PRESSURE RECONSTRUCTION AT THE INTERFACE IN DIRECT NUMERICAL SIMULATIONS OF TWO-PHASE BUBBLY FLOWS: EVALUATION OF INTERFACIAL TERMS IN THE AVERAGED MODELING.

Dynamics, pseudo-turbulence and turbulence of two-phase bubbly flows, frequently occuring in the reactors of Nuclear Power Plants, may be analysed performing Direct Numerical Simu- lations (DNS) of simplied congurations. They may be considered as numerical experiments since they provide the instantaneous evolution of the microscopic properties of the flow. These data are available to reconstruct averaged (RANS) equations in order to produce a macrospic description of the flow, more meaningful for industrial applications and useful for developing and validating new turbulence models. In particular the Two-fluid formulation, where the phases are treated separately, is proved to be a powerful tool to investigate how the presence and the properties of the dispersed phase affect turbulence of the liquid carrier phase. Indeed, when this up-scaling procedure is followed, equations for turbulent quantities may be derived too with the aim of having a better insight on the fluctuations induced both by the inhomo- geneity of the flow and by its chaotic behavior. The open-source code TrioIJK developed at the CEA is devoted to DNS. It resorts to the Front-Tracking method to advect the interfaces and solves the One-fluid formulation of the Navier-Stokes equations for incompressible fluids. The interfacial cells of the fixed-Eulerian grid show an averaged value of pressure because of the discontinuity induced by the surface tension. In the previous application the explicit assesment of the interfacial terms arising in the averaged equations was bypassed. An algorithm devoted to the reconstruction of this discontinuity at the bubble interface has been implemented in order to consider the interfacial cells as ghost cells for both the liquid and the vapor phase. The details of this implementation are presented along with test cases for its validation. The averaged momentum equation is then computed considering adiabatic conditions and neglecting phase-change. The interfacial force is evaluated explicitely for the first time, as it is pivotal to better point out the role of surface tension in bubble migration, already highligthed by the researches carried out at the CEA. Under the same hypothesis the Reynolds stress balance equation for the liquid phase is computed too. The presence of a purely liquid microscopic pressure allows a new assessment of the pressure-affected terms. Their role in the total balance is investigated. The results obtained on two simple congura- tions are reported in order to validate the previous applications of the code TrioIJK. Additional use of this post-processing tool on different configurations is feasilble to confirm the models developed at the CEA.