesn't go down the wrong path (CFRP fuselage) before eventually correcting?  Certainly SpaceX doesn't say that.

On occasion this forum has been "ahead of the curve" on certain ideas. As IE likes to say, let's try it and see what happens. 

[TheRadicalModerate]

Dozens of tonnes of wasted propellant?  In a real SpaceX engineering discussion, this would be the point where Elon Musk chimes in, "so why aren't we doing spin gravity again?"

The problems with linear thrust gravity are mathematically unavoidable. The problems with spin gravity are 'just' engineering. SpaceX never shied away from a challenge, especially if there's a big efficiency payoff at the other end (FFSC, chopstick landing, etc).

It seems the big concerns are rotational instability (solved by rotating about the primary axis), and maybe mass imbalance between ships (this could be solved by docking nose-to-nose or interstage-to-interstage, but I wonder if there's a more clever way    ).


What's that old saying that IE is always reminding us of...  "The requirements are probably wrong?" 

Nose-to-nose spin gravity involves an awful lot of re-plumbing, and long paths where the prop can pick up heat.  Beyond that, it's hard to figure out what the primary axis would be, and it'll change as the depot gets fuller.

One thing we haven't talked a lot about (or a least not in the last 50 pages) is propellant management devices.  If you put PMDs down near the sump, they may be able to hold a sufficient bolus of prop that you could switch to intermittent settling.  That would effectively replenish the bolus around the PMD, and you'd dramatically reduce the total impulse you spent on settling.

[Twark_Main]

Dozens of tonnes of wasted propellant?  In a real SpaceX engineering discussion, this would be the point where Elon Musk chimes in, "so why aren't we doing spin gravity again?"

The problems with linear thrust gravity are mathematically unavoidable. The problems with spin gravity are 'just' engineering. SpaceX never shied away from a challenge, especially if there's a big efficiency payoff at the other end (FFSC, chopstick landing, etc).

It seems the big concerns are rotational instability (solved by rotating about the primary axis), and maybe mass imbalance between ships (this could be solved by docking nose-to-nose or interstage-to-interstage, but I wonder if there's a more clever way    ).


What's that old saying that IE is always reminding us of...  "The requirements are probably wrong?" 

Nose-to-nose spin gravity involves an awful lot of re-plumbing, and long paths where the prop can pick up heat.

Then it's a good thing I gave two other options.

Personally, nose-to-nose is my least favorite of the ones I mentioned, but I wanted to get the obvious (and IMO less desirable) configurations out of the way.

Beyond that, it's hard to figure out what the primary axis would be, and it'll change as the depot gets fuller.

The primary axis will be with the depot and ships both tumbling "end over end," with both ships in a plane perpendicular to the spin axis. This gets the most mass out furthest from the axis. It doesn't change as the depot gets full.

[OTV Booster]

Conditions change throughout a transfer campaign. Geysering is more of a problem with the first propellant to enter a tank. Calls for low transfer rate or a high settling acceleration. At the end of the last topoff geysering shouldn't be an issue. A high transfer rate or low settling thrust, albeit with a heavy load, works well.

After thinking about it, geysering only happens on the receiving end.  That still makes it a problem for managing propellant blobs slamming into things and causing transient acceleration, but it shouldn't be a major cause of ullage farts.  (Team Pump notes that ullage farts aren't a problem, as long as your pumps are self-priming.)

The initial settling thrust needed to get all the props to the bottom end of the tank can be extremely low. The lower it is, the less slosh. Once the fluids are in the bottom higher acceleration will settle out bubbles and residual slosh faster.

But that's worse.  Long-term high acceleration is what chews up prop for settling.  If my numbers just up-thread are correct (and Dan points out that they're probably optimistic), then we have a real problem:  There's not enough ullage for cold-gas settling, and the amount of combusting-gas methalox you'd need pretty much dictates that you have to draw the prop straight from the mains, which limits the thrusters' chamber pressure to something like 4bar.  The Isp is still probably quite a bit better than cold gas, and you have more-or-less unlimited prop, unlike driving things off ullage cold gas, but your prop losses for settling are going to be substantial.

Once everything is where it needs to be and is settled down, the question of geysering and acceleration tradeoffs becomes prominent. There may also an issue of outlet vortex leading to pump cavitation in the delivering craft - if pumps are used. Settling and geysering will change for each transfer.

We're not talking huge amounts of power here, so I doubt that cavitation is going to be a problem.

Elon may not like another thruster design but it's too handy a tool to ignore. He may find a workaround today but chances are that someday a small thruster will save another workaround or even keep him from dropping a handy idea because it would take more development than it warrants.

I suspect that all designs whose justifications have the word "someday" in them are discarded--or at least filed until someday arrives.  However, I think that "someday" may be now.

Things would be a lot better if we had net transfer rates of about 500kg/s and we could settle at 0.1mm/sē.  But that almost certainly requires a smaller combusting gas thruster than the one used for lunar landings.

Edit to add: I think we have been ignoring something. We're dealing with two systems that can run in parallel - fuel and propellant oxidizer [FTFY]. Probably not a good idea if there's crew on board, but safe enough for routine ops?

Well, they're loading fuel and oxidizer simultaneously on the pad right now, and if they change that sequence for (eventual) crewed launches, the prop loaded first isn't going to be fully subcooled.

We've mostly been assuming that everything uses the same QD in space at is uses on the ground.  I don't see why the risk is much higher in space, but it's an area where failures of imagination are possible.

Thanks for pointing out where I got my tang tungled. I'll fix it.

IIRC, the biggest complaint about geysering was back when we were discussing connecting the ullage spaces. It was feared that geysering would pass propellent back to the originating ship. Maybe it's no big deal after all but I've got to admit that props slamming around doesn't feel like a good idea. Just a gut reaction.

That 'someday' about small thrusters was for the second time they'd be handy. As you say, 'someday' may be today. And following general SX preferences, maybe a very small thruster set in clusters to give a wide range of thrust without impossible throttling.

If Depot is stripped down to 3 Vacs and one SL, there'd be a lot of engine bay space available for small engine clusters. Gimbaling or off center clusters would make off axis thrust available to compensate for changing tanker/depot mass. The tanker might need lateral thrusters up high for that first load or two when the ship masses are near parity but not so much when the depot mass dominates. To be most effective these tanker thrusters would need to fire through the heat tiles, but if ever there was a place where a cooling gas bleed was simple to implement, this would be it. 

ISTM that unless the depot has active cooling we can depend on props eventually being near boiling, and that subcooled's big advantage is for fighting through earth gravity loss. It does effectively increase storage capacity but I expect it's going to end up near boiling by the time the depot is full, no matter what.

[Paul451]

Beyond that, it's hard to figure out what the primary axis would be, and it'll change as the depot gets fuller.

The primary axis will be with the depot and ships both tumbling "end over end," with both ships in a plane perpendicular to the spin axis. This gets the most mass out furthest from the axis. It doesn't change as the depot gets full.

The centre of rotation changes as propellant is transferred. Empty depot / first tanker CoM is going to be significantly different to full depot / empty HLS CoM. The propellant load is 5-6 times the combined dry-mass of the two ships. So effectively, the centre of current-propellant-location is the CoM of the whole system at any time. That'll start in the middle of the first tanker, and move over to the middle of the depot with each successive tanker, then back to the middle of the HLS during the last transfer.

Additionally, there's not a lot of additional mass in the rotational plane (only the flaps), so the short and intermediate axes are almost identical, making the rotation unstable. It might be solvable, by adding more systems in the rotational plane, external to the depot-ship mould-line, but it's not a minor handwavy issue that can be ignored when comparing options. Any solution will cause issues that propagate through the design and operations.

OTOH, a dozen tonnes of prop for transfer burns is 10% of the prop-mass for the tanker. So you need 10% more tankers. Ie, not quite one. Two dozen tonnes-per-transfer is one-and-a-bit extra tankers.

One or two extra tankers, or a complex AG design?


IMO, if you have a long duration (multi-decade, multi-customer) depot, servicing multiple missions per year, then I think developing an AG depot makes sense. Where the depot is significantly different from the tankers that service it. Whereas for an early design, a one-depot/one-mission fuel-and-go architecture, I'm not seeing any advantage worth the cost.

[OTV Booster]

the 100N to 1KN range is a really odd place for a methalox thruster.

let's pick the middle, say 500N.   For a cold gas thruster with Ve of 1000m/sec:  The mass flow rate is 0.5kg/sec and the kinetic energy rate is 250kW.  Typical efficiencies for all sorts of thrusters are 60% so that's 420kW input power.  That's outside the range of reasonable electrical supply for something that lasts more than a few minutes, so electrical evaporators to renew ullage, electrically heated gas thrusters, etc. are out of the question.   Something is going to have to burn.

The energy of combustion for methane is about 10MJ/kg, so the the methalox mass flow rate to get 420kW is .04kg/sec.  10x energy density by batteries, btw.

But 40 grams / second is a really small flow rate.  A landing thruster for a low grav body is going to have a mass flow rate of 100x that, nothing has that kind of throttling range.

I keep wondering if there's some sort of general need for a high amount of electrical power, and whether that can be done with a methalox generator at very low mass.  If one could generate a megawatt with a mass flow rate of 166 grams/sec and you could keep the ullage up without fuel contamination, or heat the exhaust for lower mass flow rate (or both), and generally keep all the batteries charged all the time. 

It's easier and more reliable to run electrical cables than pipes.  You don't have to worry about leaks mixing methane and lox together (but you do have to detect shorts and arcs, as one Starship found out on the test stand)

The tanker will most probably have batteries only capable of general ops but consensus points to the depot sporting all the special hardware necessary for transfer ops. It'll have PV, the QD is designed to transfer current, and it'll have loiter time between tankers to charge up a large bank of batteries to vaporize propellant. Would this be practical? IDK.


Might we be near the point where some sort of high ISP electric propulsion starts making sense? It's another gas to handle. Bummer. Maybe an extra QD outlet so the tankers can keep the depot topped up with xenon? Sounds too messy.

[Twark_Main]

IIRC, the biggest complaint about geysering was back when we were discussing connecting the ullage spaces. It was feared that geysering would pass propellent back to the originating ship. Maybe it's no big deal after all but I've got to admit that props slamming around doesn't feel like a good idea. Just a gut reaction.

I'm not sure how instead venting that liquid propellant is any better. It seems like it would be worse, in fact.

Is there some device that makes sure that only gas can pass through? If such a device exists, it seems like it could solve the problem in both cases.

[Twark_Main]

Beyond that, it's hard to figure out what the primary axis would be, and it'll change as the depot gets fuller.

The primary axis will be with the depot and ships both tumbling "end over end," with both ships in a plane perpendicular to the spin axis. This gets the most mass out furthest from the axis. It doesn't change as the depot gets full.

The centre of rotation changes as propellant is transferred. Empty depot / first tanker CoM is going to be significantly different to full depot / empty HLS CoM.

Yep.  So?

Moving the center-of-mass doesn't change the primary axis, or induce rotational instability, or shift where the propellant "pools." I'm not seeing a problem.

The propellant load is 5-6 times the combined dry-mass of the two ships. So effectively, the centre of current-propellant-location is the CoM of the whole system at any time. That'll start in the middle of the first tanker, and move over to the middle of the depot with each successive tanker, then back to the middle of the HLS during the last transfer.

I agree, in broad strokes.

There's no real need to simplify this by neglecting the dry masses. It's not that complicated. When you take the dry masses into account it reduces the CoM shift somewhat from what you said, but I'm not picky.   

Additionally, there's not a lot of additional mass in the rotational plane (only the flaps), so the short and intermediate axes are almost identical, making the rotation unstable.

I think you're confused. Maybe it's because you neglected the dry mass above?  When you also account for the dry masses (and their being off-axis from the CoM, see the parallel axis theorem), you find it dwarfs the contribution of having one set of body flaps sticking out-of-plane.

OTOH, a dozen tonnes of prop for transfer burns is 10% of the prop-mass for the tanker. So you need 10% more tankers. Ie, not quite one. Two dozen tonnes-per-transfer is one-and-a-bit extra tankers.

SpaceX won by playing a game of pennies. As many commentators have pointed out, they were the cheapest provider even before reusability.

SpaceX didn't make all the cost-optimal decisions up until now just so you can make wasteful decisions today. Ample history has shown that, yes Virginia, SpaceX will optimize cost in [present topic] too. 

You seem to believe SpaceX's cost progress is "good enough" right now, so they should rest on their laurels from here on. Whereas in reality, SpaceX is continuing their campaign of slowly and incrementally whittling down the orders-of-magnitude on the cost to Mars. By their own admission, they still have a long way to go.

One or two extra tankers, or a complex AG design?

10% is a huge performance hit — equivalent to hot staging! — and nobody is proposing a "complex" design. 

Just use that same thruster impulse "in a circle" and you get effectively unlimited ullage duration. It's quite a good trick!  For a laugh, it's easy to work out how many minutes of 1 milli-g thrust you need to induce a 1 milli-g rotation. You might be surprised at the answer!



With that newly-calculated number fresh in your mind, cast your cortex back to...


Akin Law #26  (Montemerlo's Law):  "Don't do nuthin' dumb."   


FFSC is the optimal combustion cycle, because physics. Hot staging is the optimal method of staging, because physics. Rotational ullage is the optimal (long-duration) ullage, because physics.  Starting to detect a pattern here...

[Paul451]

The centre of rotation changes as propellant is transferred. Empty depot / first tanker CoM is going to be significantly different to full depot / empty HLS CoM.

Yep.  So?
Moving the center-of-mass doesn't change the primary axis, or induce rotational instability, or shift where the propellant "pools."

Incorrect. The bottom tanks will change which end they pool, as the CoM shifts from one ship to the other.

Additionally, there's not a lot of additional mass in the rotational plane (only the flaps), so the short and intermediate axes are almost identical, making the rotation unstable.

I think you're confused. Maybe it's because you neglected the dry mass above?  When you also account for the dry masses (and their being off-axis from the CoM, see the parallel axis theorem), you find it dwarfs the contribution of having one set of body flaps sticking out-of-plane.

You propose docking two ships together in a line, and spinning them end over end.

There are three axes. One long axis down the length of both ships, and two nearly identical short axes.

You propose to rotate the pair around one of the two nearly identical short axes.

But because the two short axes are nearly identical, they are not stable.

It's possible to increase stability by putting more mass perpendicular to the axis of rotation, but that's a significant design change.

[meekGee]

Hey I lost track of the conversation.

When we're talking about accelerations, is the intent to transfer fuel using the inertial pressure head, or is the intent to just use it to ensure settling, and then pressurise the gas on top to motivate the fuel transfer? (Pressurize by burning or just solar heat input)

Looks to me like orders of magnitude difference in the required acceleration.

--

Irrespective of the fuel transfer scheme, I think docking would be a giant challenge, given that the fuel is loose and is much heavier than the  vessels.

The only way I see to dock is to accelerate both ships slowly while in formation and once the fuel is settled match speeds (while still accelerating!) and do the final docking burns.

[Twark_Main]

When we're talking about accelerations, is the intent to transfer fuel using the inertial pressure head, or is the intent to just use it to ensure settling

The second one. Team "pump" all the way. 

You propose docking two ships together in a line, and spinning them end over end.

I actually envision dorsal-to-dorsal docking, the same as existing renders.

[Paul451]

You propose docking two ships together in a line, and spinning them end over end.

I actually envision dorsal-to-dorsal docking, the same as existing renders.

You mentioned "nose-to-nose or interstage-to-interstage", and "spinning end-over-end". If you meant something else, you should have been clearer, we can't read your mind.

If you mean side-mount and "spinning end-over-end", then you are rotating around the intermediate axis and it is instantly unstable.

If you mean side-mount and spinning flat like a frisbee, then you have massively altered the way the propellant will settle, and it makes the CoM issue vastly worse. The complexity of this configuration makes other suggestions look like child's play.

If you mean something else, you should explain.

[meekGee]

When we're talking about accelerations, is the intent to transfer fuel using the inertial pressure head, or is the intent to just use it to ensure settling

The second one. Team "pump" all the way. 

Once stable, I think you don't need to continue acceleration, since surface tension will want to keep the boundary layer perpendicular to the ship axis (for minimal surface area) - unless disturbed by slosh in the depot.

Disturbances will cause waves, and if waves start to break, that's where trouble starts.  So have to flow slow.

[TheRadicalModerate]

If you mean side-mount and "spinning end-over-end", then you are rotating around the intermediate axis and it is instantly unstable.

If you mean side-mount and spinning flat like a frisbee, then you have massively altered the way the propellant will settle, and it makes the CoM issue vastly worse. The complexity of this configuration makes other suggestions look like child's play.

I assume by "side-mount", you mean dorsal-to-dorsal with noses pointed in the same direction, as in the artwork?

Another issue to consider:  As prop moves from one to the other, the CoMs of the individual ships will move, which will put shear stresses on the docking mechanisms.  I think this also tilts the axis (really axes) of inertia, which makes the rotational instability question soooooo much more complicated.

Since nobody picked up on it, I'm gonna pound the table on prop management devices down in the sumps.  If you can get and maintain a decent-sized blob of prop around the inlet, then you might be able to pump- or pressure-feed prop at exactly zero hydrostatic pressure, i.e., with no acceleration at all.

That may leave blobs of prop floating around in the main, but as long as you can occasionally nudge one or two of them into contact with the PMDs without too much splashing, you should be able to maintain a constant flow.  That would mean that you only need very small, highly intermittent settling accelerations, which would reduce the total impulse (and prop to provide that impulse) to a very small number.

That might put cold-gas thrusters back on the table.