The CEA aspires to create a numerical nuclear reactor which requires a great knowledge of single-phase and two-phase flows. In order to improve our understanding of accidental scenarios for pressurized water reactors. Turbulence in bubbly flows is comprised of SPT (Single Phase Turbulence), WIT (Wake Induced Turbulence) and WIF (Wake Induced Fluctuations) which characterize distinct phenomena. The SPT is the turbulence produced by the averaged shear, the WIT represent the temporal and turbulent fluctuations due to destabilizations and collective instabilities of wakes, and the WIF reflect the spatial fluctuations generated by the averaged wake and the potential flow around the bubbles. This work focuses on proposing a turbulence model in agreement with the current knowledge of these phenomena. We propose a tensorial three-equations modeling of turbulence, where each contribution (SPT,WIF and WIT) has its own closure. In order to achieve these objectives, a statistical database is produced from numerical experiments (direct numerical simulations) of swarms and bubble channels.