Starship On-orbit refueling - Options and Discussion

[DanClemmensen]

We therefore need
      e = 1,815,000kg *  100 m * 0.005m/s².
         = 907,500 Joules
for each spin-up and each spin-down. I have no idea how to convert this into expended propellant.

OK, I did all the elaborate math, and then realized there is a simpler way to think about this to get to the same number. Consider two masses at relative rest. These masses then accelerate on antiparallel courses to reach relative velocities that equal their tangential velocities in the tether system, and they then (conceptually) grab the ends of the tether. This is NOT how the system works in practice, but it consumes the same amount of energy This mathematically converts the energy problem into a delta-V problem. The tangential velocities in the tether system are tiny. For a 100 m radius at .42 rpm (.00707 rps) the tangential velocity is 628 m * .00707/s =  4.44 m/s.

For equal masses, multiply by 2 to get the total energy. I conclude that spin-up and spin-down use much less propellant than the RMOD needed to hook the tanker to the depot.

Because we are now using delta-V, we can easily evaluate the mass expenditure in the usual way.

[TheRadicalModerate]

This looks like an upper limit on a dry receiving tank. Once the fluid depth reaches ~one inlet diameter it can pump a bit harder and let viscosity damp geysering. Given the consumption numbers we're seeing for settling, the transfer time looks critical.

That's correct.  However, the "duh!" moment I had was realizing that, for any flow rate, there's a pump power that results in that flow arriving at ambient pressure.

FWIW, I'm building a transfer power worksheet into the prop expenditure worksheet.  The current powers are so low (single-digit watts) that I think I have a bug.  However, when I did this computation by hand up-thread, the power was also very low.  I'll post the link when I'm more confident that it's not wrong.

[Paul451]

OK, let's start over. Assume we need 5 mm/s² accelleration, and we want to use centrepital force. We mount the tanker atop the depot and then sling them from a cable with tanker toward the center of rotation, and start spinning. We need another mass at the far end of the cable. let's say that otehr mass is 1/10 the mass of our tanker+depot+propellant. For a cable that is 1100 meters, the tanker+depot CoM will be 100 meters from the center of rotation.

I agree that if the xfer time and settling-acceleration are both large, centripetal force is required instead of linear ullage thrust, but...

All the complexity of your cable and counter-weight (and their deployment as part of the docking/spin-up/spin-down/undocking sequence) exists just to allow them to both spin "tail down, nose up" for the prop transfer, while still being side-by-side.

Surely there's less complexity and risk in just sticking an extra set of propellant/gas lines and intakes in the tankers/depot/LSS tanks at the appropriate position for side-by-side rotation?

[DanClemmensen]

OK, let's start over. Assume we need 5 mm/s² accelleration, and we want to use centrepital force. We mount the tanker atop the depot and then sling them from a cable with tanker toward the center of rotation, and start spinning. We need another mass at the far end of the cable. let's say that otehr mass is 1/10 the mass of our tanker+depot+propellant. For a cable that is 1100 meters, the tanker+depot CoM will be 100 meters from the center of rotation.

I agree that if the xfer time and settling-acceleration are both large, centripetal force is required instead of linear ullage thrust, but...

All the complexity of your cable and counter-weight (and their deployment as part of the docking/spin-up/spin-down/undocking sequence) exists just to allow them to both spin "tail down, nose up" for the prop transfer, while still being side-by-side.

Surely there's less complexity and risk in just sticking an extra set of propellant/gas lines and intakes in the tankers/depot/LSS tanks at the appropriate position for side-by-side rotation?

I did not make myself clear. Sorry. I am assuming that the tanker docks atop the depot, like an SS stacked on a booster. They are not side by side. The depot would have an interface similar to the booster interface at its top end: basically a 9 meter diameter dock. The booster is assumed to deploy a QD "arm" from near its top that reaches up to connect to the QD plate on the SS (tanker, LSS, whatever).

I also assume that depot installation is permanent: it will last for many years and perform many, many propellant transfers. The tether and (large) counterweight are deployed (constructed?) once. You can think of the depot, tether, and counterweight as one really long spacecraft.

For each propellant transfer:
     start with no spin
     SS RMOD
     spin
     transfer propellant
     despin
     SS undock and depart.

[TheRadicalModerate]

Does anybody have an intelligible comparison of the viscosity of water at 20C vs methane and O2 at both boiling and slightly above freezing?

Water at 20ºC, μ=8E-4 Pa-s.
For LOX near boiling, μ=5.0E-5 Pa-s
For LCH4 near boiling μ=1.1E-5 Pa-s

I don't have the slushy versions for LOX and LCH4, but they don't matter, because prop on-orbit is almost certainly going to be near boiling.

[TheRadicalModerate]

I agree that if the xfer time and settling-acceleration are both large, centripetal force is required instead of linear ullage thrust, but...

If I'm right that, irrespective of the volumetric flow, you can always adjust pump power to put the outlet pressure at ambient, then transfer time is whatever you want it to be.

I suspect that there will be reasons for settling acceleration to be greater than 1mm/s², but if that's the case, then combusting methox thrusters are about a jillion times easier to engineer than a rotating system.  Rotating systems are terrible to make reliable, especially when you're moving their center of mass around by pumping stuff from point A to point B.

[Paul451]

we want to use centrepital force. We mount the tanker atop the depot and then sling them from a cable with tanker toward the center of rotation, and start spinning. We need another mass at the far end of the cable. let's say that otehr mass is 1/10 the mass of our tanker+depot+propellant. For a cable that is 1100 meters, the tanker+depot CoM will be 100 meters from the center of rotation.

I did not make myself clear. Sorry. I am assuming that the tanker docks atop the depot, like an SS stacked on a booster. They are not side by side. The depot would have an interface similar to the booster interface at its top end: basically a 9 meter diameter dock. The booster is assumed to deploy a QD "arm" from near its top that reaches up to connect to the QD plate on the SS (tanker, LSS, whatever).
I also assume that depot installation is permanent: it will last for many years and perform many, many propellant transfers. The tether and (large) counterweight are deployed (constructed?) once. You can think of the depot, tether, and counterweight as one really long spacecraft.

Now I'm confused. Where does the counterweight+arm attach to the depot, if the tankers are docking at the depot-nose?

[volker2020]

Not sure a nose by nose rotational docking is even possible. The mass center of a docked combination of full depot and an empty starship, will be somewhere in the upper third of the depot oxygen tank. How rotation in this case should help settle something is beyond my expertise. Apart from that, the rotation is poised to become extremely unstable. If SpaceX would make that work, it would be a marvel in itself.

[BT52]

I dont wanna be rude or anything. Any rotation is quite stupid way to overengineer.

Linear acceleration is way to go. Its well know phenomena. And furthermore they known its effects from 2nd stage.

Just copy pasta baffle system from main tanks and its almost good. Then they just need pump, power source and manipulator arm for docking adapter plate.

Maybe oversimplified view but i think that way they can reuse as many parts or experiences from ground zero stage as possible.

[edzieba]

I wonder if it would be possible to plumb fluid transfer in via the header tanks? With their small enclosed volume, you can pump props in as fast as you can and allow the violent sloshing and geysering to occur inside them. The headers already have more extensive baffling due to the need to minimise slosh during the flip manoeuvre, so even with no additional fluid management hardware and just an open line to the main tank allowing mixed phase flow, a huge amount of energy in the incoming propellant flow should be expended inside the header allowing for gentler flow into the main tank.

[DanClemmensen]

we want to use centrepital force. We mount the tanker atop the depot and then sling them from a cable with tanker toward the center of rotation, and start spinning. We need another mass at the far end of the cable. let's say that otehr mass is 1/10 the mass of our tanker+depot+propellant. For a cable that is 1100 meters, the tanker+depot CoM will be 100 meters from the center of rotation.

I did not make myself clear. Sorry. I am assuming that the tanker docks atop the depot, like an SS stacked on a booster. They are not side by side. The depot would have an interface similar to the booster interface at its top end: basically a 9 meter diameter dock. The booster is assumed to deploy a QD "arm" from near its top that reaches up to connect to the QD plate on the SS (tanker, LSS, whatever).
I also assume that depot installation is permanent: it will last for many years and perform many, many propellant transfers. The tether and (large) counterweight are deployed (constructed?) once. You can think of the depot, tether, and counterweight as one really long spacecraft.

Now I'm confused. Where does the counterweight+arm attach to the depot, if the tankers are docking at the depot-nose?

The tether connects to a spreader. The spreader has rigid cables, one for each side of the depot+tanker. The cables are about 12 m apart and maybe 50 m long and connect to a trapeze that connects to the depot near its "top", near its chopstick lift points.  After Tanker docks to depot, it can also connect to the rigid cables for lateral stability if needed, but the actual centripetal acceleration on tanker comes from its base, which sits on the depot.

The entire RMOD occurs in the de-spun state, so if necessary the depot can rotate 90 degrees to become  perpendicular to the tether so the docking port is completely clear of the tether. Then tanker docks and then depot+tanker swing back in line with the tether before tanker hooks its stabilizers onto the tether. I don't think all of this is needed. I think tanker can RMOD by maneuvering itself between the spread cables: they are farther apart than chopstick arms and RMOD can take as long as needed. Those stabilizers will never have more than a tiny force on them. Are only needed at all if the CoM of tanker+depot is "higher" than the trapeze connection point on depot (i.e., full tanker, empty depot).

[OTV Booster]

This looks like an upper limit on a dry receiving tank. Once the fluid depth reaches ~one inlet diameter it can pump a bit harder and let viscosity damp geysering. Given the consumption numbers we're seeing for settling, the transfer time looks critical.

That's correct.  However, the "duh!" moment I had was realizing that, for any flow rate, there's a pump power that results in that flow arriving at ambient pressure.

FWIW, I'm building a transfer power worksheet into the prop expenditure worksheet.  The current powers are so low (single-digit watts) that I think I have a bug.  However, when I did this computation by hand up-thread, the power was also very low.  I'll post the link when I'm more confident that it's not wrong.

Ok. Now I get it. Didn't think it through.


Hmmm. If the pump hits exactly at ambient pressure at the top of the inlet, wouldn't the flow stall out? I'm thinking the column of fluid would just make it to the lip of the inlet and no further. One tiny smidge more and it overflows the lip and fills the sump. Once the tank level reaches the top of the inlet it would continue to rise about one smidge worth, then stall out again. How many kWh pump energy in a smidge?


From a practical point of view what is the relationship between pressure and flow rate in a centrifugal pump? If it's pumping into a closed off pipe it's at high pressure but zero flow. Valve the outlet open just a tad (first cousin to a smidge) and flow starts but pressure drops. Once the outlet is fully open both pressure and volume rise and fall with RPM but is it a linear relationship? My gut says it's close. Does the relationship change facing different back pressures?


Am I overthinking this?


A random thought. If the volume and pressure are directly related, the transfer op would counterintuitively go faster at 6bar ullage pressure than at .5bar. Would it be fast enough to materially impact propellant consumption? Would the amount of makeup gas from the high pressure COPV's negate any advantage? The makeup gas will be warm and would contract in the tanks. Electric heater on the COPV outlets?


My brain is starting to hurt.

[TheRadicalModerate]

Ok. Now I get it. Didn't think it through.


Hmmm. If the pump hits exactly at ambient pressure at the top of the inlet, wouldn't the flow stall out? I'm thinking the column of fluid would just make it to the lip of the inlet and no further. One tiny smidge more and it overflows the lip and fills the sump. Once the tank level reaches the top of the inlet it would continue to rise about one smidge worth, then stall out again. How many kWh pump energy in a smidge?


From a practical point of view what is the relationship between pressure and flow rate in a centrifugal pump? If it's pumping into a closed off pipe it's at high pressure but zero flow. Valve the outlet open just a tad (first cousin to a smidge) and flow starts but pressure drops. Once the outlet is fully open both pressure and volume rise and fall with RPM but is it a linear relationship? My gut says it's close. Does the relationship change facing different back pressures?


Am I overthinking this?


A random thought. If the volume and pressure are directly related, the transfer op would counterintuitively go faster at 6bar ullage pressure than at .5bar. Would it be fast enough to materially impact propellant consumption? Would the amount of makeup gas from the high pressure COPV's negate any advantage? The makeup gas will be warm and would contract in the tanks. Electric heater on the COPV outlets?


My brain is starting to hurt.

Yeah, it's pretty counterintuitive, and I'm not sure I've understood it correctly.  I'm wondering if Poseuille only applies to static pressure, but that would be weird with an equation that has volumetric flow built into it.  But if you've got the same volumetric flow and it's incompressible, it's hard to see how there isn't dynamic pressure just from the momentum of the flow itself.

Hopefully somebody will chime in and explain it all.

[Paul451]

I dont wanna be rude or anything. Any rotation is quite stupid way to overengineer.
Linear acceleration is way to go. Its well know phenomena.

The fall back to centripetal settling is a result of the calcs for the amount of prop required for ullage burns during transfer. If you have to burn an entire extra tanker load of propellant just to do prop settling, then the technical complexity of rotation might be worth it. Perhaps not the trapeze act that Dan has proposed, but certainly the cost of adding extra sumps/vents at the required points in the tankers, depot, and LSS.

[DanClemmensen]

I dont wanna be rude or anything. Any rotation is quite stupid way to overengineer.
Linear acceleration is way to go. Its well know phenomena.

The fall back to centripetal settling is a result of the calcs for the amount of prop required for ullage burns during transfer. If you have to burn an entire extra tanker load of propellant just to do prop settling, then the technical complexity of rotation might be worth it. Perhaps not the trapeze act that Dan has proposed, but certainly the cost of adding extra sumps/vents at the required points in the tankers, depot, and LSS.

Yes, I was shocked by the amount of propellant needed to use acceleration for settling, so I started investigating rotation again. I was then shocked again by the very small amount of energy needed to use centripetal acceleration. The "trapeze act" is a whacko thought experiment, not really a proposal. To actually implement it, you would probably need an entire separate specialized SS to carry it, deploy it, and then act as the counterweight, roughly doubling the cost of the Depot.

[TheRadicalModerate]

I dont wanna be rude or anything. Any rotation is quite stupid way to overengineer.
Linear acceleration is way to go. Its well know phenomena.

The fall back to centripetal settling is a result of the calcs for the amount of prop required for ullage burns during transfer. If you have to burn an entire extra tanker load of propellant just to do prop settling, then the technical complexity of rotation might be worth it. Perhaps not the trapeze act that Dan has proposed, but certainly the cost of adding extra sumps/vents at the required points in the tankers, depot, and LSS.

Yes, I was shocked by the amount of propellant needed to use acceleration for settling, so I started investigating rotation again. I was then shocked again by the very small amount of energy needed to use centripetal acceleration. The "trapeze act" is a whacko thought experiment, not really a proposal. To actually implement it, you would probably need an entire separate specialized SS to carry it, deploy it, and then act as the counterweight, roughly doubling the cost of the Depot.

It's a shocking amount if you:

1) Use high ullage acceleration.
2) Use very low transfer flow rates.
3) Use cold gas ullage thrusters instead of combusting gas.

All three of these are interrelated.  If there are geysering or splashing problems, then higher acceleration or lower flow rates can mitigate them.  If that combo requires inefficient use of ullage prop, then going from cold gas to combustion gas dramatically increases the efficiency.

I'm still trying to figure out if my reading of the Poiseuille equation means that you can always avoid geysering.  If so, then low transfer rates are dumb, and high transfer rates are easy.  Then the only issue is whether some other kind of vibration or attitude dynamics can cause either the sending or receiving tanks to become unsettled.  If that's the case, then you need higher acceleration, which likely requires higher Isp, which requires combusting gas.

But a combustion thruster is soooooo much easier to implement than a rotating system.

[TheRadicalModerate]

I wonder if it would be possible to plumb fluid transfer in via the header tanks? With their small enclosed volume, you can pump props in as fast as you can and allow the violent sloshing and geysering to occur inside them. The headers already have more extensive baffling due to the need to minimise slosh during the flip manoeuvre, so even with no additional fluid management hardware and just an open line to the main tank allowing mixed phase flow, a huge amount of energy in the incoming propellant flow should be expended inside the header allowing for gentler flow into the main tank.

It might help on the sending side--if there's actually a problem on the sending side.  You don't want the pump to become unprimed by sucking in gas, but in general, the sending side should be more placid.

If you're using equalized pressure, I guess the main cause of unsettled conditions on the sending side would be... sucking liquid through the equalization line and dropping it into the settled prop in the sending tank.  So everything really comes back to ensuring that the receiving side stays settled enough not to suck liquid through the equalization line.

I don't think using the header helps on the receiving side.  If you receive prop into a header tank, then the header has to pump it into the main, where it will splash, which will still cause prop to get into the gas pressure equalization line.

Maybe locate the equalization lines in the header tanks?  It's a pretty hardy blob of prop that can get sucked from the main, into the header, and then into the inter-vehicle equalization.

Another possibility is simply to cover the equalization line with some kind of prop management device that prevents blobs from making it into the line, even if there's splashing.  Seems that this ought to be a pretty tractable problem.

[edzieba]

That assumes presence of an equalisation line. Initial transfer (dry receiver) - vent the incoming tank to vacuum, close the vent, and transfer prop from the pressurised sender tank (can use ullage pressure, likely no pump required*). As there is no ullage volume to compress, you can geyser and spray and slosh and vaporise as much as you want with minimal concern for a significant portion of the transfer. Eventually enough prop will boil from this vigorous action and reduced droplet size (and thus increased surface area) for autogenous pressurisation to occur and raise the pressure to match the sending tank, and at that point transfer pauses to allow for prop settling. Once prop has settled, the tank is vented to near-vacuum (low enough to minimise static boiloff, IIRC around 10kPa for CH4 and 0.15kPa for O2) and transfer can continue with the outlet well covered and the ullage vented as required to maintain that low pressure in the receiving tank. This state persists for subsequent propellant loadings. This loses some amount of gaseous prop from venting back down from equilibrium to the target low pressure, but that mass loss is relatively small: e.g. for CH4 assuming a 3 Bar sender tank pressure and the absolute worst case of the entire tank volume to be vented, the maximum mass loss is around 1.5 tonnes. That gives an upper limit for any anti-geysering hardware dry mass or low-geysering-transfer propellant consumption.


*For a 9m diameter tank, every bar of pressure the sending tank is above the receiving tank means roughly 6 MN of force trying to push prop from the sender to receiver tank.

[Twark_Main]

.This loses some amount of gaseous prop from venting back down from equilibrium to the target low pressure, but that mass loss is relatively small: e.g. for CH4 assuming a 3 Bar sender tank pressure and the absolute worst case of the entire tank volume to be vented, the maximum mass loss is around 1.5 tonnes.

Except that's not the "absolute worst case," because (as you point out) liquid propellant will be constantly evaporating to replenish the ullage gas.

It's also not the "absolute worst case" because we don't know if it will actually reliably transfer 100% of the propellant. If some is missed that needs to be counted, and even a small amount of liquid could exceed 1.5 tonnes.

You also missed the ullage thrusters. If the technique works but takes a lot longer, then that additional ullage prop mass should also be accounted for.

[edzieba]

.This loses some amount of gaseous prop from venting back down from equilibrium to the target low pressure, but that mass loss is relatively small: e.g. for CH4 assuming a 3 Bar sender tank pressure and the absolute worst case of the entire tank volume to be vented, the maximum mass loss is around 1.5 tonnes.

Except that's not the "absolute worst case," because (as you point out) liquid propellant will be constantly evaporating to replenish the ullage gas.

It's also not the "absolute worst case" because we don't know if it will actually reliably transfer 100% of the propellant. If some is missed that needs to be counted, and even a small amount of liquid could exceed 1.5 tonnes.

Only when in a vacuum state. The vents would not be opened again until the tank has reached pressure equilibrium with the sender tank, and then settles, so venting would not lose liquids (settled so no mixed phase) and pressure would not be allowed to drop before the triple point (so no flash boiling).

You also missed the ullage thrusters. If the technique works but takes a lot longer, then that additional ullage prop mass should also be accounted for.

By transferring at a high flow rate and then settling with a sealed tank, you can minimise the time at the maximum settling thrust needed (to keep the inlet covered on the sender tank) and then switch to the minimum thrust needed for the post-transfer sealed tank settling (equivalent to a cost-phase settling thrust). This is opposed to needing to keep sufficient thrust to both keep the sender tank inlet covered and keep the receiving tank from geysering for the entire transfer duration.