In view of the characteristics of the numerical simulation results of the nuclear reactor core, including the regular structures, multiple geometry duplications, large-scale grids, and the demand for refined expression of calculation results, a mesh generation method based on Delaunay triangulation was used to solve the restructuring and visualizing problem of core three-dimensional (3D) data fields. In this work, data processing and visualization of the three-dimensional refined calculation of the core were accomplished, using the triangular mesh model, hash matching algorithm, 3D visualization technology, etc. Descriptions are also given for key issues such as Delaunay triangular mesh construction, the geometric model of the reactor core, and 3D data field mapping in this work. The application results showed that the 3D physical field data, such as core power and temperature, can be accurately and efficiently displayed using the visualization technology and solution. In addition, the efficiency of design and analysis in nuclear engineering activities can also be improved significantly.

With the development of computer software and hardware technology, high-performance computing technology based on the use of a fine mesh has successfully been applied to solve challenging problems in the nuclear engineering field [

Traditionally, the analysis of core calculation data mainly includes two methods: direct text retrieval and data analysis assisted by schematic 2D images. The former method is not intuitive and inefficient in data retrieval. Although the latter method can directly observe the distribution characteristics of data in 2D space, it is still difficult to get the overall distribution of data in 3D space. The above two methods do not make full use of visualization technology to convert the resulting data generated during the scientific calculation process into image information for interactive processing and intuitive understanding. The key to the visualization of scientific computing in the field of nuclear engineering lies in the visualization of the 3D data field of the reactor core, which contains the spatial distribution of various types of physical field data in different dimensions. In the field of nuclear engineering, the generated numerical calculation data are huge with multidimensional, multivariable, and multimodel characteristics. Therefore, it is a resource- and calculation-intensive problem to fully display large-scale data [

Computer graphics processing equipment can only display limited types of primitives [

The Delaunay triangular mesh method [

Define initial mesh: As showing in part (a) of

Insert subsequent node: As showing in part (b) of

Adjust the triangular mesh: Adjust the triangular mesh according to the rule that the circumcircle of the triangle element does not contain the vertices of other triangles;

Insert the remaining nodes in a loop: Repeat steps (2) and (3) as showing in part (c) to part (i) of

Clean up outside elements: Clean the mesh elements outside the boundary of the point set to generate the final triangular mesh as showing in part (j) of

The detailed algorithm of the generation of Delaunay triangular mesh can be seen in

The advantages of this triangular method include more easily generated high-quality triangular mesh elements, strong adaptability, simple requirements for input nodes, and relatively easy programing implementation. The only input condition required is an orderly node set.

The basic process describing the application of the triangular grid modeling method to the reactor core is as follows: firstly, the triangular mesh method is used to establish a mesh model matching the geometry of the reactor core. Then, the numerical core calculation results are mapped with the geometric grid. Lastly, the 3D fine data field of the whole reactor core is visualized using professional post-processing software. In this way, nuclear engineers can understand the performance of the reactor core more accurately and intuitively.

In the process of constructing a 3D visualization mesh model of the reactor core, compared with other geometric modeling techniques, the triangular mesh modeling method has the following advantages:

Faster modeling speed: Only the data structure of the triangular mesh needs to be constructed, which contains the node and element information. There is no need to use open-source or commercial CAD libraries [

Intuitive display of results: The coloring range is relatively rich, and it can be colored on the basis of points, elements, surfaces, bodies, etc. The cross-scale rendering of the model can be refined [

Efficient data loading: The triangular mesh data structure is suitable for the storage of results and visual mapping; thus, there is no need to design an additional storage structure [

Furthermore, since there are a large number of fuel elements composed of cylindrical geometry in the core, a cylinder was used to test the effectiveness of the algorithm.

The reactor core is composed of hundreds of fuel assemblies, which are arranged in a certain layout [

Real geometric models: Based on the actual structure of the reactor core, geometric models contain accurate and complete geometric features, such as the STEP model constructed with CAD tools [

Computational grid models: For numerical calculation, computational grid models are simplified and redivided on the basis of the real geometric model [

Rendering mesh models of data field: Geometric mesh models can be used for the three-dimensional visualization analysis of spatial numerical calculation results. Generally, they fully consider the characteristics of computer graphics processing technology and use tetrahedron, hexahedron, and other discrete methods to approximate the geometric structure [

The core numerical calculation involves a large number of calculation codes, which use different data description formats. Therefore, in order to improve the efficiency of the rendering mesh model, in this work, an intermediate data format-based method was adopted to realize the decoupling of 3D visualization and calculation software.

Most 3D models are constructed using geometry engines to generate polygon meshes, which can automatically generate corresponding polygon meshes with the help of general CAD tools. The tools are characterized by strong algorithm versatility. It is difficult to associate the computational grid model, as well as optimize the rendering efficiency, for the specific structure of the core. Considering a reactor core with a regular geometric structure (commonly using basic solids such as cuboids and cylinders) and a large number of repeated structures, a triangular grid was adopted to approximate the reactor core geometry, as shown in

Parse calculation data: Combined with the characteristics of the core numerical calculation software, the corresponding data source analysis programs were developed. Data generated by the calculation software at different time steps, including the power, burnup, and neutron flux, were extracted, which were all further processed into a standard intermediate format.

Construct the computational grid: The input file of the calculation software was analyzed. The core computational grid model was constructed in an automatic or semi-automatic way.

Generate rendering mesh of fuel rods: According to the requirements of accuracy, considering the geometric parameters of the fuel rods, this work used a specific algorithm to generate the control nodes of fuel rods. Then, the control node of the fuel rods was taken as input to generate the triangular mesh on the section, before stretching it in the axial direction to generate the mesh model of fuel rods, using the Delaunay triangular mesh construction method described in Section 2.

Generate a 3D rendering mesh for reactor core: According to the layout parameters of the fuel assembly and fuel rods of the reactor core, a 3D mesh model of the entire reactor core was constructed by referencing the mesh model of fuel rods. According to the calculated data in the standard intermediate format, the core data field matching algorithm was used to realize correlation mapping between the full core three-dimensional geometric mesh model and data from the core power, burnup, flux, etc.

Map visualization attributes: The visual attribute mapping method was used to map spatial calculation data into visual attributes such as color and transparency [

In this work, the general finite element mesh model was used to describe the 3D rendering mesh model; accordingly, the complete mesh model was composed of multiple elements arranged on the basis of specific rules, while the elements were defined according to the referencing node element ID [

The geometric structure of the core was composed of a large number of repeated cylinders.

When constructing the cylindrical bottom point set, _{i} represents the

After the control node was obtained, the point-by-point insertion algorithm described in Section 2 was used to generate the Delaunay triangular mesh model of the fuel pin [

In order to accurately present the spatial distribution characteristics of the core calculation data, an interpolation algorithm was also used to complete the data mapping between the computational grid and the rendering mesh. As a result that there were tens of millions of cells in the core finite element model, the hash matching algorithm [

The “divide and leave remainder” method is a commonly used construction hash algorithm, as described in

There are three factors in the hash table method that affect the number of keyword comparisons: the hash function, the method of handling conflicts, and the filling factor of the hash table. The filling factor

The below steps take the first segment of a single fuel rod as an example to illustrate the method of establishing the mapping relationship between the geometric model and the calculated data in

Step 1: Use a triangular meshing algorithm to discretize segment 1 of the fuel rod into finite element meshes.

Step 2: Build a hash list on the basis of grid meshes and build a hash index with the grouping key.

Step 3: Use the hash function to calculate the hash address corresponding to the key code.

Step 4: Sequentially compare whether the internal element of the hash address in the grouping grid is the key code of the result data, and copy the resulting data to the mesh model to complete the mapping.

This work optimized the frequency of calling keywords when constructing the hash function. Keywords with high frequency were placed in positions with fewer comparisons in the list, whereas keywords with low frequency were placed in positions with a greater number of comparisons. In this way, the data search speed was further accelerated, thereby improving the function's ability to search massive grid data.

Considering the scale of the core three-dimensional data field and the technical difficulty of the visualization scheme, combined with the visual analysis requirements of nuclear engineers, this work adopted the method of secondary development based on EnSight software to realize the visualization of the core 3D calculation data.

The characteristics of the scheme are described below [

Applicable to very large mesh models: For the core 3D mesh visualization model constructed using the abovementioned triangular meshing method, EnSight can support the smooth display of mesh models that contain tens of millions of cells.

Standardization of core data formats: The core power, burnup, flux, and other results obtained via the above-introduced numerical calculation software can all be converted into standard data formats for EnSight.

The data flow principle of the data field 3D visualization software (referred to CorePost) is shown in

In practical applications, there are many output formats of core numerical calculation software; however, we only need to develop the corresponding data source extraction interface and convert it into an intermediate data format when using CorePost. The CorePost tool can automatically complete the other steps needed for core data field three-dimensional display, including standard data format reconstruction, sequential node-set construction, FEM triangulation mesh division, 3D model generation, unit result data matching, and simulation model visualization.

CorePost can reconstruct and create multiscale models of the entire core, fuel assemblies, fuel cells, etc. Various model operation functions are provided, such as the symmetrical expansion of the core and 3D sectioning. Multidimensional result-viewing functions are also provided, such as 1D curves, 2D sections, and 3D cloud map rendering, which allow comprehensively displaying the 3D refined display results of the core data field from both quantitative and qualitative perspectives.

^{7}.

The 3D mesh model building module was used to reconstruct and generate models of the core, fuel assemblies, fuel pins, etc. The visualization tool was then used to display the 2D curve and 3D temperature cloud map of the results with multiple scales. The results are shown in

Due to in-depth research, the wide application of high-fidelity models, and the development of high-precision algorithms in the field of nuclear engineering, massive calculation data are generated during numerical calculations of cores. As such, big data processing and visualization technologies can be effectively combined to process and analyze these data that change dynamically over time and have high-dimensional and heterogeneous data sources.

This work designed a visualization scheme for the calculation results of 3D reactor core models using the triangular mesh method. The processes mainly included data model design, data field mapping, and visualization tool development. The generation process of the triangular mesh was adaptively optimized according to the actual structural characteristics of the nuclear reactor. The achieved result performed well in terms of the loading time and processing efficiency for large-scale calculation models, thus significantly improving calculation efficiency for nuclear engineers.