In a droplet impact onto a stationary particle, I want to calculate mass conservation of VOF method (before impact vs. after impact ends).
For that, I use Reports => Volume Integrals window. In Fluent 17, there are two different options there. If "Mass Integral" is chosen for mass calculation, it shows a decrease in the existing liquid mass in the domain as solution proceeds. However, if I use "Mass" option, the calculated value remains the same before and after impact (calculated values, and their Units shown in Fluent are presented in the attached picture).
Since the difference between two method is significant (~0% error compared to 3% error), I'd like to know what is the reason and which one of them could be used for mass conservation check?
But, for "mass integral", the unit is (kg/m3).(m3)
How does velocity affect this?
Using which method is more accurate for mass conservation analysis "mass integral" or "mass"?
Thanks
Dear Sayed A Banitabaei,
"V" in the expression for mass-integral is CELL VOLUME not velocity.
The value of "mass" can be cross-checked.
Define the following custom field-function (i hope these are still around in FLUENT 17):
fn = liquid_density*liquid_volume_fraction*cell_volume
and evaluate a SUM of fn over all cells in the domain (volume integrals >> sum); fn would have a unit of kg. Check whether the value of fn is closer to "mass" or "mass-integral"....I expect it to be exactly equal to "mass".
It is interesting that the value of "mass-integral" reduces as the simulation proceeds. Referring to the theory guide of FLUENT 12, section 22.4.1 on Computing Volume Integrals....it is seen that "mass-weighted integral" takes into account rho_i (the mixture density) whilst "mass" takes into consideration rho_pi (the phase density). Since rho_i is evaluated considering all phases,
rho_i*cell_volume > rho_pi*phase_volume_fraction*cell_volume
Hence, I would expect the value of "mass-integral" to be slightly larger than that of "mass" (??!). In any case, volume conservation in two-phase flows is generally based upon the heavier (primary) phase in the domain. Hence, you should evaluate "mass" (focusing only on the droplet phase) for your conservation analysis.
I hope this helps.
Regards.
Shaswat Saincher
Hi Shaswat,
First, thank you so much for detailed explanation.
The result of custom field-function is neither close to 'mass' nor to 'mass integral':
For instance, after the impact that lamella is fully stretched (i.e. the right-hand side picture above) here are the values:
mass= 1.207643e-05 (kg)
mass integral= 1.157154e-05(kg/m3)(m3)
fn= 1.922024e-06 (no unit is mentioned)
In contrast to what was expected, the value of "mass integral" is slightly smaller than that of "mass" and it keeps decreasing as the solution proceeds.
Is it possible that we're missing a small portion of mass due to some computational or mesh/cell issues?
PS. The value of "mass" doesn't change at all during the solution but "mass integral" is decreased.
Dear Sayed A Banitabaei,
The expression: fn = liquid_density*liquid_volume_fraction*cell_volume works well in my case (numerical wave generation) as it correctly shows the amount of water mass inside the NWT (numerical wave tank) and fn remains constant throughout the simulation.
In my case of the NWT, the sum of fn over all cells in the domain is also equal to the mass-weighted integral of water volume fraction over all cells (REPORTS >> VOLUME INTEGRALS).
You can also verify your calculations by analytically estimating the initial mass of liquid in the droplet. If you are using Geo-Reconstruct, there is probably no loss of mass from the domain. If "mass" corresponds to the analytically determined value (which happens in my case), I recommend that you consider "mass" for analyzing conservation.
Best regards.
Shaswat Saincher
Thank you so much Shaswat
As my last questions:
1) considering that I'm using axissymetric solution, do i need to multiply any factor in Fn to become Cell Volume? or the value that fluent gives for cell volume already considers the revolve around X-axis?
2) is it okay if fluctuations of mass is zero? I mean, if before the impact 'mass' gives me 1.1834572 e-5 (kg) and it gives me the exact same value after lamella is completely formed, is it reasonable that mass remains perfectly conserved during the solution?
Thanks again,
Sayed
Dear Sayed A Banitabaei,
1) I think there is a Sum*2Pi type volume integral available with 2D axisymmetric simulations in FLUENT. I believe multiplying by 2*Pi with fn should account for the revolve about the x-axis.
mass= 1.207643e-05 (kg)
mass integral= 1.157154e-05(kg/m3)(m3)
fn= 1.922024e-06 (no unit is mentioned)
You can see that fn*2*Pi = "mass"
2) The fact that "mass" is perfectly conserved is slightly difficult to comprehend in a two-phase Navier-Stokes simulation because divergence of the advecting velocity field (∇.V) would never be perfectly zero. Nonetheless, if "mass" remains conserved and the same is equal to fn for the entire duration of the simulation....it helps your case and justifies the selection of Geo-Reconstruct (PLIC-VOF).
Regards.
Shaswat Saincher
Dear Shaswat Saincher,
Thank you so much! I run the simulation again and now I see a bit of discrepancy in "Mass" between before impact and when the lamella is fully stretched:
m1= 1.878348e-05
m2=1.878342e-05
mass reduction~ 0.0005%
I hope it's a reasonable value considering the divergence of the advecting velocity field.
Bests,
Sayed
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