analyticalLaval solves for the mach number and the pressure distribution inside a given laval nozzle / convergent divergent (CD) nozzle. It takes the pressures at input and output, as well as a nozzle function as input, calculated mach number and pressure distributions and the shock location (if there is a shock)

• python3.6 or newer
• see requirements.txt for others
• basic understanding of nozzle physics

git clone https://github.com/csRon/analyticalLaval.git
cd analyticalLaval
pip install -r requirements.txt

Test you installation by running

python main.py

The input of the program is defined in variables.py. The physics is defined by:

• nozzle area function area_function (should describe a A(x) of a CD nozzle)
  • x-range of the area x (only the area you want to calculate)
• input pressure pi
• output pressure po (note that pi>po)
• heat capacity ratio k (usually 1.4 for air)

You can play around a little bit with these inputs. The results will be in results folder and should be pretty self-explaining by their names.

This code comes from an older university project where it was used to validate CFD-results. To understand the derivation of the equations take a look at JoshTheEngineers awesome video (https://www.youtube.com/watch?v=b0wvwkKqoVw). If you are really interested in the derivation I can also recommend some other resources to handle the physics of CD nozzles (Unfortunately some of them are in german). Here is a list:

• https://www.aere.iastate.edu/~huhui/teaching/2017-01Sx/AerE344/class-notes/AerE344-Lecture-10-Shock_Waves_De_Laval_Nozzle.pdf
• https://itv.rwth-aachen.de/fileadmin/LehreSeminar/Thermodynamik_II/WS16_Vorlesungen/Thermodynamik_II_Kap4_Teil2von4.pdf
• https://homepages.hs-bremen.de/~kortenfr/Aerodynamik/script/node57.html

automizedDoE is licensed under the MIT license.