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-   -   Variable denisty in the contiuity and momentum equaiton (http://www.cfd-online.com/Forums/main/89005-variable-denisty-contiuity-momentum-equaiton.html)

 Hooman June 1, 2011 08:23

Variable denisty in the contiuity and momentum equaiton

Hi,

I am writing a code for a flow with a low degree of in-compressibility. So in my continuity and momentum equations, the density varies. I have never worked with variable density before so I was wondering, how does one usually decide on how the density varies and go on about solving these equations where you have velocity and density as unknowns in the continuity equations.

I would appreciate any hints.

Thanks,

H

 CFDtoy June 1, 2011 10:09

mild compressibility

Hello,
For mild compressibility - your pressure correction will have an additional term as d(rho')/dt modeled as, d(p'/C2)/dt where C = speed of sound. This will go into your ap (solving for p'). C2 can be approximated to gasConstant*temperature

No more big modifications from an incompressible code is required. merely include this this term in the P' eqn and you are all set.

ofcourse, dont forget to update rho from P - using ideal gas law.

Good luck.

CFDtoy

Quote:
 Originally Posted by Hooman (Post 310117) Hi, I am writing a code for a flow with a low degree of in-compressibility. So in my continuity and momentum equations, the density varies. I have never worked with variable density before so I was wondering, how does one usually decide on how the density varies and go on about solving these equations where you have velocity and density as unknowns in the continuity equations. I would appreciate any hints. Thanks, H

 Hooman June 2, 2011 04:44

mild compressibility

Thanks very much for you reply.

I was wondering if you knew any references on mild compressibility. I just want to know where the equations you cited come from and understand it a bit more.

I am also a bit confused because my problem was an isothermal mechanical example for an incompressible fluid. So there were no thermal terms involved. The we decided to add a bit of compressibility to it. So do you think that the equations you just told me still apply for an isothermal case?

Also I was told that pressure in this case is a state variable and can be related to the bulk modulus. What do you think of this?

H

 Hooman June 2, 2011 07:16

mild compressibility

Sorry to be asking more questions again.
I just found out that because there are more variables involved for a compressible flow, one should also solve the energy equations plus another equations. Is this true for the case of mild compressibility?

Thanks very much again!

 CFDtoy June 2, 2011 10:25

mild compressibility

For mildly compressible..you can get away with not solving for E. T can remain constant in the system, with rho changing with P only.

Quote:
 Originally Posted by Hooman (Post 310247) Sorry to be asking more questions again. I just found out that because there are more variables involved for a compressible flow, one should also solve the energy equations plus another equations. Is this true for the case of mild compressibility? Thanks very much again!

 Hooman June 3, 2011 04:52

weakly compressible

Many thanks for you help! :)

 Hooman June 3, 2011 10:30

Hi,
Can I just ask if you have any references for the equations you cited in your first reply?
Thanks,
H

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