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Y+ and Grid Types

What is Meshing in ANSYS?

Meshing means converting the computational domain to smaller subdomains to solve momentum, turbulence, and energy equations and finally obtain results for all levels of the simulated model.

Introduction

It is critical to creating a high-quality mesh to find dependable solutions and ensure numerical stability. Mesh generation, also known as grid generation in the CFD world, has evolved into its field and is still a very active area of study and development. Many existing commercial codes on the market have robust built-in mesh generators and various independent grid generating packages, demonstrating this. For the first time, creating a mesh is a daunting task, requiring judgments on the placement of discrete points (nodes) throughout the computational domain and the type of connections for each point. The mesh quality determines the success or failure of the numerical simulation.

Figure (a) shows mesh elements are Tetrahedron, hexahedron, prism/wedge, pyramid, and polyhedral. (b) Mesh topology shows the meshing hierarchy at each level.

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Mesh Generation

Mesh generation divides a continuous geometric space into discrete geometric and topological cells to form a mesh. These cells frequently form a simplicial complex. The geometric input domain is usually partitioned by the cells. Mesh cells are utilized to approximate the bigger domain in a discrete local manner. Depending on the complexity of the domain and the type of mesh sought, computer algorithms are used to produce meshes, which humans often guide via a graphical user interface (GUI). A common aim is to generate a mesh that precisely replicates the input domain geometry while having high-quality cells and not having too many cells to make subsequent calculations intractable. The mesh should likewise be fine in critical places for the following calculations (small elements).

Meshes are used to generate a computer screen and simulate physical processes such as finite element analysis and CFD. Meshes are made up of primary cells like triangles so that we can conduct operations on them like finite element calculations (engineering) and ray tracing (computer graphics). We still don’t know how to conduct these operations on complex locations and forms like a highway bridge. By doing computations on each triangle and computing the interactions between triangles, we may model the bridge’s strength or depict it on a computer screen.

Cell shapes that are commonly encountered.

Two-dimensional

The most frequent two-dimensional cell shapes are rectangles and squares. The triangle and the quadrilateral are these shapes.

Triangle

This cell has three sides and is one of the most basic mesh shapes.

Quadrilateral

This cell has a basic four-sided shape, as shown in the diagram. It’s most frequent in grids with a defined structure.

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Three-dimensional

The basic three-dimensional elements are the tetrahedron, quadrilateral pyramid, triangular prism, and hexahedron. There are triangular, and quadrilateral faces on all of them.

Tetrahedron

A tetrahedron comprises four vertices, six edges, and four triangular faces. A tetrahedral volume mesh may be created automatically in most circumstances.

Pyramid

Five vertices, eight edges, four triangular and one quadrilateral faces make up a quadrilateral pyramid. In hybrid meshes and grids, these work well as transition elements between square and triangle-faced elements and other elements.

Triangular prism

A triangular prism is made up of six vertices, nine edges, and two triangular and three quadrilateral faces. This type of layer has the advantage of efficiently resolving boundary layers.

Hexahedron

A hexahedron, sometimes known as a topological cube, has eight vertices, twelve edges, and six quadrilateral faces. It’s sometimes referred to as a hex or a block.

The accuracy of solutions in hexahedral meshes is the highest for the same cell amount.

Grid/Mesh

A mesh is a tool that separates a shape into several parts. The CFD solver uses these to create control volumes.

Terminology:

  • Cell = control volume into which domain is broken up.
  • Node = grid point.
  • Cell center = center of a cell.
  • Edge = boundary of a face.
  • Face = boundary of a cell.
  • Zone = grouping of nodes, faces, cells
  • Domain = group of node, face, and cell zones.

 

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Types of Meshes in ANSYS

The meshing in ANSYS Fluent is structurally divided into two parts:

Structured mesh

Unstructured mesh

Structured Meshes

In a Structured mesh, each element can be addressed with a row and column number because, in a Structured mesh, the mesh is produced in a completely regular manner. In contrast, this is practically impossible in an Unstructured mesh due to the lack of order in creating the mesh.

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Unstructured mesh

Unstructured CFD meshing technologies have evolved, and commercial CFD suppliers increasingly use them. They give the user more automated options for creating a mesh model and a user-friendly interface.

The standard method for creating an unstructured mesh includes the following steps:

– detecting the edges of a surface and creating nodes to construct the boundaries of each surface

– creating additional nodes on the surface and connecting them to fill the surface with data

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An O-grid consists of lines of points with the last point wrapping around and meeting the first, forming a circular ‘O’ shape. A C-grid, for example, has lines that bend in a semicircle shaped like a letter ‘C’ (basically half of an O-grid), but an L-grid has lines that bend in an L-shape formed from a quarter of an O-grid.

The following figure shows several examples.

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It takes a long time to create structured meshes for complicated geometries since it requires a lot of manual labor. Unstructured tetrahedral, hexahedral, and polyhedral meshes are employed as a result. Unstructured meshes benefit from being more adapted to fitting into complicated forms. Furthermore, volume filling may be done automatically using a Delauney triangulation or a hierarchical technique. On the other hand, Tetrahedrons tend to get overstretched in areas with high curvatures, resulting in high aspect ratios that influence the skewness of the cells; this is not the case with hexahedral cells. Additionally, aligning tetrahedral cells with the flow direction might be problematic. These two issues can stymie convergence and cause numerical diffusion or manufactured mistakes in the solution.

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Polyhedral Meshing

Polyhedral elements, which have grown more popular, are an alternative to tetrahedral meshes. Polyhedral have a higher number of near surrounding cells than tetrahedra, which is a significant benefit (typically ten, compared to four for tetrahedra). This gives gradient approximations more resolution. Polyhedral cells are formed by merging tetrahedral cells. As a result, the total cell count is lowered, as are severely skewed cells. Because of their uneven form, polyhedral cells are less susceptible to stretching. Polyhedral meshes need additional computing operations per cell due to the higher number of nodes and faces per cell and the increased number of neighbors. However, the short time to convergence compensates for this.

What is Y-Plus (Y+)?

The application of wall functions, which derive the shear stress at the wall from semi-empirical equations, is one way to describe the solution of the shear stress at a wall. The dimensionless variable y-plus represents the distance from the wall to the first grid cell’s center.

Also, Y-plus is a distance with no dimensions. In other words, Y-plus renders the vertical space between the element’s center and the wall dimensionless. This value is used to evaluate the proportionality of the grid element’s size (height) on the wall boundaries. The majority of wall rules include constraints in tolerable models Y-plus values.

On the other hand, the ratio of turbulent and laminar flow effects in a cell is represented by Y-plus. If Y-plus is low, the cell’s flow is laminar. If Y-plus is large, the current in that cell will be turbulent. As a result, if Y-plus is too small, then the flow in the cell is prolonged, and the wall functions will not be usable. Therefore, your solver may make incorrect assumptions, mainly when performing the Standard Wall Function computations. Also, if Y-plus is too large, solving the laminar/turbulent flow field in the boundary element is not too difficult, but other assumptions will be incorrect.

This number usually is about 1 in simulations without wall functions, whereas wall functions allow us to take a y+ greater than 1. The boundary layer can be divided into two regions: the inner and outer layers. The viscous sublayer (y+ <5), the buffer layer (5 <y+ <30-50), and the log-law area (y+ > 30-50) are the three zones that run from the wall to the outer layer in the former.

Wall functions

As previously stated, near-wall flow fields necessitate careful attention. Direct application of the no-slip condition and wall functions that derive the shear stress at the wall using semi-empirical equations are the two basic ways of obtaining the shear stress at a wall in RANS. The dimensionless variable y+ represents the distance from the wall to the first grid cell’s center. The first method’s y+ is usually around 1, but wall functions allow us to use a y+ greater than 1. As a result, there are fewer grid cells and, as a result, faster computing times.

The law of the wall

Viscosity and wall shear stress are important characteristics close to the wall. We define viscous scales, which are the suitable velocity and length scales in the near-wall area, based on these variables (and). The friction velocity is as follows:

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The inner layer

In dimensionless form, the law-of-the-wall for this layer is:

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From y+ = 30-50 to the outer boundary of the law-of-the-wall region, which is dependent on the Reynolds number, the log layer is valid. This layer’s law-of-the-wall can be represented in the dimensionless form as follows:

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Where B is a constant and is the von Kármán constant. This is the wall’s logarithmic law. The buffer layer is placed in the 5 <y+<30-50 areas. In this area, neither of the laws apply. The obtained expressions are illustrated in the above Figure.

Mesh Quality

The mesh quality considerably impacts the numerical computation’s accuracy and stability. Node point distribution, smoothness, and skewness are linked with mesh quality.

Checking the quality of your mesh, regardless of the type of mesh used in your domain, is critical. Different quality parameters are examined depending on the mesh cell types (tetrahedral, hexahedral, polyhedral, etc.):

  • Cell Squish is a metric for determining how far a cell deviates from orthogonality in terms of its faces.
  • On tri/tet elements, there is a skew in cell equivolume.
  • Polyhedral meshes have face squish.
  • All meshes have the same aspect ratio.

The aspect ratio is a measurement of a cell’s stretching. It’s calculated as the ratio of any of the following distances’ greatest to minimum values:

the distances between the cell centroid and the face centroids and the cell centroid and nodes. The figures below depict the aspect ratio of a unit cube as 1.732 because the maximum distance is 0.866 and the minimum distance is 0.5. Any mesh, including polyhedral meshes, can be defined using this definition.

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Use the Report Quality button on the General task page to check the quality of your mesh:

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Clustering and Node Density

Because you’re discretely defining a continuous domain, the density and distribution of nodes in the mesh determine how well the flow’s key features (such as shear layers, separated regions, shock waves, boundary layers, and mixing zones) are resolved. Poor resolution in important locations can substantially affect flow characteristics in many circumstances. The resolution of the boundary layer upstream of the point of separation, for example, is critical in predicting separation due to an adverse pressure gradient.

The boundary layer resolution also influences the accuracy of the estimated wall shear stress and heat transfer coefficient accuracy of the estimated wall shear stress and heat transfer coefficient is also influenced by the boundary layer resolution (i.e., mesh spacing near walls). This is especially true in laminar flows when the mesh adjacent to the wall must respect the laws of physics.

The boundary layer resolution also influences the accuracy of the estimated wall shear stress and heat transfer coefficient accuracy of the estimated wall shear stress and heat transfer coefficient is also influenced by the boundary layer resolution (i.e., mesh spacing near walls). This is especially true in laminar flows when the mesh adjacent to the wall must respect the laws of physics.

To obtain good quality in ANSYS Fluent meshing, we must evaluate its smoothness or quality, Skewness, aspect ratio quality, and mesh based on these patterns.

skewness

This criterion ranges from zero to one. If the element angles are ninety degrees in size, the value of skewness quality is zero, which is the best-case scenario for a computational mesh.

On the other hand, as the grid has been sharpened, the values associated with grid skewness have decreased to one, affecting the accuracy of the solution. However, due to severe curvatures in geometry, such as turbines, this criterion has occasionally exceeded 0.9, which must be controlled and limited to be a minor element.

Smoothness

Smoothing in ANSYS Meshing aims to increase element quality by shifting node locations related to other nodes and elements. The amount of smoothing iterations and the threshold metric at which the mesher will begin smoothing are controlled by the low, medium, or high options.

Also, the transition in size should be as smooth as possible. Sudden changes in cell size should be avoided because they may cause erroneous results at nearby nodes.

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Aspect Ratio

It is the ratio of a cell’s maximum to minimum side. To get the greatest results, it should ideally be equal to 1. It should be close to one for multidimensional flow. Local variations in cell size should also be kept to a minimum, with adjacent cell sizes not differing by more than 20%. A big aspect ratio can cause an interpolation inaccuracy of unacceptable magnitude.

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ANSYS Mesh Refinement?

The solution-adaptive mesh refinement function in ANSYS FLUENT lets you refine and coarsen your mesh depending on geometric and numerical solution data. ANSYS FLUENT also includes tools for designing and viewing adaptation fields tailored to specific applications.

You can Select Insert> Refinement from the context menu by right-clicking. Select Refinement from the drop-down list when clicking Mesh Control on the Context Toolbar. Scope the geometry whose mesh you wish to refine in the Details View. Choose a Refinement value between 1 (the smallest refinement) and 3 (the most refined refinement) (maximum refinement).

STUDY OF MESH INDEPENDENCE

The finer the mesh, the more precisely the geometry features can be captured, and there are more “data points” on the geometry to provide an accurate displacement and stress response.

An analyst can conduct a mesh independence (or grid independence) analysis to determine the results’ reliance on mesh density. One method is to use the strategy outlined below:

  1. On the geometry, isolate a point of interest. This might be the entire geometry of a small model. However, this is not always possible. Therefore, one might concentrate on a single area of the geometry.
  2. Obtaining the node count on a radius, chamfer, body, or named selection might be used.
  3. Refine the mesh in the desired area. There are a few best practices to follow for mesh refinement. The following are some of them:
  • Change only the mesh size. Other mesh settings, such as element type or order, should not be changed. This will ensure that the runs are compared fairly.
  • Ensure that the increase in mesh count between two runs is “significant.” By significant, we imply a minimum of 10%. This percentage is a guide based on experience and analytical judgment.
  • At least three distinct meshes should be obtained. Mesh independence may be demonstrated with just two meshes. However, mesh independence is often established after three or more passes for rather coarse beginning meshes.
  1. Compare the outcomes of the different runs. One can look for a point where a big increase in node count does not result in a significant increase in stress by plotting the number of nodes vs. stress. The analyst can plot raw data, percentages, or both.

Mesh independence plots are shown in the following Figures. Raw data and percentages are both used to show the same information. It can be seen that independent mesh stress requires a minimum of 16,000 nodes. This is 94,000-psi stress.

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