Thread Tools |
This thread is privately moderated by Montag DP, who may elect to delete unwanted replies. |
|
|
|
Discussion
Unsteady panel code for flapping wings
As part of my Master's thesis, I'm going to be investigating unsteady panel codes for flapping-wing micro air vehicles. The plan is to compare with CFD solutions to see under what conditions the panel code gives good predictions, because CFD solutions take a very long time and thus make design work tedious. Panel codes have limitations, though, especially when there's significant separation.
I thought some RCG members might be interested in the development, so I'm posting here. So far I've written a steady panel code and plan to spend the next couple weeks modifying to make it unsteady and able to simulate airfoils in flapping motion. Some details of the panel code: -Between each set of vertices for the airfoil, a vortex panel is placed. The formulation used allows for linear variation of vortex strength across the panel. There are usually at least 100 panels distributed across the surface of the airfoil. -As with any panel code, the variation of vortex strength on each panel is calculated so that the summed effect of each vortex panel and the upstream velocity is such that the airfoil is a streamline. That is, on each panel the normal component of velocity is 0. -Additionally, as with any lifting panel code, the Kutta condition is applied so that flow leaves smoothly at the trailing edge. Once the vortex strength distributions are calculated, the velocity and pressure at each panel can be computed as well. Changes required for unsteady panel code: -The normal velocity component on each panel also includes a contribution from the airfoil's flapping motion. This must be accounted for when calculating the vortex strength distribution at each time step. -As circulation bound to the airfoil changes with time, an equal and opposite amount of circulation must be shed into the wake behind the airfoil. -Vorticity shed into the wake also has an effect on the surface velocity and pressure at each point in time. -The Bernoulli equation to calculate surface pressures is more involved for unsteady flow. For now, here are some plots generated using the steady panel code. Dan ImagesView all Images in thread
|
|
Last edited by Montag DP; Dec 28, 2010 at 02:07 AM.
|
|
|
|
|
Wake roll-up
I've been working on the panel code for flapping airfoils. I have it mostly working but currently I'm struggling getting the pressure calculation working correctly (which, of course, is the most crucial part). The unsteady Bernoulli equation used to calculate it is much more involved than the steady version, and requires calculating the time derivative of the velocity potential and so on.
But, the good news is, even without that working correctly I can still make cool pictures and videos. Here's an example of what's known as wake roll-up. The airfoil is moving to the left while oscillating up and down and in pitch about its leading edge, somewhat like in the videos in my post above. As it does this, the discrete vortices shed into the wake move with the local flow field and can make some interesting patterns. In this case, four full cycles were run. I didn't time it but it took around 2 minutes in Matlab on a 4 year-old laptop, which is orders of magnitude faster than CFD takes to do the same simulation. Computational time does increase with each time step, though, because the size of the wake grows. |
|
|
|
|
|
very Low reynolds number flapping
Hi.
I am trying to do a simple 2D swimmer using flapping wings in highly viscous liquid. The swimming strokes are like this: I am trying in in Fluent using UDF and dynamic mesh. But i could not succeed in simulating. Is it possible to give me any advice for my problem? Thanks in advance Doctsh |
|
|
|
||
|
Quote:
Dan |
|
|
||
|
|
|
Nice work, I actually just finished something similar last month - an unsteady linearly varying vortex panel method with linearly varying vortex panel wake. Ah the time derivative of perturbation potential, this caused much hair loss... until I solved the problem. It is actually much simpler than I had anticipated. It turns out that the time derivative of panel potential is equal to the half the time derivative of panel circulation.
Infinitesimally either side of the panel there is a jump in tangential velocity equal to half the vorticity strength at that point on the panel. Now, recall that potential is defined as the directional integral of the velocity vector, then the result is that the jump in potential equals the circulation (or minus circulation if it is defined as anti-clockwise positive). Now, the internal potential for a closed body is constant for all time (a natural consequence of the Neumann boundary condition, or specified by the Dirichlet boundary condition) which means that the time rate of change of the OUTER surface potential (the side of interest) is exactly equal to half the time rate of change of panel circulation. This applies to each panel separately. So supposing a simple first order backward derivative stencil dPhi/dt = 0.5 * (Gamma(t) - Gamma(t-dt)) / dt (depending on how you have defined the vorticity, a minus sign may be necessary). Hope this helps! If you want, I can e-mail you the Appendix in my report that goes through this derivation.... |
|
Last edited by khyar; Apr 10, 2011 at 03:34 AM.
Reason: error
|
|
|
|
khyar,
Sounds like it's the same as mine, only with a bit more refined wake (mine just uses discrete wake points). I'd be interested in seeing that portion of your appendix, though I believe mine is working using the time derivative of perturbation potential without any simplification. Yes, that caused significant hair loss for me too, but I've done some validation of my code and it seems to check out. I calculate the actual perturbation potential at each time step and then use a simple backward derivative approximation like yours. Dan |
|
|
|
|
|
Aha, yes. With a point vortex wake I noticed that evaluating the actual perturbation potential does work okay, but there is a vertical discontinuity in the potential field directly cutting through each point vortex. This is due to the nature of the atan function. Now, with wake panels these discontinuities align with the normal vector and so they can end up crossing the body once the wake rolls up.... I tried using the atan2 function in case there were quadrant issues and this did not help matters. So if you plot the total potential field in the space around the body and wake you should see these vertical discontinuities appearing at the point vortices. If you don't, please let me know!
I used the panneled wake to tune the parameter in the discrete wake model that controls the fraction of the distance between the trailing edge and the previous wake point at which to place the newly shed vortex. It turns out that a value of 0.27 (from the trailing edge) produces the closest match to a continuous wake sheet. This lies inside the suggested range given in Katz & Plotkin (2000) of 0.2...0.3. Paul |
|
|
|
|
|
0.27... Interesting. I can't remember what value I used, but it was the one that allowed me to match the validation data as close as possible. I want to say it was somewhere in the range of 0.25-0.30, but I'd have to check.
I haven't bothered to look at the potential on a grid within the computational domain, since I was able to validate the code without looking into it. This is just a part of my Master's thesis and the real thrust for this part of it is to see whether I can successfully apply the code for a study of hovering flight in a micro air vehicle. So basically once I got the code working I just moved on to the actual application. |
|
|
Thread Tools | |
Similar Threads | |||||
Category | Thread | Thread Starter | Forum | Replies | Last Post |
Discussion | Aircraft with flapping wings/Bird attack vids | malden86 | Electric Plane Talk | 19 | Sep 29, 2010 08:14 PM |
Discussion | Membrane wings Vs single/double surface airfoil wings .. flapping and gliding | khaled_abobakr | Ornithopters | 5 | Aug 23, 2010 07:20 AM |
Question | Cutting cores for multi-panel & taper wings with ailerons | wingnutt | DLG Hand Launch Gliders & F3K | 2 | Aug 13, 2009 10:12 AM |
Slow Hawk Ornithopter Video (Flapping Wings!) | Chronister | Parkflyers | 3 | Jul 01, 2003 01:20 PM | |
Yippee! | New Flapping Wings Online Magazine | Chronister | Ornithopters | 0 | Jun 12, 2003 10:42 AM |