Computer Aided Thermal Computer Aided Thermal Fluid AnalysisFluid Analysis

Lecture 3Lecture 3

Dr. Ming-Jyh ChernDr. Ming-Jyh Chern

ME NTUSTME NTUST

Road Map for TodayRoad Map for Today

• Mesh CreationMesh Creation

• Basic conceptsBasic concepts

• Meshing techniqueMeshing technique

• User Guide Chapter 3User Guide Chapter 3

• Methodology Chapter 3Methodology Chapter 3

Spatial Description and VolumSpatial Description and Volume Discretisatione Discretisation• When we decide the When we decide the

flow problem, the flow flow problem, the flow domain has to be domain has to be divided to control divided to control volumesvolumes

• Physical variables are Physical variables are located in those located in those control volumes. control volumes.

Solution DomainSolution Domain

• The solution domain has to be bounded.The solution domain has to be bounded.• Four types of boundariesFour types of boundaries

1.1. Physical boundaries – walls or solid obstacles which Physical boundaries – walls or solid obstacles which are used to confine the flow physically. are used to confine the flow physically.

2.2. Symmetry boundaries – axes or planes beyond which Symmetry boundaries – axes or planes beyond which the flow patterns become a mirror image of itself.the flow patterns become a mirror image of itself.

3.3. Cyclic boundaries – surfaces beyond which the flow Cyclic boundaries – surfaces beyond which the flow patterns repeat itself in a cycle. patterns repeat itself in a cycle.

4.4. Notional boundaries – these are non-physical surfaces Notional boundaries – these are non-physical surfaces that serve to ‘close-off’ the solution domain in regions that serve to ‘close-off’ the solution domain in regions not covered by the other types of boundaries, e.g. not covered by the other types of boundaries, e.g. inlet and outlet boundaries.inlet and outlet boundaries.

Mesh DefinitionMesh Definition

• Active or inactive cActive or inactive cellsells

• Structure or unstruStructure or unstructure mesh.cture mesh.

Mesh Spacing Mesh Spacing ConsiderationsConsiderations

• Accuracy – determined by mesh Accuracy – determined by mesh density and distortiondensity and distortion

• Numerical stability – this is a strong Numerical stability – this is a strong function of mesh distortion.function of mesh distortion.

• Cost – It relies on the mesh density Cost – It relies on the mesh density and distortion either and influences and distortion either and influences speed of convergence and CPU speed of convergence and CPU time. time.

Mesh DistortionMesh Distortion

• Aspect ratio – Aspect ratio – bb//aa shall be close to unity as shall be close to unity as possible.possible.

• Internal angle – Internal angle – shall be close to 90 shall be close to 90oo

• Warp angle – Warp angle – shall be close to 0 shall be close to 0oo

Basic Concepts IBasic Concepts I

• Vertex – A point in 3D space, defined by a coordinate Vertex – A point in 3D space, defined by a coordinate triplet and possessing an index for identification. triplet and possessing an index for identification.

• Cell – A cell consists of vertices and a basic element for Cell – A cell consists of vertices and a basic element for computation. It is a three-dimensional object defined by computation. It is a three-dimensional object defined by vertices. vertices.

Types of Cells ITypes of Cells I

Types of Cells IITypes of Cells II

Basic Concepts IIBasic Concepts II

• Shell – A shell is a 2D cell which is only for mesh geShell – A shell is a 2D cell which is only for mesh generation. A shell is not involved in computation.neration. A shell is not involved in computation.

• Spline – a smooth curve defined by vertices along iSpline – a smooth curve defined by vertices along its length.ts length.

Basic Concepts IIIBasic Concepts III

• Patch – A patcPatch – A patch consists of sh consists of shells and is nohells and is not involved in ct involved in computation.omputation.

• Block – defineBlock – defined by 8 splines.d by 8 splines.

Meshing TechniquesMeshing Techniques

• The extrusion methodThe extrusion method

• The cell-layer methodThe cell-layer method

• The multi-block methodThe multi-block method

• The data import methodThe data import method

The Extrusion Method IThe Extrusion Method I

• This technique permits the extrusion This technique permits the extrusion of a three-dimensional mesh from of a three-dimensional mesh from an existing surface or patch.an existing surface or patch.

The Extrusion Method IIThe Extrusion Method II

• A surface or patch has to be established first.A surface or patch has to be established first.

The Extrusion Method IIIThe Extrusion Method III

• Subsequently, a three-dimensional mesh block can be Subsequently, a three-dimensional mesh block can be extruded from a surface along a specified axis.extruded from a surface along a specified axis.

Cell-layer ApproachCell-layer Approach• It is the bottom-up approaches that builds the solution domain up from It is the bottom-up approaches that builds the solution domain up from

its constituent cells, layer by layer. its constituent cells, layer by layer. • First step-Creation of verticesFirst step-Creation of vertices• Second step-Attachment of cellsSecond step-Attachment of cells• The user is free to create a complete vertex latticework first and define The user is free to create a complete vertex latticework first and define

cells afterwards, or define cells as soon as sufficient vertices are cells afterwards, or define cells as soon as sufficient vertices are created.created.

Multi-block ApproachMulti-block Approach• This is a top-down approach that requires sub-This is a top-down approach that requires sub-

division of solution domain into a series of division of solution domain into a series of shaped blocks.shaped blocks.

• Sub-division of each block into individual cells in Sub-division of each block into individual cells in an automatic fashion is possible. an automatic fashion is possible.

The data import methodThe data import method• This relies on an external CAD/CAE to perform basic geometric modelling This relies on an external CAD/CAE to perform basic geometric modelling

or mesh operation.or mesh operation.• The import data can the two basic forms: 1.entire meshes – that have beThe import data can the two basic forms: 1.entire meshes – that have be

en generated by an external CAD/CAE system such as SAMM, ICEM, and eten generated by an external CAD/CAE system such as SAMM, ICEM, and etc. 2.geometrical definitions of models – in the form of surfaces, splines, c. 2.geometrical definitions of models – in the form of surfaces, splines, and points defined by other CAD packages in IGES or VDA format.and points defined by other CAD packages in IGES or VDA format.

The data import methodThe data import method

Coordinate SystemsCoordinate Systems

• Global systemsGlobal systems– Cartesian Cartesian – CylindricalCylindrical– SphericalSpherical

• Local systemsLocal systems– CartesianCartesian– CylindricalCylindrical– SphericalSpherical– ToroidalToroidal

Vertices-Single VertexVertices-Single Vertex

Vertices-Vertex setVertices-Vertex set

Vertices-Vertex setVertices-Vertex set

Vertices-VfillVertices-Vfill

Vertices-VreflectVertices-Vreflect

Vertices-VcenterVertices-Vcenter

Vertices-GUIVertices-GUI

SplineSpline

Spline-CreationSpline-Creation

Spline-GenerationSpline-Generation

Spline-GUISpline-GUI

Homework 1Homework 1

• Purpose: practice commands regarding vertex Purpose: practice commands regarding vertex and spline.and spline.

• ContentsContents– Generate vertices along a triangle and splines connGenerate vertices along a triangle and splines conn

ecting those vertices. There must be more than onecting those vertices. There must be more than one vertex at each edge of the triangle. e vertex at each edge of the triangle.

– Generate vertices along two concentric circles and Generate vertices along two concentric circles and two splines connecting those circles.two splines connecting those circles.

– Generate vertices along an object which you design Generate vertices along an object which you design by yourself and splines connecting them. by yourself and splines connecting them.

• Due date: 29 March 2007Due date: 29 March 2007

CellCell

Cell-TypesCell-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.

Cell-Computational CellsCell-Computational Cells

Cell-Visualization CellsCell-Visualization Cells

Cell-DefinitionCell-Definition

Cell-Generation ICell-Generation I

Cell-Generation IICell-Generation II

Cell-OrientationCell-Orientation

Cell-GUICell-GUI

Multi-Block ApproachMulti-Block Approach

Multi-Block Approach-Mesh Multi-Block Approach-Mesh BlockBlock

Multi-Block Approach-Multi Multi-Block Approach-Multi BlockBlock

Multi-Block Approach-Multi Multi-Block Approach-Multi Block GUIBlock GUI

Tutorial I – 2-D FlowTutorial I – 2-D Flow

Command - vc3dCommand - vc3d