AE 618A TERM PAPER PRESENTATION

AE 618A TERM PAPER PRESENTATIONMESH METRICS IN ANSYSSAHIL BISWAS 12602SHASHWAT SAXENA 12663

ANSYSANSYS is a simulation software that enables us to predict how a body will behave in the real world.The Computational Fluid Dynamics (CFD) section in this software (Fluent) provides fluid flow analysis and the study of fluid-body interactions.The 4 major steps involved to study a bodys interaction with fluid are:GeometryMeshingSolutions SetupCalculations

MESH IMPROVEMENTOnce the mesh is generated in a software, it need not be ready for calculations and for obtaining convergence.

Hence there are some factors which determine the quality of a mesh which we need to understand so that we can improve its quality.

The 12.1 version of ANSYS came up with a new function which allows the users to viewmesh metricinformation and thereby evaluate themeshquality.

We will discuss some important ones. (NOTE: These are very general parameters and not software specific, but are easy to understand by taking reference of one, thats why ANSYS)

MESH METRICSWith the help of this presentation, we will try to explain the following :Aspect RatioSkewnessWarping FactorOrthogonal Quality

ELEMENT QUALITYThe Element Quality option provides a composite quality metric that ranges between 0 and 1. A value of 1 indicates a perfect cube or square, while a value of 0 indicates that element has zero or negative volume. For 2-D Elements quad/tri elements:

For 3-D Elements:

Where C is a constant and its value depends on the type of element.ASPECT RATIOAspect ratio is the measure of a mesh element's deviation from having all sides of equal length.It is the measure of the stretching of the cell. A high aspect ratio occurs with long, thin elements.It is equal to 1 for equilateral triangle and square.

Aspect Ratio calculation for quadrilaterals

Two lines are constructed that bisect the opposite pairs of element edges.

Then rectangles are constructed centered about each of the two lines.

The aspect ratio of quadrilateral is the ratio of longer side to a shorterside whichever rectangle is more stretched .

WARPING FACTORWarping Factor is a way to measure how far is a quadrilateral element from being planar.A high factor may indicate a condition the underlying element formulation cannot handle well, or may simply hint at a mesh generation flaw.

Warping of 0.1 is visible given the flat reference and warping of 1.0 is visually unappealing and is unacceptable.

Warping factor is computed for some quadrilateral shell elements, and the faces of bricks, wedges, and pyramids.

Twisting the top face of a unit cube by 22.5 and 45 relative to the base produces warping factors of about 0.2 and 0.4, respectively.

SKEWNESSSkewness is considered to be the best indicator of mesh quality and also is most widely used parameter.It determines how close to ideal (i.e. equilateral or equiangular) a face or cell is. Highly skewed cells can decrease accuracy and can destabilize the solution.

A value of 0 indicates equilateral cell (best) and 1 indicates a completely degenerate cell (worst cell)Quality grids have a skewness value of approximately 0.1 for 2D and 0.4 for 3D.In 2D, The presence of cells that are fair or worse indicates poor boundary node placement. You should try to improve your boundary mesh as much as possible.

How to improve the quality?Highly skewed elements exist around edges of a complex or in the regions where there is a sudden change in the element size.To reduce the skewness, growth rate of elements should not be very high.Using too many mesh control methods (sphere of influence, biased meshing etc. )is not considered good because the mesh that ANSYS generates on its own is well made specifically for the complex geometry of body.Major reason for high skewness is improper smoothing.When moving from one domain to another, the change in size of elements or the difference in element size of the two domains should not be high.

ORTHOGONAL QUALITYThe orthogonal quality for a cell is computed as the minimum of the following quantities computed for each face i :

Where Ai is the face normal vector fi is a vector from the centroid of the cell to the centroid of that face.Ci is a vector from the centroid of the cell to the centroid ofthe adjacent cell that shares the face.

Ai is the face normal vector fi is a vector from the centroid of the cell to the centroid of that face.Ci is a vector from the centroid of the cell to the centroid of the adjacent cell that shares the face.

ReferencesANSYS Meshing Users Guide (Page 122-140): http://148.204.81.206/Ansys/150/ANSYS%20Meshing%20Users%20Guide.pdfMesh Statistics: https://romeo.univ-reims.fr/documents/fluent/tgrid/ug/chp15.pdfSkewness in Meshing: www.arc.vt.edu/ansys_help/flu_ug/flu_ug_mesh_quality.htmlAspect Ratio-Wikipedia

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