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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 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 5 triplet elements positioned radially around the injector faceplate. Each triplet is composed of two 1/8 oxidizer holes and one 5/64 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. 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.
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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 4 ~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 (the only reason why they are different is due to spacing constraintsin 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 INSERT VALUE .619 inches for the oxidizer, and INSERT VALUE .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 designed 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 the faceplate and fuel manifold so that the oxidizer circulates above the fuel annulus. This is really hard to explain with words, so here are multiple 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 an annulus is optimized at 4 times the area of the orifices contained within that region, which we calculated to be INSERT VALUE and INSERT VALUE. 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. As expanded on later in the bolt calcs section, we determined that 16 bolts were necessary to withstand the pressure from the oxidizer manifold, and 10 bolts were necessary to withstand the pressure from the fuel manifold. Well actually, that's a lie – the 10 bolt configuration in the fuel manifold was more so necessary from the geometry of the injector itself; the screws must be offset from the orifices, otherwise these holes will run into each other. Therefore, since there are 5 groups of triplets, there must also be 5 pairs of screws offset from these triplets. The number of triplets also influence the number of radial bolts screwing into the faceplate, as if they are not a multiple of 5, they will run into the orifice. Since 5 does not provide the desired factor of safety, 10 radial bolts were chosen as the number of bolts securing the injector to the combustion chamber.
There are two aspects about this design that seem to be suboptimal. However, we do not know the extent to which these "aspects" will negatively impact our combustion performance. First, there are cylindrical screw heads in the oxidizer manifold region. Now, assuming the propellant is incompressible (which it may not be due to issues like cavitation, which will be discussed in another section), the presence of these screw heads will slightly increase the speed of the oxidizer as it flows around the heads; however, after the screw heads, the oxidizer will return to its original speed. This means that, assuming the fluid is incompressible, the flow of the oxidizer will be the same at each oxidizer orifice cross section, so the mixing and atomization of each oxidizer group should be the same, right? Well, yes, if not for the huge blue cylinder in the middle of the oxidizer manifold. This cylinder just needs to be here – it's unavoidable. It is the fuel inlet, or where the fuel passes through to enter the fuel manifold. What this cylinder entails is likely a bit of discrepancy between injector sprays at each element, but it is impossible to compute the extent of this discrepancy without high-fidelity modeling software. Thus, this is something we have to test during cold-flow testing.
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 instead of face seals.
, 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!That's pretty much the design! A couple more miscellaneous things are our O-ring selections – we are using a #00 series O-ring for the fuel downcomer line, a #100 series O-ring for the radial oxidizer-faceplate seal, and three #200 series O-rings for our phenolic-faceplate, chamber-faceplate, and manifold-faceplate seals.
Here is the Jupyter Notebook used to calculate many of the parameters of the injector.
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