In this paper,we propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional tran...In this paper,we propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional transverse integrated equations using the transverse integration procedure over 3D hexagonal geometry and denoted the solutions as a nodal Green's functions under the Neumann boundary condition.By applying a quadratic polynomial expansion of the transverse-averaged quantities,we derived the net neutron current coupling equation,equation for the expansion coefficients of the transverse-averaged neutron flux,and formulas for the coefficient matrix of these equations.We formulated the closed system of equations in correspondence with the boundary conditions.The proposed model was tested by comparing it with the benchmark for the VVER-440 reactor,and the numerical results were in good agreement with the reference solutions.展开更多
The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN app...The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN approaches generally utilize a fully connected network(FCN)architecture that is susceptible to overfitting,training instability,and gradient vanishing as the network depth increases.These challenges result in accuracy bottlenecks in the solution.In response to these issues,the residual-based resample physics-informed neural network(R2-PINN)is proposed.It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut(S-CNN).It incorporates skip connections to facilitate gradient propagation between network layers.Additionally,the incorporation of the residual adaptive resampling(RAR)mechanism dynamically increases the number of sampling points.This,in turn,enhances the spatial representation capabilities and overall predictive accuracy of the model.The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields.Compared with conventional FCN-based PINN methods,R 2-PINN effectively overcomes the limitations inherent in current methods.Thus,it provides more accurate and robust solutions for neutron diffusion equations.展开更多
Higher-order modes of the neutron diffusion/transport equation can be used to study the temporal behavior of nuclear reactors and can be applied in modal analysis, transient analysis, and online monitoring of the reac...Higher-order modes of the neutron diffusion/transport equation can be used to study the temporal behavior of nuclear reactors and can be applied in modal analysis, transient analysis, and online monitoring of the reactor core. Both the deterministic method and the Monte Carlo(MC) method can be used to solve the higher-order modes. However, MC method, compared to the deterministic method, faces challenges in terms of computational efficiency and α mode calculation stability, whereas the deterministic method encounters issues arising from homogenization-related geometric and energy spectra adaptation.Based on the higher-order mode diffusion calculation code HARMONY, we developed a new higher-order mode calculation code, HARMONY2.0, which retains the functionality of computing λ and α higher-order modes from HARMONY1.0, but enhances the ability to treat complex geometries and arbitrary energy spectra using the MC-deterministic hybrid two-step strategy. In HARMONY2.0, the mesh homogenized multigroup constants were obtained using OpenMC in the first step,and higher-order modes were then calculated with the mesh homogenized core diffusion model using the implicitly restarted Arnoldi method(IRAM), which was also adopted in the HARMONY1.0 code. In addition, to improve the calculation efficiency, particularly in large higher-order modes, event-driven parallelization/domain decomposition methods are embedded in the HARMONY2.0 code to accelerate the inner iteration of λ∕α mode using OpenMP. Furthermore, the higher-order modes of complex geometric models, such as Hoogenboom and ATR reactors for λ mode and the MUSE-4 experiment facility for the prompt α mode, were computed using diffusion theory.展开更多
Amidst the growing global emphasis on nuclear safety,the integrity of nuclear reactor systems has garnered attention in the aftermath of consequential events.Moreover,the rapid development of artificial intelligence t...Amidst the growing global emphasis on nuclear safety,the integrity of nuclear reactor systems has garnered attention in the aftermath of consequential events.Moreover,the rapid development of artificial intelligence technology has provided immense opportunities to enhance the safety and economy of nuclear energy.However,data-driven deep learning techniques often lack interpretability,which hinders their applicability in the nuclear energy sector.To address this problem,this study proposes a hybrid data-driven and knowledge-driven artificial intelligence model based on physics-informed neural networks to accurately compute the neutron flux distribution inside a nuclear reactor core.Innovative techniques,such as regional decomposition,intelligent k_(eff)(effective multiplication factor)search,and k_(eff)inversion,have been introduced for the calculation.Furthermore,hyperparameters of the model are automatically optimized using a whale optimization algorithm.A series of computational examples are used to validate the proposed model,demonstrating its applicability,generality,and high accuracy in calculating the neutron flux within the nuclear reactor.The model offers a dependable strategy for computing the neutron flux distribution in nuclear reactors for advanced simulation techniques in the future,including reactor digital twinning.This approach is data-light,requires little to no training data,and still delivers remarkably precise output data.展开更多
In this electronic article we use the one-dimensional multigroup neutron diffusion equation to reconstruct the neutron flux in a slab reactor from the nuclear parameters of the reactor, boundary and symmetry condition...In this electronic article we use the one-dimensional multigroup neutron diffusion equation to reconstruct the neutron flux in a slab reactor from the nuclear parameters of the reactor, boundary and symmetry condition, initial flux and?keff. The diffusion equation was solved analytically for one single homogeneous fuel region and for two regions considering fuel and reflector. To validate the method proposed, the results obtained in this article were compared using reference methods found in the literature.展开更多
Machine learning-based modeling of reactor physics problems has attracted increasing interest in recent years.Despite some progress in one-dimensional problems,there is still a paucity of benchmark studies that are ea...Machine learning-based modeling of reactor physics problems has attracted increasing interest in recent years.Despite some progress in one-dimensional problems,there is still a paucity of benchmark studies that are easy to solve using traditional numerical methods albeit still challenging using neural networks for a wide range of practical problems.We present two networks,namely the Generalized Inverse Power Method Neural Network(GIPMNN)and Physics-Constrained GIPMNN(PC-GIPIMNN)to solve K-eigenvalue problems in neutron diffusion theory.GIPMNN follows the main idea of the inverse power method and determines the lowest eigenvalue using an iterative method.The PC-GIPMNN additionally enforces conservative interface conditions for the neutron flux.Meanwhile,Deep Ritz Method(DRM)directly solves the smallest eigenvalue by minimizing the eigenvalue in Rayleigh quotient form.A comprehensive study was conducted using GIPMNN,PC-GIPMNN,and DRM to solve problems of complex spatial geometry with variant material domains from the fleld of nuclear reactor physics.The methods were compared with the standard flnite element method.The applicability and accuracy of the methods are reported and indicate that PC-GIPMNN outperforms GIPMNN and DRM.展开更多
In this study, based differential equations methods are used to solve equations because these methods are dependent on boundary value data more than other mathematical equations. We have calculated neutron flux, criti...In this study, based differential equations methods are used to solve equations because these methods are dependent on boundary value data more than other mathematical equations. We have calculated neutron flux, criticality and geometrical eigenvalue by using multi-group method and solving the neutron diffusion equation for finite and infinite cylindrical and spherical reactors in this study. For the calculation of the total neutron flux cross sections, we need the neutron diffusion equation. Thus, we have established the relationship between neuron flow and cross-section of neuron depending on neutron energy. Critical calculations have been made by comparing the results with MNCP (montecarlo n-partical) simulation methods. For necessary computer calculations, the programme, Wolfram-Matematica-7 has been used.展开更多
文摘In this paper,we propose a numerical calculation model of the multigroup neutron diffusion equation in 3D hexagonal geometry using the nodal Green's function method and verified it.We obtained one-dimensional transverse integrated equations using the transverse integration procedure over 3D hexagonal geometry and denoted the solutions as a nodal Green's functions under the Neumann boundary condition.By applying a quadratic polynomial expansion of the transverse-averaged quantities,we derived the net neutron current coupling equation,equation for the expansion coefficients of the transverse-averaged neutron flux,and formulas for the coefficient matrix of these equations.We formulated the closed system of equations in correspondence with the boundary conditions.The proposed model was tested by comparing it with the benchmark for the VVER-440 reactor,and the numerical results were in good agreement with the reference solutions.
基金supported by the Science and Technology on Reactor System Design Technology Laboratory(No.LRSDT12023108)supported in part by the Chongqing Postdoctoral Science Foundation(No.cstc2021jcyj-bsh0252)+2 种基金the National Natural Science Foundation of China(No.12005030)Sichuan Province to unveil the list of marshal industry common technology research projects(No.23jBGOV0001)Special Program for Stabilizing Support to Basic Research of National Basic Research Institutes(No.WDZC-2023-05-03-05).
文摘The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN approaches generally utilize a fully connected network(FCN)architecture that is susceptible to overfitting,training instability,and gradient vanishing as the network depth increases.These challenges result in accuracy bottlenecks in the solution.In response to these issues,the residual-based resample physics-informed neural network(R2-PINN)is proposed.It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut(S-CNN).It incorporates skip connections to facilitate gradient propagation between network layers.Additionally,the incorporation of the residual adaptive resampling(RAR)mechanism dynamically increases the number of sampling points.This,in turn,enhances the spatial representation capabilities and overall predictive accuracy of the model.The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields.Compared with conventional FCN-based PINN methods,R 2-PINN effectively overcomes the limitations inherent in current methods.Thus,it provides more accurate and robust solutions for neutron diffusion equations.
基金supported by the National Natural Science Foundation of China(No.U2267207)Science and Technology on Reactor System Design Technology Laboratory(No.KFKT-05-FWHTWU-2023004).
文摘Higher-order modes of the neutron diffusion/transport equation can be used to study the temporal behavior of nuclear reactors and can be applied in modal analysis, transient analysis, and online monitoring of the reactor core. Both the deterministic method and the Monte Carlo(MC) method can be used to solve the higher-order modes. However, MC method, compared to the deterministic method, faces challenges in terms of computational efficiency and α mode calculation stability, whereas the deterministic method encounters issues arising from homogenization-related geometric and energy spectra adaptation.Based on the higher-order mode diffusion calculation code HARMONY, we developed a new higher-order mode calculation code, HARMONY2.0, which retains the functionality of computing λ and α higher-order modes from HARMONY1.0, but enhances the ability to treat complex geometries and arbitrary energy spectra using the MC-deterministic hybrid two-step strategy. In HARMONY2.0, the mesh homogenized multigroup constants were obtained using OpenMC in the first step,and higher-order modes were then calculated with the mesh homogenized core diffusion model using the implicitly restarted Arnoldi method(IRAM), which was also adopted in the HARMONY1.0 code. In addition, to improve the calculation efficiency, particularly in large higher-order modes, event-driven parallelization/domain decomposition methods are embedded in the HARMONY2.0 code to accelerate the inner iteration of λ∕α mode using OpenMP. Furthermore, the higher-order modes of complex geometric models, such as Hoogenboom and ATR reactors for λ mode and the MUSE-4 experiment facility for the prompt α mode, were computed using diffusion theory.
文摘Amidst the growing global emphasis on nuclear safety,the integrity of nuclear reactor systems has garnered attention in the aftermath of consequential events.Moreover,the rapid development of artificial intelligence technology has provided immense opportunities to enhance the safety and economy of nuclear energy.However,data-driven deep learning techniques often lack interpretability,which hinders their applicability in the nuclear energy sector.To address this problem,this study proposes a hybrid data-driven and knowledge-driven artificial intelligence model based on physics-informed neural networks to accurately compute the neutron flux distribution inside a nuclear reactor core.Innovative techniques,such as regional decomposition,intelligent k_(eff)(effective multiplication factor)search,and k_(eff)inversion,have been introduced for the calculation.Furthermore,hyperparameters of the model are automatically optimized using a whale optimization algorithm.A series of computational examples are used to validate the proposed model,demonstrating its applicability,generality,and high accuracy in calculating the neutron flux within the nuclear reactor.The model offers a dependable strategy for computing the neutron flux distribution in nuclear reactors for advanced simulation techniques in the future,including reactor digital twinning.This approach is data-light,requires little to no training data,and still delivers remarkably precise output data.
文摘In this electronic article we use the one-dimensional multigroup neutron diffusion equation to reconstruct the neutron flux in a slab reactor from the nuclear parameters of the reactor, boundary and symmetry condition, initial flux and?keff. The diffusion equation was solved analytically for one single homogeneous fuel region and for two regions considering fuel and reflector. To validate the method proposed, the results obtained in this article were compared using reference methods found in the literature.
基金partially supported by the National Natural Science Foundation of China(No.11971020)Natural Science Foundation of Shanghai(No.23ZR1429300)Innovation Funds of CNNC(Lingchuang Fund)。
文摘Machine learning-based modeling of reactor physics problems has attracted increasing interest in recent years.Despite some progress in one-dimensional problems,there is still a paucity of benchmark studies that are easy to solve using traditional numerical methods albeit still challenging using neural networks for a wide range of practical problems.We present two networks,namely the Generalized Inverse Power Method Neural Network(GIPMNN)and Physics-Constrained GIPMNN(PC-GIPIMNN)to solve K-eigenvalue problems in neutron diffusion theory.GIPMNN follows the main idea of the inverse power method and determines the lowest eigenvalue using an iterative method.The PC-GIPMNN additionally enforces conservative interface conditions for the neutron flux.Meanwhile,Deep Ritz Method(DRM)directly solves the smallest eigenvalue by minimizing the eigenvalue in Rayleigh quotient form.A comprehensive study was conducted using GIPMNN,PC-GIPMNN,and DRM to solve problems of complex spatial geometry with variant material domains from the fleld of nuclear reactor physics.The methods were compared with the standard flnite element method.The applicability and accuracy of the methods are reported and indicate that PC-GIPMNN outperforms GIPMNN and DRM.
文摘In this study, based differential equations methods are used to solve equations because these methods are dependent on boundary value data more than other mathematical equations. We have calculated neutron flux, criticality and geometrical eigenvalue by using multi-group method and solving the neutron diffusion equation for finite and infinite cylindrical and spherical reactors in this study. For the calculation of the total neutron flux cross sections, we need the neutron diffusion equation. Thus, we have established the relationship between neuron flow and cross-section of neuron depending on neutron energy. Critical calculations have been made by comparing the results with MNCP (montecarlo n-partical) simulation methods. For necessary computer calculations, the programme, Wolfram-Matematica-7 has been used.
