Olivier Hurisse

A simple method to compute standard two-fluid models

We describe in this paper, a tool to compute approximate solutions of standard two-fluid models with an equilibrium pressure assumption. The basic approach takes its grounds in the two-fluid two-pressure formalism, and takes advantage of the relaxation techniques. The method may be used to compute either the single- or the two-pressure model, depending on the size of mesh, which is used. It is also shown on the basis of a simple numerical experiment that the local equilibrium assumption may lead to a blow-up of the numerical solution on fine meshes, even if one accounts for drag stabilizing effects.

SOME ATTEMPTS TO COUPLE DISTINCT FLUID MODELS

We present in this paper a review of some recent works dedicated to the numerical interfacial coupling of fluid models. One main motivation of the whole approach is to provide some meaningful methods and tools in order to compute unsteady patterns, while using distinct existing CFD codes in the nuclear industry. Thus, the main objective is to derive suitable boundary conditions for the codes to be coupled. A first section is devoted to a review of some attempts to couple: (i) 1D and 3D codes, (ii) distinct homogeneous two-phase flow models, (iii) fluid and porous models. More details on numerical procedures described in this section can be found in companion papers. Then we detail in a second section a way to couple a two-fluid hyperbolic model and an homogeneous relaxation model.

A Method To Couple Two-Phase Flow Models

The problem of the coupling of distinct models has recently become a challenging research topic. The need for the unsteady interfacial coupling of distinct models immediately arises in industrial projects where computational facilities require the use of different models in order to describe parts of a whole concept. For nuclear applications in the framework of nuclear power plants, it represents a challenging area, since many codes have been developped up to now, in order to cope with the system scale (corresponding to the one-dimensional simulation of the whole primary coolant circuit), the component scale (corresponding to the three-dimensional simulation of the flow inside the core, or inside the steam generator, using an homogenized approach), or the classical CFD scale. In order to reach a better understanding or representation of the flow in the nuclear plant, one actually needs to couple these codes. Owing to the great effort in the building of these codes and their validation in the past, a straightforward consequence is that the interfacial coupling should only affect the boundary conditions. This need for the coupling techniques also arises when one wishes to compute the flow in a gas turbine engine (see or http://www.stanford.edu/group/cits/ for instance).

Some Applications of a Two-Fluid Model

We present in this paper some comparisons of numerical results and experimental data in some two-phase flows involving rather high pressure ratios. A two-fluid two-phase flow model has been used herein, but we also report a few results obtained with some simpler single-fluid two-phase flow models.

Application of a Two-Fluid Model to Simulate the Heating of Two-Phase Flows

This paper is dedicated to the simulation of two-phase flows on the basis of a two-fluid model that allows to account for the disequilibrium of velocities, pressures, temperatures and chemical potentials (mass transfer). The numerical simulations are performed using a fractional step method treating separately the convective part of the model and the source terms. The scheme dealing with the convective part of the model follows a Finite Volume approach and is based on a relaxation scheme. In the sequel, a special focus is put on the discretization of the terms that rule the mass transfer. The scheme proposed is a first order implicit scheme and can be verified using an analytical solution. Eventually, a test case of the heating of a mixture of steam and water is presented, which is representative of a steam generator device.