1. Computer Aided Thermal Fluid Analysis Lecture 3 Dr. Ming-Jyh Chern ME NTUST

2. Road Map for Today Mesh Creation Mesh Creation Basic concepts Basic concepts Meshing technique Meshing technique User Guide Chapter 3 User Guide Chapter 3 Methodology Chapter 3 Methodology Chapter 3

3. Spatial Description and Volume Discretisation When we decide the flow problem, the flow domain has to be divided to control volumes When we decide the flow problem, the flow domain has to be divided to control volumes Physical variables are located in those control volumes. Physical variables are located in those control volumes.

4. Solution Domain The solution domain has to be bounded. The solution domain has to be bounded. Four types of boundaries Four types of boundaries 1.Physical boundaries – walls or solid obstacles which are used to confine the flow physically. 2.Symmetry boundaries – axes or planes beyond which the flow patterns become a mirror image of itself. 3.Cyclic boundaries – surfaces beyond which the flow patterns repeat itself in a cycle. 4.Notional boundaries – these are non-physical surfaces that serve to ‘close-off’ the solution domain in regions not covered by the other types of boundaries, e.g. inlet and outlet boundaries.

5. Mesh Definition Active or inactive cells Active or inactive cells Structure or unstructure mesh. Structure or unstructure mesh.

6. Mesh Spacing Considerations Accuracy – determined by mesh density and distortion Accuracy – determined by mesh density and distortion Numerical stability – this is a strong function of mesh distortion. Numerical stability – this is a strong function of mesh distortion. Cost – It relies on the mesh density and distortion either and influences speed of convergence and CPU time. Cost – It relies on the mesh density and distortion either and influences speed of convergence and CPU time.

7. Mesh Distortion Aspect ratio – b / a shall be close to unity as possible. Aspect ratio – b / a shall be close to unity as possible. Internal angle –  shall be close to 90 o Internal angle –  shall be close to 90 o Warp angle –  shall be close to 0 o Warp angle –  shall be close to 0 o

8. Basic Concepts I Vertex – A point in 3D space, defined by a coordinate triplet and possessing an index for identification. Vertex – A point in 3D space, defined by a coordinate triplet and possessing an index for identification. Cell – A cell consists of vertices and a basic element for computation. It is a three-dimensional object defined by vertices. Cell – A cell consists of vertices and a basic element for computation. It is a three-dimensional object defined by vertices.

9. Types of Cells I

10. Types of Cells II

11. Basic Concepts II Shell – A shell is a 2D cell which is only for mesh generation. A shell is not involved in computation. Shell – A shell is a 2D cell which is only for mesh generation. A shell is not involved in computation. Spline – a smooth curve defined by vertices along its length. Spline – a smooth curve defined by vertices along its length.

12. Basic Concepts III Patch – A patch consists of shells and is not involved in computation. Patch – A patch consists of shells and is not involved in computation. Block – defined by 8 splines. Block – defined by 8 splines.

13. Meshing Techniques The extrusion method The extrusion method The cell-layer method The cell-layer method The multi-block method The multi-block method The data import method The data import method

14. The Extrusion Method I This technique permits the extrusion of a three-dimensional mesh from an existing surface or patch. This technique permits the extrusion of a three-dimensional mesh from an existing surface or patch.

15. The Extrusion Method II A surface or patch has to be established first. A surface or patch has to be established first.

16. The Extrusion Method III Subsequently, a three-dimensional mesh block can be extruded from a surface along a specified axis. Subsequently, a three-dimensional mesh block can be extruded from a surface along a specified axis.

17. Cell-layer Approach It is the bottom-up approaches that builds the solution domain up from its constituent cells, layer by layer. It is the bottom-up approaches that builds the solution domain up from its constituent cells, layer by layer. First step-Creation of vertices First step-Creation of vertices Second step-Attachment of cells Second step-Attachment of cells The user is free to create a complete vertex latticework first and define cells afterwards, or define cells as soon as sufficient vertices are created. The user is free to create a complete vertex latticework first and define cells afterwards, or define cells as soon as sufficient vertices are created.

18. Multi-block Approach This is a top-down approach that requires sub-division of solution domain into a series of shaped blocks. This is a top-down approach that requires sub-division of solution domain into a series of shaped blocks. Sub-division of each block into individual cells in an automatic fashion is possible. Sub-division of each block into individual cells in an automatic fashion is possible.

19. The data import method This relies on an external CAD/CAE to perform basic geometric modelling or mesh operation. This relies on an external CAD/CAE to perform basic geometric modelling or mesh operation. The import data can the two basic forms: 1.entire meshes – that have been generated by an external CAD/CAE system such as SAMM, ICEM, and etc. 2.geometrical definitions of models – in the form of surfaces, splines, and points defined by other CAD packages in IGES or VDA format. The import data can the two basic forms: 1.entire meshes – that have been generated by an external CAD/CAE system such as SAMM, ICEM, and etc. 2.geometrical definitions of models – in the form of surfaces, splines, and points defined by other CAD packages in IGES or VDA format.

20. The data import method

21. Coordinate Systems Global systems Global systems – Cartesian – Cylindrical – Spherical Local systems Local systems – Cartesian – Cylindrical – Spherical – Toroidal

22. Vertices-Single Vertex

23. Vertices-Vertex set

25. Vertices-Vfill

26. Vertices-Vreflect

27. Vertices-Vcenter

28. Vertices-GUI

29. Spline

30. Spline-Creation

31. Spline-Generation

32. Spline-GUI

33. Homework 1 Purpose: practice commands regarding vertex and spline. Purpose: practice commands regarding vertex and spline. Contents Contents –Generate vertices along a triangle and splines connecting those vertices. There must be more than one vertex at each edge of the triangle. –Generate vertices along two concentric circles and two splines connecting those circles. –Generate vertices along an object which you design by yourself and splines connecting them. Due date: 29 March 2007 Due date: 29 March 2007

34. Cell

35. Cell-Types Computational Cells – Those cells are really involved in computation. Solutions are stored at those cells. Visualization Cells – Those cells are not involved in computation. They are utilized to show boundaries, baffles, and etc.

36. Cell-Computational Cells

37. Cell-Visualization Cells

38. Cell-Definition

39. Cell-Generation I

40. Cell-Generation II

41. Cell-Orientation

42. Cell-GUI

43. Multi-Block Approach

44. Multi-Block Approach- Mesh Block

45. Multi-Block Approach- Multi Block

46. Multi-Block Approach- Multi Block GUI

47. Tutorial I – 2-D Flow

48. Command - vc3d