potential flow and tangential velocity

shovaliye2 · June 11, 2020, 21:10

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?

FMDenaro · June 12, 2020, 03:41

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

sbaffini · June 12, 2020, 05:39

If you know $\textbf{n}$ you can do:

$\textbf{V}_t = \nabla \phi - \textbf{n} \left(\textbf{n} \cdot \nabla \phi\right)$

shovaliye2 · June 12, 2020, 07:12

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?

FMDenaro · June 12, 2020, 07:49

What do you mean for points P and Q being the same??

shovaliye2 · June 12, 2020, 08:20

Quote:

Originally Posted by FMDenaro

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) )

FMDenaro · June 12, 2020, 08:25

What is your idea of the function phi(x) you wrote above? How do you consider points P and Q? Think about ...

sbaffini · June 12, 2020, 12:26

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.

June 11, 2020, 21:10	potential flow and tangential velocity	#1
shovaliye2 New Member shayan Join Date: Jul 2018 Posts: 22 Rep Power: 7	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?

June 12, 2020, 03:41		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	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 shovaliye2 likes this.

June 12, 2020, 05:39		#3
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,152 Blog Entries: 29 Rep Power: 39	If you know $\textbf{n}$ you can do: $\textbf{V}_t = \nabla \phi - \textbf{n} \left(\textbf{n} \cdot \nabla \phi\right)$ shovaliye2 and aero_head like this.

June 12, 2020, 12:26		#8
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,152 Blog Entries: 29 Rep Power: 39	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. aero_head likes this.

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June 12, 2020, 07:12		#4
shovaliye2 New Member shayan Join Date: Jul 2018 Posts: 22 Rep Power: 7	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?

June 12, 2020, 07:49		#5
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	What do you mean for points P and Q being the same??

June 12, 2020, 08:25		#7
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	What is your idea of the function phi(x) you wrote above? How do you consider points P and Q? Think about ...