Rocket Propellant - Mixture Ratio

Mixture Ratio

The theoretical exhaust velocity of a given propellant chemistry is a function of the energy released per unit of propellant mass (specific energy). Unburned fuel or oxidizer drags down the specific energy. However, most rockets run fuel-rich.

The usual explanation for fuel-rich mixtures is that fuel-rich mixtures have lower molecular weight exhaust, which by reducing increases the ratio which is approximately equal to the theoretical exhaust velocity. This explanation, though found in some textbooks, is wrong. Fuel-rich mixtures actually have lower theoretical exhaust velocities, because decreases as fast or faster than .

The nozzle of the rocket converts the thermal energy of the propellants into directed kinetic energy. This conversion happens in a short time, on the order of one millisecond. During the conversion, energy must transfer very quickly from the rotational and vibrational states of the exhaust molecules into translation. Molecules with fewer atoms (like CO and H₂) store less energy in vibration and rotation than molecules with more atoms (like CO₂ and H₂O). These smaller molecules transfer more of their rotational and vibrational energy to translation energy than larger molecules, and the resulting improvement in nozzle efficiency is large enough that real rocket engines improve their actual exhaust velocity by running rich mixtures with somewhat lower theoretical exhaust velocities.

The effect of exhaust molecular weight on nozzle efficiency is most important for nozzles operating near sea level. High expansion rockets operating in a vacuum see a much smaller effect, and so are run less rich. The Saturn-II stage (a LOX/LH₂ rocket) varied its mixture ratio during flight to optimize performance.

LOX/hydrocarbon rockets are run only somewhat rich (O/F mass ratio of 3 rather than stoichiometric of 3.4 to 4), because the energy release per unit mass drops off quickly as the mixture ratio deviates from stoichiometric. LOX/LH₂ rockets are run very rich (O/F mass ratio of 4 rather than stoichiometric 8) because hydrogen is so light that the energy release per unit mass of propellant drops very slowly with extra hydrogen. In fact, LOX/LH₂ rockets are generally limited in how rich they run by the performance penalty of the mass of the extra hydrogen tankage, rather than the mass of the hydrogen itself.

Another reason for running rich is that off-stoichiometric mixtures burn cooler than stoichiometric mixtures, which makes engine cooling easier. Because fuel-rich combustion products are less chemically reactive (corrosive) than oxygenated products, vast majority of rocket engines are designed to run fuel-rich, with at least one exception for the Russian RD-180 preburner, which burns LOX and RP-1 at a ratio of 2.72.

Additionally, mixture ratios can be dynamic during launch. This can be exploited with designs that adjust the oxidizer to fuel ratio (along with overall thrust) during the flight to maximize overall system performance. For instance, during lift-off thrust is a premium while specific impulse is less so. As such, the system can be optimized by carefully adjusting the O/F ratio so the engine runs cooler at higher thrust levels. This also allows for the engine to be designed slightly more compactly, improving its overall thrust to weight performance.