Study on high-speed calculation of debris bed coolability for sodium-cooled fast reactors

Abstract

Many sensitivity calculations are necessary to evaluate the effect of the uncertainties of Core Disruptive Accident (CDA) scenarios on debris bed coolability for Sodium-cooled Fast Reactors (SFR). This paper describes a calculation model and a technique for high-speed calculations of debris bed coolability. Firstly, the detailed coolability calculation model taking into account phase change and vapor-liquid advection for a boiling zone in the debris bed is derived as a single equation. The vapor-liquid advection is based on the momentum equation including inertial, viscous, capillary and gravitational effects. In addition, the streamlined calculation which ignores inertial and gravitational effects for the boiling zone is proposed. Secondly, both the detailed and streamlined calculation models are validated through the analysis of the Sandia ACRR-D10 in-pile experiments. Then, the effects of the ignoring on debris bed coolability are evaluated through sensitivity calculations. Thirdly, the speed-up technique for the streamlined calculation model is proposed which solves the boiling zone by the combination of transient and steady state calculations and allows using coarse mesh size and time step. Owing to the technique, the calculation time becomes about 1/50. The application of the speed-up technique to the streamlined calculation model is confirmed under typical SFR conditions. Finally, it is demonstrated that the streamlined calculation model and the speed-up technique enable us to perform many sensitivity calculations in a realistic time. The model and technique developed in this study is practical to evaluate the effect of the uncertainties of CDA scenarios on debris bed coolability for SFR.

Study on application of artificial neural network to debris bed coolability calculations for sodium-cooled fast reactors

“…The application of ANN requires many data for training ANN and for validating the trained ANN. We create the data through the debris bed coolability calculations with the model by Matsuo et al (2020). In the calculations, main dominant inputs are parametrized by using LHS (McKay et al, 1979), which makes the training data and the validation data less biased.…”

“…In the calculations, main dominant inputs are parametrized by using LHS (McKay et al, 1979), which makes the training data and the validation data less biased. The details of ANN, LHS and the debris bed coolability calculation model by Matsuo et al (2020) are described in Sections 2.2, 2.3 and 2.4, respectively. Note that, the ADAM (Kingma and Ba, 2015) is used as a method for training ANN.…”

“…They confirmed that inertial and gravitational effects are small in the debris bed mainly consists of several hundred micrometers of particles. Matsuo et al (2020) developed a streamlined transient calculation model for the boiling zone and developed a speed-up technique, which allow us to use coarse meshes and time steps for the boiling zone of the debris bed in SFR which mainly consists of several hundred micrometers of particles.…”

“…Owing to the model developments as described above, we can perform coolability calculations of the debris bed with boiling with high accuracy and a short calculation time. For example, the model by Matsuo et al (2020) enables us to perform hundreds to thousands of calculations in a week with one CPU. However, the calculation speed is still not enough to perform a huge number of calculations.…”

“…Thus, the application of ANN to debris bed coolability calculations eliminates solving non-steady equations and is expected to exponentially improve the calculation speed of the debris bed coolability. Although the application of ANN requires many data for training ANN and for validating the trained ANN, we can create many data for the training and validation through the calculations with Latin Hypercube Sampling (LHS) (McKay et al, 1979) and the model by Matsuo et al (2020).…”