Why Use Vortex Generators?
Vortex Generators (VGs) can be used for various purposes such as changing stall characteristics, lowering takeoff and landing speeds and even reducing drag (typically on large transonic airliners). All of these effects result from the fact that VGs help to control and alter the boundary layer over a surface.
In my case, I wanted to improve the stall characteristics of one of my wings. The wing in question is a scratch build balsa wing that has a tendency to tip stall. To correct this problem, I designed VGs that are placed on the outboard 1/3rd of the wing. In depth details of the VG design is provided below. But first I will show you some results to prove that they work.
Frist I would like to show an image of a “clean” wing with no Vortex Generators. Figure 1 below shows the stalled clean wing fitted with tufts (aka. pieces of string). The tufts give us an idea of what the flow is doing on the surface of the wing. The image shows that the flow is very chaotic over the entire span of the wing. The result while flying is a tip stall that leads to the aircraft rolling over.
Figure 1: Clean Wing Stall
Now we can take a look at a wing stalling with Vortex Generators installed on the outboard 1/3rd span. As you can see from figure 2, the tufts behind the VGs are straight back while the rest of the tufts on the wing are again arranged in a chaotic fashion. The end result is that the wing has a much more controllable and gentle stall with no bad tip stall characteristics.
Figure 2: Wing Stall with Vortex Generators
Overall, the Vortex generators helped to mute bad stall characteristics and make the plane more controllable during a stall. The video below shows 4 stalls (2 with a clean wing and 2 with VGs). I have also provides some tips on designing your own Vortex Generators below.
Tips for Designing Vortex Generators
In this section, I will provide you with all the equations I used to design the Vortex Generators that I installed on my plane. The math is not two involving and just requires some algebra. These equations do have their limitations, which I have mentioned below, but they will serve as a good estimate on designing your VGs.
1) Determine the shape of your Vortex Generators
There are many types of Vortex Generators being used on aircraft today. For simplicity, I made simple rectangular VGs for my aircraft. Below is an image containing various styles of VGs. Ultimately, you can make them in almost any shape you want.
2) Determine Reynolds Number of flow
Before designing your VGs you need to determine what Reynolds Number you will be operating at. For this you will have to approximate or know the stall speed of your aircraft. Equation 1 below shows how to calculate this value.
Equation 1: Reynolds Number Calculation
3) Determine length of VGs and their location along the chord of your wing
Next you will need to determine the length of the VGs and where along the chord of the wing the VGs will be placed. The length of your VGs should be around 5-8% of the chord length of your wing. This is just a value that I have found to work for the square VGs I made.
The length of your VGs should be around 5-8% of the chord length of your wing.
Now you can calculate the position of the VGs along the chord. The VGs should be placed just in front of the laminar to turbulent transition of the boundary layer on your wing. This transition point is located at approximately 16% back on the wing chord from the leading edge. Thus you will want to place the leading edge of your VGs at a length equal to (16% of the chord – length of VG) back from the leading edge of your wing. This will place the VGs just in front of the laminar to turbulent boundary layer transition.
Place the leading edge of your VGs at a length equal to (16% of the chord – length of VG) back from the leading edge of your wing
4) Determine the height of your VGs
Next you will want to determine the height of your VGs. VGs work to control the boundary layer and thus they are most effective inside the boundary layer. On larger general aviation aircraft and airliners, VGs typically have a height 80% that of the laminar boundary layer right before the laminar to turbulent transition point on the wing. However, on model aircraft that will typically result in a VG with a height well less than 1/64th of an inch (my model has a boundary layer height of 0.00097 inches). This makes them very hard to manufacture and thus I made my VGs have a height of 1/8th of an inch to make them easier to handle. To calculate the height of the laminar boundary layer on your wing before the transition point you can use equation 2 below. 
Equation 2: Height of Boundary Layer Before Transition Point.
5) Calculate span wise spacing of VGs
The next step is to determine the spacing of the VGs along the span of the wing. To do this I derived an equation which determines the size of the vortex being generated by the VGs. This equation is derived from the lift equation and the equations governing vortex flow. The end result is equation 3 below. After determining the radius of the vortices being produced by the VGs, I recommend that you space the VGs at least two radiuses away from each other. I also recommend that VGs be placed at a 15 degree angle to the flow going over the wing. This will allow the VG to work effectively and produce the largest vortices. If you would like to experiment with different angles, remember to change the Coefficient of Lift (CL) for that angle.
I also recommend that VGs be placed on the outside 1/3rd to ½ span of the wing. This will make it so that the inboard sections of the wing will stall first while the outboard section continue to have smooth airflow. This will lead to gentle stalls and will help to alleviate tip stalls.
Equation 3: Radius of vortex produced by VG
6) Making and installing your VGs
The final step is to make the Vortex Generators and install them on your aircraft. To construct your VGs I recommend using some thin yet sturdy material. I made my VGs using some sturdy poster board. You could also make them from plastic folders or a similar material. If you want your VGs to be removable, I recommend gluing them to some scotch tape and then placing them on your aircraft.
To make installing the VGs easier, I recommend using a simple guide made from a piece of paper to help in aligning your Vortex Generators on the wing. Below I have included some pictures of my installed Vortex Generators to give you an idea of how they could look.
Limitations
These equations and tips have various limitations. The equations do not account for the varying velocity profile in the boundary layer when determining the size of the vortices. Some of the things I mentioned above are just things that I have found to work. Thus, if you decide to try making VGs following the steps I mentioned above and they do not work as expected, I recommend experimenting some to see what works for you.
Hope you enjoyed and happy experimenting!
For more discussion check out the RcGroups Thread at:
http://www.rcgroups.com/forums/showthread.php?t=2252309
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