Calculating pressure

Surface pressure

The APM Solver determines the surface pressure coefficient from the gradient of the doublet strength. The gradient of the doublet strength distribution is not readily available. The solver uses several algorithms to calculate the gradient. Depending on the problem, some algorithms might perform better than others.

• If the doublet_gradient_scheme option in the .conf file is set to 0 the doublet gradient will be calculated with a Constrained Hermite Taylor Series Least Squares (CHTLS) algorithm [1]. This is the default APM Solver doublet gradient scheme.

• If the doublet_gradient_scheme option in the .conf file is set to 1 the doublet gradient will be calculated with a Weighted Least Squares (WLS) algorithm.

• If the doublet_gradient_scheme option in the .conf file is set to 2 the doublet gradient will be calculated with a Linear Shape Functions (LSF) algorithm.

• If the doublet_gradient_scheme option in the .conf file is set to 3 the doublet gradient will be calculated with a Finite Differences (FD) algorithm.

The Finite Difference (FD) doublet strength gradient algorithm can be used only on structured meshes!

The images below shows a comparison of the surface pressure coefficient obtained with different doublet strength gradient algorithms.

CHTLS (left), WLS (middle), and LSF (right) results for a sphere geometry

CHTLS (left), WLS (middle), and LSF (right) results for the AGARD-AR-303 E6

Trefftz-plane loads

An alternative to the surface pressure integration is to use the far-field of Trefftz-plane approach. In general this is a more reliable approach, especially for the induced drag component. To enable the Trefftz-plane analysis set the trefftz_plane_analysis option in the .conf file to 1.

Trefftz-plane used to calculate the loads of a fixed-wing UAV

For best results when using the Trefftz-plane analysis perform an unsteady solution. The unsteady solution will allow the wake to roll-up. The Trefftz-plane analysis will be performed at the location of the third to last row of wake panels.

References

[1] Robert McDonald and Alejandro Ramos. "Constrained Hermite TLS for Mesh-free Derivative Estimation Near and On Boundaries," AIAA 2011-655. 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. January 2011.