Interaction with the body

As discussed before, the APM Solver solves for the potential flow around the body. Lift is modeled through the Kutta condition, which is imposed at trailing edges. The APM Preprocessor has the ability to find trailing edges automatically. For more information on how the APM Preprocessor finds trailing edges refer to the preprocessor section. The built-in ability of the APM Preprocessor to find trailing edges works well for simple geometries like wings. For more complex geometries, the APM Preprocessor requires additional information to find the trailing edges. Examples of more complex geometries include:

• fixed-wing aircraft

• non-planar wings

If the geometry is complex the wake should be included in the mesh file. The image below shows an unstructured mesh with and without wake. Although the APM Solver can use either of the meshes to perform simulations, the mesh with a wake (left) will give better results. Why is that?

Fixed-wing aircraft mesh with (left) and without (right) wake

First, APM Preprocessor will check if the mesh file contains a wake. If the mesh file contains a wake, APM Preprocesssor will use a different algorithm to find trailing edges. The images below show the element types resulting from the two meshes after running the APM Preprocessor.

Element types for the mesh with (left) and without (right) wake

Notice that the mesh containing a wake features elements of type 4 and 5 across the body. These elements propagate the discontinuity in the perturbation (doublet) potential, caused by the wing trailing edge, across the body. No elements of type 4 or 5 are present for the mesh without wake. The images below show the perturbation (doublet) potential solution on both meshes.

Perturbation (doublet) potential for the mesh with (left) and without (right) wake

For the mesh with wake the discontinuity in the perturbation (doublet) potential caused by the wing trailing edge propagates across the body (blue-red regions). For the mesh without wake the discontinuity is smeared (i.e. it does not propagate across the body, there are no well-defined blue and red regions). Since the pressure coefficient is determined from the gradient of the perturbation (doublet) potential, the smeared discontinuity will result in nonphyscial pressure coefficients. The image below (right) shows regions (blue) of nonphysical pressure coefficients.

Pressure coefficient for the mesh with (left) and without (right) wake

Always include a wake in the mesh if you are simulating complex geometries, i.e. fixed-wing aircraft, non-planar wings and etc.

Interactions with downstream body parts

Consider the following Cessna 210 model. The image below shows the element types.

Cessna 210 element types

As discussed previously, in order to capture the discontinuity in the potential, the wake from the main wing must propagate across the body. Due to the potential formulation of the APM Solver a steady simulation of the Cessna 210 is not going to be possible as the wake will intersect the vertical tail downstream. The intersection of the wake with the vertical tail would result in a nonphysical solution.

During unsteady simulations the APM Solver treats older (downstream) wake elements as velocity influence rather than potential influence. This allows older (downstream) wake elements to intersect the vertical tail without causing nonphysical solution.

Unsteady simulation of Cessna 210

The image above shows that the first row of wake elements extends half a chord behind the main wing trailing edge. Since downstream wake rows (second, third, etc.) are treated as velocity influence by the APM solver they can intersect the tail.