# Chemical Approach to the 3D printing fuel grain for Hybrid Rocket Propulsion
###### tags:`Project`
_Paper Author_
**Aaron Wu**

_Mt.SAC Hybrid Rocket Team_
**Gabriel Gardner, Marie Galvan, Zakaria Jafery, Ryan Lau, Aaron Wu**

_Instructor_
**Professor Martin Mason**

_Special thanks to_
Data Acquisition and Supplemental Assist: **George Gutierrez**
Mentor: **Dave Griffith, Rick Maschek**

June 6, 2022
[toc]

## Abstract
Combustion reactions are exothermic reactions that require an input of oxygen gas and heat to create the product of water vapor and carbon dioxides. Most combustion reactions involve hydrocarbons as reactants and most plastic materials are polymers composed of hydrocarbons monomers. Thus, common plastic materials are capable to undergo combustion reactions. This study will emphasize the combustions of common 3d printing materials and apply knowledge of thermodynamics. Additionally, tests are conducted with the aim to compare the fuel efficiency of each material in terms of an experimental hybrid rocket motor and provide a basis for materials' application on rocket fuel grain designs. The materials focused in this study includes polypropylene [PP plastic; (C3H6)n], polylactic acid [PLA plastics; (C3H6O3)n], Polyethylene terephthalate [PETG plastic, (C10H8O4)n], Nylon [(C12H22N2O2)n], and Acrylonitrile butadiene styrene [ABS plastic, (C₈H₈·C₄H₆·C₃H₃N)ₙ]. As a control, NOx gas is utilized as an oxidizer for each fuel grain.
For simplicity of the study, each test combustion reaction is assumed to undergo "complete combustion" https://www.youtube.com/watch?v=zEjEqnMBdEM&t=182s (this means no radical products such as HCN, NH3, NOx, CO, C; thus producing purely CO2 and H20 or also N2 with the presence nitrogen such as in ABS fuel grain)

## Hybrid Rocket Motor Design
> Figure 1: 2D design drawing of the simple 29mm hybrid rocket motor utilized in testing
From R.A.T.T. Works, Shout out to Mr. Dave Griffith.

The rocket motor design contains a compartment for the plastic fuel grain, where it is placed next to the NOX injector and stopped by the nozzle + rear closure system at the stern end of the rocket motor. The injector is used both for NOX injection and separating the combustion chamber and the OX tank. A nylon tube extends through the nozzle into the injector and is fitted with a flammable composite, APCP grain, fitting that located at the tip of the injector. Pressurized NOX is pumped from the exterior, through the nylon tube, through the injector, and into the oxidizer compartment when the system filling sequence starts. A calibrated vent is placed at the bow end of the motor to automatically release excess NOX gas when pressure in the compartment exceed the desired stress. Upon launch, the composite reload is ignited remotely by the team and the heat of the ignition generated by the APCP grain melts the nylon tubing. This allow the pumped NOX to be released into the injector with compression fitting and flows in contact with plastic fuel grain that would be ignited and will have enough of heat energy in the combustion chamber to start the combustion sequence. The combination of gaseous NOX oxidizer and flammable plastic filament fuel grain yields a hybrid propellant. During the combustion sequence of the propellant, the raise in temperature and the change in volume between the reactant and product bring high pressure in the propellant compartment and causes the gaseous product to exit the rocket motor through the nozzle into the lower pressure atmosphere.

Referencing to the thrust force equation:

## Materials of the Propellant

### Oxidizer: Nitrogen Oxide, NOX

Nitrogen oxide behave as the oxidizer in the hybrid rocket. Upon heated, the nitrous oxide decomposes into oxygen gas that is desired in the combustion process of the hydrocarbons (plastic). Consider the reaction:


### Fuel Grain: Polypropylene, (C3H6)n, PP

> Figure 2: structure of polypropylene

The density of (PP) is between 0.895 and 0.92 g/cm3. Therefore, PP is the commodity plastic with the lowest density. With lower density, the fuel grain would have a lower weight under the same dimensions.
The Young's modulus (Modulus of Elasticity) of PP is around 1300 to 1800 N/mm². With its relatively high Young’s modulus, polypropylene is tough and more resistance to elastic deformation. The Young’s Modulus is a factor to consider so the plastic undergoes a desirable compromise during combustion, between having little elastic deformation but also avoid having a sudden brittle failure at high stress.
Another factor to consider is that polypropylene is reasonably economical with the average pricing $0.08/gram
The thermal property of polypropylene include that it decomposes to propylene monomer, a colorless gas, at 300 °C to 475 °C in a nitrogen environment. Polypropylene degrades completely, without leaving any significant residue.
Under high heat, the degraded polypropylene releases propylene monomers, the combustion of propylene monomer gas is as follows:

∆H°=-3852 kJ/mol

- Heat of formation calculated by using:

| Species | heat of formation |
| -------- | -------- |
| C3H6 (g) | 20.26 kJ/mol |
| O2(g) | 0 kJ/mol |
| CO2(g) | -393.5 kJ/mol |
| H2O (g) | -241.8 kJ |

>Figure 3: heat of formation table for propylene combustion reaction

---

### Polylactic Acid, (C3H6O3)n, PLA

>Figure 4: structure of polylactic acid

PLA polymers can be from amorphous glassy polymer to semi-crystalline and highly crystalline polymer with melting temperature of 130-180 °C, and a Young’s modulus 2.7–16 GPa. Having a slightly lower modulus of elasticity than PP means it is more ductile and can elastically elongate more under tensile stress.
The high surface energy of PLA offer a good printability, allowing a flatter slicing when 3D printing. The density of PLA is around 1.25g/cm3, denser than that of PP
PLA is the most economical filament with average pricing of $0.02/g
PLA decomposes to lactic acid monomer gas at the temperature of 300–372°C
Under high temperature, the degraded polypropylene releases propylene monomers, the combustion of lactic acid monomer gas is as follows:


∆H°=-1516kJ/mol

- Heat of formation calculated by using:

| Species | heat of formation |
| -------- | -------- |
| C3H6O3 (g)| -389.42 kJ/mol |
| O2(g) | 0 kJ/mol |
| CO2(g) | -393.5 kJ/mol |
| H2O (g) | -241.8 kJ |

>Figure 5: heat of formation table lactic acid combustion reaction

- Energy released by 24.7 oz of lactic acid fuel grain:

---

### Polyethylene terephthalate, (C10H8O4)n, PETG

>Figure 6: structure of Polyethylene terephthalate

The density of polyethylene is around 1.23 g/ cm3, similar to that of PLA, denser than PP. Another factor is that PETG have a relatively low pricing, with an average of $0.04/g
The mechanical property of PETG include its Young’s modulus of around 2.0 GPa, higher than both PLA and PP. This means it is more ductile and more inclined to elastically deform under tensile stress. This can be disadvantageous if PETG extend into the nozzle and blocks the exit of the gas products from the combustion reaction
PETG plastic cannot vaporize even in high temperature. Hence, it is assumed the PETG plastic sample enters the combustion reaction in its molten state


∆H°=-4632 kJ/mol

- Heat of formation calculated by using:

| Species | heat of formation |
| -------- | -------- |
| C10H8O4 (l) | -270.518 kJ/mol |
| O2(g) | 0 kJ/mol |
| CO2(g) | -393.5 kJ/mol |
| H2O (g) | -241.8 kJ |

> Figure 7:heat of formation table Polyethylene terephthalate combustion reaction

- Energy released by 24.7 oz of Polyethylene terephthalate fuel grain

PETG plastic cannot vaporize even in high temperature. Hence, it is assumed the PETG plastic sample enters the combustion reaction in its molten state during the test.

---

### Nylon,(C12H22N2O2)n

>Figure 8: structure of Nylon 66


∆H°=-14040 kJ/mol
- Heat of formation calculated by using:

| Species | heat of formation |
| -------- | -------- |
| C12H22N2O2 (s) | -86.7 kcal/mol= -362.75 kJ/mol |
| O2(g) | 0 kJ/mol |
| CO2(g) | -393.5 kJ/mol |
| H2O (g) | -241.8 kJ |
| N2(g) | 0 kJ/mol |

>Figure 9: heat of formation table for nylon in combustion reaction

- Energy released by 24.7 oz of nylon fuel grain

>theoretical Ea
“Jellinek [6] determined that the thermal decomposition activation energy for nylon 6,6 was 223 kJ/mole. Reardon and Baker [7] reported a value of approximately 180 kJ/mole for nylon 6.”

>Explanation for source of error
According to report from U.S. DEPARTMENT OF COMMERCE, burning of Nylon are studied and found varying concentrations of radical products under different environment temperatures. for example
For example in 305°C, “Peebles and Huffman [15] heated nylon 6,6 at 305°C under vacuum and found that the major volatiles were C0 2 , NH 3 , and H2 0. In addition, they also detected cyclopentanone, 2-cyclopentylidinecyclopentanone, 2-cyclopentylcyclopentanone, hexylamine, hexamethyleneimine, hexamethylenediamine, and 1 , 2 , 3 , 5 , 6 , 7 -hexahydrodicyclopenta [ b , e ] pyridine”
https://www.govinfo.gov/content/pkg/GOVPUB-C13-f14a4cf6ab07dd4696c424f7c8669b89/pdf/GOVPUB-C13-f14a4cf6ab07dd4696c424f7c8669b89.pdf

---

### Acrylonitrile styrene acrylate, (C7H12O2)x·(C8H8)y·(C3H3N)z, ASA

> Figure 10: structure of Acrylonitrile styrene acrylate

Given Acrylonitrile styrene acrylate, or ASA, have the chemical formula of (C7H12O2)x·(C8H8)y·(C3H3N)z;
when heated, polystyrene breaks down in to acrylonitrile (C3H3N) monomer component, styrene (C8H8) monomer component, and Butylacrylate monomer (C7H12O2)

Proposed chemical combustion reaction(s):
- Combustion of acrylonitrile (C3H3N) monomer component
∆H°=-6469 kJ/mol

| Species | heat of formation |
| -------- | -------- |
| C3H3N (g) | 74.04 kJ/mol |
| O2(g) | 0 kJ/mol |
| CO2(g) | -393.5 kJ/mol |
| H2O (g) | -241.8 kJ |
| N2(g) | 0 kJ/mol |

> Figure 11: heat of formation table for acrylonitrile in combustion reaction

- Combustion of styrene (C8H8) monomer component
∆H°=-4267 kJ/mol

| Species | heat of formation |
| -------- | -------- |
| C8H8 (g) | 151.50 kJ/mol |
| O2(g) | 0 kJ/mol |
| CO2(g) | -393.5 kJ/mol |
| H2O (g) | -241.8 kJ |

> Figure 12: heat of formation table for styrene in combustion reaction

- Combustion of Butylacrylate (C7H12O2) monomer
∆H°=-3830 kJ/mol

| Species | heat of formation |
| -------- | -------- |
| C7H12O2 (g) | -375.3 kJ/mol |
| O2(g) | 0 kJ/mol |
| CO2(g) | -393.5 kJ/mol |
| H2O (g) | -241.8 kJ |

> Figure 13: heat of formation table for Butylacrylate in combustion reaction

- Energy released by 24.7 oz of ASA fuel grain, assuming 1mol ASA contain 1mol of each of its monomer:

---

### Acrylonitrile-butadiene-styrene, (C8H8)x·(C4H6)y·(C3H3N)z, ABS

>Figure 14: structure of Acrylonitrile butadiene styrene

Given polystyrene have the chemical formula of (C8H8)x·(C4H6)y·(C3H3N)z;
when heated, polystyrene breaks down in to styrene(C8H8) monomer component, butadiene (C4H6) monomer component, and acrylonitrile (C3H3N) monomer component

Proposed chemical combustion reaction(s):
- Combustion of Styrene(C8H8) monomer component

∆H°=-4267 kJ/mol

| Species | heat of formation |
| -------- | -------- |
| C8H8 (g) | 151.50 kJ/mol |
| O2(g) | 0 kJ/mol |
| CO2(g) | -393.5 kJ/mol |
| H2O (g) | -241.8 kJ |

Refer to figure 12 for heat of formation table for styrene in combustion

- Combustion of butadiene (C4H6) monomer component

-∆H°=-4816 kJ/mol

| Species | heat of formation |
| -------- | -------- |
| C4H6 (g) | 108.8 kJ/mol |
| O2(g) | 0 kJ/mol |
| CO2(g) | -393.5 kJ/mol |
| H2O (g) | -241.8 kJ |

>Figure 15: heat of formation table for butadiene in combustion reaction

- Combustion of Acrylonitrile (C3H3N) monomer component


∆H°=-6469 kJ/mol

| Species | heat of formation |
| -------- | -------- |
| C3H3N (g) | 74.04 kJ/mol |
| O2(g) | 0 kJ/mol |
| CO2(g) | -393.5 kJ/mol |
| H2O (g) | -241.8 kJ |
| N2(g) | 0 kJ/mol |

Energy released by 24.7 oz of ABS fuel grain, assuming 1mol ABS contain 1mol of each of its monomer:


## Static Tests
In the motor static tests, the motor is bolted on a static thrust tester. Upon ignition, the thrust force done by the motor onto the force sensor, located at the bow end of the motor, is recorded over time. Tests with PP, PLA, PETG and ASA fuel grains are done.

>Figure 16: Experimental thrust curve of rocket motor installed with polypropylene fuel (PP) grain

>Figure 17: Experimental thrust curve of rocket motor installed with polylactic acid (PLA) fuel grain

>Figure 18: Experimental thrust curve of rocket motor installed with polyethylene terephthalate glycol (PETG) fuel grain

>Figure 19: Experimental thrust curve of rocket motor installed with acrylonitrile styrene acrylate (ASA) fuel grain

>Figure 20: Combined plot of the experimental thrust curve(s): including PP, PETG, PLA, and ASA

In comparison between different fuel grains, the PP fuel grain, experimentally, is found to have the greatest flammability as the thrust value accelerates the soonest after ignition. From the static test and rocket launch tests, the flammability of the fuel grains are determined to have ranking: PP> PLA>PETG>ASA>Nylon

## Simulating Results

The thrust curves are measured on the statics test stand by the load cell. We then used the data to generate a thrust curve file and input it into an open-source software called Open-Rocket to simulate the performance of the rocket with the testing experimental motor.

>Figure 21: Open rocket 2D drawing representation of hybrid rocket design that is utilized in flight simulations

### PP plastic fuel grain
- Run 1
>Figure 22: Instantaneous altitude, velocity, and vertical acceleration of the rocket in PP fuel grain simulation run 1

>Figure 23: More simulation data of the rocket in PP fuel grain simulation run 1.

- Run 2

>Figure 24: Instantaneous altitude, velocity, and vertical acceleration of the rocket in PP fuel grain simulation run 2

>Figure 25: More simulation data of the rocket in PP fuel grain simulation run 2.

- Run 3

>Figure 26: Instantaneous altitude, velocity, and vertical acceleration of the rocket in PP fuel grain simulation run 3

>Figure 27: More simulation data of the rocket in PP fuel grain simulation run 3.

- Run 4

>Figure 28: Instantaneous altitude, velocity, and vertical acceleration of the rocket in PP fuel grain simulation run 4


>Figure 29: More simulation data of the rocket in PP fuel grain simulation run 4.

- Run 5

>Figure 30: Instantaneous altitude, velocity, and vertical acceleration of the rocket in PP fuel grain simulation run 5

>Figure 31: More simulation data of the rocket in PP fuel grain simulation run 5.

- Run 6

>Figure 32: Instantaneous altitude, velocity, and vertical acceleration of the rocket in PP fuel grain simulation run 6

>Figure 33: More simulation data of the rocket in PP fuel grain simulation run 6.

### PLA

- Run 1
> Figure 34: Instantaneous altitude, velocity, and vertical acceleration of the rocket in PLA fuel grain simulation run 1

> Figure 35: More simulation data of the rocket in PLA fuel grain simulation run 1.

### PETG
- Run 1
>Figure 36: Instantaneous altitude, velocity, and vertical acceleration of the rocket in PETG fuel grain simulation run 1

>Figure 37: More simulation data of the rocket in PETG fuel grain simulation run 1.

- Run 2
>Figure 38: Instantaneous altitude, velocity, and vertical acceleration of the rocket in PETG fuel grain simulation run 2

>Figure 39: More simulation data of the rocket in PETG fuel grain simulation run 2.

- Run 3
>Figure 40: Instantaneous altitude, velocity, and vertical acceleration of the rocket in PETG fuel grain simulation run 3

> Figure 41: More simulation data of the rocket in PETG fuel grain simulation run 3.

### Nylon

- Run 1
> Figure 42: Instantaneous altitude, velocity, and vertical acceleration of the rocket in nylon fuel grain simulation run 1

>Figure 43: More simulation data of the rocket in nylon fuel grain simulation run 1.

- Run 2
>Figure 44: Instantaneous altitude, velocity, and vertical acceleration of the rocket in nylon fuel grain simulation run 2

>Figure 45: More simulation data of the rocket in PETG fuel grain simulation run 2.

### ASA

>Figure 46: Instantaneous altitude, velocity, and vertical acceleration of the rocket in ASA fuel grain simulation run 1

>Figure 47: More simulation data of the rocket in ASA fuel grain simulation run 1.

### Competition

> Figure 48: Instantaneous altitude, velocity, and vertical acceleration of the competition rocket, installed with K131 motor

> Figure 49: More simulation data of competition rocket installed with K131 motor

From the simulation results, a correlation between the average velocity from launch to motor burnout and the calculated total energy released upon complete combustion can be made. The average velocity is computed from the rocket’s burnout altitude and the burnout time, knowing the rocket initially starts at rest during launch.

> Figure 50: Spreadsheet of burnout altitude, burnout time, calculated average velocity from launch to burnout, and the mean of the calculated average velocity. Highlighted in orange represents simulated failure or crashes, and are excluded in the calculation for mean of average velocity

Similar to the calculated result for energy released by the combustion of each fuel grain. The polypropylene exceed other materials and have the highest mean of average velocity from launch to motor burnout. Having the highest mean of average velocity means that the rocket gains the highest amount of kinetic energy from the combustion reaction. Thus, the Open Rocket simulation supports the results from the enthalpy of formation calculations; where the heat of formation calculation proposes that polypropylene releases the highest energy when compared to other fuel grain materials of the same mass.

## Discussion

Upon determining the enthalpy of formation of each chemical reaction. The total energy released by 24.7 oz of each fuel grain material under complete combustion is calculated. The result yields that, out of the six different fuel grain materials, polypropylene releases the highest amount of energy. Assuming 100% purity of the material, 24.7 oz of polypropylene fuel grain was able to release 64103 kJ when undergoing complete combustion.

### References on source of error
#### Source of error for Nylon
According to report from U.S. DEPARTMENT OF COMMERCE, burning of Nylon are studied and found varying concentrations of radical products under different environment temperaturesFor example in 305°C, “Peebles and Huffman [15] heated nylon 6,6 at 305°C under vacuum and found that the major volatiles were C0 2 , NH 3 , and H2 0. In addition, they also detected cyclopentanone, 2-cyclopentylidinecyclopentanone, 2-cyclopentylcyclopentanone, hexylamine, hexamethyleneimine, hexamethylenediamine, and 1 , 2 , 3 , 5 , 6 , 7 -hexahydrodicyclopenta [ b , e ] pyridine” The combustion of Nylon in real world involve complications where hydrocarbon complex are produced and the plastic does not undergo complete combustion.

#### Source of Error for ABS
“The most common products from its decomposition (like most fires) are carbon monoxide (CO) and hydrogen cyanide (HCN).”
“When polystyrene was burned at temperatures of 800–900 °C (the typical range of a modern incinerator), the products of combustion consisted of "a complex mixture of polycyclic aromatic hydrocarbons (PAHs) from alkyl benzenes to benzoperylene.” The combustion of ABS in real world involve complications where hydrocarbon complex are produced and the plastic does not undergo complete combustion

#### Sources of error for all fuel grain:
1. the assumption that the material undergoes complete combustion is unlikely in real world testing.
2. 3D printing polymers may contain impurities and will influence the completeness of the combustion reaction.
3. The effects of geometry, shape, melting point, boiling point, flash point, decomposition temperature, and the deformation of the fuel grain is not considered in study and may have been a factor that yielded our result but was unnoticed.
4. The combustion rate and the change in mass over time of the fuel grain may have affected the rocket’s performance and was not considered in this study

Why no ABS plastic thrust test? Because of the physical property of ABS, there were troubles 3D-printing the ABS fuel grain throughout the project. It requires a precise closed-air environment and high temperature to properly print the fuel grain, where the new filament can firmly attach to the older layer. Unfortunately, the process for ABS plastic was time consuming and time ran out for ABS testing in this project, but we still have chemical calculations.

## Conclusion
In this study, we examined the result of a hybrid propulsion system from the perspective of the heat of formation in terms of chemistry. We understood that the chemical approach might indicates us the best numerical number of a certain combustion reaction. In the comparison of the different material fuel grains with same mass, the enthalpy of formation calculation is supported by simulation result; where agreement is achieved between the material with the highest energy released during combustion and the material of the fuel grain that yields the highest average velocity (from launch to motor burnout). Further research can be conducted to emphasize the application and effects of reactants’ flammability and combustion rate during rocket flight. Other mechanical and thermal properties like the modulus of elasticity, tensile strengths, thermal resistivities, melting points, thermal conducting rate, and combustion rate of the material are also important factors that were noticed during experimentation of the propulsion system.
## Reference
“Complete & Incomplete Combustion | Environmental Chemistry | Chemistry | FuseSchool.” https://youtu.be/zEjEqnMBdEM?t=182.
Esmizadeh, Elnaz et al. “Degradation Behavior of Polypropylene during Reprocessing and Its Biocomposites: Thermal and Oxidative Degradation Kinetics.” Polymers vol. 12,8 1627. 22 Jul. 2020, doi:10.3390/polym12081627
Bross, David H; Ruscic, Branko “Selected ATCT Enthalpy of Formation Based on Version 1.118 of the Thermochemical Network.”, Propylene Enthalpy of Formation, Argonne National Laboratory, https://atct.anl.gov/Thermochemical Data/version 1.118/species/?species_number=71.
“Polymer Design: PET Chemicaa Recycling-Preliminary Process Flow and Data Polymer Design team,” https://www.cae.tntech.edu/~jbiernacki/CHE%204420%20S2017/S2016%20Honor%20Roll/Assignment%202.pdf”
“2-Propenoic Acid, Butyl Ester.” 2-Propenoic Acid, Butyl Ester, National Institute of Standards and Technology,　https://webbook.nist.gov/cgi/cbook.cgi?ID=C141322&Units=SI&Mask=1E9F#Thermo-Gas
“Styrene.” Styrene CAS#: 100-42-5, https://www.chemeo.com/cid/24-192-2/Styrene#ref-nist-webbook
“NIST Chemistry Webbook, SRD 69.” Gas-Phase Ion Thermochemistry, https://webbook.nist.gov/cgi/cbook.cgi?ID=C106990&Mask=1#Thermo-Gas
Xu-Wu An, Margret Månsson, Enthalpies of combustion and formation of acetonitrile,
The Journal of Chemical Thermodynamics, Volume 15, Issue 3, 1983, Pages 287-293, ISSN 0021-9614, https://doi.org/10.1016/0021-9614(83)90121-0. (https://www.sciencedirect.com/science/article/pii/0021961483901210)
Levin., Braun, Emil and Barbara C. Nylons: A Review of the Literature on Products of Combustion and Toxicity. National Bureau of Standards, 1986.
“ABS (Acrylonitrile Butadiene Styrene) Burn Test.” YouTube, MB Education, https://www.youtube.com/?watch=.