Comparison of Hexcore and Poly-Hexcore computational meshes in the aspect of air flow modeling based on the actual geometry of mining excavations

Discrete models are used in industry for many applications. In one of the most frequently used Finite Element Method (FEM) for Computational Fluid Dynamics (CFD) calculations, discrete models may be two-dimensional or three-dimensional. 2D models are used as a simplification to achieve satisfied results in the shortest computational time. 3D models, on the other hand, are used for more complex calculations. These models constitute a representation of real-world objects that have been appropriately simplified to make the calculations accurate and correct. The calculation time of a 3D model is significantly longer compared to a 2D model. For this reason, to reduce the calculation time, different types of simplifications and various types of discrete model meshes are used. In this paper, the authors made a comparison of two computational meshing technologies: Hexcore and Poly-Hexcore in the aspect of airflow modeling in mining excavations using CFD. The geometry considered in this case came from real-world excavations captured by laser scanning in the Gertruda Slant, Zloty Stok. Point cloud data was processed through feature extraction, which was subsequently utilized to create structured models of mining excavations. The results of the simulations show that taking into account such a diverse and complicated geometry and its significant lengths, reaching tens of kilometers, better results are obtained with the use of Poly-Hexcore mesh. This type of mesh allows simulations to be performed with similar accuracy in a shorter computation time. Utilizing a more modern type of mesh makes work more dynamic, which is of particular importance when conducting numerical simulations of air distribution in large and complex computational domains.


Introduction
Depending on the geometric model considered, when conducting simulation and analysis of flow with the use of Computational Fluid Dynamics (CFD), a choice is made between a 2D and a 3D model.Taking into account the efficiency, the 3D model seems to be a better choice.Considering the practicality of the application, measured by the time necessary to perform the calculations, the 2D model has the advantage.However, this model should be used only when it can represent the entire flow and the resulting simplifications will not significantly affect the calculation results [1].1295 (2024) 012007 IOP Publishing doi:10.1088/1755-1315/1295/1/012007 2 Underground mining excavations, in particular those made with the use of the blasting technique, are usually very heterogeneous geometrically, both in terms of varying cross sections and variability in the vertical and horizontal plane along the length of the excavation.For this reason, the representation of mining excavations using a 2D model will not cover the entire flow, and the simplifications used will have a significant impact on the accuracy of the results obtained.In this scenario, it is possible to use only 3D models and it is not possible to reduce the size of the geometry model as applied in [2], because real mining excavations rarely have a plane of symmetry.
Due to the high heterogeneity of the mining excavations, it is also challenging to develop a detailed geometric model for CFD simulations.Unlike unrestricted flows [3], geometry model in this case will define the computational domain.The model approach based on regular solids will again be a major simplification that will affect the results.Large, complex, and spatially spread underground structures, such as those created in the mining industry or tunneling, need a fast and reliable technique for mapping, geometry evaluation, or deformation tracking.Many examples demonstrating the application of LiDAR technology for those purposes can be found in the literature [4][5][6].When creating a geometric model of underground structures for CFD analysis of airflow concerning more details, measurement data from laser scanning on real objects under analysis can be used as well [7][8][9].
Considering the discretization of the 3D model, it should be expected that the computational mesh will consist of many elements.In the case of such complex and ununiform geometries as those resulting from the mapping of real mining excavations using laser scanning, the critical aspect is the quality of the generated computational mesh.It affects the precision of the results obtained at the expense of computing power and the time of solution [10].Underground mine ventilation networks can be tens or even hundreds of kilometers long.When conducting calculations and simulations with the use of CFD tools in such extensive computational domains, the mesh will consist of many elements, because of the extent of the computational domain, the number of which would be multiplied to maintain appropriate accuracy.
Taking into account the issues mentioned above, this paper attempts to determine the possibility of using various types of meshes for the discretization of complex geometrical models of mining excavations.These models were generated based on point clouds collected by laser scanning in a real mining environment.To solve the problem of heterogeneity and incompleteness of 3D data, features were generated according to which synthetic point clouds were created, taking into account general trends in the variability of the geometry of excavations.From the data prepared in this way, surface models of geometry defining the computational domain were created, which were discretized using the Hexcore and Poly-Hexcore techniques.The properties of both generated computational grids were compared in terms of reducing the number of grid elements and the time required for processing while maintaining satisfactory quality parameters.The created mesh models were validated by numerical simulations to check the impact of the meshing technique used on the differences in the results obtained and the time necessary to obtain a solution.
The research presented is of particular importance for CFD modeling of airflow in mining excavations.First, the analysis of airflow based on models created based on actual measurement data on excavation geometry will improve the accuracy of the results obtained.Therefore, the possibility of using spatial data from laser scanning should be sought by creating and developing appropriate methods of processing them into meshable geometries, ultimately in an automated manner.On the other hand, great emphasis should also be placed on searching for the possibility of limiting the number of discrete elements in the domain.This will lead to a reduction in the time required to obtain a solution, which is particularly important considering the extent and complexity of underground ventilation networks.

3D data acquisition
Data obtained by the same measurement technique was used for the purposes of this work.The point cloud representing the geometry of the excavation was obtained using a Velodyne VLP-16 LiDAR sensor [11] attached to a UGV (Fig. 1).However, data collected with a Terrestrial Laser Scanner (TLS) can also be used, as its structure would be the same.From the data recorded during the slow pass of the robot through Gertruda Slant in the former gold and arsenic mine in Złoty Stok, Poland [12], following the metodology described in [13], a 3D model consisting of a point cloud has been prepared (Fig. 2a) from which 25 meters have been selected for further processing (Fig. 2b).

Point cloud processing and geometry creation
As can be seen in Fig. 2b acquired point cloud is noisy, nonuniform in terms of density, and contains holes.For the reasons mentioned above, there are some problems that effectively hinder the performance of good-quality surface mesh models necessary to build computational mesh models using the FEM method for CFD simulations.Therefore, the authors use a synthetically created point cloud to address issues such as noise, non-uniformity, and holes.However, to maintain the overarching goal of using laser scanning data for CFD modeling, which is to conduct simulations based on the real geometry of excavations, synthetic point clouds are given certain features taken from measurement point clouds (Fig. 3).
In the first place, the point cloud was longitudinally sampled according to the methodology of [14].The model built from a profiles was then divided relative to four planes representing each excavation wall (Fig. 3a), on which curves describing the behavior of their geometry were drawn (Fig. 3b).The base structure of the synthetic point cloud is a uniformly sampled tunnel of a given dimension (length), resolution, and cross-sectional shape (i.e., rectangular or, as in this example, trapezoidal, following the blasting metrics in Polish copper ore mines) as presented in Fig. 4a.The features are then extracted from the original scan and applied to the model.The features include the general trajectory of the tunnel (Fig. 4b), the shapes of the walls (Fig. 4c), and additional noise useful for obtaining surfaces of the desired roughness (Fig. 4d).All parameters (such as resolutions, dimensions, strengths of features, etc.) are adjustable, which allows to introduce different variants and modifications comparable later at the stage of flow simulation.The final stage involved creating a surface mesh model using the Ball-Pivoting Algorithm (BPA) [15].

Computational meshes development
Based on a surface mesh with the same parameters, the test mesh models were developed in Ansys Fluent 2021r1 software with two techniques.The first of them, known since 2005, is a technique using Cartesian cells to fill most of the geometry with eight node cuboids and a layer of prism elements near the walls [16].On the other hand, in the transition layer between cuboidal and prism elements, the geometry is filled with tetrahedral elements.Nevertheless , Hexcore meshes contain a large number of tetrahedral elements of relatively poor quality, especially in the transition area between prism elements and cuboidal elements.This results in longer solution times and higher memory usage.
In turn, the second technique used can connect any type of mesh element to any other type of element automatically and conformally.The Poly-Hexcore mesh, applying Mosaic technology, connects octree hexahedrons of high quality from the bulk region to isotropic polyprisms in the boundary layer through Mosaic polyhedral elements.Due to this, the total element number may be reduced by 20-50% compared to the Hexcore mesh.Thus, the solver may speed up 10-50% depending on the application [17].A comparison of the meshes generated with both techniques is shown in Fig. 5.   Table 1 presents the basic parameters of the Hexcore and Poly-Hexore meshes.The Hexcore mesh is built from twice the number of elements compared to the Poly-Hexcore mesh.Furthermore, the preparation time for the Poly-Hexcore mesh is shorter by 40% compared to that for the Hexcore mesh.

Numerical simulation results comparison
Reducing the number of elements in the computational domain in the first place means shortening the time necessary to obtain a solution, however, it may potentially affect the accuracy of the results.To verify the impact of the use of a Poly-Hexcore mesh with twice as many elements as compared to the Hexcore mesh on the accuracy of the obtained results, simulations of air flow in the considered domain were carried out using both discrete models.A k-omega SST turbulence model was applied for simulation, due to the specific type of airflow in the mine.This model was verified for similar airflow modeling in mining excavations and provided accurate results [18,19].The velocity inlet was set to 3 m/s and the pressure outlet was applied to prevent reverse flow into the computational domain.Very similar results were obtained by the utilization of Hexcore and Poly-Hexcore meshes.The difference in the average air velocity values in the domain is very small and can be treated as a measurement error.Similar results of the velocity field were also obtained in cross sections at each of the stages considered in the length of the excavation.However, in the case of Poly-Hexcore mesh the computational time decreased significantly.The results are presented in Fig. 6 and Table 2.

Summary and conclusions
In this article, the authors have attempted to assess the possibility of using two computational mesh generation technologies -Hexcore and Poly-Hexcore -in the problems of air flow modeling in complex computational domains defined by the geometry of mining excavations obtained by laser scanning in underground mines.As can be seen from the results presented, both technologies allow for mesh generation with appropriate quality parameters and to simulate air distribution with satisfactory accuracy.The comparison of the results shows that the obtained values of the average air velocity in the entire domain and the average velocities and their distribution in individual cross sections along the length of the excavation are very similar.Differences in the order of hundreds of meters per second can be treated as measurement errors.On this basis, it can be concluded that the application of both meshing technologies to the problem under consideration is justified.A significant difference between meshes made with both technologies is the number of elements for which the computational domain has been discretized and the time in which it can be achieved.It was possible to make a comparison using the same hardware resources in the context of computing power and generating volumetric meshes based on the same surface mesh model.It shows that by applying Poly-Hexcore technology, it is possible to obtain similar quality parameters, reducing the number of elements by 50% compared to the Hexcore technology.Moreover, the time required to generate a mesh for a given geometry was reduced by 40%.Therefore, it can be concluded that better performance can be achieved for the problem considered using Poly-Hexcore technology.This is particularly important considering the extent of underground ventilation networks, where the reduction of the number of discrete elements in the domain and, above all, the solution time will determine the validity of simulations and analyses using CFD tools.
In the next stages of the work on modeling air flow in mining excavations based on the geometry obtained from laser scanning using CFD tools, the authors will focus on the analysis of more complex cases.Ultimately, larger domains will be considered, i.e. air flows in excavations of greater length will be modeled.By introducing sequential modeling, where the result at the outlet of the previous domain will be treated as an input to power the inlet of the next domain, it will be possible to obtain information on the airflow over a length of several kilometers, which is quite common in mine ventilation networks.Assuming constant parameters from the presented work, such as the resolution of the base point cloud, the number of surface mesh elements, and using the same meshing technology and the same hardware, the optimal length of a single section will be determined, in which calculations will be performed at one time.Moreover, more complex cases will also be considered in terms of a network of intersecting workings.The multitude of this type of intersections of workings is also very common, especially on mining fronts, where the rock mass is mined using a room-and-pillar system.In addition, discrete models with other parameters may be included in subsequent studies.The use of supercomputers would significantly reduce computation time, which is one of the most interesting issues that would allow further optimization.

Figure 2 :
Figure 2: Base 3D point cloud (a) Profile-based model coloured by the walls (b) Excavation's ceiling with curves

Figure 3 :
Figure 3: Features extraction (a) The base structure of the synthetic point cloud (b) Synthetic point cloud with general trajectory (c) Synthetic point cloud with the trajectory of the tunnel and shapes of the walls (d) Synthetic point cloud with the trajectory of the tunnel, shapes and roughness of the walls

Figure 4 :
Figure 4: Synthetic point cloud development

Figure 5 :
Figure 5: Mesh models comparison (a) Hexcore mesh -velocity field at 15 m (b) Poly-Hexcore mesh -velocity field at 15 m (c) Hexcore mesh -velocity field at 20 m (d) Poly-Hexcore mesh -velocity field at 20 m (e) Hexcore mesh -velocity field at the outlet (f) Poly-Hexcore mesh -velocity field at the outlet

Table 1 :
Meshes parameters comparison

Table 2 :
Simulation results for Hexcore and Poly-Hexcore mesh type.