Updated 11/17:
| Specification | Value |
|---|---|
| Contraction Area Ratio | 8.73 |
Chamber Diameter | 3.25 in (minimum) |
| Throat Diameter | 1.1 in (minimum) |
Characteristic Length | 57.8 in |
Chamber Length | 6 in |
Contraction Angle | 30 deg |
| Expansion Angle | 15 deg |
| Exit Diameter | 2.504 in |
| Ideal Exit Pressure | 14.04 psi |
Expansion Ratio | 5.18 |
Chamber Pressure | 445 psi |
Chamber Temperature | 3023 K (stagnation) |
| Mass Flow | 1.18 kg/s |
| Exit Mach Number | 2.7 |
| OF Mixture Ratio | 4.15 |
| Specific Impulse | 234s |
| Average Thrust | 2600 N |
Design Process
To design the chamber and nozzle, the specifications we already know include the chamber pressure, OF mixture ratio, chamber temperature, and mass flow, as these are design choices based on the tank and overall constraints, as well as the properties of the propellants. To find T0, R, and gamma, we used NASA CEA.
Chamber Geometry
For parameters such as contraction angle, expansion angle, characteristic length, and contraction ratio, constraints were chosen based on literature or previous projects.
For instance, a 15-degree, fairly gradual expansion angle in a conical nozzle is standard and known to be near the ideal value. We selected a conical nozzle design because it provides almost the same performance as an ideal bell nozzle while being much easier to machine. The ideal contraction angle is less well-defined, but values between 30 and 45 degrees are common. Given our relatively wide chamber compared to the throat (large contraction area ratio), we opted for a more gradual angle to promote better gas flow. However, this choice is not critical.
The characteristic length is defined as the total volume of the chamber (from the injector to the throat) divided by the throat area. It serves as a metric for the chamber’s overall size. This value must be high enough to allow sufficient space for gas mixing and complete combustion. If the characteristic length is too small, uncombusted propellant may be expelled through the nozzle, resulting in lost energy and reduced efficiency. Conversely, if the chamber is too large, fully combusted gases remain in the chamber longer, increasing heat stress on the components. Ideal characteristic lengths are often determined empirically, with accepted values varying for different propellant combinations. For nitrous-ethanol projects, values typically range between 20” and 300”. We selected a chamber length that provided a 2:1 length-to-diameter aspect ratio, making the chamber approximately 6 inches long from the injector to the start of contraction. This yielded a characteristic length of 57.8 inches, providing enough volume while not adding unecessary mass. Notably, extremely large values closer to 200 or 300 inches were found in engines not intended for flight.
The contraction ratio is defined as the ratio of the chamber cross-sectional area to the throat area. If this ratio is too large, the injector faceplate is exposed to excessive thermal loads due to a large surface area being in contact with hot gases. Additionally, a large contraction ratio can cause gas flow problems and result in stagnant gases near the chamber walls, exacerbating thermal issues. Conversely, if the contraction ratio is too small, there may be insufficient space to accommodate the desired injector design. This is particularly important in our design, which uses impinging triplets. Furthermore, a small contraction ratio can invalidate the assumption that chamber velocity remains near zero (M ≈ 0) compared to the throat velocity, and it reduces combustion efficiency. From available data, typical contraction ratios range from as low as 2 for large engines to as high as 10 for very small engines. Initially, we had a very large contraction ratio to fit our preferred injector design. However, we managed to reduce this ratio to around 10, which was near the upper feasible limit. The smallest chamber diameter we could achieve was 3.25 inches. We slightly increased the mass flow to attain a larger throat diameter which brought the contraction ratio below 10.
Chart of typical contraction area ratio values.
Nozzle Geometry
The sizing of the nozzle throat is critical to maintain choked flow throughout the burn.
Materials
Most of the considerations for materials with regards to the chamber and nozzle are based on the thermal loads each part will be exposed to. For instance, the nozzle will experience the highest temperatures, up to 3000 k, and we want it to degrade as little as possible. The clear material choice in this case is fine-grained (isomolded) graphite, as it is fairly easy for us to obtain, machine, and it basically never melts. It is very common to use graphite at least for the throat of the nozzle. Since our design is fairly small, to keep things simple the majority of the contraction and expansion parts of the nozzle are also graphite. For the structural wall of the chamber, we chose aluminum 6061 since it is easy to machine, strong, and light. However, aluminum can't survive the high temperatures expected in the chamber, so we have a paper phenolic liner along the chamber wall, which will ablate and keep the aluminum cool.
Reuse Considerations
One important aspect of this design is that we hope to fire this engine up to 4 times with minimal part replacements between each firing.
Sealing
As we expect the chamber to reach pressures of 445 psi, we need to seal all leak paths to prevent the hot propellant gases from escaping.
Thermal and CFD Analysis
To ensure that all parts involved do not melt and simulate the flow through the nozzle, we used Ansys Fluent to model the flow through the nozzle.
References:
1. https://ocw.mit.edu/courses/16-512-rocket-propulsion-fall-2005/resources/lecture_3/ (Exit pressure)
2. https://www.eucass.eu/doi/EUCASS2017-474.pdf (L*, contraction ratio)
3. https://ntrs.nasa.gov/api/citations/19710019929/downloads/19710019929.pdf (angles, general)
4. https://yang.gatech.edu/publications/Journal/JPP%20(2008,%20Thakre).pdf(graphite)