A LOX propellant depot with Last Minute Hydrogen

[Burninate]

Thought this idea deserved its own thread.

The normal mode for a propellant depot is to send up the fuel over the course of months or years unmanned, and then send up crew at the last minute, and depart with the crew and a bunch of the fuel.  That minimizes radiation exposure and logistical expenses.

Thus far, liquid hydrogen - LOX provides the same high thrust and around 30-50% better velocity per percentage mass expenditure than comparable chemical propellants like kerosene-LOX or hypergolic hydrazine-NTO, the traditional choice for storeable in-space propellant.  But liquid hydrogen is a deep cryogen - and boils off at the slightest whiff of heat.  Liquid hydrogen rocket stages are managed in a process of relatively quick, controlled boil-off at all times.

The conventional supposition is that this might be addressed by building a combination of active and passive cryocoolers in order to ensure Zero Boil-Off (ZBO).  This is, to put it bluntly, a Hard Problem, probably requiring considerable mass at the prop depot spent on multi-stage liquid helium refrigeration and radiators, heavy insulation, a very large, multilayer sunshield, an orbit well away from the huge thermal emitter that is Earth, and large solar panel arrays to power the process.  I have not looked very thoroughly at this challenge in the literature, but from the sound of it, solutions are low TRL.

The emerging consensus is that you can get halfway to the performance of LH2, simplify launch operations, and enable Mars ISRU besides, using another propellant combination, methane-LOX.  This is probably The Future, but I ran across this idea that seems to give hydrogen prop depots a chance:

Last Minute Hydrogen
So forget boil-off.  The stoichiometric mass ratio for hydroLOX combustion to H2O is 2 tons hydrogen to 16 tons oxygen (EDIT: but optimal ratio is 1:6, see Proponent's excellent post below).  The oxygen will keep in space, safe at 90K or so, which is achievable with passive shielding, perhaps even in LEO with some active assistance (using comparatively easy liquid nitrogen cryocooling).  Just launch the LOX and the spacecraft components over a long period of time, then (if manned) the crew capsule and the hydrogen at the last minute, and you'll have an effective hydrogen-LOX Earth Departure stage without all the hassles of ZBO.  Propellant mass is capped at 9 7 * the launch vehicle payload increment, assuming that H2 is shipped on its own separate from crew, shortly afterwards.  It's also only good for the one EDS burn, so unlike methane this is not a solution for a return stage.  Even so - we have been using liquid hydrogen rocket engines for half a century, and this enables a relatively simple EDS without the harsh mass penalty of hypergolic storeable propellants or a mission limited to a small payload mass fraction on a mega-launcher.

If you assume a 53 ton launch vehicle, with 8 launches spent on LOX, 4 launches on structure, an SEP system, supplies, and habitat, 1 launch on a crew capsule, and then 1 launch on hydrogen, you get a 14-launch mission that gets 4500m/s out of 450s Isp, good for sending 318 tons of payload to MTO.  Launch about every 8 weeks and you can do this every Mars conjunction at a steady cadence.

[MP99]

Note that hydrolox engines run at a mixture ratio of ~6:1 rather than 8:1, though that doesn't change the general principle of what you're proposing.

Cheers, Martin

[Burninate]

Well that's odd.  I wonder what the physical basis for that is.

[Proponent]

For me, the first step in understanding why stoichiometric mixture ratios (e.g., 8:1 for lox-hydrogen) are not generally optimal was to ask myself why I thought they were to begin with.  If you mix 8 g of oxygen with 1 g of hydrogen at room temperature and pressure and ignite the mixture, you can convert most of if into water.  In energy terms, that mixture ratio is quite efficient, in that other ratios would leave you with leftover hydrogen or leftover oxygen, and you'd be getting less energy out per gram of oxygen-hydrogen mixture.  So, the 8:1 ratio optimizes energy release under those conditions.

There are two problems with applying that result to a rocket engine.  First of all, we're not interested in maximizing energy release per mass of propellant.  Most of the time, what we want to optimize is something more like thrust per mass flow rate or thrust per volume flow rate.

Secondly, conditions in a rocket engine's combustion chamber are nothing like room temperature and pressure.  If you burn an 8:1 oxygen-hydrogen mixture at, say, a temperature of 3000 K and a pressure of 100 atmospheres, you're not going to get pure water as the result.  Under those conditions, molecules slam into each other hard enough and often enough to break water molecules apart.  You get significant amounts H, O, H₂, O₂, OH and H₂O.

Take a look at the two attached plots, which show chamber temperature, effective exhaust velocity and other parameters as functions of mixture ratio for lox-hydrogen and lox-methane engines operating at a chamber pressure of 10 MPa (99 atm) and a nozzle-exit pressure of 0.1 MPa (0.099 atm).  I used RPA to generate these curves.  Quantities shown in solid lines are plotted on the left-hand scale; those in dashed lines are plotted on the right-hand scale.

The solid black curve shows exhaust velocity, which is almost the same as specific impulse (aside from being measure in different units, there's also a contribution to thrust arising from amount by which the exit pressure exceeds ambient, but that's small in the cases considered here).  Typically, that's what people think about maximizing.

Now look at the lox-hydrogen plot.  Chamber temperature, in red, peaks close to the stoichiometric ratio of 8:1 (shown by the dotted brown vertical line), as you might naively expect.  But exhaust velocity peaks near 4:1, i.e., when there's a large excess of hydrogen.  Why?  Notice that the speed of sound in the chamber (blue) keeps rising as the mixture ratio decreases.  That's because the speed of sound is proportional to the square root of the ratio of specific heats times the temperature divided by the mean molecular mass.  As we dump in more and more hydrogen, temperature goes down, but the ratio of specific heats stays about the same and the molecular mass decreases, raising the speed of sound.  Now, I'm glossing over a few things here, but the speed of sound has a lot to do with how fast a gas can expand.  As the gases expand into the nozzle, their speed will be magnified, but the speed of sound sort of tells you what speed is being magnified to begin with.  The speed of sound, after all, is simply the speed at which pressure disturbances propagate.  The only thing accelerating the exhaust gases is pressure, so you can see why the speed of sound is relevant.

So why doesn't the exhaust velocity just keep increasing as mixture ratio decreases?  Well, note that the temperature decreases too.  For mixtures just a little leaner than stoichiometric, it doesn't decrease much, but around 4.5 it starts falling off pretty quickly.  That's bad, because what the nozzle is doing is converting heat into motion.  The lower the temperature in the chamber, the less heat there is to work with.

So, the fact that exhaust velocity peaks at a mixture ratio of about 4 is related to the trade-off between decreasing the molecular weight of the exhaust gases and decreasing their temperature.

So why do lox-hydrogen engines usually run at mixture ratios of 5 or 6?  Because a ratio of 4 means having an awful lot of hydrogen, and hydrogen is not very dense.  Big fuel tanks would be needed and, for a given thrust level, engines would need bigger, heavier plumbing to carry all of that hydrogen.  As result, even though specific impulse would be higher at a mixture ratio of 4, overall vehicle performance would usually be lower.  That's just another example of how you need always to keep in mind what you're optimizing for.  Optimizing for maximum chemical energy release isn't anywhere near the whole story, nor is maximizing specific impulse.

The nozzles considered here range in expansion ratio (exit area to throat area) from 50-ish at lowest mixture ratio  to 80-ish at the high end.  If we were considering low-expansion nozzles (think of relatively low-pressure first-stage engines, like the classic H-1), another effect would come into play, namely the fraction of the available energy (enthalpy) that the nozzle could convert into motion.  Basically, complex molecules keep more energy in their internal degrees of freedom (rotation, bending, stretching) than do simple molecules.  If the nozzle doesn't have a large expansion ratio, the exhaust gasses will still be quite warm and will contain a lot of wasted energy when the pass through the exit.  That problem is worse for complex molecules.  That's a long way of saying that the optimal mixture ratio depends on the expansion ratio.

Things would also look different if, say, the expansion ratio instead of the pressure ratio were kept constant.

IANARS, but I think you could say that, as a rule of thumb, the more hydrogen (or other light element, such as lithium) there is in the fuel, the further below the stoichiometric ratio the optimum will lie.

I've gone on long enough.  Let me just close by suggesting a look at the lox-methane curve.  You'll note that here, unlike in the case of lox-hydrogen, chamber temperature peaks about 3.75, a bit below the stoichiometric ratio of 4.

Oh, and the optimal mixture ratio can actually change throughout flight for a variety reasons.  Early on, for example, it might be desirable to maximize thrust at the expense of specific impulse to reduce gravity losses.

Oh, and do remember that this is a simple, 1-D, frozen-flow (chemical composition is assumed constant throughout the nozzle) calculation.  Reality will differ.

EDIT:  Corrected a few typos, cleared a bit of debris, and expanded the explanation of the role of the speed of sound, among other things.

[IslandPlaya]

Superb post Proponent!
My knowledge has been embiggened.
Thank you
 

[Remes]

Some of the advantages of propellant depots are the decoupling of risks. Bring up oxygen, bring up fuel, maybe some habitats, etc, and if everything is fine, prepare crew and start.

If you do a last minute delivery before crew lift off, this two elements are closely coupled. If the hydrogen delivery fails, everything fails. All preparations done are lost, crew and ground support waiting, etc.

In contrast: if the hydrogen is brought up months before the crew is scheduled to start and something happens, there is time to react. (For really big missions it might be worth to keep a core as backup available).

[Lar]

Superb post Proponent!
My knowledge has been embiggened.
Thank you
 

Seconded. We need to pin that post somewhere, it's such a cogent explanation.

[Lar]

Some of the advantages of propellant depots are the decoupling of risks. Bring up oxygen, bring up fuel, maybe some habitats, etc, and if everything is fine, prepare crew and start.

If you do a last minute delivery before crew lift off, this two elements are closely coupled. If the hydrogen delivery fails, everything fails. All preparations done are lost, crew and ground support waiting, etc.

In contrast: if the hydrogen is brought up months before the crew is scheduled to start and something happens, there is time to react. (For really big missions it might be worth to keep a core as backup available).

Excellent point. Suggests that having a second hydrogen tanker ready to go would be prudent. If we are getting to the level of 250+ ton 12 launch missions (corrected out 2 LOX launches from the original due to non stoich ratio, I think that's right) having another tank module ready to go might not be that big of an expense.

[sdsds]

If you do a last minute delivery before crew lift off, this two elements are closely coupled. If the hydrogen delivery fails, everything fails. All preparations done are lost, crew and ground support waiting, etc.

This leads to a mission mode where crew and hydrogen launch together. They pull into the depot, LOX up, and go.

[A_M_Swallow]

Some of the advantages of propellant depots are the decoupling of risks. Bring up oxygen, bring up fuel, maybe some habitats, etc, and if everything is fine, prepare crew and start.

If you do a last minute delivery before crew lift off, this two elements are closely coupled. If the hydrogen delivery fails, everything fails. All preparations done are lost, crew and ground support waiting, etc.

In contrast: if the hydrogen is brought up months before the crew is scheduled to start and something happens, there is time to react. (For really big missions it might be worth to keep a core as backup available).

Excellent point. Suggests that having a second hydrogen tanker ready to go would be prudent. If we are getting to the level of 250+ ton 12 launch missions (corrected out 2 LOX launches from the original due to non stoich ratio, I think that's right) having another tank module ready to go might not be that big of an expense.

The single mission to somewhere may not be extinct but IMHO will become increasingly rare.  Where a series of missions exist the LON hydrogen tank for this mission becomes the main hydrogen tank for the next mission.

[MP99]

If you do a last minute delivery before crew lift off, this two elements are closely coupled. If the hydrogen delivery fails, everything fails. All preparations done are lost, crew and ground support waiting, etc.

This leads to a mission mode where crew and hydrogen launch together. They pull into the depot, LOX up, and go.

If the payload launches with its EDS, it will need to have a big enough tank to carry the H2 load, anyway.

From the practicalities, it sounds like avoiding transfer of H2 as a deep cryogen is also an advantage.

Cheers, Martin

[MarkM]

Thanks for starting this thread, it relates to an idea that has been running in the back of my mind regarding the trade-offs between the various types of chemical propellants based on length of mission.  When does the higher ISP of hydrogen is offset by the higher mass/technology requirements of long-term storage?

[Lar]

The single mission to somewhere may not be extinct but IMHO will become increasingly rare.  Where a series of missions exist the LON hydrogen tank for this mission becomes the main hydrogen tank for the next mission.

Nod. And the next mission doesn't even (necessarily) have to be to the same place...

[muomega0]

The mission set is rather vague, as is the architecture.   So how does 'last minute' hydrogen solve BEO exploration challenges?

The first issue is crew health and trip time.  One hybrid architecture prepositions the chemical LOX/LH2 at L2 and a Mars orbit.   how does one get 'last minute' hydrogen pre-positioned in LEO, L2, and Mars depots and it what quantities?  Not specified.  The other hybrid chemical/EP architecture uses a chemical kick start, then continuous EP to reduce crew trip time.

A 7m fairing is likely the starting point for 'last minute' hydrogen, or is it multiple smaller simultaneous launches with transfer?  Volume and mass calculations not presented.   Either way then a 6 day  lunar sortie (skipping lots of details) using ACES (?) has been outlined previously--recall that ULA uses a transfer stage acting like a depot to head to lunar only.   How does one stage about a half dozen of these 'last minute'  hydrogen transfers to L2 and the Mars depots without zero (or 0.01%/day?) boiloff to meet the mission mass and cost budget  (an 10X increase from 100mT to 900 to 1200 mT)?

The LEO depot or LEO gas station allows multiple smaller LVs to supply 70% of the mass for BEO missions:  propellant.   To reduce IMLEO, raise the ISP, hence EP with less propellant but requires power, perhaps MWs.  To reduce the station keeping propellant to zero, simply add power rather than burn propellant--recall that ULA used tons of LH2 boiloff for station keeping and LOX ZBO in their depot approach--make sure you account for this in the trade.

If you produce 'last minute' hydrogen at the depot location (e.g lunar or mars or asteroid), consider how much more additional power is required if this is done in 40 days rather than 360 days.   If you include EP with its 10s of KW if not MWs of power to transfer the propellant, why not take 10 kW or so and make the LH2 zero boiloff?   Did you consider this in the trade or architecture?  What if the departure time is delayed? 

Adding ~10 kW of power and refrigerators to each depot that can last for decades versus 'last minute' hydrogen clearly has a significant number advantages.  Would you outline or quantify the advantages of 'last minute' hydrogen wrt each of its destinations.

[MP99]

The LEO depot or LEO gas station allows multiple smaller LVs to supply 70% of the mass for BEO missions:  propellant.

At 6:1, the advantage only drops to 60%. But the payload ends up being 1/3rd heavier (25% LH2).

To reduce IMLEO, raise the ISP, hence EP with less propellant but requires power, perhaps MWs.  To reduce the station keeping propellant to zero, simply add power rather than burn propellant--recall that ULA used tons of LH2 boiloff for station keeping and LOX ZBO in their depot approach--make sure you account for this in the trade.

ULA used 300s Isp for the boiloff gas used as thruster.

In LEO, I don't believe it's possible to eliminate station keeping, though you could reduce it via SEP, at the expense of having an extra liquid in the depot.

Cheers, Martin

[A_M_Swallow]

{snip}
In LEO, I don't believe it's possible to eliminate station keeping, though you could reduce it via SEP, at the expense of having an extra liquid in the depot.

A SEP tug is under development, which the ARM project may use.  Reusable SEP tugs may wish to refuel when picking up a new cargo.  This may even be the same propellant as used by the depot for station keeping.

[MATTBLAK]

LOX/CH4 Depots working in concert with S.E.P. technology could give a lot of Exploration capability.

[MP99]

{snip}
In LEO, I don't believe it's possible to eliminate station keeping, though you could reduce it via SEP, at the expense of having an extra liquid in the depot.

A SEP tug is under development, which the ARM project may use.  Reusable SEP tugs may wish to refuel when picking up a new cargo.  This may even be the same propellant as used by the depot for station keeping.

If the depot is in a fairly low LEO, then it needs a fair bit of station keeping to overcome drag. ISTR 0.1% per day of mass of the depot at 300s Isp. Call it 100 kg/day for a 100t depot.

For same depot at 3000s Isp, call it 10 kg/day.

What power / solar panels do you need for 10 kg/day SEP @ 3000s?

I suspect that will need big panels, which will increase drag, which increases panel size again (and prop consumption), which increases drag, which... . Vicious circle.

Cheers, Martin

[KelvinZero]

Reminds me of those schemes to gather gas from the upper atmosphere and recover momentum by electric propulsion. They seem particularly appropriate here since I dont think they could collect much hydrogen anyway.

The lost momentum shouldn't be proportional to mass though, it should be proportional to surface area, particularly, I imagine, the front facing surface area. Maybe a long zeppelin shape covered in solar panels? The density of liquid oxygen compared to say the ISS should help also. I wonder why I have never seen a station that looks optimized to reduce drag.

(edit) just noticed a problem with my zeppelin.. A depot probably wants to stay sun oriented to keep a shade always facing the sun.

Failing that.. orbit higher!

[MP99]

Reminds me of those schemes to gather gas from the upper atmosphere and recover momentum by electric propulsion. They seem particularly appropriate here since I dont think they could collect much hydrogen anyway.

The lost momentum shouldn't be proportional to mass though, it should be proportional to surface area, particularly, I imagine, the front facing surface area. Maybe a long zeppelin shape covered in solar panels? The density of liquid oxygen compared to say the ISS should help also. I wonder why I have never seen a station that looks optimized to reduce drag.

(edit) just noticed a problem with my zeppelin.. A depot probably wants to stay sun oriented to keep a shade always facing the sun.

Failing that.. orbit higher!

The station keeping is basically just to overcome drag. Doesn't matter what the mass is.

Cheers, Martin