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potential flow and tangential velocity

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Old   June 11, 2020, 21:10
Default potential flow and tangential velocity
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shayan
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Hello my friends.
I know u, v, and w (components of velocity in x, y and z directions) are derivative of potential velocity with respect to x,y and z respectively.
but I want to know how can I calculate Vt (tangential velocity) from potential velocity in 3 dimensional problem?
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Old   June 12, 2020, 03:41
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Filippo Maria Denaro
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The 3d case has one normal and two tangential directions, you need to specify the direction you are interested in and compute t. Grad phi
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Old   June 12, 2020, 05:39
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If you know \textbf{n} you can do:

\textbf{V}_t = \nabla \phi - \textbf{n} \left(\textbf{n} \cdot \nabla \phi\right)
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Old   June 12, 2020, 07:12
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I am solving potential velocity through below equation by boundary element method:



when I want to compute grad phi, I need to derivative mentioned equation with respect to x, y and z. am I right?

then I have terms such as:


or:


how can I evaluate these terms when points P and Q are same and the denominator of the fraction becomes zero?
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Old   June 12, 2020, 07:49
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What do you mean for points P and Q being the same??
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Old   June 12, 2020, 08:20
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Quote:
Originally Posted by FMDenaro View Post
What do you mean for points P and Q being the same??
I mean they are coincident ( they have same coordinates, for expamle P=(2,1,0) and Q is also=(2,1,0) )
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Old   June 12, 2020, 08:25
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What is your idea of the function phi(x) you wrote above? How do you consider points P and Q? Think about ...
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Old   June 12, 2020, 12:26
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If you are using this in a panel method (i.e., aerodynamics), Katz & Plotkin has everything you need to know to write a 3D panel method.

In your specific case, conside that:

1) There should be no reason to take the tangential velocity out of the gradient; if the method is working and you solve the equations correctly, the solution will be tangential to the body by the very definition of your problem (that's what you write at each control point as equation, that the solution must be tangential)

2) The self induced velocity is not computed in this way, of course, because what you are managing here is called a singularity and, guess what, the name is not random.

Not sure if these things apply to other fields as well, but in general terms you should get the point in any case.
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