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I've read somewhere that gas-gas engines (engines where both the fuel and the oxidizer enter the combustion chamber as gases) have greater efficiency of combustion as compared to liquid-liquid or gas-liquid engines. This is due to better mixing.

So, I was wondering: how much efficiency is gained by gas-gas combustion over gas-liquid combustion? And similarly, in gas-liquid combustion over liquid-liquid combustion? Are these efficiencies meaningful or marginal? Are there any other benefits to gas-gas combustion vs others (e.g. better combustion stability)?

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Combustion appears only in gaseous phase. Liquids need to vaporize in order to burn. Considering temperatures in combustion chamber this happens fast, but still part of the energy is wasted in this process. This energy varies from liquid to liquid and is called latent heat of vaporization or enthalpy of vaporization (∆Hvap). It's expressed in KJ/mol and is pressure dependent - therefore not constant even for same liquid. Also, more energy is needed as pressure rises.

As cryogenic liquids are stored at very low temperatures, they are first heated till the critical temperature, then vaporized, and finally heated to flash point when they ignite. Each step is a waste of energy compared to gases at standard temperature. If gasses are pressurized to high extent than they bring additional energy to rocket. Overall difference is not significant, between 3-5% of specific impulse, but neither negligible.

In order to precisely calculate this waste you must know working conditions of the engine such as: O/F ratio, combustion pressure, heats of vaporization at given pressure, ambient pressure etc. For reference hydrolox engine working at 68,05 atm has 4,7% lower specific impulse if you compare LH2-LOX and GH2-GOX. Therefore best in terms of specific impulse are gas-gas, followed by gas-liquid and the worst are liquid - liquid engines for the same oxidizer/fuel mixtures.

The reason we still prefer liquids is because they are denser and require less materials for rocket storage. Gasses should be compressed to several hundreds of atm in order to achieve reasonable densities. To store them you need thick walls which means a lot of dry mass added to the rocket.

At the end, despite poorer performance, liquids appear victorious. As far of combustion instabilities, liquids change volume significantly up to hundreds or even thousand times when vaporized and liquid - liquid engines are more prone to instabilities than the other two types. Instabilities rise with the increase of combustion chamber volume. For very big liquid fueled engines, like Rocketdyne F1, its a real feat of engineering to make them disappear.

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    $\begingroup$ But cryogenic liquid H2 is much better for cooling of combustion chambers than gaseous H2. $\endgroup$ – Uwe Feb 10 '20 at 23:28
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    $\begingroup$ "Combustion appears only in gaseous phase" Does this also apply for solid fuel rockets? Or solid combustion process is different to liquid combustion? I can understand how liquids have to first vaporize in order to combust, but it's a bit harder to understand how this works with solids. $\endgroup$ – Sergiy Lenzion Feb 10 '20 at 23:40
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    $\begingroup$ @LeoS Some of them like nitrocellulose based undergo thermal decomposition, they are actually mono-propellants. They don't have distinctive fuel or oxidizer, they decompose to gasses when they get enough thermal impulse. Other types are composite rocket fuels which have oxidizer (mainly ammonium perchlorate), metal fuels suspended in polymer matrix. When sufficient thermal impulse is applied oxidizer decomposes to gaseous products with oxygen as active gas, polymer undergoes pyrolisis to flammable gasses and metals are vaporized (in case of Mg and Al). $\endgroup$ – WOW 6EQUJ5 Feb 11 '20 at 0:13
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    $\begingroup$ Another thing worth considering is that for combustion like hydrolox combustion is typically not done at optimal ratios since the reaction could be 7000K which is just too hot. As a result, the loss of efficiency, may not matter that much $\endgroup$ – Oscar Smith Feb 11 '20 at 4:12
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    $\begingroup$ There are presumably also some advantages for liquid phase ingredients in rockets with a large mass flow, as a liquid injector can stuff more mass into the chamber in a given time for a given pressure and injector area. Or so I assume. $\endgroup$ – Starfish Prime Feb 11 '20 at 10:31

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