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Micro-bubble dynamics in turbulent flow

Zhang, Zhentong. Micro-bubble dynamics in turbulent flow. PhD, Energétique et Transferts, Institut National Polytechnique de Toulouse, 2019

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Abstract

This thesis is devoted to the study of the motion of small bubbles in homogeneous isotropic turbulent flows. The work addresses several questions related to the statistical description of the hydrodynamic forces exerted on a bubble as well as the stochastic modeling of their high frequency fluctuations. First, we propose a model for the acceleration of micro-bubbles (smaller than the dissipative scale of the flow) subjected to the drag and the fluid inertia forces. This model, that depends on the Stokes number, the Reynolds number and the density ratio, reproduces the evolution of the acceleration variance as well as the relative importance and alignment of the two forces as observed from Direct Numerical Simulations (DNS). Second, based on the observation that acceleration statistics conditional to the local kinetic energy dissipation rate are invariant with the Stokes number and the dissipation rate, we propose a stochastic model for the instantaneous bubble acceleration vector accounting for the small-scale intermittency of the turbulent flows. The norm of the bubble acceleration is obtained by modeling the dissipation rate along the bubble trajectory from a log-normal stochastic process, whereas its orientation is given by two coupled random walk on a unit sphere in order to model the evolution of the joint orientation of the drag and inertia forces acting on the bubble. Furthermore, the proposed stochastic model for the bubble acceleration is used in the context of large eddy simulations (LES) of turbulent flows laden with small bubbles. It can effectively reproduce effect of turbulent motion at scales smaller than the mesh resolution by adding a random contribution depending on local average dissipation rate. Comparisons with DNS and standard LES, show that the proposed model improves significantly the statistics of the bubbly phase. Third, we extend the previous results in the case of bubbles with large Reynolds number by considering non-linear drag laws. We define an effective relaxation time based on the drag coefficient to characterize bubble motion (acceleration,velocity). Eventually we study the effect of buoyancy and lift force on the bubble dynamics, and analyze the reduction of the average rising velocity in turbulent flow compared to quiescent flows. It is observed that bubbles preferentially explore region having downward fluid acceleration which contributes through the inertia force to reduction of the rising velocity. In addition, as already observed, the lift force brings preferably bubbles into downstream fluid motion which also reduce their rising velocity.

Item Type:PhD Thesis
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Institution:Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
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Research Director:
Legendre, Dominique and Zamansky, Rémi
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Deposited On:10 Jul 2020 07:36

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