### First and Second Order Turbulence Closure for Bubbly Flows

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#### Abstract

The paper presents a tow-fluid model for turbulent bubbly flows based on first and second order closure of the turbulence. In the second order turbulence closure, the Reynolds stress tensor of the liquid is split into two parts: a turbulent part produced by the gradient of mean velocity and a pseudo-turbulent part induced by bubbles displacements. Each part is computed using a specific transport equation. The reduction of this second order turbulence closure leads to an original turbulent viscosity formulation. Based on this turbulent viscosity a three equation turbulence model (k,ks,eps) is proposed. This model is applied to the computation of a turbulent bubbly wake and the numerical results clearly show that the three-equation turbulence model is able to represent the alteration of the turbulence structure of the liquid phase in bubbly flows due to the bubbles agitation *Copyright © 2014 Praise Worthy Prize - All rights reserved.*

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