On the cusp of fully grasping Method of Characteristics

[Benjies]

TL;DR

A method used to create geometries for the straightening section of rocket nozzles (as well as other systems)

'Lo all,

I've been studying the Method of Characteristics for quite some time now. I understand all the interactions between characteristic lines, and how they modify the flow Mach number and direction of the flow when these characteristic lines intersect. I have just a couple of hangups that I was hoping this forum might be able to help me with. My primary sources are here:

[1] http://mae-nas.eng.usu.edu/MAE_5540_Web/propulsion_systems/section8/section.8.1.pdf

[2] https://www.ijert.org/research/desi...method-of-characteristics-IJERTV2IS110026.pdf

In [1], at the end of section 2., the author displays that you can find the position of where the two characteristic lines intersect, and then states "thus, helping in developing the supersonic nozzle". Similar information in [2] on slide 21. Trouble is, all these paper have displayed is that you can derive the position of the characteristic line intersection, as well as the change in flow angle (theta), and finally the change in Mach number at this point downstream. But this only provides us the position of characteristic line intersection- this doesn't provide me the position of the wall of my nozzle at all. How has this given me the geometry of my wall?

I fundamentally get how the characteristic lines are generated, and how they interact during intersections. But I seem to be missing something in these sources that displays how wall contour is derived from these characteristic meshes.

Thank you!

 

[Benjies]

To be clear- I am asking for HELP with MOC- I am not sharing this for pure information! Probably should have mentioned that in my title, or something.