Injector

The injector is responsible for taking in propellant and injecting it into the combustion chamber. It needs to thoroughly mix and atomize the propellant, while also withstanding high pressure and thermal loads. For our engine design, we chose a fuel to oxidizer ratio of 1:4.5, which posed a challenge for injector geometry selection. Ultimately, an unlike impinging triplet geometry was chosen, with each triplet composed of two 7/64 oxidizer holes and one 1/16 fuel hole. Originally, the element pattern was F-O-O, but we changed this to an O-F-O because the mixing of an F-O-O configuration was not optimal. More details on both designs will be provided below. 

To calculate mass flow rates for each propellant, we can simply multiply the total mass flow by the mixture ratio fractions. For the nitrous oxide mass flow rate m_ox, we get .65 * (4.5 / 5.5) = .5318 kg/s. For the fuel mass flow rate, we get .65 * (1.5 / 5.5) = .1772 kg/s. 

Some other necessary parameters that we need are the discharge coefficient, which was calculated to be .44 using the tank model used for the engine (it's low, I know). We also need the densities of the fluids, which are rho_nitrous = 817 kg/m^3, rho_ethanol = 789 kg/m^3. The pressure drop across the injector should be 15-20% of the chamber pressure; for our engine, we chose an average pressure drop of 96 psi, which is enforced by orifice area. Finally, we can calculate the velocities of the nitrous and ethanol propellant at the outlet using Bernoulli's equation. We get v_nitrous = 40.463 m/s, and v_ethanol = 41.175 m/s. 

For a triplet design, in order to maximize mixing, the center orifice must be vertical, and the side orifices must be at the same angle from the vertical. For the oxidizer angles, we chose an angle of 30, as that would entail an included angle of 60 as recommended by Liquid Rocket Injectors (1). However, the other item to consider is impingement distance, or how far below the face plate the elements collide. Generally, the smaller the distance the better, but that also means that combustion happens closer to the faceplate, which increases risk of faceplate melting. Impingement distance is also constrained by the geometry of the injector. An impingement distance that is 5 times the length of the average diameter of the orifices is recommended, but for our design we had to use an impingement distance ~10 times the average because of geometrical constraints. Given that this rocket is a demonstrator, this choice is valid, as although it might sacrifice our performance slightly it makes our design safer. 

The other length that we need to consider is the thickness of the injector faceplate. The length of an orifice generally should range between 3-10 times its diameter; for this design we chose 5. Using simple trig, this gives us a thickness of TBD in for the oxidizer, and TBD in for the fuel. 

Now that we have our angles and our injector plate thickness, we need to start thinking about how to design a manifold. This is especially tricky since there can only be one inlet for oxidizer due to spacing constraints between the chamber assembly and tank (remember that this needs to fit inside of a rocket) so having two separate annular regions separated by a fuel annulus in the middle would be impossible. Since the length of the faceplate for fuel is smaller than the length of the faceplate for oxidizer, a clever way to design the manifold is to actually make it two parts. The fuel manifold can be the same height as the thickness of the ox faceplate minus the thickness of the fuel faceplate; placing it on the faceplate would thus create an even surface. Then, you can place the oxidizer manifold above this so that the oxidizer circulates above the fuel annulus. One can simply place O-rings where these two parts mate to prevent leakage. That probably is hard to visualize, so here's a photo (subject to change):

We created a Jupyter Notebook to calculate parameters for the injector.

Using Huzel and Huang (pp. 144-148), we calculated chamber lengths to avoid to minimize the risk of longitudinal instability. These lengths are 125, 127, and 172 inches.

Polaris Injector Calcs.ipynb