# What is density-weighted continuity equation

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 August 8, 2023, 17:01 What is density-weighted continuity equation #1 New Member   Join Date: Aug 2023 Posts: 10 Rep Power: 2 Hi everyone, I found this term as I was reading a paper, so I was just wondering what it meant by density-weighted continuity equation? I'm not so sure if it applies for multiphase flow of two fluids in CFX. Does CFX implement this in their equation? If not, how do I do that? Or if someone could explain what the text below means that would be helpful as well. Thank you so much. The part of the text from the paper I was reading: " we solve for six momentum equations, together with mass conservation and an equation for the phase fraction which involves the difference of the density-weighted continuity equations (leading to a constraint for continuity that ensures conservation of mass even in the early, not fully converged, stages of the computation)".

 August 9, 2023, 01:21 #2 Senior Member   Daniel Join Date: Feb 2017 Location: Germany Posts: 136 Rep Power: 8 Have a look in a book about the Favre averaging method of the conservation equations.

 August 9, 2023, 06:39 #3 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,582 Rep Power: 141 I think the question is about the density weighed multiphase equations, not Favre averaging equations (which are used on equations like the momentum equation as an averaging approach to get Reynolds stresses, commonly in turbulence models). The density weighted multiphase equations are explained in the CFX documentation, eqn 5-23 for continuity. Opaque and zacko like this. __________________ Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.

August 9, 2023, 07:56
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 Originally Posted by ghorrocks I think the question is about the density weighed multiphase equations, not Favre averaging equations (which are used on equations like the momentum equation as an averaging approach to get Reynolds stresses, commonly in turbulence models). The density weighted multiphase equations are explained in the CFX documentation, eqn 5-23 for continuity.
I will have a look at the documentations. Thank you very much!!

 Tags cfx, continuity equation, multiphase flow