We created a MATLAB script to calculate the geometry of our thrust chamber and injector orifice sizing. We used isentropic equations to determine the expansion area ratio for the exit, and applied a set contraction ratio to define the chamber size. This script went through extensive review, as any errors would propagate through the entire design. I will explain our thought process alongside the script.
MATLAB Script and Geometry
We used Gammas we got from our CEA run to estimate the gas constant inside of the chamber
We for a ratio for the pressure inside the chamber to the pressure of the exit which is just 1atm. Then used it to calculate our needed Mach at exit.
From the found Mach at exit we were able to get the Temperature at exit by using the CEA run temperature at chamber
Found Velocity at exit using all solved for variables
Found M* which is mass flow rate from just dividing thrust by our exit velocity.
Using M* and mixture ratio we found M* for fuel and ox
Using mass flow rate equation we got our orifice area for both fuel and ox. Then divided it by 6 and found radius of holes needed.
We got our area of the throat using mass flow of choking using temperature of the chamber, pressure of chamber and gamma.
We got a expansion rate using equation 9, and used that with our area of throat to find exit area.
Used contraction ratio from Rocket Propulsion Element to get chamber area, and then used L-Star to find volume of chamber and get the rest of the geometry