[Shiv1510]

Hi everyone

I am numerically studying oscillatory boundary layer flows in turbulent regime. I have come across many numerical (RANS, LES, DNS) studies, in which the flow is oscillated over a stationary (2D domain) infinite long flat plate in turbulent and intermittent turbulent region. However I have not able to find any studies regarding the infinite plate oscillating with fluid above it at rest (Stokes Oscillating plate problem) in turbulent or intermittent turbulent regime.

I understand they are pretty much same problem, however are there any challenges or difficulties for numerically simulating and studying the boundary layer on Oscillating plate over oscillating flow in turbulent regime?

It would be great if anyone can help me understand the difference ?

[LuckyTran]

Moving the plate is much more challenging because it typically involves a dynamic mesh that deforms following the motion of the plate.


It's very easy to prescribe flow BC's as functions of time (pressure, velocity, energy, etc.) because none of those requires the mesh to move or any special numerical treatment.

[Shiv1510]

Hi LuckyTran

Thank you so much for replying.

I may be out of my depths here, why I have to move the mesh ?

If i consider a 2D square domain with left and right as periodic boundary conditions, top as far field and bottom as wall, then move/prescribe wall nodes with sinusoidal velocity function. Is this approach wrong ?

[LuckyTran]

Actually, nevermind. I missed the part where you mentioned this was the Stoke's problem, which is a plate oscillating in the direction of the flow. I was thinking of plate oscillating up & down.


The Stokes problem is straightforward to setup. No moving mesh. Just a wall with a time-dependent velocity. If compressible, make sure you use the wave transmissive BC otherwise the acoustic waves get reflected by the farfield BC which contaminates the solution.


You don't find papers on this because an exact solution exists. There's little publication opportunity to simulating anything where an exact solution exists.

[Shiv1510]

I see. Thank you again, I really appreciate it. I am trying to simulate in turbulent region, is there an exact solution for that ? I am looking for studies conducted in the turbulent regime. Reynolds number depending on stokes Reynolds number. I did find studies regarding linear stability perturbation analysis, but nothing on numerical analysis of boundary layer in turbulent region for oscillating plate.

[LuckyTran]

In the classical Stokes problem which has exact solutions, the fluid is quiescent (i.e. left and right BC is periodic) and the flow is always spatially and temporally coherent and never adopts the random, chaotic nature of turbulence.

If you put a flow over this oscillating plate (i.e. use a velocity inlet and some sort of outlet) then you don't have exact solutions. This case is setup the same way you would do flow over a flat plate and you would approach it the same way as far as CFD is concerned. There is an academic fork here and the study branches into many different fields. The linear stability folks are predominantly Orr-Sommerfeld based in their approach, and this approach is not compatible with acoustics. You won't find many papers on this topic (more like you will find none).

The challenge with flow over oscillating plate is that the perturbations induced by the plate oscillations go like the viscous length scale. If your mesh is fine enough to resolve the acoustic fluctuations, you probably already have a DNS grid (even if you end up doing unsteady RANS).

[Shiv1510]

I see...thanks for the in depth explanation. I see now why the Oscillating plate is an issue and with RANS approach, the length scale need to be resolved. Again thank you very much for the explanation. I would just like to ask one more question.

Would there be similar problem if the flow is oscillated using a source term in momentum equation with periodic boundary conditions on the left and right side of domain ?

[LuckyTran]

Right. You just need to keep track of what length scales need to be resolved (resolving time-scales is just a matter of using a small enough time-step).


Challenges doesn't mean it's not doable. You have both the plate oscillation amplitude and frequency as parameters. Some cases are easier than others.