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So I've been screwing around with CEARUN (https://cearun.grc.nasa.gov/), which is the chemical equilibrium with applications program created by NASA. I've been using it to calculate theoretical ISP's for rocket engines using RP-1 and LOX for a variety of LOX to RP-1 mixture ratios. I've been using the 165:1 nozzle expansion ratio that the Merlin 1D vacuum uses. If we use LOX to RP-1 ratio of 2.327 (about what the Falcon 9 uses based on tank mass numbers then we get a theoretical vacuum ISP of 370.5 seconds. If we use a LOX to RP-1 ratio of 2.9 we get a theoretical vaccum ISP of 381.5 seconds. Note these are all at a chamber pressure of 9.3 MPA, which is what the merlin's use.

In reality I know the Merlin 1D vacuum has an ISP of 348 seconds, which is 93.93% the theoretical ISP. So it follows that by using this mixture ratio we'd get around 358.3 seconds of ISP after efficiency losses. So my questions pretty simple; does anyone know why spacex doesn't use a higher LOX to RP-1 mixture ratio? Doing so would seem to see a 3% increase in ISP. This is nothing to sneeze at, as that would correspond to a ~ 6% increase in orbital energy that the upper stage could achieve.

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  • $\begingroup$ How's the density specific impulse for those ratios? $\endgroup$ – Russell Borogove Jan 17 at 0:48
  • $\begingroup$ Density for ratio of 2.327 is 4.2911 kg/m3, throat velocity is 1196.4 m/s, and fuel flow per throat area is 4.2911*1196.4 = 5133.87 kg/(m2*s) For ratio of 2.9 we get a density of 4.5206 kg/m3, throat velocity is 1159.5, flow per throat area = 4.5206*1159.5 = 5241.6357 kg/(m2*s). So the mass flow, hence thrust, would be greater if you used a higher ratio. $\endgroup$ – chuckstables Jan 17 at 0:54
  • $\begingroup$ 4 kg per cubic meter doesn't sound right for RP1 and LOX. I'm asking about tanked propellant density versus impulse, but now that think about it LOX is denser, so higher O:F ratio yields better density as well. $\endgroup$ – Russell Borogove Jan 17 at 1:12
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    $\begingroup$ What does your proposed change do to the combustion chamber temperature? $\endgroup$ – Organic Marble Jan 17 at 1:56
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    $\begingroup$ Ah. That would probably be it. It raises chamber temperature by about 150 degrees kelvin, but it changes the exhaust temperature by about 400 degrees kelvin! This would mean that more regenerative cooling would be needed. Also exhaust pressure goes up by about 25%, which means that a thicker nozzle extension would be needed. $\endgroup$ – chuckstables Jan 17 at 2:26
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So I've figured it out. Turns out that increasing the LOX to RP-1 mixture ratio increases chamber temperature from about 3650 kelvin to 3750 kelvin. This would mean the engine would need more regenerative cooling and for the combustion chamber/throat.

It would also increase the temperature of the exhaust from around 1000 kelvin to around 1400 kelvin. That is a very large difference, which would inevitably require far more regenerative cooling to be run through the nozzle. This would increase engine mass/engineering complexity as you'd need larger pumps to pump more kerosene through the nozzle to cool it, which would increase the mass of the engine. This increased engine mass would partially or fully negate the benefits from the higher ISP. This isn't even mentioning the increased engine cost which would result from these changes.

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  • $\begingroup$ Nice job figuring it out! $\endgroup$ – Organic Marble Jan 17 at 23:01

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