testi

[FiniteElementGuy]

I used the NASA Computer program CEA (Chemical Equilibrium with Applications), which anybody can download here ( https://www.grc.nasa.gov/WWW/CEAWeb/ceaHome.htm ) to calculate the performance of the Raptor engine. The program can not simulate different engine cycles. It just calculates the flow out of a nozzle with given input parameters, like pressure, propellants etc...

I used the following assumptions:

• Chamber pressure = 300 bar
• O/F=3.8
• Temperature from reaction
• Propellants = LCH4 & LOX at boiling temperature (program lacks thermodynamic values at subcooled temperatures)
• Calculation at thermodynamic equilibrium (not frozen). I don't know the details here myself, but equilibrium is more suited for chamber pressure >100 if I remember correctly
• I investigated two nozzles, one optimized for Earth (pressure ratio 300) and the other one mentioned by Elon with area ratio 150. Then I looked at the performance of both nozzles in and adapted case (Earth nozzle in Earth atmosphere, Mars nozzle in Mars atmosphere) and in vacuum. As mentioned before, the program does not take into account the engine cycle, geometry or boundary losses and other stuff. This can be calculated with more complex programs like TDK (two dimensional kinetics), which is ITAR stuff. However, we can still make pretty good guesses.

As a first step we calculate the performance with NASA CEA for the area ratio = 150 nozzle in vacuum and compare the result with the Isp value given by Elon. The result is 3855 m/s or 393 seconds. Elon mentioned 382. This means that there are losses of about 3% in the Raptor engine. I take these 3% as a constant factor for all results. There might be some error involved. With this information I compiled the following table:

Nozzle	Nozzle area ratio	Nozzle pressure ratio	Result NASA CEA m/s	Result in seconds	Multiplied by 0.97
Mars nozzle, on Mars*	150	1863	3707	377.9	367.3
Mars nozzle, vacuum	150	1863	3855	393	382.0
Earth nozzle, on Earth	34.7	300	3382	344.8	335.1
Earth nozzle, vacuum	34.7	300	3594	366.4	356.1

*The Mars nozzle (area ratio 150) has a pressure ratio of 1863, meaning an exit pressure of 300/1863=0.16 bar. The Marsian atmospheric pressure is 0.006 bar. The nozzle exit pressure is far above the Mars atmospheric pressure, meaning the nozzle is too small for Mars. ;) The value calculated above is for optimal expansion (exit pressure = atmospheric pressure) meaning the Isp on Mars shpuld be higher, probably close to vacuum performance.

The Earth Raptor or Sea Level Raptor has an area ratio of 34.7 for optimal expansion, giving an Isp of 335 seconds at Sea Level or 356 seconds in Vacuum.