Probably you found an answer to your question in the meantime; however, since it is a common question of students, I want to add that you do not need to track the center or anything else. Simply use the mass averaged velocity (momentum):

let K the phase indicator function (1 for gas 0 for liquid), V the velocity vector, vol the volume of your cell (area in 2D), and sum() the summation over all your cells

bubble velocity = sum(vol*K*V)/sum(vol*K)

slip velocity = sum(vol*K*V)/sum(vol*K) - sum(vol*(1-K)*V)/sum(vol*(1-K))

[If you run compressible simulations, you must use vol*rho_gas and vol*rho_fluid]

2D bubble diameter : sqrt( 4*sum(vol*K)/Pi )

[this is the Area-circle equivalent diameter]

3D bubble diameter : cbrt ( 6*sum(vol*K)/Pi )

[this is the spherical equivalent diameter]

You can evaluate the bubble shape by searching the bounding box if it is a non-wobbling bubble - find the max and min x, y, and z of your PLIC reconstruction, zero-level when you use level set, or of your boundary compression when you use two-fluid model. For wobbling bubbles, different definitions of "shape" exist - be consistent with the experiment you want to compare.

Sikander,

What do you mean by dia?

The rise of a bubble is due to gravity and the difference in density between the gas and the liquid. A momentum balance on the bubble is the sum of forces : it includes gravity acting on the bubble, buoyant force, the drag exerted by the fluid , and a lift force which is usually neglected.

Initially, the bubble is stationary and the drag force is zero. As the bubble starts to rise and accelerates, the drag force increases, which in turn reduces the acceleration. This process continues until the acceleration drops to zero, at which time the bubble rises at a constant velocity called terminal velocity as the drag, gravity and buoyancy are balanced.

The terminal velocity, can be written as : Vt= [4*g*(ρL-ρG)*d)/3*ρL*CD]^1/2.

Regards.

Thanks Mounir for replying I mean the bubble diameter. With your answer I agree but I am asking regarding CFD how to find the gravity center for the bubble in simulation then it surely will give the terminal velocity

Not sure I understood. The shape of the bubble in steady state is stable so you can use the top of the bubble as reference. Determine the position as a function of time of the top of the bubble and you can then get its velocity.

A simple method to determine the center of the bubble is to determine the average coordinates of all nodes of the bubble phase.

Note that, depending of its size, the bubble may be non-spherical.

Sikander

I think you should write a UDF that calculates the masscenter/barycenter + the displacement over time which represents the rising velocity.

By the way, I recommend you also to use calculation on a axisymmetric 2D mesh .

And probably it is worth to mention, that your simulation result will not correlate too well with e.g. experimental results / correlations from Grace, Clift and Weber, because with a 2d simulation you are investigating the terminal rise of a cylinder instead of a sphere/ellipsoid. The drag of a cylindrical "bubble" is different, and hence the terminal rise velocity.

Probably you found an answer to your question in the meantime; however, since it is a common question of students, I want to add that you do not need to track the center or anything else. Simply use the mass averaged velocity (momentum):

let K the phase indicator function (1 for gas 0 for liquid), V the velocity vector, vol the volume of your cell (area in 2D), and sum() the summation over all your cells

bubble velocity = sum(vol*K*V)/sum(vol*K)

slip velocity = sum(vol*K*V)/sum(vol*K) - sum(vol*(1-K)*V)/sum(vol*(1-K))

[If you run compressible simulations, you must use vol*rho_gas and vol*rho_fluid]

2D bubble diameter : sqrt( 4*sum(vol*K)/Pi )

[this is the Area-circle equivalent diameter]

3D bubble diameter : cbrt ( 6*sum(vol*K)/Pi )

[this is the spherical equivalent diameter]

You can evaluate the bubble shape by searching the bounding box if it is a non-wobbling bubble - find the max and min x, y, and z of your PLIC reconstruction, zero-level when you use level set, or of your boundary compression when you use two-fluid model. For wobbling bubbles, different definitions of "shape" exist - be consistent with the experiment you want to compare.