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Old   October 23, 2009, 00:51
Default Barotropic Flow Analysis CFX
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Claudio
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Hello,

I want to perform a barotropic flow analysis in CFX, but I don't know if this is possible.

I want the density to depend only on the pressure, to analyze the effects of compressibility. I want to use the mass conservation, momentum conservation, a viscosity law plus a relation between density and pressure, such as:

dp/drho = E / rho

in which E is a bulk modulus. How can this be done? I'm using CFX 12.0.

Thanks.
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Old   October 23, 2009, 05:08
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Matthias Voß
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hi,
just write an expression for the density of your material including the pressure p(p=pabs if p_ref.=0).
Sounds so easy, maybe i am missing smth. here. Am i?

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Old   October 23, 2009, 06:46
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Glenn Horrocks
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You are correct neewbie, that should work. I have done it before to model compressibility in high pressure hydraulic systems and it works fine. It will mean you start getting acoustic waves and other compressible flow features which make convergence harder but as long as you are careful it works fine.
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Old   October 23, 2009, 07:17
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Matthias Voß
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When dealing with hydraulic systems and compressibility how did you get rid of neg.pressures while evaluating enthalpy, entropy,.. and so one? that´s what you´re referring to when saying "being careful"??

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Old   October 23, 2009, 07:35
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Glenn Horrocks
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If all you are doing is specifying a variable density (as a function of pressure as described above) then there is no enthalpy or entropy as you do not have an energy equation. The convergence difficulties simply come from compressible flow effects such as acoustic waves. The acoustic waves means another time scale has been introduced into the system which is usually orders of magnitude shorter than any other time scales, so you will probably need to use time steps much smaller than the equivalent incompressible simulation.
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Old   October 23, 2009, 08:15
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Matthias Voß
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Could one specify a smaller scale only for the momentum eq.?

hmm.. maybe won´t work, because for continuity eq. you also need a small one because they´re coupled.
Tricky.
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Old   October 23, 2009, 12:28
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Thanks a lot for your replies.

I'm a new user. Could you help me with what would be the notation when I define the density. What I don't know is how to notate the derivative of rho with respect to p.

dp/drho = E/rho

So the expression should be:

rho = drho/dp * E

As you can see, rho is part of a differential equation. Am I on the right track here using that as my density expression for the barotropic flow?

I see that the differential equation could be solved for p:

p = E * ln(rho) + C1

where C1 is an integration constant.

But according to your advice, what I need is a expression for rho.

From the previous expression, I could do:

rho = exp ( (p-C1)/E )

Would defining the density like that work?

Thanks again!
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Old   October 24, 2009, 06:01
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Quote:
hmm.. maybe won´t work, because for continuity eq. you also need a small one because they´re coupled.
Exactly. So forget it and just run small time steps to resolve the acoustic waves - well at least while the acoustic waves are doing something. If you use adaptive timestepping aiming for 3-5 coefficient loops per iteration then the solver will grow and shrink the time step as required all by itself.

Claudio I think you are heading in the wrong direction. Try this:

Look at eqn 2 here:
http://www.engineeringtoolbox.com/bu...ity-d_585.html

You then define a reference pressure, and a reference density at that reference pressure. Then you can recast the equation to give you density at any pressure using the reference density and reference pressure as the base.
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Old   October 26, 2009, 10:34
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Hi Glenn,

Equation 2 is exactly what I had in mind. What I don't understand is how to indicate to CFX that it needs to use that expression for the density. I'm using Ansys 12.0 and up to now have defined the density as constant in my simulations. In eq. 2, density is not "explicitly" defined, but rather defined as part of a differential equation. That is what I don't get. In this case, how should I define the density in CFX? In other words, where before I put a constant value, what do I write now?

On the other hand, solving that differential equation analitically is easy. I did that analysis to obtain the explicit expression for density to be plugged directly into the density definition in CFX. I believe that what you said about the reference pressure and density is the same as solving for the constant C1 in the expression in my previous post.

Thanks for you help. I hope my question was a little clearer now.
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Old   October 26, 2009, 18:00
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If you assume the bulk modulus is constant then the d(rho) and d(P) can be replaced with rho(reference)-rho and P(reference)-P. You can then rewrite in terms of rho and you're done. This is the easiest way to do it.
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