hydrolox O/F ratios

[Aeneas]

Hi all,

long time, no see... Anyway. Do you see a general problem with having a hydrolox O/F ratio close to stoichiometric? I would assume 8 is not helpful anymore because of the too high risk of unburned oxygen reacting with the chamber but let's say 7.8? So similarly close to stoichiometric as it's with Raptor (though, here, it might make sense to counter act the film cooling a bit).
Or let's phrase the question the other way: What's the highest O/F (but still fuel rich) for hydrolox that does not eat the chamber without film cooling?

Thanks and cheers,
Aeneas.

[Gliderflyer]

You could run a regen engine at stoic with no film cooling if you design it right. The reason why you might not want to is the lower O/F ratios have higher Isp due to the hydrogen in the exhaust. You can play around in CEA to see what happens with varying O/F ratios.

There might be some weird TAN case where running leaner comes out on top from a system level, but I haven't looked into those.

[Robotbeat]

You could run a regen engine at stoic with no film cooling if you design it right. The reason why you might not want to is the lower O/F ratios have higher Isp due to the hydrogen in the exhaust. You can play around in CEA to see what happens with varying O/F ratios.

There might be some weird TAN case where running leaner comes out on top from a system level, but I haven't looked into those.

Ackshually…

Conservation of energy says that with a long enough nozzle (absurdly, ridiculously long, completely impractical) in vacuum, your Isp is maximized the closer you operate to stoichiometric. The chemical energy basically all gets converted to kinetic. Adding more hydrogen at that limit actually REDUCES available chemical energy and therefore REDUCES kinetic energy of the exhaust and therefore the exhaust velocity. (The long nozzle also serves to help convert molecular rotational to translational kinetic energy.) You can recreate this in RPA-Lite or whatever, but you may run into errors with too big of a nozzle… (to get ALL the energy out, condensed droplets have to evaporate, solids need to sublimate…)

Running hydrogen rich allows you to have a shorter nozzle for a given Isp as long as you’re not at the limit. AND it reduces the peak temperatures experienced for that Isp. And that’s the real critical issue. For a given temperature, hydrogen molecules are moving faster… conservation of momentum in collisions in equilibrium… to have the same momentum as heavier molecules, the hydrogen molecules have to be moving faster. But that energy comes from somewhere: the heat capacity per unit mass is higher for hydrogen than heavier molecules. And running away from stoichiometric means you have less available chemical energy.

it’s best to think of extra hydrogen as allowing you to have high Isp without melting your nozzle. For a given temperature limit, hydrogen gets you the highest Isp.

[Aeneas]

You could run a regen engine at stoic with no film cooling if you design it right. The reason why you might not want to is the lower O/F ratios have higher Isp due to the hydrogen in the exhaust. You can play around in CEA to see what happens with varying O/F ratios.

There might be some weird TAN case where running leaner comes out on top from a system level, but I haven't looked into those.

The thing I'm touching here is the energy optimal Isp. Sure, simply maximizing Isp gets you in the quite fuel rich realm and only with large ER, as Robotbeat said, it moves closer to stoichiometric but that's not where I'm going to. In a CO2 free world with cheap electricity, the rocket fuel competition might focus on production costs. And here you want to get the most bang for your hydrogen buck. Trading some Isp for lower tank mass and much more important: lower required energy to produce a kg of hydrolox might make sense. And this requires going closer to stoichiometric.

So thanks for the estimate! That seems to support my case!

[Robotbeat]

For the first stage, I would actually go deeply oxygen rich for hydrolox. This keeps the temperatures low enough not to melt your engine and improves your density by a lot.

[deltaV]

Conservation of energy says that with a long enough nozzle (absurdly, ridiculously long, completely impractical) in vacuum, your Isp is maximized the closer you operate to stoichiometric. The chemical energy basically all gets converted to kinetic. Adding more hydrogen at that limit actually REDUCES available chemical energy and therefore REDUCES kinetic energy of the exhaust and therefore the exhaust velocity. (The long nozzle also serves to help convert molecular rotational to translational kinetic energy.) You can recreate this in RPA-Lite or whatever, but you may run into errors with too big of a nozzle… (to get ALL the energy out, condensed droplets have to evaporate, solids need to sublimate…)

Combustion isn't complete even if the mixture is stoichiometric. Unburned hydrogen wastes a lot less mass than unburned oxygen does so it's better to go a little on the fuel-rich side even if the nozzle is infinite.

[Aeneas]

For the first stage, I would actually go deeply oxygen rich for hydrolox. This keeps the temperatures low enough not to melt your engine and improves your density by a lot.

Yeah, that what Ozan said, too. But this requires reeeeally cool combustion. RPA even fails on anything larger 55 O/F...^^

Maybe dilute with nitrogen or just water?

[jasonjulius1122]

Hi all,

long time, no see... Anyway. Do you see a general problem with having a hydrolox O/F ratio close to stoichiometric? I would assume 8 is not helpful anymore because of the too high risk of unburned oxygen reacting with the chamber but let's say 7.8? So similarly close to stoichiometric as it's with Raptor (though, here, it might make sense to counter act the film cooling a bit).
Or let's phrase the question the other way: What's the highest O/F (but still fuel rich) for hydrolox that does not eat the chamber without film cooling?

Thanks and cheers,
Aeneas.

Having a hydrolox (hydrogen-oxygen) oxidizer-to-fuel (O/F) ratio close to stoichiometric can pose challenges. While an O/F ratio of 7.8 or even 8 may increase the risk of unburned oxygen reacting with the chamber, it's important to consider other factors as well. The specific design of the engine, including chamber materials, cooling techniques, and combustion stability, plays a crucial role in determining the highest viable O/F ratio without film cooling. Achieving a fuel-rich mixture can help mitigate chamber erosion, but finding the optimal balance requires careful consideration of various factors to ensure safe and efficient operation.

[Aeneas]

Having a hydrolox (hydrogen-oxygen) oxidizer-to-fuel (O/F) ratio close to stoichiometric can pose challenges. While an O/F ratio of 7.8 or even 8 may increase the risk of unburned oxygen reacting with the chamber, it's important to consider other factors as well. The specific design of the engine, including chamber materials, cooling techniques, and combustion stability, plays a crucial role in determining the highest viable O/F ratio without film cooling. Achieving a fuel-rich mixture can help mitigate chamber erosion, but finding the optimal balance requires careful consideration of various factors to ensure safe and efficient operation.

But you wouldn't deem it impossible?

[SBerger]

All existing H2/O2 engines run fuel rich.  High temperature and free O2 = not _good for the chamber walls.  The highest O/F ratio I know about is 5.8:1.  BTW (getting on my soapbox now ...), No professional propulsion engineer I have ever known in 35 yrs. in the rocket business has ever used the terms "hydrolox", "Methalaox" or "kerolox" (off the soapbox )

[1]

Every couple of years I find an excuse to read through this old post again. This thread is a good one.

https://forum.nasaspaceflight.com/index.php?topic=35169.msg1227557#msg1227557

Your mixture may vary.

[Robotbeat]

All existing H2/O2 engines run fuel rich.  High temperature and free O2 = not _good for the chamber walls.  The highest O/F ratio I know about is 5.8:1.  BTW (getting on my soapbox now ...), No professional propulsion engineer I have ever known in 35 yrs. in the rocket business has ever used the terms "hydrolox", "Methalaox" or "kerolox" (off the soapbox )

Yeah, it started being mostly enthusiasts that used those terms but it’s common now.

[sebk]

You could run a regen engine at stoic with no film cooling if you design it right. The reason why you might not want to is the lower O/F ratios have higher Isp due to the hydrogen in the exhaust. You can play around in CEA to see what happens with varying O/F ratios.

There might be some weird TAN case where running leaner comes out on top from a system level, but I haven't looked into those.

Ackshually…

Conservation of energy says that with a long enough nozzle (absurdly, ridiculously long, completely impractical) in vacuum, your Isp is maximized the closer you operate to stoichiometric. The chemical energy basically all gets converted to kinetic. Adding more hydrogen at that limit actually REDUCES available chemical energy and therefore REDUCES kinetic energy of the exhaust and therefore the exhaust velocity. (The long nozzle also serves to help convert molecular rotational to translational kinetic energy.) You can recreate this in RPA-Lite or whatever, but you may run into errors with too big of a nozzle… (to get ALL the energy out, condensed droplets have to evaporate, solids need to sublimate…)

Running hydrogen rich allows you to have a shorter nozzle for a given Isp as long as you’re not at the limit. AND it reduces the peak temperatures experienced for that Isp. And that’s the real critical issue. For a given temperature, hydrogen molecules are moving faster… conservation of momentum in collisions in equilibrium… to have the same momentum as heavier molecules, the hydrogen molecules have to be moving faster. But that energy comes from somewhere: the heat capacity per unit mass is higher for hydrogen than heavier molecules. And running away from stoichiometric means you have less available chemical energy.

it’s best to think of extra hydrogen as allowing you to have high Isp without melting your nozzle. For a given temperature limit, hydrogen gets you the highest Isp.

Ackshually… not.

Energy is not velocity. And if you're changing mixture ratio velocity is a function of both energy and molecular mass.

If you reduce energy by half but replace half of atomic mass 18 water with atomic mass 2 hydrogen you have increased velocity, not decreased it.

[Robotbeat]

Wrong. Do the conservation of energy equation.

If the exhaust energy for one second is is 4MJ, and I’m accelerating 2kg of oxygen with arbitrarily high efficiency (long, insulated nozzle, and neglecting radiative emissions, and assuming the nozzle is made of a material which will not melt), its exhaust velocity is 2km/s. If I replace that 1kg of oxygen at near zero temperature with 1kg of hydrogen gas at near zero temperature and use the same 4MJ input energy, you’re telling me the hydrogen would magically have much higher exhaust velocity?

The mistake you’re making is using volume or molar quantity instead of mass. With the same mass, and the same efficiency, the same input energy, the exhaust velocity is going to be the same.

Energy IS velocity in the equation for kinetic energy: KE = (1/2)*mass*velocity^2

The lower molecular mass of the exhaust means you’re able to achieve higher temperatures without melting your nozzle, so you can handle higher input energy per kg of propellant if you using hydrogen. But other than that, and differences in ratio of specific heats and condensation points, etc, (all of which get expanded away in an arbitrarily long nozzle), kinetic energy is just one half the mass times velocity squared.

[Robotbeat]

Rocket engines are heat engines. They are remarkable heat engines in that because they operate with extremely high internal temperatures & temperatures and can expand their gases into essentially zero external pressure, they can get extremely high Carnot efficiency compared to your run of the mill car engine. The temperature limit from expanding that exhaust to essentially zero pressure is essentially absolute zero or close enough for our purposes. So your high temperature is very high, and your low temperature is very low.

Typical rocket engines aren’t going to have a nozzle so long as to extract 99% of that energy, but 70% Carnot efficiency is attainable, and it’s common for rocket engines to achieve 50% efficiency.

[nicp]

Equipartition theorem anyone? See Wikipedia.
My understanding (from chemistry lessons 40 years ago  (so forgive me if I get this wrong) - is that the heat generated in a reaction, including combustion in a rocket engine is approximately evenly shared between 3 things...
1) Combustion products zooming around, which you can collimate with a nozzle, great! This is what we want.
2) Vibrations of the combustion product molecules, imagine springs (bonds) between the atoms of the molecule bouncing. Useless, but I think your rocket nozzle can recover some of this heat.
3) The combustion product molecules tumbling in 3 axes. Again some can be recovered. This is heat again.

So it isn't as simple as mere conservation of energy (which would imply stochiometric is best).
Your energy of combustion does not magically turn only into the kinetic energy of exhaust. You may have noticed rocket exhaust tends to be hot.
So  smaller lighter molecules in the exhaust can be better, see (as has been mentioned) typical H2/O2 engines which run around 6:1, because they have less mass to hold energy in 'tumbling' or 'jiggling' (there's a Feynman word).

I think this ratio is significantly driven by having smaller and lighter molecules in the exhaust - like unburned H2.
RL-10 is one of the highest ISP engines ever built - these guys are not stupid. They aren't going to throw away unused energy (non-stochiometric burning) for no reason.

IANARS, but if someone with real experience can talk about the equipartition theorem or tell me (with references) why I am wrong, I'd appreciate it.

Nic

EDIT: Typo
EDIT2: There's 'mv' (momentum) here too - the lighter the 'm', the bigger the 'v' which pretty much directly scales to specific impulse.

[Robotbeat]

Yeah, essentially all the spinning and vibration energy can be recovered with a long enough nozzle. Because as the kinetic/translational energy gets extracted, you’re left with energy in the other modes. But then the equipartition theorem means that after collisions, equilibrium is restored between the three modes, giving the nozzle further opportunity to extract the energy. And on and on. I was aware of all of this when I made my post, which is why I insisted on the arbitrarily long nozzle, and that’s why I referred to the ratio of specific heats here: “But other than that, and differences in ratio of specific heats and condensation points, etc, (all of which get expanded away in an arbitrarily long nozzle)”

So again, what I said was correct. It really is that simple in this limit.

And no one is calling anyone stupid. The practicalities of rockets mean you’re not going to push something to the limit like this because the weight of your nozzle will exceed the rest of your rocket if the nozzle actually has to be built out of real materials.


But the real major constraint is you want to avoid the rocket engine from melting, so your temperature is a greater limit than the energy. And when THAT is the case, hydrogen gas often wins.

[Aeneas]

All existing H2/O2 engines run fuel rich.  High temperature and free O2 = not _good for the chamber walls.  The highest O/F ratio I know about is 5.8:1.  BTW (getting on my soapbox now ...), No professional propulsion engineer I have ever known in 35 yrs. in the rocket business has ever used the terms "hydrolox", "Methalaox" or "kerolox" (off the soapbox )

That's why I asked for the limit possible. Currently the highest O/F I'm aware of is with Vulcain 2. The overall engine runs at 6.1 but they lose a lot of hydrogen in the gas generator, so in MCC, the mixture is actually at 6.74. RS-68A should be around 6.5 in MCC.

[dondar]

Wrong. Do the conservation of energy equation.

If the exhaust energy for one second is is 4MJ, and I’m accelerating 2kg of oxygen with arbitrarily high efficiency (long, insulated nozzle, and neglecting radiative emissions, and assuming the nozzle is made of a material which will not melt), its exhaust velocity is 2km/s. If I replace that 1kg of oxygen at near zero temperature with 1kg of hydrogen gas at near zero temperature and use the same 4MJ input energy, you’re telling me the hydrogen would magically have much higher exhaust velocity?

The mistake you’re making is using volume or molar quantity instead of mass. With the same mass, and the same efficiency, the same input energy, the exhaust velocity is going to be the same.

Energy IS velocity in the equation for kinetic energy: KE = (1/2)*mass*velocity^2

The lower molecular mass of the exhaust means you’re able to achieve higher temperatures without melting your nozzle, so you can handle higher input energy per kg of propellant if you using hydrogen. But other than that, and differences in ratio of specific heats and condensation points, etc, (all of which get expanded away in an arbitrarily long nozzle), kinetic energy is just one half the mass times velocity squared.

the exhaust velocity is ultimately determined by combination of conservation of energy and conservation of momentum.
final simplified formule of exaust velocity can be determined as  v_exaust=sqrt(T/M*f(M)). f(m) depends on the molecular density of the exaust. basically more particles bigger it is. In other words less molecular weight of the exhaust particles higher efficiency of the chemical engine.
It is that simple.

[dinapool]

In the context of your question, an O/F ratio of 7.8 for hydrolox could potentially be in a range where it's not too close to stoichiometric conditions and could offer a balance between efficient combustion and maintaining reasonable safety margins for chamber integrity. However, specific values for the highest O/F ratio without film cooling for hydrolox would depend on various factors, including chamber design, material properties, cooling mechanisms, and the desired level of combustion efficiency.