Responsible Engineer: Bayanni Rivera , MIT AeroAstro '27
Injector Subteam members: Jordan Bergmann, MIT AeroAstro '28; Eddy Chen, MIT AeroAstro '28; Ethan Lai, MIT AeroAstro '28; Joey Liu, MIT AeroAstro '28
Current injector for Polaris. Type: Unlike impinging triplet
The injector is responsible for taking in propellant and injecting it into the combustion chamber. It needs to must 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 5 triplet elements positioned radially around the injector faceplate. Each triplet is composed of two 71/64 8 oxidizer holes and one 15/16 64 fuel hole. This configuration was obtained by iterating the nitrous drain tank model towards the injector orifice area that would result in a mixture ratio and mass flow rate close to our target. Later on, however, we switched to halfcat sim to predict our mixture ratio. 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. That is, an F-O-O configuration results in unevenly mixed propellant, as the outer side of the resultant spray would be fuel rich while the inner side would be ox-rich.
Polaris Injector Pattern: 5 Groups of Impinging Triplets. I like to call it the star injector!
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 1.65 18 * (4.5 / 5.5) = .5318 965 kg/s. For the fuel mass flow rate, we get 1.65 18 * (1 .5 / 5.5) = .1772 215 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. The reason for this has to do with the feared combustion instability, which will be covered later on this page. 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. Studies have shown that triplet impingement angles of 60 and 90 degrees perform better than most impinging designs, with the 90 degree element slightly outperforming the 60 degree element. However, due to spacing constraints, going for a 90 degree impingement angle was not possible.
The 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 bettersmaller impingement distances correlate to increased performance, 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 by the literature, and fortunately we were able to come close to this factor with an impingement distance of INSERT VALUE.
~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 Generally, the length of an orifice generally should range between 3-10 times its diameter; for this design we chose 5~6 for the oxidizer orifices and ~3 for the fuel orifices. However, for nitrous oxide orifices in particular, one thing I wasn't sure about was whether a greater orifice length would increase the probability of the nitrous vaporizing. The literature on this is mixed – vaporization seems to depend more on the pressure downstream of the orifice (in the chamber); therefore, we will have to just observe the nitrous streams during our cold flow test. It is worth noting that the literature says that some vaporization actually improves injector performance. Using simple trig, this gives us a faceplate thickness of TBD in .619 inches for the oxidizer, and TBD in .259 inches 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 height of 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 surfacedesigned such that it creates an even surface if you place it inside a groove in the faceplate. Then, you can place the oxidizer manifold above this the faceplate and fuel manifold 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 visualizeThis is really hard to explain with words, so here 's a photo (subject to change):are a couple photos:
Ox manifold is red, fuel manifold is blue, and faceplate is white. Cross sections are taken at 0 degrees and 36 degrees. 
Here, you see that the region in which the fuel circulates (the annulus) is positioned below the region in which the oxidizer circulates. The cross-sectional area of a circulation flow region is optimized at 4 times the area of the orifices contained within that region, which we calculated to be TBD and TBD. The reason why the oxidizer annulus height is so small is because its x distance is very large.Assuming the propellant is incompressible, changing this flow area only changes circulation velocity (how fast the propellant travels radially around the annulus). A high circulation velocity should be avoided, as it increases the risk of propellant traveling unevenly through the orifices. That is, if circulation velocity is high, the propellant will have a lot of inertia, and as a result it might become pinned to one side of the orifice as it travels through it, impeding atomization and mixing.
Additionally, you will see that there are screws that screw in the oxidizer and fuel annuli into the faceplate. This is a point of uncertainty; there needs to be cylinders that protrude out of the fuel manifold that contain a screw hole and an O-ring around it to ensure to fluid leaks into the screw threads. Ideally, there is no obstruction in an annulus, so we are currently working on a way to get rid of these cylinders. We will probably just have the screws go through the fuel manifold instead of the ox manifold so that only the screw head would be obstructing flow, not an entire cylinder. However, there also needs to be a sealant to prevent fluid from leaking through the screw; we think that gaskets will do the trick. We are also using gaskets to prevent fluid from leaking from the fuel annulus; originally we had O-rings there, but due to spacing constraints we decided a gasket would be better. Although the screws in the oxidizer annulus don't secure the oxidizer manifold to the faceplate, we can ultimately just place a bunch more bolts radially around the edge of the oxidizer manifold if needed. The screws are also offset from the orifices because they run into each other if not.
Yet another thing you will notice is the placement of the igniter hole. It was quite difficult (if not impossible) to fit O-rings and screws along the faceplate surface to prevent leakage from the igniter exhaust and nitrous. It was discovered that a better way to do this was to extend the faceplate and oxidizer annulus upwards and have the O-rings be radial seals and bolts be radial bolts.
We created a Jupyter Notebook to calculate parameters for the injector.
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, with 16 bolts on the ox manifold flange and ten on the fuel manifold. The bolt calcs are promising – we were able to get very high factors of safety with them – however, the integrity of the material is more questionable. On the fuel manifold, our factor of safety (as obtained from FEA) is 1.6, and for the ox manifold it is 1.8. The radial bolts that screw the injector into the chamber also have a high factor of safety, and are offset from the orifices by 36 degrees so they don't run into the orifices. Finally, on the 0 degree cross section, you will see the fuel inlet, which comes in from the side of the injector. This is a major improvement from a previous iteration, which had the fuel entering the fuel manifold axially. This had necessitated an interpropellant O-ring seal that likely would have been compromised due to deformation of the ox manifold as a result of pressure, not to mention an increased risk of cavitation.
Although I put a lot of work into this design, there are still some aspects that I do not like about it. First, there is an interpropellant seal between the fuel and oxidizer manifold – the black represents gasket seals that prevents leakage from one manifold to another. Generally, having interpropellant seals is bad, because it has a bad failure mode (boom). I think my biggest mistake with this design was sticking to the 3-10 l/d orifice rule too rigorously. If I had made my fuel orifice very long and my oxidizer orifices very short, such that the fuel manifold was now above the ox manifold, this design would have been much easier to make, and it probably would have been more reliable. I should've adhered to the first step of SpaceX's problem solving strategy: making the requirements less dumb!
That's pretty much the design! I really hope that the injector holds up for cold flow, hotfire, and launch, but I cannot deny that there is a chance that it does not. No matter what happens, however, this has been an incredibly fun learning experience for me!
Here is the Jupyter Notebook used to calculate many of the parameters of the injectorUsing 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.
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