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Kuo Wei-Jen April 11, 1999 21:56

trailing edge problem
Hi everybody, I have a problem and need some help. As I calculated the airfoil's (NACA0012) velocity and pressure coefficient, I find that the Cp of the trailing edge can not approcach 1. or I can say that the velocity of the trailing edge can not approach zero. The Cp distribution have a large jump at the trailing edge. So, I have a question and need someone help. The question is that as you calculated the same problem, you need assign a value at the trailing edge or not. I know it must satisfied the Kutta condition. I used O-type structure grids ,finit difference method, mach no. is btw. 0.2~0.5, AOA is btw. 0~10. and full potential equation.

Thanks All

Wu Chun-Kai April 12, 1999 20:00

Re: trailing edge problem
Hi! Wei-Jen,

1) Take a note to your far free-stream boundary conditions. If your have fixed them, release them because of the conservation of circulation around the airfoil, which is varying in process of calculation.

2) I don't think it is necessary to assign a zero velocity condition at T.E. For an airfoil with a zero cross angle at the T.E.(infinite thin)(of course, NACA0012 is not the case), the velocity at the T.E. can be determined(as an asymptotic solution) and, in general, will not be a zero. I am not sure now for the case with a finite cross angle. Maybe someone can mention about that.

3) A large difference of Cp at the trailing edge may resulted from some mistakes of your finite difference descretization at the T.E., where exists a sharp corner in your mesh and more efforts are always required.

4) I have solved the potential flow for a sinlge/multiple airfoils in free stream by using the conformal mapping method. A solution can be found in seconds. Maybe you will be interested, won't you?


Praveen Chandrashekar April 14, 1999 10:09

Re: trailing edge problem
Hello Wei-Jen

I read your message when I myself was trying to solve the full potential equation. I am solving that on a structured grid with is body fitted. So the continuity equation is written in the new coordinate system. The Kutta condition is then implemented by making the derivatives of the velocity potential in the body fitted axes equal on the upper and lower ends of the trailing edge. Of course you have to put a branch cut at the trailing edge to impose the circulation. Then you will have two values of the potential at the trailing edge and along the branch cut.

I thing you should get a fairly good result by implementing the Kutta condition. For an airfoil with a non-zero trailing edge angle, the Kutta condition requires that the velocity should be zero at the trailing edge. It is important that the grid should be normal to the body surface. Otherwise, flow tangency boundary condition will not be implemented properly, which can lead to errors throughout the grid, this being an elliptic problem for subsonic flows.


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