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Biot-Savart ok, but its potential?

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Old   September 4, 2006, 10:30
Default Biot-Savart ok, but its potential?
  #1
Gerrit
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Hi All,

The induced velocity caused by a straight vortex segment is well known by the Biot-Savart law.

But what is its velocity potential delta_FI?

With all coordinates given, the ones of P, where we want to know delta_FI and the start and end point of the segment.

What is delta_FI caused by a vortex segment of length delta_l and strength Gamma????

NO 2D ANSWERS PLEASE!

Thanks for your help,

Gerrit

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Old   September 4, 2006, 13:55
Default Re: Biot-Savart ok, but its potential?
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Luca Cavagna
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Dear Gerrit, it seems you one of the few people working on potential here. I've started writing my own panel code this summer over the vacations (steady at the moment). We could stay in contact and exchange some tips about this topic. I'd say that biot-savart rule is used for Neumann panel codes. If you need to calculate the potential of a vortex-ring panel you can use a doublet. let me know if this helps. Luca
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Old   September 5, 2006, 04:14
Default Re: Biot-Savart ok, but its potential?
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Gerrit
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Hi Luca,

I just sent you a mail, let's see whether it works.

I'll repeat my reaction to you in short for people on the forum.

In fact a vortex ring is not what I'm looking for, this could indeed be replaced by a doublet panel, but then I'd use doublet panels inmediately.

I am trying to get rid of the doublet panels in the wake and to replace them (assuming steady flow) by vortex threads leaving the trailing edge in flow direction, this is why I need the change in potential delta_FI caused by a piece of vortex thread delta_l with strength Gamma.

Regards,

Gerrit
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Old   September 5, 2006, 08:28
Default Re: Biot-Savart ok, but its potential?
  #4
mar
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The best book on the panel methods is the one by katz & plotkin.

There you will find what you need if you want to use a wake of doublets' rings .

Anyway in the unsteady case the formulation of Morino is the most used one, expecially in the helicopter community.

If you are not interested in doublets but you want to use vortices you can have a look to the work of quackenbush (nasa website).

Another one is the vortex blob method...

So there are many ways to reach the same objective....

hi italian boy
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Old   September 5, 2006, 09:26
Default Re: Biot-Savart ok, but its potential?
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Gerrit
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Hi Mar,

Of course I could change the doublet panels by vortex rings, but for steady flow the vortex bars parallel to the trailing edge will cancel out, so why not starting with vortex strings in flow direction in the first place?

If you do so you need the formula I've been asking for and that one is not in the book from Katz & Plotkin!

Regards,

Gerrit
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Old   September 5, 2006, 13:10
Default Re: Biot-Savart ok, but its potential?
  #6
Peter
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Just use horseshoe vortices. Everything you need to calculate the induced velocity for a steady vortex lattice code is in Katz and Plotkin.
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Old   September 6, 2006, 03:34
Default Re: Biot-Savart ok, but its potential?
  #7
Gerrit
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Hi

As I already said, I am not looking for the velocity, I am looking for the d_potential of an infinitesimal piece d_l with a strength Gamma in 3D.

Is that in the book of Katz & Plotkin?

I didn't find it, could you please tell me the page number?

Regards,

Gerrit
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Old   September 6, 2006, 05:58
Default Re: Biot-Savart ok, but its potential?
  #8
Anton Lyaskin
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As far as I remeber there is a theorem that finite vortex filament doesn't have a potential... But why do you need d_fi? If to calculate pressure, then it can be done without it
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Old   September 6, 2006, 06:08
Default Re: Biot-Savart ok, but its potential?
  #9
Gerrit
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Oh? That's an interesting answer!

I didn't know that. I need d_FI, 'cause I wanted to replace wake panels by vortex strings in flow direction, NOT by vortex rings (which have also bars parallel to the trailing edge)!!

It would be easier to do so when it comes to rollup etc., because in case of numerical errors you won't have panels with large stretched surfaces.

It surprises me that it doesn't have a potential, because a wake of vortex rings wherein all vortex bars parallel to the trailing edge cancel out, DOES have a potential, or not?? And that should be the same.
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Old   September 7, 2006, 02:25
Default Re: Biot-Savart ok, but its potential?
  #10
Anton Lyaskin
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Yes, that's the tricky point - the complete system of your filaments (if it forms a loop in usteady case or if it has semi-infinite filaments in steady case) does have the potential, put a single finite filament doesn't. I guess the reason is that single filament doesn't satisfy Helmholtz theorems - it begins and ends in the middle of the fluid.

I've once wrote a vortex code myself, so I agree that filaments are better, mainly because of computational expences. But it's possible to calculate everything without calculating the potential - for boundary conditions you need only velocity and for pressure calculations velocity and circulation
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Old   September 7, 2006, 02:39
Default Re: Biot-Savart ok, but its potential?
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Luca
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The question is that he wants to develop a Dirichlet panel code, so he does not need to know the velocity induced by singulaties because these are needed when you write a Neumann code. I hope to be clear. Luca
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Old   September 7, 2006, 03:41
Default Re: Biot-Savart ok, but its potential?
  #12
Gerrit
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Yes, thanks Luca, this is exactly the case. I was planning to use the Dirichlet condition:

FI_inside_the_geometry = constant

Particularly, because this method is well described in the book from Katz & Plotkin.

Now that Anton is saying that a loose vortex bar doesn't have a potential it slowly starts to make sense to me. It corresponds to the way Hess & Smith solve for the integrals (ref. 10.1 In Katz and Plotkin)

So if I want the potential, I'll probably have to do the integral over the vortex bars all way downstream, then parallel to the trailing edge at infinity and then back all the way upstream up to the trailing edge. I'd even have to go along a vortex bar that sticks onto the trailing edge in order to close the circle.

In that way it wouldn't differ too much from a wake with doublet panels, the integration over the wake however, is still a bit easier.

Please correct me if I'm wrong
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Old   September 7, 2006, 03:55
Default Re: Biot-Savart ok, but its potential?
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Luca
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Maybe I'm wrong but you cannot eliminate the wake panel sides alligned with the free stream. As you correctly said you can eliminate the bars alligned with the trailing edge because you have a steady state analysis. The potential jump on this side is perfectly null because you have to do the difference between 2 neighbours. So you will have to account for many vortrex filaments starting from each node of the trailing edge panels. So I don't think it's worthwhile using a vortex filament. I think using a doublet panel it's easier because you exacly know its contribution. Luca
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Old   September 7, 2006, 05:15
Default Re: Biot-Savart ok, but its potential?
  #14
Gerrit
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Yes, maybe it's not worthwile.
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