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Mathieu Cote

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SPARCC 3.0 is an Aerospace Engineering Senior Design capstone project. This project consists of a team of seven senior Aerospace Engineering students to showcase the skills learned through school.

The aim of the project is to develop a solid propellant thruster for space use which fits inside a 2 U
(2 10x10x10 cm cubes) volume.

To achieve this, we performed extensive research and testing on solid propellants, nozzle designs, and combustion chamber materials. The project involved computational simulations, manufacturing, and experimental testing to validate the design. The results demonstrated the feasibility of using a compact solid propellant thruster for small satellite applications.

One of my core responsibilities was modeling each component as they were being designed, to ensure that all components fit together inside this volume, and that the system as a whole was able to be manufactured via iterative prototyping using 3D Printing and Water Jet Cutting.

To the left is the architecture of the SPARCC 3.0 system. The four main subsystems are Structures, Propellant, Controls, and Mechanism.

My personal responsibilities in this design were ensuring each subsystem was integrated and worked together. I also worked in a limited capacity in each subsystem, mainly controls and propellant.

The components that were the most problematic were the controls hardware, valve, and nozzle.

This page details the four most prominent responsibilities I had in the project:
Finding Pressure and Temperature of Combustion
Technical Budgets
Valve Research
ANSYS FLUENT Nozzle CFD Analysis

The combustion chamber pressure and temperature are the main driving forces behind system design.
The SPARCC 3.0 system is designed to use a custom HTPB / Ammonium Perchlorate composite propellant.
I took many different approaches to try and analytically determine the chamber pressure:

Organic Chemistry Approach:

Using the chemical structures of the HTPB hydrocarbon and Ammonium Perchlorate, attempted to determine the bonding enthalpy. Using this and the specific heats at constant pressure (Cp), the final temperature of the combustion was found to be 15,655.7 K, which is definitely incorrect.
The main issue with this method is that I used constant pressure instead of constant volume, as the volume of the combustion chamber is set to be constant (150 cc).

NASA's CEA Approach:

Using NASA's Chemical Equilibrium with Applications (CEA) to determine the equilibrium state of the combustion products, including their relative compositions and temperature.
This resulted in a chamber pressure of 127 atm and 3,297 K, which also seems quite high.
The main issue with this approach is that it seems the software is directed for constant fluid flow engines, whereas SPARCC 3.0 operates in a pulse mode, which means that the pressure values will inherently be incorrect.

Propulsion Textbook Approach:

Using rockets and compressible flow equations, the chamber temperature for a set area ratio was found assuming ideal expansion.
This resulted in a chamber temperature of 625 K, and the chamber pressure was found to be 5.13 atm, which seemed to be much more realistic than the two methods before.
These values were much more realistic, and were deemed close enough by the team to move forward with system design.

Experimental Approach:

After the above analytical approaches, the team moved forward with attempting to find these values experimentally.
The team built a scaled-down test chamber using galvanized steel pipe and ignited a 1/3 scale propellant pellet inside.
A thermometer probe was placed on the exit of the chamber in order to measure the temperature right at the exit of the chamber.
After three trials, on average the chamber temperature was found to be 1,145 K, and via the ideal gas law the pressure was found to be 9.4 atm.
These values will be compared against through further thrust tests.

SPARCC 3.0 Thermal Test Video

SPARCC 3.0 is constrained by three main budgets: mass, power, and volume.
These budgets were set via a trade study done during the SRR phase of the project.
Through each milestone of the capstone project (SRR, PDR, CDR, Showcase), these budgets are predicted to change through the development process.

AIAA Standard S-120

The bulk of my work on the technical budgets was to predict how the specifications of the current design at a given milestone will change over time.
This was done in accordance with AIAA Standard S-120, "American National Standard Mass Properties Control for Space Systems". This standard defines a "Mass Growth Analysis" which is used to define the growth of properties through the development process.

Mass Budget:

As shown on the right, six different alternatives were compared, and the average wet mass of the systems is about 6 kg. This is the maximum 'Mass Limit' that the system is allowed to reach.
The Allowable Mass is set to be 5.5 kg, which provides a 0.5 kg 'mass reserve', which is a last resort reserve to ensure the 6 kg limit is not reached.
Additionally, there is a Mass Growth Allowance (MGA) which is added to the current design's mass, which is a function of what the design is comprised of and how far along in the design process it is.

Power:

The SPARCC 3.0 system must, in any power/operation mode, not not exceed a power usage of 12 Watts. This is on the low end of the trade study, shown on the right. This also follows the AIAA S-120 standard.

Volume Budget:

The volume the entire system must take up must stay within a 2 U (20x10x10 cm) volume, with some exceptions to test stand considerations. This does not follow the AIAA S-120 standard, as it is a unique requirement of the project which requires creative placement of components.

A main requirement of the SPARCC 3.0 system is the ability to vary thrust over time.
The teams aimed to do this by using a valve at the chamber exit, while still maintaining the strict mass, volume, power, and cost budgets.
This proved very difficult for the following reasons:

Valve Type:

The initial design of SPARCC 3.0 called for a 1/4" NPT solenoid valve, however it was soon found that the design for solenoid valves means that the cross-sectional area is not constant through the valve, and would mean that the system's thrust calculations would be incorrect.
Instead, a ball valve was purchased that met the mass, power, and cost requirements, however it suffers with the operating conditions. The team has instead decided to buy the way through this risk, and choose to purchase several of the cheap valves that can easily be modified and replaced in situ if needed.

Mass/Power/Volume:

The team set very strict technical budgets:

Mass: 6,000 g
Volume: 20 cm x 10 cm x 10 cm
Power: 12 W

The valve must not exceed any of these values when integrated with the entire system.

Cost:

The SPARCC 3.0 team was given a total budget of $1,750 to finance the whole project. This means that the valve must not exceed that amount (minus the cost of the rest of the system and margin). This amount limited the valve cost to approximately $400.

Operating Conditions:

The valve for the system must be able to withstand the high operating pressure and temperature of the combustion chamber (9.4 atm and 1,145 K peak). Additionally, the use of Ammonium Perchlorate in the propellant creates Sulfiric Acid residue, which must not damage the valve.

This ball valve was verified to be able to withstand the operating conditions of the combustion chamber via a pressure test, which succesfully validated the valve, combustion chamber, and sealing solution up to 120 psi.

US Solid Stainless Steel Ball Valve 1/4" NPT

Initial axial velocity CFD of Preliminary Nozzle Design

While the team is planning to perform a thrust test to experimentally determine the thrust the system produced, there needs to be an analytical value to compare to.
An initial geometry was determined for the nozzle based on ease to manufacture in the machine shop on campus.
In doing this analysis, I learned a lot about CFD:

Meshing:

Meshing in CFD is extremely important in order to ensure that the simulation's solution is correct and to ensure convergence. I learned a lot about the importance of mesh element orthogonality and aspect ratios and how the mesh quality affects the calculation's solutions to the various equations.

Pressure vs Density based solving:

Initially, these simulations were performed using density-based solvers. However, using this method resulted in a solution that rarely converged, and changing to a pressure-based solver for the low-pressure exhaust traded some slight inaccuracies in the throat of the nozzle for a more accurate analysis of shocks in the exhaust.

Relaxation Factors:

The ANSYS FLUENT software solves several equations all at once: continuity, energy, and viscosity. The software features 'Under Relaxation Factors', which allow for control over how quickly the values in each equation is allowed to change. Increasing these factors allowed for the significant turbulent flow inside the engine to produce a much stable solution, which helps the simulation converge if it is not doing so. The lower the factors are set, the more stable the solution and the longer it takes to converge.

Boundary Conditions:

The main issue with boundary conditions I ran into was considering the pressure farfield edge using the 'pressure-farfield' boundary condition in ANSYS. This boundary condition seems to be mainly used when considering a moving control volume using a relative Mach number. Instead, I changed this boundary condition to be a 'pressure-outlet', which allowed for any outflow from the exhaust.