Modélisation des écoulements diphasiques dans les codes avancés décrivant l'accident de dépressurisation dans les réacteurs à eau sous pression

Modelling of two-phase flow in advanced codes describing the depressurization accident in pressure-water reactors

Département de Sûreté Nucléaire CEN - Fontenay-aux-Roses

Abstract

Two-phase flow modelling is one of the most important problems in the prediction of a loss-of-coolant accident because two-phase flow occurs very soon during the accident and determines the behaviour of the barriers between the radioactive products and the environment, namely the containment and the fuel cladding. For the containment, the pressure inside depends on the energy released at the break, and therefore the flow at the break. The thermomechanical behaviour of the fuel cladding is governed by the flow transient in the core. A very important aspect of two-phase flow modelling during a LOCA is that, very often, the models can only be verified on small-scale experiments. These models have then to include enough physics to be able to transpose to scale, and the transposition has to be verified on intermediate global experiments as LOBI, SEMISCALE, LOFT. To improve physics and ensure closer evaluation of safety margins, advanced codes are being developed with a special effort on two-phase flow modelling. A rigorous derivation of the equations is of course needed. This is achieved by applying the conservation principles in their integral form. Transformation by the Leibniz rule and the Gauss theorem gives the well-known instantaneous local equations (table 3). Two assumptions are necessary to get these equations, (a) and b) in table 2, but they are not very restrictive. The obtained set of equations can then be considered as rigorous, but it cannot be used practically because of mathematicaI difficulties. Moreover, experiments do not give always the local instantaneous parameters but very often average quantities. Averaged equations, therefore, are more practical. The averaging operations are of two types : - geometrical averaging leading to 2D, ID, OD models - time or statistical averaging. By cross-section averaging in the geometry fixed by assumptions c) and d) (table 2) and time or statistical averaging the set of equations of table 4 is obtained. As this set contains more unknowns than equations, it is necessary to made additional assumptions, to determine some laws and give expressions to the transfer terms. All these operations together constitute the actual modelling procedure. In modelling, the first point to be discussed is the meaning of time averaging in rapid transients as during LOCA. Use of statistical averaging or of double averaging can be substituted for time averaging but problems still remain. A very frequently used assumption is to neglect axial conduction and viscous terms. This has some consequences on the mathematical properties of the set of equations. The problem of the correlation factors for spatial profiles and turbulence is difficult in two-phase flow because of two aspects : - First, vaporization may induce heterogeneous void and velocity distribution under conditions, in which flat profiles are obtained in single phase flow. - The flows in the reactor are mostly non-established flows with strongly varying profiles. Assumptions of constant and equal to 1 correlation factors are certainly not adequate but there is a great lack of experimental data. One very important law to determine is the interaction law. This law must compensate for information lost in averaging the geometrical distribution of the phases which introduces a new variable, i.e. the void fraction. This law is generally a pressure relationship between the two phases. A crucial point in modelling is the determination of the transfer terms into which the greatest effort is put theoretically and experimentally. Theoretically some principles which have to be fulfilled by the transfer terms have been established. Studies have shown that their mathematical expressions for two-phase flow may include both algebric and derivative terms. Practical methods for determining the transfer terms are by an analytical approach based on theory, a correlation-type approach, or a combination of both. Each approach has its advantages and draw backs, especially as regards scale transposition capability. Two examples of two-phase flow modelling used in advanced codes are presented. The first one is a thermal non-equilibrium model (SERINGUE). The problem raised by this model is the determination of mass transfer. This has been achieved by a combined approach using steam-water MOBY-DICK tests. The second example is the thermal and mechanical non-equilibrium models. The main models on this type are the drift flux and two-fluid models. The characteristics of the HEXECO two-fluid model are presented. One of its important points is the use of an interaction law which relates the average pressure on the interface to the average phase pressures. This law induces derivative terms and allows the introduction of added mass terms into the momentum equations. The transfer laws of such a model are written in three steps : a) the mechanical terms are obtained by using steam-water tests ; b) with these terms, mass and energy transfers are obtained from adiabatic steam-water tests ; c) tests with heating then give the transfers between the wall and the fluid, since the transfers between the phases have already been determined. Although this seems a logical procedure, however, many difficulties arise in its application. In practice, however, a large number of numerical problems are inseparably associated with the actual modelling of two-phase flow. As a general conclusion, closer prediction of LOCA accidents and all accidents involving two-phase flow will depend on improved two-phase modelling, which can only be achieved by simultaneous progress in the understanding of fundamental and theoretical problems, such physical problems as transfer determination for example, and numerical problems.