Project Requirements

Overall

  1. Rocket 5” OD
  2. 5 kg total propellant
  3. Thrust/weight > 7 at launch
  4. Component FOS ≥ 2
  5. Components stay below melting temperature

Thrust Chamber Assembly

  1. Engine should be able to fire 4 times
  2. Contraction ratio is always < 10
  3. Propellant mixture is fuel rich
  4. Flow is always choked
  5. Injector pressure drop always > 15% of chamber pressure
  6. Minimum ṁ predicted always ≥ design ṁ and ≤ 110% of design ṁ
  7. Average MR predicted always ≥ 90% of design MR and ≤ 110% of design MR



Optimization of mass flow rate

  • Altitude decreases monotonically with mass flow rate for a fixed propellant mass.

Requirements

  • ṁ ≥ 0.6 kg/s for thrust/weight > 7
  • ṁ ≥ 1.18 kg/s for contraction ratio always < 10

We chose an optimal mass flow rate of 1.18 kg/s.


Optimization of mixture ratio

  • There is an optimum MR to maximize exit velocity.

Requirements

  • 0<MR<5.7 to be fuel rich 

We chose an optimal mixture ratio of 4.5.



Nitrous oxide drain model

Assumptions

  • We assumed a constant chosen chamber pressure, consistent with observations from [1] and [2]. A known chamber pressure is required for drain modeling.
  • To account for possible cavitation in the feed system, a compressibility correction factor is applied to ṁ and calculated to be 0.88 [3].
  • Cd is 0.48 for both lines, consistent with [1] and [2].
  • Ideal ullage gas.
  • Insulated tank.


Using the model to test possible combinations of chamber pressure, injector areas, and ullage volume, we decided on the following design values.

  • Chamber pressure
    • 445 psi
  • Injector orifices
    • 5 O-F-O triplets
    • Oxidizer orifice diameter = 5/64”
    • Fuel orifice diameter = 1/8”
  • Propellant tank
    • 15% nitrous oxide ullage to contribute to mitigating the tank pressure drop and achieve target mass flow rate




 

Performance

Design sea level thrust 

2730 N

Design sea level Isp

235 s

Design impulse

6279 Ns


References

  1. Fernandez, Margaret Mary, "Propellant tank pressurization modeling for a hybrid rocket" (2009). Thesis. Rochester Institute of Technology.
  2. https://www.halfcatrocketry.com/mojave-sphinx
  3. La Luna, S.; Foletti, N.; Magni, L.; Zuin, D.; Maggi, F. A Two-Phase Mass Flow Rate Model for Nitrous Oxide Based on Void Fraction. Aerospace 2022, 9, 828. https://doi.org/10.3390/aerospace9120828


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