# Variable denisty in the contiuity and momentum equaiton

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 June 1, 2011, 08:23 Variable denisty in the contiuity and momentum equaiton #1 Senior Member   Join Date: Jun 2010 Posts: 101 Rep Power: 7 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

June 1, 2011, 10:09
mild compressibility
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CFDtoy
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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 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
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 June 2, 2011, 04:44 mild compressibility #3 Senior Member   Join Date: Jun 2010 Posts: 101 Rep Power: 7 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? Sorry I asked too many questions. Thank you for your time. H

 June 2, 2011, 07:16 mild compressibility #4 Senior Member   Join Date: Jun 2010 Posts: 101 Rep Power: 7 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!

June 2, 2011, 10:25
mild compressibility
#5
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CFDtoy
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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 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!
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CFDtoy

 June 3, 2011, 04:52 weakly compressible #6 Senior Member   Join Date: Jun 2010 Posts: 101 Rep Power: 7 Many thanks for you help!

 June 3, 2011, 10:30 #7 Senior Member   Join Date: Jun 2010 Posts: 101 Rep Power: 7 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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