A typical mechanical turbulator consists of a strip of tape, attached to the wing surface. The chordwise position of the strip is depending on the airfoil shape. Of course it must be located in front of any laminar separation. The combined polar diagrams used on the airfoil data pages also contain the transition location, which can be considered the maximum downstream position of a turbulator; to be effective, a turbulator should be located 5 to 10% of the cord before this location. The polar diagram below shows, how to find an initial location for experiments.
Plot of the transition location in the polar diagram.
For a selected lift coefficient of Cl = 1.0, we draw a horizontal line, which intersects the transition curve for the Reynolds number of interest. moving down we can read the location from the x/c-axis. For the example, we find a value of x/c = 0.45, where laminar separation will occur, if no transition happened in front of this location. If necessary, a turbulator should be placed at x/c = 0.4 or further upstream. There is also a curve for the lower surface (T.L.), which can be used to define a turbulator position for the lower surface, but this is usually only needed for airfoils with additional camber located close to the trailing edge, as found in some full scale sailplanes.
A mechanical turbulator must have a certain minimum height to be effective. This height depends on the position of the device, because the boundary layer thickness is growing with increasing chord position. An additional parameter is the Reynolds number, which also influences the boundary layer thickness: high Reynolds numbers result in thinner boundary layers than small Reynolds numbers (at the same airfoil chord). The thickness of the transition strip must be sufficient to cause transition, but it should not be thicker than the boundary layer to avoid additional drag.
Close to the leading edge the boundary layer is very thin (1/10s of a millimeter), when the flow reaches separation, it can grow much thicker (in the order of millimeters for model airfoils). The following diagram intends to help you by giving a first guess on the thickness of a turbulator.
Turbulator height selection chart.
You enter the chart (after selecting an x/c position for the turbulator from the polars or the recommendations of the airfoil) at the top left axis. Dropping a line down to the orange band gives an upper and a lower intersection point, from each of which you draw a straight line to the right, intersecting the line matching the Reynolds number corresponding to the wings chord length. On the axis below, the approximate boundary layer displacement thickness can be found and used as a first guess for the turbulator height. The values found from the graph agree reasonably well with wind tunnel results [25], but further experiments will be necessary to find the optimum height (if such a thing exists at all).
| Example: | A wing has a chord Reynolds number of Re = 75'000. The chord length is 200 mm. The airfoil designer recommends transition at x/c = 0.4 by means of a turbulator. Entering the graph with these values a turbulator height of 0.0014 to 0.0016 times chord, which evaluates to a thickness of 0.28 to 0.32 mm. |
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