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Conference Papers Year : 2018

## Towards an innovative R$_{ij}$-$\epsilon$ model for turbulence in bubbly flows from DNS simulations

A. Du Cluzeau
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J-M. Martinez
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#### Abstract

The Euler-Euler two-fluid model for turbulent bubbly flows has been extensively studied and modelling of turbulence is necessary for many industrial applications. In addition to the single-phase flow mechanism of Shear Induced Turbulence (SIT), two-phase bubbly flows develop a pseudoturbulence linked to the wake interactions known as Bubble Induced Turbulence (BIT). In classical $R_{ij}-\epsilon$ modelling, this added phenomenon is modeled as a source term of turbulent kinetic energy in the $R_{ij}$ transport equation. Nevertheless, it has been demonstrated that SIT and BIT are statistically independent and that their physical meanings are strongly different. These results allow us to propose a splitting of the $R_{ij}$ transport equation into a transport equation for the SIT Reynolds stresses and another for the BIT Reynolds stresses.These new equations contain a lot of terms which require modelling. In this study, they are closed through physical assertions and computational results.Physical analysis based on Direct Numerical Simulations (DNS) of bubbly turbulent plane channels are performed with TrioCFD. In order to feed the RANS (Reynolds Average Navier Stokes) modelling, the up-scaling process extracts knowledge from DNS. Indeed, a method which allows to calculate the SIT and the BIT separately from the DNS is proposed. In the form of statistical profiles, all terms of the new formulation are extracted from the DNS, are analysed in order to improve our understanding of BIT and are used in support for the modelling development of an innovative $R_{ij}-\epsilon$ model.

### Dates and versions

cea-02338616 , version 1 (21-02-2020)

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• HAL Id : cea-02338616 , version 1

### Cite

A. Du Cluzeau, G. Bois, Adrien Toutant, J-M. Martinez. Towards an innovative R$_{ij}$-$\epsilon$ model for turbulence in bubbly flows from DNS simulations. TI2018 - 5th Internationnal conference on Turbulence and Interactions, Jun 2018, Les Trois ilets, France. ⟨cea-02338616⟩

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