
Nitrous Oxide injector modeling confusion
Hi everyone,
I've been designing a ethanol nitrous unlike doublet injector, and have been struggling to understand how to deal with the dual phase stuff with sizing nitrous orifices. I posted earlier about some confusions I had about the NHNE model and using it to find area.
I was doing some more research and came across this page on the MIT Rocket Team Wiki that talked about how if you lower your Cd to around 0.4-0.5 you can get away with just using the SPI equation.
I was curious, so I looked up some papers and found 2, "A Two-Phase Mass Flow Rate Model for Nitrous Oxide Based on Void Fraction" and "Experimental Study on the Mass Flow Rate of the Self-Pressurizing Propellants in the Rocket Injector."
I'm kind of stupid, so the only thing I understood from the first paper is that by doing a bunch of formulas I don't understand you can find a correction factor Y to attach to the SPI equation that can make it more accurate, but it's only recommended for single-phase nitrous injectors, and not two phase.
The paper also comes up with their own model that they call FML, but it has the same problems I have with the NHNE (Dyer edition, as they also label their equation NHNE) where the area is a variable in the SPC and in the HEM model. I also did not find any way of calculating the value of x2 in the paper, so even if I wanted to I couldn't find it.
The other paper was a little bit different and found that using the normal SPI formula and changing the Cd to 0.45, they could use the SPI formula to accurately model multiple different injector length/diameter ratios up until flow reached "critical flow," where flashing nitrous vapor chokes the flow and limits mass flow rate. In the figure you can see the critical flow happens at a certain pressure drop. My chamber pressure is going to be 350psi, and with a 20% stiffness my pressure drop is 70psi, or about 4.82 bar, which is well before the critical flow range.
Pressure drop to mass flow rate
Now to where I'm stuck. Both models, bot the Y correction factor and the Cd change to my understanding (which isn't a whole lot) model before the critical flow, and with my pressure drop being so low, I can use either one.
For the Y model, I'm confused whether I should use the Y or Y' version, as one is far more complicated than the other and I would much rather use the Y version.
For just changing the Cd, I'm hesitant about the fact that in their data, all of their mass flow rates were in grams per second, while mine are in kilograms per second. Would the difference in mass flow rate my the effect pressure drop has on critical flow be different? Would my pressure drop still be below the critical flow point? If the mass flow rate unit change doesn't matter, I would much prefer using the modified Cd SPI equation.
If I'm missing some obvious explanation in either paper or totally overthinking this, please let me know.