gridz_manual

GridZTM

Version 4.5

Zeus Numerix Pvt Ltd

March 2009

i

DISCLAIMER OF WARRANTY AND NOTICE OF COPYRIGHT

GridZTM - Copyright c© 2005 Zeus Numerix Pvt Ltd. All Rights Reserved worldwide. Nopart of GridZTM software or documentation may be reproduced, transmitted, stored in a retrievalsystem, or translated in any form without the express written permission of Zeus Numerix Pvt Ltd.

This software contains materials that are Copyright c© Zeus Numerix Pvt Ltd, IIT BombayCampus, Powai, Mumbai 400076, India. All rights reserved. GridZTM computer software is copy-righted and protected under the provisions of the Indian Copyright Act, 1957, 1994.

This Zeus Numerix Pvt Ltd software product (GridZTM) and documentation are furnishedby Zeus Numerix Pvt Ltd, under a Zeus Numerix Pvt Ltd License Agreement that contains pro-visions concerning on-disclosure, copying, length and nature of use, warranties, disclaimers andremedies, and other provisions. The software GridZTM may be used or copied only in accordancewith the terms of that License Agreement.

GridZTM should only be used by qualified persons. The determination as to who is qualifiedto use GridZTM is the obligation of the License under the License Agreement.

EXCEPT AS PROVIDED IN THE LICENSE AGREEMENT, NEITHER ZEUS NUMERIXPVT LTD, NOR THE DISTRIBUTOR SHALL BE LIABLE FOR THE NEGLIGENT PREPA-RATION OF GridZTM, OR USER’S MANUAL; OR FOR ANY TECHNICAL, EDITORIAL,OROTHER ERRORS OR OMISSIONS WHICH THE USER’S MANUAL MIGHT CONTAIN. ZEUSNUMERIX PVT LTD SHALL NOT BE LIABLE FOR INCIDENTAL, CONSEQUENTIAL,COMPENSATORY OR EXEMPLARY DAMAGES RESULTING FROM ANY SUCH NEGLI-GENT PREPARATION OR ERROR.

Zeus Numerix Pvt Ltd does not provide any warranty for GridZTM grid generator software.ZEUS NUMERIX MAKES NO PRESENTATIONS OR WARRANTIES WITH RESPECT

TO THE CONTENTS OF GridZTM - THE GRID GENERATION SOFTWARE AND DOCU-MENTATION. ZEUS NUMERIX PVT LTD SPECIALLY DISCLAIMS ANY IMPLIED WAR-RANTIES OF FITNESS OF GridZTM SOFTWARE FOR ANY PARTICULAR PURPOSE.FURTHER, ZEUS NUMERIX PVT LTD RESERVES THE RIGHT TO MAKE CHANGESFROM TIME TO TIME IN THE CONTENTS OF GridZTM SOFTWARE WITHOUT OBLIGA-TION OF ZEUS NUMERIX PVT LTD TO NOTIFY ANY PERSONS OR ORGANIZATIONSOF SUCH REVISIONS OR CHANGES.

Since GridZTM is complex and may not be entirely free from errors, we advice you to verifythe data produced by GridZTM.

TRADEMARKSCFDExpertTM,GridZTM,FlowZTM CFDTutorTM, ViewZTM, ShapeZTM, CEMExpertTM, CFDManagerTM

Zeus Numerix Pvt Ltd

Copyright c© 2006 by Zeus Numerix Pvt Ltd as an unpublished work. Proprietary data-unauthorized use, distribution, or duplication, is prohibited. All rights reserved.

Contents

1 Introduction to GridZTM 1

1.1 System Requirement and Installation Information . . . . . . . . . . . . . . . . . . 3

1.1.1 Platform Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.2 System Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1.3 Graphics Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1.4 GridZ - Linux Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 About this Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 GridZ 7

2.1 Organization of Screen and Graphics User Interface (GUI) . . . . . . . . . . . . . . 7

2.2 Using the Mouse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Using the Keyboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Changing User interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.5 Menu Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6 Toolbar Shortcuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.6.1 View Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.6.2 Geometry Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.6.3 Grid Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.6.4 2D-Block Button . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.6.5 3D-Block Button . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.6.6 Display Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.6.7 Edit Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 File Formats 19

3.1 GridZ (native) File Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Reading Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Writing Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Geometry 25

4.1 Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Point Cloud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 Line Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.4 Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.5 Piecewise Linear Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.6 NURBS Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.7 Piecewise BiLinear Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.8 NURBS Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

iii

iv CONTENTS

5 Block 35

5.1 2D Multiblock: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2 3D Multiblock: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2.1 3D MULTIBLOCK TOOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2.2 Examples: Topology, Mapping and Clustering . . . . . . . . . . . . . . . . . 51

6 Grid 59

6.1 1D Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.2 2D Structured . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.3 Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.4 Quadrilateral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.5 Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.6 Polyhedrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.7 Group TRSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.8 Cartesian Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.9 3D Structured . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.10 Surface Structured . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

7 Boundary Condition 69

7.1 Applying Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

7.2 Applying Material Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A Tutorial - Industrial Tank 73

A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

A.2 Creating Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

A.2.1 Barrel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

A.2.2 Dome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

A.2.3 Fillet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

A.2.4 Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

A.3 Volume Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

A.3.1 Creating Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

A.3.2 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

B Grid Tutorial: Generic Missile 95

B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

B.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

B.2.1 Blending Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

B.2.2 Nose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

B.2.3 Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

B.3 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

B.4 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

B.5 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

C Tutorial - Ahmed body 111

C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

C.2 Ahmed body Front Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

C.2.1 Front - Lower PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

C.2.2 Front - Upper PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

CONTENTS v

C.2.3 Front - Left PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

C.2.4 Front - Right PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

C.2.5 Front - Center PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

C.3 Ahmed body Mid-body Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

C.3.1 Mid-body 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

C.3.2 Mid-body 2- Lower PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

C.3.3 Mid-body 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

C.4 Ahmed body Rear Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

C.4.1 Rear - Lower PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

C.4.2 Rear - Upper PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

C.4.3 Rear - Left PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

C.4.4 Rear - Right PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

C.4.5 Rear - Center PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

C.5 Ahmed body Complete Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

C.6 Volume Grid for Ahmed body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

C.6.1 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

C.6.2 Mapping the faces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

C.6.3 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

D Tutorial - Geometric Funnel 141

D.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

D.2 Geometry - Creating the Central Part (AEGDBFHC) . . . . . . . . . . . . . . . . 142

D.2.1 Creating BFHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

D.2.2 Creating AEGD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

D.3 Creating the Upper and Lower Parts . . . . . . . . . . . . . . . . . . . . . . . . . . 146

D.3.1 Creating KL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

D.3.2 Scaling the PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

D.3.3 Creating OR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

D.4 Creating RT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

D.4.1 Creating the Lower Surface (OKLMTRO) . . . . . . . . . . . . . . . . . . . 150

D.4.2 Creating the Upper Surface (PJINSQP) . . . . . . . . . . . . . . . . . . . . 151

D.5 Creating the Surface (OPQSTRO) . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

D.6 Volume Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

D.6.1 Creation of Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

D.6.2 Mapping of faces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

E Tutorial - Intersecting Pipes 161

E.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

E.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

E.2.1 Semi-Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

E.2.2 Creating Carpet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

E.2.3 Carpeting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

E.2.4 Carpet Editing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

E.3 Volume Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

E.3.1 Create Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

E.3.2 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

vi CONTENTS

F Tutorial - 2D Grid Smoothening for a Blower 175

F.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

F.2 Time Required . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

F.3 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

F.4 2D Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

F.4.1 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

F.4.2 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

F.4.3 Smoothening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

G Tutorial: 3D Grid Smoothening in Dumbell 187

G.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

G.2 Time Required . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

G.3 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

G.3.1 Lobes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

G.3.2 Carpeting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

G.3.3 Central Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

G.4 Volume Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

G.5 Smoothening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

H Tutorial - Airfoil 201

H.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

H.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

H.3 Creating Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

H.4 Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

I Tutorial - Reusable Launch Vehicle (RLV) 207

I.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

I.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

I.2.1 Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

I.2.2 Creation of wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

I.2.3 Aft Wing center fin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

I.2.4 Completing Geometry of Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . 210

I.3 Volume Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

I.3.1 Creation of Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

J Tutorial: 1(a) Structured to Unstructured Voronoi Polygon 223

J.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

J.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

J.3 Block Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

J.4 Creating PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

J.5 Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

J.6 Voronoi Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

J.7 Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

K Tutorial: 1(b) Structured to Unstructured Voronoi Polygon with Clustering 229

K.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

K.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

K.3 Block Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

CONTENTS vii

K.4 Clustering in Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231K.5 Creating PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231K.6 Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232K.7 Voronoi Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232K.8 Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

L Tutorial: 2(a) Structured to Unstructured Voronoi Polygon 235L.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235L.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235L.3 Block Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236L.4 Creating Boundary PLCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236L.5 Delaunay Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237L.6 Voronoi Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238L.7 Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

M Tutorial: 2(b)Structured to Unstructured Voronoi Polygon with Clustering 241M.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241M.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241M.3 Block Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242M.4 Clustering in Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242M.5 Creating Boundary PLCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243M.6 Delaunay Triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243M.7 Voronoi Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244M.8 Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

N Tutorial: 3(a) 3D VOLUME GRID 247N.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247N.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247N.3 Block Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247N.4 Creating Boundary PLCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248N.5 Delaunay Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

O Menu 261

P Command List 271

viii CONTENTS

Chapter 1

Introduction to GridZTM

Welcome to GridZTM ! You now own one of the most robust and most effective grid genera-tor software available for industry - and you’ve just taken a big step towards creatings gridz forexecuting complex CFD problems. GridZTM is designed and developed by Zeus Numerix PvtLtd. Zeus Numerix Pvt.Ltd. is being nurtured by IIT Bombay under its Technology BusinessIncubation Plan.

Zeus Numerix has developed numerous products in the field of Computational Fluid Dynam-ics, Electromagnetics, Structural Analysis and Corrosion. A modular approach was undertakenduring the design phase so as to maximise the utility factor. While separate modules take care ofthe pre/post processing and solving, they are combined together to form the Expert suites, idealfor a complete end-to-end solution.

The softwares have been categorized according to their areas of application:CFD : CFDExpertTM suit consists of GridZTM - the pre-processor, FlowZTM - the solver andViewZTM - the post-processorCEM : CEMExpertTM suit consists of GridZTM, EMWaveZ and ViewZTM

Corrosion : CorrosionExpertTM suit consists of GridZTM, ElfZ and ViewZTM

CFDExpertTM is an advanced multi-purpose CFD software for engineering design. It has end-to-end capabilities from design to analysis. It provides accurate, fast, robust and efficient CFDsolutions. CFDExpert enables engineers to build virtual protoytpes and simulate the performanceof proposed and existing designs,thereby allowing them to improve design quality in a cost effec-tive and time saving manner.

CFDExpert is a combination of three modules:GridZ , the grid generation module.FlowZ , the solver module.ViewZ , the post-processing module.

Each module of CFD expert is a stand-alone module and is available separately. CFDExpertsolves a problem using these modules successively.

1

2 CHAPTER 1. INTRODUCTION TO GRIDZTM

CFD Technology with a difference

CFDExpertTM is a geometric modeler-cum-grid generation system with a solver and post-processor. It is a confluent of various technologies such as computer aided geometric design,computational geometry and computer graphics, structured and unstructured grid generation al-gorithims. It includes modules for CFD analysis and postprocessing. The package not only helpsin preliminary designs but also gives a continuous support for detailed design as it progresses fromlow fidelity to high fidelity optimization.

Executes Complex CFD problems easily

CFDExpertTM is extremely easy to use. It has all the capabilities that an engineer may wishfor to solve high fidelity problems. It has been extensively tested and many in-house projectsinvolving creeping flows, high speed flows, multiphase flows, heat transfer, rotating flows, etc.have been carried out using this package. The packaged has a wide applicability and can be easilycustomized to suit industrial needs.

A ‘Versatile’ CFD software

CFDExpertTM is very versatile and has many entry and exit points. You can design the ge-ometry for a problem and carry out a CFD analysis using CFDExpertTM and can independentlyproduce post-processed data with the help of this package. Alternately, you can read a grid as astandard file, and with a couple of interactive changes, copy the grid to an alternate solver. Thisfeature is important as it allows you to use CFDExpertTM either fully or in parts and by usingyour own in-house development team to carry out different parts of a job, you will save time andcut short the product development cycle.

Imperfect Geometry Perfected

CFDExpertTM allows import of CAD data in a variety of file formats from almost all ma-jor CAD packages. This ensures that your time is not spent in recreating geometry. Also, flowdomains can be created quickly and accurately from geometry definitions. CAD data files arecurrently widely used for generating geometries/ grids and since CAD data often needs correctionsdue to imperfections in the geometry,CFDExpertTM comes with a suit of repair tools to correctthese imperfections. In the design stage, you may wish to create a geometry in the absence ofCAD data, once again CFDExpertTM being a full-fledged surface modeler will help you create anygeometry quickly.

Grid Generation Mastered!

Quality grids is half the job done in CFD terms! CFDExpertTM is a master at grid generation.The Grid Module in CFDExpertTM provides both structured and unstructured grid generationoptions. You can create multi-block structured grids for high fidelity simulations or unstructuredgrids for simulations that save manpower. The CFDExpertTM multi-block structured grid gener-ation is probably the best grid generator that you may have ever come across. It has been builtpainstakingly over several man years of R & D and it lets you produce thousands of 2D and 3Dblocks and millions of grids points within hours. It also ensures that the complex topology ofyour flow domain is captured correctly. Several grid smoothening and clustering scheme options

1.1. SYSTEM REQUIREMENT AND INSTALLATION INFORMATION 3

make these grids ideal for high fidelity simulations. The mesh quality display is supported with avariety of mesh quality parameters.

Several methods of unstructured grids are available for you to create triangles in 2D, sur-face and in 3D. The conversion of triangles to quadrilaterals or polygons or direct quadrilateralgeneration is built into the unstructured grid generation module. Half-edge data structure imple-mentation lets you execute any editing operation with unbelievable speeds.

High-speed Robust Solver!

Solution module of CFDExpertTM caters to practicing engineers’ generic schemes with thehelp of generic numerical schemes that act like a block box capable of working for a large rangeof Reynolds numbers, Mach numbers and Turbulence models on one hand. On the other hand,it offers numerical schemes through its control file so that a simulation can be configured forhigh fidelity simulations by serious users. A variety of physical and chemical phenomena can besimulated simply by configuring the control file. The solver is fully compatible with CGNS (CFDGeneral Notations System) file format which is an ISO file format.

The simulation algorithms have been optimized for speed and accuracy. The code lets youexploit a multi-CPU machine or a networked UNIX / LINUX machines.

Pictures worth a Thousand Words!

CFDExpertTM post-processing capabilities support both hardware / software rendering as wellas a complete range of tools for visualizing CFD results. The tools available include 2D, surfaceand volume stream lines, streak lines and path lines. The surface of a domain can be shaded withcolour representing the physical property, through a highly useful plot that industry normallyprefers - for example, ISO surface plots for 2D, surface and volume domains. A novel feature ofthe post-processing part is creating fields by stating the algebraic / differential equations for aflow field in terms of the existing field.

1.1 System Requirement and Installation Information

SYSTEM REQUIREMENT NOTE: Please make sure that you have the necessary system soft-ware and hardware before you buy GridZTM!

1.1.1 Platform Requirement

Platform requirement of GridZTM is tabulated in

Platform CPU / Model Operating SystemWindows Intel / AMD Windows 98, 2000, XpIBM 64 bit RS 6000 AIX 5.1 or neverLinux Intel Linux kernel 2.6 or newerLinux 64 bit Intel / AMD Linux Kernel 2.6 or newerSGI R5k, R8k, R10k Irix 6.5 or newer


1.1.2 System Requirement

GridZTM requires a minimum of 100 MB of Disk space and 512 MB RAM on each machine.

1.1.3 Graphics Requirement

GridZTM requires an OpenGL accelerated card.

1.1.4 GridZ - Linux Installation

1. Log in as Root or Super User.

2. Insert GridZTM CD in the CD-Rom.

3. The CD get mounted automatically if it does not then

4. Use this Command to mount:

mount /media/cdrom

5. Install GridZTM rpm with the command:

rpm -ivh <gridz-rpm-name>

6. After installation, now we need to install the license

7. Copy GenHostid.CFDExpert executable from CD in Home and then run this exe usingCommand

./GenHostid.GridZ

8. Enter Name and Institution Name

9. This will generate a file call zeushostid

10. Send this file to your vendor and he will send you the license file

11. Write to [email protected] for any queries

GridZTM - Windows Installation

1. Log in as administrator,

2. Insert the GridZTM CD into the CDROM,

3. Go to the CDROM drive,

4. Click on executable to install GridZTM,

5. Follow the installation instruction.

1.2. ABOUT THIS MANUAL 5

1.2 About this Manual

This manual is aimed at engineers and scientists intending to use GridZ for their CFD engineeringanalysis. It is assumed that a user has a fundamental knowledge of CFD and is expected to knowthe sequence of execution of major tasks such as:

• Preparation or Importing of CAD geometry

• Generation of multi-block data

• Specification of boundary conditions, initial conditions and other parameters

Chapter 2

GridZ

Overview

2.1 Organization of Screen and Graphics User Interface (GUI)

Interactive usage requires some familiarity of the organization GridZTMGUI. A snap shot of theGridZTMscreen is shown in Fig 2.1.

Figure 2.1: GridZTMVersion 4.5

7

8 CHAPTER 2. GRIDZ

• Main MenuThe Main Menu is placed on top of canvas. The buttons are hierarchically arranged.

• View ButtonsThis is a collection of buttons placed on the top of the canvas (below the Main Menu) tohelp user to view geometry on screen.

• Selection SetThis section is used to Select / Deselect the entities and to show the details of all the entitiesin database as shown in figure. Refer fig: 2.2

Figure 2.2: Details of Selection

– DetailsPress this Button to get the details about that entity.

– Total EntityThis Button is used to get tolal number of entity in database.

– DeleteThis is used to delete the entity which is highlighted in Selection or Deselection Panel

– HideThis is used to Hide the entity which is highlighted in Selection or Deselection Panel

2.2. USING THE MOUSE 9

– Hide OthersThis is used to Hide all the entity which not highlighted in Selection or DeselectionPanel

– ShowThis is used to Show the entity which is highlighted in Selection or Deselection Panel

– Show allThis is used to show the entity in the database

– Set Center Of RotationThis button is user to set the rotation axis with respect to highlighted entity.

• Tool ButtonsThese are a set of buttons placed on the left panel of the canvas for frequently requiredoperations.

• Drawing AreaThis is a large canvas for displaying geometry, grids and post-processed data. It is sur-rounded by scroll bars, which help the user in panning, rotating or magnifying the scene.

• Command Input AreaThis area is used for keyboard input. The input data is always screened for the ranges andvalidity of input before being used. Input of expressions is supported at many importantlevels to reduce the user interaction time.

• Feedback WindowFeedback is located immediately below the input area. It provides essential feedback andguides the user in his operation.

• Pop-up WindowsMany auxiliary windows and buttons pop-up at various levels in GridZTM. Their descriptionwill be given at appropriate places.

2.2 Using the Mouse

A three-mouse button is required while executing GridZTM. The normal convention used is asfollows :

• Movement of Mouse CursorMovement of the mouse cursor in the drawing area or canvas (when no button is pressed)shows the world coordinates in the information bar located immediately on top left cornerof the canvas. When the mouse moves over any one of the buttons on the Toolbar,a briefdescription of these button appears as a Tool tip text.

• Clicking of Mouse Buttons in Drawing AreaLeft button is used for picking up points and vertices.Right button is used for picking (selecting) entities - curves, surfaces, etc.

10 CHAPTER 2. GRIDZ

• Dragging the Mouse Cursor keeping Left Mouse Button PressedPressing the left button pressed and dragging the cursor helps in panning the scene. Sim-ilarly pressing the left button and dragging the scroll bar is used for scrolling a windowor panning, rotating, or scaling a scene on the drawing area, depending upon the optionselected from the ones beside the view buttons.

• Dragging the Mouse Cursor keeping Right Mouse Button PressedDragging the mouse cursor keeping right button pressed helps in zooming the view.

• Dragging the Mouse Cursor keeping Middle Mouse Button PressedThis action is equivalent to rotation of the geometry in the drawing area about some axis.

2.3 Using the Keyboard

GridZTMdoes not use any special keys from keyboard. However, following keys need to be men-tioned:

1. Enter key Press the Enter-key to indicate that feeding data is over.

2. Tab key You can move from one input area to the next, if such an input area is presentedto you.

3. Q key This key is used to exit from a rubberband mode, used for drawing points/curveswith freehand.

4. K key: This key will take you to command line, where you can enter a command to beexecuted. Also, after typing a partial command, use the TAB key to see the possiblecommands. The Command List is given at the end of the User Manual.

Note : Expressions are case sensitive. A white space is not acceptable. A wrong expressionor invalid data is indicated by an error message.

2.4 Changing User interface

A User can change the User Interface according to his requirement. By Dragging the MouseCursor keeping Left Mouse Button Pressed, a user can change the look and feel of the software.User can move Control Panel, ToolBar and Feedback Window. The user can delete it oradd it whenever required. as shown in figure.Refer fig: 2.3

2.5 Menu Buttons

A User is guided through the Menu buttons logically for his/her actions. Only the ‘leaves’ of thetree trigger an action in the menu as shown in Fig 2.4

2.6. TOOLBAR SHORTCUTS 11

Figure 2.3: GUI-change

2.6 Toolbar Shortcuts

2.6.1 View Buttons

1. File Open

2. File Save

3. Set Default View

4. Fit to Window

5. World View

6. Isometric View

7. Zoom In

8. Zoom Out

9. Undo

10. Redo

11. Picking On/Off

12. Show All Points

13. Show Boundary Points

14. Show Directions

15. Display Normals

12 CHAPTER 2. GRIDZ

Figure 2.4: Hierarchy of Menu Buttons

Figure 2.5: View Buttons

16. Geometry Rendering

17. Capture Image

Refer fig: 2.5

2.6.2 Geometry Buttons

Show Geometry Tools as shown in Fig 2.7

Figure 2.6: Geometry Icon

1. Draw Free Points

2. Draw Piecewise Linear Curve (PLC)

3. Draw NURB Curve (BSC)

4. Move Point to New Position

5. Move Entity to New Position

6. Get Distance between 2 Points


Figure 2.7: Geometry Tools

7. Stitch Curve

8. Split Curve

9. Curve Open/Close

10. Reverse Curve

11. Extract Point

12. PLC Equal Arc

2.6.3 Grid Buttons

Show Grid Tools as shown in Fig 2.9

Figure 2.8: Grid Icon

Figure 2.9: Grid Tools

1. Invert Normal

2. Stitch Surface

3. Reset Faces

4. Select Faces

5. Deselect Faces

6. Tag Faces

14 CHAPTER 2. GRIDZ

2.6.4 2D-Block Button

Show 2D-Block Tool as shown in Fig 2.11

Figure 2.10: 2D-Block Icon

Figure 2.11: 2D-Block Tool

1. Sequential Block Traversal

2. Block Traversal Through Edges

3. Block Traversal Around Vertex

4. Edge Traversal

5. Vertex Traversal

6. Show no Grids

7. Show Grids in Current Block

8. Show Grids in All Blocks

9. 2D MB Summery

10. Change Mapping Order

11. Delete Selected 2D Block

12. IJ Traversals

13. Reverse Traversal Direction


Figure 2.12: 3D-Block Icon

Figure 2.13: 3D-Block Tool

2.6.5 3D-Block Button

Show 3D-Block Tool as shown in Fig 2.13

1. Block Traversal

2. Block Traversal Thru Faces

3. Face Traversal

4. Edge Traversal

5. Vertex Traversal

6. IJK TRaversal

7. Show Wireframe

8. Show Current Faces

9. Show Grid Current Block

10. Show All Faces All Blocks

11. Show Volume Grid Current Block

16 CHAPTER 2. GRIDZ

12. Show Volume Grid All Block

13. Show all Mapped Surface

14. Reverse Traversal Direction

15. Show/Hide Mapping Guide Lines

16. Change Mapping Order

17. Show Current All Block

18. Map Face

19. Map Edge

20. Delete Selected Block

21. MultiBlock Summary

2.6.6 Display Buttons

Show Display Tools as shown in Fig 2.15

Figure 2.14: Display Icon

Figure 2.15: Display Tools

1. Front View

2. Back View


3. Top View

4. Bottom View

5. Left Side View

6. Right Side View

7. Show All Points

8. Show Boundary Points

9. Show Direction

10. Display Normals

11. Hidden Line (ON/OFF)

12. Geometry Rendering

2.6.7 Edit Buttons

Show Edit Tools as shown in Fig 2.17

Figure 2.16: Edit Icon

Figure 2.17: Edit Tools

1. Delete Last

2. Delete Selected

3. Delete Deselected

4. Delete by Type

5. Delete All

6. Copy Selected

18 CHAPTER 2. GRIDZ

7. Move Selected

Next chapter: File Formats

Chapter 3

File Formats

This Chapter gives a brief overview of the file formats supported by GridZTM.The Various file formats supported by GridZTM are -Read

GridZ (native) FilesGridZ (native binary ) FilesCGNS Grid FilesSTL FilesDXF FilesParametric Files

- PLC ( Piecewise Linear Curve) Curve- BSC ( B-Spline Curve) Curve

IGES FilesWrite

GridZ (native) FilesGridZ (native binary) FilesSTL FilesCGNS Grid FilesTecplotPlot 3D

The user is expected to be acquainted with all the standard file formats mentioned above(except GridZ - the native file format). Nevertheless, a brief summary of each file format is given,while GridZ file format is explained in detail.

3.1 GridZ (native) File Format

You can use the GridZ file format exclusively for archiving, storing and manipulating files contain-ing Geometric entities. This format supports archival of Free Points, Segments(vectors), Planes,PLCS’s (Piecewise Linear Curves), BSC’s (B-Spline Curves), NURBC (Non-uniform Rational B-Spline Curves), PBLS’s (Piecewise BiLinear Surfaces), BSS’s (B-Spline Surfaces), NURBS (Non-Uniform Rational B-Spline Surfaces), RS (Surface of Revolution), TRSP (Triangulated SurfacePatch), QDSP (Quadrilateral Surface Patch) and PYSP (Polygonal Surfaces Patch). The entitiescarry adequate information and hence can be used in structured or unstructured grids.

19

20 CHAPTER 3. FILE FORMATS

GridZ format is an ASCII format, where records (lines) are separated by carriage return andline feed. The format has no header. It contains information entity by entity. Information foreach entity starts with a record of that given entity ID and entity name followed by entity specificinformation. Information of each entity ends with a record containing string END. The last recordof the file provides a summary of different types of entities archived in the file.

The information archived in each entity is geometric in nature and will not write the colour ofthe entity. Also, only essential information is stored for example: in a triangulated surface, onlycell-vertex connectivity is written.

GridZ File format example of a File containing a Single PLC is given below -

31 PLC0 4-7.15555556e+01 -5.18518519e+00 7.67406640e-05-1.34814815e+01 3.71851852e+01 -2.37036800e-055.58518519e+01 3.62962963e+01 -9.21480560e-051.05629630e+02 -5.77777778e+00 -9.98517520e-050 END0 0 1 0 0 0 0 0

Observe the following -

• Entity number (31) for PLC

• Entity name PLC

• Open/Close Flag (0 for open )

• Number of points (4)

• Co-ordinates (x, y, z) of each point , with one point per line.

• END to indicate End of Data for the entity.

• In the last line, we get a summary of number of all Entities present in the file.

Some Common entities and their entity numbers are given below-

• -2 - Free Point

• 21-Point Cloud

• 4 - Plane

• 1 - Line (Segment)

• 31 - PLC

• 1001 - Nurbs Curve

3.2. READING FILES 21

• 151 - PBLS

• 2001 - Nurbs Surface

• 162 - Triangulated Patch

• 13001 - Polygon Patch

Note that all Geometries, TRSP’s, QDSP’s and PYSP’s must be stored as GridZ files.

In case of there being multiple entities being saved in a file, the entities will appear in theorder in which they occur in the Selection Set i.e. the entity selected last comes first.

3.2 Reading Files

We start off with the file formats supported for reading files.

a) CGNS

CGNS (CFD General Notation System) was initially developed by NASA and Boeing startingin 1994. CGNS is now becoming a popular standard for the CFD (Computational Fluid Dynam-ics) community to allow the transfer of data using a standard data file format. The CGNS systemfacilitates the exchange of data between sites and applications with the intention of eliminatingthe work currently spent converting formats and to allow various CFD codes and pre- and post-processing codes to readily import data from diverse sources. Many of the major CFD codes andpost-processors have or will soon be providing CGNS data I/O capabilities.CGNS consists of a collection of conventions, and software implementing those conventions, forthe storage and retrieval of CFD data. The system consists of two parts:(1) A standard format for recording the data.(2) A software that reads, writes, and modifies data in that format.CGNS is a database format that includes the mesh, the solution, boundary conditions, and otherinformation. A CGNS file reader can potentially interrogate a CGNS file and determine exactlywhat information it contains. Then it can intelligently choose the data that it wants to access.The mesh can be structured or unstructured. The data can be stored at the nodes or cell-centers.The standard continues to grow and change. Currently, ICEM CFD Engineering is the lead de-veloper of the CGNS software library, which is distributed worldwide as freeware.

b) DXFAutoCAD DXF (Drawing Interchange Format, or Drawing Exchange Format) is a CAD data fileformat, developed by Autodesk as their solution for enabling data interoperability GridZTM readsfiles in DXF format, versions supported by AutoCAD 2000 upwards.

c) IGESThe Initial Graphics Exchange Specification (IGES) (pronounced eye-jess) defines a neutral dataformat that allows the digital exchange of information among Computer-aided design (CAD)systems. Using IGES, a CAD user can exchange product data models in the form of circuit dia-grams, wireframe, freeform surface or solid modeling representations. Applications supported byIGES include traditional engineering drawings, models for analysis, and other manufactur- ingfunctions


A list of the entities that can be read in GridZTM are -

Entity number and type ( Notes)

• 110 Line

• 116 Point

• 120 Surface of revolution

• 126 Rational B-spline curve

• 128 Rational B-spline surface

• 144 Trim Surface

• 142 Trim Curve

• 122 Tabulated Cylinder

• 108 Plane

• 104 Composite Curve

• 140 Offset Surface

• 124 Transformation Matrix

d) STLSTL (stereolithography) files describe only the surface geometry of a three dimensional objectwithout any representation of color, texture or other common CAD model attributes. It describesa raw unstructured triangulated surface by the unit normal and vertices (ordered by the right-hand rule) of the triangles using a three-dimensional Cartesian. STL ASCII format is supportedwith this software.

f) Script files

This is a special file format which records history of all commands ordered or executed in asession. The recording of the session can be controlled by using the Start/Stop buttons presentbelow the Selection Set.

3.3 Writing Files

Here, only those file formats not encountered before are explained.

a) Tecplot

TEC files are used by the TECPLOT program which is a visualization program for technicaldata especially when a user has an application program (fluid flow solver, engineering stress pro-gram, aeronautic simulator, heat flow program), that produces lots of data.

3.3. WRITING FILES 23

TEC files are ASCII-type and color is not associated with the data, but can be added duringpostprocessing by the TECPLOT program or by associating variables “R”, “G” and “B” withdata; for instance with 2D or 3D data and can have time dependence data. Geometric data isstored, but the user can also store associated quantities such as pressure, temperature or velocity.Also, the data is grouped into zones whose meaning is determined by the user.

b) Plot 3D

The PLOT3D structure file used for file input is fixed format ASCII-type and can be createdin an interactive session of GridZTM or manually with a text editor. Plot 3D file format is sup-ported by the Plot 3D software which does Post Processing specifically for CFD.

Next chapter: Geometry

Chapter 4

Geometry

Module Geometry occupies the apex of the heirarchy of the entire process of geometry generation.Once into module geometry we can create all possible points, curves or surfaces through a varietyof ways as systematically listed below.

4.1 Point

• CreateMenuGeometry −− > Point −− > Create

1. Rubberband: Creates free points using the left mouse button. Press the middlemouse button or press Q to stop creating more points. Note that this option does notwork when we are in the isometric view. Also, the point created last can be deleted bya right click.

2. XYZ Co-ordinates: Creates a point by giving the X,Y,Z values for each point. Fill inthe required values for each point. This option is especially useful for creating precisepoints using exact coordinates.

3. From Algebra of N Points: Creates ‘n’ number of points using an expression. Touse this option you require two or more points. This option comes with a pop-upwindow which has entries as follows:

– No. of Copies: Enter the number of copies (including the existing Points) re-quired.

– U min: Enter minimum value for a variable (parameter) u. Default value is 0.

– U max: Enter maximum value for a variable (parameter) u. Default value is 1.

– Algebraic Equation: Enter the appropriate algebraic equation depending on therequired distribution of interpolated Points. The default expression is u∗p1+(1−u) ∗ p2. p1 and p2 stand for the first and second selected point respectively.

• ExtractThis option extracts points from different entities. You have to ‘pick’ the entity before youselect any of the options available under extract.

25

26 CHAPTER 4. GEOMETRY

MenuGeometry −− > Point −− > Extract

1. From Point Cloud : Extract all points from Point Cloud.

2. From Line Segment : Extracts all points from a Line Segment.

3. From PLC : Extracts all points from a Piecewise Linear curve (PLC). The PLC is notretained after this operation.

4. From PBLS : Extracts all points from a Piecewise Bilinear Surface (PBLS). The PBLSis retained after this operation.

5. From Triangulation : Extracts a point from a Triangulated Surface Polygon (TRSP).

6. From Triangulation Boundary : Extracts a point from a TRSP Boundary.

7. From Polygon : Extracts a point from a Polygon.

8. From Polygon Boundary : Extracts a point from a Polygon Boundary.

9. Vertex of 2D Block : Extract a point from selected vertex of 2D Block.

10. Vertex of 3D Block Extract a point from selected vertex of 3D Block.

• IntersectionMenuGeometry −− > Point −− > Intersection

1. Line X Line : Creates a point at the intersection of two intersecting line segments.To perform this operation you require two line segments such that they intersect eachother.

2. Curve X Curve : Creates points at the intersection of two Piecewise Linear curves/B-spline curves. To perform this operation, you require two Piecewise Linear curves/B-spline curves such that they intersect each other.

3. Curve X Surface : Creates a point at the intersection of a surface and a curve. Toperform this operation, you need one surface and one curve intersecting each other.

4. Surface X Surface : Creates points at the intersection of the two selected surfaces.

4.2 Point Cloud

• ConvertMenuGeometry −− > Point Cloud −− > Convert

From Points : This menu is use to group more than two points.

• EditMenuGeometry −− > Point Cloud −− > Edit

Attributes: This menu is use to add attributes to point cloud

4.3. LINE SEGMENT 27

4.3 Line Segment

• CreateMenuGeometry –> Line Segment – > Create

1. Axis Parallel : Creates a line segment parallel to X, Y or Z axes after feeding in therequisite information.

2. Cross Product : Creates a line segment perpendicular to the two line segments se-lected.

• ConvertMenuGeometry –> Line Segment – > Convert

2 Points : Converts a line segment from 2 points. To perform this operation you willrequire two points.

• ExtractMenuGeometry –> Line Segment – > Extract

From PLC : Extracts a line segment from a PLC. To perform this operation you willrequire a PLC with only two points.

• EditMenuGeometry –> Line Segment – > Edit

1. Alter Magnitude : Magnifies a line segment.

2. Scale Magnitude : Scales a line segment.

3. Mirror : It flips the line segment about it’s first point along the direction of the linesegment.

4.4 Plane

• CreateMenuGeometry –> Plane – > Create

1. Line Segment : Creates a plane from line segment.

2. From 3 Points : Creates a plane passing through three points.


3. Plane Parallel : Creates a plane parallel to a plane or perpendicular to a line segment.

4. Principle Plane Parallel : Creates a plane parallel to the X, Y or axes as specified.

5. From Co-efficient : Creates a plane using four coefficients a, b, c, d to give a plane withequation ax + by + cz + d = 0.

4.5 Piecewise Linear Curve

PLC: Linear Discretization of Segments

• CreateMenuGeometry –> Piecewise Linear Curve – > Create

1. Rubberband : Creates a PLC from free points, which in turn are made by left clickingat appropriate positions. Press the middle mouse button or press Q to stop creatingmore points. Note that this method doesn’t work in isometric view. Also, the pointcreated last can be deleted by a right click.

2. Algebra of N PLC : Creates n number of PLCs between 2 PLCs (having equal num-ber of points) using interpolation. This option comes with a pop-up window which hasentries as follows:

No. of Copies : Enter the number of copies (including the existing PLC’s) required.

U min : Enter minimum value for a variable (parameter) u. Default value is 0.

U max : Enter maximum value for a variable (parameter) u. Default value is 1.

Algebraic Equation : Enter the appropriate algebraic equation depending on therequired distribution of interpolated PLC’s. The default expression is u∗ c1+(1−u) ∗ c2. c1 and c2 stand for the first and second selected curves respectively.

3. From Expression : This options creates a PLC from an expression. Clicking on thisoption opens a box with following options:

0 for Open/1 for Close : This tells whether the PLC to be created is to be Openor Closed.

No. of Points : Enter the number of points required on the PLC to be created.


U max : Enter maximum value for a variable (parameter) u. Default value is 2*pi.

Expression for x : Enter appropriate expression for x co-ordinate, of the PLC to beconstructed, in terms of the parameter u. Default expression is 10 ∗ cos(u).

Expression for y : Enter appropriate expression for y co-ordinate, of the PLC to beconstructed, in terms of the parameter u. Default expression is 10 ∗ sin(u).

Expression for z : Enter appropriate expression for z co-ordinate, of the PLC to beconstructed, in terms of the parameter u. Default expression is 0. As is evident,the default PLC created is a circle of radius 10.

• ConvertMenu

4.5. PIECEWISE LINEAR CURVE 29

Geometry –> Piecewise Linear Curve – > Convert

1. From Points : Converts free points into a PLC.

2. From Segment : Converts a line segment into a PLC.

3. PLC Equal Arc : Creates specified no. of equidistant points (including the end-points)on selected PLC.

4. Split PLC : Splits a PLC into two PLCs at a previously selected (picked) point. Thisoption creates two PLC’s along with the original PLC, giving 3 PLC’s in all.

5. Split two Intesecting PLCs Splits intersecting PLCs which are intersects each other.This option will create np. of PLCs depending upon the no. of intersection viz oneintersection will lead to creation of four PLCs.

6. Stitch 2 PLC : Stitches 2 PLCs into 1 PLC at previously selected points. The pointson the two PLCs must overlap to enable stitching. This option creates a new PLCalong with the original PLC’s, giving 3 PLC’s in all. Also the direction of each PLCmust be consistent(i.e both of them must be in the same orientation).

7. Stitch PLCs in loop : Stitches ’n’ number of PLCs into 1 PLC at previously selectedpoints. The points on the n PLCs must overlap to enable stitching. This option createsa new PLC along with the original PLC’s, giving n+1 PLC’s in all. Also the directionof each PLC should be consistent.

8. Join 2 PLC : Joins 2 selected PLCs by drawing a straight line between the last pointof the PLC selected first and the first point of the second selected PLC, to create asingle PLC. The PLC’s obviously need not have a common endpoint, as is necessaryfor option 5.

• ExtractMenuGeometry –> Piecewise Linear Curve – > Extract

1.From PBLS : Extracts multiple PLCs from PBLS.

2. All from PBLS : Extracts a PLC from a PBLS. Select two points on the PBLS first.Note that the 2 points selected are in the same direction ( u or v).

3. From PBLS Boundary : Extracts a PLC from the boundary of a PBLS boundary.

4. NURBC Equal Parameter : Creates a PLC having points located at equal distancesin parametric space from the NURBS Curve. The operation tries to maintain thecurvature of the original curve.

5. NURBC Equal Arc : Creates a PLC from a NURBS Curve having points located atequal distances.

6. Trim Surface Boundary Curve : Extracts a PLC from the boundary of a Trim sur-face boundary

7. From TRSP Boundary : Extracts a PLC from the boundary of the TRSP.

8. From Polygon Boundary : Extracts a PLC from the boundary of the polygon.

9. Edge of 2D Block : Extract PLC from the selected edge of 2D Block.


10. Edge of 3D Block : Extract PLC from the selected edge of 3D Block.

• EditMenuGeometry –> Piecewise Linear Curve – > Edit

1. Open/Close : Opens/closes a PLC

2. Insert Point : Inserts a single point at selected position on a PLC

3. Delete Point : Deletes a single selected point on a PLC

4. Deform : Deforms a PLC for a required range by providing X,Y,Z values.

5. Reverse : Reverses the direction of a PLC, such that the first point becomes the lastpoint.

• IntersectionMenuGeometry –> Piecewise Linear Curve – > Intersection

1. PBLS X PBLS : Generates PLC’s as an intersection of two PBLS’s.

• QueryMenuGeometry –> Piecewise Linear Curve – > Query

Quality - Displays the variation of geometric properties of PLCs. A separate dialogue boxis opened wherein the information of the selected PLCs can be obtained. Right click onthe parameters button to get the options for the information. The exit button is usedto exit from the quality box. The input range button is used to input the percentagerange after selecting the parameter.Note the selected entities must contain PLCs only.

4.6 NURBS Curve

NURBS Curve: Smooth Discretization of Segments

• CreateMenuGeometry –> Nurbs Curve – > Create

1. Rubberband NURBS : Creates a rubberband Nurb curve from free points, whichin turn are made by left clicking at appropriate positions. Press the middle mousebutton or press Q to stop creating more points. Note that this method doesn’t workin isometric view. Also, the point created last can be deleted by a right click.

4.7. PIECEWISE BILINEAR SURFACE 31

2. From Algebra of N NurbCurves : Creates ‘n’ number of Nurbs curves between 2Nurb curves (having equal number of points) using interpolation.

3. From Expression :This options creates a Nurbs curve from an expression.

4. Circle : Creates circular nurbs curve with the input specifications.

5. Ellipse : Creates an ellipse nurb curve with the input specifications.

6. Circular Arc : Creates circular arc nurbs curve with the input specifications.

7. Elliptical Arc : Creates an elliptical arc nurb curve with the input specifications

8. Curve Offset : Creates a similar curve offset by the dimensions as input by the user.

• ConvertMenuGeometry –> Nurbs Curve – > Convert

1. From Points : Convert points into a Nurbs Curve.

2. From PLC as Control Polygon : Convert PLC as a control polygon into a Nurbscurve.

3. Reverse Curve : Reverses the direction of a Nurbs Curve, such that the first pointbecomes the last point.

• ExtractMenuGeometry –> Nurbs Curve – > Extract

1. Loft U curves from NURBS : Extracts Loft U curves from Nurbs curves by theprocess of lofting.

2. Loft V curves from NURBS : Extracts Loft V curves from Nurbs curves by theprocess of lofting.

4.7 Piecewise BiLinear Surface

• CreateMenuGeometry –> Piecewise BiLinear Surface – > Create

1. From Algebra of N PBLS : Creates ‘n’ number of PBLS between 2 PBLS (havingequal number of points) using interpolation.

2. From Expression :This options creates a PBLS from an expression. Clicking on thisoption opens a box with the following options:

2. Offset Surface : Create a offset surface for the top selected PBLS along the unit normaldirection. This unit normal direction is computed on individual points

0 for Open/1 for Close For U : This tells whether the PBLS to be created is tobe Open or Closed. Default value is 0.


No. of Points for U Direction : Enter the number of points in the U directionrequired on the PBLS to be created. Default value is 30.


U max : Enter maximum value for a variable (parameter) u. Default value is 2*pi.

0 for Open/1 for Close For V : This tells whether the PBLS to be created is tobe Open or Closed. Default value is 0.

No. of Points for V Direction : Enter the number of points in the V directionrequired on the PBLS to be created. Default value is 30.

V min : Enter minimum value for a variable (parameter) u. Default value is 0.Module

V max : Enter maximum value for a variable (parameter) u. Default value is 2*pi.

Expression for x : Enter appropriate expression for x co-ordinate, of the PBLS to beconstructed, in terms of the parameter u. Default expression is 10∗cos(u)∗(cos(v)).

Expression for y : Enter appropriate expression for y co-ordinate, of the PBLS to beconstructed, in terms of the parameter u. Default expression is 10∗sin(u)∗(cos(v)).

Expression for z : Enter appropriate expression for z co-ordinate, of the PBLS tobe constructed, in terms of the parameter u. Default expression is 10 ∗ sin(v).As is evident, the default PBLS created is a sphere of radius 10.

• ConvertMenuGeometry –> Piecewise BiLinear Surface – > Convert

1. From PLCs : Convert PLCs into a PBLS. This function can also be executed by typingPBLS in the command line.

2. From four Open PLCs : Convert four connected PLCs into a PBLS.

3. From Driven Curve : PBLS is created by driving the profile curve along the directioncurve. Here the first PLC amongst the selected entities acts as the direction curve whilethe second PLC acts as the profile curve.

4. Split PBLS : Splits a PBLS into 2 PBLS. Deselect all, then ‘Pick’ a boundary gridpoint where you want to split the PBLS and click on this option.

5. Stitch PBLS : Stitches 2 PBLS (having equal number of grid points on opposite sides)into a single PBLS. ‘Pick’ a point on each PBLS successively where you want to stitchthe PBLS and click on this option.

• ExtractMenuGeometry –> Piecewise BiLinear Surface – > Extract

1. Current 2D Block : Extracts a PBLS from a selected face of a 2D Block.

2. All 2D Blocks : Extracts PBLS of all 2D blocks.

3. Face of 3D Block : Extracts a PBLS from the selected face of a 3D Block.

4. I Layer Of 3D Block : Select a particular layer and use this option to extract thePBLS from a particular face of a 3D Block.

4.8. NURBS SURFACE 33

5. J Layer Of 3D Block : Select a particular layer and use this option to extract thePBLS from a particular face of a 3D Block.

6. K Layer Of 3D Block : Select a particular layer and use this option to extract thePBLS from a particular face of a 3D Block.

7. Mapped Surface of 3D Block : Extract PBLS from mapped surface of 3D Block.

8. Face by Label : Extracts PBSL from selected label name of 3D Block.

9. NURBS Equal Parameter : Creates a PLC having points located at equal distancesin parametric space from the NURBS Curve. The operation tries to maintain thecurvature of the original curve.

10. NURBS Equal Arc : Creates a PLC from a NURBS Curve having points located atequal distances.

11. Patch From PBLS : Creates a PBLS which is a subset of the top selected PBLSin the selection set. For this, two points should be picked which would indicate twodiagonally opposite boundary end points of the required PBLS.

• EditMenuGeometry –> Piecewise BiLinear Surface – > Edit

1. Delete Row/Column : Deletes a row/Column of the PBLS.

2. Self Stich : Stitch the boundary of same Surface.

3. Change Point Change number of grid points is u and v direction.

4. Deform : Deforms a PBLS for a required range by providing an expression for theX,Y,Z values in terms of the old values.

5. Make Uniform Normal as first PBLS : Changes the orientation of specific no. ofPBLS in the selection set as the top selected one. Keep the PBLS whose orientationyou dont want to change as the first PBLS in the selection set. Enter the requirednumber of PBLS in the pop-up window.

• QueryMenuGeometry –> Piecewise BiLinear Surface – > Query

Quality :Displays the variation of geometric properties of PBLS. A separate dialogue boxis opened wherein the information of the selected PBLS can be obtained. Right click onthe parameters button to get the options for the information. The exit button is usedto exit from the quality box. The input range button is used to input the percentagerange after selecting the parameter. Note the selected entities must contain PBLS only.

4.8 NURBS Surface

• CreateMenuGeometry –> Nurbs Surface – > Create


1.Surface of Revolution : Creates a nurbs surface of revolution consistent with the datainput in the pop-up menu.

2.Offset Surface : Creates a similar surface offset by the dimensions as input by the user.

3.Cone : Creates conical nurbs surface with the input specifications.

4.Cylinder : Creates a cylinder as mentioned above.

5.Sphere : Creates a sphere as mentioned above.

6.Torus : Creates a torus as mentioned above.

• ConvertMenuGeometry –> Nurbs Surface – > Convert

1. From PBLS : Convert PLCs into a Nurbs Surface. This function can also be executedby typing PBLS in the command line.

2. Lofting NURBC : Converts NURBCs into a Nurbs Surface by the process of lofting.

2. Reverse Surface : Reverse the Surface.

• ExtractMenuGeometry –> Nurbs Surface – > Extract

1. Base Surface of Trim Surface : Extracts the base/parent surface of the trim surface.The Trim surface is the trimmed NURBS surface This tool will extract the NURBSsurface which was trimmed.

Next chapter: Grid

Chapter 5

Block

5.1 2D Multiblock:

• Create

Menu

Block −− > 2D Multiblock −− > Create

1. Init Block - A 2D block with lower left corner as origin and the upper right cornerspecified by the user in the command box opened is created. Thus a block is initialized.The grid points inside the block is 17*17. This parent Block can be divided into childblocks using vertex, box and slit. It can be scaled and deformed. The 2D Block issaved in CGNS file format.

2. Insert Vertex - By inserting a vertex, Four blocks are created. The vertex is insertedby mouse; i.e. the point at which you click the mouse, the parent block is divided intofour blocks.

3. Insert Slit - This option creates a slit inside a block and divides the block into 6 blocks.There is no information across the slit. The size of the slit is given manually by movingthe mouse. There are two faces at the slit which can be mapped separately on twoPLCs.

4. Insert Dummy Slit - This option is same as the earlier one. It divides the currentblock into 6 blocks. However, there is only one face at the slit across which informationcan be transferred. Also, only one PLC can be mapped from this face. In short, thereare no two separate faces at the dummy slit. It is simply a face shared by two blocks.

5. Insert Box - A box is created inside the block, which is divided into 9 blocks with thisbox as a hole. The edge of the box is a boundary wall, with no information passingthrough this box. There is no grid inside it as it is hole. A box is created by movingthe mouse.

6. Insert Dummy Box - This option is similar to dummy slit, with a dummy box created;but the box created is not a hole. It is a block and contains all the neighboringinformation. A box is created by moving the mouse.

7. Input Values - This option is used for creating a vertex, a slit or a hole by giving therequired co-ordinates . After clicking this option, in the command box enter 0 if vertexis to be created or 1 for slit or 2 for hole. Then a command box will be opened whereinfill the required co-ordinates.

35

36 CHAPTER 5. BLOCK

8. On Block - First select a block using block traversal option on the toolbar. This optionis used for creating a block within a selected 2D block. The block is created concentricto the selected 2D block and is half in the area.

9. On Edge - First select a block and one edge using block traversal and edge traversaloptions on the toolbar. This option is used for creating a block within a selected 2Dblock with one edge lying on the selected edge of the selected block. The block iscreated symmetrically with half the area of the selected block with one edge lying onthe selected edge of the selected block.

10. On vertex - First select a block and one vertex using block traversal and vertex traver-sal options on the toolbar. This option is used for creating a block within a selected2D block with one vertex common. A block is then created with half the area of theselected block and a common selected vertex inside the selected block.

11. Plane Cutter - This option helps to create 2D blocks by cutting the existing planes.The graphical interphase helps the user with a better visualisation.

• Convert

Menu

Block −− > 2D Multiblock −− > Convert

1. PBLS to Block - Converts the selected PBLS in to 2D Block

2. TRSP to Block - Converts the top selected TRSP into a 2D block.

3. Paste Edge - This option pastes the selected edge to the neighboring blocks for con-nectivity. The unpasted edge can be pasted. After pasting the edge, block traversingcan be done.

4. Unpaste Edge - This option unpastes the selected edge which is highlighted so thatthere is no connectivity with the neighbouring blocks.

5. Paste a Block - Pastes the selected block with neighbouring blocks

6. Unpaste a Block - Unpastes the selected block from the neighbouring blocks

7. Paste all Blocks - This option pastes all the blocks in the present interface

8. Unequal Abutting - Converts the current edge as an un-equal abutting interface

9. Equal Abutting - Converts the current unequal abutting interface to equal abuttinginterface

10. Set Periodic Boundary - To assign the periodic conditions, Rotational and Trans-lational, for the selected edge

11. Reset Periodic Boundary - To remove the assigned periodic conditions, Rotationaland Translational, from the selected edge

• Extract Menu Block −− > 2D Multiblock −− > Extract

From Face of 3D Block - Current face of Block3D is added as a Block2D

• Edit Topology

Menu

Block −− > 2D Multiblock −− > Edit Topology

5.1. 2D MULTIBLOCK: 37

1. Collapse a block - This option is used to collapse the selected block.

2. Delete Block - After clicking this option, one can delete a selected block.

3. Pick and Delete Block - Click here and Pick inside any block to delete it.

4. Edit Operation - After clicking this option command Box appears of Edit Operation.

Following options are available under the Edit Operation Command Box.

1. Move All Blocks - With this option all blocks of the 2D topology are moved to thespecified coordinates.

2. Move Block - With this option a block can be moved. Select a block and click theoption, then enter distances through which the block should move in the commandbox opened.

3. Move Edge - From this option an edge can be moved. Select an edge and click theoption, then enter distances through which the edge should move in the command boxopened.

4. Move Vertex - From this option a vertex can be moved to the required co-ordinatepoint. Select a vertex and click the option, then enter the XY Co-ordinate in thecommand box where the vertex should be moved.

5. Scale All Blocks - With this option all blocks of the 2D topology are scaled by thespecified factor of scaling.

6. Scale Block: - From this option a block can be scaled. Select a block and click theoption, then enter scale factor in the command box.

7. Scale Edge - Any edge of a block can be scaled according to topology. click this optionand select the edge by picking two end points and then entering the scale factor in thecommand box.

8. Rotate All Blocks - With this option all blocks of the 2D topology are rotated by thespecified angle about a specified axis.

9. Rotate Block - From this option a block can be rotated . Select a block and click theoption, then enter angle of rotation in degrees in the command box and then enter theaxis about which block is to be rotated 0 for x axis, 1 for y axis and 2 for z axis in thecommand box. The block rotate about its center.

10. Rotate Edge - Click this option and select the edge by picking two end point andthen you have to enter the angle of rotation and click OK. The angle is given in degree,also the edge rotate about its center.

11. Deform All Block - All Block can be deformed using this option. The equations fordeformation must be entered in the command box opened.

12. Deform Block - The selected block can be deformed using this option. The equationsfor deformation must be entered in the command box opened.

13. Deform Edge -The selected edge can be deformed using this option. The equationsfor deformation must be entered in the command box opened.

• Edit Grid

Menu

Block −− > 2D Multiblock −− > Edit Grid

38 CHAPTER 5. BLOCK

Change Grid Points - Changes the number of grid points in the current edge of theselected 2D block

• Clustering

Menu

Block −− > 2D Multiblock −− > Clustering

1. All Blocks -Clustering is effected on all the blocks.

2. One Block -Clustering is effected only on one block.

3. One Edge -Clustering is effected only along one edge.

4. Remove Clustering -Declusters the blocks.

5. Remove One Edge Clustering -Declusters a clustered edge.

6. Distance First Point -This option enables the user to evaluate the distance from thecurrent edge to the first point in the present block

• Map / Unmap

Menu

Block −− > 2D Multiblock −− > Map /Unmap

1. Map Edge - Edge of a 2d block is mapped with a PLC using this option. The edgetakes the shape of PLC and also the number of point on it.

2. Map Face - Maps the current face of the selected 2D Block with the selected PBLS

3. Map Vertex - A vertex of a block is mapped with a point. Traverse the block and thenthe required vertex to be mapped with the point. The vertex move to the position ofthe top selected point.

4. Map Edge with Nurb Curve - Maps the current edge of the selected 2D Block withthe selected NURB Curve

5. Map Face with Nurb Surface - Maps the current face of the selected 2D Block withthe selected NURBS Surface

6. Unmap Vertex - A vertex of a block is unmapped . Traverse the block and then therequired vertex to be unmapped .

7. Unmap Edge - Edge of a 2d block is unmapped using this option by traversing to therequired edge.

8. Unmap Face - Unmaps the current face of the selected 2D Block

9. Retrieve Topology - This option retrieves the original topology of the 2D block sys-tem.

• Grid Motion

Menu

Block –> 2D Multiblock –> Grid Motion

1. Block Specification: This option enables the user to specify the selected block as Mov-ing Frame of Reference or Sliding Frame of Reference


2. Edge Specification: This option enables the user to specify the sliding interfaces inthe computational domain. Following informations are required for this option.

2.a Interface Type: To set the interface type

2.b Sliding Label: The label for the selected edge

2.c Sliding Group Label: Assigns the selected edge to a pariticular group/set of edges.

• Quality

Menu

Block –> 2D Multiblock −− > Quality

Current Block - Displays the information on the Quality of the cells in the current blocks

All Blocks - Displays the information on the Quality of the cells for all the blocks

5.2 3D Multiblock:

The most elementary method of structured grid generation is based on abstraction of the domaininto square blocks and mapping. The second method of multiblock structured grid generation isthat of extrusion of 2D blocks into 3D blocks. Both these methods has been explained here.

Abstraction of Domain Method

It is the process in which the domain is abstracted into a square topology. It is an interactiveprocess, the user has to use two types of modules (a) Module topology and (b) Module geometry.The complete process can be understand with the help of Fig.Refer Fig No 5.1.

In module geometry, the user first creates geometry, or import a CAD file and do otheroperations like CAD clean-up and repair. The surface of geometry thus available are inspectedto see if multiblock can be made. If necessary surfaces are stitched or split to produce requiredmultiblock surface grids.

The first step in module multiblock is abstraction of domain suitable for surface topologyproduced above. This depends upon shape of the body and outer domain. The user has toimagine this abstracted domain. This abstracted domain is created block by block.

Once the surface geometry and 3D topology are generated, the surface is required to assign tofaces of abstracted topology. This requires interaction of geometry and block topology, both areviewed simultaneously on the screen. A curve may also be assigned to an edge of topology usingvarious mapping tools. After geometry is assigned to the multiblock topology, TFI grid is auto-matically generated in the domain. Quality checks are done on the TFI grid and if required gridcan be smoothened using Laplace smoothener. Grid enhancement features includes increasingnumber of grid points in high priority region. This can be achieved either by increasing numberof points or by moving grid points from lower priority region to higher priority region. The finalstep is to apply appropriate boundary condition on faces of blocks. The grids can be saved at anyintermediate step in CGNS format.

Extrusion of 2D Blocks

40 CHAPTER 5. BLOCK

Surface Structured Grid

Decide Topology

CAD File Import / Generate Geometry

CAD Clean−up, Repair

Final Grid (CGNS Format)

and Splitting

Checks

Module Geometry Module Multiblock

Apply Boundary Conditions

Assign Geometry to Topology

Grid Enhancing, Quality

Create Multiblock Topology

Decide the Domain

Figure 5.1: Abstraction of domain method


1. Surface Block

In case of surface grids, the number of Cartesian coordinates are three but number ofparameters defining surface are two and hence computational space has two parameters.Thus surface block can be considered as intermediate between 2D block and 3D block. The2D grid can be considered as a special case of surface grid with the third coordinate set tozero. So surface blocks are generated from the boundary surfaces of the complex domain onwhich multiblock grid is to be generated.

2. Generation of 3D Blocks from Surface Blocks

The surface blocks can be extruded in normal direction to generate 3D blocks. Ones thesurface blocks of the domain is created, 3D blocks are generated by extruding surface blocksin normal direction. In this method multiblock topology depend on the split of surfaceblocks. The surface block forms the base of the newly created 3D blocks. The user isprovided with option of mapping the upper face of 3D block same as base face. Else theupper face is mapped to flat surface.

A three dimensional grid of any geometry is generated using 3-D blocks, which have gridsinside. Creation of 3-D blocks and then doing all operation like scaling, moving, cutting plane,clustering and mapping etc is done using all the GUI option in Block -3D Multiblock and toolbarShow 3D Option. For creating a 3D grid for any geometry, first a 3D grid topology is created andthen mapping is done on the geometry.

5.2.1 3D MULTIBLOCK TOOLS

• Create

Menu

Block −− > 3D Multiblock −− > Create

1. Block - A 3D block can be created by exporting a 2D block to 3D or directly creatinga block. A block of dimension (30*30*30) with the grid point(17*17*17) in it is cre-ated.Pickability of block, face edge and vertex in 2d or 3d block is not applicable, onlytraversal is allowed and all the operation can be done on the particular block or allblocks. Face, edge and vertices of the block can be traversed using the face, edge andvertex traversal from the tool bar. Another block can also be created on the selectedface of the existing block from these option by giving the length of the required block.

2. On Face - Using the Face Selector Option on Toolbar, select a face in the parent block. Then, click this option again to divide the parent block into appropriate number ofchild blocks. Refer Figs on the following page:

3. 0n Vertex - Block is created on the vertex of the existing block by giving the appro-priate value between 1 to 8 (in case of 17 grid points in IJK direction). It omits thespecified number of points on the three edges and breaks the existing block into fourblocks.

4. On Edge - Block is created on the edge of the existing block by giving the appropriatevalue the value between 1 to 8 (in case of 17 grid points in IJK direction). It omitsthe specified number of points on the two faces and breaks the existing block into fiveblocks. Refer the immediate figure for the same:

42 CHAPTER 5. BLOCK

Figure 5.2: Split when intersecting block touches parent block face shared by single block

Figure 5.3: Splitting when intersecting block touches parent block face shared by two blocks


Figure 5.4: Split when intersecting block touches parent block edge.

5. In Block - Using the ”In Block Selector” Option on toolbar, select a face in the parentblock . Then, click this option again to divide the parent block into appropriate (sevenin this case) number of child blocks. Refer the figures to follow :

Figure 5.5: Parent block

6. Plane Cutter - Select the IJK plane to be cut using the ’IJK plane traversal’ thenusing this option, Plane of a block can be cut to divide the block in that direction.Refer to the figure below:

• Convert

Menu

Block −− > 3D Multiblock −− > Convert

1. From 2D Block : 2D block is converted into 3D blocks by giving the no. of layers andthen the dimensions of each layer in the command box. The 2D grid is also retainedafter making 3D block, it can be deleted.

44 CHAPTER 5. BLOCK

Figure 5.6: Seven children formed by splitting parent block

2. Paste a Block : When a block is created, it does not know its neighbouring blocks andthere is no connectivity. This option helps to paste the Block to the neighboring blocksfor connectivity. After pasting the block, block traversing can be done.

3. Unpaste a Block : This option unpastes the current block which is highlighted so thatthere is no connectivity with the neighbouring blocks.

4. Paste a Face : Pastes two faces of a block for connectivity.

5. Unpaste a Face : This option unpastes all the face,i.e. there is no connectivity betweenany faces As a result, face traversal can’t be done.

6. Paste All Blocks : Pastes a block with all the neighbouring blocks for connectivity.

7. Unpaste All Blocks : This options unpastes all the blocks thereby losing the connec-tivity with rest of the blocks.

8. Equal Abutting : This option will convert the present interface, edge/face, as equalabutting interface

9. Un-Equal Abutting : Converts the present interface, edge/face, as un-equal abuttinginterface

10. Periodic Boundary : Assigns the periodic boundary conditions, Rotational or Trans-lational, for the current face of the selected 3D Block

11. Remove Periodic Boundary : Removes the periodic boundary conditions from thepresent face

12. Coarsen Grid : This operation coarsens the existing finer grid for all the blocks

• Edit Topology

Menu

Block −− > 3D Multiblock −− > Edit Topology


Figure 5.7: Splitting of a block by an internal face

1. Collapse Face : Collapses the selected face on a 3D multiblock.

2. Move Face by Lable : This option moves the selected labelled face in the requireddirection by entering the values for x,y,z.

3. Delete Blocks : After clicking this option command box appears for Delete Option.

Following options are available under the Delete Option Command Box.

a. Delete Current Block : Current selected block is deleted.

b. Delete All Blocks : By using this option all the blocks get deleted.

c. Delete Block In Plane : Blocks in a plane are deleted.

d. Delete Block in Row : By using this option all the blocks in a row get deleted.

e. Delete Block by Label : By using this option all the blocks with selected label nameare deleted.

4. Deform : A block can be deformed by this option by entering the XYZ values. AnExpression can also be given for deformation.

5. Edit Operation : This command provides additional edit operation options.

Following options are available under the Edit Operation Command Box.

a) Move Vertex By Translation : This option moves the vertex of the block (if it isnot mapped) by entering the values for x,y,z. The vertex of block is selected by vertextraversal.

b) Move Edge By Translation : With this option you can move the selected edge if itis not mapped by entering the values for x,y,z.

c) Move Face By Translation : With this option you can move the selected face byentering the values for x,y,z.

46 CHAPTER 5. BLOCK

d) Move Block By Translation : With this option you can move the selected block tothe required position by entering the values for x,y,z. Mapped block can not be moved.

e) Move All Blocks Translation : With this option you can move all the blocks to therequired position by entering the values for x,y,z.Blocks can not be moved if any faceedge or face is mapped of any block.

f) Move all Blocks by Rotation :With this option the blocks can be rotated about achosen axis by a chosen angle.

g) Copy all Blocks by Rotation : This command copies all the blocks and rotates usingthe specified angle and the axis of rotation

h) Move All Blocks by Scaling : With this option you can scale all the blocks to re-quired shape by entering the values for x,y,z. Scaling can not be done for mappedblock.

i) Copy All Blocks by Scaling : With this option you can scale all the blocks to re-quired shape by entering the values for x,y,z. Scaling can not be done for mappedblock.

6. Optimum Partition : This command performs the partitioning the blocks for effiecientparrallel computing.

• Clustering

Menu

Block −− > 3D Multiblock −− > Clustering

Clustering is done for better grid quality at the surface of geometry or at the sharp discon-tinuous surface. Clustering can be done for a edge, face, block or all blocks. After clickingthis option, a window is opened and then required value is given for clustering. For cluster-ing select a block and then its edge on which clustering is done. Clustering is done beforesmoothening. The following figures give a schematic representation of clustering:

1. Clustering : Clustering is done for all blocks which is connected to the selected block.

2. Remove Clustering : All Clustering is removed from this option, after removing clus-tering, again clustering can done.

3. Remove One Edge Clustering : This option remove clustering of only the selectededge.

4. Change Grid Points : This option changes the number of grid points on the selectededge equally and also in all the connected blocks.

5. Distance First Point :It gives the distance of the first point from the surface of theblock.

6. Uncluster Topology : This option removes the clustering for entire topology

• Map / Unmap

Menu

Block −− > 3D Multiblock −− > Map / Unmap

Once the geometry and Topology of 3D multiblock is created, mapping is done for grid.


Figure 5.8: Example to explain clustering propagation

Figure 5.9: Clustering a single block

48 CHAPTER 5. BLOCK

Figure 5.10: Clustering an edge of a block

1. Map Vertex : Vertex of a block is mapped with a given point with is only in theselection set. After mapping, the vertex of the block moves to the position of thepoint. After mapping the vertex or the blocks can not be moved.

2. Map Edge : This option maps the edge of the block with a PLC which is already inthe selection set. The direction of the curve and the direction of the edge should bein the same direction. After mapping, the edge takes the shape of the PLC and it’sgrid changes to the points on the PLC. After mapping, edge and the block can not bemoved, number of points can not be changed and clustering cannot be done on thatedge.

3. Map Face : This option maps the selected face of the block with a PBLS which istop selected. Before mapping, mapping order should be checked from the option.show3D option - show/hide mapping guide line and if it is not correct mapping order canbe changed from the option change mapping order. After mapping, the face takesthe shape of the PBLS and also its grid change to the points on the PBLS. Aftermapping, face and the block can not be moved, number of points can not be changedand clustering cannot be done on that edge. Refer to the following figures to get anidea of mapping:

4. Unmap Vertex : If you have mapped the vertex wrongly then using this option youcan Unmap the vertex. Then vertex can be moved or mapped again.

5. Unmap Edge :If you have mapped the edge wrongly then using this option you canUnmap the edge. Then edge can be moved or mapped again.

6. Unmap Face :If you have mapped the face wrongly then using this option you canUnmap the face. Then face can be moved or mapped again.

7. Map Edge with Nurb Curve : This option maps the current edge with the selectedNURB Curve.

8. Map Face with Nurb Surface : This option maps the current face with the selectedNURB surface.


Figure 5.11: Unmapped face and block topology

Figure 5.12: Mapped face and block topology

9. Convert PBLS mapping to NS : This option converts the PBLS mapping to NURBSurface mapping.

10. Unmap All Edge : This option unmap’s all edges of the block.

11. Retrieve Topology : This option retrieve the topology by unmapping all the ver-texes, edges and faces. The vertexes, edges and faces can be mapped again. Thevertexes may not come to its initial position but the edges, faces become straight butall vertexes, edges and faces is unmapped.

• Attributes

Menu

Block −− > 3D Multiblock −− > Attributes

1. Set Face Label: Assigns the Label for the selected face

2. Show Block Label: Displays the blocks based on the selected Labels (Blocks whichhave same labels will be displayed)

3. Show Abutting Interface: Displays the abutting interfaces in the present block

4. Remove Label by: Removes the labels assigned to the blocks

5. Set Label: This operation assigns the label for the current block

• Grid Motion

Menu

Block –> 3D Multiblock –> Grid Motion

50 CHAPTER 5. BLOCK

1. Block Specification: This option enables the user to specify the selected block as Mov-ing Frame of Reference or Sliding Frame of Reference

2. Face Specification: This option enables the user to specify the sliding interfaces in thecomputational domain. Following informations are required for this option.

2.a Interface Type: To set the interface type

2.b Sliding Label: The Label for the selected face

2.c Sliding Group Label: Assigns the selected face to a pariticular group/set of faces

• Rendering:

Block –> 3D Multiblock –> Rendering

1. All Blocks : With this option you can render all the blocks. For removing rendering,click this option again.

2. Current Block : Shows the rendering of the current block.

3. Surfaces : With this option you can rendered all the surfaces of blocks.

4. Surface Grids : With this option you can rendered the surface grids for geometry.This option show the Wireframe of geometry and the outer blocks.

5. Mapped Surfaces : All mapped surfaces can be rendered for better visualization.

6. Mapped Surface Grid : Shows the Surface Grids of the mapped surface only.

7. Show Layer in Plane : Displays the grid at the current planein in all the blocks. Awindow opens for the plane selection. The plane can be traversed by modifying I, J,K, values.

Show Label : Shows Label name given to block.

• Query

Menu

Block −− > 3D Multiblock −− > Query

Block by No. : Traverses to the required block according to the number input in thecommand line.

Block by Name : Traverses to the required block according to the name input in thecommand line.

Negative Check : Checks the negative volume of the block selected.

Negative Check All Blocks : This option check the negative volume of all the blockand inform the block name and number and negative volume. For removing negativevolume, smoothening is done also clustering can be done.

• Quality

Menu

Block –> 3D Multiblock –> Quality

Current Block : Displays the information on the Quality of the cells of the selected block

All Blocks : Displays the information on the Quality of the cells for all the blocks


Layerwise Current Block : Displays the information on the Quality of cells at the se-lected plane (layer) for the current block

Layerwise All Blocks : Displays the information on the Quality of the cells at the selectedplane for all the blocks

5.2.2 Examples: Topology, Mapping and Clustering

We conclude this chapter by providing a few figures of various examples of topology,mapping andclustering.

Figure 5.13: Split when intersecting block touches parent block vertex

Next chapter: Grid

52 CHAPTER 5. BLOCK

Figure 5.14: Split Block Topology by intersecting block inside the parent block (27 blocks case)

Figure 5.15: Split Block1 by internal face becomes 4 child blocks as split propagation affectsparent block twice


Figure 5.16: Split block using face can result in possible 8 child blocks.

Figure 5.17: Choosing an edge inside the block for splitting

54 CHAPTER 5. BLOCK

Figure 5.18: Choosing a vertex inside the block for splitting

Figure 5.19: Domain shape change grid density


Figure 5.20: Global grid clustering in possible by splitting a block

Figure 5.21: Edges of blocks around Ahmed body (see surface grids of one block)

56 CHAPTER 5. BLOCK

Figure 5.22: Grids on faces of Ahmed body (see Clustered grids close and in wake of body

Figure 5.23: Single block of Pickup Van grids


Figure 5.24: Blocks of Hypersonic Research Vehicle

58 CHAPTER 5. BLOCK

Chapter 6

Grid

6.1 1D Grid

1D grid refers to 1 dimensional grid made up by grid points on a PLC.

• ConvertMenuGrid −− > 1d Grid −− > Convert

1. Divide in Equal Arc - Divides the curve (PLC) into equal parts by creating the givennumber of points at equal distance on the curve. The actual shape of the curve ischanged as well as the number of points as the initial points are not retained. Thenumber of points are given in the command box after clicking on the option, providedonly one curve (PLC) is in the Selection Set; else the operation is carried out on thetop(last) selected curve.

2. Divide in Equal Arc Keep Corners - Divides the curve (PLC) into equal parts bycreating the given number of points at equal distances on the curve. The initial shapeof the curve is not changed as it keeps the initial points on the curve and adds moreequally-spaced points on the curve. The no. of point are given in the command boxafter clicking on the option, provided only one curve (PLC) is in Selection Set; else theoperation is carried out on the top(last) selected curve.

3. Enhance - The no of points on a PLC is changed with more no of points at placeswhere there are more points already. The desired number of points are given in thecommand box. The enhanced curve is created along with the original curve.

4. Cluster - This option does clustering of grid points on the curve (PLC). A window isopened and the input is given for clustering. A clustered curve is created along withthe original curve. If this is not required, it can be deleted while retaining the originalcurve.

1. Cluster function: Different functions (Forexample exponential, logarithm, trigono-metric, hyperbolic etc) are given and the points are created as per the variation ofthe function.

2. Clustering type: Clustering can be done from one end of the curve or both endsas desired. Both options are available here..

59

60 CHAPTER 6. GRID

3. Total no. of points desired: Total number of desired points are given in thisbox for clustering.

4. % of total length: The % length of second point should be given . Forexamplevalue (0.2) tell thats the length between first and second point is 0.2 % of actuallength.

5. Carpet - This option drops a carpet on a 1D grid. See ‘Introduction to Carpeting’explained later in this chapter

• ExtractMenuGrid −− > 1D Grid −− > Extract

From TRSP Boundary - Extracts the curve (PLC) from the TRSP boundary. Similaroption is available in geometry –> PLC –> Extract

• QualityMenuGrid −− > 1D Grid −− > Attributes −− > Quality

Quality - Displays the variation of geometric properties of PLCs. A separate dialoguebox is opened wherein the information of the selected 1D grids or the PLCs can beobtained. Right click on the parameters option to get the options for the information.The exit option is used to exit from the quality box. The input range option enablesthe user to specify the percentage range after selecting the parameter.

Note: The selected entities must contain only PLCs.

6.2 2D Structured

This section describes the creation of a 2D Structured grid.

• Create

Menu

Grid −− > 2D Structured −− > Create

1. Four Open PLC - Generates 2D Grid from four open PLCs,provided they have samenumber of points and a reverse order of tangent

2. One PBLS as mapped - A single PBLS mapped into a single block 2D Grid

3. One PBLS as unmapped - A single PBLS is converted into a single block 2D Gridwithout mapping

3. Two Curves - Creates a 2D block from 2 open curves such that the 2 blocks are theopposite edges of the block created. Also the number of points on the curves shouldbe same

4. All PBLS as mapped - Maps all the PBLS into 2D blocks

5. All PBLS as unmapped - Converts all the PBLS into 2D blocks without mapping

6.3. TRIANGLES 61

• Convert

Menu

Grid −− > 2D Structured −− > Convert

1. Swap Tsi and Eta Grid lines - Tsi grid lines are made into Eta grid lines and vice-versa. After swapping the grid lines, the normal to the PBLS is changed.

2. Swap Tsi Grid lines - Tsi grid lines are swapped with other grid lines (e.g. Eta gridlines). After swapping the grid lines, the normal to the PBLS is changed.

3. Swap Eta Grid lines - Eta grid lines are swapped with other grid lines (e.g. Tsi gridlines). After swapping the grid lines, the normal to the PBLS is changed.

4. Invert Normal - Normal to the PBLS is inverted.

• Edit

Menu

Grid −− > 2D Structured −− > Edit

Generic 2D Smoothener - Smoothens a 2D grid.Whether to smoothen current block (0for no 1 for yes), then remaining blocks (0 for no and 1 for yes) and the maximum noof iterations are given in the command box, rest values are taken as default.

• Query

Menu

Grid −− > 2D Structured −− > Attributes −− > Quality

Quality -Displays the variation of geometric properties of PBLS or a 2D structured grids. Aseparate dialogue box is opened wherein the information of the selected 2D structuredgrids or the PBLS can be obtained. Right click on the parameters button to get theoptions for the information. The exit button is used to exit from the quality box. Theinput range button is used to input the percentage range after selecting the parameter.Note the selected entities must contain 2D structured grids only.

6.3 Triangles

This section deals with operations on a 2D Unstructured Grid.

• Create

Menu

Grid −− > Triangles −− > Create

Delaunay - This is one of the methods for creating a 2D Unstructured Grid (TriangulatedSurface) from closed curves (PLCs). Triangulated surface is created inside a closedcurve having any number of points. Inside this closed curve, any number of closedcurves can be made having required number of points. This closed curve will becomethe boundary line (there can be no grid points inside this). The maximum length ratio

62 CHAPTER 6. GRID

of all triangles and the maximum area is also controlled by giving these values.An important point to remember is that when this option is used for some PLC, therespective PLC must not contain any overlapping since that makes a zero length edgeand the triangulation will fail.

Sphere - This option creates the Sphere, discretized with triangles. User needs to specifythe radius of the sphere and the number of faces (triangles) in the Sphere.

Cube - This option creates the Cubic surface with triangulation. User needs to specifycube’s size and the number of surfaces (triangles) in the cube.

• Convert

Menu

Grid −− > Triangles −− > Convert

1. Stitch two polygon - Stitches two Polygon to create triangles.

2. Self Stitch : This utility stitches the open boundaries of a polygonal surface [TRSP]if they intersect. The user may be require to call it again if some of the commonboundaries are not stitched.

3. From PBLS by inserting point - Converts the PBLS to 2D triangle by insertion ofpoint.

4. From PBLS by Inserting Edge - Converts the PBLS to 2D triangle by insertion ofan edge.

5. Generate Mesh Using OpenGL lib :Input : NURBS surface , tolerance value. Ituses OpenGL lib function to triangulate the surface. The main task of lib functionis to triangulate a surface for rendering them. Thus the resultant surface mesh maynot be of good quality. The tolerance value controls the deviation of the triangulatedsurface from the inputted nurbs surface.

6. Generate Mesh using Advancing Front :Input : NURBS surface, tolerance value,Trim surface The advancing front algorithm is used to triangulate the nurbs/trimsurface. tolerance [same as above]. The edge length of the triangles to be generatedwud be decided by the tolerance value. Hence, the triangles will be of uniform areas

• Edit

Menu

Grid −− > Triangles −− > Edit

1. Smoothen Grid -Triangulated surface is smoothened by maximizing the minimum an-gle and minimizing the maximum angle. It puts the vertex in the centre of the neigh-boring vertices for a better grid. Thus it carries out local smoothening along withMin-max and Max-min.

2. Min - Max - 2D Unstructured grid (triangulated surface) is smoothened by minimizingthe maximum angle of all triangles.

3. Max - Min - 2D Unstructured grid (triangulated surface) is smoothened by maximizingthe minimum angle of all triangles.

4. Insert Point - Inserts a point inside a triangle. The triangle is selected by selecting 3vertices. Also the point is inserted at the centroid of the chosen traingle.

6.4. QUADRILATERAL 63

5. Delete point - Display all grid points of a TRSP. Then select a point to be deleted.After selecting any point on it, click on this option to delete.

6. Merge 2 neighboring faces -Display all the grid point of a TRSP. Select two pointson it that make an edge, the respective edge can be deleted.

7. Swap edge -By selecting the two points of the edge, it can be swapped in other direc-tion. The edge however should not be a boundary edge.

8. Collapse Edge - Collapses an edge from a the traingle whose edge is chosen.

9. Collapse Face - Collapses a chosen face. a face can be selected by picking three pointsonthe face

10. Collapse All Degenerate Faces - Collapses all degenerate faces. No picking is re-quired. The tool will detect faces with area less than the specified tolerance and collapsethem.

11. Uniform Normals - If the Normals in the domain are in different directions, thisoption uniforms the Normals in a particular direction. User can invert them if required.

12. Invert Normals - Changes/inverts the orientation of the normals of the surfaces.

13. Deform - The TRSP is deformed by feeding in the equations for deformation.

• Query

Menu

Grid −− > Triangles −− > Query

1. Consistency: This option checks for the consistency of the Triangles.

2. Quality: Displays the information of the quality of the generated triangles

6.4 Quadrilateral

• Convert

Menu

Grid −− > Quadrilaterals −− > Convert

From PBLS - Converts PBLS into 2D quadrilateral.

From Block3D Face - Current face of Block3D is added as Quad entity.

6.5 Polygons

Polygons are 2D Unstructured grids having more than 2 edges.

• Convert

Menu

Grid −− > Polygons −− > Convert

1. Stitching Polygons - Select two polygons. They must have common boundary points.They can be stitched using this option. A stitched polygon along with original twopolygons is created.

64 CHAPTER 6. GRID

2. Voronoi from Triangles - triangles are converted to Voroni polygons. The originaltriangulation is not retained. Voroni polygons are shown by blue colour.

• Edit

Menu

Grid −− > Polygons −− > Edit

1. Smoothen - Smoothens the grid by maximizing the minimum angle and minimizingthe maximum angle of polygon.It puts the vertex in the centre of the neighboringvertices for a better grid. Thus it carries out local smoothening along with Min-maxand Max-min.

2. Insert Point - A point can be inserted inside a triangle of a polygon. Just select a faceby left clicking on the face of the required triangle of the polygon and click this option.

3. Delete Point - Display all grid points of a Polygon. Then select a point to be deleted.After selecting any point on it, click on this option to delete.

4. Merge 2 Neighboring Faces - Display all grid points of a Polygon. Then select twopoints constituting the edge to be deleted. After selecting the points , click on thisoption to delete.

5. Swap Edge - By selecting the two points of the edge, it can be swapped in otherdirection. The edge however sh

6. Collapse Edge - Collapses an edge from a the traingle whose edge is chosen.

7. Collapse Face - Collapses a chosen face. a face can be selected by picking three pointsonthe face

8. Collapse All Degenerate Faces - Collapses all degenerate faces. No picking is re-quired.The tool will detect faces with area less than the specified tolerance and collapsethem. This tolerance can be using set-tolerance command.

9. Uniform Normals - If the Normals in the domain are in different directions, this optionuniforms the Normals in a particular direction. User can invert them if required.

10. Invert Normals - Changes/inverts the orientation of the normals of the polygons.

11. Deform - The polygon is deformed by feeding in the equations for deformation.

6.6 Polyhedrons

Polyhedrons are 3D Unstructured grids having more than 7 edges.

• Create

Menu

Grid −− > Polyhedrons −− > Create

1. Delaunay - Creates Delaunay 3D unstructured grid

• Convert

Menu

Grid −− > Polyhedrons −− > Convert

6.7. GROUP TRSP 65

1. From Multiblock - Creates polyhedrons from multiblock.

• Edit

Menu

Grid −− > Polyhedrons −− > Edit

1. Split - Select points on a polyhedron and splits it into 2 polyhedrons having a commonboundary points.

2. Stitching Polygons - Select two polyhedrons. They must have common boundarypoints. They can be stitched using this option. A single stitched polyhedron from theoriginal two polyhedrons is created.

• Attributes

Menu

Grid −− > Polyhedrons −− > Attributes

1. From 3 Points - Displays the attributes of polyhedrons created from 3 points

2. Reset Faces - Displays the attributes polyhedrons with reset faces

3. Select Faces - Displays the attributes of polyhedrons with selected faces

4. Deselect Faces - Displays the attributes of polyhedrons with deselected faces

5. Tag Faces - Displays the attributes of polyhedrons with tagged faces

6.7 Group TRSP

• Group TRSP

Menu

Grid −− > Group TRSP

1. Convert From TRSP: - This option is used to group many Triangulated Surface Patch(TRSP) into one Group TRSP. All the properties are same as Single TRSP.

6.8 Cartesian Grid

• Cartesian Grid

Menu

• Grid −− > Cartesian Grid

1. Generate Point Cloud - The ‘Starting Coordinate’ i.e. the start point of the domain.It should not be a negative value. The ‘Domain Size’ is calculated based on the length,height and width of the domain. ‘Constant Distance’ should be given in (i, j, k)direction. These are the constant (dx, dy, dz ) spacing between two points in each ofthe direction. They should be multiples of the length, height and width respectively.

66 CHAPTER 6. GRID

2. Create Output file - This generates an output file for BARC Tab - Solid: Input theinformation associated with each additional entity. The number of Solids text box willhave a number equal to the number of INTERSECTION point clouds in the database.This means the computation of point clouds was carried out for these many GROUPTRSP entities. Tab - Domain: Input the domain information which will be enteredin the grid output file. The last domain information entered in the ‘Domain PointsGenerator’ GUI will be highlighted. The domain size should be such that it covers allthe GROUP TRSP entities in the database. Click on the Create button to generatethe binary grid output file

6.9 3D Structured

• 3D Structured

Menu

Grid −− > 3D Structured −− > Edit

1. Laplace Smoothener - This operation improves the quality of the grids in the currentblock by Laplace Smoothener algorithm

2. Laplace Smoothener for all Blocks - This operation improves the quality of thegrids in all the blocks by Laplace Smoothener

3. Generic Gridder - Generic gridder improves the quality of the grids by modifyinginternal boundary. Laplace Smoothener algorithm, discussed above, does not modifythe boundaries

6.10 Surface Structured

Introduction to CarpetingIt is not always possible to mathematically define all geometric figures easily, specially in cases

where there are intersections of surfaces or very complex geometric shapes. Carpeting techniquescome handy in these cases. Carpeting works as follows. There is a Carpet which is a PBLS witha large number of points which is dropped on a group of PBLS or on a single triangulated surfaceto take the shape on the surface on which it is dropped.

Note: Before carpeting, if there are more than one TRSP then stitch them together to makea single TRSP. Also, PBLS and TRSP cannot be carpeted together and hence, must be carpetedseparately.

After the carpet is dropped, it becomes a single PBLS taking the required shape. Editing acarpet has to be done like splitting, deleting some part, etc. to get the final required shape as aPBLS.

Carpeting Options in GridZ are explained in the following menu commands.

• Create

Menu

Grid −− > Surface Structure −− > Create

1. From Rectangle as a Carpet 1. A virtual bounding box is created around a PBLSby automatically finding the minimum and maximum coordinates of a group ofPBLS or a single TRSP.

6.10. SURFACE STRUCTURED 67

2. The face of the bounding box with its principle normal along +z axis is taken asa carpet by default and is dropped in the -z direction always.

3. The number of grid points for the carpet must be entered in the command box afterclicking this option. The number is usually high to get better results approximatelyaround 10,000. The maximum limit is about 1,85,000.

2. Carpet User defined 1. A PBLS or TRSP is made by the user and is stored ascarpet.input in the directory where the GridZ runs.

2. Then the PBLS or the TRSP on which carpeting is to be done is opened. Thenthe option of carpet user defined is clicked.

3. Carpeting is done along the principle normal direction of the carpet.

3. Bounded Carpet 1. This option is used when only a particular portion of a carpetis to be dropped

2. A PBLS or TRSP is made by the user and is stored as carpet.input in the directorywhere GridZ runs.

3. Then the PBLS or the TRSP on which carpeting is to be done is opened. Thenthe option of bounded carpet is clicked.

4. Then in the command box the starting and ending values of u and v parametersis to be given, that is the portion of the carpet to fall.

5. Carpeting is done along the principle normal direction of the carpet.

Refer to the Tutorial on Intersecting Pipes for an example of carpeting.

Next chapter: Solver

68 CHAPTER 6. GRID

Chapter 7

Boundary Condition

In a numerical simulation, it is impossible and unnecessary to simulate the whole universe. Gen-erally we choose a region of interest in which we conduct a simulation. The interesting regionhas a certain boundary with the surrounding environment. Numerical simulations also have toconsider the physical processes in the boundary region. In most cases, the boundary conditionsare very important for the simulation region’s physical processes. Different boundary conditionsmay cause quite different simulation results. Improper sets of boundary conditions may introducenonphysical influences on the simulation system, while a proper set of boundary conditions canavoid that. So arranging the boundary conditions for different problems becomes very important.While at the same time, different variables in the environment may have different boundary con-ditions according to certain physical problems.

This chapter describes the boundary condition options available in GridZ. The information inthis chapter is divided into the following sections:

For Grid Smoothning For Compressible Flow Solver For Incompressible Flow Solver For Elec-tromagnetic Solver For Stress Analysis Solver For Acoustics Solver For Corrosion Solver

Each sections has boundary conditions for the respective problem.

7.1 Applying Boundary Condition

Inflow : BCInflow/ BCInflowSubsonic/ BCInflowSupersonic:Inflow boundary condition is given to the faces of the blocks from where the flow enters into theentire domain. The inflow can be subsonic or supersonic, accordingly the flow tags are given tothe faces. If the solver can recognize itself that the flow is subsonic or supersonic then BCInflowBC tag can be given.

OutFlow: BCOutflow/ BCOutflowSubsonic/ BCOutflowSupersonic:Outflow boundary condition is given to the faces of the blocks from where the flow exit from thedomain. the outflow can be subsonic or supersonic, according to the flow tags are given to thefaces.If the solver can recognize itself that the flow is subsonic or supersonic then BCOutflow BCtag can be given.

69

70 CHAPTER 7. BOUNDARY CONDITION

Wall: BCWall/ BCWallInviscid/ BCWallViscous/ BCWallViscousHeatFlux/BCWallViscousIsothermal/BC Degenerate Line:These tags are given to boundary wall. The BC wall can be inviscid or viscous; accordingly thefaces of the blocks are tagged for computational work, so that solver knows what kind of boundarycondition exists at the wall. If it knows all by itself, then BCWall tag can be given for that faceof the block.

Boundary Conditions Apply Options:

1. On Edge: Assigns the selected BC on current edge. Applicable for 2D multiblock only.

2. On Face: Assigns the selected BC on the current face. Applicable for 3D multiblock only.

3. On Plane: Assigns the selected for the interfaces in all the blocks at current plane.For 2D multiblock a IJ plane selector shall pop up. For 3D multiblock the plane should befirst selected using the IJK traversal

4. Label: Assigns boundary condition for the edges/faces of 2D/3D multiblocks with the selectedlabel. This can also be used to change te label.

5. Change Boundary Condition: Enables the user to change the selected current BC to se-lected new BC. It can also be used to change the label of the current selected BC. Applicableto all the edges/faces having current selected BC.

Boundary Conditions Show Options:

Displays all the BCs applied on the top selected entity. The entity can be either 2D multiblockor 3D multiblock or a polygon. The display can be adjusted to either mesh or smooth.

7.2 Applying Material Condition

Currently Electrode, Anode and Cathode material conditions can be given to any polygonal mesh.Though it can be applied to a open surface but the solver will required it to be a water-tight body.

To add a material condition on a set of points

1 Click on New This will activate few textboxes.

2 Enter label name

3 Click on Select. This will display all the points of the entity. Left click and drag onthe polygonalentity to select required points. This step will mark the selected triangles in dark green incolor.

4 Select the material condition

5 Click on Add to add the selection.

Note that thought not explicitly checked, all points having same material condition should beinterconnected.

7.2. APPLYING MATERIAL CONDITION 71

To deselect some points to an existing material condition

1 Go the the required material condition using previous/next buttons

2 Click on Deselect. The selected poins will be highlighted. Left click and drag onthe polygonalentity to deselect required points.

3 Click on Modify

To view selected pointsClick View The selected points will be displayed in yellow color.

To remove current selectionClick Remove This will remove the current selection identified by the label name.

Error Messages

ERROR: Found Zero New Points: When user tries to add set of points for a selection whichwere already present inthe selection.

ERROR: Vertices Not Found For Deselection: When use tries to deselect those points whichdoesnt exist inthe selection.

ERROR: Empty Label or Material Condition Not Selected: If label is not entered before clickingAdd button.

ERROR: No Points Selected: If user has not selected any points for the new selection.

72 CHAPTER 7. BOUNDARY CONDITION

Appendix A

Tutorial - Industrial Tank

A.1 Introduction

The purpose of this Tutorial is -

• To create a database (Geometry model) for an Industrial tanking/piping application .

• To learn to create ‘Volume Grids’.

Pre-requisites

• Basic concepts of creating Geometries and Manipulation.

• Basic concepts of 3D Multiblocks creation, Mapping, etc.

Time Required

• 2-3 hours.

A.2 Creating Geometry

A.2.1 Barrel

1. Create a curve for the barrel using point command.

Menu CommandModule Geometry –> Point –> Create –> XYZ Coordinate.

Create the following 4 points:

Point x Co-ord y Co-ord z Co-ord

1. 250 0 02. 300 200 03. 300 300 04. 250 500 0

73

74 APPENDIX A. TUTORIAL - INDUSTRIAL TANK

2. Create PLC from the 4 points.Menu CommandModule Geometry –> Piecewise Linear Curve –> Convert –> From Points.

3. Add points to the PLC by using the PLC Equal Arc option.Menu CommandModule Geometry –> Piecewise Linear Curve –> Convert –> PLC Equal ArcEnter value 100 in the dialog box.

4. Make 25 copies of the PLC(excluding the one already there) by rotating the PLC about theY axis through 3.6o each.ToolbarShow Edit Tools –> Copy Geometry EntityFill in the following values:Top SelectedRotationy3.6No. of copies 25Set MatrixApply,CanceliRefer Fig.No A.1

Figure A.1: Barrel PLC’s

5. Create PBLS from the interpolated PLCs.Module Geometry –> Piecewise Bi-Linear Surface –> Convert –> From PLCsRefer fig A.2

6. Make 3 copies of the PBLS by rotating the whole PBLS through 90o about the Y axis.ToolbarShow Edit Tools –> Copy Geometry Entity

Fill in the following values:Top Selected

A.2. CREATING GEOMETRY 75

Figure A.2: Barrel PBLS

Rotationy90No.of copies 3Set MatrixApply,CancelRefer Fig.No A.3

Figure A.3: Barrel

7. Select All Entities from the Selection Set and Hide all PBLS.


A.2.2 Dome

1. Create the curve from the given expression.Menu CommandModule Geometry –> Piecewise Linear Curve –> Create –> From Expression.Fill the following values:010atan(62.5/150)pi/2162.5*cos(u)162.5*sin(u)0Apply,CancelRefer Fig.No A.4

Figure A.4: Expression Dialog Box

2. Translate the PLC through 100,437.5,0.ToolbarShow Edit Tools –> Move Geometry EntityFill in the following values:Top SelectedTranslation100,437.5,0


Set MatrixApply,Cancel

3. Make 25 copies of the PLC by rotating the PLC about the Y axis through 3.6o each.ToolbarShow Edit Tools –> Copy Geometry EntityFill in the following values:Top SelectedRotationy3.6No. of copies 25Set MatrixApply,CancelRefer fig A.5Refer fig A.6 for the PLC

Figure A.5: Copy Dialog Boxi

4. Create a PBLS from the interpolated PLCs:Module Geometry –> Piecewise Bi-Linear surface –> Convert –> from PLCsRefer fig A.7

5. Make 3 copies of the PBLS by rotating the whole PBLS through 90o about the Y axis.


Figure A.6: Dome PLC’s

Figure A.7: Dome PBLS


6. ToolbarShow Edit Tools –> Copy Geometry EntityFill in the following values:Top SelectedRotationy90 degreeNO. of Copies 3Set MatrixApply.CancelRefer fig A.8

Figure A.8: Dome


A.2.3 Fillet

1. Create PLC from the expression.Menu CommandGeometry –> Piecewise Linear Curve –> Create –> From Expression.Use the following values : 0, 10, 0, pi/2, 50-50*cos(u), 50-50*sin(u), 0. Refer fig A.9

2. Translate the PLC to (50,600,0).ToolbarShow Edit Tools –> Move Geometry EntityFill in the following values:Top SelectedTranslateX=50,Y=600,Z=0Set MatrixApply,Cancel


Figure A.9: Fillet PLCsee figure C.11

3. Make 25 copies of the PLC by rotating the PLC about the Y axis through 3.6o each.ToolbarShow Edit Tools –> Copy Geometry EntityFill in the following values:Top SelectedRotationy3.6No. of Copies 25Set MatrixApply,CancelRefer Fig.No A.10

Figure A.10: Fillet PLC’s

4. Create a PBLS from the interpolated PLCs:


Module Geometry –> Piecewise Bi-Linear Surface –> Convert –> From PLCsRefer fig A.11

Figure A.11: Fillet PBLS

5. Make 3 copies of the PBLS by rotating the whole PBLS through 90o about the Y axis.ToolbarShow Edit Tools –> Copy Geometry EntityFill in the following values:Top SelectedRotationy90No. of copies 3Set MatrixApply,CancelRefer fig A.12

Figure A.12: Fillet



A.2.4 Pipe

Bent Pipe

1. Extract the boundary PLC from the Upper face of the Fillet.First, pick the PBLS.Toolbar

Go to picking mode by clicking on Picking ON/OFF.If the boundary points are not displayed clicked on Show Boundary Points to see bound-ary point of PBLS.

Click on any two points on the boundary PLC from upper surface of fillet. Then extractthe PLC.

2. Menu CommandModule Geometry –> Piecewise Linear Curve –> Extract –> From PBLS. Thiswill ensure that all 4 PLCs will be extracted from upper surface of the fillet.

3. Translate all 4 PLC’s to 100,-650,0.ToolbarShow Edit Tools –> Move Geometry EntityFill in the following values:All Selected TranslationX=100, Y= -650, Z=0Set matrixApply,Cancel

4. Make 10 copies of each PLC by rotating each PLC about the Z axis through 10o each. Selectone PLC at a time and Rotate it about the z axis.ToolbarShow Edit Tools –> Copy Geometry EntityFill in the following values:Top SelectedRotationZ10No of copies 9Set MatrixApply,CancelRefer Fig. No A.13


Figure A.13: Bent Pipe Frame

5. Create a PBLS from the interpolated PLCs:

Module Geometry –> Piecewise Bi-Linear Surface –> Convert –> From PLCsGenerate all four surfaces of bend pipe by same procedure mentioned above.

6. Translate all PBLS’s by X= -100, Y=650, Z=0.ToolbarShow Edit Tools –> Move Geometry EntityFill in the following values:All SelectedTranslation-100, 650, 0Set MatrixApply,CancelRefer fig A.14

Straight Pipe

1. Extract the PLCs from the left face of Bent Pipe.First, pick the PBLS -ToolbarGo to picking mode by clicking on Picking ON/OFFIf the boundary points are not displayed clicked on Show Boundary Points to see bound-ary point of PBLS.

Click on any two points on the boundary PLC from upper surface of Bent Pipe. Thenextract the PLC-Menu Command


Figure A.14: Bent Pipe

Geometry –> Piecewise Linear Curve –> Extract –> From PBLS.In this way all the 4 PLCs must be extracted from upper surface of Bent Pipe.

2. Translate all 4 PLC one by one to -250,0,0 and Copy it.ToolbarShow Edit Tools –> Copy Geometry EntityFill in the following values:Top SelectedTranslation-250,0,0Set MatrixApply,Cancel

3. Interpolate between the 2 PLCs to get 25 PLCs in allMenu CommandModule Geometry –> Piecewise Linear Curve –> Create –> Algebra of N PLCs.Use the following values:No of Copies: 25U Min: 0U max: 1Algebraic Equation: c1*u+c2*(1-u)

4. Create PBLS from the Interpolated PLCsModule Geometry –> Piecewise Bi-Linear Surface –> Convert –> From PLCsCreate One by One all 4 PBLS by the same procedure. Refer fig A.15

A.3. VOLUME GRID GENERATION 85

Figure A.15: Straight Pipe

A.3 Volume Grid Generation

A.3.1 Creating Topology

The topology to be created is shown in fig A.16

Figure A.16: Topology

1. Create a BlockMenu Command

2. Block –> 3D Multiblock –> Create –> Block

3. Enter the following value:30,30,30 Refer fig A.17


Figure A.17: Dialog box

4. Translate blockMenu Command

5. Block –> 3D Multiblock –> Edit Topology –>Edit Operations.

6. Fill in the following values:movetranslationblocko15-15ApplyRefer fig A.18

7. Scale BlockMenu CommandBlock –> 3D Multiblock –> Edit Topology –> Edit operation.

8. Fill in the following values:movescaling0.50.50.5Apply

9. Select the top face of the block . Then move the face by 485 in y direction.Menu CommandBlock –> 3D Multiblock –> Edit Topology –> Edit operations.

10. Enter the following values: 0,485,0



11. Create block on top of the block made .Select the upper face of the block.Menu CommandBlock –> 3D Multiblock –> Create –> Block.

12. Create a block at distance 100.

13. On top of this create a block at distance 50.

14. Similarly on top of this create blocks at distance 100, 100.

Refer fig A.19

A.3.2 Mapping

1. Mapping of the tank is to be done to get the grid as shown in fig A.20

After rendering mapped surfaces we will get fig A.21

2. Open the PBLS file of tank using read as Zeus Numerix file format. For ease of mapping,rotate the whole PBLS by 45 degrees about Y axis.



Figure A.20: Mapped 3D Blocks

ToolbarShow Edit Tools –> Move Geometry Entity

3. Fill in the following values:All Selectedy45Set MatrixOK

In this way, all PBLS’s are rotated.

4. From the 3D Block Toolbar, using the traverse block option Select the lowermost block tomap the barrel.

5. Select the option Show current block. Select a vertical face of this block using traverse faceoption in the Toolbar.


Figure A.21: Rendering of Mapped Blocks

Refer fig:A.22

6. Select the PBLS directly opposite to the selected block face and from the Toolbar click showmapping lines and click change mapping order, until the correct order is obtained as shownin fig A.23

7. Next map the face.Menu CommandBlock –> 3D Multiblock –> Map / Unmap –> Map Face .

8. Enter 100 in the command box. Refer fig A.24

9. Check the mapping by doing rendering of mapped facesMenu CommandBlock –> 3D Multiblock –> Attributes –> Rendering –> Rendering MappedSurfaces.

10. Click the option again to get back to the normal view mode.

11. Similarly, map all the remaining PBLS upto the Bent pipe. The step by step blocks areshown in the given figures A.25 to A.28.

12. Next select the free circular face of the bent pipe. Create a new block at a distance of 250by creating block as shown in creating topology. Refer fig A.29

13. By above mapping methods, map the Straight pipe. Refer fig A.30


Figure A.22: 3-D MultiBlock tool


Figure A.23: Mapping Step1

Figure A.24: Mapping Step2

14. Finally, paste all the blocksMenu commandBlock –> 3D Multiblock –> Convert –> Paste all Blocks

15. See the mapped tank by rendering mapped surfaces as explained in Section on Mappingearlier on in this tutorial.

The volume grid is now completed.


Figure A.25: Mapped Barrel

Figure A.26: Mapped Dome

Figure A.27: Mapped Fillet


Figure A.28: Mapped Bent Pipe

Figure A.29: Create Block for Straight Pipe

Figure A.30: Mapped Straight Pipe

Appendix B

Grid Tutorial: Generic Missile

B.1 Introduction

• The purpose of this Tutorial is to acquaint the user with the basics of creating geometryand topology on GridZTM.

Time Required

• The time required to complete this tutorial is about 1-2 hours.

B.2 Geometry

The required Generic Missile Geometry is as shown in B.1

Figure B.1: Required Geometry of Generic Missile

B.2.1 Blending Surface

1. Create a Curve of the blending surface using command.Menu Command

95

96 APPENDIX B. GRID TUTORIAL: GENERIC MISSILE

Geometry –> Piecewise Linear Curve –> Create –> From Expression.Use the following values :Open(0)/Close(1)–> 0No. of points = 40Umin –> pi/2Umax –>pi/2+atan(1.95/4)X –> 4.5*cos(u)Y –> 4.5*sin(u)-4Z–> 0Apply, Cancel

Figure B.2: Dialog box for PLC from expression

2. Curve created shown in B.3

Figure B.3: PLC From Expression

3. Make 10 copies of the curve by rotating the curve about X-axis 9 degree each.Control PanelShow Edit Tools –> Copy Geometry Entity

B.2. GEOMETRY 97

Fill in the following values in the Dialog Box shown in B.5Top SelectedRotationX = 9No. of copies = 10 Set Matrix, Apply, Cancel

Figure B.4: Dialogue Box

4. Create PBLS from the Interpolated PLCsMenu CommandGeometry –> Piecewise Bi-Linear Surface –> Convert –> From PLCs

5. Make 3 copies of PBLS bt rotating PBLS through 90 Degree about X-axis.Control PanelShow Edit Tools –> Copy Geometry EntityFill the following values:Top SelectedRotationX = 90No. of copies = 3 Set Matrix, Apply, Cancel


Figure B.5: 10 PLC creted

PBLS creted from PLC Required Blending Surface

6. Save it in the ZEUS .pbls file format.

B.2.2 Nose

1. Extract the boundary curve from the leading edge of Blending Surface.First pick the surface.

Menu CommandGo to picking mode by clicking on Picking ON/OFF icon in Toolbar Buttons.

Figure B.6: Picking ON/OFF Icon

If boundary points are not displayed clicked on Show Boundary Points icon in toolbarbuttons to see boundary points of surface.

B.2. GEOMETRY 99

Figure B.7: Show Boundary Points Icon

Click on any two boundary points of blending surface.then extract the curve using com-mand.Menu CommandGeometry –> Piecewise Linear Curve –> Extract –> From PBLS.

In this way all the 4 PLCs should be extracted from the leading edge of the BlendingSurface.See B.8

Figure B.8: Required PLCs

2. Deselect and Hide the Blending Surface. Right click on the PBLS’s in the selection set andclick Select/Deselect. Then All PBLS’s will appear in the Deselected Box. Again rightclick on these PBLS in the Deselected column and click on Hide.

3. Check the direction of the curve.Toolbar ButtonsClick on Show Direction icon shown below to see direction of curve.Note :Direction of all the curves should be same.Refer fig: B.9

Figure B.9: Show Geometry Direction Icon

4. Create a surface from 4 curvesMenu CommandGrid –> 2D Structured –> Create –> Four Open PLC


This will create a structured grid, we have to extract the surface from this grid.Menu CommandGeometry –> PBLS –> Extract –> Current 2D Block

Delete the BLOCK2D from Database Summary

5. Deform the Surface and get the desired shapeMenu CommandsGeometry –> PBLS –> Edit –> DeformFill the following values in the dialog box:x = -sqrt(0.05*0.05-y*y-z*z)-1.95y = yz = zOK

6. Delete the previous surface from Database Summary.

Figure B.10: Required PBLS

Figure B.11: Blending Surface with the Nose

7. Save it in the ZEUS .pbls file format.

B.2. GEOMETRY 101

B.2.3 Cylinder

1. Extract the boundary curve from the Trailing edge of Blending Surface.First pick the surface. Go to Pick Mode .ToolbarPicking ON/OFF

If boundary points are not displayed clicked on Show Boundary Points in toolbar buttonsto see boundary points of surface.

2. Click on any two boundary points of one of the PBLS of the blending surface.then extractthe curve using command.Menu CommandGeometry –> Piecewise Linear Curve –> Extract –> From PBLS.

3. Translate a curve to (10,0,0) and copy it.Control PanelShow Edit Tools –> Copy Geometry EntityFill the following values:Top SelectedTranslationX=10,Y=0,Z=0Set Matrix,Apply,Cancel

Figure B.12: Required PLC

4. Interpolate between the 2 PLCs to get 50 PLC in all.Menu CommmandGeometry –> Piecewise Linear Curve –> Create –> Algebra of N PLCsUse the following values:No. Of Copies = 50Umin =0Umax =1Algebra Equation = c1*u+c2*(1-u)OK


5. Create PBLS from the interpolated PLCs.See B.13Menu CommandGeometry –> Piecewise Bi-Linear Surface –> Convert –> From PLCs

Figure B.13: Required Interpolated PLCs

6. Make 3 copies of PBLS by rotating the PBLS through 90 degree about X axis.Control PanelShow Edit Tools –> Copy Geometry EntityFill the following values:Top SelectedRotationX = 90No. of copies = 3Set Matrix, Apply, Cancel

7. Your Geometry is complete. Select all and save it in ZEUS format.See B.14

Figure B.14: Required Geometry of Generic Missile

B.3. TOPOLOGY 103

B.3 Topology

1. Create a BlockMenu Command:Block –> 3 D Multiblock –> Create –> Block.A dialogue box will appear with values:X=30,Y=30,Z=30,Press OK

2. Translate block usingMenu Command:Block –> 3 D Multiblock –> Edit Topology –>Edit Operations. A dialog box will appear as shown in the B.15. Thus select Move Block By from thedrop down menu and fill in the following values.

Figure B.15: Dialog box for moving a block

Enter the following values: -10, -15, -15.See B.16 for Block Position.

3. Now Create a Block on the trailing edge side face of a block created in the last step. Selectthe face by using face traversal option in the Show 3D Block Tools.Menu Command:Block –> 3 D Multiblock –> Create –> On Face.A Selector Box will appear on the screen,which will have two boxes as showm in B.17.


Figure B.16: Required Block Position

Figure B.17: Selector Box

4. Choose the right hand box to select the face and the left hand box to bring that face of theblock closer to the geometry. This is done to enable better Mapping.See B.18.

5. Bring all the Faces of the Block closer to the geometry,except the face at the back of themissile .This is done to obtain better Grid. See B.19.

6. Now divide this Block into no. of parts as your Geometry i.e into 3 parts.Menu CommandBlock –> 3 D Multiblock –> Create –> Plane Cutter.

Choose an innermost block by using Block Traversal option in Show 3D Block Tools.An ijk Traversal Dialogue Box will appear on the screen as shown in figure:-Traverse the plane in i direction and cut it as required by your geometry, as shown in B.20.Make two cuts, one near the end of blending surface and other near the trailing edge of thegeneric missile

After second cut see B.21.

7. Topology is complete. Save the block in CGNS format with .cgns ext.

B.4. MAPPING 105

Figure B.18: Block On Face

Figure B.19: Enclosed Geometry

B.4 Mapping

1. Open the PBLS file of of the Missle using read as Zeus Numerix file format.

2. From the 3D Block Toolbar, using the traverse block option Select the frontmost blockto map the Nose.Select the option Show current block. Select a vertical face of this block using traverseface option in the toolbar.

3. Select the Nose PBLS and Face block directly opposite to it and from the toolbar clickShow Mapping Lines and click Change Mapping Order, until the correct order isobtained as shown in B.22.

4. Then Map the face.Menu CommandBlock –> 3 D Multiblock –> Map / Unmap –> Map Face .Enter Nose in the command box.

5. Check the mapping by doing Rendering of Mapped facesMenu CommandBlock –> 3 D Multiblock –> Rendering –> Rendering All Block.


Figure B.20: Plane Cutter1

Figure B.21: Plane Cutter2

6. Delete the PBLS which has been mapped. See All Block Rendered B.23.

7. Similiarly Map all the faces of the blending surface see B.24. Use the block faces exactlyinfront of the PBLS for mapping.

8. Delete the PBLS which has been mapped. Mapped Blending surface see B.25. .

9. Check the mapping by doing Rendering of Mapped facesMenu CommandBlock –> 3 D Multiblock –> Rendering –> Rendering Mapped Surfaces.See B.26.

10. Click the option again to get back to the normal view mode.

11. Similarly Map all the remaining PBLS.

12. Completely Mapped Generic Missile.See B.27.

13. The Volume Grid is complete.See B.28.

B.5. CLUSTERING 107

Figure B.22: Face to be mapped with Nose

Figure B.23: All Blocks Rendered

B.5 Clustering

1. Before Clustering ,delete all the blocks inside the Geometry.Select the block to be clustered using the Block traversal option given in 3D BlockToolbar.Menu Command3DBlock –> Edit Topology –>– Delete Selected Block

2. Now select the Block from the Blending Surface and the Edge of the Block parallel to whichgrid lines are. This selection can be done using Show 3D block Tools options. Then selectthe vertex on that edge,towards the face,where you want more no.of Grid points. Rememberwe cannot do clustering on the edges which are mapped. Then go toMenu Command3dBlock –>– Clustering –>– ClusteringFill the following values:ExponentialOne SideNormalAll Block


Figure B.24: Showing Mapping lines for Blending Surface

Figure B.25: Mapped Blending Surface

Volume50.01OK

See B.29.

3. Now select the last BLock i.e. one behind the Geometry and do the clustering in the similiarmanner.

4. save it CGNS format with .cgns extension.

B.5. CLUSTERING 109

Figure B.26: Rendered Surface

Figure B.27: Mapped Missile

Figure B.28: Volume Grid OF Missile


Figure B.29: Clustering Box

Appendix C

Tutorial - Ahmed body

C.1 Introduction

Ahmed body is a simplified car model created by Ahmed et al in 1980’s to investigate the behaviorof newly developed turbulence models for complex geometry cases.

The Ahmed body is made up of a round front part, a movable slant plane placed in the rearof the body to study the separation phenomena at different angles, and a rectangular box, whichconnects the front and the rear slant plane as shown in figure C.1.

Figure C.1: Ahmed body

To create the Ahmed body in GridZTM, we begin by creating surfaces for the Front, Mid-Body,and Rear portions.

C.2 Ahmed body Front Surface

We have divided the front surface into 5 parts:

• Lower PBLS

• Upper PBLS

111

112 APPENDIX C. TUTORIAL - AHMED BODY

• Left PBLS

• Right PBLS

• Center PBLS

C.2.1 Front - Lower PBLS

1. Create a PLC from the given expression.

• Menu CommandGeometry –> Piecewise Linear Curve –> Create –> From Expression.

• Use the following values:0, 30, 0, pi/2, 100-100*cos(u), 100-100*sin(u), 0. Referfig C.2

Refer fig C.3 for the PLC.

Figure C.2: PLC - From Expression (Command Box)

2. Deform the Curve (x,y,y). A new deformed PLC is created (Refer to the isometric view forbetter understanding).

• Menu CommandGeometry –> Piecewise Linear Curve –> Edit –> Deform

Fill in values - see figure C.4

3. Delete previous PLC.

Refer fig C.5 for the PLC’s.

• Select the initial PLC with a right-click of the mouse and delete it using this option.

C.2. AHMED BODY FRONT SURFACE 113

Figure C.3: PLC - From Expression

Figure C.4: Deform - From Expression

4. Create a copy of the deformed PLC by scaling (1,1,-1)

• ToolbarShow Edit Tools –> Copy Geometry EntitySelect And Fill in the following ValuesTop SelectedScaling11-1No. Copies 1set matrixApply , Cancelsee figure C.6


Figure C.5: Isometric View

5. Translate the 1st deformed PLC (0,0,-389) and Move it.

• ToolbarDeselect All from Selection Set

• Right click on first deformed PLC, click on select option to select it

• ToolbarShow Edit Tools –> Move Geometry EntityTop SelectedTraslation00-389set matrixApply , Cancelsee figure C.7

Refer fig C.8 for the Translated PLC.

6. Between the 2 PLCs, interpolate 35 copies of PLCs using Algebra of N PLCs. 35,0,1,c1*u+c2*(1-u)

• Menu CommandGeometry –> Piecewise Linear Curve –> Create –> Algebra of N PLCs

• Fill in the following values: 35,0,1,c1*u+c2*(1-u), see figure C.9

7. Create a PBLS from the interpolated PLCs

• Writepbls from plcs in Command Line OR


Figure C.6: Scaling Option

• Use commandGeometry –> Piecewise Bi-Linear Surface –> convert –> Piecewise LinearCurve

You have now created the Lower PBLS of the Front of the Ahmed body. See figure C.10

C.2.2 Front - Upper PBLS

1. Scale the Lower PBLS (1,-1,1) and create a copy.

• ToolbarShow Edit Tools –> Copy Geometry EntityTop SelectedScaling1-11No. of Copies - 1set matrixApply,Cancelsee figure C.11


Figure C.7: Translation Option

2. Translate the new PBLS (0,288,0) and Move it.

• ToolbarShow Edit Tools –> Move Geometry EntityTop SelectedTraslation02880No. of Copies 1set matrixApply,Cancel

The upper PBLS has been created as shown in figure C.12

C.2.3 Front - Left PBLS

1. Extract a boundary PLC from the left side of the Upper PBLS.

• ToolbarClick Pick an Entity button,

• Click iso-metric view button


Figure C.8: Translated PLC

Figure C.9: Algebra of N PLCs

• Click show boundary points button

• Left click on any two points on the boundary PLC from the left side of the UpperPBLS in the ’PICKING ON MODE’

• Menu CommandGeometry –> Piecewise Linear Curve –> Extract –> From PBLS

• Follow the same procedure as above to extract PLC from left side of the lower PBLS

2. Deselect All and select each PLC one after another.

• ToolbarSelect only two extracted PLCs by a right click on each extracted PLC ORwith the help of selection set

3. Between the 2 PLCs, interpolate 25 copies of PLCs using Algebra of N PLCs (25,0,1,c1*u+c2*(1-u)


Figure C.10: Front Lower PBLS

Figure C.11: Scaling Option

• Menu CommandGeometry –> Piecewise Linear Curve –> Create –> Algebra of N PLCs.

• Fill in the following values: 25,0,1,c1*u+c2*(1-u), see figure C.13

The image will appear as shown in figure C.14.


• Writepbls from plc in the Command Line Input OR

• Use CommandGeometry –> Piecewise Bi-Linear Surface –> Convert –> Piecewise LinearCurve

C.2.4 Front - Right PBLS

1. Extract a boundary PLC from the right side of the upper PBLS.


Figure C.12: Upper and Lower PBLS of Front surface

Figure C.13: Values for Algebra of N PLCs

• ToolbarClick on Pick an Entity button And also put on the Boundary points ofPBLS

• Left click on any two points on the boundary PLC from the right side of the UpperPBLS, as earlier.


• Follow the same procedure as above to extract PLC from right side of the lower PBLS

2. Deselect All and select PLCs which are extracted from right side Lower and Upper PBLS




Figure C.14: Left side PLCs for Surface 1

• Fill in the following values:25,0,1,c1*u+c2*(1-u)


• Write pbls from plc in the Command Line Input.

Four PBLS of the Front Surface are created - as shown in figure C.15

Figure C.15: The Four PBLS of Front Surface

• Click On Show Display Tools in the Command Buttons, from that click on Left SideView.This will give the Left Hand Side View of the geometry or PBLS.

C.2.5 Front - Center PBLS

1. Extract a PLC from the inner side of the Lower PBLS.

• ToolbarClick Pick an Entity And Put ON the Bondary Points


• Left click on any two points on the inner boundary of the Lower PBLS.


• Left click on any two points on the inner boundary of Upper PBLS and extract thePLC

2. Deselect All and select PLCs which are extracted earlier.



• Fill in the following values:25,0,1,c1*u+c2*(1-u)


• Write pbls from plcs in the Command Line Input.


Figure C.16: Ahmedbody Front Surface

Note: Save the file as a .pbls file.

1. Select All

2. Save File as front.pbls

3. Delete All to clear the canvas.

While creating the Front Surface of the Ahmed body you have learned the method to:

• Create PLCs

• Extract PLCs from PBLS


• Reset Transformation matrix and Scale

• Reset Transformation matrix and Translate

• Interpolate between PLCs

• Create N PLCs using algebraic equations

• Create PBLS

In the next sections you will have to refer to commands provided in the Ahmed body Frontsurface to create the rest of the Ahmed body. The steps and values are provided.

C.3 Ahmed body Mid-body Surface

The middle body surface is divided into THREE surfaces(Mid-body 1,Mid-body 2,Mid-body 3).Each surface is made up of FOUR PBLS (Lower, Upper, and two sides). The steps to create thesurfaces are the similar, the only exceptions in each surface are the coordinates.

• Mid-body 1

• Mid-body 2

• Mid-body 3

C.3.1 Mid-body 1

Mid-body 1 - Lower PBLS

1. Enter coordinates for two end points P1 and P2.

• Menu CommandGeometry–> Point –> Create–> XYZ Co-ordinates

• Enter coordinates for P1- X=100, Y=0, Z=0

• Similarly enter the coordinates for P2- X=182, Y=0, Z=0

2. Create PLC from points

• Menu CommandGeometry–> Piecewise Linear Curve –> Convert–> From Points

• The PLC Equal Arc option - Which divides the PLC into equal number of partsGeometry–> Piecewise Linear Curve –> Convert–> PLC Equal Arc

• Toolbar

Click on Show All Points This will show all points on the PBLS. To put itOFF click again on the same button.

C.3. AHMED BODY MID-BODY SURFACE 123

3. Now translate and make ONE copy of above PLC.

Show Edit Tools –> Copy Geometry Entityput values as X=0,Y=0,Z=-389 Give No. Of Copies as 1 , Apply , Cancel.

4. Using command Algebra of N PLCs create 35 copies.Geometry –> Piecewise Linear Curve –> Create –> Algebra Of N-PLC

5. Create a PBLS from the PLCsGeometry –> Piecewise Bi-Linear Surface –> Convert –> From PLCs The newlygenerated PBLS is nothing but the Mid-Body - Upper PBLS

6. Deselect All and Select the newly created PBLS.

Mid-body 1 - Upper PBLS

1. Translate and make ONE copy of PBLSShow Edit Tools –> Copy Geometry Entity Use values as X=0, Y=288, Z=0 GiveNo. of Copies as 1 , Apply , Cancel.

2. The generated copy of PBLS is nothing but the Mid-Body 1 - Lower PBLS.

Mid-body 1 - Left PBLS

• Put ON the Boundary points.

1. Extract a boundary PLC from the left side of the Lower PBLS.


3. Deselect all

4. Select TWO extracted PLCs

5. UsingGeometry –> Piecewise Linear Curve –> Algebra of N PLCs create 25 copies

6. Create a PBLS from the PLCs with command used in creating Mid-Body - Lower PBLS

Mid-body 1 - Right PBLS

• Make ONE copy and Translate the above created Left PBLS to X=0, Y=0, Z=-389 withthe help of Copy Geometry Entity.



1. Select All

2. Save File as midbody1.pbls



Figure C.17: Mid-body 1 Surface

C.3.2 Mid-body 2- Lower PBLS

1. Enter the XYZ Coordinates for two end points P1= X=182, Y=0, Z=0 and P2=X=822,Y=0, Z=0.

2. Create PLC from the 2 points

3. Use the PLC Equal Arc specify no.as 50

4. Show All Points

5. Copy and Traslate the above PLC using Copy Geometry Entity tool with values X=0,Y=0, Z=-389 Give No. of copies as 1

6. Using Algebra of N PLCs create 35 copies

7. Create a PBLS from the PLCs which gives the Mid-Body Lower PBLS.


1. Copy and Traslate above PBLS using Copy Geometry Entity tool with values X=0, Y=288,Z=0

2. Put No. of copies as 1


1. Extract a boundary PLC from the left side of the Lower PBLS.


3. Select the extracted PLCs

4. Using command Algebra of N PLCs create 25 copies

5. Create a PBLS from the PLCs.

C.3. AHMED BODY MID-BODY SURFACE 125


1. Make ONE copy and Traslate above PBLS with values X=0, Y=0, Z=-389




1. Select All



C.3.3 Mid-body 3

Mid-body 3 - Lower PBLS

1. Enter coordinates for two end points P1= X=822, Y=0, Z=0; P2= X=874, Y=0, Z=0

2. Create a PLC from the two end points


4. Display All Points

5. Make one Copy and Translate above PLC using values X=0, Y=0, Z=-389

6. No. of copies 1


8. Create a PBLS from the PLCs



1. Make one Copy and Traslate the above Lower PBLS

2. For Traslation use values as X=0, Y=288, Z=0

3. No. of Copies 1


1. Extract a boundary PLC from the left side of the Lower PBLS

2. Extract a boundary PLC from the left side of the Upper PBLS

3. Deselect all

4. Select extracted PLCs




1. Make one Copy and Traslate Left PBLS

2. Translation values X=0, Y=0, Z=-389

3. No. of Copies 1




1. Select All



C.4. AHMED BODY REAR SURFACE 127

C.4 Ahmed body Rear Surface

C.4.1 Rear - Lower PBLS

1. Enter coordinates for two end points Point1= X=874, Y=0, Z=0; and Point2= X=1044,Y=0, Z=0


3. Use the PLC Equal Arc specify no. as 20


5. Make ONE copy and Translate the above PLC with values X=0, Y=0, Z=-389

6. No. of copies 1



9. Deselect All


Figure C.20: Rear Lower PBLS

C.4.2 Rear - Upper PBLS

1. Enter coordinates for two end points Point1= X=874, Y=288, Z=0; and Point2= X=1044,Y=145.3, Z=0




5. Make ONE copy and Translate above PLC with values X=0, Y=0, Z=-389

6. No. of copies 1




C.4.3 Rear - Left PBLS

1. Extract a boundary PLC from the left side of the Lower PBLS

2. Extract a boundary PLC from the left side of the Upper PBLS

3. Deselect all

4. Select the extracted PLCs.

5. Using command Algebra of N PLCs create 25 copies.


C.4.4 Rear - Right PBLS

1. Make ONE copy and Translate the above PBLS with values X=0, Y=0, Z=-389

2. No. of copies 1

C.4.5 Rear - Center PBLS

To close the rear-end of the Ahmed body

1. Extract a boundary PLC from the rear side of the Lower PBLS

2. Extract a boundary PLC from the rear side of the Upper PBLS

3. Deselect all

4. Pick-select (right-click) each PLC





1. Select All

2. Save File as rear.pbls


C.5. AHMED BODY COMPLETE SURFACE 129

Figure C.21: Rear Surface

C.5 Ahmed body Complete Surface

To save the Ahmed body as a single surface PBLS, open each of the saved .pbls files one after.The whole Ahmed body will appear on screen. Refer fig C.22

1. Select All

2. Save File as Ahmedbody.pbls


Figure C.22: Ahmedbody - PBLS


C.6 Volume Grid for Ahmed body

Volume grid of the Ahmed body is generated by making the initial topology using 3D multiblocksand then mapping the faces of the blocks with the surface PBLS of the ahmed body.

C.6.1 Topology

.There are two ways of creating it.

• Make the 2D-Multiblocks and export it to 3D-multiblocks

• Create a block and then create another blocks on its faces and similarly creates all blockswhich is not a good idea here as the number of blocks here is more.

Here, only the first method is explained.The topology to be created for the ahmed body is shown in figures C.23, C.24, C.25.

Figure C.23: Initial Topology view 1


C.6. VOLUME GRID FOR AHMED BODY 131


Creating Topology by method1

Instead of creating the 2D multiblock directly, we go from the basics. First we create a PLC fromspecific points; from which we make a PBLS. This PBLS is then converted to a 2D block; whichfinally is exported to 3D.

1. Create a PLC from the following points:

Refer Fig.6.25

Menu Command

• Geometry –> Points –> Create –> XYZ Cordinates

• Give values stated above in the command box opened.

• x=0. y = 0

• x= 2088. y = 0

• x= 2196.3009 y = 0

• x = 2277.5366 y = 0

• x = 2915.7385 y = 0

• x = 2973.7568 y = 0

• x = 3140.0761 y = 0

• x = 7316.0761 y = 0

2. Use the points to create a PLC from them: Menu CommandGeometry –> PLC –> Convert –> from points.

3. Make four copies of this PLC by translating along Y axis.

• Make ONE copy and Translate the above PLC using values (x=0,y=2*282.3560,z=0)


• No. of Copies 1

• Repeat the above step on the newly formed PLC with respective translation values:(0,282.3560,0) and (0,2*282.3560,0).

• Menu command: Convert these PLCs to PBLS usingGeometry –> Piecewise Bi-Linear Surface –> Convert –> From PLCs

4. Now we convert this PBLS into a 2-D blocks.

Menu CommandBlock –> 2D Multiblock –> Convert –> PBLS to BLOCKRefer fig: C.26

Figure C.26: PBLS to 2D block

Now we export this 2D block into 3D. Menu CommandBlock –> 3D Multiblock –> Convert –> From 2D MultiblockRefe fig: C.27

• No. of layers in z-direction= 3

• Distance of 1st layer= 2*382.9211 ; where 382.9211 is the length of theAhmed Body along Z-dir. After putting value click Next.

• Distance of 2nd layer= 382.9211 Click Next.

• Distance of 3rd layer= 2*382.9211

• Select Unmapped

• Save this file with a suitable name in CGNS(.cgns) file format

• Now the job at hand is to fit the geometry of the Ahmed Body created in to the 3DMultiblock that we have created. Note that you donot forget to save the 3DBlockcreated in ’.cgns’ format. When you reopen this file first select the file extension asCGNS(.cgns) in File type menu.

• Since, throughout the process we have been careful enough to create the block accordingto the dimensions of the geometry, the final fitting would not be very tedious. We justopen the .pbls file of Ahmed Body in the 3D block created; followed by some very basictransformation operations.


Figure C.27: Export 2D to 3D

• Initially when the .pbls and .cgns files are opened, the geometry is offset from thetopology.The figure below gives a clear view of the orientation obtained.

Menu commandShow Edit Tools –> Move Geometry Entity. Enter the following values in the com-mand box opened. x= 2100, y=565, z=1148.7633.

5. Save the file in CGNS GRID file after completing all blocks. Go to save option on toolbar,there in the list of formats choose CGNS, choose directory, give a file name like topologyand extension .cgns i.e. topology.cgns and click on Save button.

6. The final positioning of the Ahmed Body in the topology is shown in the figure 7.27.

C.6.2 Mapping the faces

1. Open the Surface grid file of the Ahmed body and deselect all from the icon ”deselect all”.

2. Select one PBLS for mapping using the picking option on the toolbar.fig C.30 Click on thisicon, the cursor will become a point and then right click on the required PBLS. fig C.31.

3. Move to the corresponding block which should be mapped with Block Traversal through

Face tool and then click the icon ”show current/all block option” on the 3D Blockoptions toolbar, to show only the current block. fig C.32.


Figure C.28: Relative Orientation wrt the Topology

4. Traverse the face of the block which is to mapped with the selected PBLS. and then Click

the Icon ”show/hide mapping guide lines” on the 3D block options toolbar for knowingthat mapping vertices are correct or not. If not then click the icon ”change mapping order”

to make it correct. fig C.33.

5. Then Map the face.

Menu CommandBlock–> 3DMultiBlock–> Mapped/unmapped–> Map face. fig C.34.

6. Mapped surface is checked from the following option:

Menu CommandBlock–> 3DmultiBlock –> Attributes –> Rendering –> Rendering mapped surface. fig C.35.Click on it again to get back normal block.

NOTE: For a proper mapping of the faces, the end points of each surface should be matchedexactly, else mismatch in the number of points does not allow the desired mapping.

The following figures are the various mapping steps:

7. Similarly mapped each PBLS of the Ahmed body as done above and check that all face ismapped or not. fig C.40.


Figure C.29: Correct position of the Ahmed Body

Figure C.30: Pick Entity Icon

8. Save the Mapped Blocks in the CGNS GRID file in the same way as topology was savedgiving it a different name.

C.6.3 Clustering

Clustering is done on a grid to increase the no. of grid points near the body over which flow isto be solved since at those areas more accurate results are desired and the flow changes are morenear the body as compared to places away from the body. Clustering cannot be done on theface of the block which is mapped. It is done on the other faces which are normal tothe mapped face.

1. Traverse to the block where clustering is to be done then traverse edges and vertex using the”traverse edge”, ”traverse vertex” option in the 3D Block toolbar and then use the Menucommand

Block –> 3D Multiblock –> Clustering –> All Blocks Enter the following valuesin the command box opened Exponential, one side, 30 , 2, .2. Refer fig C.41 andfig C.42.

2. Similarly clustering is done in all the required direction following the same procedure. Incase of wrong clustering, remove the clustering using the option


Figure C.31: Select a PBLS to be mapped

Figure C.32: Select a corresponding block

Block –> 3D Multiblock –> Clustering –> Remove Clustering and then do theclustering again.

3. To See the effect of Clustering in All Blocks just use Command-Blocks –> 3D Multiblock –> Rendering –> Show Layer in Plane

4. Save the 3D grid in CGNS grid file.


Figure C.33: Mapping lines in correct order

Figure C.34: Mapped block

Figure C.35: Rendering the mapped surface


Figure C.36: Mapped blocks





Figure C.40: Final mapped blocks


Figure C.41: Before Clustering

Figure C.42: After Clustering

Appendix D

Tutorial - Geometric Funnel

D.1 Introduction

The purpose of this Tutorial is -

• To create a Geometry model for a Funnel. Refer figure D.1

Figure D.1: Funnel - Wireframe

• To take over from where the preceding (Industrial Tank) tutorial leaves off.

• To help the user learn how to create Volume Grids .

Pre-requisites

• Basic Creation of Geometries and Manipulation.

• Basic concepts of 3D Multiblocks, Mapping, etc.

Time Required

• This tutorial requires about 6-8 hours for completion.

141

142 APPENDIX D. TUTORIAL - GEOMETRIC FUNNEL

D.2 Geometry - Creating the Central Part (AEGDBFHC)

D.2.1 Creating BFHC

1. Create a point (5,0,0).

• Menu CommandModule Geometry –> Point –> Create –> XYZ Coordinate.

• Enter the values 5, 0, 0

2. Make 9 copies of the Point by rotating it about the Z axis through 10o each.

• ToolbarShow Edit Options –> Copy Geometry EntityFill in the following values:Top SelectedRotationz, 10No.of Copies 9Set MatrixApply,Cancel

• Refer figure D.2 for the points created.

Figure D.2: Points

3. Create PLC from the points.

• Menu CommandModule Geometry –> Piecewise Linear Curve –> Convert –> From Points.

4. Divide the PLC into equal number of arcs.

• Menu CommandModule Geometry –> Piecewise Linear Curve –> Convert –> PLC EqualArc. Enter value 13 in command line.

D.2. GEOMETRY - CREATING THE CENTRAL PART (AEGDBFHC) 143

5. Translate the PLC to x = -5.5

• ToolbarShow Edit Options –> Move Geometry EntityFill in the following values:Top SelectedTranslation-5.5, 0, 0Set MatrixApply,Cancel

• Refer fig D.3

Figure D.3: Translated PLC

6. Make 15 copies of the PLC by rotating the PLC about the Y axis through 4o each time.

• ToolbarShow Edit Options –> Copy Geometry EntityFill in the following values:Top SelectedRotationy,4No. of Copies 15Set MatrixApply,Cancel

• Refer figure for viewing the PLC created D.4

7. Create PBLS from the interpolated PLCs.

• Enter pblsfromplcs in command line Input. Refer fig D.5

8. Make 2 copies of the PBLS by rotating it about the Y axis through 60o each time.


Figure D.4: Interpolated PLC’s

Figure D.5: PBLS


Refer fig: D.6

D.2.2 Creating AEGD

1. Create a point (3,0,0).


D.2. GEOMETRY - CREATING THE CENTRAL PART (AEGDBFHC) 145

Figure D.6: PBLS’s - 1

Enter the values 3, 0, 0

2. Make 9 copies of the Point by rotating it about the Z axis through 10o each.

• ToolbarShow Edit Options –> Copy Geometry EntityFill in the following values:Top SelectedRotationz,10No. of Copies 9Set MatrixApply,Cancel




• Menu CommandGeometry –> Piecewise Linear Curve –> Convert –> PLC Equal Arc.

• Enter value 13 in command line.

5. Translate the PLC to x= -4.5

• ToolbarShow Edit Options –> Move Geometry EntityFill in the following values:Top SelectedTranslation-4.5, 0, 0


Set MatrixApply,Cancel

6. Make 15 copies of the PLC by rotating the PLC about the Y axis through 4o each time.



• Enter pblsfromplcs in command line Input.

8. Make 2 copies of the PBLS by rotating it about the Y axis through 60o each time.


Refer fig: D.7

D.3 Creating the Upper and Lower Parts

D.3.1 Creating KL

1. Create a point (-4.5,0,0).


• Enter the following values -4.5, 0, 0

2. Make 15 copies of the Point by rotating it about the Y axis through 4o each.

D.3. CREATING THE UPPER AND LOWER PARTS 147

Figure D.7: PBLS’s - 2





• Menu CommandModule Geometry –> Piecewise Linear Curve –> Convert –> PLC EqualArc.


5. Make 2 copies of the PLC by rotating it about the Y axis through 60o each.

• ToolbarShow Edit Options –> Copy Geometry EntityFill in the following values:Top SelectedRotationy,60No. of Copies 2Set Matrix


Apply,Cancel

Refer fig: D.8

Figure D.8: PLC ”KL”

D.3.2 Scaling the PBLS

• Select the larger funnel boundary which was created first (BFHC).

• Scale the PBLSs by (9/11,1,9/11)Show Other Option –> Reset Transformation MatrixShow Other Option –> Set Scaling Matrix

• Fill in the following values: 9/11, 1, 9/11

D.3.3 Creating OR

1. Create a point (-12.5,0,0).


• Enter the values -12.5, 0, 0

2. Make 9 copies of the Point by rotating it about the Y axis through 10o each.

• ToolbarShow Edit Options –> Copy Geometry EntityFill in the following values:Top SelectedRotationy,10No. of copies 9Set MatrixApply,Cancel

D.4. CREATING RT 149





• Enter value 16 in the command line.

Refer fig: D.9

Figure D.9: PLC ”OR”

D.4 Creating RT

1. Deselect All and Create 2 points with co-ordinates (0, 0, 12.5) and (12.5, 0, 12.5).


• Enter the values 0, 0, 12.5 and 12.5, 0, 12.5





• Enter value 16 in the command line.


Creating TM

1. Deselect All and Create 2 points with co-ordinates (12.5, 0, 0) and (12.5, 0, 12.5).


• Enter the values 12.5, 0, 0 and 12.5, 0, 12.5






D.4.1 Creating the Lower Surface (OKLMTRO)

1. Deselect all and select PLC OR and the first PLC of arc KL.

2. Check direction’s of both the PLCs. If they are not same then change the direction.

• Menu CommandModule Geometry –> Piecewise Linear Curve –> Edit –> Reverse

3. Interpolate between these two PLC’s to get 13 copies.

• Menu CommandModule Geometry –> Piecewise Linear Curve –> Create –> Algebra of nPLC’s

• Enter the value 13 in the command line.


5. Menu CommandModule Geometry –> Piecewise Bi-Linear Curve –> Convert –> From PLC’s

Refer fig: D.10

6. Similarly, create the other 2 PBLS’s by selecting the 2 respective PLC’s and proceeding asshown in the previous steps.

D.5. CREATING THE SURFACE (OPQSTRO) 151

Figure D.10: Lower Surface

D.4.2 Creating the Upper Surface (PJINSQP)

1. Select only the three PBLS of lower surface (OKLMTRO).Then translate them to y=6.

• ToolbarShow Edit Options –> Move Geometry EntityFill in the following values:All SelectedTranslation0,6,0Set MatrixApply,Cancel

Refer fig: D.11

Figure D.11: Upper Surface

D.5 Creating the Surface (OPQSTRO)

1. Deselect all PBLS’s.


• Extract PLC PQ,QS,SN from PJINSQP. Select two points on required PLCMenu CommandGeometry –> Piecewise Liner Curve –> Extract –> From PBLS

• Extract PLC OR,RT,TM from ORTMLKO in a similar manner.

• Take PQ and OR and interpolate PLCsMenu CommandGeometry –> Piecewise Liner Curve –> Create –> Algebra of N PLC

• Enter No of PLC as 13

• Create PBLS from the interpolated PLCs.

• Make all PBLS of OPQSTRO in same fasion.

• In a similar manner create the PBLS PJKO, INML, SNMT, EGLK, JIHF, FEAB,HCDG

• Rotate all PBLS about the Y axis through 180o.

• ToolbarShow Edit Options –> Move Geometry EntityFill in the following values:All SelectedRotationy,180Set MatrixApply,Cancel

2. For mapping split the PBLS FBCH, PKKO, PQRO, QSTR, NSTM and INML horizontallyalong Y = 3. This is done by selecting two points that have y co-ordinate = 3 and splittingthe PBLS

• Menu CommandGeometry –> Piecewise Linear Curve –> Convert –> Split PLC

3. Similarly cut the above PBLS horizontally at Y = 5.

4. Check the normals of all PBLS. If they do not direct outside the volume then change it using

• Menu CommandGrid –> 2D Structured –> Convert –> Invert Normal

5. Save the surface grid in ZEUS file type.

D.6. VOLUME GRID 153

Figure D.12: Complete PBLS

Figure D.13: Rendered Geometry

D.6 Volume Grid

Volume grid of the Geometric Funnel is generated by creating multiblocks and mapping the facesof the block with the surface PBLS of the funnel.

D.6.1 Creation of Topology

First the TOPOLOGY of volume grid should be generated.

1. Create a 5 x 6 x 3 block as shown in D.14

• Menu CommandModule Block –> 3DMultiBlock –> Create –> Block

2. Move the block by (-2.5,0,-3)

• Menu CommandModule Block –> 3DMultiBlock –> Edit Topology –> Move Block. Referfig D.15


Figure D.14: Initial Block

Figure D.15: Moved Block

3. Create a block on the face of the block in z direction of a required length by traversing theface to the required position.. Refer fig D.17

• Menu CommandModule Block –> 3DMultiBlock –> Create –> BlockEnter the following values: 3

4. Similarly create all the blocks by traversing block and then traversing face and creating blockon it of required values according to the Topology shown in fig D.18, fig D.19, fig D.20,.

5. Value for all blocks is to be 3

6. Divide all blocks along J-direction at two different distance using plane cutter.

• Menu CommandModule Block –> 3DMultiBlock –> Create –> Plane Cutter


Figure D.16: Scaled Block

Figure D.17: New Block

• Enter the value for J

7. Paste all the blocks for connectivity between all adjacent block.

• Menu CommandModule Block –> 3DMultiBlock –> Convert –> Paste All Blocks

8. Save the file in CGNS GRID file after completing all blocks.

D.6.2 Mapping of faces

1. Open the Surface grid file of the Geometric Funnel and deselect all from the icon ”deselectall” (only surface grid(PBLS) can be selected or deselected) Refer fig D.21


Figure D.18: Topology - Front View

Figure D.19: Topology - Side View

2. Select one PBLS for mapping from the option ”select one entity”. Refer fig D.22

3. Move to the block which should be mapped with the selected face by Block Traversal andthen click the icon ”show current/all block option”, to show only the current block. Referfig D.23

4. Traverse the face of the block which to be mapped with the selected PBLS. Click the Iconshow/hide mapping guide lines for knowing that mapping vertexes is correct or not. if notthen click the icon ”change mapping order” to make it correct. Refer fig D.24

5. Map the face.

• Menu CommandModule Block –> 3DMultiBlock –> Mapped/unmapped –> Map face. Referfig D.25


Figure D.20: Topology - Isometric View

Figure D.21: Mapping

6. While mapping change the grid points where it is required.

• Menu CommandModule Block –> 3DMultiBlock –> Clustering –> Change Grid Points.

7. Mapped surface is checked from the option.

• Menu CommandModule Block –> 3DMultiBlock –> Attributes –> Rendering –> RenderingMapped surface. Refer fig D.26

8. Similarly map each PBLS of the geometric funnel as done from 8 to 13 and check that allface is mapped or not.. Refer fig D.27

9. Delete the block which is not required by traversing to the block to be deleted by usingtraverse block option on the toolbar.


Figure D.22: Mapping - One face selected

Figure D.23: Mapping - Display Current Block

• Menu CommandModule Block –> 3DMultiBlock –> Edit Topology –> Delete SelectedBlock.


Figure D.24: Mapping - Correct Mapping Order

Figure D.25: Mapped Face

Figure D.26: Rendered Mapped Face


Figure D.27: Rendered Mapped Surface-

Figure D.28: Mapped Funnel

Appendix E

Tutorial - Intersecting Pipes

E.1 Introduction

• The purpose of this Tutorial is to acquaint the user with the concept of Carpeting.

Pre-requisites

• Ahmed Body, Funnel,and Tank tutorials

• Fundamentals of Carpeting

Time Required

• The time required to complete this tutorial is about 8 - 10 hours.

E.2 Geometry

The required PBLS is as shown in fig E.1.

Figure E.1: Required Geometry of Intersecting Pipes

161

162 APPENDIX E. TUTORIAL - INTERSECTING PIPES

E.2.1 Semi-Cylinders

1. Create a hollow semi cylindrical pipe.

• Menu CommandGeometry –> Piecewise Bi-Linear Surface –> Create –> From Expression.

• Use the following values 30, 0, pi. 30, 0, 200. 10*cos(u), 10*sin(u), v.

2. Rotate the created PBLS.

• ToolbarShow Edit Tools –> Copy Geometry Entity

• Fill in the following values:Top SelectedRotationy90Set MatrixApply, Cancel

3. Translate the PBLS.

• ToolbarShow Edit Tools –> Move Geometry Entity

• Fill in the following values:Top SelectedTranslation 0, 0, 100Set MatrixApply, Cancel

• A T-shaped connection is thus created, as shown in fig E.2.

• Save the 2 PBLS’s as a .pbls Zeus Numerix data file.

E.2.2 Creating Carpet

1. Create the Carpet, which is nothing but a rectangular PBLS, on lines similar to creatingthe PBLS surface in the previous section.

• Menu CommandGeometry –> Piecewise Bi-Linear Surface –> Create –> From Expression.

• Use the following values : Refer fig E.3. 100, 0, 50. 100, 0, 50. u-25, 30, v+75.

Check that the normal to the Carpet points in the direction in which it needs to be dropped(Here, the downward direction). This is done by using the shortcut on the Toolbar.

E.2. GEOMETRY 163

Figure E.2: Input Semi-cylindrical Pipes

Figure E.3: Carpet

• ToolbarShow Display Options –> Display Normals

If the normals are not in the required direction, then reverse them.

• Menu CommandGrid –> 2D Structured –> Convert –> Invert Normal.

• Refer fig E.4 and Refer fig E.5

2. Save the correct Carpet as carpet.input in the Run directory if full verson of GridZTM isavailable or if only the GridZTM executable is available, then save the file in the homedirectory in the Zeus Numerix format.

E.2.3 Carpeting

1. Open the file containing the T-shaped connection only and not the carpet. Create thebounded Carpet.


Figure E.4: Input Pipes along-with Carpet

Figure E.5: Input Pipes with Carpet (top view)

• Menu CommandGrid –> Surface Structured –> Create –> Bounded Carpet (object pbls)Referfig E.6

• In the command box enter the values (2,99,2,99) . This represents the starting andending of u and v parameters of pbls to fall on the input cylinders one set in tsi directionand one in eta direction.

• Carpeting will start and a PBLS will be created, as shown in fig E.7.

2. Delete the original 2 PBLS’s which formed the T-shaped structure and retain only the newCarpeted PBLS. Refer Refer fig E.8.

E.2. GEOMETRY 165

Figure E.6: Carpeting Dialog Box

Figure E.7: Un-edited Carpet with original cylinders

E.2.4 Carpet Editing

1. Take the new PBLS. We need to delete the unwanted parts of this PBLS.

2. First, choose the option which displays the all points.

• ToolbarShow All Points

3. Left Click on the required two points where the PBLS needs to be cut. Split the PBLSthere.

• Menu CommandGeometry –> Piecewise Bi-Linear Surface –> Convert –> Split PBLS.

4. The PBLS will be split, giving rise to 3 PBLS’s- one original and 2 new (split) ones. Removethe original PBLS and the unwanted PBLS.


Figure E.8: Required un-edited Geometry

5. Repeat this process on all unwanted PBLS’s,keeping in mind to save regularly in differentfiles for easy retrieval in case you make some error. Take care not to delete the intersectedregion. Sometimes splitting has to be done twice to delete a part i.e. when a PBLS is splitin such a way that the required portion of the cylinder is cut too.

6. 3 PBLS will be created.Refer fig E.9.

Figure E.9: Edited Carpet

7. Then Split the 3 PBLS into a total of 18 PBLS in order to make a volume grid.

8. Display the boundary points by selecting the direct icon on the Display Toolbar.

9. Save the file as geometry.pbls

10. On correct editing, we get the required surface.Refer fig E.10,fig E.11.

E.3. VOLUME GRID GENERATION 167

Figure E.10: Final Geometry

Figure E.11: Final Geometry (top view)

E.3 Volume Grid Generation

E.3.1 Create Topology

1. The topology to be created is shown in fig E.12,fig E.13,fig E.14.

2. Open the file geometry.pbls

3. Create Block with default values Menu commandBlock –> 3D Multiblock –> Create–> Block

4. Scale BlockMenu commandBlock –> 3D Multiblock –> Edit Topology –> Edit Operations –> Scale allBlocks Feed in Value (0.3, 0.3,0.3)

5. Translate blockMenu commandBlock –> 3D Multiblock –> Edit Topology –> Move Block byFeed in values (-4.5, 0, 115)


Figure E.12: Topology


6. Translate FaceSelect face in -y direction and translate by (1.5) in y directionSelect face in -z direction and translate by (-5) in z directionSelect face in -x direction and translate by (-5.5) in x directionSelect face in +x direction and translate by (5.5) in x direction

Menu commandBlock –> 3D Multiblock –> Edit Topology –> Edit Operation

7. So finally we have a rectangular block approximately covering a section of the pipe.

8. Now Create a Block by selecting a face in -Z direction Menu commandBlock –> 3D Multiblock –> Create –> BlockFeed in values 20

9. Create a Block by selecting a face of new block in -Z directionMenu commandBlock –> 3D Multiblock –> Create –> BlockFeed in values 15



10. select the second block we created that is the middle one and select the +X direction face.

11. Create a Block by selecting a face of same block in +X directionMenu commandBlock –> 3D Multiblock –> Create –> BlockFeed in values 14.5

12. Select all PBLS. Now press button in Toolbar to show all boundary points.

13. Select the first block we created and select the face in -x direction. Create a plane cutterby the button described below.Drag the scale in I to match with intersection of two PBLSshown by boundary points and press OK. Use same method to create a plane cutter onother side of the parent block. Now go to last of the first four blocks we created. Performsame operation on this block to create one block for every PBLS.

Menu commandBlock –> 3D Multiblock –> Create –> Plane Cutter

14. The initial topology will look like Refer fig E.12.

15. Paste all the blocksMenu CommandBlock –> 3D Multiblock –> Convert –> Paste all blocks

16. Save the topology as a .cgns grid file.

E.3.2 Mapping

1. Mapping of the Pipes is to be done to get the grid as shown inRefer fig E.15. After renderingmapped surfaces we will get Refer fig E.16.

2. Open the PBLS file of tank using read as IITZeus file format and the Topology using CGNSGrid format

3. From the 3D Block Toolbar, using the traverse block option Select the first block to mapthe first part of the pipe.


Figure E.15: Mapped 3D Blocks of Intersecting Pipes

Figure E.16: Rendered Mapped Intersecting Pipes

4. Select the show current block. Select top face of this block using traverse face option in theToolbar.

5. Select the base PBLS opposite to the selected block face and from the Toolbar click showmapping lines and click change mapping order, until the correct order is obtained as showninRefer fig E.17.

6. Then map the face.Menu commandBlock –> 3D Multiblock –> Mapped/Unmapped –> Map Face.Refer fig E.18.

7. Check the mapping by doing rendering of mapped faces.Menu commandBlock –> 3D Multiblock –> Rendering –> Mapped SurfacesClick it again to get back to the normal block

8. Similarly map the 2 sides that are in front of the other two pbls of the first part of the pipe.A block as shown in fig E.19 will be obtained.

9. Similarly Map all the remaining Pbls. The step by step blocks are shown in the given inthe figures.


Figure E.17: Mapping Step 1

Figure E.18: Mapping Step 2

10. Paste all the blocksMenu commandBlock –> 3D Multiblock –> Convert –> Paste all Blocks

11. For creating the blocks from fig 19 - 22, only the top faces are mapped of the correspondingblocks, the side and bottom faces of blocks are not mapped, this gives rise to a disorientationas shown in fig E.20.

12. To rectify them, extract a PLC from correct edge of disoriented block such that it in extractoption of PLC in module geometry. Then select proper edge of the block and map the edgeto get block with base matching exactly. Then translate this PLC to the next required baseof block by distance at which the next block is created by the user. Repeat mapping edgethere also.Refer fig E.21.

Menu commandBlock –> 3D Multiblock –> Mapping/Unmapping –> Map Edge

13. In the process, one side of block at the extreme of pipe two will be collapsed to 0 area.There will be two such blocks.


Figure E.19: Mapped Surface

Figure E.20: Distorted Base

14. At the intersection also there will be a base not matching exactly . Repeat the PLCextraction there also and map the edge.

15. Paste all blocks again.

16. See the mapped Pipes by rendering mapped surfaces as explained in Step 8 - RenderedMapped Intersecting Pipes

17. The Volume Grid is now completed.


Figure E.21: Mapping Edge to match Base

Figure E.22: Mapped Surface of pipe 1

Figure E.23: Mapped Intersecting Region 1


Figure E.24: Mapped Iintersecting Region 2 Surface

Figure E.25: Mapped Pipe 2 Surface

Appendix F

Tutorial - 2D Grid Smoothening for aBlower

F.1 Introduction

This tutorial is to acquaint the user with the making of a 2D grid. The 2D grid of the blower iscreated by making PLCs of Blower Refer fig F.1 and then creating a topology of 2D multiblocksand mapping it with the PLCs. The user must be familiar with menu commands and the toolbar,so expansions of menu tree is not provided everywhere.

Figure F.1: Geometry of the Blower

Pre-requisites

• Ahmed Body, Tank, and Funnel tutorials

• Fundametals of 2D structured grids

F.2 Time Required

• 6 - 8 hours

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176 APPENDIX F. TUTORIAL - 2D GRID SMOOTHENING FOR A BLOWER

F.3 Geometry

1. Create a point (x=20, y=0, z=0)Menu CommandModule Geometry –> Point –> Create –> X,Y,Z co-ordinatesRotate this points and create 10 copy.

2. ToolbarFill the following values:Show Edit Tools –> Copy Geometry EntityTop SelectedRotationz7.2No. of copies 10Set MatrixApply,Cancel

3. Convert PLC from the points and then from PLC Equal arc , make 25 points on the curve.Menu CommandModule Geometry –> PLC –> Convert –> From PointsModule Geometry –> PLC –> Convert –> PLC Equal ArcFeed in the value 25 in the command box . After converting the plc from points delete allthe points in the selection box.

4. Rotate the PLC with an angle of 72 degree about Z-axis and create 4 copies to complete acircle.

5. ToolbarShow Edit Tools –> Copy Geometry EntityFill the following values:Top SelectedRotationz72No. of copies 4Set MatrixApply,Cancel

6. Create a point (30, 0, 0). Rotate it by 72 degree about Z-axis and create a PLC from twopoints and make 25 points on it from PLC Equal Arc. Next, rotate this PLC by 72 degreeand create 4 copies.Menu CommandModule Geometry –> Point –> Create –> X,Y,Z co-ordinatesRotate this points and create 10 copy.

F.3. GEOMETRY 177

7. ToolbarShow Edit Tools –> Copy Geometry EntityFill the following values:Top SelectedRotationz72No. of copies 1Set MatrixApply,Cancel

8. Convert PLC from the points and then from PLC Equal arc , make 25 points on the curve.Menu CommandModule Geometry –> PLC –> Convert –> From PointsModule Geometry –> PLC –> Convert –> PLC Equal ArcFeed in the value 25 in the command box . After converting the plc from points delete allthe points in the selection box.

9. Rotate the PLC with an angle of 72 degree and create 4 copies to complete a circle.ToolbarShow Edit Tools –> Copy Geometry EntityFill the following values:-Top SelectedRotationz72No. of copies 4Set MatrixApply,Cancel

Refer fig F.2

Figure F.2: Basic Geometry

10. Now Create an airfoil consist of 2 PLC at the corner of the pentagon created.Refer fig F.3


Figure F.3: Airfoil for Fan Geometry

11. Rotate the airfoil with an angle of 72 degree about Z-axis and create 4 copies.Refer fig F.4

Figure F.4: Blower with Fans Geometry

12. Create a point (76,46,0) and rotate it with an angle of 7.2 degree about Z-axis and create10 copy. and covert points into PLC and then 25 points on the PLC from PLC Equal arc.

13. Rotate this PLC with an angle of 72 degree about Z-axis and make 4 copies.Refer fig F.5

14. Create two points (110,-67,0) and (106,-112,0) and create PLC from points and then create25 points on the PLC. Menu CommandModule Geometry –> Point –> Create –> X,Y,Z co-ordinatesModule Geometry –> PLC –> Convert –> From Points

Refer fig F.6

15. Now join the PLC with the outer circle by making two PLCs.

1. Delete the PLC on the circle directly opposite to the PLc created in the above step.Refer fig F.7

2. Now extract the boundary point of the plc created from two points in the above step.Andalso extract the boundary point of the plc opposite tom it on the circle(Check your ge-

F.4. 2D GRID GENERATION 179

Figure F.5: Blower Geometry Incomplete

Figure F.6: Blower Incompleted Geometry

ometry requirment and do accordingly).Create a Plc from those points.Using PLC fromPoints.Similiarly do it for the other PLC of the pipe from Blower.Refer fig F.8

16. The 2D blower geometry is complete. Save the file as a Zeus Numerix data file.

F.4 2D Grid Generation

2D grid of blower is created by making 2D-MultiBlock topology and then mapping it with thegeometry created of PLCs.

F.4.1 Topology

1. Create points (20,0,0), (30,0,0), (70,0,0),(90,0,0) and (100,0,0). Convert it to a PLC. MenuCommandModule Geometry –> Point –> Create –> X,Y,Z co-ordinatesModule Geometry –> PLC –> Convert –> From Points

2. Rotate the PLC Toolbar


Figure F.7: Blower Incompleted Geometry

Figure F.8: Blower Completed Geometry

Show Edit Tools –> Copy Geometry EntityFill the following values: Top SelectedRotationz72No. of copies 5Set MatrixApply.Cancel

3. Convert it to PBLS.Menu CommandModule Geometry –> PBLS –> Convert –> From PLC

Refer fig F.10

4. Convert PBLS to 2D block and delete the PBLS.

5. Menu CommandModule Block–> 2DMultiBlock –> Convert –> PBLS to Block.Refer fig F.11


Figure F.9: Blower Topology

Figure F.10: Creation of PBLS for a 2D Block

6. Delete the outer four blocks out of five according to the topology (Refer fig F.9) by traversingto the block and using commandModule Block –>2DMultiblock –> Edit Topology –> Delete Block.Refer fig F.12

7. The Topology of 2D Blower is complete. Save this as a .cgns file.

F.4.2 Mapping

1. Traverse the block to the middle blocks and UNPASTE THE EDGE where Airfoil PLCshas to be mapped.

2. Menu CommandModule Block –> 2DMultiblock –> Convert –> Unpaste edge.

3. Select one PLC and map it with respective edge of the Block.

4. Menu CommandModule Block–>2DMultiblock –> Mapped/Unmapped –> Mapped –> MapEdge. fig11.

5. We can also use option ”Undo” incase of wrong mapping or Unmapp the edge.


Figure F.11: PBLS to 2D Block

Figure F.12: Editing Topology

6. After mapping all edges save the grid in CGNS file format.

F.4.3 Smoothening

1. Menu CommandModule Grid –> 2D Structured –> Edit –> 2D Generic Smoothener.

2. Enter the following values: 100,0.4, 0, 0. The remaining values are default and need notbe changed.


Figure F.13: Creation of PBLS for 2D Block

Figure F.14: Final 2D Block


Figure F.15: Before Smoothening


Figure F.16: After Smoothening

Appendix G

Tutorial: 3D Grid Smoothening inDumbell

G.1 Introduction

The purpose of this tutorial is to acquaint the user with the concept of smoothening. The tutorialconsists of 3 sections:

• Creating Geometry for the dumbell

• Creating the Volume Grid

• Smoothening the 3D Grid

Pre-requisites

• Industrial Tank and Intersecting Pipes Tutorials

• Concept of Carpeting

• Concepts of smoothening

G.2 Time Required

This tutorial requires about 3-4 hours for completion.

G.3 Geometry

The geometry consists of 2 spherical lobes and on central cylindrical portion as shown in fig G.1

G.3.1 Lobes

A lobe will consist of 2 basic parts - one being a hemisphere while the other being a hemispherewith a portion chopped off to coincide with the flat face of the central cylinder. Refer fig G.2

1. We first create that part of the lobe which is not completely hemispherical. For this, createa curve of the circle

187

188 APPENDIX G. TUTORIAL: 3D GRID SMOOTHENING IN DUMBELL

Figure G.1: Dumbell Geometry

Figure G.2: Lobe

• Menu CommandModule Geometry –> Piecewise Linear Curve –> Create –> From Expres-sion.

• Use the following values: 0, 10, pi/2, 3*pi/4, 40*cos(u), 40*sin(u), 0

2. Translate this PLC by 40/√

(2) units along X axis.

• ToolbarShow Edit Option –> Move Geometry Entity

• Fill in the following values:Top SelectedTranslation40/sqrt(2)00Apply,Cancel

G.3. GEOMETRY 189

3. Make 9 copies of the PLC by rotating the PLC about the X axis through 10o each.

• ToolbarShow Edit option –> Copy Geometry Entity

• Fill in the following values:Top SelectedRotationx10No. of copies 9Apply,Cancel


• ToolbarMOdule Geometry –> Piecewise Bi-Linear Surface–> Convert –> FromPLCs.

5. Make 3 copies of the PBLS by rotating the whole PBLS through 90o about the X axis.

• ToolbarShow Edit Option–>Copy Geometry Entity

• Fill in the following values:Top SelecedRotationx90No. of copies 3Apply,Cancel

Refer fig G.3

6. Store the set of 4 PBLS’s as an Zeus data file curve.pbls and then Delete All.

Now we create the hemispherical region.

7. Create a point with co-ordinates (40, 0, 0)


• Enter the following value: 40, 0, 0

8. Make 9 copies of the point by rotating it about the Z axis through 10o each.


Figure G.3: Lobe - Part1


• Fill in the following values:Top SelecedRotationz10No. of copies 9Apply,Cancel

9. Create a PLC from the 10 points.


10. Make 9 copies of the PLC by rotating the PLC about the X axis through 10o each.


• Fill in the following values:Top SelecedRotationx10No. of copies 9Apply,Cancel

G.3. GEOMETRY 191

11. Create PBLS from the interpolated PLCs. Module Geometry –> Piecewise Bi-LinearSurface –> Convert –> From PLCs

12. Translate the PBLS along X axis through distance of 40/sqrt(2)

• ToolbarShow Edit Option–> Move Geometry Entity

• Fill in the following values:Top SelecedTranslation40/sqrt(2)0oApply,Cancel



• Fill in the following values:Top SelecedRotationx90No. of copies 3Apply,CancelRefer fig G.4

Figure G.4: Hemisphere - With Degeneracy


14. Store the 4 PBLS’s together as an IITZeus file hemis.pbls.

15. We observe that there exists a degeneracy at the rightmost point. To overcome this, wecarpet the hemispherical surface by a PBLS extracted from the cross-section of the lobe.

G.3.2 Carpeting

1. One by one, extract 4 PLC’s from the leftmost edges of the 4 PBLS’s which form thehemispherical surface.

• Deselect All PBLS’s and then select just one PBLS.

• Select (Left Click) any 2 points on the PLC to be extracted.

• Extract the PLC.

• Menu CommandModule Geometry –> Piecewise Linear Curve –> Extract –> From PBLS.

2. Repeat the above procedure to get 4 PLC’s.

3. Create a 2D structured grid from the 4 PLC’s. Note that all 4 PLC’s must be traversed inthe same direction to get the correct grid.

• Menu CommandModule Grid –> 2D Structured –> Create –> Four Open Curves.

4. Extract a PBLS from the 2D Grid. Refer fig G.5

Figure G.5: Carpet

• Menu CommandModule Geometry –> Piecewise Bi-linear Surface –> Extract –> Current2D Block.

5. Then delete all the PLC’s and 2D Block to get just the PBLS, which will act as our carpet.Store this as an Zeus file carpet.input. Note that the carpet file must be stored in the samefolder which contains the executable program of GridZTM.

6. Delete the carpet and open hemis.pbls

G.3. GEOMETRY 193

7. Stitch all PBLS together one by one.

• Menu CommandModule Geometry –> PBLS –> Convert –> Stitch PBLS.

8. Convert the new PBLS to triangulated surface. We thus obtain the TRSP’s. Refer fig G.6

• Menu CommandModule Grid –> Triangles –> Convert –> From PBLS by Inserting Point.

Figure G.6: Hemisphere - TRSP

9. Delete all the PBLS.

10. Carpet the TRSP.

• Menu CommandModule Grid –> Surface Structured –> Create –> Bounded Carpet.

• Enter the following values: 2, 9, 2, 9

11. Delete the TRSP’s to leave just the Carpeted PBLS. Refer fig G.7

12. Store this as an Zeus file finalhemis.pbls.

13. Open curve.pbls also. We now have 5 PBLS’s in all.

14. Scale each PBLS to get the mirror image in the YZ plane.

• ToolbarShow Edit Option –> Copy Geometry Entity


Figure G.7: Hemisphere - Carpeted

• Fill in the following values:All SelectedMirrorxNo. of copies 1Set MatrixApply,Cancel

15. Translate only the newly created PBLS’s along -X axis by 120 units. Select newly created5 PBLS’s and deselect rest 5 PBLS’s.

• ToolbarShow Edit Option–> Move Geometry Entity

• Fill in the following values:All SelecedTranslation-12000Set MatrixApply,Cancel

16. Store all 10 PBLS’s as shown in fig G.8 as lobes.pbls

Note that there can occur slight misalignment of PBLS’s at the edges, especially at the edgescommon to the carpeted region and other PBLS’s. This discontinuity can be removed by stitching2 PBLS’s and then splitting them.

G.3. GEOMETRY 195

Figure G.8: Lobes

G.3.3 Central Cylinder

1. Deselect all entities. Select a PBLS from the right lobe and it’s corresponding (mirrorimage) from the left lobe. Extract 2 PLC’s from the 2 PBLS’s which on interpolation willform 1/4th curved surface of the cylinder.For extracting the PLC’s, follow the same procedure as shown in 1st point of section 4.2

2. Delete all items except for the 2 PLC’s.

3. Interpolate between the 2 PLC’s to get a set of 60 PLC’s

• Menu CommandModule Geometry –> Piecewise Linear Curve –> Create –> Algebra of NPLC’s



• Module Geometry –> Piecewise Bi-Linear Surface –> Convert –> FromPLCsRefer fig G.9


• ToolbarShow Edit Option–> Copy Geometry Entity

• Fill in the following values:Top SelecedRotationx90No. of copies 3Set MatrixApply,CancelRefer fig G.10


Figure G.9: Central Cylinder - 1 PBLS

Figure G.10: Central Cylinder

6. Save the cylinder as cylinder.pbls

Opening the files finalhemis.pbls, curve.pbls and cylinder.pbls gives us the entire dumbell ge-ometry.

G.4 Volume Grid

The volume Grid for this dumbell is relatively easy, as it involves mapping just 3 block faces.

1. Creates blocks of lengths 30, 120, 30 along the X axis. The lengths along Y and Z axes ofeach block are 30 units. Refer fig G.11

2. Open the Zeus file containing the entire Dumbell Geometry. Map one surface at a time, oneblock at a time, to get the volume grid for the entire dumbell. Refer figures G.12, G.13, G.14.

G.5 Smoothening

The mapped blocks we have created need to be smoothened now. The procedure for this is asfollows -

G.5. SMOOTHENING 197

Figure G.11: Blocks

Figure G.12: 1 Lobe Mapped

1. View the internal grids of a lobe using the I J K Layer Traversal option from the Toolbar.

• ToolbarShow 3D Block Option –> I J K Layer Traversal

• Move the scroll bars to get image as shown in fig G.15

2. Smoothen the Grid.

• Menu CommandModule Grid –> 3D Structured –> Edit –> Generic Smoothener

• We’ll be using Laplace Smoothening. Enter the following values: 1, 100. The restare default values which need not be changed and which are not necessary for Laplacesmoothening anyway.

3. On completing the desired number of iterations, we get the smoothened 3D grid as shownin fig G.16. Especially note the green region.


Figure G.13: 2 Lobes Mapped

Figure G.14: Entire Dumbell Mapped

Figure G.15: Before Smoothening

G.5. SMOOTHENING 199

Figure G.16: After Smoothening

Appendix H

Tutorial - Airfoil

H.1 Introduction

• The purpose of this Tutorial is to acquaint the user with the concept of Triangulation gridand Boundary condition.

Pre-requisites

• Must be familiar with PLC,PBLS and Blocks.

• Fundamentals of Grid (structured and unstructured).

• Airfoils in arranged order.

Time Required

• The time required to complete this tutorial is about 30 min.

H.2 Geometry

The geometry provided is as shown in fig J.1

Figure H.1: Geometry of cascade Air Foil.

1. Open the airfoils geometry.

201

202 APPENDIX H. TUTORIAL - AIRFOIL

2. Close all the open PLCs. Select each airfoil one by one and go to options to close the plcs,if the airfoil has open PLCs.

• Tool BarShow Geometry Tools –> Curve Open/Close.

Save the file as geometry.plc in the Zeus format.

H.3 Creating Boundary

1. Create the Boundary, which is nothing but a rectangular PLC close loop.

• Menu CommandBlock –> 2D multiblock –> Create –> init block.

• Use the following values :100,100.

• Select the lower edge,by edge transversal option.

• Tool Bar2D Block Tools –> Edge Transversal.

• Move the edge to the given values (0,-150,0).

• Menu CommandBlock –> 2D Multiblock –> Edit Topology –> Move Edge.

• Use the following values :0,-150,0.

• Similarly transfer the right hand side edge to the 300,0,0.

• And transfer the left hand side edge to the -200,0,0.

2. Create Boundary PLC by extracting from all the edges of 2D block created,first select therequired edge by edge transversal.

• Menu CommandShow 2D Block Tools –> Edge transversal.

3. Now after selecting the Edge extract the PLC.

• Menu CommandGeometry –> Piecewise Linear curve –> Extract –> Edge of 2D Block.

4. After Extracting all the PLC now we have to join them to form the close loop.

• Menu CommandGeometry –> Piecewise Linear curve –> Convert –> Stitch PLCs in loop..

• It forms the single PLC of the same geometry which is an open PLC. Now we have toclose the loop.

• Tool BarShow Geometry Tools –> Curve Open/Close

• Save the boundary as a boundary.pbls Zeus data file.

the required boundary with geometry is as shown in fig J.2

H.4. GRID GENERATION 203

Figure H.2: Boundary

H.4 Grid Generation

To create the grid first open both files - boundary.plc and the geometry.plc.Note: Before creating the TRSP check that the curves follow the same direction.

• View the direction of all the PLCs.

• Tool barShow OrientationPlease note that direction of outer boundary and the one of the inner foil is reverse to theother two foils.

• If you don’t make changes in their directions, the TRSP obtain will be of the type one shownin fig J.3 which is a wrong TRSP.

Figure H.3: Wrong TRSP obtained

• To correct the wrong TRSP, first, Deselect all and then select a boundary PLC and reversethe direction of the curve.

• Tool BarShow Geometry Option –> Reverse Curve


• Similarly change the direction of the airfoil which was also in the reverse direction.

• First, Deselect all. Next, select the boundary plc followed by the selection of inner foils. Ifyou don’t follow this step then the TRSP obtain will be of the type one shown in fig J.4- awrong TRSP.So follow the steps given above.

Figure H.4: Wrong TRSP obtained

• Menu CommandGrid –> Triangles –> Create –> Delaunay

• In the box, click on Length with value 1.7.

• Save the figure as a airfoil.cgns CGNS data file.

• TRSP obtain is shown in fig J.5

Figure H.5: Flow around a cascade airfoil(Length).

• To generate a grid with the area option do the following:Menu Command

H.4. GRID GENERATION 205

Grid –> Triangles –> Create –> Delaunay

• In the box, click for Area with value 10.

• Save the figure as a airfoil2.cgns CGNS data file.

• TRSP obtain is shown in fig L.1

Figure H.6: Flow Around a Cascade Airfoil (Area).

Appendix I

Tutorial - Reusable Launch Vehicle(RLV)

I.1 Introduction

• This tutorial is an advanced level of creating complex Geometry (RLV- Reusable LaunchVehicle). Note that here,every detail of generating the geometry is not given. The conceptof generating Geometry is same as done in previous tutorials.

• The complete dimensions of the geometry is given in the NASA Technical paper (NASA-94-tm4533.pdf). The Geometry is created as per specified dimension. the Nose fin , speedbrake and Tip fin is not included in the geometry.

• The dimension are shown in figures I.1 to I.5

Figure I.1: Technical 1

207

208 APPENDIX I. TUTORIAL - REUSABLE LAUNCH VEHICLE (RLV)


Pre-requisites

• Detailed concepts of creation of geometries and Grid generation, as demonstrated in pre-ceding tutorials like ahmed body, tank, intersecting pipes, geometric funnel.

Time RequiredThis tutorial requires about 18 - 20 hours for completion.

I.2 Geometry

For creating geometry of RLV, the complete Aircraft is divided into 9 parts, with the cylinderbeing divided lengthwise into 6 parts plus 2 wings and 1 aft center fin. All parts can be createdseparately and then opened together for the complete geometry.

I.2.1 Cylinder

1. The cylinder is divided along the circumference into 8 parts bearing in mind the topologyneeded for generating grid from geometry.

2. The Cone is created by creating a curve of required radius which is then rotated about theX-axis. The set of PLC’s are then converted to a PBLS. The number of PBLS’s thus is 8as shown in I.6. The number of PLC’s in each PBLS will remain constant for all furthercylindrical surfaces to ensure connectivity.

3. Similarly create the 2nd circular part of length 8.12 and radius 18.8 such that it is tangentto the cone at point of join (Refer diagram). The number of PBLS’s is 8. Note that the

I.2. GEOMETRY 209


number of points on circumference should be same as cone. Refer I.7

4. Create the cylindrical part (3rd part) by rotating the PLC of length 6.52 (ref. Diagram).Refer I.8

5. The 4th part is not the complete cylinder, as the lower part is attached to the wing. So,we create that part while creating the wing. The side part is straight and cylindrical. ReferI.9

6. The 5th part is also like the 4th. It ends at the beginning of aft. central fin. The lower partis flat and the lower side is attached to the wings.

I.2.2 Creation of wing

For creating wing, a PLC of airfoil shape is generated. the shape of airfoil is according toNACA0010-10 airfoil. To create the wing PBLS, we -

1. Scale the same PLC(airfoil)

2. Create a copy by translating the PLC to required positions for wing root

3. Interpolate between both to make N number of PLCs

4. Create a PBLS from them.

5. Split the PBLS (wing) into 7 parts as shown in the I.10 to match the fuselage of the aircraft.

6. Create copies of all PBLS’s of wing in negative Z direction to create the right wing.



I.2.3 Aft Wing center fin

The Afterward center fin is created as given in the I.11. The central curved part is divided into3 parts (2 sides and 1 central).The fin is then translated to the required position.

I.2.4 Completing Geometry of Airfoil

All the gaps between the wings, fin and cylinder are created by extracting the appropriate bound-ary PLC’s and interpolating between them. The lower surfaces of 5th and 6th parts are flat (ReferI.12). The complete RLV is thus created as is shown in I.13

I.3 Volume Grid

Grid of the RLV (Reusable Launch Vehicle) is generated by making the multiblocks and mappingthe faces of the block with the surface PBLS of the RLV geometry.

I.3.1 Creation of Topology

The topology of the geometry created for RLV is shown in following I.14 to I.18.Blocks are created with this topology in mind.

There are two ways of creating the Topology. One way is to make the 2D Multiblock andexport it to 3D Multiblock; the other is to create one block, then create blocks on it’s faces andsimilarly creates all blocks, although this is not a good idea here as the number of block is more.So we follow the first method.

I.3. VOLUME GRID 211


Creation of 2D Multiblock

We first create XY plane of the topology and then export it along z-direction to get 3D multiblock.A 100 X 100 size 2D block is created first. We can create as many blocks as needed inside it byinserting vertex or box to get the required topology. then the topology can be scaled to actualsize.

1. Create a 2D block of 100 by 100.

• Menu CommandBlock –> 2D Multiblock –> Create –> Init Block. Refer I.19

2. The block is divided into 4 blocks by inserting the values of a vertex. The vertex co-ordinateis given according to the topology. Similarly, a block can also be created inside the blockthat will break the block into 9 parts.

• Menu CommandBlock –> 2D Multiblock –> Create –> Input Values. Refer I.20

3. Delete the blocks which are not required and then Scale the 2D blocks to the actual topologysize as shown in the topology figure.

4. Export the 2D blocks to 3D blocks by giving the number of layers and then dimensions oflayers. 2D multiblock is exported in positive Z-direction.


Figure I.6: Cone

Figure I.7: Second cylindrical part

• Menu CommandBlock –> 3D Multiblock –> Convert –> From 2D Block

5. Move the entire topology to the required position by giving X,Y,Z values.

• Menu CommandBlock –> 3D Multiblock –> Edit topology –> move all block. Refer I.18

6. Paste all the blocks.

• Menu CommandBlock –> 3D Multiblock –> Convert –> Paste all block


Figure I.8: Third cylindrical part

Figure I.9: Fourth cylindrical part

7. 3-d block topology is completed. Now mapping is done for grid of RLV. Save this file as aCGNS GRID file.

Mapping the faces

1. Open the Surface grid file of the RLV and deselect all entities. (Only surface grid(PBLS)can be selected or deselected). Refer I.21

2. Select one PBLS for mapping. Traverse to the block which should be mapped. Use optionfor Block Traversal on the Toolbar. Then click the icon ”show current/all block option”, toshow only the current block. Refer I.22

3. Traverse to the face of the block which is to be mapped with the selected PBLS. Use optionfor Face Traversal on the Toolbar. Then Click the Icon ”show/hide mapping guide lines”


Figure I.10: Wing

Figure I.11: Center Fin

for viewing whether the mapping of vertices is correct or not. If not then click the icon”change mapping order” to make it correct. Refer I.23

4. Map the face.

• Menu CommandBlock –> 3D Multiblock –> Mapped/unmapped –> Map Face Refer I.24

Degenerate surface

The nose cone of the RLV is degenerate i.e. one edge of each block around it collapses. Sofor degenerate blocks after mapping each face of the cone, the option Paste all Blocks isused for connectivity of the blocks.


Figure I.12: PBLS of RLV

5. Select one PBLS of the nose cone, traverse the block to the required position and then mapit as done earlier. Refer I.25

6. After mapping use the option paste all blocks for connectivity.

• Menu CommandBlock –> 3D Multiblock –> Convert –> Paste All Blocks

7. Mapped surface is rendered and checked from the option.

• Menu CommandBlock –> 3D Multiblock –> Attributes –> Rendering –> Mapped Surface.Refer I.26

8. Similarly map each PBLS of the RLV as done in steps 1 to 4 and check whether all facesare mapped or not.

9. Save the Complete Mapped Blocks as a CGNS GRID file.


Figure I.13: Rendered Surface of RLV

Figure I.14: Front View


Figure I.15: Front Central View- Magnified

Figure I.16: Side View


Figure I.17: Central View - Magnified

Figure I.18: Isometric View


Figure I.19: 2D Block

Figure I.20: Child Blocks


Figure I.21: RLV Surface + All Blocks

Figure I.22: Mapping - One PBLS selected


Figure I.23: Mapping - Correct Mapping Order

Figure I.24: Mapped Face

Figure I.25: Mapping - Degenerate Surface


Figure I.26: Mapping - Rendered RLV

Appendix J

Tutorial: 1(a) Structured toUnstructured Voronoi Polygon

J.1 Introduction

• The purpose of this Tutorial is to acquaint the user with the concept of:

• Unstructured Grids.

• Forward Facing Step.

• Voronoi Diagram.

Pre-requisites

• Familiarity with making PLC, PBLS and BLOCKS.

• Fundamentals of Structured Grid.

Time Required

• The time required to complete this tutorial is about 1 hour.

J.2 Geometry

The required geometry is as shown in fig J.1

J.3 Block Geometry

1. Create a block.

• Menu CommandBlock –> 2D Multiblock –> Create –> Init Block.

• Use the following values :X=150,Y=50.

• Insert the Vertex inside the block, using the Menu Command Block –> 2D Multi-block –> Create –> Input value

223

224APPENDIX J. TUTORIAL: 1(A) STRUCTURED TO UNSTRUCTURED VORONOI POLYGON

Figure J.1: GEOMETRY

• Use the following values :X=30.Y=10.

2. Create the Forward Facing Step.

3. Delete the block which ranges from:X=30 to X=150,Y=10.

• Menu CommandBlock –> 2D Multiblock –> Edit Topology –> Delete Block

• Save the block as a step.cgns CGNS data file.

The required geometry is as shown in fig J.2

Figure J.2: Forward facing Step-Block

J.4 Creating PBLS

To create PBLS, convert all the blocks into the corresponding PBLS with the steps given below.

• Menu CommandGeometry –> PBLS –> Extract –> All 2D Blocks.

J.5. GRID GENERATION 225

• Save the PBLS as a step.pbls ZEUS data file.

the required PBLS”S are as shown in fig J.3.

Figure J.3: Required PBLS”S

J.5 Grid Generation

To create the TRSP Grid follow these steps:

• ToolbarDeselect all –> Picking On –> Click on any one PBLS

• Menu CommandHere there are two options for generating grids:Grid –> Triangles –> Convert –> From PBLS by inserting EdgeGrid –> Triangles –> Convert –> From PBLS by inserting Edge

• Similarly Convert All the PBLS’S to TRSP’S

• Stitch ALL the TRSP’S into ONE.

• ToolbarDeselect All –> Picking On –> Choose Any TWO TRSP’S

• Menu CommandGrid –> Triangles –> Convert –> Stitch

• Save the TRSP as a reverse.trsp ZEUS data file.

The trsp obtained is as shown in Refer fig J.4.


Figure J.4: Required TRSP.

J.6 Voronoi Generation

To create the Voronoi Diagram follow this step:

• Menu CommandGrid –> Polygons–> Convert –> Voronoi From Triangles

• Save it in the IITZEUS format with .trsp extension.

The Voronoi Diagram obtained is as shown in Refer fig J.5.

Figure J.5: Required Voronoi

J.7 Boundary Condition

To fix the Boundary Condition:

• ToolbarDeselect all from the selection box. Then with Picking ON mode choose Voronoi.Click Show Boundary Points

J.7. BOUNDARY CONDITION 227

• With Picking On,choose three points on the Voronoi. Choose Two Boundary points ofVoronoi”S that EDGE through which fluid ENTERS the body and choose any one morepoint between them. The sequence will be like first, second and last point on the edgerequired.

• Menu CommandBoundary Condition –> Apply, Choose On EdgeEnter BC inflow and give label as inflow.


• With Picking On,choose three points on the Voronoi. Choose Two Boundary points ofVoronoi”s that EDGE through which fluid EXITS the body and choose any one more pointbetween them. The sequence will be like first, second and last point on the edge required.

• Menu CommandBoundary Condition –> Apply, Choose On EdgeEnter BC outflow and give label as outflow.

• Save the file in .cgns format.

Appendix K

Tutorial: 1(b) Structured toUnstructured Voronoi Polygon withClustering

K.1 Introduction

• The purpose of this Tutorial is to acquaint the user with the concept of:

• Unstructured Grids.

• Forward Facing Step.

• Voronoi Diagram.

Pre-requisites

• Must be familiar with PLC,PBLS and BLOCKS.

• Some background of grid (structured).

Time Required


K.2 Geometry

The required geometry is as shown in K.1

K.3 Block Geometry

1. Create a block.



229

230APPENDIX K. TUTORIAL: 1(B) STRUCTURED TO UNSTRUCTURED VORONOI POLYGON WITH CLUSTERING

Figure K.1: GEOMETRY

• Insert the Vertex inside the block, using the Menu Command.Block –> 2D Multiblock –> Create –> Input Value



3. Delete the block which ranges from:X=30 to X=150,Y=10.



The required geometry is as shown in K.2

Figure K.2: Forward facing Step-Block

K.4. CLUSTERING IN BLOCK 231

K.4 Clustering in Block

1. Choose a block.

• Menu CommandBlock –> 2D Multiblock –> Clustering –> All block.

• Use the following values :exponential,one side,grid points=35,2,.001.

2. Similarly do clustering in all the blocks.

3. Save the block as a step.cgns CGNS data file.

The required Clustered Block is as shown in K.3

Figure K.3: Clustering in Block

K.5 Creating PBLS

Convert all the blocks into the corresponding pbls’s.

• Menu CommandGeometry –> PBLS –> Extract –> Current 2D Block.

• Toolbar to select the next block to be converted to PBLSClick Sequential Block Traversal

• Save the PBLS as a step.pbls ZEUS data file.

The required PBLS’S are as shown in K.4.


Figure K.4: Required PBLS”S

K.6 Grid Generation

Now to create the TRSP Grid.

• ToolbarDeselect all –> Picking On –> Click on any one PBLS.

• Menu CommandHere there are two options for generating grids:(i) Grid –> Triangles –> Convert –> From PBLS by inserting Edge(ii) Grid –> Triangles –> Convert –> From PBLS by inserting Point

• Similarly Convert All the PBLS’S to TRSP’S

• Stitch ALL the TRSP’S into ONE by selecting two at a time, using the following Toolbarsand Menu CommandDeselect All –> Picking On –> Choose Any Two TRSP’SGrid –> Triangles –> Convert –> Stitch

• Save the TRSP as a reverse.trsp ZEUS data file.

The trsp obtained is as shown in K.5.

K.7 Voronoi Generation

Now to create the Voronoi Diagram.


• Save it in the IITZEUS format with .trsp extension.

The Voronoi Diagram obtained is as shown in K.6.

K.8. BOUNDARY CONDITION 233

Figure K.5: Required TRSP.

Figure K.6: Required Voronoi

K.8 Boundary Condition

Now we have to give the Boundary Conditions.







• Menu Command

Enter BCOutflow and give label as outflow.


Appendix L

Tutorial: 2(a) Structured toUnstructured Voronoi Polygon

L.1 Introduction

• The purpose of this Tutorial is to acquaint the user with the concept of Unstructured Grids.

Pre-requisites

• Must be familiar with PLC,PBLS and BLOCKS.

• Some background of grid (structured).

Time Required


L.2 Geometry

The geometry is as shown in fig L.1

Figure L.1: Geometry

235

236APPENDIX L. TUTORIAL: 2(A) STRUCTURED TO UNSTRUCTURED VORONOI POLYGON

L.3 Block Geometry

1. Create a block.



2. Create the Forward Facing Step Block.

3. Delete the block which ranges from X=30 to X=150,Y=10.

• Menu CommandBlock –> 2D Multiblock –> Edit topology –> Delete Block


The required geometry is as shown in fig L.2

Figure L.2: Forward facing Step

L.4 Creating Boundary PLCS

First extract all the boundary PLCS from the Blocks.

• ToolbarClick Sequential Block Traversal

• Click Edge Traversal

• Menu CommandGeometry –> PLC –> Extract –> Edge Of 2D Block.

• Delete the internal PLCs

• Stitch all the PLC”S left.

• Menu CommandGeometry –> PLC –> Convert –> Stitch PLC’s in Loop.

L.5. DELAUNAY TRIANGULATION 237

• The PLC obtained would be OPEN,CLOSE it.

• Menu CommandGeometry –> PLC –> Edit –> Open/Close.

• Check At Entity Information in selection set.

• Save the boundary as a boundary.pbls ZEUS data file.

The required Boundary PLC”S are as shown in fig L.3.

Figure L.3: Required Boundary PLC”S

L.5 Delaunay Triangulation

A triangulation is a subdivision of an area (volume) into triangles (tetrahedrons). In a Delaunaytriangulation the circumcircle (circumsphere) of every triangle (tetrahedron) does not containany points of the triangulation. The Delaunay triangulation is the dual structure of the Voronoidiagram.

Applications

• Simulation of the growth of crystal

• Metallurgy (examination of alloys)

• Cartography, town planning

• Computation of neighbouring problems (computational geometry)

• Mesh generation for finite elements methods, stereolithography, visualization of surfaces,etc.

Create a Delaunay Triangle

• Menu CommandGrid –> Triangles –> Create –> Delaunay


• Enter length =1.7.Preview.Ok

• Save the figure as a reverse.trsp ZEUS data file.

• enter Area =25.Preview.Ok


The DELAUNAY TRIANGLE (Length) obtained is as shown in Refer fig L.4.

Figure L.4: DELAUNAY TRIANGLE-Length

The DELAUNAY TRIANGLE (Area) obtained is as shown in Refer fig L.5.

Figure L.5: DELAUNAY TRIANGLE-Area

L.6 Voronoi Generation



• DO it once for Delaunay obtained by length and area each.

L.7. BOUNDARY CONDITION 239

• Save it in the ZEUS format with .trsp extension.

The Voronoi Diagram (Length) obtained is as shown in Refer fig L.6.

Figure L.6: Required Voronoi-Length

The Voronoi Diagram (Area) obtained is as shown in Refer fig L.7.

Figure L.7: Required Voronoi- Area

L.7 Boundary Condition






• Similarly Pick the outflow.


Appendix M

Tutorial: 2(b)Structured toUnstructured Voronoi Polygon withClustering

M.1 Introduction

• The purpose of this Tutorial is to acquaint the user with the concept of Unstructured Grids.

Pre-requisites

• Familiarity with PLC,PBLS and BLOCKS.


Time Required


M.2 Geometry

The required geometry is as shown in fig M.1

Figure M.1: Geometry

241

242APPENDIX M. TUTORIAL: 2(B)STRUCTURED TO UNSTRUCTURED VORONOI POLYGON WITH CLUSTERING

M.3 Block Geometry

1. Create a block.

• Menu CommandBlock –> 2DMulti Blocklock –> Create –> Init Block.




• Menu CommandBlock –> 2D MultiBlock –> Edit Topology –> Delete Block


The required geometry is as shown in fig M.2

Figure M.2: Forward facing Step Block

M.4 Clustering in Block

1. Choose a block.

• Menu CommandBlock –> 2D MultiBlock –> Clustering –> All block.

• Use the following values :exponential,one side,grid points=35,0.001.

2. Similiarly do Clustering in all the blocks.

3. Save the block as a step.cgns CGNS data file.

Clustered Block is as shown in fig M.3

M.5. CREATING BOUNDARY PLCS 243

Figure M.3: Clustering in Block

M.5 Creating Boundary PLCS

Extract all the boundary PLCS from the Blocks



• Menu CommandGeometry –> PLC –> Extract –> Edge Of 2d block.


• Stitch all the PLC’S left.






The required Boundary PLC”S are as shown in fig M.4.

M.6 Delaunay Triangle

Delaunay Triangulation

A triangulation is a subdivision of an area (volume) into triangles (tetrahedrons). The Delau-nay triangulation has the property that the circumcircle (circumsphere) of every triangle (tetra-hedron) does not contain any points of the triangulation. The Delaunay triangulation is the dual


Figure M.4: Required Boundary PLC”S

structure of the Voronoi diagram.

Applications

• Simulation of the growth of crystal

• Metallurgy (examination of alloys)

• Cartography, town planning

• Computation of neighbouring problems (computational geometry)

• Mesh generation for finite elements methods, stereolithography, visualization of surfaces,etc.

Creating Delaunay Traingulation

• Menu CommandModule Grid –> 2D triangles –> Create –> DELAUNAY

• Enter length =1.7.Preview.Ok


• enter Area =25.Preview.Ok


DELAUNAY TRIANGLE (Length) obtain is as shown in Refer fig M.5.

DELAUNAY TRIANGLE (Area) obtain is as shown in Refer fig M.6.

M.7 Voronoi Generation


M.8. BOUNDARY CONDITION 245

Figure M.5: DELAUNAY TRIANGLE-Length

Figure M.6: DELAUNAY TRIANGLE-Area


• DO it once for Delaunay obtained by length and area each.

• Save it in the IIT/ZEUS format with .trsp extension.

The Voronoi Diagram (Length) obtain is as shown in Refer fig M.7.The Voronoi Diagram (Area) obtain is as shown in Refer fig M.8.

M.8 Boundary Condition



• With Picking On,choose three points on the Voronoi. Choose Two Boundary points ofVoronoi”S that EDGE through which fluid ENTERS the body and choose any one more


Figure M.7: Required Voronoi-Length

Figure M.8: Required Voronoi- Area

point between them. The sequence will be like first, second and last point on the edgerequired.


• Similarly Pick the outflow.


Appendix N

Tutorial: 3(a) 3D VOLUME GRID

N.1 Introduction

• The purpose of this Tutorial is to acquaint the user with the concept of 3D Volume Grids.

Pre-requisites

• Familiarity with PLC,PBLS and BLOCKS.


• Fundamentals of Unstructured Grid.

Time Required


N.2 Geometry

The required geometry is as shown in fig N.1

N.3 Block Geometry

1. Create a block.



• Insert the Vertex inside the block, using the Menu Command Block –> 2D Multi-block –> Create –> Input value



247

248 APPENDIX N. TUTORIAL: 3(A) 3D VOLUME GRID

;

Figure N.1: Geometry




The required geometry is as shown in fig N.2

Figure N.2: Forward facing Step Block

N.4 Creating Boundary PLCS

Extract all the boundary PLCS from the Blocks



N.5. DELAUNAY TRIANGULATION 249

• Menu CommandGeometry –> PLC –> Extract –> Edge Of 2D block.


• Stitch all the PLC’S left.






The required Boundary PLC”S are as shown in fig N.3.

Figure N.3: Required Boundary PLC”S

N.5 Delaunay Triangulation

Delaunay Triangulation

A triangulation is a subdivision of an area (volume) into triangles (tetrahedrons). The De-launay triangulation has the property that the circum-circle (circumsphere) of every triangle(tetrahedron) does not contain any points of the triangulation. The Delaunay triangulation is thedual structure of the Voronoi diagram.

Creating Delaunay TriangulationDELAUNAY TRIANGLE (Area) obtain is as shown in Refer fig N.4.

• Menu CommandModule Grid –> 2D triangles –> Create –> Delaunay


Figure N.4: DELAUNAY TRIANGLE-Area

• Enter Area =25. Preview, OK


• Translate the grid. First select only the Polygon and translate it.ToolbarCopyPut the following values: Top Selected Entity, Translation: 0,0,50

• open boundary.pbls

• Translate new PLC to that of the same values as the polygon using the method explainedearlier - with only the PLC selected.

• Choose two PLC’s and make N PLCMenu CommandGeometry –> PLC –> Create –> Algebra of N PLC.

• Put value for no. of PLC as 10

• Convert PLCS to PBLSMenu CommandGeometry –> PBLS –> Convert –> From PLC’s.

• Convert the PBLS to trianglesMenu CommandGrid –> Triangles –> Convert –> From PBLS by inserting edge.

• Select two adjusting POLYGON and stitch themMenu CommandGrid –> Triangles –> Convert –> Stitch

• Make them all as one surface.

• Save As ready

N.5. DELAUNAY TRIANGULATION 251

• Make PolyhedronsMenu CommandGrid –> Polyhedrons –> Create –> Delaunay

• Specify input as ready. Write output file. Insert number of surfaces: 1.Click on OK. Thejob has now been fired and will run in the background.

List of Figures

2.1 GridZTMVersion 4.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Details of Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 GUI-change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Hierarchy of Menu Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5 View Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.6 Geometry Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.7 Geometry Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.8 Grid Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.9 Grid Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.10 2D-Block Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.11 2D-Block Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.12 3D-Block Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.13 3D-Block Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.14 Display Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.15 Display Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.16 Edit Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.17 Edit Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.1 Abstraction of domain method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2 Split when intersecting block touches parent block face shared by single block . . . 42

5.3 Splitting when intersecting block touches parent block face shared by two blocks . 42

5.4 Split when intersecting block touches parent block edge. . . . . . . . . . . . . . . . 43

5.5 Parent block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.6 Seven children formed by splitting parent block . . . . . . . . . . . . . . . . . . . . 44

5.7 Splitting of a block by an internal face . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.8 Example to explain clustering propagation . . . . . . . . . . . . . . . . . . . . . . . 47

5.9 Clustering a single block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.10 Clustering an edge of a block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.11 Unmapped face and block topology . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.12 Mapped face and block topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.13 Split when intersecting block touches parent block vertex . . . . . . . . . . . . . . 51

5.14 Split Block Topology by intersecting block inside the parent block (27 blocks case) 52

5.15 Split Block1 by internal face becomes 4 child blocks as split propagation affects parent block twice 52

5.16 Split block using face can result in possible 8 child blocks. . . . . . . . . . . . . . . 53

5.17 Choosing an edge inside the block for splitting . . . . . . . . . . . . . . . . . . . . 53

5.18 Choosing a vertex inside the block for splitting . . . . . . . . . . . . . . . . . . . . 54

5.19 Domain shape change grid density . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

253

254 LIST OF FIGURES

5.20 Global grid clustering in possible by splitting a block . . . . . . . . . . . . . . . . . 55

5.21 Edges of blocks around Ahmed body (see surface grids of one block) . . . . . . . . 55

5.22 Grids on faces of Ahmed body (see Clustered grids close and in wake of body . . . 56

5.23 Single block of Pickup Van grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.24 Blocks of Hypersonic Research Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . 57

A.1 Barrel PLC’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

A.2 Barrel PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

A.3 Barrel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

A.4 Expression Dialog Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

A.5 Copy Dialog Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

A.6 Dome PLC’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

A.7 Dome PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

A.8 Dome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

A.9 Fillet PLC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

A.10 Fillet PLC’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

A.11 Fillet PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

A.12 Fillet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

A.13 Bent Pipe Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

A.14 Bent Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

A.15 Straight Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

A.16 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

A.17 Dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

A.18 Dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

A.19 Dialog box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

A.20 Mapped 3D Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

A.21 Rendering of Mapped Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

A.22 3-D MultiBlock tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.23 Mapping Step1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.24 Mapping Step2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.25 Mapped Barrel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.26 Mapped Dome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.27 Mapped Fillet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.28 Mapped Bent Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.29 Create Block for Straight Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.30 Mapped Straight Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

B.1 Required Geometry of Generic Missile . . . . . . . . . . . . . . . . . . . . . . . . . 95

B.2 Dialog box for PLC from expression . . . . . . . . . . . . . . . . . . . . . . . . . . 96

B.3 PLC From Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

B.4 Dialogue Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

B.5 10 PLC creted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

B.6 Picking ON/OFF Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

B.7 Show Boundary Points Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

B.8 Required PLCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

B.9 Show Geometry Direction Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

B.10 Required PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

B.11 Blending Surface with the Nose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

LIST OF FIGURES 255

B.12 Required PLC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

B.13 Required Interpolated PLCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102B.14 Required Geometry of Generic Missile . . . . . . . . . . . . . . . . . . . . . . . . . 102

B.15 Dialog box for moving a block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103B.16 Required Block Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

B.17 Selector Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

B.18 Block On Face . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105B.19 Enclosed Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

B.20 Plane Cutter1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106B.21 Plane Cutter2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

B.22 Face to be mapped with Nose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

B.23 All Blocks Rendered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107B.24 Showing Mapping lines for Blending Surface . . . . . . . . . . . . . . . . . . . . . . 108

B.25 Mapped Blending Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108B.26 Rendered Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

B.27 Mapped Missile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

B.28 Volume Grid OF Missile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109B.29 Clustering Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

C.1 Ahmed body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111C.2 PLC - From Expression (Command Box) . . . . . . . . . . . . . . . . . . . . . . . 112

C.3 PLC - From Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

C.4 Deform - From Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113C.5 Isometric View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

C.6 Scaling Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115C.7 Translation Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

C.8 Translated PLC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

C.9 Algebra of N PLCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117C.10 Front Lower PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

C.11 Scaling Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118C.12 Upper and Lower PBLS of Front surface . . . . . . . . . . . . . . . . . . . . . . . . 119

C.13 Values for Algebra of N PLCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

C.14 Left side PLCs for Surface 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120C.15 The Four PBLS of Front Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

C.16 Ahmedbody Front Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121C.17 Mid-body 1 Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

C.18 Mid-body 2 Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

C.19 Mid-body 3 Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126C.20 Rear Lower PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

C.21 Rear Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129C.22 Ahmedbody - PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

C.23 Initial Topology view 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

C.24 Initial Topology view 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130C.25 Initial Topology view 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

C.26 PBLS to 2D block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132C.27 Export 2D to 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

C.28 Relative Orientation wrt the Topology . . . . . . . . . . . . . . . . . . . . . . . . . 134

C.29 Correct position of the Ahmed Body . . . . . . . . . . . . . . . . . . . . . . . . . . 135

256 LIST OF FIGURES

C.30 Pick Entity Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

C.31 Select a PBLS to be mapped . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

C.32 Select a corresponding block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

C.33 Mapping lines in correct order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

C.34 Mapped block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

C.35 Rendering the mapped surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

C.36 Mapped blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

C.37 Mapped blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

C.38 Mapped blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

C.39 Mapped blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

C.40 Final mapped blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

C.41 Before Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

C.42 After Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

D.1 Funnel - Wireframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

D.2 Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

D.3 Translated PLC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

D.4 Interpolated PLC’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

D.5 PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

D.6 PBLS’s - 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

D.7 PBLS’s - 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

D.8 PLC ”KL” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

D.9 PLC ”OR” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

D.10 Lower Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

D.11 Upper Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

D.12 Complete PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

D.13 Rendered Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

D.14 Initial Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

D.15 Moved Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

D.16 Scaled Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

D.17 New Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

D.18 Topology - Front View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

D.19 Topology - Side View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

D.20 Topology - Isometric View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

D.21 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

D.22 Mapping - One face selected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

D.23 Mapping - Display Current Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

D.24 Mapping - Correct Mapping Order . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

D.25 Mapped Face . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

D.26 Rendered Mapped Face . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

D.27 Rendered Mapped Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

D.28 Mapped Funnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

E.1 Required Geometry of Intersecting Pipes . . . . . . . . . . . . . . . . . . . . . . . . 161

E.2 Input Semi-cylindrical Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

E.3 Carpet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

E.4 Input Pipes along-with Carpet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

E.5 Input Pipes with Carpet (top view) . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

LIST OF FIGURES 257

E.6 Carpeting Dialog Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

E.7 Un-edited Carpet with original cylinders . . . . . . . . . . . . . . . . . . . . . . . . 165

E.8 Required un-edited Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

E.9 Edited Carpet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

E.10 Final Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

E.11 Final Geometry (top view) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

E.12 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

E.13 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

E.14 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

E.15 Mapped 3D Blocks of Intersecting Pipes . . . . . . . . . . . . . . . . . . . . . . . 170

E.16 Rendered Mapped Intersecting Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . 170

E.17 Mapping Step 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

E.18 Mapping Step 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

E.19 Mapped Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

E.20 Distorted Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

E.21 Mapping Edge to match Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

E.22 Mapped Surface of pipe 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

E.23 Mapped Intersecting Region 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

E.24 Mapped Iintersecting Region 2 Surface . . . . . . . . . . . . . . . . . . . . . . . . . 174

E.25 Mapped Pipe 2 Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

F.1 Geometry of the Blower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

F.2 Basic Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

F.3 Airfoil for Fan Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

F.4 Blower with Fans Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

F.5 Blower Geometry Incomplete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

F.6 Blower Incompleted Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

F.7 Blower Incompleted Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

F.8 Blower Completed Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

F.9 Blower Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

F.10 Creation of PBLS for a 2D Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

F.11 PBLS to 2D Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

F.12 Editing Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

F.13 Creation of PBLS for 2D Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

F.14 Final 2D Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

F.15 Before Smoothening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

F.16 After Smoothening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

G.1 Dumbell Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

G.2 Lobe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

G.3 Lobe - Part1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

G.4 Hemisphere - With Degeneracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

G.5 Carpet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

G.6 Hemisphere - TRSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

G.7 Hemisphere - Carpeted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

G.8 Lobes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

G.9 Central Cylinder - 1 PBLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

G.10 Central Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

258 LIST OF FIGURES

G.11 Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197G.12 1 Lobe Mapped . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197G.13 2 Lobes Mapped . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198G.14 Entire Dumbell Mapped . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198G.15 Before Smoothening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198G.16 After Smoothening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

H.1 Geometry of cascade Air Foil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201H.2 Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203H.3 Wrong TRSP obtained . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203H.4 Wrong TRSP obtained . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204H.5 Flow around a cascade airfoil(Length). . . . . . . . . . . . . . . . . . . . . . . . . . 204H.6 Flow Around a Cascade Airfoil (Area). . . . . . . . . . . . . . . . . . . . . . . . . . 205

I.1 Technical 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207I.2 Technical 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208I.3 Technical 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

I.4 Technical 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210I.5 Technical 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211I.6 Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212I.7 Second cylindrical part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212I.8 Third cylindrical part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213I.9 Fourth cylindrical part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213I.10 Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214I.11 Center Fin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214I.12 PBLS of RLV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215I.13 Rendered Surface of RLV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

I.14 Front View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216I.15 Front Central View- Magnified . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217I.16 Side View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217I.17 Central View - Magnified . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218I.18 Isometric View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218I.19 2D Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219I.20 Child Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219I.21 RLV Surface + All Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220I.22 Mapping - One PBLS selected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

I.23 Mapping - Correct Mapping Order . . . . . . . . . . . . . . . . . . . . . . . . . . . 221I.24 Mapped Face . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221I.25 Mapping - Degenerate Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221I.26 Mapping - Rendered RLV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

J.1 GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224J.2 Forward facing Step-Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224J.3 Required PBLS”S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225J.4 Required TRSP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226J.5 Required Voronoi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

K.1 GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230K.2 Forward facing Step-Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

LIST OF FIGURES 259

K.3 Clustering in Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231K.4 Required PBLS”S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232K.5 Required TRSP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233K.6 Required Voronoi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

L.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235L.2 Forward facing Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236L.3 Required Boundary PLC”S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237L.4 DELAUNAY TRIANGLE-Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238L.5 DELAUNAY TRIANGLE-Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238L.6 Required Voronoi-Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239L.7 Required Voronoi- Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

M.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241M.2 Forward facing Step Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242M.3 Clustering in Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243M.4 Required Boundary PLC”S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244M.5 DELAUNAY TRIANGLE-Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245M.6 DELAUNAY TRIANGLE-Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245M.7 Required Voronoi-Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246M.8 Required Voronoi- Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

N.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248N.2 Forward facing Step Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248N.3 Required Boundary PLC”S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249N.4 DELAUNAY TRIANGLE-Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

260 LIST OF FIGURES

Appendix O

Menu

1. File

→ OpenSaveSave AsExit

2. Edit

→ UndoRedoDatabase

3. Tools

→ Operations Last Selected Entity

→ Zeus Style Zeus Style

4. Geometry

→ Point Create RubberbandXYZ co-ordinatesAlgebra of N Points

Extract From Line SegmentFrom PLCFrom PBLSFrom TriangulationFrom Triangulation BoundaryFrom Polygon

261

262 APPENDIX O. MENU

From Polygon BoundaryVertex Of 2D BlockVertex Of 3D Block

Intersection Line X LineCurve X CurveCurve X SurfaceCurve X Plane

Query U/V Value on Surface

→ Line Segment Create Axix ParallelCross Product

Convert 2 Points

Extract From PLC

Edit Alter MagnitudeScale MagnitudeMirror

→ Plane Create Point and Line SegmentFrom 3 PointsPlane ParallelPrinciple Plane ParallelFrom Co-efficient

→ Piecewise Lin− Create Rubberband−ear Curve Algebra of N PLC

From ExpressionConvert From Points

From SegmentPLC Equal ArcSplit PLCStitch 2 PLCStitch PLCs in LoopJoin 2 PLC

Extract From PBLSAll From PBLSFrom TRSP BoundaryFrom Polygon BoundaryFrom PBLS BoundaryEdge Of 2D Block

263

Edge Of 3D BlockNURBC Equal ParameterNURBC Equal Arc

Edit Open / CloseInsert PointDelete PointDeformReverse

Attributes Display CurvatureDisplay Tangent

Intersection PBLS X PBLS

Query Quality

→ Nurbs Curve Create Rubberband NURBSRubberband NURBS as PLCAlgebra of N NurbCurvesFrom ExpressionCircleEllipseCircular ArcElliptical ArcCurve Offset

Convert From PointsFrom PLC as Control Polygon

Extract Loft U curves from NURBSLoft V curves from NURBS

Edit Change DegreeChange NameOpen / Close

Attributes Display CurvatureDisplay TangentDisplay PolygonCurve

→Piecewise Bi− Create From Algebra of N PBLS−Linear Surface From Expression

From Expression File


Convert From PLCsSplit PBLSJoin 2 PBLSStitch PBLS

Extract From BSS/RSCurrent 2D BlockAll 2D BlockFace of 3D BlockI Layer Of 3D BlockJ Layer Of 3D BlockK Layer Of 3D Block

Edit Delete Row/ColumnDeform

Attributes Display NormalDisplay U DirectionDisplay V Direction

Query Quality

→ Nurbs Surface Algebra of N surfacesFrom ExpressionSurface of RevolutionTabulated CylinderOffset SurfaceConeCylinderSphereTorus

Convert From PBLSLofting NURBSC

5. MODULE BLOCK

→ 2D Multiblock Create Init BlockInsert VertexInsert SlitInsert Dummy SlitInsert BoxInsert Dummy BoxInput Valueson Blockon Edgeon Vertex

265

Convert PBLS To BlockTRSP to BlockPaste EdgeUnpaste Edge

Edit Topology Collapse BlockDelete BlockDelete EdgeMove VertexDrag VertexScale EdgeRotate EdgeMove EdgeScale BlockRotate BlockMove BlockScale All BlocksRotate All BlocksMove All BlocksDeform TopologyDeform BlockDeform EdgeDeform Vertex

Edit Grid Change Grid Points

Clustering All BlocksOne BlockOne EdgeRemove ClusteringRemove One Edge Clustering

Map / Unmap Map VertexMap EdgeMap BlockUnmap VertexUnmap EdgeUnmap BlockRemap VertexRemap EdgeRemap BlockRetreive Topology

Attributes Show NeighboursRender All BlocksSet Edge Label


→ 3D Multiblock Create BlockOn Face SelectorOn FaceOn VertexOn EdgeIn Block SelectorIn Block*27 BlocksPlane Cutter*Cross Cutter Select*Cross Cutter

Convert From 2D BlockPaste a BlockUnpaste a BlockPaste a FaceUnpaste a FacePaste All BlocksUnpaste All Blocks

Edit Topology Delete Selected BlockDelete Block in PlaneDelete All BlocksDelete Blocks in RowDeformMove Vertex ByMove Vertex ToMove Edge ByMove Face ByMove Block ByMove All BlockRotate All BlockScale All Block

Clustering All BlocksOne BlockOne FaceOne EdgeRemove ClusteringRemove One Edge ClusteringForce All BlocksForce Remove ClusteringChange PointDistance First Point

Map / Unmap Map Vertex

Map Edge

267

Map FaceUnmap VertexUnmap EdgeUnmap FaceForce Unmap FaceSingle numpstsRetreive Topology

Set Face Label

Rendering All BlocksCurrent BlockSurfacesSurface GridsMapped SurfacesMapped Surface Grid

Query Block by No.SurfacesNegative CheckNegative Check All BlocksTFI refineShow Negative Volume

6. MODULE GRID

→ 1D Grid Convert Divide in Equal ArcDivide in Equal Arc Keep CornersEnhanceClusterCarpet

Extract From TRSP Boundary

Query Quality

→ 2D Structured Create Four Open PLCOne PBLSTwo CurvesAll PBLS

Convert Swap Tsi and Eta Grid LinesSwap Tsi Grid LinesSwap Eta Grid LinesInvert Normal


Edit Generic 2D smoothener

Query Quality

→ Triangles Create Delaunay

Convert StitchFrom PBLS by inserting EdgeFrom PBLS by inserting Point

Edit SmoothenMin-MaxMax-MinInsert PointDelete PointMerge 2 neighboring facesSwap EdgeCollapse EdgeCollapse FaceCollapse all Degenerate facesUniform NormalInvert NormalDeform

Query Consistency

→ Quadrilaterals Convert From PBLS

→ PolygonConvert

Stitching PolygonsVoronoi from triangles

EditSmoothenInsert PointDelete PointMerge 2 neighboring facesSwap EdgeCollapse EdgeCollapse FaceCollapse all Degenerate facesUniform NormalInvert NormalDeform

→ Polyhedrons Create Delaunay

269

Convert From Multiblock

Edit SplitStitch

Attributes From 3 PointsReset FacesSelect FacesDeselect FacesTag Faces

→ Surface Structure Create From a Rectangle as a Carpet (object trsp)From a Rectangle as a Carpet (object pbls)From a PBLS as a CarpetCarpet User Define (object trsp)Carpet User Define (object pbls)Bounded Carpet (object trsp)Bounded Carpet (object pbls)Nurbs Tessellator in FileQuality

Query From a Rectangle as a Carpet (object trsp)From a Rectangle as a Carpet (object pbls)From a PBLS as a CarpetCarpet User Define (object trsp)Carpet User Define (object pbls)Bounded Carpet (object trsp)Bounded Carpet (object pbls)Nurbs Tessellator in File

Query From a Rectangle as a Carpet

7. MODULE Boundary Condition

→ For Grid SmootheningApplyShow

→ For Compressible Flow SolverApplyShow

→ For Inompressible Flow SolverApplyShow

→ For Electromagnetic SolverApplyShow


→ For Stress Analysis SolverApplyShow

→ For Acoustics SolverApplyShow

→ For Corrosion SolverApply

8. Help

→ AboutGenerate HostIDWhat Is This

END SESSION

Appendix P

Command List

271

272 APPENDIX P. COMMAND LIST

No. Commands Operation

1 open tuiOpenFile -1

2 resetView tuiResetView 0

3 showAllPoints tuiShowAllPoints -1

4 undo tuiUndo 0

5 redo tuiRedo 0

6 select tuiSelectEntity -1

7 deselect tuiDeselectEntity -1

8 show tuiShowEntity -1

9 hide tuiHideEntity -1

10 point tuiCreatePointFromCoordinates -1

11 render tuiRenderCommand 1

12 panLeft tuiPanLeft -1

13 panRight tuiPanRight -1

14 panUp tuiPanUp -1

15 panDown tuiPanDown -1

16 rotateUp tuiRotateUp -1

17 rotateDown tuiRotateDown -1

18 rotateLeft tuiRotateLeft -1

19 rotateRight tuiRotateRight -1

20 rotateAbout tuiSetCenterOfRotation 1

21 enablePicking tuiEnableDisablePicking 1

22 disablePicking tuiEnableDisablePicking 1

23 pick tuiPickPoint 2

24 movePointOnEntity tuiMovePointOnEntity 0

25 executeScript tuiExecuteScript 1

26 cutPlane tuiCutPlane -1

27 delete last tuiDeleteLast 0

28 delete selected tuiDeleteSelected 0

29 delete deselected tuiDeleteDeselected 0

30 delete all tuiDeleteAll 0

31 copy tuiCopy 1

32 move tuiMove 1

33 set translation tuiTranslation 3

34 set rotation tuiRotation 2

35 set scaling tuiScaling 3

273


51 point n point tuiPointNpoint -1

52 point from coordinates tuiPointXYZ -1

53 point extract from pbls tuiPointFromPbls -1

54 point extract from plc tuiPointFromPlc -1

55 point extract from line tuipointFromLine -1

56 point extract from tribdry tuipointFromTriBdry -1

57 point extract from poly tuipointFromPoly -1

58 point extract from tri tuipointFromTri -1

59 point extract from polybdry tuipointFromPolyBdry -1

60 point extract from 2dblock tuipointExtractVertex2dblk -1


101 line axis parallel tuiLineAxisParallel -1

102 line cross product tuiLineCrossProduct -1

103 line from two points tuiLineFrom2Points -1

104 line alter magnitude tuiLineAlterMagnitude -1

105 line scale magnitude tuilineScaleMagnitude -1

106 line mirror tuilineMirror -1

107 line extract from plc tuilineFromPlc -1


126 plane from three points tuiPlaneThreePoints -1

127 plane parallel tuiPlaneParallel -1

128 principle plane tuiPlanePrinciplePlane -1

129 plane from coefficient tuiPlaneFromCoefficient -1

130 plane from line tuiplaneFromLine -1


153 plc between two plcs tuiPlcNPlc -1

154 plc from expression tuiPlcExpression -1

155 plc join tuiPlcJoin -1

156 plc extract all from pbls tuiPlcAllPbls -1

157 plc from points tuiplcFromPoints -1

158 plc open close tuiplcOpenClose -1

159 plc split tuiplcSplit -1

160 plc extract trsp bdry tuiplcTrspBdry -1

161 plc extract poly bdry tuiplcPolyBdry -1

162 plc extract pbls bdry tuiplcPblsBdry -1

163 plc extract from pbls tuiplcPbls -1

164 plc extract from block2d tuiblock2dExtractPlc -1

165 plc from points tuiPlcFromPoints 0

166 plc stitch tuiPlcStitch 0

167 plc stitch in loop tuiPlcStitchInLoop 0



201 pbls from expression tuiPblsExpression -1

202 pbls from plcs tuiPblsPlcs -1

203 pbls stitch tuiPblsStitch -1

204 pbls extract from current block tuipblsBlockToPbls -1

205 pbls extract all blocks tuipblsAllBlockToPbls -1


251 nurbc from expression tuiNurbcFromExpression -1

252 nurbc from circle tuiNurbcCircle -1

253 nurbc from ellipse tuiNurbcEllipse -1

254 nurbc from circular arc tuiNurbcCircularArc -1

255 nurbc from elliptical arc tuiNurbcEllipticalArc -1

256 nurbc offsetcurve tuiNurbcOffset -1

257 nurbc n nurbc tuiNurbcNnurbc -1

258 nurbc extract u tuiNurbcExtractU -1

259 nurbc extract v tuiNurbcExtractV -1

260 nurbc from points tuiNurbcFromPoints -1

261 nurbc as control polygon tuiNurbcControlPolygon -1


301 nurbs from cone tuiNurbsCone -1

302 nurbs from cylinder tuiNurbsCylinder -1

303 nurbs from sphere tuiNurbsSphere -1

304 nurbs from torus tuiNurbsTorus -1

305 nurbs n nurbs tuiNurbsNnurbs -1

306 nurbs from nurbc tuiNurbsFromNurbc -1

307 nurbs from pbls tuiNurbsFromPbls -1

308 nurbs from expression tuiNurbsFromExpression -1

309 nurbs revolve tuiNurbsRevolve -1

310 nurbs offsetsurface tuiNurbsOffset -1

275


351 block2d init block tuiblock2dInitBlock -1

352 block2d onblock tuiblock2dOnBlock -1

353 block2d onedge tuiblock2dOnEdge -1

354 block2d onvertex tuiblock2dOnVertex -1

356 block2d undo tuiblock2dundoBlock -1

357 block2d redo tuiblock2dredoBlock -1

358 block2d collapse block tuiblock2dCollapseBlock -1

359 block2d delete block tuiblock2dDeleteBlock -1

360 block2d move vertex tuiblock2dMoveVertex -1

361 block2d scale edge tuiblock2dscaleEdge2D -1

362 block2d rotate edge tuiblock2drotateEdge2D -1

363 block2d move edge tuiblock2dMoveEdge2D -1

364 block2d scale block tuiblock2dscaleBlock2D -1

365 block2d rotate block tuiblock2drotateBlock2D -1

366 block2d move all blocks tuiblock2dmoveAllBlock2D -1

367 block2d scale all blocks tuiblock2dscaleAllBlock2D -1

368 block2d rotate all blocks tuiblock2drotateAllBlock2D -1

369 block2d move block tuiblock2dmoveBlock2D -1

370 block2d map vertex tuiblock2dmapVertex -1

371 block2d map edge tuiblock2dmapEdge -1

372 block2d map block tuiblock2dmapBlock -1

373 block2d unmap edge tuiblock2dunmapEdge -1

374 block2d unmap block tuiblock2dunmapBlock -1

375 block2d unmap vertex tuiblock2dunmapVertex -1



378 block2d set edge label tuiblock2dSetLabel -1

379 block2d show boundary cond tuiblock2dShowBoud -1

380 block2d set boundary cond tuiblock2dSetBounCond -1

381 block2d cluster all block tuiblock2dClusterAllBlock -1

382 block2d cluster one block tuiblock2dClusterBlock -1

383 block2d cluster one edge tuiblock2dClusterEdge -1

384 block2d remove clustering tuiblock2dRemoveClustering -1

385 block2d convert trsp to block tuiblock2dTrspToBlock -1

386 block2d convert pbls to blocks tuiblock2dPblsToBlocks -1

387 block2d unpaste edge tuiblock2dUnpasteEdge -1

388 block2d paste edge tuiblock2dPasteEdge -1

389 block2d input values tuiblock2dInputValues -1

390 block2d change grid points tuiblock2dChangeGridpts -1

391 block2d deform block tuiblock2dDeformBlock -1

392 block2d deform edge tuiblock2dDeformEdge -1

393 block2d deform vertex tuiblock2dDeformVertex -1

394 block2d deform topo tuiblock2dDeformTopo -1

395 block2d blk from 2 open plc tuiblock2d2OpenPlc -1

396 block2d blk from 4 open plc tuiblock2d4OpenPlc -1

397 block2d remove edge clustering tuiblock2dRemoveEdgeClustering -1

398 block2d delete edge tuiblock2dDeleteEdge -1

399 block2d retrive topo tuiblock2dRetriveTopo -1

400 block2d insert vertex tuiblock2dinsertVertex -1

401 block2d insert slit tuiblock2dInsertSlit -1

402 block2d insert dummy slit tuiblock2dInsertDummySlit -1

403 block2d insert box tuiblock2dInsertBox -1

404 block2d insert dummy box tuiblock2dInsertDummyBox -1

405 block2d traverse block tuiblock2dBlockTrav -1

406 block2d traverse block thru edge tuiblock2dBlockTravThruEdge -1

407 block2d traverse block around ver tuiblock2dBlockTravAround -1

408 block2d traverse vertex tuiblock2dTravVertex -1

409 block2d traverse edge tuiblock2dTravEdge -1

277


451 block3d move vertex tuiblock3dMoveVertex -1

452 block3d move edge tuiblock3dMoveEdge -1

453 block3d move face tuiblock3dMoveFace -1

454 block3d move block tuiblock3dMoveBlock -1

455 block3d move all block tuiblock3dAllMoveBlock -1

456 block3d scale all block tuiblock3dScallAllBlock -1

457 block3d move vertex3d to tuiblock3dMoveToVertex -1

458 block3d delete all block tuiblock3dDeleteAllBlock -1

459 block3d delete selected block tuiblock3dDeleteBlock -1

460 block3d delete block from row tuiblock3dDeleteBlockinRow -1

461 block3d map vertex tuiblock3dmapVertex -1

462 block3d unmap vertex tuiblock3dunmapVertex -1

463 block3d map edge tuiblock3dmapEdge -1

464 block3d unmap edge tuiblock3dunmapEdge -1

465 block3d rotate all block tuiblock3dRotateAllBlock -1

466 block3d init block tuiblock3dInitBlock -1

467 block3d unpaste face tuiblock3dUnpasteFace -1

468 block3d paste face tuiblock3dPasteFace -1

469 block3d unpaste block tuiblock3dUnpasteBlock -1

470 block3d paste block tuiblock3dPasteBlock -1

471 block3d unpaste all block tuiblock3dUnpasteAllBlock -1

472 block3d paste all block tuiblock3dPasteAllBlock -1

473 block3d export 2d to 3d tuiblock3dExport2DTo3D -1

474 block3d show boundary cond tuiblock3dShowBoud -1

475 block3d set face label tuiblock3dSetLabel -1

476 block3d change grid pts tuiblock3dChangeGridpts -1

477 block3d set boundary cond tuiblock3dSetBounCond -1

478 block3d cluster all block tuiblock3dClusterAllBlock -1

479 block3d cluster one block tuiblock3dClusterBlock -1

480 block3d cluster edge tuiblock3dClusterEdge -1

481 block3d extract vertex tuiblock3dExtractVertex -1

482 block3d extract edge tuiblock3dExtractPlc -1

483 block3d extract I layer tuiblock3dExtractILayer -1

484 block3d extract J layer tuiblock3dExtractJLayer -1

485 block3d extract K layer tuiblock3dExtractKLayer -1

486 block3d extract face tuiblock3dExtractFace -1

487 block3d deform topo tuiblock3dDeformBlock -1

488 block3d remove edge clustering tuiblock3dRemoveEdgeClustering -1

489 block3d remove clustering tuiblock3dRemoveClustering -1

490 block3d render current block tuiblock3dRenderCurrentBlock -1

491 block3d render surfaces tuiblock3dRenderSurfaces -1

492 block3d render mapped surface tuiblock3dRenderMappedSurfaces -1

493 block3d render all blocks tuiblock3dRenderAllBlocks -1

494 block3d render surface grid tuiblock3dRenderSurfaceGrid -1

495 block3d render mapped surface grid tuiblock3dRenderMapSurfaceGrid -1



496 block3d map face tuiblock3dmapFace -1

497 block3d unmap face tuiblock3dunmapFace -1

498 block3d retrive topo tuiblock3dRetriveTopo -1

499 block3d add block tuiblock3dAddBlock -1

500 block3d on face selector tuiblock3dOnFaceSel -1

501 block3d on face tuiblock3dOnFace -1

502 block3d on edge tuiblock3dOnEdge -1

503 block3d on block selector tuiblock3dInBlockSel -1

504 block3d plane cutter tuiblock3dPlaneCutter -1

505 block3d on vertex tuiblock3dOnVertex -1

506 block3d goto blknum tuiblock3dGotoBlkNum -1

507 block3d goto blkname tuiblock3dGotoBlkName -1

508 block3d negative volume oneblk tuiblock3dNegVolBlk -1

509 block3d negative volume allblk tuiblock3dNegVolAllBlk -1

510 block3d delete blk from plane tuiblock3dDeleteBlkFromPlane -1

511 block3d on block tuiblock3dInBlock -1

512 block3d edge traversal tuiblock3dTravEdge -1

513 block3d face traversal tuiblock3dTravFace -1

514 block3d traverse thru face tuiblock3dTravThruFace -1

515 block3d block traversal tuiblock3dTravBlock -1

516 block3d vertex traversal tuiblock3dTravVertex -1

517 block3d delete all blk tuiblock3dDeleteAllBlk -1

518 block3d reverse traverse tuiblock3dReverseTrav -1

519 block3d change mapping order tuiblock3dMappingOrder -1


551 intersection line line tuiLineIntersection -1

552 intersection plc plc tuiPlcIntersection -1

553 intersection pbls pbls tuiPblsIntersection -1

554 intersection pbls plc tuiPblsPlcIntersection -1


600 2dstucture pbls to block tui2dstucturePblsToBlock -1

601 2dstucture allpbls to blocks tui2dstuctureAllPblsToBlocks -1


650 grid plc enhance tuigridPlcEnhance -1

651 grid plc divide keep corners tuigridPlcKeepCorners -1

gridz_manual

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