Starship On-orbit refueling - Options and Discussion

[Twark_Main]

Still trying to get a handle on this.

The advantage of dropping the pressure in the depot tanks is not that the liquid is colder, but rather that the vapor is colder, because it boiled off at a lower temperature.  That makes it much easier for the cryocooler to liquefy it back to a temperature that would be heavily subcooled if the system suddenly went up to flight pressure.

1. No, the advantage is that the liquid is colder.

2. This is harder for the cryocooler, because it's maintaining a larger delta-T.

The advantage of dropping the pressure is that you can maintain subcooled prop with "just" a boil-off liquefying cryocooler, rather than needing to switch to a heavier cryocooler design which uses heat exchangers in the tanks.

the prop will have heated up during the time it took the tanker to launch and do the RPOD, and will likely be at the boiling point for 6bar (or whatever on-orbit flight pressure is).  So the largest, quickest transfer of heat power into the depot is probably the prop transfer itself, not the leakage from the outside.

I don't know how you deal with that.

Yep, that's one of the advantages of subcooling your depot: the "extra cold" helps you deal with excess heat soak in transfer plumbing etc during on-orbit refilling, which reduces (or ideally eliminates) wasteful venting during pre-chill.

I suspect, if you're going to deal with subcooling at all, you then need a multi-stage cooler, which runs until all that heat accumulated during flight has been removed.  Then the last stage (optimized solely for returning low-pressure vapor at low temperature to the liquid state) can run, and the other stages can shut down.  But this doesn't help in terms of the power requirements to deal with the pulse of transferred heat that arrives with new prop.

There's no issue. The depot propellant is just slightly less subcooled after the transfer, and the cryocooler gradually pulls the temperature back down. So the thermal inertia of the propellant itself smooths out the "pulse."

[TheRadicalModerate]

Still trying to get a handle on this.

The advantage of dropping the pressure in the depot tanks is not that the liquid is colder, but rather that the vapor is colder, because it boiled off at a lower temperature.  That makes it much easier for the cryocooler to liquefy it back to a temperature that would be heavily subcooled if the system suddenly went up to flight pressure.

1. No, the advantage is that the liquid is colder.

2. This is harder for the cryocooler, because it's maintaining a larger delta-T.

The advantage of dropping the pressure is that you can maintain subcooled prop with "just" a boil-off liquefying cryocooler, rather than needing to switch to a heavier cryocooler design which uses heat exchangers in the tanks.

That's what I said.  The LOX boil-off vapor will be at, say, 65K instead of 90K, so a small delta-T ill return it to liquid slightly less than 65K.  Then, after it's transferred at 65K and brought up to fight pressure, it'll still be at 65K-ish, and therefore deeply subcooled, even though it was near boiling in the depot.

This way, the cyrocooler never has to use liquid as an input.

the prop will have heated up during the time it took the tanker to launch and do the RPOD, and will likely be at the boiling point for 6bar (or whatever on-orbit flight pressure is).  So the largest, quickest transfer of heat power into the depot is probably the prop transfer itself, not the leakage from the outside.

I don't know how you deal with that.

Yep, that's one of the advantages of subcooling your depot: the "extra cold" helps you deal with excess heat soak in transfer plumbing etc during on-orbit refilling, which reduces (or ideally eliminates) wasteful venting during pre-chill.

Are you talking about pre-chill for the transfer itself?  Yes, that's a problem, but I've been assuming that it's solvable only by sacrificing some prop to condition the lines.  The trick is to make the lines short and insulated.

I think the best place to place the cryocooler(s) is in the ullage space of the mains in the depot.  That way, it's guaranteed to get the cold boil-off that occurs when the pressure is low.

I suspect, if you're going to deal with subcooling at all, you then need a multi-stage cooler, which runs until all that heat accumulated during flight has been removed.  Then the last stage (optimized solely for returning low-pressure vapor at low temperature to the liquid state) can run, and the other stages can shut down.  But this doesn't help in terms of the power requirements to deal with the pulse of transferred heat that arrives with new prop.

There's no issue. The depot propellant is just slightly less subcooled after the transfer, and the cryocooler gradually pulls the temperature back down. So the thermal inertia of the propellant itself smooths out the "pulse."

The cryocooler should never need an effective power greater than the steady-state heat leaking into the tanks--except when it receives a bolus of new prop. Then it needs to get that new prop down to the equilibrium temperature and pressure, which requires considerably more power to do without having to vent a bunch of boiloff.

[J]

[...] without having to vent a bunch of boiloff.

Is there any information about the engines to be
used for settling propellant during transfer? I had
assumed that (especially if using subcooled
propellants chilled by reducing tank pressure)
any venting of boil-off would be done through
these engines.

If the propellant was cooled entirely by boiling at
transfer (by reducing the pressure from 6 bar to
.2 bar), it looks like it would require boiling off
about 10% of the propellant. If the depot has
tanks large enough to accommodate this and
still fully fill the target tanks with subcooled
propellant, then over a 100 ton of ullage gas
is "vented" through the settling thrusters. That's
plausibly 200m/s, depending on the ISP of the
thrusters. That is ... not quite nothing.

[Slarty1080]

Will the Tanker Starship just have stretched tanks capped with an aerodynamic shell? Or will it have a dedicated "tanker" LOX tank in the payload bay? I would have thought the former, to save the mass penalty of an extra bulkhead, but if so they will presumably have to fix the existing LOX autogenous pressurization method first else there is a danger of introducing carbon dioxide and water ices into orbital storage tanks.

[OTV Booster]

Still trying to get a handle on this.

The advantage of dropping the pressure in the depot tanks is not that the liquid is colder, but rather that the vapor is colder, because it boiled off at a lower temperature.  That makes it much easier for the cryocooler to liquefy it back to a temperature that would be heavily subcooled if the system suddenly went up to flight pressure.

1. No, the advantage is that the liquid is colder.

2. This is harder for the cryocooler, because it's maintaining a larger delta-T.

The advantage of dropping the pressure is that you can maintain subcooled prop with "just" a boil-off liquefying cryocooler, rather than needing to switch to a heavier cryocooler design which uses heat exchangers in the tanks.

That's what I said.  The LOX boil-off vapor will be at, say, 65K instead of 90K, so a small delta-T ill return it to liquid slightly less than 65K.  Then, after it's transferred at 65K and brought up to fight pressure, it'll still be at 65K-ish, and therefore deeply subcooled, even though it was near boiling in the depot.

This way, the cyrocooler never has to use liquid as an input.

the prop will have heated up during the time it took the tanker to launch and do the RPOD, and will likely be at the boiling point for 6bar (or whatever on-orbit flight pressure is).  So the largest, quickest transfer of heat power into the depot is probably the prop transfer itself, not the leakage from the outside.

I don't know how you deal with that.

Yep, that's one of the advantages of subcooling your depot: the "extra cold" helps you deal with excess heat soak in transfer plumbing etc during on-orbit refilling, which reduces (or ideally eliminates) wasteful venting during pre-chill.

Are you talking about pre-chill for the transfer itself?  Yes, that's a problem, but I've been assuming that it's solvable only by sacrificing some prop to condition the lines.  The trick is to make the lines short and insulated.

I think the best place to place the cryocooler(s) is in the ullage space of the mains in the depot.  That way, it's guaranteed to get the cold boil-off that occurs when the pressure is low.

I suspect, if you're going to deal with subcooling at all, you then need a multi-stage cooler, which runs until all that heat accumulated during flight has been removed.  Then the last stage (optimized solely for returning low-pressure vapor at low temperature to the liquid state) can run, and the other stages can shut down.  But this doesn't help in terms of the power requirements to deal with the pulse of transferred heat that arrives with new prop.

There's no issue. The depot propellant is just slightly less subcooled after the transfer, and the cryocooler gradually pulls the temperature back down. So the thermal inertia of the propellant itself smooths out the "pulse."

The cryocooler should never need an effective power greater than the steady-state heat leaking into the tanks--except when it receives a bolus of new prop. Then it needs to get that new prop down to the equilibrium temperature and pressure, which requires considerably more power to do without having to vent a bunch of boiloff.

If there is always some propellant in the depot (a reasonable assumption) it has the means of prechilling the transfer plumbing before the transfer. Conditioning produces vapor. Vapor is chilled back into liquid. Once the plumbing is conditioned only an ongoing trickle keeps it that way while waiting for the target to arrive.


Depending on battery power sounds dicey. It is needed for nightside ops, but the whole process? With four operational pads there are conceivably two transfer ops per 24hours and possibly four. If it's one transfer every couple of days the trades might work out. A lot of unknowns. Steady state thermal input of the depot. Temp/pressure of arriving props. Thermal impact of transfer. The total power requirements of the whole process.


A long time ago I was noodling the idea of a detachable and maneuverable power module mostly made up of PV, batteries and electric thrusters. It would allow the mothership to take care of business without PV getting in the way. One version would use charged up batteries to recharge the mothership, another would exchange battery packs. In this application it might be able to maneuver to act as a thermal shade, at least part time. Maybe an idea for depot V2. Incidentally, it gives an additional reason to trick out the depot with an arm.

[Twark_Main]

Still trying to get a handle on this.

The advantage of dropping the pressure in the depot tanks is not that the liquid is colder, but rather that the vapor is colder, because it boiled off at a lower temperature.  That makes it much easier for the cryocooler to liquefy it back to a temperature that would be heavily subcooled if the system suddenly went up to flight pressure.

1. No, the advantage is that the liquid is colder.

2. This is harder for the cryocooler, because it's maintaining a larger delta-T.

The advantage of dropping the pressure is that you can maintain subcooled prop with "just" a boil-off liquefying cryocooler, rather than needing to switch to a heavier cryocooler design which uses heat exchangers in the tanks.

That's what I said.  The LOX boil-off vapor will be at, say, 65K instead of 90K, so a small delta-T ill return it to liquid slightly less than 65K.

Ahh, I should have said that the heat lift is higher. This is why the cryocooler has to work harder at low pressure.

Any boil-off based system will have this same property of negligible delta-T, whether or not it uses low pressure.

the prop will have heated up during the time it took the tanker to launch and do the RPOD, and will likely be at the boiling point for 6bar (or whatever on-orbit flight pressure is).  So the largest, quickest transfer of heat power into the depot is probably the prop transfer itself, not the leakage from the outside.

I don't know how you deal with that.

Yep, that's one of the advantages of subcooling your depot: the "extra cold" helps you deal with excess heat soak in transfer plumbing etc during on-orbit refilling, which reduces (or ideally eliminates) wasteful venting during pre-chill.

Are you talking about pre-chill for the transfer itself?  Yes, that's a problem, but I've been assuming that it's solvable only by sacrificing some prop to condition the lines.  The trick is to make the lines short and insulated.

Again, you don't necessarily have to accept this "sacrifice" if using subcooled propellant. The propellant can be used to "ullage collapse" the gas and avoid venting.

I suspect, if you're going to deal with subcooling at all, you then need a multi-stage cooler, which runs until all that heat accumulated during flight has been removed.  Then the last stage (optimized solely for returning low-pressure vapor at low temperature to the liquid state) can run, and the other stages can shut down.  But this doesn't help in terms of the power requirements to deal with the pulse of transferred heat that arrives with new prop.

There's no issue. The depot propellant is just slightly less subcooled after the transfer, and the cryocooler gradually pulls the temperature back down. So the thermal inertia of the propellant itself smooths out the "pulse."

The cryocooler should never need an effective power greater than the steady-state heat leaking into the tanks--except when it receives a bolus of new prop. Then it needs to get that new prop down to the equilibrium temperature and pressure, which requires considerably more power to do without having to vent a bunch of boiloff.

Again subcooling avoids venting, so I don't know why you're so eager to prematurely accept defeat here.

"Considerably more power" depends on your desired cadence. The minimum required thermal power is actually the same, as long as you can accept long chill-down time. How fast you want the refilling cycles determines how "considerable" the power requirements get.

The point is, you never need some huge powerful cryocooler that's sized to chill the propellant as it's transferring, or to (ideally quickly) pre-chill the tanker or plumbing while everything's docked in orbit. This is what you really want to avoid, because now you can spread that cooling load over 3 days instead of 3 hours.

[TheRadicalModerate]

[...] without having to vent a bunch of boiloff.

Is there any information about the engines to be
used for settling propellant during transfer?

Short answer:  no.  But settling isn't going to be something that only happens during prop transfer.  Even when storing prop, periodic settling will be required to move bubbles that formed around hotspots to the top of the tank, where they can either be cryocooled or vented.  Without that settling, a bubble at the bottom of the tank could push liquid into the vents, which would be bad.

No clue how often this would need to happen, or for what duration.  1 minute every 5 hours?  Over a two-month accumulation and storage period, that would be 8600 seconds.  Then figure 45 minutes of continuous settling for 15 prop transfers: another 41,000 seconds, for a total of ~50,000 seconds per mission.

If we use an average mass for the depot of 1000t (negligible when empty, 2000t when full), and we want an acceleration of 0.0005G = ~0.005m/s², then we need an average thrust for settling of 5kN.  I doubt cold gas at low pressure will generate more than Isp=50s, which would therefore require 510t of prop.  That's not great.

On the other hand, if we use hot (combusting) methalox, we get 7x the Isp, which drops the settling consumption to 73t.  Still not great, but quite a bit better.

Lots of guesswork going on here:  Maybe we only need to drive the bubbles to the top every 10 hours.  Maybe settling acceleration only needs to be 0.001m/s².  But things can get out of hand pretty quickly.

I expect to see at least two different sizes of hot gas thrusters:  one that's maybe 500-1000N, for settling and fine attitude adjustment, and one that's ~50-100kN for coarse attitude adjustment, small-delta-v maneuvers, and use as landing thrusters.  But those are both SWAGs.

If the propellant was cooled entirely by boiling at transfer (by reducing the pressure from 6 bar to .2 bar), it looks like it would require boiling off about 10% of the propellant.

First, "boiling at transfer" won't work, because it's a non-equilibrium process.  The prop temperature doesn't magically drop the moment the pressure drops; it requires enough boiloff to remove enough heat (via enthalpy of vaporization) to get to the equilibrium temperature.

If you use this kind of cooling in the depot, I think this goes to the argument I was having with Twark.  Yes, you can just drop the pressure, and the ensuing boiloff will eventually equilibrate to the low boiling temperature, which will become subcooled when you then increase the pressure.  But if you have a cryocooler, and it has more power than needed to deal with the heat leakage into the tanks, you can reduce the ullage pressure over time, by removing more vapor from the tank and turning it into somewhat colder prop.  That in turn is lowering the liquid temperature by a second method, rather than relying only on the enthalpy of vaporization to pull heat out of the liquid (and therefore lower the temperature).

The question is whether you can design a cryocooler where the temperature drop is small, but constantly moving lower.  Usually, these things need a specific inlet and outlet temperature, with an effective amount of heat removed. 

But you also need additional coolers to deal with the sudden pulses of warm prop that arrive when tankers dump stuff in that's been launched and spent a while on-orbit, with no cooling at all.  So maybe you have a multi-stage cryocooler, and you only use the coldest stage for storage, once you've reached your low-pressure boiling temperature (which will become your flight-pressure subcooled temperature).

Will the Tanker Starship just have stretched tanks capped with an aerodynamic shell? Or will it have a dedicated "tanker" LOX tank in the payload bay? I would have thought the former, to save the mass penalty of an extra bulkhead, but if so they will presumably have to fix the existing LOX autogenous pressurization method first else there is a danger of introducing carbon dioxide and water ices into orbital storage tanks.

Given the relative ease with which SpaceX can control the stacking order of tank rings and domes, I'd guess that they'll just eat into the barrel (aka the payload bay) rings.  I suspect the barrel has already gotten shorter by a ring or two between v2 and v3 (hard to tell, because they've reduced the skirt size somewhat by using an EDome and sinking the RVacs a ways into the dome itself), the depot may only have 3-4 ring segments available for re-jiggering.  Each segment should hold 100t of sorta-subcooled prop.

Having two sets of tanks is an enormous pain.  Re-jiggering is easy.

[TheRadicalModerate]

Ahh, I should have said that the heat lift is higher. This is why the cryocooler has to work harder at low pressure.

Any boil-off based system will have this same property of negligible delta-T, whether or not it uses low pressure.

Does it?  As long as the mass flow stays the same, shouldn't the heat removed stay the same?  I suspect that there's some additional energy to run the vapor through the system faster (or maybe even to compress it), but I'd guess that it's fairly small.

Are you talking about pre-chill for the transfer itself?  Yes, that's a problem, but I've been assuming that it's solvable only by sacrificing some prop to condition the lines.  The trick is to make the lines short and insulated.

Again, you don't necessarily have to accept this "sacrifice" if using subcooled propellant. The propellant can be used to "ullage collapse" the gas and avoid venting.

The only way you have genuinely subcooled prop is when you quickly raise the tank pressure.  Until then, low pressure prop will only be in equilibrium at its boiling temperature.  That temperature just happens to be lower.

If you bubble hot vapor from line conditioning through that prop, it's just gonna boil the amount of heat you extract from it.  Might as well put it into the ullage space directly and take your lumps.

This, and the fact that tanker prop will be near boiling if not at boiling when it's transferred into the depot, is why I think you need to be able to have more lift power (using your term/dt) than the leakage power.  Otherwise, you'll need to vent enough vapor to remove that heat pulse from the tanks.

Here's a question:  Suppose you have a near-empty HLS or other target Starship.  It not only has hot lines, it has hot tanks.  How much power (or vented prop) is needed to condition the entire tank?

"Considerably more power" depends on your desired cadence. The minimum required thermal power is actually the same, as long as you can accept long chill-down time. How fast you want the refilling cycles determines how "considerable" the power requirements get.

The point is, you never need some huge powerful cryocooler that's sized to chill the propellant as it's transferring, or to (ideally quickly) pre-chill the tanker or plumbing while everything's docked in orbit. This is what you really want to avoid, because now you can spread that cooling load over 3 days instead of 3 hours.

Oh, I wasn't thinking it was chill-as-you-transfer.  But it does need to be powerful enough to start collapsing the vapor before the pressure limits are reached.  I suspect that's not possible for, say, the first load of prop into the depot, but it ought to be doable with some additional power when, say, the fifth load of prop is being transferred into the four previous ones, all of which have had the heat removed to be in equilibrium.

There will always be a trade between over-designing the cryocooler and allowing some venting.  That trade space goes all the way from no cryocooler at all, using only venting to remove the heat, to no venting, with a humungous cryocooler to collapse vapor as soon as it is produced.

[Twark_Main]

[...] without having to vent a bunch of boiloff.

Is there any information about the engines to be
used for settling propellant during transfer?

Short answer:  no.  But settling isn't going to be something that only happens during prop transfer.  Even when storing prop, periodic settling will be required to move bubbles that formed around hotspots to the top of the tank, where they can either be cryocooled or vented.  Without that settling, a bubble at the bottom of the tank could push liquid into the vents, which would be bad.

No clue how often this would need to happen, or for what duration.  1 minute every 5 hours?  Over a two-month accumulation and storage period, that would be 8600 seconds.  Then figure 45 minutes of continuous settling for 15 prop transfers: another 41,000 seconds, for a total of ~50,000 seconds per mission.

Intermittent jostling will do more harm than good. You need to run the ullage thruster long enough for the bubbles to rise to the top (in "slow-mo" no less).

How is any of this better than slowly spinning, again?

So maybe you have a multi-stage cryocooler, and you only use the coldest stage for storage, once you've reached your low-pressure boiling temperature (which will become your flight-pressure subcooled temperature).

The "multi-stage" coolers are staged in series, not in parallel. If you shut off one stage then the whole thing stops working.

Ahh, I should have said that the heat lift is higher. This is why the cryocooler has to work harder at low pressure.

Any boil-off based system will have this same property of negligible delta-T, whether or not it uses low pressure.

Does it?  As long as the mass flow stays the same, shouldn't the heat removed stay the same?  I suspect that there's some additional energy to run the vapor through the system, but I'd guess that it's fairly small.

It's a higher heat lift between the (now colder) propellant and the radiator panels.

Are you talking about pre-chill for the transfer itself?  Yes, that's a problem, but I've been assuming that it's solvable only by sacrificing some prop to condition the lines.  The trick is to make the lines short and insulated.

Again, you don't necessarily have to accept this "sacrifice" if using subcooled propellant. The propellant can be used to "ullage collapse" the gas and avoid venting.

The only way you have genuinely subcooled prop is when you quickly raise the tank pressure.

This pressure rise will happen more-or-less immediately in the piping. You can also raise the pressure in the main tanks, of course.

If you bubble hot vapor from line conditioning through that prop, it's just gonna boil the amount of heat you extract from it.  Might as well put it into the ullage space directly and...

Raise the pressure in the main tanks. Great idea. 

This, and the fact that tanker prop will be near boiling if not at boiling when it's transferred into the depot, is why I think you need to be able to have more lift power (using your term/dt) than the leakage power.  Otherwise, you'll need to vent enough vapor to remove that heat pulse from the tanks.

No venting is needed for that "heat pulse". You just raise the pressure in the tank. The tank pressure follows the tank temperature, not the other way around.

So when a "pulse" of heat arrives, you don't say "oops, I have to maintain this low pressure, I guess I need to boil off and vent a bunch of propellant so it gets back to the same pressure it was this morning." 

[TheRadicalModerate]

No venting is needed for that "heat pulse". You just raise the pressure in the tank. The tank pressure follows the tank temperature, not the other way around.

So when a "pulse" of heat arrives, you don't say "oops, I have to maintain this low pressure, I guess I need to boil off and vent a bunch of propellant so it gets back to the same pressure it was this morning."

I'm pretty sure you have a conservation of energy problem here.  If you add a bunch of heat (aka energy), it doesn't matter through what states that heat is distributed.  You still have to get rid of it before the system will reach equilibrium.

There are only two ways to do that:  vent vapor containing the heat, or transfer the heat to radiators via cryocooling.  One loses mass, the other requires more power than is needed to maintain equilibrium in the face of heat leaking into the tanks from radiation.

The only exception I can think of to this is if your depot can accommodate extremely high pressures indefinitely.  Since that exception isn't available to us, you have to get rid of the heat that's incompatible with the state you want the prop in.

[OTV Booster]

No venting is needed for that "heat pulse". You just raise the pressure in the tank. The tank pressure follows the tank temperature, not the other way around.

So when a "pulse" of heat arrives, you don't say "oops, I have to maintain this low pressure, I guess I need to boil off and vent a bunch of propellant so it gets back to the same pressure it was this morning."

I'm pretty sure you have a conservation of energy problem here.  If you add a bunch of heat (aka energy), it doesn't matter through what states that heat is distributed.  You still have to get rid of it before the system will reach equilibrium.

There are only two ways to do that:  vent vapor containing the heat, or transfer the heat to radiators via cryocooling.  One loses mass, the other requires more power than is needed to maintain equilibrium in the face of heat leaking into the tanks from radiation.

The only exception I can think of to this is if your depot can accommodate extremely high pressures indefinitely.  Since that exception isn't available to us, you have to get rid of the heat that's incompatible with the state you want the prop in.

You bring up a point. In a very early build SpaceX, maybe Elon himself, specifically said that the intent was to rate the tanks to 6bar operating and 6.4bar (IIRC) as margin. Then they did a test to destruction and said that the tank met those numbers.


Are these numbers still valid? Is it possible that that the numbers have moved upward for exactly the reason above? We've seen more testing but I don't remember any announcements of test criteria. I'm not on twitX so what I know is from NSF.


I was about to ask the impact of 12bar tanks but that needs so many loose assumptions that it's pointless. Still, higher tank pressure might be in the toolbox.

[TheRadicalModerate]

Still, higher tank pressure might be in the toolbox.

Higher max tank pressure should allow a cryocooler designed for ZBO to be lower power.  If you bring in warm prop, with a total heat that's above what you want for equilibrium conditions by x joules, and heat leakage from space is y watts, then you need to remove the x joules in a time t that is sooner than when the pressure from that heat will build up to the point where the depot has to vent.  So the total effective cooling power y + x/t will be lower.

What happens if we dump a tanker's worth of warm prop at flight pressure into the depot?  Two things:

1) If we assume perfect mixing, then the liquid temperature will rise from initialDepotTemp to:

newDepotPropTemp = initialDepotPropMass * initialDepotTemp + transferredPropMass * transferredPropTemp / (initialDepotPropMass + transferredPropMass)

2) Vapor pressure will rise to:

newDepotPressure = (R  / molarMass) * (initialDepotGasMass * initialDepotTemp + transferredGasMass * transferredTemp) / newUllageVolume

That new, likely increased pressure may have driven the new liquid mass to be subcooled, in which case we'll have:¹

timeBeforePressureStartsToRise = liquidPropSpecificHeat * (boilingTemp(newPressure) - newDepotPropTemp) * newLiquidMass / leakagePowerFromSpace

So, to the extent that higher pressure gives us a bigger boiling point-to-subcooled temperature spread, that reduces the amount of power the cryocooler needs to provide.  Note three things, however:

1) If the current pressure is less than the max tankage pressure, you have still longer for the cooler to do its thing, which means the cooler can be even lower power.

2) The cooler is working over a bunch of different conditions, from the depot being completely empty except for the first load of prop transferred in, to it being completely full.  There are likely some trades to be made to handle that whole space.

3) It's not the end of the world if max pressure is reached, because the tank will just vent.  But you're losing some useful prop mass when it happens.

_____________
¹Note that I'm ignoring liquid saturation curve effects.  I think that's a decent approximation.

[OTV Booster]

Still, higher tank pressure might be in the toolbox.

Higher max tank pressure should allow a cryocooler designed for ZBO to be lower power.  If you bring in warm prop, with a total heat that's above what you want for equilibrium conditions by x joules, and heat leakage from space is y watts, then you need to remove the x joules in a time t that is sooner than when the pressure from that heat will build up to the point where the depot has to vent.  So the total effective cooling power y + x/t will be lower.

What happens if we dump a tanker's worth of warm prop at flight pressure into the depot?  Two things:

1) If we assume perfect mixing, then the liquid temperature will rise from initialDepotTemp to:

newDepotPropTemp = initialDepotPropMass * initialDepotTemp + transferredPropMass * transferredPropTemp / (initialDepotPropMass + transferredPropMass)

2) Vapor pressure will rise to:

newDepotPressure = (R  / molarMass) * (initialDepotGasMass * initialDepotTemp + transferredGasMass * transferredTemp) / newUllageVolume

That new, likely increased pressure may have driven the new liquid mass to be subcooled, in which case we'll have:¹

timeBeforePressureStartsToRise = liquidPropSpecificHeat * (boilingTemp(newPressure) - newDepotPropTemp) * newLiquidMass / leakagePowerFromSpace

So, to the extent that higher pressure gives us a bigger boiling point-to-subcooled temperature spread, that reduces the amount of power the cryocooler needs to provide.  Note three things, however:

1) If the current pressure is less than the max tankage pressure, you have still longer for the cooler to do its thing, which means the cooler can be even lower power.

2) The cooler is working over a bunch of different conditions, from the depot being completely empty except for the first load of prop transferred in, to it being completely full.  There are likely some trades to be made to handle that whole space.

3) It's not the end of the world if max pressure is reached, because the tank will just vent.  But you're losing some useful prop mass when it happens.

_____________
¹Note that I'm ignoring liquid saturation curve effects.  I think that's a decent approximation.

Yeah, I knew that. 

[OTV Booster]

Still, higher tank pressure might be in the toolbox.

Higher max tank pressure should allow a cryocooler designed for ZBO to be lower power.  If you bring in warm prop, with a total heat that's above what you want for equilibrium conditions by x joules, and heat leakage from space is y watts, then you need to remove the x joules in a time t that is sooner than when the pressure from that heat will build up to the point where the depot has to vent.  So the total effective cooling power y + x/t will be lower.

What happens if we dump a tanker's worth of warm prop at flight pressure into the depot?  Two things:

1) If we assume perfect mixing, then the liquid temperature will rise from initialDepotTemp to:

newDepotPropTemp = initialDepotPropMass * initialDepotTemp + transferredPropMass * transferredPropTemp / (initialDepotPropMass + transferredPropMass)

2) Vapor pressure will rise to:

newDepotPressure = (R  / molarMass) * (initialDepotGasMass * initialDepotTemp + transferredGasMass * transferredTemp) / newUllageVolume

That new, likely increased pressure may have driven the new liquid mass to be subcooled, in which case we'll have:¹

timeBeforePressureStartsToRise = liquidPropSpecificHeat * (boilingTemp(newPressure) - newDepotPropTemp) * newLiquidMass / leakagePowerFromSpace

So, to the extent that higher pressure gives us a bigger boiling point-to-subcooled temperature spread, that reduces the amount of power the cryocooler needs to provide.  Note three things, however:

1) If the current pressure is less than the max tankage pressure, you have still longer for the cooler to do its thing, which means the cooler can be even lower power.

2) The cooler is working over a bunch of different conditions, from the depot being completely empty except for the first load of prop transferred in, to it being completely full.  There are likely some trades to be made to handle that whole space.

3) It's not the end of the world if max pressure is reached, because the tank will just vent.  But you're losing some useful prop mass when it happens.

_____________
¹Note that I'm ignoring liquid saturation curve effects.  I think that's a decent approximation.

Situation: depot is mostly empty. It needs some keep alive propellant for maneuvering and settling when the first tanker shows up. It is crucial this propellant not boil off or the depot will be unable to mate up. Even if the tanker were able to take over operations it's doubtful it could work with a totally inert depot.


Empty or full, the depot will have the same environmental thermal load. The variables are the vagaries of orbit (high beta, etc),  cryo cooler impact, internal pressure and time. At minimum, in these circumstances the cooler needs to be capable of cooling the props enough to counteract the worst case thermal input and drop the props temp to just short of slush at the lowest acceptable internal pressure.


But wait. Why at low pressure when it's easier at high pressure? Because when that first tanker shows up it can not stuff propellant into the depot if 1) the depot is already at max pressure, 2) a pressure differential is needed to move the props, and 3) the new prop needs conditioning and there is no point in letting the old prop add to the workload. Long term storage at high pressure, and low pressure (with highly sub chilled props) when taking on more propellant.


This pattern will hold for every transfer. The difference will be the volume of props that have to be chilled from high pressure near slush to low pressure near slush.
After the last tanker load the propellant can stay at high pressure up to and including transfer to the target ship but sending over lower temp low pressure props might handle the target tank conditioning with more grace. It might be a good thing to reclaim the conditioning vapor.


My gut says that multiple small cryocoolers will do better than one large monolithic cooler. Parallel or series? IDK. Maybe a mix.

[TheRadicalModerate]

Situation: depot is mostly empty. It needs some keep alive propellant for maneuvering and settling when the first tanker shows up. It is crucial this propellant not boil off or the depot will be unable to mate up. Even if the tanker were able to take over operations it's doubtful it could work with a totally inert depot.

Empty or full, the depot will have the same environmental thermal load...

Flow a tonne or two of methalox into COPVs and insulate the bejeezus out of them.  If that's the only problem, it's straightforward.  Thrusters are going to have different feed plumbing no matter what.

But wait. Why at low pressure when it's easier at high pressure? Because when that first tanker shows up it can not stuff propellant into the depot if 1) the depot is already at max pressure, 2) a pressure differential is needed to move the props, and 3) the new prop needs conditioning and there is no point in letting the old prop add to the workload. Long term storage at high pressure, and low pressure (with highly sub chilled props) when taking on more propellant.

The low pressure is to depress the boiling point, so the liquid stabilizes at the desired subcooled temperature, and so the cryocooler only have to use gas as an input.  If you only had to worry about transfer pressure differential problems, temporarily fiddling with the pressure is easy.  So is using a pump.

Note!  Prop density is almost entirely a function of temperature, so if you store prop at low pressure and it's boiling at that pressure, if you suddenly raise the pressure, it's now subcooled and still at your target density.

My gut says that multiple small cryocoolers will do better than one large monolithic cooler. Parallel or series? IDK. Maybe a mix.

It has to be series.  I can't remember the rationale behind it, but you want to have fairly small temperature drops across each cryocooler stage, so the output of a warmer one feeds the input of the next colder stage.

However, there's nothing to prevent you from turning off the warmer-to-not-quite-as-warm stages as the vapor temperature (= boiling temperature, more or less) drops.  Just feed in the vapor directly to the most appropriate stage and turn the upstream stages off.

[Twark_Main]

However, there's nothing to prevent you from turning off the warmer-to-not-quite-as-warm stages as the vapor temperature (= boiling temperature, more or less) drops.  Just feed in the vapor directly to the most appropriate stage and turn the upstream stages off.

What cryocooler model are you seeing where the second-to-last stage is also capable of reaching cryogenic temperatures?   

I am not aware of any such cryocoolers existing, but maybe you can enlighten me.

Note that I'm excluding ultra-cryogenic coolers that can reach a few degrees above absolute zero. Obviously that hardware would be massive overkill for this purpose, and wouldn't be well suited to operating at these higher temperatures anyway.

[OTV Booster]

Situation: depot is mostly empty. It needs some keep alive propellant for maneuvering and settling when the first tanker shows up. It is crucial this propellant not boil off or the depot will be unable to mate up. Even if the tanker were able to take over operations it's doubtful it could work with a totally inert depot.

Empty or full, the depot will have the same environmental thermal load...

Flow a tonne or two of methalox into COPVs and insulate the bejeezus out of them.  If that's the only problem, it's straightforward.  Thrusters are going to have different feed plumbing no matter what.

But wait. Why at low pressure when it's easier at high pressure? Because when that first tanker shows up it can not stuff propellant into the depot if 1) the depot is already at max pressure, 2) a pressure differential is needed to move the props, and 3) the new prop needs conditioning and there is no point in letting the old prop add to the workload. Long term storage at high pressure, and low pressure (with highly sub chilled props) when taking on more propellant.

The low pressure is to depress the boiling point, so the liquid stabilizes at the desired subcooled temperature, and so the cryocooler only have to use gas as an input.  If you only had to worry about transfer pressure differential problems, temporarily fiddling with the pressure is easy.  So is using a pump.

Note!  Prop density is almost entirely a function of temperature, so if you store prop at low pressure and it's boiling at that pressure, if you suddenly raise the pressure, it's now subcooled and still at your target density.

My gut says that multiple small cryocoolers will do better than one large monolithic cooler. Parallel or series? IDK. Maybe a mix.

It has to be series.  I can't remember the rationale behind it, but you want to have fairly small temperature drops across each cryocooler stage, so the output of a warmer one feeds the input of the next colder stage.

However, there's nothing to prevent you from turning off the warmer-to-not-quite-as-warm stages as the vapor temperature (= boiling temperature, more or less) drops.  Just feed in the vapor directly to the most appropriate stage and turn the upstream stages off.

Parallel for when there's a heavy thermal load and little time.  Example: high beta, the last tanker load got delayed and is near boiling and another tanker is inbound right behind it. Serial for deep cooling.


Sounds like both. Maybe two or more parallel feeding into one.

[TheRadicalModerate]

What cryocooler model are you seeing where the second-to-last stage is also capable of reaching cryogenic temperatures?

What do you mean by "cryogenic temperatures"?  A temperature at which the target fluid is liquid?

You need something that's capable of reducing ullage gas of a fairly wide variety of temperatures to a temperature that's just above the boiling point.  So maybe you want a cascade of pulse tubes, each of which can lower the temperature of the gas by a fixed amount, with the last one feeding into something like a Joule-Thomson cooler, which only really works to liquefy things?

This sounds pretty heavy, and no doubt there's something better to be designed by somebody who knows what they're doing.  I doubt it will be off-the-shelf.  At this point, we don't even have a good grip on what kind of power the whole system needs if it's to be ZBO or near-ZBO.  That's likely the top-level constraint on what's possible.

[Twark_Main]

What cryocooler model are you seeing where the second-to-last stage is also capable of reaching cryogenic temperatures?

...

Note that I'm excluding ultra-cryogenic coolers

What do you mean by "cryogenic temperatures"?

LOX temperatures, as opposed to LH2 temperatures.

[TheRadicalModerate]

What cryocooler model are you seeing where the second-to-last stage is also capable of reaching cryogenic temperatures?

What do you mean by "cryogenic temperatures"?

LOX temperatures, as opposed to LH2 temperatures.

That's a pretty big range.  At 6bar, boiling is 111K.  At 0.5bar, it's 83K.  You could also wind up with superheated ullage gas from the autogenous system and a tanker, depending on how rendezvous and prox ops are done.  So you may need to cool gas from ~130K all the way down to 83K.  And there are different pressure ranges to accompany that temperature range.