From experiments to eulerian two-fluid

gas-liquid models for turbulent bubbly flows

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In spite of the progress achieved in the adaptation of the CFD codes to bubbly flows modelling, some important difficulties subsist; in particular the ability to predict phase distribution remains limited by the inadequate modelling of the turbulence and of the interfacial forces. At the same time, number of experimental researches has been achieved during the two last decades and we have now number of databases concerning basic bubbly flows configurations. These experimental studies have greatly enhanced our understanding of two-phase flow mechanisms. The analysis of experimental results show that the presence of the dispersed phase alters considerably the liquid turbulence structure. With regard to turbulence modelling, the experimental results suggest that we have to go up to turbulence closure level so that we may take into account the effect of the bubbles on the redistribution mechanism. In order to attain this objective, second order turbulence modelling is required. On the other hand the turbulence is proved to have in important effect on the phase distribution phenomenon. Two important questions are thus preamble to the elaboration of efficient prediction tools applied to gas-liquid systems especially when transfer problems are considered. The first question is related to the predetermination of the turbulence structure of the continuous phase as it is altered by the dispersed phase and the second concerns the prediction of the void fraction and bubbleπs size distributions. In the two-fluid modelling to be presented, we precisely attempt to improve the prediction of two-phase bubbly flows by laying emphasis on two aspects of the interfacial interactions :

- First, we develop a turbulence model adapted to bubbly flows in order to describe accurately the Reynolds stress tensor in each phase. In this model, the Reynolds stress tensor of the continuous phase is split into two parts, a turbulent dissipative part produced by the gradient of mean velocity and by the bubbles wakes, and a pseudo-turbulent non-dissipative part induced by the bubbles displacements, each part is predetermined by a transport equation.

- Second, we take into account the turbulent correlations issued from added mass in the expression of the force exerted by the liquid on the bubbles: this turbulent contribution, which is customary ignored, is proving to be important in the phase distribution phenomena especially in bubbly flows under micro-gravity condition;

The application of the eulerian-eulerian two-fluid modelling allows an accurate representation of the turbulence and of the void fraction in number of basic bubbly flows (grid, uniform shear, 2D thin shear bubbly flows and wall bubbly flows) with moderate void fractions (up to 15%). In this presentation the most prominent steps of the modelling will be presented, and the results will be commented in order to specify the basic requirements in the elaboration of general CFD codes applied to Gas-liquid bubbly flows.