For a Grid Fin, what would be the most optimal way of finding the lift to drag ratio?
Because Navier-Stokes computations are involved you'll probably want to use a computer with computation fluid dynamics (CFD) software.
I am thinking about comparing lift to drag ratios of square lattice Grid Fins but with different geometrical parameters (such as thickness of the grid fin, the number of cells inside the fin).
This article: "Navier-Stokes Computation of Grid Fin Missile Using Hybrid Structured-Unstructured Grids" (Nov 2006), by You-qi DENG, Ming-sheng MA, Ming ZHENG and Nai-chun ZHOU explains that many factors must be considered:
The airflow is very complex.
I know that the lift to drag ratio depends on the aspect ratio, but I couldn't find anything about Grid Fins for this.
There are many designs, and adjustments to formulas that must be verified by wind tunnel testing.
For example: "Swept-back grid fins for reduced drag" National University of Singapore:
Figure 1: Conventional grid fin (left) and swept-back grid fin (right).
Figure 2: Mach number contours across grid fins for freestream Mach number 1.045: conventional grid fin (left) and swept-back grid fin (right).
Figure 3: Drag coefficient of grid fins from experiments and from numerical simulations. Swept-back grid fins have 30% less drag in the velocity range explored.
See how when you do the calculations the results you actually obtain in wind tunnel testing are markedly different.