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Dealing with weakly compressible flows

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Old   September 9, 2020, 08:56
Default Dealing with weakly compressible flows
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John Applesmith
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I have read that there is some literature to suggest that incompressible solvers fail to propagate mass flux accurately in pulsatile (transient) flows and this effect is worsened in FSI problems.

I suspect my simulation of pulsatile blood flow through a bi-leaflet prosthetic heart valve is prone to this- there is very low mass inflow at the inlet despite changing the time-step, domain size and inherent geometry. Are there any methods in Ansys CFX for treating the flow as weakly incompressible since there are local sharp pressure drops near the leaflet but the flow overall is very much incompressible? One paper "imposed a speed of sound of 15.7 m/s on the fluid (with the effective value being in the order of 1570 m/s)" but I'm not sure how to do this in Ansys. I'm using the immersed boundary method (like the paper) and assuming rigid leaflets.
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Old   September 9, 2020, 20:00
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I recommend thinking about the original statement (that incompressible solvers fail to propagate mass flux accurately) before proceeding.

If the fluid has a small amount of compressibility and you have a configuration where that would be important (eg closing a valve on a long water pipe line) then if you model this with an incompressible solver then of course your results will be wrong. Here the small amount of compressibility in liquid water is important and that generates the water hammer effect. If you don't model that small amount of compressibility you will be wrong.

But if the flow does not have significant compressibility and you model it with an incompressible solver your results will be fine. For instance if the flows are slow and the velocities small (such as your heart valve case) then an incompressible solver will be fine. I think you will find it is other effects which case the inaccuracy, such as deformation of the walls which cause the problem.

So I think your original statement is incorrect and only applicable in limited circumstances. It is certainly not a general statement and I find it hard to believe it is applicable to your case.

Having said that, if you want to model your fluid as weak compressible then define your fluid to have density as a function of pressure. I would recommend using the bulk modulus of water (or your fluid if you have it) so the weak compressibility you add is physically realistic. The simulation will be a bit harder to run as you will now have pressure waves propagating around, but if they are weak it should be OK.

Note the restrictions on fluid models with immersed solids. See the documentation for that.

Your comment about somebody imposing a speed of sound of 15.7 m/s on the fluid sounds very dodgy. This sounds like they were using a very poor solver to have to impose such a unrealistic condition as that. This does not sound like a procedure you should copy.
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Old   September 17, 2020, 15:24
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Quote:
Originally Posted by ghorrocks View Post
I recommend thinking about the original statement (that incompressible solvers fail to propagate mass flux accurately) before proceeding.

If the fluid has a small amount of compressibility and you have a configuration where that would be important (eg closing a valve on a long water pipe line) then if you model this with an incompressible solver then of course your results will be wrong. Here the small amount of compressibility in liquid water is important and that generates the water hammer effect. If you don't model that small amount of compressibility you will be wrong.

But if the flow does not have significant compressibility and you model it with an incompressible solver your results will be fine. For instance if the flows are slow and the velocities small (such as your heart valve case) then an incompressible solver will be fine. I think you will find it is other effects which case the inaccuracy, such as deformation of the walls which cause the problem.

So I think your original statement is incorrect and only applicable in limited circumstances. It is certainly not a general statement and I find it hard to believe it is applicable to your case.

Having said that, if you want to model your fluid as weak compressible then define your fluid to have density as a function of pressure. I would recommend using the bulk modulus of water (or your fluid if you have it) so the weak compressibility you add is physically realistic. The simulation will be a bit harder to run as you will now have pressure waves propagating around, but if they are weak it should be OK.

Note the restrictions on fluid models with immersed solids. See the documentation for that.

Your comment about somebody imposing a speed of sound of 15.7 m/s on the fluid sounds very dodgy. This sounds like they were using a very poor solver to have to impose such a unrealistic condition as that. This does not sound like a procedure you should copy.
Thanks for replying,

The water hammer effect is very important to my simulation as this study is focused on cavitation (and so the sharp pressure transients). I have assumed rigid leaflets as well as rigid artery walls- do you think that could be more of a reason for the low mass inflow than the compressibility?
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Old   September 17, 2020, 19:52
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Water hammer and cavitation are totally different physics. Why do you think they are linked? (Is that what your last comment was implying?)

If you are studying blood flow in a heart-like gizmo I would think the following will be important:
* The fluid is incompressible
* water hammer and cavitation will not occur, the flows are not long or fast enough.
* The fluid might have some non-newtonian properties (blood is non-Newtonian)
* The walls have a lot of deformation. Pressure pulses in the fluid case significant stretching of the artery walls.

I suspect you have confused wall deformation with weak compressibility. Could this be correct? You cannot model deforming walls by making the fluid weakly compressible. You model deforming walls by modelling deforming walls (obviously).
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Old   September 18, 2020, 10:15
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Originally Posted by ghorrocks View Post
Water hammer and cavitation are totally different physics. Why do you think they are linked? (Is that what your last comment was implying?)

If you are studying blood flow in a heart-like gizmo I would think the following will be important:
* The fluid is incompressible
* water hammer and cavitation will not occur, the flows are not long or fast enough.
* The fluid might have some non-newtonian properties (blood is non-Newtonian)
* The walls have a lot of deformation. Pressure pulses in the fluid case significant stretching of the artery walls.

I suspect you have confused wall deformation with weak compressibility. Could this be correct? You cannot model deforming walls by making the fluid weakly compressible. You model deforming walls by modelling deforming walls (obviously).
Cavitation and water hammer are linked because the rapid closure of prosthetic leaflets has been known to induce sharp pressure drops in the flow field near the leaflet- known as the water hammer effect. These pressure drops can cause cavitation bubbles (as in the Edwards-Duromedics valve). The water hammer effect has been explicitly mentioned as one of the mechanisms for causing isothermal hydrodynamic cavitation in mechanical heart valves from the literature I have been researching (Peter Johansen, Mechanical heart valve cavitation. Expert Review of Medical Devices)

I have not confused the deformation with the compressibility of the fluid- I was wondering including which of those physical phenomena would help fix my problem of achieving valid results at the boundary. I suspect the deformation more so. As this is flow in relatively large arteries, every single paper has assumed Newtonian blood as my supervisor advised me to.
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Old   September 18, 2020, 22:45
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If you are getting water hammer and cavitation effects in a blood pumping device then it is a seriously aggressive device. OK, I will take your word on that.

I would recommend you do some studies to see which of all these effects is important. The best and quickest way is to do some simplified analytical work to estimate how big the wall deformations and blood compressibility are. If you need to you can simulate both options and get it from there, but this is a lot more work.

To answer your original question, you can easily add compressibility of any amount to CFX by defining density as a function of pressure. You can make this realistic by getting the variation from the bulk modulus, or you can use any bogus bulk modulus you like to change it if you like. But as you might have guessed from my comments, I think this approach is ill-advised, you should model the thing with the correct physics and not add dodgy physics just to patch over some tricky numerics. It should work fine with the correct physics.
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