Potential theory
 

Hi! I have a question about the potential theory. I don´t understand why one property of potential flows is to be irrotational. When I have a foil with a certain angle and Kutta-condition, this causes a lift due to rotation, right? For me that´s a contradiction. Thank you! Martin

Re: Potential theory
 

When you're dealing with potential flows about an airfoil you do indeed require circulation in order to deal with non-symmetrical systems or airfoils at an angle of attack.

In some potential theories there needs to be a jump in the solution (a branch cut) to ensure that your solution isn't multi-valued. Across this branch cut the potential can jump - the circulation around the airfoil is related to the jump in the potential. The flow is still irrotaional though - which is required in order to use potential theory in the first place. The concept of rotationality (is that even a word!) is related to rotation but only in a local sense. A good discription of rotational flows can be found in Achieson's: "Introductory fluid mechanics".

I'm unsure of whether this is the case for ALL potential flows - this is certainly the case in my own work (2D transonic flow) however. Hope this vague explanation is of some use - not bad for 1am though!

B

Re: Potential theory
 

Hi !

Irrotational doesn't mean that you don't have circular motion.Take the vortex equation... The pure vortex in potential theory is called irrotational vortex. The word "irrotational" says that that the vorticity is zero. But the vorticity is nothing but: omega = C * nabla X V = C * curl(V). In potential theory velocity comes from a potential function: V=nabla(phi) Now, results that omega=C * nabla X nabla (phi) = curl(nabla(phi)) = 0, therefore the flow is irrotational.