ntkFoam: An OpenFOAM based neutron transport kinetics solver for nuclear reactor simulation

Abstract Due to the complexity of detailed nuclear reactor numerical simulation, especially the complicated geometry and multi-physics coupling properties of the advanced reactor, a nuclear reactor kinetics solver for nuclear reactor engineering and design needs to be developed. Based on the open source C++ software OpenFOAM, this work establishes a neutron transport kinetics solver, namely ntkFoam, for the nuclear reactor kinetics simulation, from the governing equations to the detailed implementations. The coupling between multi-group neutron transport equations and the delayed neutron precursor balance equations are considered with using the finite volume method. By introducing the inverse power method to the OpenFOAM, the k-eigenvalue problems are calculated, and by coupling the neutron transport and delayed neutron precursor calculations using the Euler implicit scheme, the transient kinetics problems are simulated. Numerical results show that the proposed ntkFoam can simulate the multi-group neutron transport kinetics problem accurately and flexibility, and both the regular and irregular mesh configurations can be adopted. This work can provide some new perspectives and foundations to nuclear reactor coupling calculations.

[1]  Yang Yang,et al.  Overview of Computational Fluid Dynamics Simulation of Reactor-Scale Biomass Pyrolysis , 2017 .

[2]  Konstantin Mikityuk,et al.  GeN-Foam: a novel OpenFOAM® based multi-physics solver for 2D/3D transient analysis of nuclear reactors , 2015 .

[4]  SN transport method for neutronic noise calculation in nuclear reactor systems: Comparative study between transport theory and diffusion theory , 2018 .

[5]  Liangzhi Cao,et al.  Auto MOC—A 2D neutron transport code for arbitrary geometry based on the method of characteristics and customization of AutoCAD , 2008 .

[6]  J. Duderstadt,et al.  Nuclear reactor analysis , 1976 .

[7]  Gene H. Golub,et al.  Calculation of Gauss quadrature rules , 1967, Milestones in Matrix Computation.

[8]  Aleksandar Jemcov,et al.  OpenFOAM: A C++ Library for Complex Physics Simulations , 2007 .

[9]  Giorgio Locatelli,et al.  Generation IV nuclear reactors: Current status and future prospects , 2013 .

[10]  Song-Charng Kong,et al.  High-Resolution Particle-Scale Simulation of Biomass Pyrolysis , 2016 .

[11]  Anatoli Paul Ulmeanu,et al.  Reliability modelling of medium voltage distribution systems of nuclear power plants using generalized stochastic petri nets , 2006, Comput. Math. Appl..

[12]  E. Lewis,et al.  Computational Methods of Neutron Transport , 1993 .

[13]  Mohammad Asadzadeh,et al.  Chebyshev spectral-S_N method for the neutron transport equation. , 2006 .

[14]  S. Patankar,et al.  Finite volume method for radiation heat transfer , 1994 .

[15]  Hongchun Wu,et al.  A least-squares finite-element Sn method for solving first-order neutron transport equation , 2007 .

[16]  G. Verdú,et al.  Multigroup neutron diffusion equation with the finite volume method in reactors using MOX fuels , 2017 .

[17]  Richard C. Martineau,et al.  Hybrid PN-SN with Lagrange multiplier and upwinding for the multiscale transport capability in Rattlesnake , 2017 .

[18]  B. Ganapol.  A more efficient implementation of the discrete-ordinates method for an approximate model of particle transport in a duct , 2015 .

[19]  C. Demazière,et al.  Fine-mesh deterministic modeling of PWR fuel assemblies: Proof-of-principle of coupled neutronic/thermal–hydraulic calculations , 2014 .

[20]  Rizwan Uddin,et al.  A lattice Boltzmann framework to simulate boiling water reactor core hydrodynamics , 2009, Comput. Math. Appl..

[21]  Nishimura Tatsuo,et al.  Development of Discrete Ordinates SN Code in Three-Dimensional (X, Y, Z) Geometry for Shielding Design , 1980 .

[22]  C. Daw,et al.  Modeling the impact of bubbling bed hydrodynamics on tar yield and its fluctuations during biomass fast pyrolysis , 2016 .

[23]  Chi-Wang Shu,et al.  High order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD , 2001 .

[24]  C. Alejaldre,et al.  Identification of safety gaps for fusion demonstration reactors , 2016, Nature Energy.

[25]  Dalin Zhang,et al.  Steady and transient solutions of neutronics problems based on finite volume method (FVM) with a CFD code , 2015 .

[26]  Wei Li,et al.  Finite volume lattice Boltzmann scheme for neutron/radiative transfer on unstructured mesh , 2017 .

[27]  Chi-Wang Shu.  High-order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD , 2003 .

[28]  John C. Lee,et al.  A time-dependent neutron transport method of characteristics formulation with time derivative propagation , 2016, J. Comput. Phys..

[29]  Tanay Mazumdar,et al.  Solution of the neutron transport equation by the Method of Characteristics using a linear representation of the source within a mesh , 2017 .

[30]  Song-Charng Kong,et al.  Characterizing Effects of the Shape of Screw Conveyors in Gas–Solid Fluidized Beds Using Advanced Numerical Models , 2015 .

[31]  Development of a finite volume inter-cell polynomial expansion method for the neutron diffusion equation , 2016 .

[33]  Toshikazu Takeda,et al.  3-D Neutron Transport Benchmarks , 1991 .

[34]  A. Ullah,et al.  Multi-scale CFD modeling of gas-solid bubbling fluidization accounting for sub-grid information , 2018 .

[35]  Yahui Wang,et al.  Lattice Boltzmann solution of the transient Boltzmann transport equation in radiative and neutron transport. , 2017, Physical review. E.

[36]  Yahui Wang,et al.  GPU accelerated lattice Boltzmann method in neutron kinetics problems , 2019, Annals of Nuclear Energy.

[37]  Yahui Wang,et al.  High-order lattice Boltzmann method for multi-group neutron diffusion solution , 2019, Progress in Nuclear Energy.

[38]  Mohammad Asadzadeh,et al.  Chebyshev spectral-SN method for the neutron transport equation , 2006, Comput. Math. Appl..

[39]  Oleg P. Iliev,et al.  A fast algorithm for 3D simulation of thermal stratification in containment pools of nuclear power plants , 2014, Comput. Math. Appl..

[40]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[41]  Ruipeng Chen,et al.  The steady states of a non-cooperative model arising in reactor dynamics , 2016, Comput. Math. Appl..

[42]  B. Rokrok,et al.  Mesh-free RBF collocation method to solve the multi-group SN neutron transport equation in arbitrary domains , 2018, Annals of Nuclear Energy.

[43]  Carlo Fiorina,et al.  Extension of the GeN-Foam neutronic solver to SP3 analysis and application to the CROCUS experimental reactor , 2017 .