Results with K-Epsilon Model |

Method |

The available experimental results are the bubble distribution in columns with upward flow, downward flow and flow in weightless conditions. To obtain these values with Fluent, vertical lines are created in the column and for each one, the average DPM (Discrete Phase Model) Concentration is calculated. Then these concentrations are plotted in function of the radius.

Results |

With such a simulation, the velocity profile coincide with the expected one.

__Velocity profile__

__Bubble concentration in the column versus non-dimensional Radius (experimental results)__

__Average bubble concentration in the column versus Radius (computational results)__

This wrong distribution can be explained by the wrong direction of the rebound of bubbles on the wall. To solve this problem, new computations were done with the LES-model.

__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 *V _{p}* 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.

Continuous phase |

*Velocity magnitude*

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.

Dispersed phase |

*Particles evolution*

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.

*DPM concentration*

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 |

With this model, the bubbles are free to evolve in 3 Dimensions. Like this, the simulations show that the bubbles evolve from the axis to the wall and then to the axis in a sole plane, and then evolve to a random plane.

However, the problem of direction of reflection to the wall is not corrected.

Bubble trajectory - Front view |
Top view |

Espeyrac Lionel Pascaud Stéphane |
Presentation Physics CFD Results Conclusion |