A Fault in Airfoil Theory
That May Bear on Wind Energy
Drawing From Airfoil Theory vs. Photo Of Actual Streamlines
Drawing From Wind Blade Patent Application vs. Photo Of Actual Streamlines
Added to this is the missing fact that the airflow velocity is not only increased above the airfoil near the leading edge as indicated but is increased also beneath the airfoil near the trailling edge, which causes a lowered pressure there as well.
Corrective measures are sometimes being considered. The vortex generators introduced on the downwind sides of blades have the purpose of increasing the Coanda Effect. However, experience has shown a relatively small effect gained. A possible solution is offered by a second blade element. The element may be a thin flap added under the trailing edge as superimposed in the photo - as is - on the left.
In the image on the right, a better view of the potential effect of this second element is gained. An approximate conversion of the image to the Earth Frame of Reference is obtained by means of skewing. The flow attack angle ahead of the stagnation point then is fixed at minus 90 degrees beneath the airfoil to eliminate the blade tangential velocity vector. It becomes quite clear that the additional element beneath the airfoil moves to the rear providing more effective blade width as shown. If the flow streamlines were adjusted to suit, a better deflection of the entire trailing flow downward and closer to the blade chord line would be seen. Greater airflow deflection, of course, means more power production.
Answers such as this are needed. Small one kilowatt turbines using double element blade concepts have been a remarkable success. Shows to go (!).
The theory which sets the flow lines to follow the airfoil surfaces closely and leave the trailing edge smoothly following its direction is found in early aviation theory publications¹ (page segment copied in "fair use" on the left for review purposes).
What is happening here is that a "clockwise flow circulation" has been postulated around the airfoil profile. The strength of this circulation, termed "gamma" and notated by the Greek letter Γ, is being determined by how well the flow thereby adjusted deflects sufficiently to leave the trailing edge smoothly. This has been given a name: "The Kutta-Joukowsky Condition".
The value of gamma found thereby is seen as the last line in the analysis. But the underlying assumptions have made this analysis superficial and unwarranted. The flow has momentum that overrides any circulation present. The actual value of this parameter can not be found in this manner. In fact, the actual value has never been adequately studied and found as is presently known. There is some deflection occurring but how much is a more complex problem than this. Suffice it to say that this logic has been given more credence than is justified. The evidence from practice now demonstrates that the "Kutta-Joukowsky Condition" is not a valid deflection theory hypothesis. Wind turbine blade design is better approached without it.
And yes, small wind turbines can sometimes readily and quickly cover gaps in the theories. Small is beautiful (!).
¹ From page 52 of Theory of Wing Sections by Abbott and von Doenhoff, 1959, ISBN 486-60586-8, Dover Publications Inc., Mineola, NY.
AIRFLOW DEFLECTION THEORY BRIEFLY Some excitement is present here. A formula for the aerodynamic force, F = m dot delta V, quite well known in other flow field problems involving flow changes, can form the basis for a wind turbine blade theory, the flow seeing, as it does, deflection by the blades. A derivation can be even provided. Aviation theories, as developed in the textbooks mentioned below and often seen in wind energy studies, always find the pressures on the blade surfaces, the determination of which is considered to be de rigeur. But pressures are only a step in the process of the ultimate findings - the blade driving and bendback forces. The pressures, so exhaustively determined, must then be integrated with further exhaustive effort along the blade surfaces in completing the solution. Here in this different approach, the forces are found directly without the unnecessary step of finding the pressures. The confusion on this point continues to lack resolution. This information has a bearing on the value of the NoDrag Flap concept being given study and mentioned above. So it is quite clear that a lack of understanding existed and may still exist of the theoretical foundations of this potential advance. Click on these three links, Page 1 (233kb), Page 2 (127kb), and Postscript (7kb).