Development of Galerkin Finite Element Method Three-dimensional Computational Code for the Multigroup Neutron Diffusion Equation with Unstructured Tetrahedron Elements

Seyed Abolfazl Hosseini 한국원자력학회 2016 Nuclear Engineering and Technology Vol.48 No.1

In the present paper, development of the three-dimensional (3D) computational code basedon Galerkin finite element method (GFEM) for solving the multigroup forward/adjointdiffusion equation in both rectangular and hexagonal geometries is reported. Linearapproximation of shape functions in the GFEM with unstructured tetrahedron elements isused in the calculation. Both criticality and fixed source calculations may be performedusing the developed GFEM-3D computational code. An acceptable level of accuracy at a lowcomputational cost is the main advantage of applying the unstructured tetrahedron elements. The unstructured tetrahedron elements generated with Gambit software are usedin the GFEM-3D computational code through a developed interface. The forward/adjointmultiplication factor, forward/adjoint flux distribution, and power distribution in thereactor core are calculated using the power iteration method. Criticality calculations arebenchmarked against the valid solution of the neutron diffusion equation for InternationalAtomic Energy Agency (IAEA)-3D and Water-Water Energetic Reactor (VVER)-1000 reactorcores. In addition, validation of the calculations against the P1 approximation of thetransport theory is investigated in relation to the liquid metal fast breeder reactorbenchmark problem. The neutron fixed source calculations are benchmarked through acomparison with the results obtained from similar computational codes. Finally, ananalysis of the sensitivity of calculations to the number of elements is performed.

Sensitivity Analysis of the Galerkin Finite Element Method Neutron Diffusion Solver to the Shape of the Elements

Seyed Abolfazl Hosseini 한국원자력학회 2017 Nuclear Engineering and Technology Vol.49 No.1

The purpose of the present study is the presentation of the appropriate element and shapefunction in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using theGalerkin finite element method in both rectangular and hexagonal reactor cores. Thespatial discretization of the equation is performed using unstructured triangular andquadrilateral finite elements. Calculations are performed using both linear and quadraticapproximations of shape function in the Galerkin finite element method, based on whichresults are compared. Using the power iteration method, the neutron flux distributionswith the corresponding eigenvalue are obtained. The results are then validated against thevalid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependencyof the results to the type and number of the elements, and shape function order,a sensitivity analysis of the calculations to the mentioned parameters is performed. It isshown that the triangular elements and second order of the shape function in eachelement give the best results in comparison to the other states.

High accurate three-dimensional neutron noise simulator based on GFEM with unstructured hexahedral elements

Seyed Abolfazl Hosseini 한국원자력학회 2019 Nuclear Engineering and Technology Vol.51 No.6

The purpose of the present study is to develop the 3D static and noise simulator based on Galerkin FiniteElement Method (GFEM) using the unstructured hexahedral elements. The 3D, 2G neutron diffusion andnoise equations are discretized using the unstructured hexahedral by considering the linear approximationof the shape function in each element. The validation of the static calculation is performed viacomparison between calculated results and reported data for the VVER-1000 benchmark problem. Asensitivity analysis of the calculation to the element type (unstructured hexahedral or tetrahedron elements)is done. Finally, the neutron noise calculation is performed for the neutron noise source of typeof variable strength using the Green function technique. It is shown that the error reduction in the static calculation is considerable when the unstructuredtetrahedron elements are replaced with the hexahedral ones. Since the neutron flux distribution andneutron multiplication factor are appeared in the neutron noise equation, the more accurate calculationof these parameters leads to obtaining the neutron noise distribution with high accuracy. The investigationof the changes of the neutron noise distribution in axial direction of the reactor core shows thatthe 3D neutron noise analysis is required instead of 2D.

Development of Galerkin Finite Element Method Three-dimensional Computational Code for the Multigroup Neutron Diffusion Equation with Unstructured Tetrahedron Elements

Hosseini, Seyed Abolfazl Korean Nuclear Society 2016 Nuclear Engineering and Technology Vol.48 No.1

In the present paper, development of the three-dimensional (3D) computational code based on Galerkin finite element method (GFEM) for solving the multigroup forward/adjoint diffusion equation in both rectangular and hexagonal geometries is reported. Linear approximation of shape functions in the GFEM with unstructured tetrahedron elements is used in the calculation. Both criticality and fixed source calculations may be performed using the developed GFEM-3D computational code. An acceptable level of accuracy at a low computational cost is the main advantage of applying the unstructured tetrahedron elements. The unstructured tetrahedron elements generated with Gambit software are used in the GFEM-3D computational code through a developed interface. The forward/adjoint multiplication factor, forward/adjoint flux distribution, and power distribution in the reactor core are calculated using the power iteration method. Criticality calculations are benchmarked against the valid solution of the neutron diffusion equation for International Atomic Energy Agency (IAEA)-3D and Water-Water Energetic Reactor (VVER)-1000 reactor cores. In addition, validation of the calculations against the $P_1$ approximation of the transport theory is investigated in relation to the liquid metal fast breeder reactor benchmark problem. The neutron fixed source calculations are benchmarked through a comparison with the results obtained from similar computational codes. Finally, an analysis of the sensitivity of calculations to the number of elements is performed.

Adaptive group of ink drop spread: a computer code to unfold neutron noise sources in reactor cores

Seyed Abolfazl Hosseini,Iman Esmaili Paeen Afrakoti 한국원자력학회 2017 Nuclear Engineering and Technology Vol.49 No.7

The present paper reports the development of a computational code based on the Adaptive Group of InkDrop Spread (AGIDS) for reconstruction of the neutron noise sources in reactor cores. AGIDS algorithmwas developed as a fuzzy inference system based on the active learning method. The main idea of theactive learning method is to break a multiple inputesingle output system into a single inputesingleoutput system. This leads to the ability to simulate a large system with high accuracy. In the presentstudy, vibrating absorber-type neutron noise source in an International Atomic Energy Agency-twodimensional reactor core is considered in neutron noise calculation. The neutron noise distribution inthe detectors was calculated using the Galerkin finite element method. Linear approximation of theshape function in each triangle element was used in the Galerkin finite element method. Both the realand imaginary parts of the calculated neutron distribution of the detectors were considered input data inthe developed computational code based on AGIDS. The output of the computational code is thestrength, frequency, and position (X and Y coordinates) of the neutron noise sources. The calculatedfraction of variance unexplained error for output parameters including strength, frequency, and X and Ycoordinates of the considered neutron noise sources were 0.002682 #/cm3s, 0.002682 Hz, and0.004254 cm and 0.006140 cm, respectively.