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Finite aspect ratio effects on airfoil coefficients

Airfoils data are only available in infinite 2D data. For finite data, a logical assumption is probably that the lift coefficient will be always lower than infinite airfoil lift while the drag coefficient is higher in small angle of attack and lower when angle of attack is large.

NACA0015 data modified for different aspect ratio using Viterna Corrigan model

Lift and drag coefficients for finite aspect ratio airfoil at small angle of attack before stalling can be estimated quite accurately from infinite aspect ratio airfoil data by using the Lanchester Prandtl theory (Abbott, 1959). The equations below show that the angle of attack increases for the same value of lift or in another word, the lift decreases like the figure above. The drag coefficient will increases too although it shows both possibility of increasing and decreasing in the equation. The stall angle increase but still with the same value of maximum lift coefficient at stall even though it is much logical to expect that the maximum lift decrease with aspect ratio too.

Viterna and Corrigan model (Lissamen, 1994) provide a mean to modify the airfoil data after the stalling angle of attack till 90degree. After the infinite data got modified by Prandtl equation, the Viterna model uses only 3 values from the resulting infinite data to estimate the lift and drag coefficients after stalling. It estimates that the finite lift and drag coefficients are lower in fully stalled condition which is fine. However, as the maximum lift (at stall) coefficient remains the same (only angle of attack increases) from the previous Prandtl modification, it results in a higher lift coefficient after the stall point (around the lift dip) than the infinite span airfoil.

The top figure shows the result of applying the Viterna and Corrigan model to Sheldahl NACA0015 airfoil data. The lift coefficient right after stalling only decreases a bit compare to the infinite span airfoil. If this airfoil behaviour is true, the performance of VAWT at medium tip speed ratio range can be greatly improved by finite airfoil.

References

Spera, D. A. (Editor) (1994), Wind turbine technology: Fundamental concepts of wind turbine engineering. New York, ASME Press.

Last updated at November 6, 2002
Comments are welcomed