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December 18, 2015, 11:18 
number of equations/variables in VOF model

#1 
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Hi members,
the VOF model (for a turbine in my case) uses the momentum and continuity equation. In the VOF, the momentum equation is solved for the mixture, while the continuity equation is solved for the secondary phase. The further equation that the sum of the VOF is equal to 1. But, since there are two phases, is there a missing equation?? Because if I model a single phase problem, the continuity and monentum equations are enough, but for a two phase flow, I need more equations. The further equation that the sum of the VOF is equal to 1 is not sufficient... Could anyone explain this to me better? Where I am wrong? Thank you 

December 21, 2015, 21:00 

#2 
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The volume fraction is not solved for the primary phase, if you know the sum of the two volume fractions is 1 then it makes sense to just compute the primary phase faction from the logic that the sum is 1, why would you want to solve another equation when you can just calculate the volume fraction of the primary phase by 1vf of secondary phase.
That is what the solver actually does. 

December 22, 2015, 10:13 

#3 
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Thank you for your response.
My doubt is this. Consider a single phase problem, without turbulence and incompressible flow (water). Solving the continuity and momentum equation the solver calculates pressure and velocity in each point. Two equations for two variables are satisfactory. But when the phases are two (with VOF method), I need the mixture pressure, the mixture velocity and the volume fraction of the secondary phase in each point, thus 3 variables, and I need an additional equation. The equation sum(phases)=1 is used to calculate the primary phase volume fraction, but only after that the secondary phase volume fraction has been calculated by the previous three ones (my doubt pertains to the third equation...). Thank you!! 

December 22, 2015, 19:23 

#4 
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As far as i understand the continuity equation is used to solve for the interface between the faces and only the momentum equations are shared.
Read section 17.3 in the fluent theory guide, the full explanation is there, 

December 23, 2015, 10:40 

#5 
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Thank you.
therefore, the solver solves the phase continuity equation for the secondary phase, then it calculates the primary phase volume fraction by (alpha_2=1alpha_1) and then solves both the momentum and the continuity equation for the mixture. Thank you 

January 14, 2020, 20:48 

#6  
Member
Soumitra Vadnerkar
Join Date: Aug 2018
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Quote:
I hope it is right (please someone confirm), because, this thing have been bugging me since a long time. 

Tags 
continuity equation, equations, momentum equation, phase equation, vof 
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