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Hello, @truffaldino,
Thank you for your response. So, mathematically, the circulation is constant whatever the line if this line enclose the wing, even if I take a circle of radius equal to hundred times the chord of the wing. I recognize that I am not surprised by your response, because mathematically, I agree with you. But, in a CFD case, when we use a farfield boundary condition, on which we impose the velocity, it is clear that the circulation through this boundary condition is zero, because the velocity vector is constant along this boundary, and so the integral is zero. So, we could say that we impose a zero circulation around our wing !? Am I stupid or there is something which I don't well understand ? |
William: It is good that you are paying attention to fluid dynamics fundamentals.
The difference between "mathematical" case an one with imposed boundary conditions is that in the former the external forces act from the airfoil surface only, while in the latter the external force is imposed from the both boundary and the airfoil. If your boundary is far enough from the airfoil, the "defect" in circulation close to the airfoil (but far enough from the boundary layer) will be small (proportional to the ratio between the airfoil chord to the distance to the boundary) . Roughly speaking you have to satisfy both Joukowsky-Kutta condition and BC. When you are close to the airfoil Joukowsky-Kutta condition makes much more bigger contribution to the circulation than the BC at far boundaries. So, choose the contour that is far enough from the external boundary and also where effect of boundary layer/wake is negligible (the flow is practically inviscid at the distance of a few boundary layer sizes from the airfoil surface). This can be contours with distance from the airfoil surface ranging from airfoil chord to several bl sizes. Truffaldino |
Thank you very much, @truffaldino,
Yes, it is the never-ending problem of CFD that it is only an approximation of the analytical theory of fluid mechanics. We have to keep this in mind... Thank you very much for your response which confirms what I thought but what I wasn't able to accept ! Putting words on it sure helped me. I will make some exercises and tests ot 'see' that you are right. :) Even if I know that you are. Thank you for your help ! William |
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