26 Sep 2022

Application of simulation to debris-bed formation in an actual plant

Background of THERMOS development

In a severe accident, molten fuel is released from the reactor vessel into the reactor cavity, forming a debris bed. Understanding the debris-bed formation and cooling process ex-vessel is essential for accident analysis and MCCI (Molten Core Concrete Interaction) countermeasures. Although melt in the reactor cavity spreads with multidimensional solidification, MELCOR only handles debris in one dimension and cannot analyze debris behavior in-depth. Therefore, understanding the mechanisms and quantifying uncertainty factors is difficult. To address this issue, we are developing THERMOS, a multidimensional analysis code that performs an in-depth numerical evaluation of debris-bed formation and cooling caused by the release of molten material from the reactor vessel. The results of applying the code to the simulation of debris-bed formation in an actual plant are introduced in this paper.

Current status of development of ex-vessel debris behavior analysis method

We are developing and verifying a coupled code system of JBREAK and MSPREAD, two of THERMOS’s main modules. JBREAK uses a 3D interface tracking method to simulate the molten-jet breakup and formation as well as the agglomeration of entrained droplets. Based on the shallow water equation, MSPREAD[1,2] simulates the melt spread, crust growth, and cooling of partially solidified molten debris. 
To exchange the time-dependent storage property from JBREAK to MSPREAD, we developed an algorithm that converts 3D momentum flux into 2D momentum flux in the horizontal plane. To synchronize the differences in time steps, the Gap-Tooth method was used. The molten debris is ejected from the reactor vessel as a mixture of metals with low solidus temperatures and oxides with high solidus temperatures, and its viscosity depends exponentially on the solid fraction. To predict melt spreading in the cavity, it is necessary to consider a wide range of debris compositions, morphologies (melts, solids, particles, and agglomerates), temperatures, and solid fractions based on the accident progression analysis. Although it is necessary to provide THERMOS with in-vessel debris information as the initial or boundary conditions, this is outside the scope of THERMOS analysis. Based on the accident progression analysis results in MELCOR, we developed an interface method to provide THERMOS with the temperature, flow rate, composition, and physical properties of the melt released from the reactor vessel. In particular, depending on the scenario, this method provides THERMOS with debris release histories, such as the location of the reactor vessel failure, melt flow rate, and melt temperature. THERMAT, which is the unique material property library developed for THERMOS, provides thermophysical properties such as density, specific heat, thermal conductivity, viscosity coefficient, solidus, and liquidus used in both codes. The solidification ratio affects these properties, and it can be given by the lever rule or the nonlinear model obtained by the thermodynamic equilibrium theory. Viscosity is expressed by the Ramacciotti model, which takes into account the effect of the solid fraction due to partially solidified molten debris. This code structure enables the investigation of the expected phenomena under realistic accident scenarios.

Computational Space © NRA
Fig. 1 Computational Space © NRA

An example of analysis capabilities

The computational space, as shown in Fig. 1, includes a weir and two sumps, simulating a typical BWR. According to the melt release history analyzed by MELCOR, the debris consisted of mass fraction (Zr:SS:SSOx=5E-21:0.987:0.013) and approximately 2,700 kg of melt was released during 400.0 seconds. The analysis of debris behavior after 15 sec and 100 sec is shown in Fig. 2, where MSPREAD calculates the temperature, thickness, viscosity distribution of the melt, and solid fraction, and the typical dynamics of molten debris from impacting the floor to flowing out of the pedestal into the annulus. The debris thickness distribution has a high peak at the drop position and a lower distribution further away from the drop position, indicating that debris-bed formation varies depending on the drop position. The analytical results show that the solid fraction of debris is very low immediately after the molten jet is dropped, and as the debris spreads, the heat transfer area increases, the solid fraction cools, and the viscosity increases. It was demonstrated that melt spreading is strongly influenced by the solid fraction and that it is important to evaluate the composition, morphology (melt and particles), and solidus temperature of debris ejected from the reactor vessel. The developed analytical method can predict the complex distribution of debris, which contributes to accident analysis and the reduction of uncertainties related to the initial conditions and boundary conditions of MCCI analysis. The actual phenomenon is that debris falls into the reactor cavity multiple times. However, this analysis only covers the first debris fall. In the future, we intend to improve the analysis code to handle multiple drops of jets and to conduct an analysis considering an accident such as the one that occurred in TEPCO’s Fukushima Daiichi Nuclear Power Station.

Analysis result by JBREAK-MSPREAD © NRA
Fig. 2 Analysis result by JBREAK-MSPREAD © NRA

[1] Hotta, A., et al., “Development of a horizontal two-dimensional melt spread analysis code, THERMOS-MSPREAD Part-1: Spreading models, numerical solution methods and verifications”, Nuclear Engineering and Design, Vol. 386, 111523, 2022.
[2] Hotta, A., et al., “Development of a horizontal two-dimensional melt spread analysis code, THERMOS-MSPREAD Part-2: Special models and validations based on dry spreading experiments using molten oxide mixtures and prototype corium”, Nuclear Engineering and Design, Vol. 387, 111598, 2022.

Wataru Kikuchi
Nuclear Regulation Authority (NRA)