Figure 1: Nested structure around a Wind Turbine Blade
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Every geometry is unique, posing a new challenge for meshing and thereby pushing the limits of the grid-generator. At times the requirements are so unique that it lays the foundation for a new gridding technique. One such need is the gridding requirement for multi-scale problems, where the geometric scale varies by a large ratios ranging from many kilometers at one extreme to a few millimeters at the other. Such geometric domains demand special kind of grids, which can make a smoother transition from the smallest cells to the largest ones in the general field.
One classical example for multi-scale problems is the oil field simulation. Oil reservoirs stretch for miles, while the pipelines have pipes with diameters of the order of a few inches. To resolve the pipe geometry, low aspect ratio small size cells needs to be used, while the vast domain demands large sized coarse elements. Similar gridding needs arise in applications like analysis of wind turbine farm, injectors in combustion, heat transfer in and around thin pipes in biological flows, etc.
Figure 2: Perforated well in a full field reservoir.
For such cases, the conventional unstructured and cartesian grinding methodologies fits the bill easily as the underlying grinding philosophy easily caters to such needs of local refinement without overshooting the total grid count. However, these approaches have their own bag of concerns in the form of lack of flow alignment, presence of hanging nodes, etc.
A Daunting Task
For a traditional structured grid generator, multi-scale problems would be a daunting task. The underlying gridding approach causes the fineness of the refined grids near the smaller geometric features to propagate into the field, thereby unnecessarily increasing the cell count, without bringing any practical computational benefit. In fact, it increases the computational time and also unnecessarily demands larger computational resources.
Figure 3: Area Nesting to capture the Wake region behind a Venus entry capsule.
Propagation of the fineness, results in presence of high aspect ratio cells in the flow domain. Though this may not be an issue with the present day robust CFD algorithms, they may not be the preferred elements for certain flow problems sensitive to grid aspect ratio.
Overcoming the Limitations
This handicap of the structured multi-block is overcome by making use of the ingenious technique called nesting. It is a method of generating self-similar fractal-like topology, which perfectly allows high resolution of small geometric features along with placing coarser, large-size elements in less active regions of the flow field with 1-1 connectivity. It smartly couples the flow alignment features of structured grid with the low aspect ratio mesh elements size scaling capability of unstructured methodology.
Like the unstructured grids, the local refinements is not propagated to the external domain, but are smoothly and consistently transitioned to large scale as needed. This is an effective adaptive refinement technique without any hanging nodes. The nested structure loops back multiple times around the small scale geometric feature or within a defined region, thereby constraining the high density in and around the region of interest.
Figure 4: Nesting to capture the boundary layer of a transport aircraft.
The fundamental idea behind nesting is stacking up of elementary topological elements in a recursive way, there by creating a ‘nest’ like structure around the region of interest. The topology-building concept of nesting was build around the blocking strategy called clamping. Figure 5 shows the block structure for both clamping and nesting. Nesting is a more aggressive variant of clamping, in which the transition from denser to sparser blocks happens more rapidly. Here in GridPro, clamping based block-building strategy is used in internal flow cases while nesting is used in external flow problems.
Figure 5a: Clamping, gradual reduction in number of blocks.
Figure 5b: Nesting, rapid reduction in number of blocks
The following set of images, gives an illustration of the nested refinement technique. The topology has a self-similar structure with high resolution in the bottom and sparse resolution at the top. This entire process is automatic. All the user needs to do is specify the low density and high-density region and the topology gets automatically generated. The construction of self-similar structure helps in smooth transition from high-density region to low-density region.
Figure 6a. Nested topology and grid.
Figure 6b. Zoomed view of box region in figure 6a.
Figure 6c. Zoomed view of box region in figure 6b.
Based on different meshing requirements, nesting comes in various flavors out of which forward nesting and area nesting are the notable one’s. Forward nesting being 1D in nature helps in generating a high density grid around a specific geometric feature, while area nesting being 2D in nature is good at generating a cloud of points in a specific region of the flow field.
A video showing Area Nesting using GridPro.
A video showing the Reverse Nesting using GridPro.
Application of Nesting
This simple, robust and powerful tool finds application in almost all Engineering fields including Oil and Gas, Turbo machines, Aerospace, Marine. Nesting is very effective in capturing small geometric features like vortex generators, probes, etc., they are ideal for grids used in analysis of turbine blades with cooling holes, capturing flow phenomenon’s like confluent boundary layer, wake, vortex, etc., flow field around ships, submarines, aircrafts, land vehicles like cars and trains. Sometimes even quirky cases like analysis of flow past a hair strand or flow past a golf ball, etc. can be a good candidate for nesting. Also, instances where there is need for reduction in cell aspect ratios, nesting can come in handy. Following are some videos showing nested grids around vortex generators, train and submarine.
A video showing Nested Mesh around a Train
A video showing Nested mesh around a Submarine.
A video showing usage of Nested Mesh to capture Vortex Generators
Limitation for Multi block solvers in Nesting
Though nesting is powerful and highly automatic, it has one inherent drawback of generating way too many blocks. In fact, the number of blocks increases exponentially with the number of levels. The positivity of generating grids with reduced cell count comes at the expense of increased block count. This may not be an issue for an unstructured solver, which will be sensing the grid as one single domain with unstructured hex cells. However, the tool calls for scalability of multi-block solvers since it has to deal with a lot of smaller blocks.
Figure 7: Nested grid for bullet configuration.
Though the number of blocks are huge, nesting is a very effective tool since most of the CFD solvers are unstructured in nature. Being fast, efficient and automatic, this gridding tool is perfectly capable of handling complex geometries and parametric geometric modifications, and an ideal reliable choice for multi-scale problem.
Resources for Further Reading:
“Automatic nested refinement – a technique for the generation of high quality multi-block structured grids for multi-scale problems using gridpro”, Krishnakumar Rajagopalan, Peter. R. Eiseman, Engineering with Computers, November 2005, Volume 21.