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Solution of the bound circulation

Hi Professor Marten,

I have reviewed your doctoral thesis and the theoretical section of the Qblade  manual and would like to ask some questions about your iterative calculation of bound  circulation.

The work you have done seems to inherit and carry forward the A Van Garrel. In this part, the algorithm of lift line is mentioned.I don’t know if I understand this part correctly:

1.We should first know the Angle of attack, and then query the lift coefficient corresponding to the Angle of attack to obtain the lift force of the panel.

2.By looking up the table and calculating the lift force, the Kutta-Joukowski theorem is used to solve the attachment ring quantity.


Let my try to break the iteration down into simple steps:

1. At the first step of the iteration, we assume a bound circulation (bound vortex elements or lifting line) of zero. This allows us to compute the angle of attack (AoA) from kinematic and geometric considerations since the induced velocity is zero.

2. Next, we obtain an AoA distribution for the blade and evaluate the lift coefficient (Cl), drag coefficient (Cd), and moment coefficient (Cm) from polar data.

3. Using the Kutta-Joukowski theorem, we calculate a circulation distribution from the lift distribution and update the strength of the vortex elements on the blade. Since the circulation is now nonzero, the bound vortex elements induce a velocity, which changes the AoA that the blade sees. As a result, the Cl, Cd, and Cm values need to be updated.

4. We repeat this process until the change in circulation is small enough to achieve convergence.

I hope this help you to understand the iteration procedure…



robytian has reacted to this post.

Hi Professor Marten,

Your answer gives me a lot of help,Because I want to realize this part of your work, I still have some details to consult you:

1.Regarding your first step, how to calculate the AoA if the bound ciculation is zero, I have learned that the Kuta-Joukowski theorem is the formula for lift coefficient and lift force, and if one term in the formula is zero, how can the other term be a real number?Do you have any formulas for reference?

2.The second step is that according to the magnitude of the Angle of attack, interpolation gets the relevant parameters, which is no problem.

3.This step is based on the Kutta-Joukowski formula to calculate the bound circulation, how to get the lift in the formula? Is lift obtained by looking up the lift coefficient of the table? Is there a reference formula for this part of lift calculation?

4.What I understand is that after calculating the AoA, you get the lift coefficient, calculate the lift, calculate the  bound circulation, update the AoA, update the lift coefficient.  In addition, among the above steps, which steps involve updating the velocity, and this velocity takes into account the induced velocity generated by the vortex, right?

I’m sorry that I have so many questions, because I found that the descriptions of these questions are not clear after consulting many papers, so I ask you. Thank you for your patient answer.


Hi Rob,

I think the best overall description of the iteration procedure is still found in Arne van Garrels report: Development of a Wind Turbine Aerodynamics Simulation Module, which also includes all formulas for each step. Check the overview on page 12. The lifting line free vortex wake implementation in QBlade is mostly based on this work.