|Results with K-Epsilon Model|
Nevertheless, the bubbles concentration is not correct. Indeed there are only short differences
between the three types of flow and the distribution does not follows physical laws. In upward
flow bubbles go to the axis whereas in downward flow bubbles go to the wall. In weightless
conditions, up and down notions are non-sense and bubbles are more equally distributed in the
column because not subject to gravity.
Bubble concentration in the column versus non-dimensional Radius (experimental results)
Average bubble concentration in the column versus Radius (computational results)
Bubble trajectory with the 2D K-Epsilon model (upward flow)
|LES model - Dispersed phase study (without flow)|
In order to determine the particle final velocity, we write a simplified equation of motion of particles :
The drag, due to viscous dissipation behind the bubble, is defined as :
Writing that Vp is established, the equation of motion aims to the result of the final particle velocity :
In order to determine if the software correctly calculates this velocity, we inject different particles and we find the graph presented below :
Particle final velocity versus Radius
It appears that the evolution of the particle final velocity does not vary like R² but like R !!!
|LES model - Interaction study (with flow)|
This study is limited to an upward flow. We first analyze the continuous phase flow. After the convergence of this phase, we implement the injection defined before and we analyze the results in comparing them with the experimental observations. Conclusions of this study are now presented.
The velocity profile presented is the same in all the flow thanks to the periodic conditions. Its shape corresponds to the boundary-layer theory.
Subgrid turbulent kinetic energy
The subgrid kinetic energy is more important near the wall. The turbulent intensity is more important because of the wall interaction.
This picture shows that the particles oscillate in a zone near the axis and after several iterations, the particle goes near the wall as predicted in the theory. We deduce that the theory is correct and that the particles, after reflecting the wall, will go up and stay near the wall. But the interaction bubble-wall does not be established as predicted and the bubbles go down. Consequently, the flow is like a downward one and the particle goes near the axis.
=> This transversal oscillation, due to an incorrect rebound, goes on during all the simulation.
For an upward flow, we have demonstrated that DPM concentration must be greater near the wall. Consequently, the result presented here is not correct. The particles tends to stay in a zone 2mm far from the axis.
|Results with 3D K-Epsilon Model|
Bubble trajectory - Front view