Figure 1: Structured multi-block meshing of a wire-wrapped nuclear fuel rod assembly.
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This article is a part of the series on Nuclear fuel rods CFD.
Part 1: Thermal Hydraulics of Wire Wrapped Nuclear Fuel Rods
Part 2: Role of Structured Meshes in Nuclear Fuel Rods CFD
Part 3: Automated Structured Meshing of Wire-Wrapped Fuel Rods
In this article, we cover aspects of meshing wire-wrapped nuclear fuel rod assembly using GridPro, more precisely on the automation of the meshing process which is scalable, versatility and robust with a high level of mesh quality control.
Introduction
The geometry of the fuel rod bundle with helically wrapped wires is complex. The helical nature of the wire along the rod length makes meshing challenging for both structured and unstructured meshing algorithms. Adding to the complexity are the presence of high acute angle wire-rod junction and the small gaps between the wire and neighbouring rod. The geometric complexities mentioned above are intimidating enough for a user to look for solutions other than structured mesh. But as we discussed in our previous article, Structured meshes seem to be the Holy grail for Thermal Hydraulics of the Nuclear Fuel Rods. Empathizing with the needs of the community, we at GridPro have developed an automation script that focuses on providing a solution that will provide the user the highest quality mesh with minimal input. Our goal was to build a solution that would be
- Automatic
- Flexible
- Scalable
- User Controllable
- Versatile
Though the above objectives are conflicting in nature, we wanted to provide a solution that would require minimal input and have the turnaround time as that of an unstructured mesher and provide all the benefits of a structured mesh-like high quality, Multi-Grid Scalability, and user control in terms of mesh size and refinement. Over the years, with GridPro our goal is to provide a platform for automating Structured Multi-Block Meshing. For self-replicable configurations like nuclear fuel rod assembly, it is possible to nearly reach these ideal requirements using the tools in GridPro. The following sections elaborate on this aspect in greater detail.
Automation
Normally, the block generation step in the multi-block approach is time and labor-intensive. However, nuclear fuel rod assemblies being self-replicable is favorable for automation. In GridPro, automation of fuel rod assembly was possible by adopting a template-based approach. Standard templates for a single rod are built for different rod wire configurations. Picking the right template and providing more details is the first input the user provides for the automation.
The automation script requires the following inputs,
- Rod diameter,
- Wire diameter,
- Pitch of the wire
- Distance between two rods, as shown in Figure 2.
- Number of rings, as shown in Figure 3.
When the script is executed, the blocking for the single rod configuration is replicated and translated and merged to complete the topology building for the entire bundle.
Scalability
The scalability with respect to nuclear fuel bundle can be reasoned as,
- Scalability based on the number of rods.
- Scalability based on different sizes of mesh.
Scalability in terms of the number of rods The scripting strategy ensures that the user is able to extract the full benefit of structured multi-block strategy, The regularity of the patterns makes the number of rings as a parameter that can be used to scaled the model from a mere single rod configuration to a 7-rod bundle when it is a single ring, 19 rods for 2 rings to the farthest extent of 8 rings for a 217-rod full-scale configuration.
Scalability based on different sizes of mesh One of the main tasks of a CFD analyst is to find the right mesh size for their configuration with all the local limitations in mind. GridPro’s multi-block approach is very conducive for scalability w.r.t grid refinement as well. The blocking or topology can create a series of sequential grids as required for a grid-convergence study by changing a single parameter or by providing a sequential ratio. The edge density of each block is modified based on the user input to get a family of grids. The algorithm reads the parameters and ensures that there is no deterioration in grid quality when subjected to grid refinement.
Local grid-refinement
As discussed in our previous article, because of the need to accurately model sensitivity to heat transfer, the meshes in the contact regions between wires and rods, may need more refinement. For configurations like wire-wrapped fuel rod assembly, where geometric scales differ by a large magnitude, the ability to do local mesh refinement could be a lifesaver since the cell count could be kept under desirable limits and make the simulation computationally feasible.
When the flow trips over the wire placed across its flow path vortices are generated. Fine mesh points are needed to discretize the region in the near vicinity of the wire, especially in the wake region where the vortices are present. Also, the location where the wire comes in contact with the rod is susceptible to shoot-up in temperature. Such hot spot regions need high-resolution meshes to accurately predict the local temperature. Figure 7 shows the local grid refinement at the wire-rod junction. Local refinement by Enriching in GridPro ensures that the refinement is contained locally and is not allowed to propagate to the larger domain.
Figure 8: Accurate geometric capturing of the thin wire with an optimal number of cells.
Figure 8, shows the local refinement by Enrichment along the entire length of the rod, in the near vicinity of the wire. The ratio of rod diameter to wire diameter is nearly 20:1. The mesh element size needed to discretize also varies by the same ratio. Enrichment in GridPro ensures appropriate resolution of the thin wire and smooth transition to the bigger cells used to discretize the rods without abnormal shoot-up in cell count.
Optimizing cell count
From a numerical point of view, hexahedral elements are the most efficient elements. They consume the least memory and computing time per element. The grid built using hex elements are well aligned to the flow and hence well adapted for long and thin shear layers on the wall and in the wake. Compared to the unstructured grids, to fill a volume of space with a fixed edge length, the hex meshing approach needs the least number of cells. One of the major advantages of hex meshing is its ability to generate high aspect ratio grids without any deterioration in cell quality. This ability, unlike in the unstructured approach helps in generating grids with directional refinement. In the case of fuel rod meshing, this is a powerful asset, as it helps to reduce the cell count in the rod axial direction and more optimally refine the grid in the other two directions.
A study by TerraPower shows that they were able to reduce the cell count by 27 million i.e a reduction of 32% in total cell count by employing stretched structured grids in the axial direction without compromise in solution accuracy. This simple ability helps in a drastic reduction of computational time also. Further, the additional cells in the non-axial direction help in accurate capturing of the flow physics in the sub-channel assemblies.
Quality
Generating meshes with high quality is always the goal of a CFD Analyst who is looking beyond pretty images. Hence, ensuring cell quality parameters like skew, aspect ratios, face warpage, negative volumes, right-handedness is very essential before performing large and complex CFD analyses like nuclear-fuel rod subassemblies. In GridPro, internally the algorithm ensures that essential quality criteria are met. For example, the algorithm strives to place cells adjacent to the wall as orthogonally as possible and also maintain the cell angles larger than 20 degrees and lesser than 160 degrees. Management of the cell aspect ratios is easy and efficient. By varying the edge density, the cell aspect ratio can be modified. Block smoothing algorithm ensures that there is a smooth variation of cells in the domain and the cell aspect-ratio are kept in the range of 10-50 – a range well acceptable to most CFD solvers to obtain good solution convergence.
The generated blocks are not rigid. Automatic block smoothing ensures the gradual transition of the cell size from the region of high density to coarser regions and avoids jumps in cell size. The algorithm tries to ensure that the growth rate in adjacent cell volume is always lesser than 2. Further, block smoothening ensures maintenance of grid quality even in narrow gaps and high acute regions. In GridPro, gaps as small as 4 microns have been meshed with cell quality well within acceptable limits. Solutions obtained on grids generated with these tools are also of superior quality. Blocks are placed aligned to the fluid flow. The presence of hexahedral cells aligned to the predominant flow direction ensures a drastic reduction in discretization errors. Further, the blocks generated in GridPro have a one-to-one connected interface. Since there are no non-matching grid interfaces, there is no degradation in the flow prediction.
Versatility
In GridPro it is easy to accommodate different variants of wire-rod junctions. Researchers regularly test with different variants of the wire-rod configuration, such as point contact between wire-rod, sharp angle wire-rod intersection, filleted wire-rod intersection, square cross-section wires, wires represented by thin sheets, etc. Out of these, the first three are challenging to mesh, while the other variants are easily manageable.
The point contact case is geometrically not meshable as the wire tangentially comes in contact with the rod. Instead, they are slightly approximated by providing as small a gap. Figures 13a and 14a show a grid with a gap of 4 microns. Even in this micro-gap, the cell quality is well maintained and the fineness is locally contained.
Figures 13b and 14b shows the second case of displaced wire, where the wire is offset by a larger margin resulting in the creation of an acute-angle intersection between wire and rod. The geometric acuteness is accurately captured with fine grid points. Sometimes, studies are done with the wire physically not touching the rod. Figure 14a shows a mesh for such a geometric variant with a small gap. Accurate capturing of these narrow gaps with high-resolution grids having high cell quality is key to obtaining accurate reliable solutions. Tools in GridPro help to meet the meshing requirement of all the possible variants regularly used in the nuclear fuel rod assembly simulations.
Conclusion
With this, we come to the end of this Part 3 in the series on Nuclear fuel rods. For adequate resolution of the geometry and flow field, meshes with a sufficiently large number of cells are essential. Since, the number of elements is proportional to storage requirements and computing time, for many large-scale 3D problems like nuclear fuel rod subassemblies, Engineers usually end up compromising between desired accuracy level and the number of cells. Using GridPro, the need to make such a compromise can be eliminated. Optimized grids can be automatically generated for wire-wrapped nuclear fuel-rod bundles in no time and with ease. Whether it is a 7-rod bundle or a 217-rod bundle the time and effort are just the same.
Case Studies
CFD computational studies using GridPro’s structured multi-block meshes for wire-wrapped nuclear fuel rod assembly have been made by TerraPower . Here is the link to the case study. Fuel_Rods_TerraPower_Casestudy
Nuclear Fuel Rods Series
- Part 1: Thermal Hydraulics of Wire Wrapped Nuclear Fuel Rods
- Part 2: Role of Structured Meshes in Nuclear Fuel Rods CFD
- Part 3: Meshing Wire-Wrapped Fuel Rod Bundle with GridPro
References
1. “Best Practice Guidelines for the use of CFD in Nuclear Reactor Safety Applications“, NEA/CSNI/R(2007)5, JT03227125, 15-May-2007.
2. “Best Practice Guidelines for the Use of CFD in Nuclear Reactor Safety Applications – Revision“, Nuclear Safety, NEA/CSNI/R(2014)11, February 2015.
3. “Computational Fluid Dynamics for Nuclear Reactor Safety-5“, Workshop Proceedings, 9-11, September 2014, Zurich, Switzerland.
4. . “CFD Investigation of Wire-Wrapped Fuel Rod Bundles and Flow Sensitivity to Bundle Size”, L.M. Brockmeyer et al, NURETH-16, Chicago, IL, August 30-September 4, 2015.
5. ” CFD calculations of wire wrapped fuel bundles : modelling and validation strategies“, Ulrich Bieder et al, NEA-CSNI-R–2011-14, INIS Volume 44, Issue 33, 2012.
