A comparison of three algorithms applied in thermal-hydraulics and neutronics codes coupling for lbe-cooled fast reactor

Highlights

• The OSSI method, FPI method and ABN method have been implanted in the coupling process.

• The ABN method combines the advantages of JFNK method and OSSI method.

• The ABN method balances accuracy and computational cost in mild transients.

Abstract

In this research, the Operator-Splitting semi-implicit (OSSI) method, fixed-point implicit (FPI) method and Approximate Block Newton (ABN) method have been applied to the coupling of thermal-hydraulics code COBRA and neutronics code SKETCH-N. In the OSSI method, there’s only one data exchange within a time step. In the FPI coupling, an iteration convergence has been added to the OSSI coupling framework to ensure the coupling results converged. And in the ABN method, a variant of Jacobian-free Newton Krylov method has been applied, which removes the Jacobian matrix construction and storage. Three temporal schemes have been validated through a PWR control rod bank ejection benchmark to show their applicability. Moreover, a LBE-cooled fast reactor control rods withdrawal accident applying two time steps has been simulated. And the results indicate that the ABN method applied in the mild transient generally outperforms the other two methods in both the convergence speed and the computational cost.

Introduction

There is a strong coupling relationship between the physical fields inside the reactor core, such as neutron flux, fuel temperature, and coolant temperature fields and so on (Xu, 2004). For example, in the fission process, the heat has been released by the neutron and particles collision and transferred into the coolant, changing the temperature and density fields. In turn, the macroscopic cross sections depend strongly on the thermal-hydraulics variables. In order to deeply describe the relationship among these fields, the equations involved in this domain must be considered together. However, owing to the limited computational resources, the solution will be extremely challenging along with more physic fields. So, the early reactor analysis divides the phenomenon in the reactor into individual fields. And each code puts emphasis on one field and connects other fields with coupling parameters defined by the users. However, this can only predict the accident procedure qualitatively, not quantitatively. Hence, covering as many physical fields as possible in the solution will be of importance to reduce the reactor safety margin and improve economy.

Along with the upgrade of computational approach and technology, reactor codes can better predict multi-physics by coupling codes in different fields. This method cannot only effectively utilize the existing codes but also avoid the complex work for code development and validation. The traditional coupling method utilizes semi-implicit algorithm, which performs separate physics solvers sequentially. This method is also called Semi-Implicit Operator-Splitting (OSSI) method and widely used in the early couplings, such as DYNSUB code (Gomez-Torres et al., 2012), TRAC-PF/MOD3 (Bandini et al., 1998) and so on. Owing to the semi-implicit algorithm, the whole coupling variables are not updated simultaneously and transient problems are all solved in small time step to reduce errors. Then the implicit fixed-point implicit (FPI) method (Gomez-Torres et al., 2012) emerged to improve this problem. This method is based on the OSSI method framework, adding an iteration loop on the frame of the explicit process, which ensures that the coupling parameters are converged within every time step and hence allows a relatively larger times step size. Olsen (Olsen and Dufek, 2017: S1738573317304242.) has coupled the Monte Carlo solver and a xenon feedback solver and proved that the FPI method can result in large spatial oscillations of the neutron flux distribution. Similarly, the divergence has also happened in Andrew’s coupling research (Yeckel et al., 2009)and illustrates that the FPI method often fails to converge and has difficulty in choosing relaxation factors. At present, the Jacobian-free Newton Krylov method (JFNK) (Knoll and Keyes, 2004) is the most promising hotspots among continually studied fully implicit method. For example, in the development of Multiphysics Object Oriented Simulation Environment (MOOSE) (Moose, 2014), the JFNK method presents mathematical structure to solve nonlinear partial differential equations (PDEs) that often arise in simulation of nuclear processes. This method treats all the physic fields equations as a whole problem to solve, which needs to do massive modification to the original source codes. Furthermore, the Jacobian matrix in the JFNK method is challenging to build and store, especially for the large-scale nuclear reactor models. Hence, regarding the existing simulation codes, a variant of JFNK method- Approximate Block Newton (ABN) (Mylonakis et al., 2017) emerged and it allows limited modifications to the source codes. Besides, this algorithm removes the difficulties of the Jacobian matrix construction and storage, and makes the black-box solver coupling possible. Meanwhile, based on the previous research on the ABN method, this method shows higher convergence and stability.

The lead-cooled fast reactor has the characteristics of high power density, irradiation and operation temperature, which posts a significant challenge restricting the development of lead-based cooled fast reactors (Zhang et al., 2020). For example, the high coolant temperature and flow velocity cause severe corrosion to the structural materials. So the coupling simulation involving neutron-physic and thermal–hydraulic fields is urgently needed in the advanced reactors design and research. As the most promising GEN-IV reactor, a series of coupling studies surrounding the lead-based fast reactor have been launched. Based on ELSY (European Lead cooled System) reactor (Chandra and Roelofs, 2010), Aufiero (Aufiero et al.,) has performed the coupling among the neutronic, the thermal-elastic and the fluid-dynamic phenomena upon both in steady-state operation and during two transient scenarios. Chen hongli (Chen et al., 2016) has applied the CFD/neutron kinetics coupled code FLUENT/PK to design a conceptual lead cooled fast reactor SNCLFR-100 and analyzed major accident scenarios. Bonifetto (Bonifetto et al.,) has developed a 2D + 1D full-core coupling platform- FRENETIC and benchmarked against the pure thermal-hydraulics and neutronics results. In addition to the above research, there’re also many other applications of coupling methods but mostly in OSSI or FPI algorithms. So far, there’s no ABN method applied in the lead-based fast reactor design and analysis.

In this study, based on the sub-channel code COBRA-IV (Stewart et al., 1977) and neutron diffusion code SKETCH-N (Zimin et al., 2001.[in print], 2001.), three algorithms have been implanted into two solvers. Then the NEACRP PWR control rod ejection accident benchmark (Finnemann and Galati, 1992) has been adopted to validate three methods applicability. The relative power and fuel doppler temperature will be compared with the reference results. At last, three algorithms computational performance will be compared based on a lead–bismuth eutectic (LBE) cooled fast reactor rod withdrawal accident.