I am currently doing a school research project attempting to find the effect of single-slotted flaps and slats on an airfoil's (NACA 2412 or similar) lift coefficient. I will be using a small homemade wind tunnel to see the lift force that a small airfoil model generates with and without the use of high-lift devices, and backing the claims up using CFD data. The model will be a simple wing that is essentially an elongation of a 2D airfoil.
When designing the slotted flap, there seems to be very little information on how the geometry of the flaps is created nor is there much data on existing designs. There are many research papers investigating the effect of high-lift devices, but almost none explain how their designs were produced or why they used the flap that they did. Essentially, how the flap takes its shape. For example, in Theory of Wing Sections, various slotted flaps were tested for their max lift coefficients, but the book does not specify how these designs are created (see image). The same goes for slats.
My question is, how are these various designs of flaps and slats produced mathematically and how can I replicate this design process for my airfoil? The flaps and slats do not need to be perfect, but I will have to justify what led me to the design that I will be using in my experiment.
Alternatively, I can also use proven designs of high-lift devices from existing airplanes such as a C172 or experimentally optimised ones. Unfortunately, I was not able to find any of those. If anyone is aware of existing single-slotted flap and slats schematics, it would also be very much appreciated.
I am aware that someone asked a similar question but it was deemed too broad. Hope this isn't.