# Geometry

Meshing Limitations: Due to the automatic methods to create the y+1 mesh currently there are some limitations to what can be meshed. Many single and multi-element airfoils have been successfully meshed. However, if either of the following two things happen then there will probably be meshing problems. Improvements are constantly being made and it is hoped that these limitations will be eventually removed.

1. If the airfoil length is very small and/or the speed very low such that the Reynolds number becomes rather low then the layers in the boundary layer will not generate properly. There will be a warning that will pop up if the Reynolds number is too low to create a proper mesh.

2. We have not been able to adequately mesh an airfoil with Gurney flap. This is something we are currently actively working to correct. But for the moment is not recommended that Gurney flaps be added to any airfoil.

## Geometry Requirements

For the Airfoil tool, the airfoil geometry is input as coordinate sets. (Currently, coordinate set input is the only supported format.) The coordinate set(s) is then used to generate a surface (or surfaces for multiple elements) which is used for analysis.

### How the coordinate set(s) must be created:

• The coordinates need to be scaled in meters.

• The leading edge point should be located at (0, 0) for the most forward wing part. For multi-element cases each element will be entered as a separate part. Be sure that each of the elements are located in the proper position relative to each other when input (i.e. the leading edge of the second element will be at some point other than (0, 0)) so that when all elements are plotted on the same graph they show proper relative position to each other. (Image 1 is an example of this.)

• The coordinates must be entered such that the first ordinate is in the chord-wise direction and the second ordinate is in the thickness direction. This application sees these as (x, z) pairs. (Image 1)

• Coordinates must be ordered such that they are continuous around the airfoil section. See the Image 1 describing this. The first and last point of the ordered set will be connected when generating the surface mesh; therefore, they should not be the same point.

Image 1: Example of user coordinate position inputs.

• Due to the methods used for volume meshing, it is necessary that there not be any sharp edges on the airfoil.

• It is recommended that trailing edges have thickness no less than 0.2% of the chord. For example, if the chord length of the airfoil is 1 m then the minimum thickness of the trailing edge is 2 mm. Obviously, thicker trailing edges are acceptable. Note that trailing edges might include the rear edges of a cove region in a multiple element airfoil.

• We have had a few cases where a sharp leading edge is designed into the airfoil. The mesher will create an appropriate mesh if the half angle between the points is no less than 45 degrees. This can be achieved (in the sharp leading edge case) by moving the leading edge point slightly to create the desired half angle. See Image 2 for an example. Note this image was created for illustration purposes. Often the required shift is so slight that it is not visible when viewing the whole airfoil. Image 3 shows this done for an example airfoil.

Image 3: Slightly blunted sharp Leading Edge - Auto-meshing result.

### Spline Feature

• A Hermite spline feature has been incorporated into the application. It is not required that you use the spline feature if you input 200 or more points to define the airfoil. Note, however, that at higher angles of attack it has been seen that when higher numbers of points (~400) are used to define the airfoil, it shows the most consistent results. A description of how to use the spline feature is below in the "Creating Airfoil Parts" section.

• The mesher will capture 0.0015625*chord spacing in the high curvature regions like the leading edge and will have 0.003125*chord spacing over the rest of the airfoil (including multiple elements. The spacing of the input coordinate set does not need to be any finer than this spacing because it will not be captured in the mesh. For a multiple element airfoil, the smaller elements will take less coordinates to obtain this spacing but will still require a minimum of 200 coordinate pairs.

### How the coordinate set is used in TS Aero 2D Airfoil

• The final set of points input when creating the geometry is used to create the surface stl required by the mesher. Therefore, if the points around the leading edge are not fine enough to define the leading edge curve, then a faceted and/or pointed leading edge can be the result. If you follow the guidelines above when creating the airfoil surface, then this pitfall is less likely to happen.

### Where to find airfoil coordinate sets

• This Airfoil Tools web site is recommended for obtaining airfoil coordinates. Be aware that coordinates downloaded and generated on this web site will usually have a pointed trailing edge. You MUST blunt the trailing edge to no less than 0.2% of the chord as described above before uploading them into the application.

## Creating Airfoil Parts

When working with multi element airfoils each element of the airfoil is entered as a separate part.

### Create Basic Part

• To input a data set select Geometries and then select Create Basic Part (middle button). Name the element as desired. For example main, flap1, flap2, etc. Note: The part names cannot start with numbers or special characters.

### Edit Part

• Once the part is created, it must be edited to input the coordinates. Select the part that was just created and you should see something like Image 4.

• Select the part type as Airfoil.

• Double click on the first entry for the airfoil coordinates and either enter by hand or copy and paste a set of coordinates into the table.

• Once coordinates are input then they are plotted in the application. This allows you to check that there are no problems with the coordinates. You can zoom and scroll to view the different regions of the airfoil by selecting the tools on the right side of the graph. (Image 5)

• Note that for the example shown here there are not enough points defining the airfoil. This can be seen by the message shown at the bottom of the coordinate set (Image 6)

### Interpolate Surface points

• You will not be allowed to save the part until there are enough points to well define the airfoil surface.

• You must choose the area you want to interpolate over by selecting rows. You may add points over a region of the airfoil (for example the leading edge) or the whole airfoil depending on what rows you select.

• Once you have selected the rows you want to interpolate over, then the interpolate selected rows button becomes active and you can select it.

• To interpolate over multiple areas (for example if you want to add points around the leading edge and the trailing edge but not in the middle), select one area then interpolate and then select the other area and then interpolate. Each section must be done individually.

### Save part

• You must Save the part before navigating from this screen or you you will loose the airfoil you created. Scroll to the bottom of the screen and select the green Save button. (You can see the Save button placement, inactive, in Image 6.)

Repeat as necessary for multiple element cases.

Image 4: Create a Basic Part

Image 5: Airfoil plotted

Image 6: Too few Airfoil coordinates notification

Image 7: Interpolate coordinates

## Airfoil Geometry Notation

Within the simulation, the user will also be expected to include the reference chord length of the airfoil which will be used for meshing and results purposes. For multi-element cases it is up to the user to decide if the chord length is the length of the main element or is the overall length of all elements together.

Results are coefficient values and are non-dimensionalized by chord length and flow conditions.