Safety evaluation of light-water nuclear reactors with respect to severe accidents confronts the problem of fission products and actinides released into the reactor coolant system (RCS). The SOPHAEROS code models radionuclide transport and is developed as part of the ASTEC integral code, Van Dorsselaere et al. (1999), and validated, in particular, on Phébus-FP tests, Schwarz et al. (1999). The status of SOPHAEROS v2.1 - modelling, validation, application and development activities - is outlined here.
The RCS is decomposed into a 1-D sequence of control volumes each comprising one or several freely-oriented truncated cones. The following table summarizes the phenomena modelled in a volume.
|| homogeneous nucleation|
| turbulent (eddy) impaction
|| heterogeneous nucleation (reversible)|
| diffusion, turbulent or laminar (Brownian)
|| sorption on metal-alloy surfaces|
|| vapour-phase chemistry|
|| condensation on surfaces (reversible)|
| bend impaction
| agglomeration (gravitational, Brownian, turbulent)
| mechanical resuspension
| inter-volume aerosol fall-back
Some modelling details are worth noting.
The present treatment of aerosols is single component, i.e. distribution of species among the size classes is ignored. The size distribution is discretized over a fixed grid of up to 50 size classes.
Approaches to homogeneous nucleation were appraised, Martin (1997), before choosing the Girshick et al. (1990) model. Vapour is nucleated beyond a critical saturation determined as a function of the minimum number of molecules in an embryo particle and a critical classical nucleation rate. Key assumption: an embryo can be described with macroscopic properties (surface tension).
Vapour-phase chemistry uses thermodynamics to calculate equilibrium. Two databases supply physico-chemical properties the larger, covering ~800 species, arising from identifying 65 pertinent elements and methodically assessing species in relevant conditions, Mason and Kissane (2000).
Mechanical resuspension occurs in turbulent flow (Re > 2300 here) and dry conditions (solid deposits, superheated steam). The model uses the ECART code approach, F. Parozzi (1992). When aerodynamic forces (drag plus lift due to turbulent bursts) exceed adhesion (gravity, intermolecular attraction, friction), the resultant force determines the resuspension rate.
The mass-balance equations resulting from the above intra-volume phenomena combined with inter-volume transport produce a nonlinear system solved numerically by a Newton-Raphson method. This implicit method allows the coupling between condensation/evaporation on/from aerosols, agglomeration and fall-back to be handled correctly while leading to satisfactory code run times.
VALIDATION AND APPLICATIONS
The table below summarizes the data sources for purely aerosol phenomena. A wide-ranging review of the experimental database has started with the intention of redefining the full validation matrix.
Main Phenomena Studied
|| eddy impaction; impaction in bends|
|| eddy impaction; impaction in bends|
|| turbulent diffusion; eddy impaction|
|| impaction in bends; sedimentation|
|| thermophoresis; eddy impaction; mechanical resuspension|
IRSN is currently performing a Probabilistic Safety Analysis level 2 for French 900MW PWRs where Sophaeros (as part of ASTEC V1) is used to predict fission-product release into the containment.
In the short term, model developments include: a more mechanistic model for mechanical resuspension; deposition due to aerosol impaction in contractions and more complex geometries; and retention in water pools occurring in the RCS for a number of accident sequences. Longer-term developments may address gas-phase chemical kinetics and steam condensation onto aerosols (cold-leg breaks) as well as the single-component aerosol treatment (representative experiments, such as Phébus FP, should determine whether aerosols are relatively homogeneous in the RCS).
SOPHAEROS is a suitable tool for prediction of fission-product transport with a reasonable level of accuracy and an acceptable calculation time. The code, now a robust and relatively mature tool, provides a sound basis for completing modelling of the relevant phenomenology.