Higher Order Panel Method / BEM Current State Overview

Discussion in 'Hydrodynamics and Aerodynamics' started by DCockey, Mar 12, 2011.

  1. DCockey
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    DCockey Senior Member

    It may not be any quicker than other methods. There can be advantages with some types of mixed boundary conditions (combination of velocity and potential) if the solved for values of the potential and normal velocity are located at the same locations as the collocation points where the boundary conditions are applied. Numerical stability may be inherently better.

    Panel centroid and normal at the centroid are not used.

     
  2. DCockey
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    DCockey Senior Member

    If the computational domain is too small there will be "blockage" effects similar to what happens when a large model is tested in a small wind tunnel or tow tank. Various outer boundary conditions have been formulated to try to minimize these effects, similar to attempts to use slotted walls or conformal walls in wind tunnels.

    The zonal method I was investigating located the inner boundary of the panel method outside of the region where viscous effects were significant including boundary layers, recirculation bubbles, and wakes. This is different than panel methods with added calculations for boundary layers which I've also used. The outer boundary conditions for the RANSE solver come from the panel method. Iteration between the RANSE solver and the panel method is needed.
     
  3. DCockey
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    DCockey Senior Member

    The methods I'm considering use bi-linear and bi-quadratic distributions of singularities. The challenge and potential weakness is the efficient evaluation of the integrals. The methods start with a reasonably rigourous Green's function approach rather than distributing singularities until the results converge properly.
     
  4. BYDE
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    BYDE Junior Member

    So, summing up:
    Your method has the collocation point (BCs) and control point (singularity) at the same location. This as it is in the 'normal' non de-singularized methods. But, as a difference with them, this common location is at one of the corner points instead that at the centroid of the panel.
    Is it right?

    Well, in general I'm a Naval Architect not a mathematician, so I don't have the knowledge to discuss in detail the numerical properties of your concept. I have experience in panel methods for ship hydrodynamics, and I did a broad literature review about them (which includes aerodynamics BEM).
    To my knowledge, I can tell you that I've never seen a method based on your concept. (as this was your original question)





    Yes, I also use this technique but only on the free surface panels.
    It's the opposite way though: collocation points (BCs) stay on the actual surface, while the panels (hence corner points and centroid where the singularity is located) are moved off. Not really 'off' either: for the free surface they're moved above it. For a closed body in a single-phase fluid (as your case), the panels are moved inward, inside the body.
     
  5. BYDE
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    BYDE Junior Member

    Ok, but how is the PM useful in providing the outer conditions? Because the PM gives a solution only on the surface of the body, not on the domain. Unless you place nodes in all the domain too, but then it becomes as slow as the RANS code.
     
  6. DCockey
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    DCockey Senior Member

    The zone for the RANSE solver and the zone for the potential flow panel method overlap. The boundary condition for the inner boundary of the potential flow solver is derived from the velocities of the RANSE solver. The boundary condition for the outer boundary of the RANSE zone is derived from the potential flow solution. Once the potential flow solution is known along the boundary of the potential flow zone, the velocity anywhere in the potential flow field can be obtained by an integration along the boundary. Iteration is required between the two solvers.
     
  7. Leo Lazauskas
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    Leo Lazauskas Senior Member

    I use bi-quadratic and higher in Michlet and Flotilla.

    Are you considering free-surface effects yet? Or is it for bodies in free air?

    Here's another useful reference to the de-singularised approach where attention was paid to convergence.

    D.C. Scullen,
    "Accurate computation of nonlinear free-surface flows",
    PhD Thesis, The University of Adelaide, 1998.
    http://www.scullen.com.au/DSc/Publications/scullen_98_a4.pdf
     
  8. BYDE
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    BYDE Junior Member

    Ok, I understand it. Does it work well?
    To be frank I'm not really amazed by this concept, it seems to me like it'd greatly complicate the whole process while giving little advantages.
    With an unstructured mesh you can obtain a rather low time-demanding farfields mesh, not comparable to BEM ok but still quite fast on a modern computer. And I still have concerns about stability and robustness of your method.
    It's just my impression though.

    Stability and reliability are first issues imo for CFD codes, even before time.
    Nowadays a RANS computation with a few millions cells takes just some hours in parallel on, say, 4-6 processors (so a low-end infrastructure). I think your method, even if good, may have a short life in the near future as available cpu power will keep increasing.
    Right now BEM are mainly used within optimization codes (it's my case for example), and for them you must assure a very high reliability of your solution process.
     
  9. DCockey
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    DCockey Senior Member

    Bodies in free air or near the ground to date.

    The 2D version was implemented and extensively tested. It worked very well, was stable and converged to the exact answer (for problems with an exact answer) as the panels size was refined. The stability and convergence were insensitive to the arrangment of panels. It was also able to handle mixed boundary conditions with no difficulty. By mixed boundary conditions I mean problems with mixtures of normal velocity, tangential velocity, and the velocity at an arbitrary angle specified over different portions of the surface. Unfortunately I no longer have a copy of the code nor of the results.

    The extension to 3D has not been implemented. I've worked out two different approaches; one based on velocity and one on a combination of potential and velocity. Coding is needed to go further, and I need to decide whether I want to invest the time. Currently I have several other projects which are higher priority.

    I am interested in including a free surface boundary, either using linearized Havelock type sources as the Green's function, or the full non-linear problem with a moving surface. I think a method such as the one I'm considering has potential for the non-linear problem since the potential, velocity and pressure are solved for directly at the same locations used for the geometry of the surface. My guess is that could help with stability and convergence.
     
  10. DCockey
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    DCockey Senior Member

    A zonal approach with overlapping zones using a RANSE solver for the the inner zone and a panel method/BEM with Havelock sources for the outer zone has the potential for significantly reducing the sized of the RANSE mesh when calculating the flow around a boat or ship on the free surface. My idea is the outer zone would not require any input by the user beyond the setting the location of it's inner boundary. Considerable work would be required to implement it though. It could be an appropriate topic for a PhD dissertation. No guarentees though.

    I agree that stability and reliability are primary considerations for any numerical method. Without those you really don't have anything. But those are not sufficient. I've seen examples in the past where what was required for stability and convergence raises questions about the accuracy of the results.
     
  11. BYDE
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    BYDE Junior Member

    yeah, sounds like some years of phd work! dirty work.. :)
    well, the only 'zonal approach' cfd i'm aware of (which i like also) is for hull hydrodynamics: bem for the bow (where wave phenomena matter), rans for the stern (where viscous phenomena matter more).
    I think FLOWTECH uses it very well, or they used it some years ago at least.
    Same purpose of reducing the comp. time, but you see that it's a different 'zonal subdivision' than in your method. That's the closest thing I know anyway

    Regards
     
  12. tspeer
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    tspeer Senior Member

    Panair (Boeing A502 code) is a potential flow panel code that uses higher order than constant panel strengths. The source strength varies linearly and the doublet strength varies quadratically. See NASA CR 3250. Quadpan is another one, but I don't know if it is generally available.

    AFAIK, Panair was pretty much the high-point of panel code development before CFD went to Euler and RANS solutions.
     
  13. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Katz and Plotkin describe the Panair method in their book. I don't think it wouldt be too hard to implement.

    Leo.
     
  14. DCockey
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    DCockey Senior Member

    Thanks for the PanAir reference. Very much appreciated. I looked at PanAir in the early eighties but had forgotten about it. My recollection is that PanAir uses collocation points located on the interior of the panels. Also, the way it deals with continutity of singularity strength across panel edges is different than what I'm proposing. The combination of collocation points at the corner nodes and the way I handle singularity continuity across panel edges when there is a slope discontinuity is what I think is unique. The two go together.

    I'll have to get a copy of Katz and Plotkin. I moved out of aerodynamics just before the first edition was published in 1991.
     

  15. Zeeshan Riaz
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    Zeeshan Riaz New Member

    Bem

    Dear All,

    I have written a code with triangular elements and collocation point at nodes and getting good results and I have use the quadrature technique to avoid the singularities. But the code is linear and can only predict the lift of lifting surface for small angle of attack. Can anybody suggest how can I include the non-linearity to cater for higher angle of attacks.

    Regards

    Zeeshan
     
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