When we look at the structural analysis and flow analysis programs, we see that it is a structure that works by solving the equations related to the problem to be solved by numerical methods. Here, the input values and properties differ for each part of the geometry, and iteratively solved with numerical methods and a stepwise solution is achieved for each point. The structures that allow the geometries to be introduced to analysis programs are actually the structures we weave around our own geometry, similar to a spider web, and are called mesh.
Speaking for the analyses, we see that the geometry is divided into these mesh particles and the solutions are made on them. In fact, many parameters such as how long the solution will take and how reliable its accuracy will be vary depending on this mesh structure. The mesh structure can consist of triangular and rectangular pieces for 2 dimensions. Each of these parts represents an element, and for mesh structures, how many elements they consist of is critical to the solution.
Structural Mesh vs Fluid Mesh Difference
If a comparison is made between Structural Analysis and flow analysis, it is seen that flow analysis equations are more complex than structural equations. In order to better observe the features of the flow at different points, it would be better to create a more detailed and good mesh structure than structural analysis. However, in order to carry out the structural analysis, the geometry should be knitted with a square mesh structure, that is, it should be covered with a structured mesh. In flow analysis, it is possible to solve with both structures called structured or unstructured mesh.
What Should Be Considered While Meshing
As we mentioned above, we can say that having a good mesh structure means ensuring the accuracy of the solution. Of course, the setup and boundary conditions we will create for the solution are as important as the mesh structure, but the mesh structure is important as it is the first step.
Is a mesh with more elements always better for the same geometry and problem? It is one of the important questions for understanding the logic of mesh structure. It is not always the case that a high-element mesh is a good better mesh. In cases where it is not necessary, excessively discarded mesh structures may have no effect other than prolonging the solution time. For the number of mesh elements, the optimum number of elements should be determined by the process we call independence from the mesh, and this number should be processed.
Mesh Independence Process
The ideal mesh element number is tried to be determined while making the mesh independence process. In this process, the same solution scheme is repeated by creating mesh structures with different number of elements. It is tried to find the ideal number of elements by reducing the number of elements between the number of elements that give similar and correct results.
Important Parameters
There are some parameters that are as important as the number of elements for mesh structures. These are Aspect ratio, Skewness and Orthogonal Quality values.
Aspect Ratio
Aspect ratio is one of the parameters to be considered while creating the mesh structure. For some solvers (e.g. OpenFoam) the aperture ratio must be kept below a certain value. The aspect ratio is a measure of the stretching of a cell. It is computed as the ratio of the maximum value to the minimum value of any of the following distances: the distances between the cell centroid and face centroids, and the distances between the cell centroid and nodes.
Skewness
The skewness value is one of the values that should be especially checked. It represents the height to base ratio for triangular mesh elements. While making the solution, the skewness value must be less than 1 as it will create an impossible triangular element and cause an incorrect solution. For this value, the range of 0.5 – 0.8 is considered ideal.
Orthogonal Quality
Orthogonal quality is computed with vector mechanics. The program makes calculations by using the face normal vector. The vector from the cell centroid to the centroid of each of the adjacent cells. And the vector from the cell centroid to each of the faces. It sounds complex. But what you need to know about ‘Orthogonal Quality’ is, that 0 is the worst and 1 is the best.
Boundary Layer for Flow Analysis
Speaking specifically about flow analysis, the flow progresses by forming certain boundary layers while moving on geometries. Generally, in flow problems, the most critical parts are characterized as boundary layer parts, so these parts must be carefully modeled in the mesh structure. While forming the boundary layer in the mesh structure, as a result of determining the parameters such as the first layer thickness, the boundary layer is formed by increasing the layer thickness with a certain increase rate. While determining the number of layers of the boundary layer, the element dimensions of the mesh structure formed around the boundary layer are taken into account, and the number of layers is determined by trying to capture the square geometry for the structured mesh structure and the equilateral triangle geometry for the unstructured mesh structure in the last layer. While determining the first layer thickness, the so-called Y+ value is used and this value should generally be less than 1. The parameters affecting the Y+ value are given in the formula set below.
As seen here, Y+ value depends on velocity drag, dynamic viscosity value and first layer thickness. By entering the desired Y+ value, the first layer thickness is calculated and inflation is tried to be created over this calculation.
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Author: Berkay Çakır
Editor: Halit Yusuf Genç
Engineer For Space 