Embedded Files
Nozzle Design Calculations
Physics Based Model
Physics Based Model
Using the system model, I was able to make a nozzle design code that takes a desired force as an input and outputs the throat and exit diameter of the thruster.
Using the system model, I was able to make a nozzle design code that takes a desired force as an input and outputs the throat and exit diameter of the thruster.
Flow Assumptions
Flow Assumptions
Isentropic- Ideal Conditions
k =1.4
Choked Flow Conditions
Pressure ratio is high enough to maximize flow through nozzle
To design an iterative model for the thruster design using a force input, I chose to use Cold gas thrusters Specific impulse to calculate the mass flowrate required to produce a the force without defining a throat area
this method is less computationally intensive then running through a range of areas that could meet the mass flowrate requirement
This equation were taken from :
B. McBride and S. Gordon, "Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications," NASA, 1996.
ISP can be directly calculated using This isentropic relationship which then can be manipulated to find the mass flowrate :
The Isentropic ISP equation was taken from this paper:
S. L. Nothnagel, "Development of a Cold Gas Propulsion System," Massachusetts Institute of Technology, Mass, 2011
To get the theoretical exit pressure, exit temperature and Mach number of the system, I used the isentropic equations from:
J. D. Anderson, "Fundamentals of Aerodynamics, Fifth Edition," McGraw-Hill, 2007.
The throat diameter of the nozzle, can be solved by taking the mass flowrate from the ISP equation using this choked mass flow rate equation found in :
J. D. Anderson, "Fundamentals of Aerodynamics, Fifth Edition," McGraw-Hill, 2007.
Applying Nozzle Design Calculations:
Create a System of Equations to Solve for Throat and Exit Area
The equations mentioned above and the system model can now be combined into a MATLAB script to create a system of equations to solve for the nozzle geometry. This process will have to be iterative since the starting assumption of the exit pressure is atmospheric. The code converges in less the 5 epochs.
The code will spit out all the information onto a text file that then can used as a design cataloged for the designer.
Note: after testing this design theory, using area ratio to calculate Mach number is not as accurate as using the Pressure ratio. if the chamber pressure is sigifigantly lower then the stagnation pressure, the Mach number will be severely off.
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