MESH CONSIDERATIONS Chapter 5

Training Manual May 15, 2001 Inventory # Mesh Considerations Mesh used affects both solution accuracy and level of computational effort. Typical CFD meshes require more elements than typical solid mechanics problems. Concentrate mesh density toward steep gradient regions. –Wall boundary layer –Shear layer –Separation regions –Shock waves Transitions from high-to-low mesh density regions should be gradual to avoid numerical instabilities. 3-D element shapes may be mixed.

Training Manual May 15, 2001 Inventory # Finite Element Mesh Rapid Change in Element size is not good. –Can occur with free meshing. Aspect Ratio — depends on local behavior of solution. –10:1 in regions with significant gradients may be high. 100:1 in regions without gradients may be fine. Included Angles — Approximate recommended limits. –25 < Angle < 155 –Acceptable included angles depend upon variable gradients in the region.

Training Manual May 15, 2001 Inventory # Finite Element Model Problems Un-referenced nodes –Some geometry with nodes not connected into elements –Free Meshing Difficulty –Generally must clear area/volume & remesh Element Errors –Duplicate elements –Overlapping volumes –Degenerate elements –Unsupported element generated –Bad Shapes Generated

Training Manual May 15, 2001 Inventory # Examples of Poor Meshes Incompatibility - the faces of adjacent elements must line up. The faces of adjacent elements must match up. If they do not, unspecified boundaries result. 1

Training Manual May 15, 2001 Inventory # Another Example of Poor Meshing Change in element size is too great. 1

Training Manual May 15, 2001 Inventory # Free Meshing Free meshes are usually not a problem; this one shows too great a change in element size. 1

Training Manual May 15, 2001 Inventory # Triangles and Quadrilaterals Both of the meshes shown use the same lesize commands. The quadrilateral mesh is preferred because it enables better resolution at a boundary.

Training Manual May 15, 2001 Inventory # Pipe Cross Section 1 A pipe cross section using a center square. Using a center square, the pattern allows for mesh refinement towards the pipe walls. Element sizing near the “center square" is not quite uniform. A quarter of a circle can be free meshed with all hexes. May require use of higher order quadrature for element integration

Training Manual May 15, 2001 Inventory # Another Pipe Cross Section 1 This mesh pattern which uses more volumes and enables more uniform spacing near the center.

Training Manual May 15, 2001 Inventory # Mixing Triangles and Quadrilaterals 1 An example of using triangles to provide a transition in the number of elements in the transverse direction. Note that the mesh is not as good near the walls in the triangle region.

Training Manual May 15, 2001 Inventory # Mixing Triangles and Quadrilaterals (continued) 1 Using boundary areas preserves the ability to control the boundary layer spacing with a mapped quad mesh.

Training Manual May 15, 2001 Inventory # Using the Mesh Tool The preceding cross sections can be extruded or swept into the third dimension to create a mesh with Hexahedral and, where necessary, Wedge elements. It may not always be possible to create a mapped mesh The mesh tool is useful to mesh irregular areas or volumes –These can also be extruded into three dimensions

Training Manual May 15, 2001 Inventory # Layered Meshing Generates line-graded free meshes in 2D for: –lines with small variation in element size along line –steep transition in element size and number normal to line Use Mesh Tool Specifications –Desired element size at the wall –Thickness of inner LAYER1 (uniformly sized elements) Distance or number of rows –Thickness of outer transitional region - LAYER2 Size of elements increases by transition factor to global element size

Training Manual May 15, 2001 Inventory # Layered Meshing Controls Mesh Tool

Training Manual May 15, 2001 Inventory # Controls for a Very Fine Mesh... Global Distance between lines: 1.0 Size at wall:.01 LAYER1 Size factor is 3.0 LAYER2 1.5

Training Manual May 15, 2001 Inventory # … Resulting In A Very Fine Mesh

Training Manual May 15, 2001 Inventory # Comments on the Layered Mesh... Note that this mesh, although quite fine at the walls, is not optimized for this duct configuration. Generally in these cases higher aspect ratio elements would be used near the walls. The layered meshing is most appropriate for curved surfaces such as cylinders in cross flow.

Training Manual May 15, 2001 Inventory # Alternate Example Same wall element size:.01 Inner Layer 1 element thick Size factor of 4 for transitional layer

Training Manual May 15, 2001 Inventory # Alternate Mesh

Training Manual May 15, 2001 Inventory # Free Meshing - Quads Smartsizing is available Settings!

Training Manual May 15, 2001 Inventory # Circle (r=10) - Smartsize = 6 (Default - no esize)

Training Manual May 15, 2001 Inventory # Circle (R=10) - Smartsize = 1 (Finest) But this has four elements with included angles near 180 o

Training Manual May 15, 2001 Inventory # Adjustments Prep7 > Checking Ctrls > Shape Checking: CHANGE SETTINGS To use this feature, one must temporarily redefine element as a shell 63….

Training Manual May 15, 2001 Inventory # With 150 degrees specified

Training Manual May 15, 2001 Inventory # More Quad Free Meshing Half Circle : r = 10 Esize: 0.5 Smartsize : Default (6)

Training Manual May 15, 2001 Inventory # Mesh Refinement Convenient when mesh is NOT mapped Take the previous mesh and do a minimum refinement at the outer edge…. Choose Refine “at Lines” Click Refine The Picker Appears (then pick lines) Generally use minimum refinement in the resulting dialog box...

Training Manual May 15, 2001 Inventory # Resulting refinement...

Training Manual May 15, 2001 Inventory # Mesh Tool and Transition elements Another pipe cross section –Use two cylinders, one solid and one hollow…. –Glue them together –Further operation necessary to control radial spacing

Training Manual May 15, 2001 Inventory # Preparation Rotate the working plane 90 about the X axis and divide the two volumes into four. Add the lines together as shown (picture shows only the front lines merged)

Training Manual May 15, 2001 Inventory # Some line sizing Set the four azimuthal lines to 20 divisions apiece. In the radial direction, use 15 elements with a spacing ratio of 4. Flip the lines if necessary to get small elements near the outer edge.

Training Manual May 15, 2001 Inventory # The Cross section Using the mesh tool, mesh the outer regions with a mapped quadrilateral mesh Mesh the inner two areas with a free triangle mesh

Training Manual May 15, 2001 Inventory # Sweeping Set the number of divisions (and ratio) in the axial direction and then sweep the mesh… It is best to combine the lines and copy the line divisions to the back areas before doing the sweeping. You may allow ANSYS to choose the source and target areas.

Training Manual May 15, 2001 Inventory # The Result Quadrilaterals > Hexahedrals Triangles > Wedges

Training Manual May 15, 2001 Inventory # Transition Elements: More In this case it is possible to map mesh hexahedrals directly in the two outer volumes. The inner volumes could then be meshed with tetrahedral elements. Pyramid elements would be automatically created to provide the transition between the hexahedral and tetrahedral faces. The extrusion of the cross section involving wedges is probably preferable if long aspect ratio elements are to be created. (I.e. the pipe is long….)

Training Manual May 15, 2001 Inventory # Three Dimensional Meshing Intersection of Two Pipes The World Itself is quite three - dimensional In this Example two intersecting cylinders are created –Large annular cylinder –Smaller inlet region Goal: Mesh each cylinder with only Hexahedral elements Techniques illustrated –Solid Modeling Boolean Operations –Sweeping process Display the grid of the working plane. Set the working plane to a spacing of 1.0, a snap increment of 1.0, and have it extend 10 units in all directions

Training Manual May 15, 2001 Inventory # Step 1 : Create The Annular Cylinder Choose the isometric viewInner Radius is 3 Outer radius is 7 Stretch out from z = 0 to some distance such as z=50.. (“back up” the view as necessary …..) The Result…

Training Manual May 15, 2001 Inventory # Step 2: Add the Inlet 1 - Move working plane to 0,0,4. –It is convenient to align with the global cartesian axes first…. 2 - Rotate WP +90 about Y axis 3 - Create Solid cylinder with center y=5 units up from origin of working plane, stretch to radius of 2 and then pull to local z = 15

Training Manual May 15, 2001 Inventory # Result of Step 2….. At this point, the two cylinders occupy some of the same volume. The overlap must be eliminated.

Training Manual May 15, 2001 Inventory # Step 3: Split the Small Inlet Preprocessor> (Modeling) Operate>Divide> Volume by Area Pick Volume (OK) Pick Area (OK) Note when Using Picker: Keep depressed until correct item is highlighted The Inlet cylinder is being trimmed by the surface of the middle cylinder

Training Manual May 15, 2001 Inventory # Result of Division Adjust the display: –Colors from Utility Menu > Plot Ctrls > Numbering… (turn on volume numbers) –Change view via Utility Menu > Device Options: Vector Mode –Plot Volumes

Training Manual May 15, 2001 Inventory # Step 4: Delete the Extra Volume Preprocessor >(Modeling) Delete> Volumes and Below…. Volume 2 has been replaced by Volumes 3 and 4. The volume inside the big cylinder is now deleted. Pick the one shown and OK Note that from revision to revision, changes in the way boolean operations are performed may change entity numbering schemes...

Training Manual May 15, 2001 Inventory # Geometry Modifications Divide the annular cylinder into two cylinders: –Move the working plane to z = 8 (Step 5) –This enables meshing most of the annular cylinder with a mapped mesh –Divide the resulting two annular cylinders at y=0 into a top half and a bottom half (Step 6) Using the area of the inlet which projects onto the surface of the annular cylinder, make a volume which extends back through the cylinder (Step 7) Overlap this volume with the cylinder and the Inlet (Step 8) Delete the resulting extra volume (Volumes and Below) (Step 8) Details of performing these steps follows…..

Training Manual May 15, 2001 Inventory # Step 5: Divide Cylinder Realign working plane (WP) with global cartesian coordinate system and then offset to 0,0,8. Then divide the Annular Cylinder by the working plane

Training Manual May 15, 2001 Inventory # Step 6: Divide the Two annular cylinders Rotate WP 90Deg about X axis Divide both new cylinders by WP. Result: 5 volumes Turn off wireframe

Training Manual May 15, 2001 Inventory # Step 7: Make Volume by Projecting Area through Cylinder Preprocessor >Operate > Extrude > -Areas- along Normal.. Choose area where the inlet cylinder has been split in two (use isometric view…) Make sure to use a negative value, making sure it is enough to penetrate the annular cylinder completely

Training Manual May 15, 2001 Inventory # Solid model has now been properly connected Step 8: Clean up the Volumes OVERLAP the two Volumes highlighted Delete the “extra” volume (and below)

Training Manual May 15, 2001 Inventory # The Four Volumes Near the Intersection This is the region of interest…. The remainder of the annular cylinder is left to the student ! There should be 6 volumes all told.

Training Manual May 15, 2001 Inventory # Step 9: Line Combinations Select the Two Annular volumes near the intersection Add lines (LCOMB) - delete existing lines (Operate > Add) Generally, it will be best to combine the lines to make 180 degree sections where ever two 90m degree segments occur.

Training Manual May 15, 2001 Inventory # Step 10: Line Divisions Mesh divisions - Annular Cylinder (Meshtool-Lines-Set) –20 Azimuthal –14 Axial –10 Radial Before Meshing Define Element types 2D and 3D –63,141

Training Manual May 15, 2001 Inventory # Step 11: Mesh sweeping Source Area Target Area –Larger one is source Set ESIZE 0.4 First Mesh the Source Area, then perform sweep

Training Manual May 15, 2001 Inventory # Esize 0.4 Pick larger area as Source to ensure proper element size… Target Source Second Sweep

Training Manual May 15, 2001 Inventory # Sweeping Through Annular Volumes.. Meshtool Select –Volume –Source Area –Target Area Options Box Available It is possible to mesh the target area first to see what mesh will be extruded. It is later deleted.

Training Manual May 15, 2001 Inventory # Resulting mesh patterns Now the surface of the “plug” will be used to sweep through the inlet volume Q2

Training Manual May 15, 2001 Inventory # These two areas must be mapped meshed before the sweeping operation… Set number of divisions along cylinder to 18. (In some cases, it is not necessary to mesh the side areas…) Step 12: Mesh Division for Small Inlet ….

Training Manual May 15, 2001 Inventory # Step 13: Mesh via Pick Corners... The mapped mesh is created through the Mesh Tool - “Pick Corners” The same four corners for each of the two areas:

Training Manual May 15, 2001 Inventory # Surface Mesh of the Inlet A 2D non-planar element type such as Shell63 should be defined so that a surface mesh can be created. Resulting surface Mesh

Training Manual May 15, 2001 Inventory # Step 14: Mesh Inlet via Sweep Use Option to Clear Areas afterward Meshtool –Sweep –Hex/Wedge –Auto Pick In this case, ANSYS can automatically pick the source and target areas…..

Training Manual May 15, 2001 Inventory # Resulting Mesh So Far !!!

Training Manual May 15, 2001 Inventory # The Underside The line divisions have already been done….

Training Manual May 15, 2001 Inventory # Voila!!

Training Manual May 15, 2001 Inventory # Notes The meshing of the other two volumes of the annular area is straightforward and is left to the student… This mesh can now easily be used for a mixing analysis following the application of the appropriate solid model boundary conditions. The “the Back End” of the annular cylinder can be made an inlet or a wall, and a velocity applied to the small inlet… Challenge to the User –Mesh the same configuration with a combination of hexahedral and tetrahedral elements….