Appendix A Mesh Quality

1. Appendix AMesh Quality ANSYS MeshingApplication Introduction

2. Overview Mesh Quality Metrics in ANSYS Meshing Skewness Aspect Ratio Worst Element Mesh Quality Considerations for the FLUENT Solver General Considerations Impact of Mesh Quality on the Solution Mesh Quality Considerations for the CFX Solver Factors Affecting Mesh Quality CAD Issues Mesh Resolution and Distribution Meshing Method Inflation Strategies to Improve Mesh Quality CAD Cleanup Virtual Topology Pinch Controls Sensible Mesh Sizings and Inflation Settings General Recommendations Workshop A.1 Virtual Topology for an Auto Manifold Workshop A.2 FLUENT and CFX Mesh Quality Metrics

3. Mesh Quality Metrics in ANSYS Meshing • Mesh Metrics are available under Mesh Options to set and review mesh metric information and to evaluate mesh quality • Different physics and different solvers have different requirements for mesh quality • Mesh metrics available in ANSYS Meshing include: • Element Quality • Aspect Ratio • Jacobian Ration • Warping Factor • Parallel Deviation • Maximum Corner Angle • Skewness

4. Skewness Two methods for determining skewness: Based on the Equilateral Volume deviation: Skewness = Applies only to triangles and tetrahedra Default method for tris and tets Based on the deviation from a Normalized Angle deviation: Skewness = Where is the equiangular face/cell (60 for tets and tris, and 90 for quads and hexas) Applies to all cell and face shapes Used for prisms and pyramids Mesh Quality Metrics optimal (equilateral) cell actual cell circumsphere 0 1 Perfect Worst

5. Mesh Quality Metrics aspect ratio = 1 high-aspect-ratio quad aspect ratio = 1 high-aspect-ratio triangle • Aspect Ratio • Aspect for generic triangles and quads is a function of the ratio of longest side to the shortest side of the reconstructed quadrangles (see User Guide for details) • Equal to 1 (ideal) for an equilateral triangle or a square

6. Mesh Quality Statistics in ANSYS Meshing • The min, max, averaged and standard deviation for the selected mesh metric are shown for the surface mesh (after Preview Surface Mesh generation) and for the volume mesh (after Preview Inflation layer or Generate Mesh generation) • The worst elements can be highlighted using the Show Worst Elements under the Mesh object in the Tree Outline

7. Mesh Quality Considerations for FLUENT FLUENT requires high quality mesh to avoid numerical diffusion Several Mesh Quality Metrics are involved in order to quantify the quality, however the skewness is the primary metric The aspect ratio and cell size change mesh metrics are also very important In worst scenarios and depending on the solver used (density based or pressure based) FLUENT can tolerate poor mesh quality. However some applications may require higher mesh quality, resolution and good mesh distribution The location of poor quality elements helps determine their effect Some overall mesh quality metrics may be obtained in Ansys Meshing under the Statistics object Additional mesh quality metrics may be retrieved in FLUENT GUI under Mesh/Info/Quality from the menu, or using the TUI commands ‘mesh/quality’

8. Mesh Quality Requirements for FLUENT The most important mesh metrics for Fluent are: Skewness Aspect Ratio Cell Size Change (not implemented in Ansys Meshing) For all/most applications: For Skewness: For Hexa, Tri and Quad: it should be less than 0.8 For tetrahedra: it should be less than 0.9 For Aspect Ratio: It should be less than 40, but this depends onthe flow characteristics More than 50 may be tolerated at the inflation layers For Cell Size Change: It should be between 1 and 2. • Poor mesh quality may lead to inaccurate solution and/or slow convergence • Some applications may require even lower skewness than the suggested value

9. Skewness and the Fluent Solver High skewness values are not recommended Generally try to keep maximum skewness of volume mesh < 0.95. However this value is strongly related to type of physics and the location of the cell FLUENT reports negative cell volumes if volume mesh contains degenerate cells. Classification of the mesh quality metrics based on skewness: * In some circumstances the pressure based solver in Fluent can handle meshes containing a small percentage of cells with skewness ~0.98.

10. Impact of the Mesh Quality on the Solution Example (max,avg)CSKEW=(0.912,0.291) (max,avg)CAR=(62.731,7.402) Mesh 1 VzMIN≈-90ft/min VzMAX≈600ft/min Large cell size change (max,avg)CSKEW=(0.801,0.287) (max,avg)CAR=(8.153,1.298) Mesh 2 VzMIN≈-100ft/min VzMAX≈400ft/min

11. Mesh Quality Considerations for CFX • Mesh quality requirements are somewhat different for the CFXsolver than for the FLUENT solver due to the difference in thesolver structure for the two codes • Fluent uses a a cell-centered scheme, in which the fluid flow variables are allocated at the center of the computational cell, and the mesh-element is the same as the solver-element • CFX employs a vertex-centered scheme for which the fluid flow variables are stored at the cell vertex, and the solver-element or control volume is a “dual” of the mesh-element. This means that the vertex of the mesh-element is the center of the solver-element

12. Mesh Quality Considerations for CFX • The CFX solver calculates 3 important measures of meshquality at the start of a run and updates them each time themesh is deformed • Mesh Orthogonality • Aspect Ratio • Expansion Factor +--------------------------------------------------------------------+ | Mesh Statistics | +--------------------------------------------------------------------+ Domain Name: Air Duct Minimum Orthogonality Angle [degrees] = 20.4 ok Maximum Aspect Ratio = 13.5 OK Maximum Mesh Expansion Factor = 700.4 ! Domain Name: Water Pipe Minimum Orthogonality Angle [degrees] = 32.8 ok Maximum Aspect Ratio = 6.4 OK Maximum Mesh Expansion Factor = 73.5 ! Global Mesh Quality Statistics : Minimum Orthogonality Angle [degrees] = 20.4 ok Maximum Aspect Ratio = 13.5 OK Maximum Mesh Expansion Factor = 700.4 ! Good (OK) Acceptable(ok) Questionable (!)

13. Mesh Orthogonality in CFX • Orthogonality measures alignment of: • ip-face normal vector, n, & • node-to-node vector, s. • Orthogonality Factor = n·s, >1/3 desirable • Orthogonality Angle = 90º-acos(n·s), >20º desirable • Are these different than Max/Min Face Angles in CFD Post? YES! • Face angles correspond to angles between edges • One can have an acceptable Face Angle and an unacceptable Orthogonality Angle if an element is skewed in two directions…

14. Mesh Expansion Factor in CFX Expansion factor measures how poorly the nodal position corresponds to the control volume centroid • Mesh Expansion Factor ≈ ratio of largest to smallest element volumes surrounding a node,<20 is desirable • The Mesh Expansion Factor is essentially identical to the Element Volume Ratio in CFD Post

15. Mesh Aspect Ratio in CFX Aspect ratio measures how stretched a control volume is • Aspect Ratio = maximum of the ratio of largest to smallest ip-areas for each element surrounding a node,<100 is desirable • The Aspect Ratio is very similar to the Edge Length Ratio in CFD Post

16. Significance of Mesh Quality in CFX • Sources of discretisation error • non-orthogonality introduces errors in flux approximations • large mesh expansion introduces errors in storage and source approximations • Amplification of discretisation error • corrections to reduce errors caused by non-orthogonality can create unphysical influences • Difficulties solving linearised equations • large aspect ratios require use of more significant digits(i.e. use of double precision solver) Why is geometrical mesh quality important?

17. Factors Affecting Mesh Quality CAD Issues Small edges, sharp edges and faces Small gaps/passages between edges and faces Unconnected geometry entities CAD issues need to be fixed to avoid this

18. Factors Affecting Mesh Quality Mesh Resolution and Distribution Geometry with abrupt changes, discontinuities and/or small gaps may require more resolution, and Mesh distribution where appropriate to be able to predict physical conditions Inappropriate resolution and distribution may lead to large cell size change, aspect ratio and/or skewness

19. Factors Affecting Mesh Quality Type of Size Function Inappropriate usage (or no usage at all) of Advanced Size Functions (ASF) may lead to poor mesh quality Use Curvature ASF for geometries with dominant curvature features Use Proximity ASF for geometries with gaps or narrow components Use Curvature and Proximity ASF in geometries having a combination of these features ASF may be used to avoid this !

20. Factors Affecting the Mesh Quality Meshing Method Inappropriate usage of Meshing Method (Automatic, Tetrahedrons, Sweep, MultiZone and CFX-Mesh) may lead to large skewness The selection of the Meshing Method depends on the geometry and application It is a good practice to use Show the Sweepable Bodies under the Mesh object in the Tree Outline Many applications may take advantage of Patch Conforming and Sweep Meshing Method A relatively “good” mesh in terms of max skewness, however the average and standard deviation are large

21. Factors Affecting Mesh Quality Inflation Inappropriate: Surface mesh quality Choice of the inflation surfaces Inflation Option Inflation algorithm (layer compression or stair-stepping) Inflation parameters Advanced Inflation Options may lead to poor mesh quality! Affected Inflation

22. Strategies to Improve Mesh Quality CAD cleanup Use CAD or DM to: Simplify the geometry Merge small edges Merge the faces in order to reduce the number of faces Avoid narrow faces Keep volume gaps only where important Decompose the geometry Remove unnecessary geometries Add geometries Repair the geometry After split edge/Project edge/merge face in DM

23. Strategies to Improve Mesh Quality Virtual topology Use VT in order to simplify details at geometry level in AM Can be added under Model object in the Tree Outline Mesh may be improved by creating virtual edges/faces If the resulting surface mesh is distorted consider fixing the geometry issue in DM or CAD After virtual merging of narrow face with wide face

24. Strategies to Improve Mesh Quality Pinch Controls Allow to remove small features (small edges or narrow faces) at the mesh level Intended for Patch-Conforming Tetrahedral Method When it is defined the small features are “pinched-out” from the mesh when pinch criteria are met Pinch locations are detected automatically with Pinch Controls under Mesh object in the Tree Outline

25. Strategies to Improve Mesh Quality Sensible Mesh Sizings and Inflation Settings The minimal size decreased 2X in order to fit the narrow geometry. As a result the mesh quality has been improved. Local face sizing may also be used

26. General Recommendations A volume mesh may be considered inacceptable if it satisfies one or more the following conditions: Very high skewness for FLUENT meshes(> 0.98) Degenerate cells (skewness ~ 1) High aspect ratio cells Negative volumes Cell Quality can be improved by: Improving surface mesh quality Moving mesh nodes CAD to fix geometric problems such as sharp angles, small edges, merge faces unite and/or decompose the geometries Clean-up tools in DM to simplify the geometries and their entities Different methods, global and local sizings and parameters in the ANSYS Meshing Application Pinch Controls in the ANSYS Meshing Application to avoid small features Virtual topology in the ANSYS Meshing Application in order to simplify the geometry Strategies to Improve Mesh Quality

27. Miscellaneous If the model contains multiple parts or bodies the mesh metric information can be shown by highlighting them under the Geometry object in the Tree Outline The Body of Influence (BOI) technique may be used also to control the mesh quality and appropriate local resolution More advanced mesh statistics including histograms can be exhibited by FE Modeler Mesh Metrics in FEM Different mesh quality metricscan also be viewed in CFD Post

28. Workshop A.1 Virtual Topology for anAuto Manifold

29. Goals This workshop uses the manifold geometry from workshop 5.2. Recall that this geometry contains many problematic small faces and sharp angles. In workshop 5.2, the Patch Independent method was used to produce a good quality mesh without modifying the geometry. In this workshop Virtual Topology will be used to “remove” the problematic geometry and then the default Patch Conforming meshing method will be used.

30. Starting the Project Launch ANSYS 12.0 Workbench Click on Component Systems in the Toolbox on the LHS of the main panel Double click the Mesh option to add it to the Project Schematic In the Project Schematic right-click on Geometry and select Import Geometry > Browse. Select the file Auto-Manifold.agdb

31. Named Selections Next, make sure that Named Selections will be brought into Meshing: Right-click on cell A2 and then select Properties Ensure Named Selections is checked, and the Named Selection Key is blank Close the Properties window

32. Edit the Mesh • Edit the Mesh (cell A3) • The Meshing window will open • Start by suppressing the fluid region and meshing the solid: • Select the Body selection icon from the toolbar • Select the inner fluid region, sothat it is highlighted in green, andthen right-click and selectSuppress Body

33. Mesh Settings • Select Mesh from the Outline tree • In the Details view set the Physics Preference to CFD • The assumption here is that heat transfer will be solved in the solid region using a CFD solver • Expand the Sizing section in the Details view and set: • Span Angle Center = Medium • Min Size = 1.0 mm • Max Face Size = 10.0 mm • Max Tet Size = 10.0 mm • Right-click on Mesh in the Outline tree and select Preview Surface Mesh • Since the body is not sweepable, the Patch Conforming method will be applied by default

34. Examine the Mesh • The Patch Conforming method meshes each individual surface. This produces a poor quality mesh on some surfaces in this geometry. Examine the surface mesh and look for regions of poor mesh quality. By switching between Geometry and Mesh in the Outline tree relate regions of poor mesh quality to the underlying surface geometry. Some examples are shown here:

35. Adding Virtual Topology • Virtual Topology allows you to merge adjacent surfaces, removing undesirable surface geometry feature and producing a higher quality mesh • Right-click on Model (A3) in the Outline tree and select Insert > Virtual Topology • A Virtual Topology entry is added to the Outline tree • In the Details view note that the Behaviour is set to Low • Right-click on Virtual Topology in the Outline tree and select Generate Virtual Cells • This automatically creates virtual cells using a “Low” merging strategy. “Medium” and “High” strategies are likely to result in more faces being merged into virtual cells

36. Virtual Topology • When Virtual Topology is selected in the Outline tree the viewer shows all virtual cells that have been created • Examine the new surface geometry and note that most of the problematic faces have been merged to produce a cleaner surface geometry • In the Details view change the Behaviour to Medium • Right-click on Virtual Topology in the Outline tree and select Generate Virtual Cells • Note that more faces have been merged into virtual cells • Try generating virtual cells using the High option for Behaviour • This does not work as well for this geometry as shown to the right • Switch back to the Medium option and generate the virtual cells again

37. Examine Improved Mesh • Re-create the surface mesh and examine the regions that previously showed poor mesh quality • You should find that the surface mesh has been greatly improved • There are still some regions where the mesh quality could be improved. The arrows below shows one of these locations. • If you zoom in and examine the geometry here you will find a kink at the edge of the surface

38. Adding Virtual Cells Manually • You can manually add Virtual Cells to improve the mesh further • Pick the Face selection icon from the toolbar • Orient the view approximately as shown below (note the X-Y axes) • Check that Virtual Topology is selected from the Outline tree • Select the four faces shown below, then right-click and select Insert > Virtual Cell 3 1 2 4

39. Examining Improved Mesh • Re-create the surface mesh and examine the region again • You should find an improved surface mesh • You can continue adding Virtual Cells as necessary • In some cases the automatic virtual cell creation may merge faces that you do not want to merge. You can delete individual virtual cells by selecting the Virtual Face from below the Virtual Topology entry in the Outline tree and right-clicking to delete. • Right-click on Mesh and select Generate Mesh to create the final solid mesh

40. Viewing the Fluid Body • The next step is to create the mesh for the fluid region • In the Outline tree expand the Geometry > Part section • Right-click on the first solid and select Hide Body to hide the solid region • Right-click on the suppressed (second) solid and select Unsuppress Body • With the second solid selected, in the Details view expand the Graphical Properties section and set the Transparency to 1

41. Adding Inflation • Select Virtual Topology from the Outline tree • Virtual Cells have already been created on the fluid region from earlier • Check that the automatic virtual cells look reasonable • There should be no small surfaces remaining in the model • The next step is to add inflation to the fluid walls • Right-click on Mesh and select Insert > Inflation • In the Geometry field you need to select the solid body corresponding to the fluid region from the Viewer then click Apply • Once this has been selected click on No Selection in the Boundary field so that the Apply / Cancel buttons appear

42. Creating the Fluid Mesh • Now select one of the faces from the model that is not an inlet or outlet • Select Extend to Limits from the toolbar as shown: • All the fluid walls should now be selected • Click Apply in the Boundary field in the Details view • To generate the final mesh right-click on Mesh and select Generate Mesh

43. Checking the Mesh Quality • Expand the Statistics entry and set theMesh Metric to Skewness. Note that theMax Skewness is within the acceptable rangefor the FLUENT solver. • If you had generate the mesh without VT, theMax Skewness would have been considerablyhigher Without Virtual Cells

44. Fluid Region Mesh NO VT VT

45. Workshop A.2 FLUENT and CFX Mesh Quality Metrics

46. Goals This hands on tutorial will demonstrate how the Meshing Application in ANSYS is used to generate a CFD mesh for an internal flow domain The geometry represents portions of an aerospace valve region, decomposed into 3 bodies The goal is to produce a conformal hybrid CFD mesh including hex, pyramid, prism and tetrahedral elements including pinch controls and to examine mesh quality metrics for the Fluent and CFX solver preferences

47. Creating a Meshing System Launch ANSYS Workbench from the START menu Click on Component Systems in the Toolbox on the LHS of the WB main panel Double click the Meshoption

48. Right click (RMB) on the Geometry button and select Import Geometry (the question mark on the button goes away once a geometry file is imported) Import the Aero-Valve.agdb file from the tutorial folder Double click on the Mesh button in the Project Schematic to launch the Meshing Application Importing the Geometry

49. Geometry The original geometry is a Solid part and the Fluid region was extracted out in DesignModeler (DM). Other operations performed in DM; A parameter was defined for the position of the valve Some outlet ports were closed One multi-body part was created and a given the name “Fluid” and the material “Fluid” Individual bodies were re-named and Named Selection was used to define the Inlet and Outlet Fillets were added to somesharp corners to improvemesh quality

50. Meshing Options • In the Meshing Options panel select the following meshing options: • Physics Preference • CFD • Mesh Method • Automatic • Click OK after youmake the selection • In Units, make sure the setting is mm