Starship On-orbit refueling - Options and Discussion

[OTV Booster]

.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.

The sender, depot or tanker, will need to retain enough propellant to maneuver away from the receiver. In addition, a tanker needs props to leave orbit and the depot need enough so it doesn't boil dry - maybe until the next campaign. With some judicious baffling there shouldn't be a problem with exposing the outlet.

[eriblo]

.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.

The sender, depot or tanker, will need to retain enough propellant to maneuver away from the receiver. In addition, a tanker needs props to leave orbit and the depot need enough so it doesn't boil dry - maybe until the next campaign. With some judicious baffling there shouldn't be a problem with exposing the outlet.

Tankers will presumably have header tanks for their own needs.

[eriblo]

What do people mean when they talk about geysering? Cryogenic geysering is as far as I know related to cryogenic liquids in long pipes under enough acceleration and external heating that convection becomes important. I am not sure how this applies to millig propellant transfer?

[OTV Booster]

.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.

The sender, depot or tanker, will need to retain enough propellant to maneuver away from the receiver. In addition, a tanker needs props to leave orbit and the depot need enough so it doesn't boil dry - maybe until the next campaign. With some judicious baffling there shouldn't be a problem with exposing the outlet.

Tankers will presumably have header tanks for their own needs.

Is the header used for deorbit? Thought it was only used post fireball.

[OTV Booster]

What do people mean when they talk about geysering? Cryogenic geysering is as far as I know related to cryogenic liquids in long pipes under enough acceleration and external heating that convection becomes important. I am not sure how this applies to millig propellant transfer?

Rad Mod came up with this to describe the impact of too high a transfer pressure on the receiver. If the inlet plume punches through the settled propellant it would be geyser like.

[TheRadicalModerate]

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...

That only solves half the problem, though.  The sending tank's pressure will be dropping, increasing the back pressure on the system.  To solve that, you either need to have really big pumps to drop the sending tank's ullage pressure so much that the prop pool boils, or you need a heater to boil prop on the sending side to keep the pressure up. Neither of these is an efficient solution, either energy-wise nor prop efficiency-wise.

In contrast, the equalization line doesn't require any more gas to be wasted as ullage, needs tiny little pumps, doesn't require heaters in the mains, and is less complex in general.  The geysering/splash problem is likely a real one, but if it can't be solved with a bit of clever configuration of the pump outlet, then just putting a PMD around the equalization inlet probably solves it.

[OTV Booster]

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.

I've been noodling this from the pumps POV. In looking at the relationship between volume and pressure I could not find a single practical constant to serve as an anchor.


One extreme is pumping against a closed valve and the other extreme is the valve open to an infinite vacuum.


Against a closed valve there would be max pressure and zero flow. Depending on the motor design there would be either a limitation on RPM, a high current draw, or some combination of both.


Opening the valve into an infinite vacuum, the pressure would be minimum, the flow maximum and again depending on motor design, an increase in RPM, a drop in current draw, or some combination.


Current draw could be held constant as could RPM but the two seem to be so intermingled I can't figure out what I'm modeling let alone the practical implications. Maybe assume a synchronous, constant RPM AC motor for modeling despite the DC motor that would probably be used in the ship? Doesn't feel useful.


Yeah, we need a pump engineer.

[eriblo]

I personally do not expect to see gas transfer/equilization lines. If they do pressure/temperature driven pumping (which I currently expect) then there is obviously no need and for electrical pumping I do not think it is worth the hassle of extra outlets, lines and connections.

If you build up to much pressure differential you let the propellants slosh a bit until it decreases enough and then you continue. If you are in a hurry you might trade a bit of venting against extra RCS propellant.

[DanClemmensen]

Yeah, we need a pump engineer.

...or maybe a plumber. 

In the mundane world of water piping, a pump is characterized by its flow rate against a particular backpressure. Backpressue is usually quoted in "head", which is the height of a water column.   Plumbers compute the expected backpressure of a pipe system by summing the piecewise backpressures, where each fitting has a backpressure spec and there is a forumula to compute the backpressure of a length of pipe based on its length and diameter.

Clearly the backpressures will be different for other fluids.

[Nevyn72]

So what is easier to pump, a cryogenic liquid or a gas?

Is it more efficient to pump the liquid from the tanker to the depot and let ullage gas flow from the depot and return to the tanker to balance volumes?

Or is it better to pump ullage gas from the depot to the tanker and have that 'push' the liquid through?

Note: this presupposes the use of a gas equalisation line.

[eriblo]

So what is easier to pump, a cryogenic liquid or a gas?

Is it more efficient to pump the liquid from the tanker to the depot and let ullage gas flow from the depot and return to the tanker to balance volumes?

Or is it better to pump ullage gas from the depot to the tanker and have that 'push' the liquid through?

Note: this presupposes the use of a gas equalisation line.

To first order pumping power is volumetric flow times pressure differential. Gases have ~1000 times larger volume...

But as I stated previously I am not sure you need to move the gas with autogenous pressurization. Once you get past the transients the gas pressure is the vapor pressure at the temperature of the liquid. If you compress the gas on one side it will start condensing into the liquid while an expanding gas volume will be replenished by the liquid boiling. Since the mass of the liquid is generally much higher than that of the ullage gas the resulting temperature changes are relatively small as long as everything mixes well. Splashing and sloshing would be beneficial as long as the liquid outlet is submerged.

[OTV Booster]

I personally do not expect to see gas transfer/equilization lines. If they do pressure/temperature driven pumping (which I currently expect) then there is obviously no need and for electrical pumping I do not think it is worth the hassle of extra outlets, lines and connections.

If you build up to much pressure differential you let the propellants slosh a bit until it decreases enough and then you continue. If you are in a hurry you might trade a bit of venting against extra RCS propellant.

That last is the detail where the devil resides. How much venting? How much settling propellant? How long to transfer?


No ullage crossover and using thermal/pressure to power the transfer is mechanically simplest and avoids risk of recirculating splatter, but is it a path to acceptable propellant consumption? I really have not a clue.


There are times I wish I were more of a numbers guy.

[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...

That only solves half the problem, though.  The sending tank's pressure will be dropping, increasing the back pressure on the system.  To solve that, you either need to have really big pumps to drop the sending tank's ullage pressure so much that the prop pool boils, or you need a heater to boil prop on the sending side to keep the pressure up. Neither of these is an efficient solution, either energy-wise nor prop efficiency-wise.

Starting from a 0.1 Bar receiver tank and a 3 Bar sender tank, with the sender tank 2/3 full of prop (1/3 ullage volume) and the receiver tank empty of prop, the entire fluid propellant volume could be transferred to the receiver without any pumping or venting (final state: receiver 2/3 full with prop, 0.3 Bar ullage pressure, sender filled entirely with with 1 Bar ullage).
A worse case would be a sender tank almost entirely full of fluid prop with only a small ullage head volume, attempting to fill an empty tank: the equilibrium state with the maximum fluid transfer volume (assuming valves shut at ullage pressure equilibrium to avoid oscillation, the same starting pressures as previously, and tanks of equal volume) would mean that you can have no less than ~20% of the sender tank as ullage volume to complete a full fluid transfer from replenished ullage pressure alone (final equilibrium stage being the sender at 0.6 Bar all ullage, and the receiver 80% full of liquid prop with the ullage at 0.5 Bar).
The key trick is that all one needs to do to transfer more than that 80% capacity that is to vent the receiver again, and you now once again have a pressure differential to work with to complete transfer.

In contrast, the equalization line doesn't require any more gas to be wasted as ullage, needs tiny little pumps, doesn't require heaters in the mains, and is less complex in general.  The geysering/splash problem is likely a real one, but if it can't be solved with a bit of clever configuration of the pump outlet, then just putting a PMD around the equalization inlet probably solves it.

Whether you pump fluids directly or pump the ullage gas, it still requires a pump to be added, along with a power supply for that pump (power that could also be used for boiling prop to replenish ullage gas). Pumping the ullage gas is also not as simple as it appears, as for the same volumetric gas flow rate you do not get the same flow of liquid prop. It also requires the propellants in the receiver tank be settles and stratified during the transfer process or else the ullage recirc line will ingest liquids as well as gas (resulting in prop that needs to be resettled and repumped), whereas transfer to a sealed receiver allows for slosh and geysering during the transfer process, only the sender tank needs to keep the outlet covered with liquid prop.

[livingjw]

Is geysering during propellant transfer really a problem in space?  Heat transfer will be small, transfer pump pressures are low and there is no gravity to accelerate the vapor. Just trying to get a handle on the concerns.

John

[eriblo]

Is geysering during propellant transfer really a problem in space?  Heat transfer will be small, transfer pump pressures are low and there is no gravity to accelerate the vapor. Just trying to get a handle on the concerns.

John

I thought so too  Unfortunate word choice:

What do people mean when they talk about geysering? Cryogenic geysering is as far as I know related to cryogenic liquids in long pipes under enough acceleration and external heating that convection becomes important. I am not sure how this applies to millig propellant transfer?

Rad Mod came up with this to describe the impact of too high a transfer pressure on the receiver. If the inlet plume punches through the settled propellant it would be geyser like.

[OTV Booster]

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...

That only solves half the problem, though.  The sending tank's pressure will be dropping, increasing the back pressure on the system.  To solve that, you either need to have really big pumps to drop the sending tank's ullage pressure so much that the prop pool boils, or you need a heater to boil prop on the sending side to keep the pressure up. Neither of these is an efficient solution, either energy-wise nor prop efficiency-wise.

Starting from a 0.1 Bar receiver tank and a 3 Bar sender tank, with the sender tank 2/3 full of prop (1/3 ullage volume) and the receiver tank empty of prop, the entire fluid propellant volume could be transferred to the receiver without any pumping or venting (final state: receiver 2/3 full with prop, 0.3 Bar ullage pressure, sender filled entirely with with 1 Bar ullage).
A worse case would be a sender tank almost entirely full of fluid prop with only a small ullage head volume, attempting to fill an empty tank: the equilibrium state with the maximum fluid transfer volume (assuming valves shut at ullage pressure equilibrium to avoid oscillation, the same starting pressures as previously, and tanks of equal volume) would mean that you can have no less than ~20% of the sender tank as ullage volume to complete a full fluid transfer from replenished ullage pressure alone (final equilibrium stage being the sender at 0.6 Bar all ullage, and the receiver 80% full of liquid prop with the ullage at 0.5 Bar).
The key trick is that all one needs to do to transfer more than that 80% capacity that is to vent the receiver again, and you now once again have a pressure differential to work with to complete transfer.

In contrast, the equalization line doesn't require any more gas to be wasted as ullage, needs tiny little pumps, doesn't require heaters in the mains, and is less complex in general.  The geysering/splash problem is likely a real one, but if it can't be solved with a bit of clever configuration of the pump outlet, then just putting a PMD around the equalization inlet probably solves it.

Whether you pump fluids directly or pump the ullage gas, it still requires a pump to be added, along with a power supply for that pump (power that could also be used for boiling prop to replenish ullage gas). Pumping the ullage gas is also not as simple as it appears, as for the same volumetric gas flow rate you do not get the same flow of liquid prop. It also requires the propellants in the receiver tank be settles and stratified during the transfer process or else the ullage recirc line will ingest liquids as well as gas (resulting in prop that needs to be resettled and repumped), whereas transfer to a sealed receiver allows for slosh and geysering during the transfer process, only the sender tank needs to keep the outlet covered with liquid prop.

It looks like your model looks only at the ullage pressure and ignores plumbing losses and head from increasing liquid depth in the receiver. It's a starting point, IIUC.


The worst case would be a 1350t capacity tanker with 150t of propellant pumping the last load into a 1600t capacity depot. IIRC you are a proponent of using a standard tanker as a depot and not stretching the tankers beyond 1200t. Don't remember if you advocate for keeping the tanker at 1200t and separate tanks in the cargo space.


As much as I dislike separate tanks for delivery, the ullage thrust/consumption problem might be a strong argument in its favor.

[TheRadicalModerate]

If you build up to much pressure differential you let the propellants slosh a bit until it decreases enough and then you continue. If you are in a hurry you might trade a bit of venting against extra RCS propellant.

That last is the detail where the devil resides. How much venting? How much settling propellant? How long to transfer?

No ullage crossover and using thermal/pressure to power the transfer is mechanically simplest and avoids risk of recirculating splatter, but is it a path to acceptable propellant consumption? I really have not a clue.

I think I know why the Poiseuille results are so non-intuitive:  they don't include dynamic pressure.  They're a solution for a flow in equilibrium, but the non-equilibrium case requires the volumetric flow to be established.  So the dynamic pressure of the flow can still cause geysering.

So, two choices for limiting geysering:

1) Limit geysering by starting the pumping operation at low power/high acceleration, then gradually increase power and decrease acceleration as the pool fills.  The pool will then provide viscous damping as the flow rate inceases.

2) Assuming that only some small amount of prop will blob up and hit the equalization inlet, let it.  Soon enough, the pool will be deep enough that viscous damping will prevent geysering.  You wind up wasting a bit of energy re-pumping prop that recirculated, but it's probably a trivial amount.

A final note on how to limit recirculation:  For ullage acceleration a and geyser velocity v_g,  a blob will fall back into the pool before hitting the equalization inlet if the height h between the top of the pool and the inlet is greater than v_g²/(2a).  This is really just a limiting condition on how much geysering you can tolerate.

[TheRadicalModerate]

Is geysering during propellant transfer really a problem in space?  Heat transfer will be small, transfer pump pressures are low and there is no gravity to accelerate the vapor. Just trying to get a handle on the concerns.

John

I don't know.  Assuming that there's actually a pump, then there are two potential problems:

1) So many free-floating blobs in the receiver get sucked into the pressure equalization line between the tanks that transfer efficiency drops asymptotically to zero.  I think this is unlikely, unless the pool viscosity is so low that geysering can occur in an almost-full tank, when the geyser and the equalization inlet can be close together.

Solutions:
a) Lower the outlet flow when the receiver pool is shallow, then increase it as viscosity and pool depth conspire to eliminate the geysering.
b) Put the opposite of a PMD around the equalization inlet, designed to guid the occasional blob away from the inlet and down the walls, back to the main pool

2) Free-floating blobs crash into the tank walls with enough momentum to set up some sort of vibration/resonance in the system, causing slosh in the sending tank, which eventually leads to the outlet being uncovered.

Solutions:
a) Create reasonable baffles.
b) If liquid can come through the equalization outlet, make sure it doesn't splash into the sending pool.
c) Deal with the fact that the outlet will occasionally get uncovered, and make sure that the pump can re-prime itself. 

Note:  a self-priming pump may be annoying, but it's nothing like the amount of annoyance that'll occur if a pressure-fed system has the same problem and uncovers the inlet.  Then you're talking about having to re-establish the pressure differential between tanks, which could take hours.

I'm inclined to think that the geysering problem is something that needs some engineering applied to it, but that it's far from an insurmountable problem.

[eriblo]

Is geysering during propellant transfer really a problem in space?  Heat transfer will be small, transfer pump pressures are low and there is no gravity to accelerate the vapor. Just trying to get a handle on the concerns.

John

I don't know.  Assuming that there's actually a pump, then there are two potential problems:

1) So many free-floating blobs in the receiver get sucked into the pressure equalization line between the tanks that transfer efficiency drops asymptotically to zero.  I think this is unlikely, unless the pool viscosity is so low that geysering can occur in an almost-full tank, when the geyser and the equalization inlet can be close together.

Solutions:
a) Lower the outlet flow when the receiver pool is shallow, then increase it as viscosity and pool depth conspire to eliminate the geysering.
b) Put the opposite of a PMD around the equalization inlet, designed to guid the occasional blob away from the inlet and down the walls, back to the main pool

2) Free-floating blobs crash into the tank walls with enough momentum to set up some sort of vibration/resonance in the system, causing slosh in the sending tank, which eventually leads to the outlet being uncovered.

Solutions:
a) Create reasonable baffles.
b) If liquid can come through the equalization outlet, make sure it doesn't splash into the sending pool.
c) Deal with the fact that the outlet will occasionally get uncovered, and make sure that the pump can re-prime itself. 

Note:  a self-priming pump may be annoying, but it's nothing like the amount of annoyance that'll occur if a pressure-fed system has the same problem and uncovers the inlet.  Then you're talking about having to re-establish the pressure differential between tanks, which could take hours.

I'm inclined to think that the geysering problem is something that needs some engineering applied to it, but that it's far from an insurmountable problem.

One problem is that cryogenic geysering is an existing well known fenomen that can be a problem for (or even destroy) cryogenic piping on launch vehicles and tank farms. You are talking about the tank inlet jet splashing while filling a tank.

[TheRadicalModerate]

One problem is that cryogenic geysering is an existing well known fenomen that can be a problem for (or even destroy) cryogenic piping on launch vehicles and tank farms. You are talking about the tank inlet jet splashing while filling a tank.

Fair enough.  Let's call it... fountaining?  Something that implies that mass flow from the inlet is coming out with sufficient momentum to break the surface tension of the existing inlet pool.