Pressure wave reflection at wall boundaries
 

Hi all,

Apologies, this question needs quite a bit of explaining. I'm running transient simulations of a mostly closed container (for the purposes of this, it's essentially a box with a throughflow of air), where the flow is being excited by a regular series of sparks. The sparks are modelled as a localised energy source term, applied as a square wave in time (i.e. source term on for 50% of the time then abruptly turned off for the other half cycle). The spark frequency is selected to be the primary resonant frequency for the domain - so the pressure wave formed by the spark reflects off the end of the box, and then is added to by the next spark along. This is modelling an experimental setup.

My concern is exactly what is happening numerically as the pressure wave reflects from the endwalls, and how better to simulate what is happening in reality. As my transient simulations are of a resonant condition, I have been building up peak-to-peak pressure wave variations approximately 2 orders of magnitude larger than were measured experimentally. My understanding of how CFX handles wall boundaries is that it enforces a dp/dn=0 condition at the wall; which in my interpretation is equivalent to having a perfectly rigid solid wall, resulting in a perfect reflection of the pressure wave - i.e. no attenuation/absorption at all.

The questions that I would really like some help with if anyone is able to shed any light are:

• Is my understanding of how pressure waves reflect off walls in CFX correct? (I.e. that there will be no attenuation and all the energy bound up in the pressure wave will rebound).
• Is there any way of tuning or representing the partial absorption of (pressure wave) energy at a wall boundary? My only idea thus far is to place a thin layer of porous material in front of each wall boundary, but I've not yet wholly convinced myself that this will give me a physically realistic representation.

I've not managed to find the guidance that I'm after in the CFX documentation, so any help that anyone can offer would be gratefully appreciated!
Thanks!

Yes, walls are implemented as dp/dn=0, along with no slip for momentum. Yes, this results is almost no attenuation. There will be a small amount of attenuation from viscosity and more from numerical dissipation but these are likely to be small.

If you want the wall to absorb a bit of energy you need to work out exactly what the physics of that absorbtion is. A porous material is one way, but does not appear to match your experiment very well. A better way is to make the wall flexible and model it using either a rigid body or even better FSI - this is likely to be more accurate to the experimental results but much harder to model.

But before you do any of that I recommend you check a few basics. Inlet and outlet boundaries are notorious for causing spurious reflections. Are you sure that your results are not being affected by spurious reflections from the boundaries? What have you done to mitigate this effect?

Once you have checked spurious reflections you should then do a time step, mesh size and convergence criteria sensitivity analysis to make sure that your model setup is accurate enough to capture the effects you are looking for.

Thanks for the response - that's most helpful. Inlet/outlets are quite remote and around 90 degree bends from the chamber that is resonating (mimicking the experimental rig directly), so there are no significant reflections at those boundaries (also confirmed by viewing pressure contours in post-processing).

The exact details of the absorption at the point of reflection itself are actually unimportant - this is a bit of a strange CFD case where the region of interest is a complex mixing region a fair bit away from the walls, and it is the interaction of the spark, jet and the pressure wave that is important. Thus, I think that I can probably get away with using a porous layer to artificially introduce some loss rather than incurring the expense of going to FSI.

Thanks once again!

In my previous work modelling engine manifolds I got reflections from the inlet and outlet boundaries despite them being around many bends and a very long distance away. In my experience the best way to reduce boundary reflections is to expand the pipe out into a large area (mimicking a pipe going into atmosphere) and then put the boundary on the large area. There are also non-reflecting boundaries available as a beta feature but these are new and I am not very familiar with them.

I am a bit puzzled that you think adding dissipation to the wall reflection wall is the correct approach. This is because in reality wall reflections have almost no dissipation - that is why you can hear echoes and it is easy to set up a standing wave in a closed pipe. If you are getting dissipation then either your wall has some strange behaviour (such as it is not rigid) or there is an interaction with something else and the something else is causing the dissipation.

Just a note about adding a porous region: The porous region is going to need quite large loss coefficients to cause significant dissipation. This means that your porous region is going to cause spurious reflections itself - there will be a reflection when the wave hits the porous region, another when the wave hits the rigid wall behind the porous regions and another when the reflected wave leaves the porous region. Be aware that this approach may well cause more problems than it fixes. This is why I am suggesting you investigate the real physical source of the dissipation and correctly model that dissipation mechanism rather than introducing a new artificial dissipation which may have bad side effects.