[aakie]

Dear OpenFOAMers,

I have been working on a 6DOF solver (pimpleDyMFoam) to simulate a transverse (1DOF) freely-oscillating cylinder in 2D. The idea was to verify the model by running the same cases that have been run in the numerical papers of:

Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: Forced and free oscillations. 2009. A. Placzek et al.

Flow-induced vibration of a circular cylinder at limiting structural parameters. 2001. D. Shiels et al.

For most of the cases the simulations were successful. Successful means: the results agreed well with the results from the two papers.
Yet, some cases have appeared to diverge. With divergence, I mean that the oscillation amplitude starts to grow with the lift force (unbounded). FYI: all the residuals showed convergence. I have attached an image to show you the 'divergent' behavior. Remarkably, the beginning part of the solution agrees well with literature. Yet, at one point it looks like a numerical instability enters and the solution starts to diverge.

A summary of my Mesh properties/CFD settings:

- Mesh has a domain of 100Dx100D (it is a square).
- The mesh has 30.096 cells and is based on an O-grid block around the cylinder
- Flow is resolved in 2D
- The following non-dimensional input parameters have been used for this specific, diverging case: U* = 0.71, m* = 15, c* = 0, k* = 29.68, Re = 100
- I use standard BC for a cylinder (Uniform inlet velocity, zero ref. pressure at the outlet, movingWallVelocity (0 0 0) around cylinder wall and pointDisplacement of cylinder is calculated.
- Concerning the structural solver, I dont use relaxation. There is only a spring and damper mounted to the cylinder, in the vertical (transverse to the flow) direction, 1 DOF. The damping is indeed zero, yet in other cases this was no problem at all. All the rotational DOF's have been left out.
- I use an adjustable timestep with Co_max = 0.7. Al the disc. schemes used are 2nd order. The final residuals have been put on a tolerance of 1e-08. For the p-U coupling I use the PIMPLE family, with 2 outer and inner Correctors.
- The case has been run in parallel on four processors.

Things I have tried before to change;
- I played with the two relaxation parameters in the dynamicMeshDict.
- I set the PIMPLE settings more tight (nOut = 10, nIn = 5, tolerances).
- I have set the linear solver tolerances very tight (1e-14).
- I have tried a fixed timestep
- I have tried a couple of different disc. schemes (all 2nd order).
- I changed the structural solver (CrankNicloson vs. sympletic)

All these settings still lead to divergence in the time series.

In the attachment you can find the case files. Personally, I think it has something to do with the weakly-coupled FSI solver that pimpleDyMFoam uses. I have read in a couple of papers that it is possible that artificial instabilities are caused by the weakly-coupled solver (known as negative numerical damping) which eventually leads to divergence. Yet, I still believe with the right CFD settings (I think the mesh is not the problem here) this artificial instability could be avoided. Especially since the paper of A. Placzek et al. used an weakly-coupled solver themselves. Furthermore, I run the same case with a strongly-coupled FSI solver (implicit). It turned out that almost no sub-iteration was required, implying that a weakly-coupled solver would also yield satisfactory results.


I am out of ideas at this moment and I am wondering if some of you has faced a similar problem before with the 6DOF solver (numerical divergence). Please let me know if you have any advice/tips/tricks on this matter. Thanks in advance! And feel free to ask for more information

[aakie]

Bump! I am very eager to hear your opinion!

[aakie]

So apparently when I changed the structural solver from CrankNicolson (implicit) to symplectic (explicit), the divergence stopped. Would anybody know why this is happening or have a reference?

[khaab22]

Hey, If you were able to figure out, can you tell me what you did wrong & possibly even share the case files ??
I'm getting the same problem & struggling from a long time.

Thanks in advance .

[Zhi Cheng]

Hi! Excuse me, can I know how to get the oscillating amplitude change or the spring length change? like your pic showing the change of y?
Best regards,
ZHI CHENG