NACA 4415 Airfoil Calculation

Rotor blade design is a key element in determining the efficiency of a wind turbine. A crucial precursor to a final rotor blade design is to select one or more 2D airfoil sections to form a smooth blade profile. A wind tunnel study of a 2D airfoil (NACA 4415), typical of an airfoil used by wind turbine rotors, is compared with predictions made by our Panel Flow add-on.

Wind TurbineWind TurbineThe study, conducted in the Ohio State University Aeronautical and Astronautical Research Laboratory 7x10[feet] Subsonic Wind Tunnel, produced an extensive array of data that included pre- and post-stall aerodynamic coefficients. The subsonic speeds of the tests make them ideal for comparison with simulation results from our Panel Flow add-on. Also the tests provide pressure-coefficient profiles at various angles of attack (alpha), and lift and form drag coefficients, which should be well predicted by our panel method for pre-stall conditions.

The wind tunnel data were not corrected for tunnel wall effects. Using our Panel Flow add-on it is possible to make an estimate for the alpha correction necessary to eliminate the wall effects and therefore mimic free air.


To simulate a 2D airfoil in our 3D simulation, the 2D airfoil section was extended 5 chord lengths in the span-wise direction using our Builder add-on. Symmetry was also enabled, effectively doubling the span to 10 chord lengths. All data were extracted on the symmetry plane to maximize the distance to the ends and thus minimize end effects on the extracted data.

A wake was specified as originating at the airfoil trailing edge. An automated, pseudo time-stepping, force-free technique was used to convect wake elements downstream.

Surface Pressure Coefficient Contours
Surface pressure coefficient contours and wake elements for alpha = 16 are shown above.

Time was coupled to alpha using our Transient add-on. Caedium then performed an automated alpha traverse, calculating steady-state solutions at each angle.


Increasing alpha by 0.7 degrees for all our calculations resulted in excellent agreement with the experimental lift and drag coefficients at Reynolds number = 2x106 in the pre-stall range. This correction most likely accounts for the wind tunnel wall effects in the tests, thus decreasing the test results’ alpha by 0.7 degrees would be equivalent to free air for the tests at Reynolds Number = 2x106.

Lift Coefficient Plot
The lift coefficient plot above shows excellent agreement between our computation and the experiment within the linear range between stalls. During and after stall, viscous effects dominate the flow, thus our inviscid computation, as expected, does not agree with the experiment.

Form Drag Coefficient Plot
The form drag coefficient plot above shows good agreement between our computation and the experiment within the same range as that for the lift coefficient. Note that total drag (skin friction drag + form drag) was not measured in the experiment. Inviscid methods, such as the panel method used by our Panel Flow add-on, cannot predict skin friction without modifications.

Shown below are a series of pressure coefficient distribution comparisons between our computation and the experiment at various experimental alphas within the range showing good agreement with the lift coefficient. Note that lines represent the computation and open circles represent the experiment.

Pressure Coefficient Distribution Alpha = -3.98
Pressure Coefficient Distribution Alpha = -1.93
Pressure Coefficient Distribution Alpha = 0.15
Pressure Coefficient Distribution Alpha = 2.03
Pressure Coefficient Distribution Alpha = 4.12
Pressure Coefficient Distribution Alpha = 6.14
Pressure Coefficient Distribution Alpha = 7.95

Notice the reasonably good agreement of all the computations with the experimental pressure coefficient distributions for the range of alphas shown.

Try For Yourself

The sym project file for this study can be viewed in Caedium or you can investigate this case yourself using our Panel Flow add-on. To take advantage of the automated alpha sweep you will need to use our Transient add-on.

The most convenient way to view and edit this case is to use our Professional add-on that combines all the add-ons used during this example.


NACA 4415 Tutorial

Check out our tutorial Flow Over an Airfoil for more on the NACA 4415 airfoil.

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