Author Topic: Q&A Fuel and oxidizer mass ratios (Read 39818 times)

Slarty1080 · « **on:** 01/27/2020 01:18 pm »

I’m in discussion with someone on another forum who says that all rocket engines tend to burn fuel rich. My understanding was that rocket engines are very much oxygen rich in almost all cases. Can someone confirm (or contest) my belief? Any references to actual figure would be very helpful especially for Raptor and the RS25.

mmeijeri · « **Reply #1 on:** 01/27/2020 01:29 pm »

Fuel-rich simply means more fuel than the stoichiometric ratio, in other words more fuel than can be burned completely with the oxidiser, not more fuel than oxidiser by mass. You will typically have more considerably more mass in oxidiser than fuel. You were likely talking past each other and both meant the right thing, though the person you were talking to was technically correct terminology-wise.

e of pi · « **Reply #2 on:** 01/27/2020 01:45 pm »

As a worked example, the stoichiometric ratio for reacting hydrogen and oxygen is an O:F (mass) ratio of 8:1. However, most engines like J-2, RL-10, and SSME run with a propellant mix that ranges from 5:1 or 6:1. In other words, they're running with less substantially less oxygen than the "ideal" reaction, and thus are fuel-rich in chemistry terms though oxygen still makes up >80% of the propellant mix.

Working the equations for kerosene is a little more complex because it doesn't have as clearly defined a formula, but it works out to a mass ratio for ideal combustion of about 3.4:1 to 3.5:1. The F-1 engine burned at about 2.27:1, while the RD-180 uses about 2.72--thus, again, both are running fuel rich in chemical terms though the propellant mix is more than two thirds oxygen.

For extra fun, you can get into "oxygen rich" or "fuel rich" staged combustion, where the preburner's mixture ratio varies radically from the ratio of the main chamber. The RD-180 is an oxygen-rich staged combustion engine--it runs all the oxygen but not quite all the kerosene through the preburner and turbopumps to avoid the carbon deposits ("coking") that results from high-temperature combustion of kerosene. However, once the remaining kerosene is injected at the main combustion chamber, the final reaction overall is fuel-rich.

Slarty1080 · « **Reply #3 on:** 01/27/2020 05:39 pm »

So if you were manufacturing hydrogen and oxygen by electrolysis of water (only) for an O2/H2 burning engine you would be short of hydrogen or would end up with excess oxygen? And related to this if you were making methane and oxygen using the sabatier reaction (oxygen and hydrogen from electroylsis of water and carbon dioxide as required) for a raptor engine you would similarly end up with an excess of oxygen?

e of pi · « **Reply #4 on:** 01/27/2020 06:02 pm »

Quote from: Slarty1080 on 01/27/2020 05:39 pm

So if you were manufacturing hydrogen and oxygen by electrolysis of water (only) for an O2/H2 burning engine you would be short of hydrogen or would end up with excess oxygen? And related to this if you were making methane and oxygen using the sabatier reaction (oxygen and hydrogen from electroylsis of water and carbon dioxide as required) for a raptor engine you would similarly end up with an excess of oxygen?

Making a hydrogen/oxygen propellant mix from water would indeed end up with excess oxygen. Making methane is a little more complex since there's a few ways to do it. It depends on if your hydrogen feedstock is water or pure H2, and which reactions you're using. If you purely ran water electrolysis and atmospheric CO2 for the inputs to a sabatier process, I think you would end up with oxygen excess.

Proponent · « **Reply #5 on:** 01/27/2020 08:36 pm »

There are lots of factors determining the optimum O/F. Isp can usually be increased by running a bit richer (lower O/F) than stoichiometric, in part because the molecular weight of the fuel is usually lower than that of the oxidizer (over simplifying a bit), resulting in a higher sound speed for the exhaust products. There is a lengthy discussion here.

To increase Isp for a given nozzle expansion, one also wants a low ratio of specific heats in the exhaust, in other words, more simpler molecules that have fewer ways to retain energy. That's a reason you might want more H₂ and less H₂O in the exhaust of an O₂-H₂ engine.

Though we often forget this, maximization of Isp is not in and of itself desirable, in that it's often better to run at an O/F that gives a slightly higher overall density, so that tankage of a given size will hold a little more impulse. The trade between Isp and density depends on the required delta-V and the relationship between propellant volume and vehicle mass.

In fact, the ideal O/F changes with time. Just to illustrate the concept, suppose you had a rocket of fixed overall volume sitting on the launching pad that could easily operate and any mixture ratio. Now consider the first drop of propellants burned. That mass of that drop will not need to be accelerated, so it might as well pack the most impulse possible, i.e., it should be optimized for maximum impulse density (impulse per unit volume). Subsequent drops of propellant should be weighted more and more toward Isp, as their masses matter.

Optimum O/F might be affected by other things too. Consider the Saturn V's third stage, which achieved orbital insertion and was then restarted a few hours later for trans-lunar injection. While the stage was coasting in LEO, hydrogen was boiling off. There was very little boil-off of oxygen, however, because boiled-off hydrogen was used to cool the lox. The fact that lox was relatively stable while hydrogen was a wasting asset affects the optimal O/F for the TLI burn, under the constraint of a fixed size or mass of the stage.

In the example of lox-hydrogen propellant cycle, where the propellants come from ISRU, the overabundance of oxygen might lead one to run engines at a higher O/F to maximize the efficiency of the entire system (including the propellant production part), at the modest expense of vehicle mass efficiency. You always need to keep in mind what it is you're maximizing (hint: it's never Isp).

Slarty1080 · « **Reply #6 on:** 01/27/2020 08:48 pm »

Thanks for putting me straight - I have owned up to the mistake on the other site and will keep this in mind in future.

Hog · « **Reply #7 on:** 01/30/2020 07:14 pm »

RS-25 run at approx 6:1.

libra · « **Reply #8 on:** 02/19/2020 01:01 pm »

Random question related to my pet peeve, suborbital refueling...
Since the O/F ratio of kerolox and keroxide are 3 and 7 respectively...
100 tons of props should be
- 87.5 mt H2O2 and 12.5 mt of kerosene
- 75 mt and 25 mt of kerosene
I was wondering if the second one would need to transfer fuel with oxidizer even with such a different O/F... the difference in mass is not that big, it is proportionally that the difference is large...

e of pi · « **Reply #9 on:** 02/19/2020 01:19 pm »

Quote from: libra on 02/19/2020 01:01 pm

Random question related to my pet peeve, suborbital refueling...
Since the O/F ratio of kerolox and keroxide are 3 and 7 respectively...
100 tons of props should be
- 87.5 mt H2O2 and 12.5 mt of kerosene
- 75 mt and 25 mt of kerosene
I was wondering if the second one would need to transfer fuel with oxidizer even with such a different O/F... the difference in mass is not that big, it is proportionally that the difference is large...

I don't think that's a chemistry question--it's a vehicle design and operational procedure question. If you don't transfer a balanced mix of fuel and oxidizer and instead try to transfer just fuel, then you need oversized oxidizer tanks on the vehicle receiving the transfer, while needing oversized fuel tanks on the tanker vehicle which would reduce the benefit of using identical vehicles for suborbital refueling.

You'd need to make a study of whether the benefit of only having to transfer one fluid makes up for the loss of design commonality or whatever modularity is needed to swap oversized fuel tanks into a tanker and oversized oxidizer tanks into an orbiter or of simply having larger and heavier tanks in every vehicle capable of accommodating both a tanker's load of fuel and an orbiter's load of oxidizer, which is a pretty detailed operational and design question.