Predicting Pressure Distributions Using CFD

University of Newcastle upon Tyne, Dept. of Civil Eng., Structural Eng.

Wind Loading on a Fabric Structure 1

Predicting Pressure Distributions on Surfaces of Arbitrary Geometry from CFD –

a preliminary study

By

I Gede Adi Susila

Thesis submitted to the Department of Civil Engineering

University of Newcastle upon Tyne

in partial fulfilment of requirement for the degree of

Master of Science

in

Structural Engineering

APPROVED:

P. D. Gosling, Supervisor

August 2001

Newcastle upon Tyne

Keywords: Wind Loads, Fabric Membrane Structure, Cable-suspended roof, published data, CFD method, LES (Large Eddy Simulation- Smagorinsky +Lilly model viscosity).



Predicting Pressure Distributions on Surfaces of Arbitrary Geometry

from CFD – a preliminary study

Abstract

Structural fabric membrane for many years have been applied and developed for large span

enclosures for variety of purposes. More recently, structures that combine highly flexible cable

integrated with fabric membranes have been designed as structural integral system. Accurate

assessment of wind load distribution is important because the large surface area usually projected

by a fabric membrane structure means that wind pressure is a significant load case. The

requirement to predict wind loading on structures of complex geometry form is absolutely needed.

Computational Fluidal Dynamic (CFD analysis) is highly pointed to solve a number of wind

tunnel test problem on the computer simulation. Large-eddy simulation (LES) technique with the

Smagorinsky eddy-viscosity model has been applied in order to predict pressure coefficients for 3-D

domes and catenoid models. “Fluent” has been used to analyze the flows. Published data of Maher

and the ASCE have been used as the basis guideline to enable wind loading to be applied

appropriately.

Plan view: pressure coefficients

for y/d = ½ (hemisphere) Maher’s

Plan view of pressure coefficient contour

y/d=h/D=1/2 on CFD

Table of Mean pressure coefficient around the

sphere under LES simulation

0.621

0.318

-0.744-0.289

-1.2

-0.441

-0.144

-1.5

-1

-0.5

0

0.5

1

0 30 60 90 120 150 180

Angle, @ (degree)

mean external Cp

Cp Around Wall

Result of LES computations are compared with those from laminar models as well as those from

turbulent models based on Reynolds–average Navier-Stokes equation (RANS model) and those

from experiment. The numerical experiment results for all models with various configurations to be

exited by the turbulent wind forces were identified. The LES results from 3D computational agreed

very well with the experimental or published data. For the dome case of h/d=1/2 ratio, the result can

be sort it out into the maximum positive Cp=+0.621 and the maximum negative in the centre of

dome is Cp = -1.2. The coefficient offered was quit similar to the published data of Cp=+0.6 and

Cp=-1.0, respectively.

In the limited study presented in this dissertation, CFD has been shown to a reasonable

prediction of wind pressure distributions. Conceivably it could replace some wind tunnel tests.

However, further study of CFD applied to the structural engineering problem is still needed in

order to evaluate the reliability of the numerical results.

Keywords: Wind Loads, Fabric Membrane Structure, Cable-suspended roof, published data, CFD

method, LES (Large Eddy Simulation- Smagorinsky +Lilly model viscosity).

Corresponding author: E-mail: [email protected] / [email protected] /

[email protected]

Present Address: 11 Sedgley Road, Crumpsall, Manchester, M8 5AG. UK.



Table of Contents

List of Figure ............................................................................................................. vii

List of Table .............................................................................................................. xv

Chapter 1. Introduction .......................................................................................... 1

Chapter 2. Literature Review................................................................................. 5

2.1 Introduction ................................................................................................ 5

2.2 Cable-Suspended Structures ....................................................................... 5

2.3 Fabric Membrane Structures ...................................................................... 17

2.4 Computational Fluid Dynamic (CFD) for Wind Loading.......................... 23

2.5 Wind Tunnel Test ....................................................................................... 35

2.5.1 Wind Tunnel Techniques................................................................... 37

2.5.2 Small Wind Tunnel............................................................................ 43

2.6 Conclusion.................................................................................................. 43

Chapter 3. Numerical Methods .............................................................................. 44

3.1 Introduction ................................................................................................ 44

3.2 Finite Element Theory and CFD Methods Reviews................................... 44

3.2.1 The CFD Code................................................................................... 51

Pre-processor .................................................................................... 51

Solver................................................................................................. 51

Post-processor.................................................................................... 52

3.2.2 Fluid Flow Problem and Governing Equations on CFD ................... 53

3.2.3 General Fluid Dynamic Background................................................. 60

3.3 General Strategies and Procedures ............................................................. 62

AutoCAD Reviews ............................................................................ 63

Pre-processor: GAMBIT Reviews .................................................... 64

Solver: Fluent Reviews...................................................................... 67

Post-processor.................................................................................... 68

3.4 Detail of Model Experimental .................................................................... 68



3.4.1 Single Cooling Tower Model ............................................................ 70

3.4.1.a Detail Procedure and Instruction ........................................... 71

3.4.1.b The Result of the Laminar Flows of Cooling Tower ............ 77

3.4.1.c The Result of the Turbulent Flows under Large Eddy

Simulation (LES) of Cooling Tower ..................................... 82

3.4.2 Multiple Cooling Tower model ......................................................... 86

3.4.2.a The Result of the Turbulent Flows under Large Eddy

Simulation (LES) of Multiple Cooling Tower ...................... 88

3.4.3 Single Sphere Model ......................................................................... 93

3.4.3.a The Result of the Turbulent Flows under Large Eddy

Simulation (LES) of Single Sphere ....................................... 95

3.4.4 Multiple Sphere Model...................................................................... 97

3.4.4.a The Result of the Laminar of Multiple Sphere ...................... 99

Chapter 4. Experimental Methods......................................................................... 101

4.1 Introduction ................................................................................................ 101

4.2 Experimental Work Procedure ................................................................... 103

4.2.1 1:1000 Scale Model of Cooling Tower and Sphere Model ............... 103

4.2.2 Wind Tunnel Testing and Requirement............................................ 104

4.3 Published Experimental Data and Comparison with CFD result ............... 107

4.3.1 Published Data for Sphere/Domes problem ............................. 107

4.3.2 Published Data for Hyperbolic Cooling Tower problem ......... 108

4.3.3 Comparison and Discussion of Published data to the

CFD result ................................................................................ 109

4.3.3.a Single Cooling Tower. ........................................................... 109

4.3.3.b Single Sphere......................................................................... 112

Chapter 5. Conclusions ........................................................................................... 115

5.1 Introduction ................................................................................................ 115

5.2 Wind Tunnel Testing.................................................................................. 115



5.3 Wind loading test on CFD method............................................................. 115

5.3.1 Comparison reliability between Laminar and Turbulent problem

flow model in CFD method ............................................................ 116

5.3.2 Comparison between published data and CFD method study

of wind loading to fabric membrane structure................................... 116

5.4 General Conclusion and Recommendations

Bibliography............................................................................................................. 118

Appendix 1 ............................................................................................................... 119

Appendix 2 ............................................................................................................... 120

Appendix 3 ............................................................................................................... 123

Appendix 4 ............................................................................................................... 149

List of Figures

Figure 1.1 Tent Model ............................................................................................... 1

Figure 1.2 Membrane Roof Model ............................................................................ 1

Figure 1.3 Illustration of wind acting on fabric structure.......................................... 2

Figure 1.4. Example contour of pressure coefficient ................................................ 3



Figure 2.1.Static behaviour and various types of suspended roof ............................. 6

Figure 2.2 various types of suspended roof............................................................... 6

Figure 2.3 Behaviour of cable system ....................................................................... 6

Figure 2.4 Deflection of cable system....................................................................... 7

Figure 2.5 Wind pressure distribution ....................................................................... 9

Figure 2.6 Antisymmetric wind load effect............................................................... 9

Figure 2.7. Circular plan referencing cable system. .................................................. 9

Figure 2.8. Stadium Detail by Irwin cs & Inc. Figure2.9-10..................................... 11

Figure 2.9. Mean force coefficient ............................................................................ 12

Figure 2.10. Mean deflection at φ=900 ...................................................................... 12

Figure 2.11. Structure Layout.................................................................................... 12

Figure 2.12. Wind Pressure Distribution, by Yasui, cs included Figure2.11 ............ 12

Figure 2.13. La-Plata Stadium by Rocha cs, & included Figure2.14-15.................. 13

Figure 2.14. Mean wind pressure, α=1800 .............................................................. 16

Figure 2.15 Standard Deviation of wind pressure, α=1800 ....................................... 16

Figure 2. 16 Hybrid double-layer system by Ando,cs............................................... 16

Figure 2.17. Wind pressure coefficient Distribution. ................................................ 16

Figure 2.18. Millennium Dome by Kronenburg, A & B ........................................... 17

Figure 2.19 Membrane in tension by Shaeffer .......................................................... 19

Figure 2.20 Hyperbolic surface of membrane .......................................................... 19

Figure 2.21The hangar structural scheme by Kazakevitch........................................ 20

Figure 2.22 Pressure distribution on the membrane roofing at any surface (a) the stage of

erection, β=0; ε=0.5%- on upper surface, 2-the net values on the upper and lower surfaces;(b), (c) The completed stage (on the upper surface); 3,4 in

section a; 3-β=900, ε=0.5%; 4-β=900 , ε=8%, etc.e by Kazakevitch ...... 20

Figure 2.23 Structural section, Park Dome Kumamoto (1999)................................. 22

Figure 2.24 General Approach Design Tensile Membrane Structure by Campbell (2000) 23

Figure 2.25 Visual Post-processing, Voogt (1990).................................................... 24

Figure 2.26 Stubwing and pressure measurement Voogt (1990)............................... 24

Figure 2.27 Calculation grid in a close vicinity of the cube, Mikkelsen &

Livesey (1995) ...................................................................................... 25



Figure 2.28 Cp value shown as isobar for an angle of 00 Mikkelsen & Livesey

(1995..................................................................................................... 25

Figure 2.29 Comparison between full-scale, model scale and numerically predicted Cp for h/z0= 180 ......................................................................................... 25

Figure 2.30 The computational grid in close vicinity of the obstacle, Lakehal (1998)

.............................................................................................................. 26

Figure 2.31 Pressure coefficient distribution at the symmetry plane, Lakehal (1998)

.............................................................................................................. 26

Figure 2.32 Comparison of pressure coefficient distribution at a horizontal plane z/H for different approach flow angles:/, Lakehal (1998) ............................................... 27

Figure 2.33 Unstructured hexahedral meshes around typical building configuration, Kim & Boysan (1999) ...................................................................................... 28

Figure 2.34 Flow over the curved two-dimensional hill- predictions using four different turbulence models, bottom left: pressure distribution and bottom right; skin-friction distribution. Kim & Boysan (1999) .......................................................................... 29

Figure 2.35 Distribution of pressure coefficient (Cp) on 1:1:0.5 building of conical vortex at the

roof corner predicted by revised model k-ε ( k-ε−φ model by Kawamoto, 1995 30

Figure 2.36 Conical vortex at the roof corner predicted by LES, by Murakami, 1997 30

Figure2.37 Computational model of the AIJ project by Tamura,cs. ......................... 33

Figure 2.38 Kinetic turbulent energy: a). Smargorinsky model, b). Dynamic SGS model, by Tamura,cs ............................................................................................. 34

Figure 2.39 Mean pressure coefficient on the roof: a). Smargorinsky model, b). Dynamic SGS model, by Tamura,cs ............................................................................ 34

Figure 2.40 Heler-type dry-cooling tower, by Su,cs. ................................................ 35

Figure 2.41 Computational region and coordinate system, by Su, cs. ...................... 35

Figure 2.42 Contour of pressure in the horizontal plane (Z=9m, cross wind speed of 5 m/s), by Su, cs........................................................................................................ 35

Figure 2.43. Experimental planning and execution process diagram........................ 38

Figure 2.44. Representative data flow. ...................................................................... 39

Figure 2.45 Dome geometry and coordinate system, by Uematsu............................ 40



Figure 2.46 Distributions of the mean and rms pressure coefficient Cp and

C’p H/D =1/4, by Uematsu................................................................. 40

Figure 2.47 Tapping arrangement and wind direction definition for single dome test, by Letchford,cs .......................................................................................... 42

Figure 2.48 Comparison of mean pressure coefficient along centerline of a smooth dome, by Letchford,cs .......................................................................................... 42

Figure3.1 Three-dimensional stress on an element, by Logan .................................. 45

Figure 3.2 Tetrahedral solid element, by Logan........................................................ 46

Figure 3.3 Mass flow in and out of fluid element, by Versteeg & Malalasekera...... 55

Figure 3.4 Stress components on three faces of fluid element, by Versteeg & Malalasekera 56

Figure 3.5 Stress components in the x-direction, by Versteeg & Malalasekera........ 56

Figure 3.6 (a) Boundary condition for an internal flow problem Versteeg & Malalasekera 58

Figure 3.6 (b) Boundary condition for external flow problem, by Versteeg & Malalasekera 59

Figure 3.7 Velocity profiles at different locations downstream of an obstacle, by Versteeg & Malalasekera......................................................................................... 59

Figure 3.8 by Potts (MMM336) ................................................................................ 60

Figure 3.9 by Potts (MMM336) ................................................................................ 60

Figure 3.10 Example mesh geometric in AutoCAD.................................................. 63

Figure 3.11 Arranged position of inlet, outlet and wall boundaries in AutoCAD .... 63

Figure 3.12 The geometry that will be exported from AutoCAD ............................. 63

Figure 3.13 Arranged model generated, domain, and floating element (tetrahedral) 65

Figure 3.14 Arranged position of inlet, outlet and wall boundaries in AutoCAD .... 66

Figure 3.15.a Sphere Elevation.................................................................................. 69

Figure 3.15.b Cooling Tower Elevation .................................................................... 69

Figure 3.16 Computational domain development ..................................................... 69



Figure 3.17 Sketch of Heler-type dry cooling tower (De1.igs of IGES file) ............ 70

Figure 3.18 Internal count space................................................................................ 70

Figure 3.19 Domain of Single Cooling Tower .......................................................... 71

Figure 3.20 Computational region and coordinate system. ....................................... 71

Figure 3.21. Surface mesh on rear of cooling tower ................................................. 72

Figure 3.22 Brick and Cooling tower ........................................................................ 73

Figure 3.23 Elements within a specified quality range of 0.6 upper and 0. 7 lower ratios 74

Figure 3.24 Plot the residual of laminar flow and number iteration converged at 118. 76

Figure 3.25 Plot the residual of turbulent flow and 427 number iteration converged 77

Figure 3.26.a Pressure coefficient contour of the whole body from the top of plan (Coded De1) ...................................................................................................... 77

Figure 3.26.b Pressure coefficient contour of the whole body from side elevation .. 78

Figure 3.26.c Diagram pressure coefficient in distance position of the model to the sources. ................................................................................................. 78

Figure 3.26.d Pressure coefficient contour occurred at z = 0.2 H ~ 32 m (Plane-5) . 79

Figure 3.26.e Diagram pressure coefficient at z =0.2 H ~ 32 m (Plane-5)................ 79

Figure 3.26.f Pressure coefficient contour occurred at z = 0.45 H ~ 72 m (Plane-6) 80

Figure 3.26.g Diagram pressure coefficient at z = 0.45 H ~ 72 m (Plane-6) ............ 80

Figure 3.26.h Pressure coefficient contour occurred at z = 0.7 H ~ 112 m (Plane-7) 81

Figure 3.26.i Diagram pressure coefficient at z = 0.7 H ~ 112 m (Plane-7) ............. 81

Figure 3.27.a Pressure coefficient contour of the whole body from the top of plan (Coded De11) .................................................................................................... 82


Figure 3.27.c Diagram pressure coefficient in distance position of the model to the sources 82





Figure 3.27.f Pressure coefficient contour occurred at z = 0.45 H ~ 72 m (Plane-6) 84

Figure 3.27.g Diagram pressure coefficient at z = 0.45 H ~ 72 m (Plane-6) ............ 84

Figure 3.27.h Pressure coefficient contour occurred at z = 0.7 H ~ 112 m (Plane-7) 85

Figure 3.27.i Diagram pressure coefficient at z = 0.7 H ~ 112 m (Plane-7) ............. 85

Figure 3.28 Sketch of Multiple Cooling Tower (De5.igs of IGES file).................... 86

Figure 3.29 Domain of Multiple Cooling Tower ...................................................... 86

Figure 3.30. Grid mesh generating of imported file IGES from AutoCAD in Gambit. 87

Figure 3.31. Surface mesh on rear of multiple cooling tower ................................... 87

Figure 3.32 Brick and Cooling tower ........................................................................ 87


Figure 3.34.a Pressure coefficient contour of the whole body from the top of plan . 88


Figure 3.34.c Diagram pressure coefficient in distance position of the model to the sources. 89



Figure 3.34.f Pressure coefficient contour occurred at z = 0.45 H ~ 58.5 m (Plane-6) 91

Figure 3.34.g Diagram pressure coefficient at z = 0.45 H ~ 58.5 m (Plane-6) ......... 91

Figure 3.34.h Pressure coefficient contour occurred at z = 0.7 H ~ 91 m (Plane-7) . 92

Figure 3.34.i Diagram pressure coefficient at z = 0.7 H ~ 91 m (Plane-7) ............... 92

Figure 3.35 Sketch of Single Sphere (De3.igs of IGES file)..................................... 93

Figure 3.36 Domain of Single Sphere. ...................................................................... 93

Figure 3.37. Grid mesh generating of imported file IGES from AutoCAD in Gambit and already meshed on rear of sphere surface. ........................................................ 94



Figure 3.38. Brick and Sphere ................................................................................... 94

Figure 3.39 .The mesh developed on domain............................................................ 94


Figure 3.41.a Pressure coefficient contour of the whole body from the top of plan (Coded De31) 95



Figure 3.42 Sketch of Multiple Sphere (De4.igs of IGES file) ................................. 97

Figure 3.43 Domain of Multiple Sphere.................................................................... 97

Figure 3.44. Grid mesh generating of imported file IGES from AutoCAD in Gambit 98

Figure 3.45. Surface mesh on rear of multiple cooling tower ................................... 98

Figure 3.46. Brick and Sphere ................................................................................... 98





Figure 4.1a: 1:1000 Scale Model of Single Sphere .................................................. 101

Figure 4.1b: Sketch Model of Single Sphere............................................................. 101

Figure 4.2a: 1:1000 Scale Model of Single Sphere .................................................. 101

Figure 4.2b: Sketch Model of Multiple Sphere ........................................................ 101

Figure 4.3a: 1:1000 Scale Model of Single Cooling Tower..................................... 102

Figure 4.3b: Sketch Model of Single Cooling Tower .............................................. 102

Figure 4.4 a: 1:1000 Scale Model of Multiple Cooling Tower ................................ 102

Figure 4.4b: Sketch Model of Multiple Cooling Tower........................................... 102



Figure 4.5 Typical open-circuit wind tunnel ............................................................. 104

Figure 4.6 Scheme the open-circuit of small wind tunnel......................................... 104

Figure 4.7.a – c Photo Small Wind Tunnel ............................................................... 105

Figure 4.8. Open or closed –throat wind tunnel. ....................................................... 106

Figure 4.9. Elevation of circular dome rising directly from the ground.................... 107

Figure 4.10. Plan view: pressure coefficients for y/d = ½ (hemisphere)................... 107

Figure 4.11. Plan view: pressure coefficient for y/d = ¼ .......................................... 107

Figure 4.12. Distribution of local mean pressure coefficient around the throat of the cooling tower (ASCE, 1987) ....................................................................................... 108

Figure 4.13. Distribution of local mean pressure coefficient at different height around the hyperbolic throat of the cooling tower (ASCE, 1987).......................... 108

Figure 4.14. Distribution of root – mean square pressure coefficient around throat of a hyperbolic cooling tower (ASCE, 1987) ................................................................ 109

Figure 4.15. Guiding the angle to describe the pressure coefficient around throat combine with various of a different height measurement. .......................................... 111


Figure 2.48 Comparison of mean pressure coefficient along centreline of a smooth dome, by Letchford, cs ......................................................................................... 113



List of Tables

Table 2.1 Details of model roof materials ................................................................... 21

Table 3.1 Laminar and turbulent flow model ............................................................ 61

Table 3.2 Turbulent flow equations for compressible flows,

by Versteeg & Malalasekera...................................................................... 61

Table 4.1 Limiting values of Cpe and values CL for domes rising directly from the ground.

................................................................................................................. 108

Table 4.2 Distribution of local mean pressure coefficient around the hyperbolic Cooling

Tower ro represented the fabric structure by CFD method under Large Eddy

Simulation (LES-Smagorinsky &Lilly)................................................... 109

Table 4.3 Distribution of local mean pressure coefficient at different heights around the

Cooling Tower to represented the fabric structure by CFD method under Large

Eddy Simulation (LES-Smagorinsky & Lilly) ........................................ 110

Table 4.3.a. Distribution of local mean pressure coefficient at different heights around the

Cooling Tower to represented the fabric structure by CFD method under

Large Eddy Simulation (LES-Smagorinsky & Lilly)........................... 110

Table 4.3.b. Distribution of local mean pressure coefficient at different heights around the



Table 4.3.c. Distribution of local mean pressure coefficient at different heights around the



Table 4.4 Mean pressure coefficient around the sphere under LES simulation ........ 114



Chapter 1 Introduction

Fabric membrane structures utilize advanced technology that enables large span structure to

be built as lightweight and easily deployable. Fabric structures include tents, pressurised and air

supported, sails and inflatable that resist applied load by a combination of curvature and tension (pre-

stress) roofing system.

Fig.1.1 Tent Model

The tents models have been used with

considered perfect advanced material of a

membrane roof with predominantly tensile

forces. A historical review of suspended roofs

suggests that the tent is the earliest version of a

tension roof, (Fig. 1.1).

Fig.1.2 Membrane Roof Model

The tent structure has given inspiration to

improve model structures. Fabric membrane

structures have constructed for a large stadium,

aircraft hangar, wide roofing on entertainment

building and much more variety of purposed,

(Fig.1.2).

More recently, light fabric membrane structures combined with cable suspended roof are considered

as integral system structures. However, a more accurate assessment of load distribution also

considering extreme climate or weather condition effects is important for a complete and accurate

understanding of behaviour of the system structure.

The large surface area usually projected by a fabric membrane structure means that wind

pressure is a significant load case. It may also be could be strongly influenced by the basic

structural form of the roof. However, a problem exist is predicting the applied loading to

membrane roof structures estimates of wind loading to complex geometric form are required.

Industry provided data of CFD (Computational Fluidal Dynamic) and relatively small number of

wind tunnel test form the basis of an approach to enable wind loading to be applied appropriately.



The aim of wind tunnel test and CFD is to provide information on local wind patterns,

coefficient of wind pressure, and wind-induced structural vibration. The use of wind tunnels is to

determine the response of a structure to wind forces and to determine the pattern of wind flow to

leeward of a structure. Investigations are carried out on the eddy formation behind model

membrane structures to find the frequency and strength of oscillatory forces on the structure of a

turbulent air-stream, and on the simulation of natural boundary layer effect, (Fig.1.3).

The objective of the present research is to develop procedures for accurate and efficient

analysis, particularly to estimate wind loading on non-conventional structures and complex geometry

with criteria to the design of tent structures or cable suspended roofs. In this study testing and CFD

analysis of scale models are used to obtain a better understanding of how these structures behave

under wind loading conditions. The specific contribution of qualitative observations and quantitative

measurements of the behavior of the model could be used to supplement failure criteria in related

design procedures and serve as a basis for analytical and physical comparisons.

On CFD method, the initial design model structures were developed on AutoCAD in order to

generate the complex geometric of shape model structures desired. Mesh model structure was

exported into Gambit, which is a pre-processing CFD to assembled and associate with Fluent.

Fig.1.3 Illustration of wind acting on fabric structure

A shape of wind tunnel model was also

created on Gambit, which the model

structure generation was placed in the

middle of tunnel model. The mesh

generation resulted by Gambit will then

exported to the Fluent. The Fluent as a

solver then associated a particularly need in

which the model appropriately generated.

Using facilities available, boundary conditions can be applied in order to specify in which condition

approached. Fluent solver will process the mesh through running iteration for time period depend on

number of element generation. The result of model generation can be obtained and displayed as

contour pressure distribution or velocity distribution as well as data script, (Fig.1.4).



Fig.1.4. Example contour of pressure coefficient

Several model structures were used in this particular cases such as Sphere, Cooling Tower,

China hat model and tandem combination on each model in CFD. The same model tried to involve in

wind tunnel too. In wind tunnel model, there were used lamp shade, small ball, and bowl and fiber-

glass resin as basic material to perform the shape model of fabric membrane structure. All models

measured approximately in 150mm x 150mm each of plan area. The shape of structures model were

constructed look like dome/sphere and China hat model represented cooling tower model. All of them

were investigated under low-speed wind tunnel testing.

When the airflow approaches a building, it is impinged around and over the surface of

building. The force will create areas of pressure or suction on part of building such as facades, gables

and roof. In this study, the material building is fabric membrane structure and cable suspended so that

leads to the extraordinary buildings geometric developed. It is the significant requirement to evaluate

wind loading by CFD method or wind tunnel test. Once model structure has been examined

completely, the result can be combined to the standard method of wind loads in order to analysis a

structure related. The important result expected is local mean pressure coefficient (2

21 V

pCp

ρ= )

known as dimensionless pressure, it will then combined with the area pressure coefficient. The area

pressure coefficient is integration the local mean pressure coefficient over a surface area such as the



roof, gable, etc or part of building faced the wind and then divided by the area yields the area pressure

coefficient, which can be used conveniently for determining the wind loads on specific area of

building. The pressure coefficient being indicated by a positive Cp value and a negative value

(suction pressure). The pressure counted at any point on the surface is also a fraction of the dynamic

pressure (qs). Relationship to the building design is when value of dynamic pressure (qs) combined

with pressure coefficient whether is external or internal. Since the combination between dynamic

pressure and coefficient pressure occurred, the wind load can be obtained and then can be applied to

the building design.

Data from the computer simulation model and from wind tunnel testing or published data

were collected, tabulated, and assessed. Comparable experimental results of CFD model simulations

are discussed, conclusions are drawn, and recommendations for further research are presented.

Procedures considering is intended to develop more relevant, efficiently, and effectively in order to

know wind-loading distribution of the membrane structure presented.



Chapter 2 Literature Review

2.1 Introduction

The use of permanently installed fabric membranes structure is increasing all the time.

Typical structures constructed basically similar form to a normal building or integrated an

extraordinary with whatsoever curvature form make it, however those have roof materials sheet

replaced with fabric membranes (layer skin). This type structures under investigation, which has

combined with cable suspended roof. Both of material structures are focused as large areas of

research, using numerical and experimental methodologies. Many experimental and numerical

researches have been established regarding wind loading using wind tunnel test and numerical

methods on CFD (Computational Fluid Dynamic). However, a dearth of numerical as well as

experimental research has been performed regarding wind load on variety of shape fabric membrane

structures. Type of research can be found on pressurized arch, beam structure, and inflatable

combined fabric membrane structures, these structural types have not been research to extent of many

types of shape of structural supported membrane structure.

Examples of research conducted on variety of shape of fabric membrane structure, and cable-

suspended are presented. Consideration of various research methods and different aspect of the

structure have been balanced. The research presented here is aimed to evaluate the need for further

analysis and investigation of cable-suspended supported membrane structures.

2.2 Cable-Suspended Structures

Cable-suspended roof has been used for many years ago. The ancient style of roofing system

is tents, which are motivated to form an advance model structure of a membrane roof on the cable

suspended. The historical of tent combined with cable is a review of suspended roofs suggest that the

earliest version of tension roof. (Prem Krisnha 1978, p.1). The cable structure would be supported the

membrane that is majority resisted pressure of wind load.

The suspended roof was acting on which is the lower tension flange of the cable net and the

upper compression flange is replaces by the edge ring or by the anchoring, (Fig.2.1b). Thus, it is

consist of two cable rows that can only take two-dimensional tension so that is mean the structure will

take a small compression only when pre-stressed without any shear taken or has no shear rigidity.



Refer to these form

that the original form

of the roof could

equilibrate a given

load only with the

addition

Fig.2.1.Static behavior and various types of suspended roof

of shear, then the actual suspended

roof is forced to change its shape

into a new form that will be able to

carry the load without shear. That

is clear; the form adopted is one of

funicular surface of the load. Since

the cables are able to

Fig.2.2 various types of suspended roof.

take a compressive force; the suspended roof given a shape that it may be possible to pretension the

cables. Hyperbolic surface shown in (Fig.2.2) that has an opposite curvature in two cable directions.

Nonlinear behavior shown by cables when loaded, and there are varies of degree non-linearity

with the types of cable structure and also the loading. A cable has to follow the funicular curve in

order to sustain loads. It undergoes large geometric adjustments, particularly when the loading is

concentrated or un-symmetric. Figure2.3. shows feature

Fig.2.3 Behavior of cable system

of the behavior of a

cable, this to a

smaller or larger

degree is applicable

to cable-roof system

and poses a serious

problem in analysis.

(Prem Krisnha 1978,

p.3-5).

B A



z

x

Fig.2.4 Deflection of cable system

f

lqH

8

2

= 1.1

)(8

)( 2

mWf

lqqhH

+

∆+=+ 1.2

8

)()()(

2lqq

hWWHhfHf mm

∆+=++ 1.3

The characteristic of the behavior of the cable is that their deformation is relatively large, and affects

the system of internal forces. Horizontal component of the cable force is due to the load f to let the

cable sag, (Fig.2.4a) which can be magnitude on Eq.1.1. By increasing load ∆q, the cable elongation

has been changed, which increased the sag on cable by Wm and resulted addition horizontal force by

h, written on Eq.1.2. On an antisymmetric load qant case, the only matter has changed is its shape with

no changed by arising force of H due to q, shown on, (Fig.7b). (Szabo & Kollar, 1984, p.16-18).

There are considered a cable segment as the basic structural element in suspended roof.

Governing equations and the analysis of a freely hanging cable are important to understand, so

that a special section on it would be written in Appendix 1.

The cable is a strand or a rope made out of high-strength steel wire. The strand as well as the

rope is protected with a uniform coating of pure zinc. Cables are available in standard size along with

the appropriate fittings to facilitate cable connections with each other and also to other structural

members. The breaking strength of cables is in the region of 1380 N/mm2 and the modulus of

elasticity is of the order of 138 to 166 kN/mm2. (Prem Krisnha 1978, p.18-19).

In cable suspended roofs, the system of cables carries the roof load directly and as such

has a primary structural function. The cable system also serves a false work for erection of

cladding. The need for large-span roofs is quit often governed by functional and aesthetic

requirement, rather than by economic or structural consideration.

For the general design considerations that the problem encountered that suspended roof would

be considered cause of the significantly in the design and construction of long span roofs, such as the

need for a more accurate assessment of load distribution. Related to the suspension cable, there are



also have a problem of the provision of adequate static stiffness, avoiding the occurrence of flutter;

anchorage and pre-tensioning of cables and the design of the supporting structure and etc., which

assumed special importance for suspended roof. Site condition could be strong influence on basic

structural form of the roof. If site condition doesn’t permit build individually, a large span suspended

roof can be profitably planned between two buildings of adequate strength, which will serve as

anchor for the cable.

The material cable roof suspended structure can be broadly subdivided into two-the

supporting structure and the roof cladding. The supporting structure may be constructed of plain,

reinforced, or pre-stressed concrete, steel, or a combination of the two. The final choice will be

governed by aesthetic and structural considerations and economics. The cladding can be further

subdivided into: (1) cables and their connections, (2) auxiliary framework that supports the

decking and is placed over the cables, (3) roofing which is the external waterproofing skin, and

(4) the insulating layer.

The durability of cable can only be defined by design life expectation of the structure, which

the materials are designed for permanent and temporary use. Application material cable supported

roof was not involved in the specification of building codes so that is much more needing concern on

fire protection due to the fire causes creep to the cable. Cable roof are generally classified as flexible

material structures because the restriction of allowable deflection on these system doesn’t it same to

the conventional of beam and slab structure. The necessary considerations of cable structures are

deflection on the system and the limited slopes occurred. (Prem Krisnha, 1978, p.22-23). Many

experimental and numerical researches have been done in order to manage the wind acting.

The wind load acting to the light and widen the roof surface structures dominantly, which is

measured per unit area of horizontal projection. The loading intensity can be specified in between two

hanging cables and two bracing cable. The cables are anchored in boundary structures that may

consist of column or anchored in arches. Simplified system is the cable net was composed of a system

of simple tension members and the joint in the net are frictionless hinges. (See fig.2.1-2.2). However,

the consideration static loading, temperature changes and support movements are enclosed, which the

distributed load (Mollmann, 1974, p. 162-163). The load distribution would be supported in any

direction by the suspended cable.



The cables structures are able to take a compression force in term of pre-stresses state the

suspended roof has given a shape that it would be possible to pre-tension the cable. That is way the

roof and the net should form a hyperbolic surface. The dynamic effect of the wind load action on

suspended roof partly causes a tendency for the entire structure to vibrate and partially way give rise

to local “flutter”. (Szabo & Kollar, 1984, p. 14). The cable specification would be more interesting to

be defined in all aspect structures term with the reliability proved as primarily structures. Response

structures of cable can be defined from the potential strength in tensile.

The basic of the cable behavior is that the changing their shape without elongation

according to the balance the antisymmetric load with unchanged the cable force. Since that

happened, the load distribution affected the cable defection that mostly due to the wind load.

(Szabo & Kollar, 1984. p.30-31). In the case of antisymmetric load it is a significant change of

the cable shape. It can be shown in figure 2.5.a.b, which is the change of the row of cables in one

direction and the other case is that, the row of cables

Fig.2.5 Wind pressure distribution

Fig.2.6 Antisymmetric wind load effect

Fig.2.7. Circular plan referencing cable system. Note: fig. 2.5-2.7 by Szabo, cs.

Tan α = 2.

α = 63025’

Sin α = 0.89.

changed in both directions, shows in

fig. 2.5c. That is convenient taken as

a basis those cable which intersect

each other at their quarter points.

Figure 2.7 indicated the ratios of a

circular ground plan. The affinity to

the elliptic ground plan figure 2.5

and 2.6, so that the same ratio can

be retained.



The proportions of the loads (qx and qy) taken by the cables, including deflection wx and wy of the

two perpendicular cables at their point of intersection (figure 2.6a). The two divisions load and

the deflection of the two cables at the point intersection can be written into:

qqq yx =+ 1.4

x

x

xn

lxq

w8

2

89.02

= 1.5

y

y

yn

lyq

w8

2

89.02

= 1.6

Explanation of figure 2.6b is somewhat more complicated due to only the y-direction cable is

able to change its shape without elongation. Eq. 1.6 gives the deflection of the y-direction cable

at the quarter point. On the other hand, the deflection of the x-directional cable can be determined

by approximation of the static cable behavior:

1

2

16

3

AEf

lhwk = 1.7

f

lqh

8

2∆= 1.8

At its quarter point, ¾ of the greatest deflection occurs

x

qxxEAfx

lxqw

)()79.0(

)89.0(

128

3

4

3

1

4

= 1.9

x

qxxEAfx

lxqw

)(512

9

1

4

= 1.10

(J Szabo & L. Kollar, 1984. p.31-47)

In order to gain design load of the fabric structure, that is very dominantly factor of wind load

involved so that is needed to investigate wind behavior on the fabric structure shape in some

cases.

This kind of building type has been researched (e.g. Irwin & Wardlaw 1973; Marcelo Rocha,

Sandro Cabral & Jorge Riena, 2000; Yasni, Marukawa, Katagiri, Katsumira, Tamura & Watanabe,

1999). Attempt to understand the structural characteristics have been undertaken with numerical and



experimental approaching methods. This research would be conducted to the appropriate design

methodology research.

Irwin and Wardlaw, 1973 performed wind tunnel test on retractable fabric roof for the

Montreal Olympic Stadium in Canada, (Fig.2.8). The physical structure has a cable-supported

membrane that is attached to a rigid structure. The potential roles on it have physical quantities of

cable-supported membrane roof behavior under wind action in the following measurement:

MF (mass of roof fabric per unit area),

Mc (mass of cable per unit length),

ρ ( density of air),

b (typical length of roof),

KT (slope of tension versus strain curve for warp or weft direction),

Ks (slope of shear loading versus shear strain curve for warp or weft direction),

U (mean wind speed),

µ (viscosity of air),

E (Young’s modulus),

A (areas of roof),

D (aerodynamic drag cable per unit length),

g (gravitational acceleration),

∆p (excess of internal over external pressure in zero wind),

ζ (damping ration in vacou),

VI (internal volume covered by roof),

γ (ratio of specific heats for air),

PI (absolute internal pressure).

An appropriate

set drawn are:

µ

ρUb,

bg

U2

,

b

M F

ρ,

bU

KT

2ρ,

T

s

K

K,

2b

MC

ρ,

22bU

EAC

ρ,

bU

D2ρ

,

ζ , 2U

p

ρ

∆, γ ,

I

I

VU

bP2

3

ρ,

2U

PI

ρ

γ

They have got internal pressure (pi) and the mean force coefficient as function of wind speed that is

changed the deflection of the roof altering mean pressure distribution, (Fig.2.9 & 2.10) The

experimental method also resulted the non-dimensional parameter (∆p/ρU2) described the relationship

of an excess of internal pressure, density of air, and mean wind speed function.



Fig. 2.8. Stadium Detail by Irwin cs & Inc. fig.2.9-10

From the conclusion drawn, added

mass effect is significant and may in

some case dominant for lightweight

membrane. Fabric membranes are

sensitive to wind tunnel noise and

thorough knowledge of the acoustic

environment in wind tunnel is

essential in interpreting the data. On

present roof, the deflections due to

wind were significant.

Fig. 2.9. Mean force coefficient

Fig. 2.10. Mean deflection at φ=900

From the experimental above can be described that is significant influence of wind pressure

distribution to the fabric membrane and the cable, which resulted the significant deflection also

vibration measurement.

Yasri, Marukawa, Katagiri, Katsumura, Tamura, and Watanabe (1999), was also performed

wind tunnel testing on cable suspended roof of long span structures in Japan. Since the dead load of a

long-span structure’s roof is relatively small, it is important to estimate wind-induced response to

structure. They built two different models that are catenary’s-shape as a sag roof and wave-shape as a

rise roof supported by cable, which the structures are combination between the cable and truss beam.



Fig.2.11. Structure Layout

This the experiment method

considered, they developed the

distribution of the mean wind

pressure coefficient and fluctuating

wind pressure coefficient. They

utilized the Monte Carlo simulation

for producing wind pressure

simultaneously at multiple points.

Fig.2.12. Wind Pressure Distribution, by Yasui, cs included Fig.2.11

Fluctuating wind pressure over the roof surface described of pi (t), (i=1,2, m) was a stationary

Gaussian process with a cross spectrum density function Sij (ω), (i, j =1, 2, m) and mean value is 0.

The fluctuating wind pressure can be estimated from:

1),...,,2,1;...,,2,1(2

exp1 1

0

−===

= ∑

−

=

jNnmiN

knjX

Np

N

k

ik

d

in

π 1.11

where k is indicated the frequency and d is indicated an estimate value. Xk is an element of the

complex vector defined by

kkk Ht

NX ζ

∆=

2 1.12



∆=

mk

ik

k

k

mmkmikkmkm

iikkiki

kk

k

mk

ik

k

k

HHHH

HHH

HH

H

t

N

X

X

X

X

ζ

ζ

ζ

ζ

.

.

.

.

.

.

......

....

....

....

...

...

...

...

2

.

.

.

.

.

.

2

1

21

21

2221

11

2

1

Hk is obtained by the LLT decomposing the cross spectrum density:

S(ωk) = Η(ωk) Η∗Τ(ωk) 1.13

×

=

∗

∗∗

∗∗∗

)(0

.

.

.

)(...)(

)(...)()(

)(...)()(

...

...

...

)()(

0)(

1

12111

21

2221

11

kH

kHkH

kHkHkH

kHkHkH

kHkH

kH

mm

m

m

mmmm ω

ωω

ωωω

ωωω

ωω

ω

αα

where ζ ik is the complex number defined by ζ ik = ζ ik + jη ik.

Here ζ ik and jη ik are mutually independent Gaussian probability variables. Using random variables

below:

E[ζ ik] = E[jη ik] = 0,

E[ζ2 ik] = E[jη2

ik] = 0.5.

The wind pressure ζ ik was obtained in terms of complex Fourier coefficient Xik , determined from

iik

i

j

jkijkik

ik H

HX

−

=∑

−

=

1

1

ζ

ζ 1.14

They were drawn conclusion that the high sporadic negative pressure obtained in the wind tunnel

test to observe the wind pressure at the edge of the roof. The power spectrum of the fluctuating

wind pressure obtained from the simulation is in good agreement with the experimental done.

From the experimental above can be described that is significant vertical displacement occur effected

by wind load to the structure as well as resulted wind pressure distribution.

Marcelo Rocha, Sandro Cabral, and Jorge Riera (2000) performed experimental research on

wind tunnel testing as well as numerical methods, which is used Proper Orthogonal Decomposition

(POD) method and Monte Carlo simulation of the tenstar cable roof structure of the La Plata Stadium,



in La Plata, Argentina. In addition, the impressive of shape roof model presented to cover the

stadium, which is divided into two alternatives

(A)

model solution of

complete and partial

cover of the field.

(B)

Fig. 2.13. La-Plata Stadium by Rocha cs, & included fig.2.14-15

From the experiment

conducted, they

evaluated the mean wind

pressure fluctuation, and

standards deviations of

the pressure field.

The POD method explained vector of wind pressure time series measured in n given point of a

surface as p (t) = [p1 (t), p2 (t), pn (t)] and associated by µp = [µp, µp, µp]. Second statistical moments

of wind pressures in the form of a covariance matrix:

Cp = Sp Rp SpT, 1.17

Where

=

=

1...

....

....

....

...1

...1

,

...00

...

...

...

0

0

21

221

112

2

1

nn

n

n

n

RpSp

ρρ

ρρ

ρρ

σ

σ

σ

are the diagonal matrix of wind pressure standard deviations and the symmetric matrix of correlation

coefficient, respectively. Aware from the correlation coefficients, to define a zero time gap, that is,



Cp,ij=ρijσi σj = E {[pi (t) - µI][pj (t) - µj]} = E {pi (t) pj (t)} - µi µj 1.18

The correlation coefficient matrix can be subjected as Orthogonal Decomposition, which is

accomplished by solving eigenvalue-eigenvector:

Rpzj = λj zj 1.19

Where the n solutions (λj zj), j =1, 2, n. used to assemble the matrices

=

=Λ

nnnn

n

n

nzzz

zz

zzz

Zpp

...

....

....

....

...

...

,

...00

...

...

...

0

0

21

22221

11211

2

1

ρ

λ

λ

λ

Λp is diagonal matrix of the square roots of the eigenvalues; λj and Zp are the corresponding

orthonormal eigenvector, zj. Reconstitute of the correlation matrix as

Rp = (Zp Λp) (Zp Λp)T 1.20

The optional covariance matrix as

Cp = (Sp Zp Λp) (Sp Zp Λp)T 1.21

On the other hand, general derived equation of Monte Carlo simulation was also presented in this

research, which is similar to the previous research above. They drawn discussion by mean of

theoretical and practical example, which was depend on whether a global or a local structural

response to wind pressure loads required. The POD method presents a fast convergence rate for

global response, while for local response the effective correlation length of the pressure process

taken into consideration on Computational Dynamic Fluid (CFD).

Fig.2.15 Standard Deviation of wind pressure,



Fig. 2.14. Mean wind pressure, α=1800 α=180

0

Ando, Ishii, Suzuki, Masuda, Saito, (1999), was also performed wind tunnel test on

construction of a double membrane air supported structure, which are consisted of cable suspended,

membranes roof and few steel part. Since lightweight of long span structures can be built in Japan

(1997), it is important to estimate wind-induced response to structure. They built a 1/500 scale model

to validate the design of “Ukigumo Dome”, which resembles a floating cloud. The main roof of the

dome is a cable reinforced double layer air-inflated as hybrid double-membrane air supported

structure (fig.2.16). They were conducted wind tunnel test with velocity pressure setting at q=

301.8kgf/m2, which is designed load of return period of 500 years in Kumamoto. From the scale

model, they obtained wind pressure coefficient around the roof, (fig.2.17). The coefficients of the

windward, leeward and central sides are determined to be –1.1, +0.15 and –0.4, respectively.

Fig. 2. 16 Hybrid double-layer system by Ando,cs

Fig. 2.17. Wind pressure coefficient Distribution.

They were concluded that is the first building was constructed the movement roof with double

membrane air-supported structure. It is obvious that wind loading was very important influence to the

membrane structure since large area surface of roof exist and historical record of relatively high-

speed wind occurred.

Due to the cable-suspended structure is flexible, it is highly important to understand the

response to wind loading for this research. Any prediction about behavior of cable suspended roof

combined with membrane structure can be involved so that should be studied, in order to recognize

the distribution pressure of passing wind on these structures.

2.3 Fabric membrane Structures



For many years fabric membrane structures has been used for a main component building

structure. The roofing system would perhaps have used animal skin to form tents, which are

considered perfect example of an advance structure of a membrane roof with dominantly tensile

force. In between the tension members would have membrane attached or stretched over the

boundary surface fitted. (Prem Krisnha 1978, p.1). The earlier structures (tents) built is not yet have

improvement. It is because of the impermanent nature. The technology developed the fabric

membrane and new material involved so that they have begun to be perceived as architecture and

engineering structure.

Sophisticated construction technique and complexity of requirement would be introduced as

modern tensile membrane engineering system of portable as well as permanent building at the present

day. “Perhaps the most high-profile building to be erected in UK this century is the Millennium

Experience Dome,” which are using material cable, fabric membrane and several steel erections. The

dome is an understatement of 320 meters in diameter, over 100 meters to the top of the mast, and

more than 1000 meters around its circumference is using PTFE-coated fabric and galvanized cable.

Fig.2.18. Millennium Dome by Kronenburg, (A)

(B)

The form of spherical tensioned fabric cap was taken by the enclosure. Tensioned steel cables

arranged radially on the surface of structure is supported the skin-membrane, supported and braced

from the columns by hanging and tie-down cables at 2 meter interval. (Kronenburg, 2000, p.13-14).

Portable architecture using membrane structures are rose that is not only due to increased

performance and longer lifetime but also because the adaptation of computer-aided design as well as

computer program package to support the design structure.

However, for the simple point, these structures are still designed to resist the basic loading

criteria as conventional building. The original dead load of these structure relatively small, however



the imposed live load and wind pressure much more significant to influence the structural design.

Wind pressure would be relatively difficult to generate on the building, which has complex

geometries. The shape of structure basically governed by the physical principles that are begins with

produced a stable structures with the membrane surface should have double curvature and defined

mathematically as a hyperbolic paraboloid. The geometry of the membrane is established through a

shape generation technique to ensure static equilibrium of the system. (Birdair Technical Info, 2001).

The relationship between basic loading system and generated geometry of membrane roof should be

involved in order to collect data loading on design structure.

The advantage and appeal of fabric structures are because the lightweight efficiency in long

span application and not easily constructed. The typical materials involved are PTFE (Teflon)-coated

fiberglass, silicone coated fiberglass and vinyl-coated polyester that are inherently waterproof and

require little maintenance. PTFE is chemically inert, resistant to moisture and microorganisms and

has low deterioration. There is no bending and shear stiffness of cable combined with membrane

occurred due to they rely on their form and internal pre-stress alone to perform the same function.

Since they depend only on internal tensile forces, there are relatively simple equation would be under

laid. (Shaeffer, 1996, ix).

“Designer often attracted to fabric structure are intrigued with the wide range of forms which

ca be built. Although the range of possible forms is extensive these are not ‘free-form’ structure.”

Conforming to the physical principals must be governed is because behavior as limited characteristic

of the material form. In tensile behavior, combining or weaving numerous linier tension components

generally makes membranes. That is mostly using cable suspended with the membranes structurally

and visually acts as tension surface. (Shaeffer, 1996, p.5.1-5.4).



Fig. 2.19 Membrane in tension by Shaeffer

Planar axial forces of membrane surface usually

resist loads. Applying a pressure load at any

point will tent to increase the tension in one

direction and decrease it in the opposite. This

will force the surface to deform until the axial

force of the surface balance the applied load.

Suction load will increase the membrane

tension in other direction. (Figure 2.19)

Every point on a stable tension surface should be satisfied the axial equilibrium of:

∑ =0Fx ,∑ =0Fy and∑ =0Fz

Fig. 2.20 Hyperbolic surface of membrane

Cone-like or hyperboloid surface are

generated when a membrane is stretched

between two vertically displaced

concentric boundaries. The similar size

and shape to the cooling tower form, or

may be significantly different must

supported tent forms to develop in order

to associate to the membrane structure.

Simple physical model can be seen in figure 2.20, which the range of viable forms and proportions is

significantly increased by the use of radial cable. Principle curvature generally follows meridional

lines and an opposite sense of curvature was set as perpendicular to the meridional lines.

The lightweight structure had been studied by Frei Otto (1967) that was mainly researched on

model studies of shape of air-supported structures. There are wires tied over the membrane represent

cable or net. The result of experimental research method is estimation of membrane stress that can be

made on measuring the principle radii of curvature. Tension support can be introduced in the form of

grid to reduce the radii of curvature of the membrane.

The fabric membrane structure as much like a thin sheet that is light and has flexible nature.

The wind load is dominantly affected to the whole of applying load on the structure so that is



necessary to gain the wind pressure acting to the structure. Kazakevitch, (1998) was performed the

requirement of experimental investigation in the wind tunnel of wind load on the membrane roof.

Fig. 2.21

The hangar structural scheme by Kazakevitch. Fig. 2.22 Pressure distribution on the membrane roofing

surface (a) the stage of erection, β=0; ε=0.5%- on upper surface, 2-the net values on the upper and lower surfaces;(b), (c) The completed stage (on the upper surface); 3,4 in section a;

3-β=900, ε=0.5%; 4-β=90

0 , ε=8%,etc.e by

Kazakevitch

The cylindrical membrane roof model at Riga Airport in Latvia determinate the wind pressure

distribution and wind flow visualization over the roof surface in wind tunnel testing. Method to

determine characteristic of natural dynamic of membrane system was described base on the complete

Vlascov equations. The roof for hangar developed in the form of a cylindrical membrane roof of 108

m span and 60 m wide. (see fig. 2.21)

The roof model was created on scale 1:250 and intended to determine wind pressure distribution

along the upper and lower surface. The integral aerodynamic coefficients were calculated by means

the integration over the appropriate surface:

∫ ∑ ∆===−

σ

σσ ii

i

xnpS

dxnpqSqS

XC ),(cos

1),(cos

11 1.22



By analogy

∑ ∆=−

i

iii ynpS

C σ),(cos1

1.23

∑ ∆=−

i

iii znpS

C σ),(cos1

1.24

where S is the area of the horizontal projection of the model roofing surface. It was measured of pi

as the pressure mean aerodynamic coefficient at any point I, pi’ = pi/q defined as the net pressure,

and the dynamic wind pressure; q=ρV/2,ρ the air flow density, V the velocity of the undisturbed

flow, ∆σI the area of the element around point I, and ni the normal to the surface at point i. The result

of the experimental was obtained on the wind pressure distribution along the upper and lower roofing

surface. (see figure 2.22)

Wind tunnel tests have proven useful to achieve design relevancy. Many kinds of membrane

structures were also investigated to collect the relevant data. Irwin and Wardlaw, 1976 performed the

experiment using fabric membrane of 1420 denier Kevlar 49 and 100 denier Kevlar 29 in wind tunnel

testing that defined the independent of the elastic properties to the membrane (see figure 2.8-2.10).

The Montreal Stadium was completed in 1987 using a polyurethane and PVC-coated Kevlar fabric.

The details of full scale and model roof materials can be summarized in table below.

Table. 2.1 Full Scale Model

Fabric 1420 denier Kevlar 49 closely

woven

100 denier Kevlar 29 woven as an open net

Airtight Coating PVC on both side High density polyethylene sheet on

underside

Mass Kevlar 1.1 kg/m2, Coating 1.1

kg/m2

Total 2.2 kg/m2

Kevlar 0.009 kg/m2, Coating 0.006 kg/m

2

Adhesive 0.005 kg/m2, Total 0.02 kg/m2

Approximate KT

Approximate KS/KT

16 MN/m

6.2 x 10-4

0.14 MN/m

20 x 10-4

The result of experiment affected the natural frequency, and deflections under static load. The

evidence released that the behavior of tensioned membrane in wind not sensitive to their elastic

properties and very little strain of the membrane deflection. In addition, added mass is very



significant effect on the lightweight membrane and very sensitive to the effect of acoustic

environment.

Wind tunnel testing completed by Ando, Ishii, Suzuki, Masuda, Saito, (1999) on a double

membrane air supported structure. The structural system involved is “Park Dome Kumamoto” which

is the main roof of the dome is a cable reinforced double layer air-inflated membrane. The double

membrane air supported structure is 107 m with conical trapezoide steel ring frame at the center

maintains the thickness and shape of the air-supported structure. The 48 cables run radially at the

upper and the lower regions between the ring frame and the exterior ring truss. The upper and lower

rings have diameters of 10.6 m and 36.6m, respectively, and the ring frame is 14 m high.

Fig. 2.23 Structural section, Park Dome Kumamoto (1999)

The membrane is PTFE

coated glass fiber fabric

covered those structure. The

result of the experimental

research on wind loading is

distribution of wind pressure

coefficient which they set the

velocity pressure at q = 301.8

kgf/m2.

The wind pressure coefficient of the roof is collected. (See figure 2.16-2.17, page 13). To gain a

better understanding of the behavior of these types of structure so that need more wind tunnel testing

should be advocated. This kind structures was the first building with double-membrane air-supported

structure, which is the original system applied as lightweight and built as a long span structure. That

is mean large areas membrane surface roof will invoked by mostly wind loading that is need more

investigation on every time want to build new structure. Thus, it will led the further study on wind

load induced on membrane structures by such as procedure of experimental or numerical methods.



2.4 Computational Fluid dynamic (CFD) for Wind Loading

Campbell (2000) on in

his paper provided an overview

of the utilization of computing

in the design and construction

of tensile membrane structure.

This paper pursued general

methodology in the design and

construction of tensile

membrane structure is

illustrated in figure 2.21. It can

be described from flow chart

that is wind loading became

highly order demand to the

analysis design structure, so

that will be regarded in all

process design.

Boundary & Support Definition

SHAPE(Form Finding)

SHAPEArchitectureEvaluation

PrestressEvaluation

STRUCTURAL

Evaluation

Support StructureModel

SizeInitial Element

ANALYSIS

PresstresShape

ElementSize

Pattern BoundaryDefinition

(Pattern Surface)SHAPE

(Cutting Templates)PATTERN

Joint DesignDetailing

(Element Size)DESIGNErection/Stressing

Sequence Difinition

Analysis

Typically Non-

automated

Process Process

automated

Typically

Fig. 2.24. General Approach Design Tensile Membrane Structure by

Campbell (2000)

A part from general approach design flowchart is may be prescribed boundary pre-stress to patterning

of shape of structure generation. It is belief that would be easier to generate a shape module due to the

ability of the digital computer as well as to analyze the system structure. It is highly recommended to

pursue CFD method become a part of approaching design to predict wind loading to the structure, it is

because the wind load basically very significant would applied mostly to those kind of structures. It is

connected closely to the geometry modeling in CFD code with kinds of the design structures to

develop related to fabric membrane.

For the first time, CFD introduced in aircraft industry and on aerodynamic industry related. In

ship design, CFD methods were mainly focused to integrate the geometry and analysis of ship. CFD

methods to be used in close combination with wind tunnel testing by Voogt (1990) to investigate



during development phase of Fokker 50 &100 project Aircraft prototype and to analyze candidate

shapes of airplane. The basis of CFD analysis can reduce significantly the number of wind tunnel

model test. Furthermore, the analysis of flow in a free flight environment cannot be obtained on wind

tunnel analysis. However, the combination of both methods is essential to reduce design cycle times

and the potential development risk. Any attempts to gain a better understanding of critical flow

phenomena using CFD methods may be extended predict wind behavior to fabric membrane

structures. “The aerodynamic design process is aimed to get a number of aerodynamic requirements

under certain geometric constraints. In the computational cycle a configuration is optimized for a set

of selected parameters at the design condition”. Results of the computational can be visualized on

graphic terminals, figure 2.25. In order to running the program, there are closely connected with CFD

is geometry modeling. CFD has been a vital element in the design of the Fokker 100 wing, which one

of example visual post-processing illustrated a changing isobar pattern on a wing. The relevant result

of research to this study is indication of pressures computed as illustrated in figure 2.26.

Fig. 2.25 Visual Post-processing, Voogt (1990)

Fig. 2.26 Stubwing and pressure measurement Voogt

(1990)

Prediction of wind effect on building surface was conducted by Mikkelsen and Livesey

(1995) with concern on comparison of computed result to wind tunnel test and full-scale

measurements. The research conducted evaluation on numerical K-ε model Kamaleon II, to predict

wind pressure on structure surface. The 3D domain of 0.6x0.6x0.6 m3 corresponded to cube of

0.05x0.05x0.05 m3 was generated on computer program. The pressure distribution was calculated on



different wind angle approached of 00, 50, 150, 250, 350, & 450, and one sample pressure coefficient

presented in figure 2.28

2

21

oU

PoPCp

ρ

−= 1.25

where Cp = pressure coefficient, P=local pressure, Po=reference pressure, ρ=air density and

Uo=free-stream velocity.

Fig. 2.27 calculation grid in a close vicinity of the cube, Mikkelsen &

Livesey (1995)

Fig.2.28 Cp value shown as isobar for an angle of 0

0

Mikkelsen & Livesey (1995)

The calculation was a steady-state, which the isothermal flow condition consisting of 45 x 39 x27

cells (see figure 2.27). The density was higher in the vicinity of the house and a particular cell

matched each pressure tap location in the full-scale model test. One example pressure distribution can

be seen in figure 2.28.

Fig. 2.29 Comparison between full-scale, model scale and numerically predicted Cp for h/z0= 180

Comparison between full-scale and

numerically prediction can be

described in figure 2.29. The pressure

distribution Cp result indicated

closely match with the wind tunnel

test and either numerical prediction of

pressure distribution as well as the

drag coefficient indicated slightly

higher value than those by wind

tunnel experimental.



It is significant to pursue the literature of CFD in order to understand of how the data obtained

in the way of correlation to the real world condition. The attempt to qualify of wind-induced pressure

on building, place in extraordinary geometry is crucial so that need to under take suitable model

approach. One example research presented the global force acting on an obstacle to define the flow

field at the symmetry plane by Lakehal (1998).

Fig. 2.30 The computational grid in close vicinity of the obstacle, Lakehal (1998)

Fig. 2.31 pressure coefficient distribution at the sysmetry plane, Lakehal (1998)

He admitted research on the Kupka building with reduced in model scaled of 1:200 with a sharp

round-walled geometry provided by 1/10 building height. It can be seen in figure 2.30, the developed

mesh generation of the Kupka building model and one of example result of coefficient pressure

distribution can be seen in figure 2.31. Generating CFD codes on the model structure is used base on

Reynolds-average Navier-Stokes (RANS) equations and large-eddy simulation (LES). In this

research, the modeling app

roach based on solving RANS equations, using standard version of k-ε turbulence model adapted for

airflow simulation. The three dimensional steady-state flows are described by the Navier-Stoke

equations, which express mass and momentum conservation. Reynolds averaging procedure and the

eddy-viscosity concept, which obtained a system equation expressed nonorthogonal co-ordinate

system ),,( χηξξ =i

3,2,1,0 ==∂

∂m

U

m

m

ξ 1.26

( )

∂

∂Γ+

∂

∂−=

∂

∂Γ−

∂

∂ m

k

j

i

j

k

m

m

im

j

i

iim

m

U

J

pU

JUU ββ

ξξ

ββ

ξξ

ξξξ 11

127



where U is the contravariant velocity expressed in term of the covariant components ξU by

Um= ξβ j

i

jU and i

jβ the cofactor of i

p

j

ξξ

∂∂

in the Jacobian (J) of the transformation p

ii ξξ ⇒ , which

reads

,3,2,1, =

∂

∂

∂

∂

∂

∂

= mJ

p

m

p

m

p

m

χ

ξ

η

ξ

ξ

ξ

1.28

p=p/ρ + 2/3k represents the increased pressure (p=pressure, ρ= fluid density and k = turbulent kinetic

energy), and tvv+=Γ the effective viscosity (laminar + turbulent). The eddy-viscosity is determined

according to the algebraic expression ε

µ2

kCvt = which involves the turbulent scalars (k) and its rate

of dissipation (ε). In k-ε model, the turbulent quantities k and ε are obtained from transport equations

and describing mean flow

)(1 −+ −=

∂

∂Γ−

∂

∂φφφ β

ξ

φφ

ξSSJ

JU m

j

j

m

m

, m=1,2,3 1.29

φ stands for either k or ε, where the net source/ink part are given. For k and ε equations by (G-ε) and

(C1G –C2ε)ε/k, the diffusion coefficients Γφ by Γ/σφ. G represents the rate of production of turbulent

kinetic energy resulting from the interaction of the turbulent motions and mean flow.

∂

∂+

∂

∂

∂

∂= n

i

n

jn

j

n

in

j

n

iUUU

J

vG β

ξβ

ξβ

ξ

ξξξ

2

1 , m=1, 2, 3 1.30

The empirical constants are assigned the standard values, so that Cµ=0.09; C1=1.44; C2=1.92;

σk=1; and σε=1.3. Those are the basic formulation of Navier-Stokes applied to the model

turbulent in CFD. Numerically prediction pressure distribution using CFD indicated fairly well

performance pressure coefficient or non-dimensional data respected to the inflow wind profile. The

result of research is pressure coefficient distribution (Cp= (p-po)/1/2ρUB2 , where po = reference

pressure) on windward and leeward side of model which was compared between computational

method and the experimental result, (see fig. 2.32) and also the example of pressure coefficient

distribution can be seen in figure 2.31.



In their conclusion, the RANS equations predicted airflow features and induced loads on a three-

dimensional building-like model with complex boundaries. In the light of different results, the

numerical procedure can be used to simulate realistically pressure-induced effect of a turbulent flow

over a building. So that means, in this study, the behavior of wind load acting on the fabric membrane

structure hopefully could be predicted. The promising aspect of CFD procedure to further

investigation on wind behavior can be adapted.

In order to achieve successful application on model used the CFD, it needed concerning on

mesh and turbulence modeling. Regarding to the assessment, Kim and Boysan (1999), performed

turbulence modeling, which is determined the fidelity of computational on the environmental

application. Using CFD software FLUENT, they employing structured mesh for complex geometries

that is often made a very difficult of adequate mesh structure applied. However, unstructured meshes

have been generated over the typical building group using commercial preprocessors. The turbulence

models to be discussed based on Reynolds-averaged Navier-Stokes (RANS) equation and large eddy

simulation (LES) in lieu of increasingly important role it plays.



Fig. 2.33 Unstructured hexahedral meshes around typical building configuration, Kim & Boysan (1999)

The issue of turbulence modeling of

computational simulation for environment

application presented, which was applied

environmental flow such as atmospheric

boundary layer to a smooth terrain and bluff

bodies. They tried to explore the principle

the needed of mean wind speed data and

atmospheric turbulence data to accumulate

accurately of presented atmospheric wind

and its effects on building and structure.

The complex model environmental such as topography around building, the flows of 3D, and the

flows encountered in urban areas have tried to resolve. (Fig.2.33) Using the commercial CFD

software FLUENT resulted prediction pressure and skin-friction distributions as ell as the periodic

vortex shedding in turbulence flow over a square cylinder which was compared with the k-ε

turbulence model on surface-mounted cube.

Fig. 2.34 Flow over the curved two-dimensional hill- predictions using four different turbulence models, bottom left: pressure distribution and

bottom right; skin-friction distribution. Kim & Boysan (1999)

The numerical approach

predicted pressure

distribution on surface

structures, prediction of

flow over the curve,

production of turbulent

kinetic energy and to

predict periodic of vortex

shedding in turbulent

flow.

They also defined that is significant improve the accuracy of numerical solutions for turbulent flows

and the CFD demonstrated potential economical solver proposed for turbulent models. In their

conclusion, the major issue that determine successful application of CFD to building aerodynamics

that the unstructured mesh has a great potential to significantly save time and effort for mesh



generation. Large eddy simulation will play an increasingly more important role, especially in dealing

with turbulence modeling issue. In this study case, LES would be delighted to try in generating

unstructured mesh on membrane structure model. It is due to the LES shown more significantly

improve the accuracy of numerical solution for turbulent flows.

Muakami, (1997&1998) conducted research on CFD method, which the new trends in

turbulence models for Computational Wind Engineering (CWE) is presented. Since CWE is known as

a difficult problem to analyze of the flow around bluff body by CFD, he admitted research on current

status and future trends in computational wind engineering with some reviewing another research to

be compared and an overview of turbulence model applied in CWE-1997. One example from several

research is the basic shape of the rectangular cylinder or bluff body that used model rectangular

cylinder with D/B and H/D (B: breadth, H: height and D: depth). He performed research that belief

about analysis of bluff body flows by LES (Large Eddy Simulation) can predicted the flow around it

much more accurately than the k-ε model does. It can be seen in figure 2.36. In this term, a very

confident appreciation given, which is decided the LES method shows the best reproduction of

experimental data, next is the RSM (Reynolds Stress Model), and the k-ε model gives the poorest

result. “In the recent LES computations the conventional Smagorinsky SGS (subgrid scale) model has

replaced by the dynamic SGS model. The development of the dynamic SGS model is one of the most

significant improved in the world of CFD. The appearance of dynamic LES makes it possible to

predict the velocity and pressure field around a bluff body with higher accuracy.

Fig. 2.35 Distribution of pressure coefficient (Cp) on 1:1:0.5 building of conical vortex at the roof corner

predicted by revised model k-ε ( k-ε−φ model by Kawamoto, 1995

Fig. 2.36 Conical vortex at the roof corner predicted by LES, by Murakami, 1997.



The new trends in LES were the improvement of a dynamic SGS model that was proposed recently

by Germano with paper “A dynamic subgrid scale eddy viscosity model. 1991” and revised by Lilly

“A proposed modification of the Gerrmano subgrid-scale closure method” 1992. These analytical

models considered under realistic condition that the CFD estimation could gain sufficient result on

wind-interaction problems. The standard Smagorinsky model (S model) has been widely used in the

computation of LES. A simple eddy-viscosity type assumption is used for modeling the SGS stress:

SGS stress __

jijiij UUUU −=τ , 1.30

Eddy-viscosity model in S model: ijSGSkkijij Sv231 −=− τδτ 1.31

25.01.0:)( 2 −∆= SSSGS CSCv , 1.32

∂

∂+

∂

∂=

i

j

j

iij

x

u

x

uS

2

1, 1.33

21)2( ijij SSS = 1.34

In the standard dynamic SGS model based on the s model (DS), C (=CS2) is determined. The

empirical model function fµ is required for damping vSGS in the area near the wall.

SfCv SSGS

2)( µ∆= 1.35

)25/exp(1+

−−= nxf µ 1.36

The dynamic mixed model (DM) 2was proposed by Zang, 1993 and Vreman, 1994 as a linear

combination of the DS model and the scale-similarity model revision . The basic DM model

equations are shown in Eqs.1. 32 and 1.33

kkijijij

elsimilarityscale

kkijij

ModelySmagorinsk

ijSGSkkijij BBSSCBBSv δδτδτ312

mod

31

31 22 −+∆−=−+−=−

−

1.37

jijiij uuuuB −= 1.38

In order to determine coefficient C in LES, the model of SGS stress τij and procedure for determining

coefficient C can be seen below.

∂

∂+

∂

∂+−

∂

∂+

∂

∂−=

∂

∂+

∂

∂

i

j

j

i

ij

jij

ji

t

i

x

u

x

uv

xx

p

x

uu

x

uτ

1.39



(a) Base Model

• S model

ijkkijij SSC 231 2 ∆−=− τδτ

∂

∂+

∂

∂=

i

j

j

iij

x

u

x

uS

2

1

21)2( ijij SSS =

• Scale-similarity (Bardina) model

ijij B=τ

jijiij uuuuB −=

• Filtered bardina model

))(( jjiiBijijij uuuuCCL −−++=τ

jijiij uuuuL −=

jiijjiij uuuuuuC )()( −+−=

• Mixed model

kkijijijkkijij BBSSC δτδτ312

31 2 −+∆−=−

(b) Procedure for determining )( 2SCC =

• tuning

optimizing CS according to flow characteristics based on numerical

experiment (standard S model; CS=0.1 (channel flow) ~ CS=0.25

(isotropic turbulence))

• dynamic procedure with double filtering

Germano identity

stresssoleduuuuT ijjijiijijij Re:$ˆˆˆ$ −=−= τ

• Lilly’s least-square method (optimization of C at each point)

elDSM

MC

kl

ijijmod:

$

2

1

2−=

elDMM

HMC

kl

ijijijmod:

)($

2

1

2

−−=

ijijij SSSSM 22 ˆˆˆˆ ∆−∆=

)(ˆˆ

ˆˆˆˆ

jijijijiij uuuuuuuuH −−−=

1.40

1.41

1.42

1.43

1.44

1.45

1.46

1.47

1.48

1.49

1.50

1.51

1.52

1.53



• Ghosal’s localization model

[ ]∫ += )()(),()( xfdyyCyxKxC

where [ ]+, denotes the positive part K and f are defined as functions of

ijij SSˆˆˆ

2 2∆=α and ijij SS2ˆ2∆=β

• Meneveau’s Lagrangian dynamic model

elLDSI

ItxC

MM

LM mod:2

1),( −=

elLDMI

IItxC

MM

HMLM mod:2

1),(

−−=

∫ ∞−−=

t

ijijLM dtttWtMtI '''' )()()($

∫ ∞−−=

t

ijijMM dtttWtMtMI '''' )()()(

∫ ∞−−=

t

ijijHM dtttWtHtMI '''' )()()(

W(t-t’) : weighting function.

1.54

1.55

1.56

1.57

1.58

1.59

1.60

ix three component of spatial coordinate (I=1, 2, 3; streamwise, lateral, vertical (or spanwise))

f time-averaged value of f

ijS strain-rate tensor

S scale of strain –rate

∂

∂+

∂

∂=

2

2

1

i

j

j

i

x

u

x

u

iu three component of velocity vector

p pressure

Uo time-averaged value of u1 at the inflow boundary for the case of 2D square cylinder.

Cp instantaneous pressure coefficient )2//()( 2oo UppCp ρ><−=

<po> reference static pressure

vt eddy viscosity

k turbulent energy, 2/''jiuuk =

ε dissipation rate of k

''jiuu Reynolds stress

The S model is so simple and well designed that is has been applied to many flow fields and has

attained great success. The conclusions are drawn that pointed at the advantages of dynamic LES over



the standard LES. It is very promising for accurately predicting the flow around a bluff body. Another

conclusion are the CWE applications reviewed that the difficulties in applying CFD to wind

engineering problem are caused by 1) large Reynolds number, 2) impinging at the front wall, 3) sharp

edges of the bluff body, 4) remaining effect of flow obstacle at outflow around a bluff body, etc. An

evaluation of problems is based of proper choice of turbulent particularly in CWE. The basis

measures for the selection and evaluation of turbulence model are 1) prediction accuracy and 2) CPU

time required. One disadvantage of using LES is that too much CPU time is required. Since that

happened rapid evolution of CPU hardware needed to overcome the restriction and application of

LES to CWE problems is realized in near future in widely.

Another research has represented by Tamura, Kawai, Kawamoto, Nozawa, Sakamoto and

Ohkuma, (1997) of numerical prediction of wind loading on buildings and structures using CFD

related to large eddy simulation (LES) and the k-ε model for turbulent flows. In AIJ (Architectural

Institute of Japan ) concerned on model of a low rise building with (breadth: depth: height = 1:1:0.5)

have been computed by a member of working group measured the flows and the pressure around it. A

half cube on a flat plate was adopted as a computational model of a low-rise building. (Fig.2.37)

Fig.2.37 Computational model of the AIJ project by Tamura,cs.

Regarding to the current status of CFD

technology in wind engineering, they

submitted a questionnaire to the wind

and structural engineers in research

institutes and private companies that

they obtained conclusion of the CFD

technique is widely

.



Fig 2.38 by Tamura,cs

used for application in wind engineering,

especially environmental problems and

structural engineers are planning to use

the CFD technique for wind-load

estimations. In this research, one of

testing is concerned to the sub grid-scale

model of LES.

Fig 2.39 by Tamura,cs

One of the example case

is adopted the standard

Smagorinsky model and

another one is adopted the

dynamic SGS model.

The result of the two LES cases has not deviated from each other, however they shown a different

result in the space-time cross-correlation of fluctuating pressure on the roof.(Fig.2.38 and 2.39). The

conclusion drawn that in the case of LES, the numerical scheme has an important role for the

computed result so that CFD technique could have reliability to predict wind loading on building and

structures from view points of numerical accuracy and computational costs.

Su, Tang, & Fu (1997) were conducted research that analyzed fluid flow and thermal

performance of a dry-cooling tower under cross wind condition. Numerical simulation using finite

element volume (FVM) is 3-D structure shape generated on NSRT (Numerical Simulation in

Turbulence Research) software, which has been developed by them of CFD method. The Heler’

cooling tower model invoked cross wind that resulted turbulence flow around and pressure contour. It

is concerned to the temperature distribution, which air is played role over the tower. However, small

portion of wind behavior to the surface of cooling tower have been presented. The horizontal

crosswind acting to the tower affected that has resulted contour pressure distribution. It can be seen in

figure 2.42.



Fig. 2.40 Heler-type dry-cooling tower, by Su,cs.

Fig. 2.41 Computational region and coordinate system,

by Su, cs.

The contours of pressure in the

horizontal plane Z=9m indicated

lower pressure due to the

pressure close to the side surface

of the tower and because of the

large velocity of air. Fig. 2.42 Contour of pressure in the horizontal plane (Z=9m, cross wind speed of 5 m/s), by Su, cs.

The results were compared with the respective experiment and the agreement is satisfactory. It is

more concerned to the heat transfer on tower. Although the research is done for the heat transfer,

however it can gave inspiration of general type of dry cooling tower model and has correlation to the

shape of the membrane structure model.

2.5 Wind Tunnel Test

A theoretical calculation of the wind load on a structure is quite difficult, which were the

fundamental equations generated on the mechanics of airflow are very complicated and so many

parameters in boundary conditions for the system of equations. Even nowadays, since the evolutions

of advanced computer introduced, there are very few cases can be obtained on numerical calculations

of wind loads on structures in turbulent flow. An actual and most accurate measurement for

determining wind loads will be on full-scale structures that is belief impossible in practice. So the

most appropriate method for that is using model tests in a wind tunnel. (Dyrbye, & Hansen, 1997, p.

177)



“The purpose of wind tunnel tests is to provide designers with information on local pattern,

wind loads, and wind-induced structural vibration having an accuracy far exceeding that can be

obtained from predictions based on other less expensive means such as theory, numerical analysis,

expert judgment (consulting), and so on” (Liu, 1991, p.147). The use of wind tunnel tests steadily

increased to improve design on many kind of structures shape. Due to the distributions of wind

pressure and flow pattern around the structures may not be given by building code and standard as

well as from any other source, so that the wind tunnel was the only way to generate the information.

The wind tunnel test may be considered only use low-speed wind tunnels because it makes

possible use model that can be prepared early in design cycles and to minimize cost. To gain a better

understanding of wind loading on two model structures such as sphere/dome and cooling tower

model, there are some references could be involved. Distribution of local mean pressure coefficient

on circular cylinder and hyperbolic cooling tower represented on wind engineering by Liu, 1991,

p.92-97, that explaining about the similarity of pressure distribution around both the structures later.

The average value derived is the data from several studies (full scale measurement) described in

ASCE (1987).

As the basic consideration of wind force, that is defined a stream of air moving at velocity V

exerts a force q per unit area, where q is dynamic head of air expressed below: 2

2

1 Vq ρ= . 1.61

The total pressure remains constant at all the points that is stated by Bernoulli’s equation of 2

22

12

2

12

11 VpVp ρρ +=+ 1.62

where p1, p2 are the static pressures at two points in the air stream, ρ is the air density, and V1, V2 are

the corresponding air velocities. (Sachs, 1978, p. 2)

The flow pattern of incompressible flow around circular cylinder perpendicular to the flow

depend on the Reynolds number that is expressed as

Re = ρ VD/µ 1.63

where ρ is the density of the fluid, V is the velocity of the fluid relative to the cylinder, D is the

cylinder diameter, and µ is the dynamic viscosity of the fluid. Local mean pressure coefficient can be

derived by the pressure p at an arbitrary point on a structure in non-dimensional as follows:

2

2

1 V

pCp

ρ= 1.64



Where Cp is the dimensionless pressure (pressure coefficient). The pressure p is measured above

ambient pressure. The velocity is that at a reference height, and ρ is the density of air. To understand

the pressure fluctuation at various parts of a building, the good correlation of pressure occurred

between windward external and the internal pressure produced by a windward opening. The pressure

fluctuations on a building caused by free stream turbulence carried in approaching and the signature

turbulence by the structure itself.

The theory said that the building encounters a slowly varying large eddy in the wind, the flow

around the building at any time t regarded quasi-steady. In this term, the pressure p at any location

varies expressed:

2

)()(

2tV

Cptpρ

= 1.65

Where p (t) is pressure at time t and V (t) is the free-stream velocity at t. (Liu, 1991, p.72-91.)

2.5.1 Wind Tunnel Techniques

Wind tunnel test on a structural model are needed when the full-scale structure difficult to

analyses. The use of wind tunnels is to determine the response of a structure to wind forces and to

ascertain the pattern of wind flow to leeward of a structure. Investigation is carried out on the eddy

formation behind bluff bodies to find the frequency and strength of oscillatory forces; on the structure

of a turbulent air-stream, and on the simulation of natural boundary layer effect.

In general the wind tunnel test developed for aircraft work that is also suitable for

structural model testing. Basically, two types of wind tunnel known that are open jet and closed

jet. In the open jet tunnel the working section, where the model situated, has no side walls so that

the air-stream is spilled out by model, and the force and pressure reading are artificially low. The

closed jet tunnel has sided wall, constraint the air flow past the model, so that forces and pressure

are artificially high. Measurements are made by conventional instrumentation, such as force and

moment balances and pressure manometers and the stiffness and damping of flexible structures is

either simulated in the model or by mounting a rigid model on springs with eddy-current

damping. (Peter Sachs, 1978, p. 95)

Guidelines for wind tunnel experiment (Barlow, Rae, & Alan Pope, 1999, p. 460-462) can be

described that is a rather commonsense listing of requirement for initiating and executing a successful



aerodynamic experiment as the following step below. It was included block diagram adapted from

AGRADAR 3043 in figure 2.43.

1. Clearly state the problem being addressed and define the purpose of the experiment. A clear

statement of the problem being addressed will often critical in obtaining efficient application

of their professional knowledge and skills or in avoiding a serious misunderstanding about

what persons involved in the planning and execution of the experiment in sufficient time so

that they can be mentally and physically prepared. The expected result from an experiment

must have associated expected accuracy and precision that are the minimum goals in order

that the objectives can be met. These accuracy and precision requirements should be a part of

the problem statement. Maximum advantage must be taken of results from previous

experiments, theories, and computations, as they are available in the professional literature or

from corporate records.

D e f i n e d P u r p o s e s o f E x p e r i m e n t & R e q u i r e d A c c u r a c i e s o f t h e R e s u l t s

D e s i g n t h e E x p e r i m e n t- R e q u i r e d o u t p u t p a r a m e t e r s- M e t h o d s t o e v a l u a t e u n c e r t a i n t y- T e s t m e t h o d s- I n s t r u m e n t a t i o n n e e d s

- A c c u r a c i e s r e q u i r e d t o m e e t n e e d s- M o d e l c o n f i g u r a t i o n- M e a s u r e m e n t r e q u i r e d- C o r r e c t i o n s r e q u i r e d a n d m e t h o d s

E n u m e r a t e e r r o r s o u r c e s a n d e s t i m a t e

e f f e c t s o f u n c e r t a i i n t i e s o n r e s u l t s

R e s u l t s

A c c e p t a b l e ?

C a n

I m p r o v e m e n t sN o

Y e s

P r o c e e d w i t h

P r e p a r a t i o n s

S t a r t t e s t a n d

m o n i t o r d a t a

R e s u l t s

A c c e p t a b l e ?

N oM e a s u r e m e n t

P r o b l e m ?

N o

S t o p

s e a r c h f o r A l t e r n a t i v e

b e m a d e ?

t o t h i s t e s t !

Y e s

N o

N o

C o n t i n u e

T e s t

Y e s

P u r p o s e

A c h i e v e d ?

S o l v e

P r o b l e m

Y e s

D o c u m e n t O u t c o m eI n c l u d e f i n a l e v a l u a t i o n o f Y e s

u n c e r t a i n t y w i t h r a n d o m a n ds y s t e m a t i c c o n t r i b u t i o n si d e n t i f i e d a n d q u a n t i f i e d .

Fig. 2.43 Experimental planning and execution process diagram.

2. Identify the outcomes needed, including the ranges of values of parameters that will provide

the information to resolve the problem. This will imply a range of operating states and



configuration geometries. There will imply an accuracies and precisions associated with each

variable or parameter that should be identified.

3. Identify feasible model provisions and compatible facilities. This will require conceptual and

preliminary design of the models and fixtures. It will require identifying any wind tunnel

boundary corrections to be applied along with tare, interference, and other data corrections. It

will require assessment of the impact of these choices individually and in sum on the accuracy

and precision of the outputs.

4. Prepare run schedules and configuration change implications. Embedded in these decisions

will be the degree to which replication, randomization, and blocking can contribute to the

enrichment of the data to be obtained.

Compare the resources needed and resources available. Iterate step 1-4 until a match is

obtained.

Prepare a clear guide for the conduct of the experiment. Make sure all persons involved

understand the required actions procedures. Make sure all persons, materials, models,

instrumentation, and software will be available at the time and place for executing the

experiment.

5. Initiate the experiment. Provide for monitoring of all processes and data gathering. Include

process evaluation of achieved accuracies and precisions of measurements.

6. Conduct data analyses to provide quantitative evaluation of the achieved accuracies and

precisions. This information should be provided to the aerodynamicists and other project

personnel as a part of data package so that the product decisions can include appropriate

consideration of outcome uncertainties.

AGRAD AR 3043 contains an extensive example of an application to forces and pressure test that the

data flow diagram included in figure 2.44.



Experimental Aerodydnamic Coefficient

Model DeformationCorrections

Boundary & SupportCorrections

Math Model

Flow Angle

Buoyancy

Prior Data

Calibrations

Tares

Data Acquisition

Pre

ssu

re R

efer

ence

Mo

del

Pre

ssure

Tem

per

ature

Sen

sors

Oth

er T

ran

sduce

rs

An

gle

Sen

sors

Balance

System(s)Encoders

Mo

del

F

orc

es

Iner

tial

F

orc

es

Tem

per

atu

re

Posi

tio

nin

gS

yst

ems

Wind Tunnel Environment

Fig. 2.44 Representative data flow.

There will very useful for a planning process an experiment with emphasis on the inclusion of

uncertainty evaluation.

The model would be developed in wind tunnel usually of ideal as small as possible, but there

are obvious because of practical limitation. These are not always due to the difficulty of simulating

fine detail such as no exactly sharp edges on our modeling. In practice, the model size is determined

by sensitivity of the balance in force and moment measurements, and by the size of pressure tubing

and it’s positioning in pressure test. For the flexible models the size is determined by comparative

mechanical properties of the model and full-size materials. (Peter Sachs, 1978, p. 105)

Uematsu, Yamada, Inoue, and Hongo, (1997) performed a different type of model testing

with the intention on wind-induced dynamic behavior to a rigidly jointed single–layer lattice

dome with a long span. The dynamic response of nine latticed domes with a span of 120 m was

analyzed in the time domain. They concerned the experimental method of characteristic of

fluctuating wind pressure on domes and the mean pressure distribution as well as wind pressure

coefficient (Cp & C’p). This type of structure has seldom been used due to many unsolved

problem regarding the structural design and the wind-induced vibration is one of those problems.



Since such a single-layer dome is a long span, the dynamic changes should be considered in the

wind resistant. It is very different characteristic of material used from the study of fabric

membrane structure, where the fabric membrane is usually light, flexible and tends to deflect and

oscillate under turbulent wind force. The geometry of the wind tunnel models is schematically

illustrated in figure 2.45 and one of example result of pressure distribution can be seen in figure

2.46.

Fig. 2.45 Dome geometry and coordinate system, by Uematsu.

Fig. 2.46 Distributions of the mean and rms pressure coefficient Cp and C’p H/D =1/4, by Uematsu.

They drawn conclusions of research, which the preset results, may give a reasonable basis for

evaluation the dynamic response to the dome shape. The result of them can be used as a reference

for further research of dome/sphere shape model structure. It very grateful to perusing the

literature related to the wind loading with wind tunnel studies to collect information data

experimental from the real structural modeled. However, in order to simplified, validation,

comparison and many considerations that is important to pursue model experimental using

computer program simulation.

Letchford and Sarkar, (2000) performed wind tunnel test on rough and smooth parabolic

domes, which simultaneous pressure measurement involved simulation atmospheric boundary

layer flow. Mean and fluctuation pressure distribution have compared with earlier studies for

similar shape and Reynolds number. The previous wind tunnel studies have undertaken by

Maher’s classical study, Ogawa, and Taylor. The differences between them is that Ogawa and

Taylor were presented measurement of fluctuating pressures and Taylor was the only one

presented contour maps of maximum and minimum point pressure for hemispheres and truncated



spheres. A complication of wind tunnel model studies of these types of structures is because the

curved surface, which leads to Reynolds number effects.

Reynolds numbers defined as µ

ρDU

where ρ and µ are fluid properties, D is the base diameter

and U is the mean velocity at the top of model height. The Reynolds numbers ware used in the

range of each in dealt with Maher used R in the range of 6 x 105- 18x 105, Taylor dealt with R in

the range from 1x105 to 3 x 105, and Ogawa also investigated a range of turbulent intensities with

Reynolds numbers ranging from 1.2 x 105 to 2.1 x 105. The wind tunnel used is closed circuit, 1.8

m wide with a ceiling adjustable to ~1.8m. There is an upstream fetch of approximately 15m for

developing appropriate simulations of the earth’s atmospheric boundary layers. A model dome

was constructed with a base diameter (D) of 480 mm and height (h) of 150mm. The research was

estimated pressure coefficient, which all pressure stated as non-dimensionalized by the mean

dynamic pressure (1/2ρU2) at the top of the dome. ∆p is the instantaneous pressure difference

between the surface pressure and a reference pressure in the wind tunnel.

Fig. 2.47 Tapping arrangement and wind direction definition for single dome test, by Letchford,cs

Fig. 2.48 Comparison of mean pressure coefficient along centerline of a smooth dome, by Letchford,cs

They were governed equation as:

221 U

pCp

ρ

∆= Mean pressure coefficient, 1.66

221 U

pCp rms

rmsρ

∆= Standard deviation pressure coefficient, 1.67

221

ˆˆU

ppC

ρ

∆= Mean peak maximum pressure coefficient, 1.68



22

1 U

ppC

ρ

(( ∆

= Mean peak minimum pressure coefficient, 1.69

hU

UG

1

3ˆ

= Gust velocity ratio 1.70

The corresponding coefficients are

2

ˆˆ

G

pCpC = Mean maximum pseudo-steady pressure coefficient, 1.71

2G

pCpC

(

(= Mean minimum pseudo-steady pressure coefficient. 1.72

They specified conclusion that mean and fluctuating pressure distributions are well approximated

by a spherical dome of the same height to diameter ratio. The pressure distributions were

independent of Reynolds number in the range 2.3 x 105-4.6 x 105 defined by velocity at top of

dome and base diameter. In this study, hemisphere is one of the structural geometry on fabric

membrane structures under wind force acting investigated. Regarding to the previous research,

the result can be referenced to further study to the similar shape geometry with variation on

material structure involved.

Published data by Maher’s classical study of the dome surface can be described in

Chapter 4, which will be compared with the CFD result. Those tables and diagrams involved are

based on the work of Maher in 1965 and some by Blessmann in 1971, both of the result of them

that arrived in general conclusions. Mean and fluctuation pressure distribution will have

compared with those earlier studies.

2.5.2 Small Wind Tunnel

Regarding the impression of useful the large wind tunnel with a large jet and more speed, the

smaller wind tunnel might be considered in order to minimize cost as the fundamental advantages

with the economically in operation. Small tunnel is much less in cost to build and less run as well as

carried out the smaller model generated and time consuming.

“The key to successful experiments made in a small tunnel is to have a clear understanding of

the likely role of Reynolds number on the objects of the experiments. That is a matter of whether the

relevant effect of Reynolds number in small wind tunnel.” There are not exactly true, that has no

effect of Reynolds number on such cases. However, small wind tunnel is often used for instruction in



the methods of experimentation and the result has done well. “Pressure distribution measurement on

airfoils can be instructive even at relatively low Reynolds numbers. For a given airfoil shape the

distribution does not change drastically with Reynolds numbers so long as angle of attack is well

below stall. Many experiment concerning wind tunnel wall corrections are suitable for small tunnel.

These tend to be little affected by Reynolds numbers”. (Barlow, Rae, & Alan Pope, 1999, p. 665).

2.6 Conclusion

“The quantitative analysis of the behavior of fabric structures under severe loadings, has

developed to the point where they can now, be engineered in every way to the same performance

criteria as a permanent structure” (Russell, 2000). More specific research need for the fabric

membrane structure, which is considered the structure as an integrated whole without analyzed in

separately structural components. By applied CFD methods and subjecting scale model of fabric

membrane structure model to wind loading simulation, a more understanding of the behavioral of

them will be pursued.



Chapter 3 Numerical Methods

3.1 Introduction

Numerical study was investigated wind loading on the fabric membrane structure that

mostly occurred on roof surface. Using Computational Fluid Dynamics (CFD) methods,

prediction and evaluation of wind loads impinging to the membrane structure is being assessed

with concerned on developing models structure.

The CFD can solve some problem in which allow the immediate solution of the flow field

without advancing in time and space. High-speed digital computer instrumentation needed in

order to advance the practical simulation. Some computers package contributions also required

for complex problem might be developed. In this case, some programme computer package can

be involved since they can be associated to the main program solver. Since the latest role of CFD

in engineering, prediction problem became in confident to generate in three-dimensional fluid

dynamics. The simple and the complex model immediately can be identified using the computer

package. One of them is AUTOCAD package that possibly can develop the initial model

generation. The reason this package involved is because the availability and the handling ability

on it in order to maximise productivity in CFD.

In term of CFD code, there are three components of the CFD codes have been used are

GAMBIT as pre-processor programme and FLUENT as a programme solver. The post-processor

is GSVIEW of postscript-based generation to translate the dynamic result display of model

developed. Those are mostly governed by the finite element method, which have been translated

into a computational programme, particularly on fluid dynamic.

Such as the principle methods, understanding of how the computational simulation work

is significant in which the theory involved, including the theory of finite element methods as the

basic of computational fluid dynamic developed.

3.2 Finite Element Theory and CFD Method Reviews

Computational Fluid Dynamics is the analysis of systems, which are fluid flow and other

associated phenomena involved in computer-based simulation. The technique of this is applications

of finite element methods for fluids where the wide range application area copes and very powerful

pursued.



Three dimensional or solid elements considered is useful for the stress analysis of general three-

dimensional bodies that require more-precise analysis than is possible through two dimensional or

axisymmetric analyses. The basic three-dimensional element is tetrahedron, which is used in the

development of the shape function, stiffness matrix and force matrices in term of a global coordinate

system. Referencing the theory of basic development on three dimensional, Finite Element published

by Logan (1986) derived to consider the three dimensional infinitesimal element in Cartesian

coordinate with dimensions dx, dy, & dz, and normal and shear stress.

σ

ττ

σσ

τ

ττ

τ

Fig.3.1 Three-dimensional stress on an element, by Logan

Normal stress are perpendicular to

the faces of the element, and are

presented byxσ ,

yσ , and zσ . Shear

stress act in the faces (planes) of

the element, and are presented

byxyτ ,

yzτ , zxτ and etc. The

moment equilibrium of element on

Appendix 2 are given by

yxxy ττ = , zyyz ττ = xzzx ττ = 2.1

The element strain/displacement relationship are obtained on Appendix 2 are given by

x

ux

∂

∂=ε ,

y

vy

∂

∂=ε

z

wz

∂

∂=ε 2.2

where u, v, and w are displacement associate with the x, y, and z directions. The shear strain γ are

given by

yxxy

x

v

y

uγγ =

∂

∂+

∂

∂= ,

zyyzy

w

z

vγγ =

∂

∂+

∂

∂= , xzzx

z

u

x

wγγ =

∂

∂+

∂

∂= 2.3

where, only three independent shear strains exist. Representing the stress and strains by column

matrices as



=

zx

yz

xy

z

y

x

τ

τ

τ

σ

σ

σ

σ}{ ,

=

zx

yz

xy

z

y

x

γ

γ

γ

ε

ε

ε

ε}{ 2.4

The stress/strain relationship for an isotropic material are given by

[ ] }{}{ εσ D= 2.5

where {σ} and {ε} are defined by Eq. 2.4 and the constitutive matrix [D]is given by

[ ]

−

−

−

−

−

−

−+=

2

21

02

21

002

21

0001

0001

0001

)21()1(

vSymmetry

v

v

v

vv

vvv

vv

ED 2.6

In this study, developing the tetrahedral element is focused that it is because in CFD method, the

model and the domain approached by tetrahedral discretization. Tetrahedral element considered is

shown in figure 3.2 with corner nodes 1, 2, 3, and 4.

Fig. 3.2 Tetrahedral solid element, by Logan

2.7

There is three degree of freedom per node, or twelve total degree of freedom per element. For a

compatible displacement field, the element displacement functions u, v, and w must be linear along

=

4

4

4

1

1

1

.

.

.

}{

w

v

u

w

v

u

d



each edge because only two points (the corner nodes) exist along each edge and the functions must be

linear in each plane side of the tetrahedron. The linear displacement function as

u(x, y, z) = a1 + a2x + a3y + a4z 2.8

v(x, y, z) = a5 + a6x + a7y + a8z 2.9

w(x, y, z) = a9 + a10x + a11y + a13z 2.10

Skipping the straightforward but tedious detail, would be obtain

})()(

)(){(6

1),,(

4444433333

2222211111

uzyxuzyx

uzyxuzyxV

zyxu

δγβαδγβα

δγβαδγβα

+++++++

+++++++= 2.11

where 6V is obtained by evaluating the determinant

=

444

333

222

111

1

1

1

1

6

zyx

zyx

zyx

zyx

V 2.12

and V represents the volume of the tetrahedron. The coefficients αi, βi, γi, and δi (I=1, 2, 3, 4) in Eq.

(2.11) are given by

=

444

333

222

1

zyx

zyx

zyx

α

−=

44

33

22

1

1

1

1

zy

zy

zy

β

=

44

33

22

1

1

1

1

zx

zx

zx

γ

−=

44

33

22

1

1

1

1

yx

yx

yx

δ 2.13

and

−=

444

333

111

2

zyx

zyx

zyx

α

=

44

33

11

2

1

1

1

zy

zy

zy

β

−=

44

33

11

2

1

1

1

zx

zx

zx

γ

=

44

33

11

2

1

1

1

yx

yx

yx

δ 2.14

and

=

444

222

111

3

zyx

zyx

zyx

α

−=

44

22

11

3

1

1

1

zy

zy

zy

β

=

44

22

11

3

1

1

1

zx

zx

zx

γ

−=

44

22

11

3

1

1

1

yx

yx

yx

δ 2.15

and



−=

333

222

111

4

zyx

zyx

zyx

α

=

33

22

11

4

1

1

1

zy

zy

zy

β

=

33

22

11

4

1

1

1

zx

zx

zx

γ

−=

33

22

11

4

1

1

1

yx

yx

yx

δ 2.16

Expressions for v and w are obtained by simply substituting vi’s for all ui’s and then

wi’s for all ui’s in Eq. 2.11. The displacement expression for u given by Eq. 2.11, with similar

expressions for v and w, can be written equivalently in expanded form in term of the shape functions

and unknown nodal displacements as

=

4

4

4

1

1

1

4421

4321

4321

.

.

.

00000000

00000000

00000000

w

v

u

w

v

u

NNNN

NNNN

NNNN

w

v

u

2.17

where the shape functions are given by

V

zyxN

6

)( 11111

δγβα +++=

V

zyxN

6

)( 22222

δγβα +++=

V

zyxN

6

)( 33333

δγβα +++=

V

zyxN

6

)( 44444

δγβα +++= 2.18

The element strains for the three-dimensional stress state are given by

+

+

+=

=

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

zu

xw

yw

zv

xv

yu

zw

yv

xu

zx

yz

xy

x

y

x

γ

γ

γ

ε

ε

ε

ε}{ 2.19

Using Eq. (2.17) in Eq. (2.19), would obtained

{ } [ ]{ }dB=ε 2.20



where

[ ] [ ]4321 BBBBB = 2.21

The sub matrix 1B in Eq. 2.21 is defined by

=

xz

yz

xy

x

y

x

NN

NN

NN

N

N

N

B

,1,1

,1,1

,1,1

,1

,1

,1

1

0

0

0

00

00

00

2.22

Sub matrices 2B , 3B and 4B are defined by simply indexing the subscript in Eq.2.22 from 1 to 2, 3,

and 4, respectively. Substituting the shape functions from Eq. 2.18 into 2.22, 1B is expressed as

=

11

11

11

1

1

1

1

0

0

0

00

00

00

6

1

βδ

γδ

βγ

δ

γ

β

VB 2.23

with similar expressions for 2B , 3B and 4B . The element stresses are related to the element strains by

{ } [ ]{ }εσ D= 2.24

where the constitutive matrix for an elastic material is given by Eq. 2.23

The element stiffness matrix is given by

[ ] [ ] [ ][ ]∫∫∫=v

TdVBDBk 2.25

Since both matrices [B] and [D] are constant for the simple tetrahedral element, Eq.2.25 can be

simplified to

[ ] [ ] [ ][ ]VBDBkT

= 2.26

where, V is the volume of the element. The element stiffness matrix is order of 12 x 12.

The element body force matrix is given by



[ ] [ ] { }∫∫∫=v

TdVXNfb 2.27

where [N] is given by the 3 x 12 matrix in Eq. 2.17, and

{ }

=

b

b

b

Z

Y

X

X 2.28

For constant body forces, the nodal components of the total resultant body forces can be distributed to

the nodes in four equal parts. The surface forces are given by

[ ] [ ]

= ∫∫z

y

x

s

T

p

p

p

Nfssurface

onevaluated3,2,1

2.29

where px, py, and pz are the x, y, and z component, respectively, of p. Simplifying and integrating Eq.

2.29 that can be shown as

=

0

0

0

}{3123

z

y

x

z

y

x

z

y

x

S

s

p

p

p

p

p

p

p

p

p

f 2.30

where S123 is the area of the surface associated with nodes 1, 2, and 3.

The formulation of tetrahedral element review is concerned to the developing finite element

volume related to the CFD methods. “The cornerstone of computational fluid dynamics is the

fundamental governing equations of fluid dynamics-the continuity, momentum and energy

equations”. Anderson (1996). The basic equations of fluid motion are always to follow the philosophy

of:



• Appropriate fundamental physical principle from the law physics, such as

a. Mass is conserved.

b. F=ma (Newton’s 2nd law)

c. Energy is conserved.

• Applied the physical principle to the suitable model of the flow.

• To extract the mathematical equations which embody such physical principles.

The physical meaning of substantial derivative is important to establish a common notation in

aerodynamics development.

3.2.1 The CFD Code From the reference “An Introduction to CFD -The Finite Volume Method” by Versteeg & Malalasekera, (1995), CFD codes and formulations are derived. CFD codes are structured around the numerical algorithms that can solve fluid flow problems. The CFD code contained three main elements that are: 1) a pre-processor, 2) a solver and 3) a post-processor. Brief examine the function of each of these elements derived:

1. Pre-processor Pre-processing consist of the input of a flow problem to a CFD program by means of an operator-friendly interface and the subsequent transformation of this input into a form suitable for use by the solver. The user activities at the pre-processing stage involved

• Definition of the geometry of the region of interest: the computational domain.

• Grid generation –the sub-division of the domain into a number of smaller, non-overlapping

sub-domains: a grid (or mesh) of cells (or control volumes or element)

• Selection of the physical and chemical phenomena that need to be modelled.

• Definition of fluid properties.

• Specification of appropriate boundary conditions at cells, which coincide with or touch the

domain boundary. The solution to a flow problem (velocity, pressure, temperature etc) is defined at nodes inside each cell. The accuracy of a CFD solution is governed by the number of cells in the grid, which is fineness of the grid generation, the more accurate result gain. It is dependent how good the computer hardware related to the iteration time assumption.

At present it is still up to the skills of the CFD user to design a grid that is a suitable compromise between desired accuracy and solution cost. In order to maximise productivity of CFD personnel all major codes now include their own CAD-style interface and/or facilities to import data from proprietary surface modellers and mesh generators.

2. Solver

In outline the numerical methods that form the basis of the solver perform the following steps:



• Approximation of the unknown flow variables by means of simple functions.

• Discretisation by substitution of the approximations into the governing flow equations and

subsequent mathematical manipulations.

• Solution of the algebraic equations. The theory of finite elements has been developed initially for structural stress analysis. A standard work for fluids applications is Zienkiewickz and Taylor (1991). The finite difference formulation was originally developed the finite volume method as basic of CFD technique established. The finite volume method concerned with most well-established and thoroughly validated general purpose CFD technique. It is central to four of the five main commercially available CFD codes: PHOENICS, FLUENT, FLOW3D and STAR-CD. The numerical algorithm consists of the following steps:

• Formal integration of the governing equations of fluid flow over all the (finite) control

volumes of the solution domain.

• Discretisation involves the substitution of a variety of finite-difference-type approximations

for the terms in the integrated equation representing flow processes such as convection,

diffusion and sources. This converts the integral equations into a system of algebraic

equations.

• Solution of the algebraic equations by an iterative method.

3. Post-processor

As in pre-processing a huge amount of development work has recently taken place in the post-

processing field. Owing to the increase popularity of engineering workstations, many of with have

outstanding graphics capabilities, the leading CFD package are now equipped with versatile data

visualisation tools. These include:

• Domain geometry and grid display

• Vector plots

• Line and shaded contour plots

• 2D and 3D surface plots

• Particle tracking

• View manipulation (translation, rotation, scaling etc.)

• Colour postscript

More recently these facilities may also include animation for dynamic result display and in addition

to graphics all codes produce trusty alphanumeric output and have data export facilities for further

manipulation external to the code. As in many other branches of CAE the graphics output capabilities

of CFD codes have revolutionised the communication of ideas to the non-specialist.



3.2.2 Fluid Flow Problem and Governing Equations on CFD

In solving fluid flow problems, it need to be aware that the underlying physics is complex and

the results generated by a CFD code are at best as good as the physics embedded in it and at worst as

good as bits operator. Elaborating on the latter issue first, the user of a code must have skills in a

number of areas. Prior to setting up and running a CFD simulation there is a stage of identification

and formulation of the flow problem in terms of the physical and chemical phenomena that need to be

considered.

Performing the actual CFD computation itself requires operator skills of a different kind.

Specification of the domain geometry and grid design is the main tasks at the input stage and

subsequently the user needs to obtain a successful simulation result. The two aspects that characterise

such a result are convergence of the iterative process and girl independence. The solution algorithm is

iterative in nature and in a converged solution the so-called residuals – measures of the overall

conservation of the flow properties – are very small. Progress towards a converged solution can be

greatly assisted by careful selection of the settings of various relaxation factors and accelerations

devices. The only way to eliminate errors due to the coarseness of a grid is to perform a grid

dependence study, which is a procedure of successive refinement of an initially coarse grid until

certain key results do not change. Then the simulation is grid independent. Optimisation of the

solution speed requires considerable experience with the code itself, which can only be acquired by

extensive use. There is no formal way of estimating the errors introduced by inadequate grid design

for a general flow. Good initial grid design relies largely on an insight into the expected properties of

the flow. The only way to eliminate errors due to the coarseness of a grid is to perform a grid

dependence study, which is procedure of successive refinement of an initially coarse grid until certain

key results do not change. Then the simulation is grid independent. A systematic search for grid-

independent result forms an essential part of all high quality CFD studies.

Every numerical algorithm has its own characteristic error patterns. Well-known CFD

euphemisms for the word error are terms such as numerical diffusion, false diffusion or even

numerical flow. At the end of a simulation the user must make a judgement whether the results are

‘good enough’. It is impossible to assess the validity of the models of physics and chemistry

embedded in a program as complex as a CFD code or the accuracy of its final result by any means

other than comparison with experimental test work. Anyone wishing to use CFD in a serious way



must realise that it is no substitute for experimentation, but a very powerful additional problem-

solving tool. Validation of a CFD code requires highly detailed information concerning the boundary

conditions of a problem and generates a large volume of results. To validate these in a meaningful

way it is necessary to produce experimental data of similar scope

CFD computation involves the creation of a set of numbers that (hopefully) constitutes a

realistic approximation of a real-life system. One of the advantages of result, but in the prescient

words of C. Hastings (1955), written in pre-IT days: ‘The purpose of computing is insight not

number’. The underlying message is rightly cautionary. The main outcome of any CFD exercise is

improved understanding of the behaviour of a system, but since there are no cast iron guarantees with

regard to the accuracy of a simulation we need to validate our results frequently and stringently.

It is clear that there are guidelines for good operating practice, which can assist the user of

CFD code and repeated validation plays a key role as the final quality control mechanism.

However, the main ingredients for success in CFD are experience and a through understanding of

the physics of fluid flows and the fundamentals of the numerical algorithms. Without these it is

very unlikely that the user gets the best out of a code.

The governing equations of fluid flow represent mathematical statements of the conservation

laws of physics, as written by Aderson, (1996) in this paper, page 48. The first step in the derivation

of the mass conservation equation is to write down a mass balance for the fluid element.

Rate of increase of mass in fluid element

=

Net rate of flow of mass into fluid element

The rate of increase of mass in the fluid element is

zyxt

pzyx

tδδδδδρδ

∂

∂=

∂

∂)( 2.31

It is needed to account for the mass flow rate across a face of the element which is given by the

product of density, area and the velocity component normal to the face. From Figure 3.3, it can be

seen that the net rate of flow of mass into the element across its boundaries is given by

zxyy

vvzyx

x

uuzyx

x

uu δδδ

δ

ρρδδδ

δ

ρρδδδ

δ

ρρ

∂−+

∂+−

∂−

2

1.

)(

2

1.

)(

2

1.

)(

yxzz

wwyxz

z

wwzxy

y

vv δδδ

δ

ρρδδδ

δ

ρρδδδ

δ

ρρ

∂+−

∂−+

∂+−

2

1.

)(

2

1.

)(

2

1.

)( 2.32



Flow, which are directed into the element produce an increase of mass in the element and get a

positive sign and those flows that are leaving the element are given a negative sign.

ρ ρδ

δ

ρ ρδ

δ

ρ ρδ

δ

ρ ρδ

δ

ρ ρδ

δ

ρ ρδ

δ

Fig.3.3Mass flow in and out of fluid element, by Versteeg & Malalasekera

The rate of increase of mass inside the element is equated to the net rate of flow of mass into the

element across its face (Fig. 3.3). All terms of the resulting mass balance are arranged on the left hand

side of the equals sign and the expression is divided by the element volume δxδyδz.

This yield

0)()()(

=∂

∂+

∂

∂+

∂

∂+

∂

∂

z

w

y

v

x

u

t

p ρρρ 2.33

or in more compact vector notation 0)( =+∂

∂udiv

t

pρ 2.34

Equation (2.34) is the unsteady, three-dimensional mass conservation or continuity equation at a

point in a compressible fluid. The first term on the left hand side is the rate of change in time of the

density (mass per unit volume). The second term describes the net flow of mass out of the element

across its boundaries and uts called the convective term.

For an incompressible fluid (i.e.a liquid) the density ρ is constant and equation (2.34)

becomes

div u = 0 2.35

or in longhand notation

0=∂

∂+

∂

∂+

∂

∂

z

w

y

v

x

u 2.36



In term of momentum equation in three dimensions, the Newton’s second law states that the rate

of change of momentum of a fluid particle equals the sum of the forces on the particle.

Rate of increase of momentum of fluid particle

= Sum of forces on fluid particle

The rates of increase of x-,y- and z- momentum per unit volume of a fluid particle are given by

Dt

Dw

Dt

Dv

Dt

Duρρρ 2.37

We distinguish two types of forces on fluid particle:

• Surface forces - pressure forces and viscous forces

• Body forces -gravity force, centrifugal forces, Coriolis & Electromagnetic force

The state of stress of a fluid element is defined in terms of the pressure and the nine

viscous stress components show in figure 3.4.

τ

τ

τ

τ

τ

τ

τ

τ

τ

τ

τ

τ

ττ τ

ττ

Fig.3.4Stress components on three faces of fluid element, by Versteeg & Malalasekera

The pressure, a normal stress, is denoted by

p. Viscous stresses are denoted by ι. The

usual suffix notation ιij is applied to

indicate the direction of the viscous

stresses. The suffices I and j in ιij indicate

that the stress component acts in the j-

direction on a surface normal to the i-

direction.

Forces

aligne

d with

the

directi

on of

a co-

ordina

te axis

ττ

δ

δδ

ττ

δ

ττ

δ

ττ

δ

ττ

δ

δδ

ττ

δ

Fig.3.5 Stress components in the x-direction, by Versteeg & Malalasekera

First we consider the x-

components of the forces

due to pressure p and

stress components ιxx, ι.yx

and ι.zx show in figure

3.4. The magnitude of a

force resulting from a

surface stress is the

product of stress and area.



get a positive sign and those in the opposite direction a negative sign. The net force in the x-

direction is the sum of the force components acting in that direction on the fluid element.

On the pair of faces (E, W) have

zyxx

xx

ppzyx

xx

x

pp xx

xxxx

xx δδδδ

ττδ

δδδδ

δ

ττδ

δ

∂++

∂+−+

∂−−

∂−

2

1.

2

1.

2

1.

2

1.

zyxxxx

p xx δδδδτ

δ

∂

∂+

∂−= 2.38

The net force in the x-direction on faces (N,S) is

zyxy

zxyy

zxyy

yxyx

yx

yx

yx δδδτ

δδδτ

τδδδτ

τ∂

∂=

∂

∂++

∂

∂−−

2

1.

2

1. 2.39

The final net force in the x direction on the T and B is given by

zyxz

yxzz

yxzz

zxzx

zx

zx

zx δδδτ

δδδτ

τδδδτ

τ∂

∂=

∂

∂++

∂

∂−−

2

1.

2

1. 2.40

The total force per unit volume on the fluid due to these surface stresses is equal to the sum of

Eq. 2.38, Eq. 2.39 and Eq. 2.40 divided by the volume δxδyδz:

zyx

p zxyxxx

∂

∂+

∂

∂+

∂

+−∂ τττ )(

Without considering the body force, overall effect can be included by defining a source SMx of x-

momentum per-unit volume per unit time. The x-component of the momentum equation is:

Mxzxyxxx Szyx

p

Dt

Du+

∂

∂+

∂

∂+

∂

+−∂=

τττρ

)( 2.41a

The y-component of the momentum equation is:

My

zyyyxyS

zy

p

xDt

Dv+

∂

∂+

∂

+−∂+

∂

∂=

τττρ

)( 2.41b

The z-component of the momentum equation is:

Mzzzyzxz S

z

p

yxDt

Dz+

∂

+−∂+

∂

∂+

∂

∂=

)( τττρ 2.41c

Energy equation involved is derived from the first law of thermodynamics which states that

he rate of change of energy of a fluid particle is equal to the rate of heat addition to the fluid particle

plus the rate of work done on the particle.

Rate of increase of

energy of fluid particle

= Net rate of heat added to

fluid particle

+ Net rate of work done on

fluid particle.



The energy equation can be specified often as the sum of internal (thermal) energy i, kinetic energy ½

(u2+ v2+ w2) and gravitational potential energy. The energy E equation is:

Ezzyzxz

zyyyxyzxxyxx

STgradkdivz

w

y

w

x

w

z

v

y

v

x

v

z

u

y

u

x

upudiv

Dt

DE

++

∂

∂+

∂

∂+

∂

∂+

∂

∂+

∂

∂+

∂

∂

+

∂

∂+

∂

∂+

∂

∂+−=

)()()()(

)()()()()()()(

τττ

ττττττρ

2.42

The energy is became E = i +½ (u2+ v2+ w2).

The motion of a fluid in three dimensions is described by a system of five partial differential

equations: mass conservative Eq. 2.34, x-, y-, and z moment equations Eq. 2.41a-c and energy

equation Eq. 2.42. The state of substance in thermodynamic equilibrium is used ρ and T as state

variables for state equation of pressure p and specific internal energy i:

p=p(ρ, Τ) and i=i(ρ, Τ) 2.43

For a perfect gas the following equations of state are useful:

p=ρRT and i=CvT 2.44

Finally, a command differential form for all the flow equations identified as transport equation and

developed integrated forms which are central to the finite element volume CFD method: for steady

state processes derived as:

∫ ∫ ∫+Γ=A A CV

dVSdAgradndAun φφρφ )(.)(. 2.45

and for time-dependent processes

dVdtSdtdAgradndAundtdVt

t t CVt At ACV

∫ ∫ ∫∫ ∫∫ ∫∫∆ ∆∆∆

+Γ=+

∂

∂φφρφρφ )(.)(.)( 2.46

Generating model on CFD method is difficult without knowing a great deal about flow before

solving a problem..

Fig.3.6 (a). Boundary condition for an internal flow problem Versteeg & Malalasekera

It is very difficult to specify the

precise number and nature of

allowable boundary conditions

on any fluid/fluid boundary in

the far field. For the convenient

attempt, the boundary condition

for flow problem specified in

figure below



Fig.3.6 (b) Boundary condition for external flow problem, by Versteeg & Malalasekera

It is obvious that flow inside a CFD solution domain is driven by the boundary conditions. The

difficulties are encountered in obtaining solution, therefore paramount importance that supplied

physically realistic and well-posed boundary conditions are applied. The boundary conditions mostly

affected the rapid of divergence of CFD simulation. A set of ‘best’ boundary condition for viscous

fluid flows, which included the inlet, outlet and wall condition. The finite volume method

implementation included three conditions, constant pressure, symmetry and periodicity, which are

physically realistic and very useful I practical calculations. Some permissible state combination in

subsonic flows:

• Walls only

• Wall and inlet and at least one outlet

• Wall and inlet and at least one constant pressure boundary

• Wall and constant pressure boundaries

Position of outlet boundaries is became a significant matter to contribute in how the flow

can behave effectively. “If outlet boundaries are placed too close to solid obstacles it s possible

that the flow will not have reached a fully developed state which may lead to

Fig. 3.7 Velocity profiles at different locations downstream of an obstacle, by Versteeg & Malalasekera

sizable errors. It is

imperative that the outlet

boundary is placed much

more further downstream

than 10 height downstream

of the last obstacle to give

accurate result” (fig. 3.7)



3.2.3 General Fluid Dynamic Background

Definition of fluid is a substance, which cannot sustain shear stresses whilst at rest. The fluid

problem generally interested in microscopic, rather than molecular scale behaviour that possibly

assumed as a continuous and homogeneous substance. Physical of air justified of 1m cubes contains

27x1024 molecules and the viscosity of air is the resistance to continuous shearing due to a property of

the fluid, which has value of µ =1.82x10-5 kg/m.s at 200 C known as the dynamic viscosity or

absolute viscosity.

Newton’s law of viscosity for fluid is the relationship between shear stress τ and rate of shear

strain γ, with the constant of proportionality being the dynamic viscosity:

µγγµτ == )(dt

d 2.47

or shear stress = dynamic viscosity x rate of shear strain. While the rate of shear strain is equal to the

velocity gradient normal to the shear plane:

dn

dcµτ = 2.48

τ µ

Fig. 3.8 by Potts (MMM336) Fig. 3.9 by Potts (MMM336)

Considering steady flow of fluid along a duct of uniform cross sectional flow area (A) at velocity

(c)(figure 3.9). The net volume of fluid crossing plane x-x is thus dV= A.c.dt, and the net mass is

ρ.A.c.dt. Alternatively, volume flow rate Q (= dV/dt) = A.c and mass flow rate is m (=dm/dt) = ρ.A.c.

In CFD method the consideration of the laminar and turbulent flows can be approached from

the definition and also can be specified the behaviour of air by using pipe model in order to know the

differences between them. A simple comparison of both flow features is discussed. The physical

model for the laminar is described by the figure below in left part, on the other hand, the turbulent

behaviour can be described in right part of the table below:



Table 3.1 Laminar and Turbulent flow model

A

turbulence model is more focused due to the more complicated problem faced. The turbulent

model can be simplified as a computational procedure to close the system of mean flow equation

described on table below:

Table 3.2 Turbulent flow equations for compressible flows, by Versteeg & Malalasekera

Continuity

0)( =+∂

∂Udiv

t

pρ 2.49

Reynolds equations

MxSz

wu

y

vu

x

u

Ugraddivx

PUUdiv

t

U

+

∂

∂−

∂

∂−

∂

∂−+

+∂

∂−=+

∂

∂

)''()''()'(

)()()(

2 ρρρ

µρρ

2.50a



MySz

wu

y

v

x

vu

Vgraddivx

PVUdiv

t

V

+

∂

∂−

∂

∂−

∂

∂−+

+∂

∂−=+

∂

∂

)''()'()''(

)()()(

2 ρρρ

µρρ

2.50b

MzSz

w

y

wu

x

wu

Wgraddivx

PWUdiv

t

W

+

∂

∂−

∂

∂−

∂

∂−+

+∂

∂−=+

∂

∂

)'()''()''(

)()()(

2ρρρ

µρρ

2.50c

Scalar transport equation

ΦΦ +

∂

∂−

∂

∂−

∂

∂−+ΦΓ=Φ+

∂

Φ∂S

z

w

y

v

x

ugraddivUdiv

t

)''()''()''()()(

)( ϕρϕρϕρρ

ρ 2.51

For most engineering purposes that is unnecessary to resolve the details of the turbulent

fluctuations. The effect of turbulence on the mean flow is the only effect usually sought. Large

eddy simulations are considered in order to investigate the effect to the model problems. Large

eddy simulation (LES) are turbulence models where the time-equations are solved for the mean

flow and the largest eddies and where the effect of smaller eddies are modelled. Large eddy

simulations are at present at the research stage and the calculations are too costly considered in

general purpose computational. Nowadays, anticipation may be already done the improvement in

computer hardware or may change the perspective in the future. Some LES equations have

derived in Eq. 1.30-1.60 in Chapter 2.

3.3 General Strategies and Procedures

In CFD method, the computer hardware and software must be available in order to

accommodate model data and then run the computer programme so that can be identified the

prediction result of wind load acting on the fabric membrane building model.

The Sun Ultra 5 series workstations in the University of Newcastle upon Tyne are all licensed

to run Fluent version 5 and Gambit. The Fluent 5 is the latest version CFD software from Fluent

Inc., and is a state-of-the-art commercial CFD solver, using the latest unstructured mesh approach.

However, Fluent 5 does not have any internal facilities for mesh generation, and the necessary grids

must be produced using a separate package of Pre-processor. The latest and (most powerful) pre-

processor can be used is Gambit that is supplied by Fluent. Inc too.



Creating grid model in Gambit need understanding to identify menu function of software and

must be familiar wait. In order to gain a good and clean result, Gambit has Graphics User Interface or

“GUI” as guide information and as tutor via Netscape. Creating mesh structure model to present

fabric membrane structures are far more difficult due to the shape model of structure usually as a

complex geometry. For the simple shape, the model can be generated directly in Gambit, or when has

no choice that is need time consumed to generate the model. Due to the ability of Gambit to associate

another programme computer package, the geometric mesh model can be developed in such as CAD

programme, that is depend on how far can be used too those programme.

1. AutoCAD Reviews

In this study, AutoCAD programme package has been used to generate grid model structure.

In this commercial package, the three-dimensional model can easily be generated due to wide range

of ability to specify interface in accurately. AutoCAD offers two methods for creating 3D model:

surface modelling and solid modelling. Several kinds of simple models are presented below is 3D

surface modelling generated that are concerned.

Fig.3.10 Example mesh geometric in AutoCAD



Fig.3.11Arranged position of inlet, outlet and

wall boundaries in AutoCAD

Fig.3.12 The geometry that will be exported from AutoCAD

Thus, is because the fabric membrane structure developed is based on surface with mostly

curving.

Using AutoCAD’s 3D capabilities, simple object can be created by manipulation of current 3D

surface available. There are some basic shape available for 3D model such as cone, sphere/dome,

torus, pyramid and also have surface developed that such as edge surface, 3D mesh, revolved

surface, tabulated surface, and ruled surface.

Generating model initially in AutoCAD is much more promised due to easier to arrange

the shape of model and to decide easily the dimension of domain as well as the shape of

tunnel/domain generation. It is important part in order to fulfil the requirement the position of

outlet boundary, which can be seen in figure 3.7. The domain must be arranged in deal with the

base point of coordinate (x,y,z = 0,0,0)It is because when importing done, the domain should

created again if only model imported to Gambit with the same domain pattern in AutoCAD. It is

unnecessary when importing included the domain depend on kind of domain developed.

Once the geometry of model structures completed as in example in figure 3.12, the model

is ready to export into Gambit. Initially, it is important to create such as an IGES file before

exporting, in order to associate between the programme consoles. IGES file is the file interface

from the AutoCAD that can only be read by Gambit. The IGES files can be easily operated on

Mechanical Desktop 4 as family of AutoCAD programme. Such as a simple save to IGES file or

imported directly, IGES file has been created. Since that happened the IGES file needed to

transfer to the Gambit as a pre-processor.



2. Pre-processor: GAMBIT Reviews

The model structures actually can be created directly in Gambit. However, sometime when a

complicated structure model has been created, it will spend such along time in generation. This

procedure is naturally on the way and relevant problem need time consumed. Developing such as

model structure in Gambit is depend on how the user familiar with the programme, more experience

on it much more helpful. Fortunately, when processing model still has a problem, CAD program is

the alternative ways to produce model structures.

In this study, creating initial model structure has been done in AutoCAD, the IGES file has been

created and has already transferred into Gambit. Processing geometry in Gambit has need through the

guideline or using the tutorial of importing and cleaning up the dirt geometry in order to have a right

way in developing. In general term of Gambit procedure, it can be summarised about importing IGES

file in the following item below:

• Importing an IGES file

• Connecting edges, using manual and an automatic method

• Merge face

• Creating a triangular surface mesh, or others

• Mesh a volume with a tetrahedral mesh or using different volume mesh

• Prepare the mesh to be read into Fluent 5.

In term of importing and cleaning geometry, there are strategies of how to dealt with and

passed through the pre-processor (Gambit) before solved by the Solver (Fluent 5). Creating a fully

unstructured tetrahedral mesh around a China hat as an example problem in Gambit, firstly the model

geometry imported as an IGES file.

The tutorial will be guided the step that would typically follow to prepare an imported CAD

geometry for meshing. It is the geometry “dirty” that is needed to clean up the geometry using the

tool available in Gambit. A very obvious tutorial guided how to do the right thing fixed the gap

automatically either during mesh importing or subsequently by means of the “connect edge”

command.



Fig.3.13 Arranged model generated, domain, and floating element (tetrahedral)

The original CAD geometry is not modified during the fixing process; the modifications

required to eliminate the gaps are made using ”virtual” geometry. Some edges in the original

geometry are very short and will be eliminated using the “vertex connect” command. Other edges are

not automatically connected, because they are farther apart than the specified tolerance, it is needed to

connect such edges manually.

The imported geometry includes a number of small surfaces, the edges of which may

unnecessarily constrain the mesh generation process. Using the “merge faces” command, GAMBIT

allows to easily combined these surfaces prior to meshing. It can then have GAMBIT automatically

create a triangular mesh on the China hat model, it can be seen in figure 3.13 B. Since the imported

geometry consists only of the China hat, it is need to create a suitable domain around the China hat

model structure in order to conduct a CFD analysis (this is loosely equivalent to placing the structure

in a wind tunnel)(fig.3.11). The remainder of the tutorial shown how to add a real box around the

structure, use virtual geometry to create some missing faces, and finally stitch all faces together into a

A B

C

D



single volume. This volume can then be meshed (without any decomposition) using a tetrahedral

meshing scheme or using another suitable mesh volume. (Fig. 3.13A-D)

Fig.3.14 Arranged position of inlet, outlet and wall boundaries in AutoCAD

The next attempt in Gambit process

is set a boundary type to the domain

in which condition flow to be

specified. In order for the mesh to be

properly transferred to Fluent, the

edges must be assigned boundary

types, such as wall, inlet, outlet, etc.

In this general example, velocity inlet

created on the tunnel

where moving air while other side of tunnel as the outflow and mostly of all side of tunnel is wall or

only two side of tunnel is wall with free edges on the top. Figure 3.13 show the boundary or vicinity

requirement so that when model structure completely passed through the examination in this process,

the mesh developed can be appreciated by the Fluent. Finally, once the boundary type has been set,

the mesh is ready to transfer to the Fluent (solver). In the main Gambit window, the command is File

�Export�Mesh�Accept.

3. Solver: Fluent Reviews

Starting Fluent 5, firstly need to define as 3D base in order to specify the 3D environment

identification, which is same orientation developed in the previous process. The next step is

defining viscous model and fluid properties. In the main Fluent window, that is

Define�Models�Viscous. Laminar is a default viscous model have got, if it was intending to

solve a turbulent flow, then another turbulence models such as k-epsilon, Reynolds stress and

Large Eddy simulation can be selected. Then, material fluids need to define whether is default or

define as a special ‘custom’ of fluid material to be selected.

Boundary condition of zone will be identified as default automatically by this programme.

In the main Fluent window, that is Define�Boundary condition�Set. When it is continued the



example problem above, boundary conditions will appear as zone identified that are velocity inlet

zone, wall zone and outflow zone. In order to update the velocity inlet motion, it is allowed a

value data entry to be set. The next term of Fluent solution is iterative solution for flow field, in

the main Fluent window, the following command step is Solve�Controls�Solution. Iterative

solution of the governing conservation equations is the important part due to the non-linearity of

equations must be solved until the iterative process is converges. Final solution can be recorded

by using residual monitor available in order to judge convergence behaviour on graph of residual

against iteration numbers. During iteration, time to be consumed that are depend on how the

simple or complex problem have. It is long time to be consumed when such as turbulent model

solved due to more complex governing equation developed. Once the iteration has convergence,

how the solution is progressing can be checked. In the main Fluent window, Display�Velocity

Vectors/Contour�Pressure�Pressure coefficient�Display. The graphical display window will

show the velocity vectors or contour of pressure coefficient, zooming needed to view the velocity

field in more detail if desired.

In Fluent, data resulted as graphical and diagram. Simple command direction File�Hardcopy,

the data can be obtained. The default graphics display window on the screen shows plots with a black

background and colored objects (foreground). At this point, to preview the hardcopy, Preview, which

is the desired case for hardcopy printouts. 4. Post-processor

As an explanation before by Versteeg and Malalaseker, other facilities may also included in order

to manipulate the dynamic result display into an addition graphical. As in many other programme

graphics output capabilities, thus can be connected to CFD codes, which have revolutionised the

communication of ideas to the non-specialist.

Once the graphical has been resulted on Fluent, its mean processing of the whole step

development of the numerical methods are nearly finished. Graphical data and diagram can be simply

obtained from Fluent. It is simple to command (File�Hardcopy), the data can be printed out directly

to printer. There are several types of file association can arranged the dynamic graphical in order to

present data properly. In this study, graphical and diagram data saved as a format file under GSview

programme. In order to organise data graphical and diagram into a different format file, the graphical



as well as diagram can be saved as EPS or PS format with colour postscript based development. It is

as an alternative procedure to produce graphical format on project report or any journal.

It is a procedure review done due to the availability of programme and in order to make smooth

transfer into different programme rather than to printout directly from Fluent or Unix cluster. A

difficult arrangement established on these programme during presenting graphical and diagram data

on paper. However, there are impressive format graphical and diagram presented directly on

computer monitor display.

3.4 Detail Of Model Experimental

In this study, pursued numerical simulation of tensile membrane structures are developed in

CFD simulation as an engineering tool presented wind tunnel. The model structures generated are

placed on tunnel model of computational domain. The main structures models developed are sphere,

and cooling tower. Those models are presented a basic shape of fabric membrane structures. The

model represented variations of structures that consist of cable suspended roof that support fabric

membranes. The structures shape models have chosen due to the needed to compare, the result of

CFD methods to the published data available of the previous research.

At the first stage of the project, it was planned to solve the common specified problem in

wind engineering by CFD methods that adopted as a computational model of a low-rise building with

sphere and cooling tower model developed. (Figure 3.15.a & b).

Fig. 3.15. a Sphere Elevation

Fig. 3.15. b Cooling Tower Elevation

In this study, position of the velocity inlet, the wall and the outflow are arranged such as

described below. These pattern of outflow/outlet boundaries are placed at 20 times the height of

the obstacle (20 H) which was the same as in experiments performed by Tamura, cs. This distant

is long enough in order to avoid the possibilities that the flow reached the range across a wake

region with recalculation which my lead to measurement error. The typical velocity inlet was



placed at 10 times the height of model (10H), while the wall can be arranged between 7H and

10H that are depended on the amount of volume element generation needed. It is important

because of the limitation of space disk on the computer availability. The bigger domain have, the

bigger quota space disk needed. The top wall was also placed at 10 times height of model (10H).

Somewhat further conditions that the outlet boundary is placed at least at 10H as the typical

literature reviewed before (fig. 3.7). However the outlet boundary placed much longer than 10H

downstream of the last obstacle to give accurate result.

Fig. 3.16 Computational domain development

The model detail preparation was adopted as a computational model of a low-rise building

with sphere and cooling tower model developed. Each of the basic models has been modified as a

multiple model. There are several model involved including combination of each member that is

described below:

3.4.1 Single Cooling Tower Model



This model was adopted from the

original Heler type dry-cooling tower.

The model developed is simple shape

rather than the real one with other

component such as the water pipes,

radiator, support beam, etc. It is because

the shape of it is nearly the same as the

requirement of the fabric membrane

Fig. 3.17 Sketch of Heler-type dry cooling tower (De1.igs of IGES file)

structures shape. The other reason is the needed of published data availability to compare with the

further result. In this particular case, the model was arranged to the same shape and dimensional to

the model developed in the experimental method (wind tunnel). It is because much easier to make

model in AutoCAD and exported to Gambit. Providing model in the experimental method more

difficult or need time to spend. Once the model has developed in the experimental or in wind tunnel

test, the shape model can be are developed the same as the model in wind tunnel test immediately.

The cooling tower model was measured as height (H = 16 cm), the top diameter (D2 = 10.5

cm), and the bottom structures (D1= 20.5 cm). Creating geometry in CFD was selected as a default of

measurement in meter. Again, it is more useful to make model in small scale in order to reduce the

space disk consumed. This model was modified into smaller scale in CFD, that was made as H=1.6

m, D2=1.05m and D2=2.05m, respectively.

Fig. 3.18 Internal count space

The cooling tower has divided into 6 (six) surfaces with every

connection have a rib. This model was used 6 ribs and 1cover on the

top, while there is no surface on the bottom. (Figure 3.17). A part of

cooling tower geometry includes a number of small surfaces will be

generated as constrain the mesh generation process as figure 3.18.

Using the “merge faces” command, GAMBIT allows to easily combining these surfaces prior to

meshing. In GAMBIT, then automatically create a triangular mesh on every surface of the model, in

figure 3.18.



x

z

y

Fig. 3.19 Domain of Single Cooling Tower

In this particular case, there are domain

developed, which is based on the height of

model situated in the suitable place. The

dimensional of domain developed is 48 x

22.4 x 16 with unit a long x direction as the

length, y direction as

wide and z direction as the height of domain respectively. For the study of cooling tower, the

computational region developed is shown in figure 3.20. Beside of that is only half of

Fig. 3.20 Computational region and coordinate system.

the field simulation can present

the whole simulation. However,

in this study the whole body of

model simulation involved in

order to know the pressure

pattern distribution in fully

three-dimensional. In CFD

method the capacity and

capability of computer is

absolutely needed. In this case,

because of the limitation capacity of disk space quota at about 128-140 MB and the speed limit of 128

MB RAM, relatively small grid number of mesh generated. The grid number for the cooling tower

simulation is 30 x 10 x 20, i.e. 30 grids in the main flow direction, 10 grids along the circumference

of the tower and 20 grids in wide direction. 3.4.1. Detail Procedure and Instruc3.4.1. Detail Procedure and Instruc3.4.1. Detail Procedure and Instruc3.4.1. Detail Procedure and Instruction:tion:tion:tion: In this report is a procedure that enables to solve 3-D of cooling tower in flow problem with

the CFD program, Fluent. In this stage, the notation should already be familiar with used in this

module, or can be described in the learning module, Fluent and Gambit-General Information.

Log on and launch Fluent:



1. Log onto one of the UNIX cluster computers. It is useful completed the Gambit learning

module for generating the grid.

2. To begin Gambit and Fluent from the UNIX % command prompt: Fluent. nit

3. To start working in Gambit, type: gambit De1-dev x11

Note: De1 is the example case of the cooling tower problem.

4. From main menu, specified Fluent 5 is the base of solver.

Read the grid points and geometry of the cooling tower (in Gambit); used importing and cleaning up model design procedure.

1. Selected a solver (Fluent 5)

2. Imported the IGES file from AutoCAD as the import source of the developing cooling tower

geometric: File �� Import �� IGES

3. Selected the cooling tower model (De1.igs) in the files list.

4. Checked the connectivity-based in colouring geometry: Specify colour mode.

Note: Since the models were already arranged on AutoCAD that is can be reduced and eliminated

the short edges depend on the knowledge on the model developed. If it is needed to eliminate very

short edges, there are connection facilities available: Geometry �� Edge �� Connect/Disconnect

edges. Since, there is no problem the connection between vertex and the sort edges, the step

process can be continued.

5. Created a surface mesh on the face of the cooling tower body: Mesh �� Face �� Mesh Faces.

In this case, mash faces developed on model is triangular element of pave type generation

with 10 interval count spacing, shown in figure 3.18.

Fig. 3.21. Surface mesh on rear of cooling tower

Note: the surface

mesh of model body

can be removed from

display in order to

make easier to see in

the next steps.



6. Created a brick around the cooling tower body: Geometry �� Volume �� Create volume. The

width (x) =48, depth (y) =22.4, and height (z) =16, shown in figure 3.19.and 3.22.

Fig. 3.22 Brick and Cooling tower

7. Removed unwanted geometry: Geometry �� Volume �� Delete Volumes.

8. Created straight edges on one of the line nearly to the bottom of model: Geometry �� Edges

�� Split/merge edges. Two times performed split of the nearly line in order to make another

surface connection between the model and the domain developed. Create straight edges

between two point/vertex: Geometry �� Edge �� Create Edge (Fig.3.22)

9. Created faces at the bottom wall plane, where the model is mounted: Geometry �� Face ��

Form face. Once the face can be made, the face creations need to be verified: Geometry ��

Face �� Summarize/query faces/total entities.

10. Created volume: Geometry �� Volume �� Form volume. It can be applied in the stitch faces

form to accept the selection of the faces to create volume.

11. Created mesh the edges: Mesh �� Edge �� Mesh Edges. The mesh created on the faces of the

cooling tower is used a fine mesh and for the volume, more coarse mesh created. This can be

done by instructed the Gambit to gradually change the mesh density between the coarse and

the fine meshes. Its mean, to specify the distribution of nodes along the some edges in the

geometry.

12. Created mesh the volume: Mesh �� Volume �� Mesh Volumes. The tetrahedral or hybrid

from the elements option menu under schema in the mesh volume form of Tgrid was selected

with interval count at 30.

13. Examined the volume mesh: Examine mesh. It can be identified mesh volume created, aspect

ratio, how many nodes created and the skew of floating element volume created. The 3D



element or mesh volume can be evaluated of 111841 mesh volume and creating 23738 nodes

developed with 1: 4 of aspect ratios.

Fig. 3.23 Elements within a specified quality range of 0.6 upper and 0. 7 lower ratios

14. Set Boundary Types: Zones �� Specify Boundary Types. It is defined the velocity inlet zone

in the surface of entry boundary, the outflow zone in the surface of exit boundary and the rest

is wall or free boundary. (Fig. 3.20.)

15. Exported the mesh and saved the session problem: File �� Export �� Mesh ��Accept. To

save the current session: File � Exit (Gambit asked whether the session will be saved or not)

Read the grid points and geometry of the cooling tower in flow domain (in Fluent):

1. Selected File��Read ��Case. In Select File, select De1.msh from the listing of available files

shown, then OK. Fluent will read in the grid geometry and mesh that was previously created

by Gambit. Some information is displayed on the main screen. If all went well, it should give

no errors, and the word Done should appear.

2. Verified the integrity of the grid: Grid�� Check. Look for any error messages that indicate a

problem with the grid. If the grid is not valid, it will have to return to Gambit and regenerate

the grid.

3. Look at the grid: Display �� Grid ��Display. A new window opens up showing the grid. If

this window is too big, rescale it by dragging the edges of the window. It is best if the

graphical display window is small enough that both it and the Fluent window are both visible

simultaneously.

4. The graphical display can be zoomed-in or zoomed-out with the middle mouse button.



Define the boundary conditions:

1. In Fluent, Define ��Models ��Viscous. Laminar flow is the default and the further

investigation will also provided Turbulent flow calculations, where both of model flows are

specified in Fluent. ��OK.

2. The boundary conditions need to be specified. In Gambit, the boundary conditions were

declared, i.e. wall, velocity inlet, etc., but actual values for inlet velocity, etc. were never

defined. This must be done in Fluent. In Fluent: Define �� Boundary �� Conditions, and a

new Boundary Conditions window will pop up.

3. In Boundary Conditions, selected name of velocity inlet or whatever named, which is the left

side of the computational domain. �� Set.

4. In Velocity Inlet, change Velocity Specification Method to Magnitude and Direction. Change

Velocity Magnitude to 1 m/s. ��OK.

5. The fluid needs to be defined. In Boundary Conditions, select fluid, and Set. The default

fluid is air, which is the fluid we desire in this problem. Select air as the Material Name in the

Fluid window, and ��OK.

Note: Defining �Material is the air as the default material name with default the density of 1.225

(kg/m3) and viscosity of 1.7894 x 10 –5 (kg/m-s). Leave the Materials window.

6. Return to the Boundary Conditions window. The default boundary conditions for the wall and

the outflow are okay, so nothing needs done to those

7. Finally, Close the Boundary Conditions window.

Set up some parameters and initialize:

1. In Fluent: Solve ��Initialize ��Init. The default initial values of velocity and gage pressure

are all zero. The convergence can be sped up slightly be giving more realistic values of the

initial velocity distribution. Apply, Init and Close.

2. As the code to monitor iterates, "residuals" are calculated for each flow equation. These

residuals represent a kind of average error in the solution - the smaller the residual, the more

converged the solution. In the main window, Solve �� Monitors ��Residual. In Residual

Monitors, turn on Plot in the Options portion of the window. The Print option should already

be on by default. Here, Print refers to text printed in Fluent, and Plot causes the code to plot

the residuals on the screen while the code is iterating.



3. The convergence criteria need to be set. In Fluent, Solve��Iterate to open up the Iterate

window. The Number of Iterations can be predicted into small or big numbers depend on the

model developed. For Laminar flow problem, iteration set up to 250, and for the Turbulent

flow problem the iteration set until 1600 and ��Iterate. The main screen will listed the

number of the residuals after every iteration, while the graphics display window will plot the

residuals as a function of iteration number. It can be seen in figure 3.24 (laminar) and 3.25

(turbulent).

4. Once the convergence criteria of the iteration has archived, the graphical and diagram data

can be exploited in order to collect the target data. Since there are several measurements can

be obtained, the only criteria of suitable data has been selected, and collected as a report

project. It is because the relevant issue such as of pressure coefficient is the significant data

targeted. In Fluent: Contour �� Pressure �� Pressure Coefficient �� Display. In this stage,

graphical contour and plot of diagram can be collected. The result selected can be printed out

directly to the printer or can be saved as a variety of file format desired. In this study, the

pressure coefficient contour as well as the diagram has saved in .EPS format in order to link

with the other post-processor programme.



Fig. 3.24 Plot the residual of laminar flow and number iteration converged at 118.



Fig. 3.25 Plot the residual of turbulent flow and 427 number iteration converged

3.4.1. B The Result of the Laminar Flows of Cooling Tower



Fig. 3.26.a Pressure coefficient contour of the whole body from the top of plan (Coded De1)

Fig. 3.26.b Pressure coefficient contour of the whole body from side elevation



Fig. 3.26.c Diagram pressure coefficient in distance position of the model to the sources.



Fig. 3.26.d Pressure coefficient contour occurred at z = 0.2 H ~ 32 m (Plane-5)

Fig. 3.26.e Diagram pressure coefficient at z =0.2 H ~ 32 m (Plane-5)



Fig. 3.26.f Pressure coefficient contour occurred at z = 0.45 H ~ 72 m (Plane-6)



Fig. 3.26.g Diagram pressure coefficient at z = 0.45 H ~ 72 m (Plane-6)

Fig. 3.26.h Pressure coefficient contour occurred at z = 0.7 H ~ 112 m (Plane-7)



Fig. 3.26.i Diagram pressure coefficient at z = 0.7 H ~ 112 m (Plane-7)

3.4.1. C The Result of the Turbulent Flows under Large Eddy Simulation

(LES) of Cooling Tower





Fig. 3.27.f Pressure coefficient contour occurred at z = 0.45 H ~ 72 m (Plane-6)



Fig. 3.27.g Diagram pressure coefficient at z = 0.45 H ~ 72 m (Plane-6)





3.4.2 Multiple Cooling Tower model

This model was also

adopted from the original

Heler type dry-cooling tower,

which was tight together of

four cooling tower with

connection in between, figure

3.28. This shape is

developed is because the

inspiration of the shape of

tent that nearly has the same

curve as the domination of



the fabric membrane

structures, figure 1.2.

Fig. 3.28 Sketch of Multiple Cooling Tower (De5.igs of IGES file)

The cooling tower model was measured as height (H = 13 cm), the top diameter (D2 = 7 cm each),

and the bottom structures (D1= 22 cm).

This model geometry was modified in CFD with was selected as a default of measurement in

meter. It is smaller scale developed that was made as H=1.3 m, D2=0.7m and D2=2.2m, respectively.

This multiple cooling tower has also divided into several surfaces with every connection has a rib.

This model was used 6 ribs and 1cover on the top, while there is no surface on the bottom. (Figure

3.17). A part of cooling tower geometry includes a number of small surfaces will be generated as

constrain the mesh generation process as figure 3.18. The domain developed was based on the

height of model

x

z

y

Fig. 3.29 Domain of Multiple Cooling Tower

situated in the suitable place. The

dimensional of domain developed is 39 x

18.2 x 13 in unit with along of x direction as

the length, y direction as wide and z

direction as the height of domain

respectively.

For this investigation, the computational region developed is typically as shown in figure 3.20. The

grid number for the cooling tower simulation is 35 x 10 x 25, i.e. 35 grids in the main flow direction,

10 grids along the circumference of the tower and 25 grids in wide direction. Detail procedure and

instruction was typical information to be described start from page 71 above.



Recapitulation to read the grid points and geometry of the multiple cooling tower (in

Gambit) can be described in figure scheme below with the same procedure in importing and

cleaning up model design.

Fig. 3.30. Grid mesh generating of imported file IGES from AutoCAD in Gambit.

��

Fig. 3.31. Surface mesh on rear of multiple cooling tower

Creating a brick around the multiple cooling tower body of the width (x) =39, depth (y) =18, 2, and

height (z) =13, can be described below in figure 3.32.

Fig. 3.32 Brick and Cooling tower


Examining the volume mesh is part of evaluating the reliability of element developed. It can be

identified mesh volume created, aspect ratio, how many nodes created and the skew of floating

element volume created. The 3D element or mesh volume can be evaluated of 34683 meshes volume

and creating 162937 nodes developed with 1: 7 of aspect ratios, which domain developed as 4 wall, 1

velocity inlet and 1 outflow. There is different meshes volume developed when the domain is as 3

walls, 1 velocity inlet and 2 outflows. The meshes volume developed is 29765 elements and 15042

nodes with aspect ratio of 1:7.

By defining Velocity Inlet Magnitude typically at 1 m/s and the material air with default the

density of 1.225 (kg/m3) and viscosity of 1.7894 x 10 –5 (kg/m-s), then the Fluent will processed the

flow problem Typical process has been applied as well to process iteration prediction into a numbers



depend on the model developed. Typical Laminar flow problem, iteration set up to 250, and the

Turbulent problem iteration set until 1600. After process, numbers of iteration of the laminar is 104

and 308 iteration for turbulent

The graphical and diagram data can be exploited, since the convergence criteria of the iteration

have archived. There are several data and graphical measurement obtained with the only criteria of

suitable data selected, and collected. The relevant issue to wind loading is pressure coefficient is the

significant data targeted, that described below:

3.4.2. A The Result of the Turbulent Flows under Large Eddy Simulation (LES)

of Multiple Cooling Tower

Since the turbulent flows have the opportunity to present more promises result of the relevant

pressure coefficient issue, so that the result of turbulent flows under Large Eddy Simulation (LES)

presented. In this case, all the result as graphical

Fig. 3.34.a Pressure coefficient contour of the whole body from the top of plan



Fig. 3.34.f Pressure coefficient contour occurred at z = 0.45 H ~ 58.5 m (Plane-6)

Fig. 3.34.g Diagram pressure coefficient at z = 0.45 H ~ 58.5 m (Plane-6)




3.4.3 Single Sphere Model

This model was

adopted from the original

domes as the arched roof

based on the Maher and

Blessmann. The shape

developed is the basic of

domes structures inspiration,

which is used to be a fabric

membrane structures, figure

3.35. This model is a circular

dome rising directly from the

ground with y/d = ½.

Fig. 3.35 Sketch of Single Sphere (De3.igs of IGES file)

The sphere model was measured as height, y or H = 7.5 cm, and diameter of bottom structures is D =

15 cm. Another model of circular dome formatted as y/d =1/4 and y/d =1/6 are also developed, which

are presented in Appendix 3.

The model geometry was modified in CFD with was selected as a default of measurement in

meter. A smaller scale developed of H=0.75 m, and D=1.5m, respectively. The single sphere has

divided into 8 (eight) surfaces with every connection have a rib. The surface of the sphere is known

as smooth domes in the field of researcher. In this term, the geometry developed is involved small

interval (10 interval meshes) of surfaces will be generated as constrain the mesh generation process as

similar prospect in figure 3.18. The domain developed was based on the height of model, which is

situated in the suitable place.

The dimensional of domain

developed is 22.5 x 10.5 x 7.5 in

unit, which are long x direction as

the length, y direction as wide and z

direction as the height of domain



x

z

y

Fig. 3.36 Domain of Single Sphere.

respectively.

The computational region developed is typically as shown in figure 3.20. The grid number for the

single sphere simulation is 35 x 8 x 20, i.e. 35 grids in the main flow direction, 8 grids along the

circumference of the tower and 20 grids in wide direction. Detail procedure and instruction was

typical information to be described start from page 71 above.

Recapitulation to read the grid points and geometry of the single sphere (in Gambit) can be

described in figure scheme below with the same procedure in importing and cleaning up model

design.

Fig. 3.37. Grid mesh generating of imported file IGES from AutoCAD in Gambit and already meshed on rear of sphere surface.

��

Fig. 3.38. Brick and Sphere

Creating a brick around the multiple cooling tower body of the width (x) =22.5, depth (y) =10.5, and

height (z) =7.5, can be described above in figure 3.38.



Fig. 3.39 .The mesh developed on domain.


To evaluate the reliability of element developed the volume meshes need to be examined. The

examining identified the mesh volume created, aspect ratio, how many nodes created and the skew of

floating element volume created. The 3D element or mesh volume can be evaluated of 120838

meshes volume and creating 25504 nodes developed with 1: 4 of aspect ratios, which domain

developed as 4 wall, 1 velocity inlet and 1 outflow. There is different meshes volume developed when

the domain is as 3 walls, 1 velocity inlet and 2 outflows. The meshes volume developed is 25519

elements and 120909 nodes with aspect ratio of 1:4.

Typical process has been applied as well to process iteration prediction set up to 250 for laminar

flow and set up 1600 iteration for turbulent problem flows. The result is 88 iteration for laminar and

470 iterations for turbulent problem. Velocity Inlet Magnitude defined at 1 m/s and the material air

with default the density of 1.225 (kg/m3) and viscosity of 1.7894 x 10 –5 (kg/m-s), then the Fluent will

processed the flow problem

The graphical and diagram data can be obtained since the convergence has been archived. Several

data and graphical measurement collected that is described below:



3.4.3. A The Result of the Turbulent Flows under Large Eddy Simulation (LES)

of Single Sphere




3.4.4 Multiple Sphere Model

This model was

arranged of four single

spheres that are tight

together. In this particular

case, the geometry of multi

sphere developed is inspirited

by the tensile structure and

portable structure published

literature. The shape

developed is among of the

four sphere is model of

circular dome rising directly

from the ground with y/d =

½. That is created as fabric

membrane structures, (figure

3.42)

Fig. 3.42 Sketch of Multiple Sphere (De4.igs of IGES file)

The multiple sphere model was measured as height, y or H = 7.5 cm, and diameter of bottom

structures is D = 25 cm.

The model geometry was modified in CFD with was selected as a default of measurement in

meter. A smaller scale developed of 1/10 of the real model that is H=0.75 m, and D=2.5m,

respectively. On every single sphere has divided into 8 (eight) surfaces with every connection has a

rib. In Gambit process, the geometry developed is small interval (10 interval meshes), which the

surfaces generated as constrain the mesh generation process as similar potential in figure 3.18. The

domain developed was based on the height of model, which is situated in the suitable place.

The dimensional of domain developed is the

same as the single sphere due to the same

height that is 22.5 x 10.5 x 7.5 in unit,

which are long x direction as the length, y



x

z

y

Fig. 3.43 Domain of Multiple Spheres.

direction as wide and z direction as the

height of domain respectively.

The computational region developed is typically as shown in figure 3.20. The grid number for the

single sphere simulation is 35 x 10x 25, i.e. 35 grids in the main flow direction, 10 grids along the

circumference of the tower and 25 grids in wide direction. Detail procedure and instruction was

typical information to be described start from page 71 above.

Recapitulation of the grid points and geometry of the multiple spheres (in Gambit) with the same

procedure in importing and cleaning up model design can be described in figure scheme below:

Fig. 3.44. Grid mesh generating of imported file IGES from AutoCAD in Gambit

��

Fig. 3.45. Surface mesh on rear of multiple cooling tower

Creating a brick around the multiple cooling tower body of the width (x) =48, depth (y) =22.4, and

height (z) =16, can be described below in figure 3.39.

Fig. 3.46. Brick and Sphere




The examining identified of the mesh volume created were evaluated 163452 meshes volume and

34763 nodes developed with 1: 4 of aspect ratios, which domain developed as 4 wall, 1 velocity inlet

and 1 outflow. There is different meshes volume developed when the domain is as 3 walls, 1 velocity

inlet and 2 outflows. The meshes volume developed is 162937 elements and 34683 nodes with aspect

ratio of 1:4.

Typical process has been applied as well to process iteration prediction set up to 250 for laminar

flow and set up 1600 iteration for turbulent problem flows. The result is 99 iterations for laminar and

error result in iterations for turbulent problem. Velocity Inlet Magnitude defined at 1 m/s and the

material air with default the density of 1.225 (kg/m3) and viscosity of 1.7894 x 10 –5 (kg/m-s), then

the Fluent will processed the flow problem

The graphical and diagram data can be obtained since the convergence has been archived. Several

data and graphical measurement collected that is described below:

3.4.4 .a The Result of the Turbulent Flows under Large Eddy Simulation (LES)

of Multiple Spheres




In this particular case, the result of laminar flows problem can be described in Appendix

3. In addition, one example of turbulent flow problem (RAN) has also been investigated. For

further detail, all result from CFD method can be described in Appendix 3 and any other reason

for this decision can also drawn in the summary of this study.



Chapter 5. Conclusion

5.1 Introduction

Four scale models were constructed, and wind load testing of these models have been

observed regarding the behaviour of fabric membrane structure including two models as an

additional test. The conclusion drawn from observations will be summarized below, along with

recommendations for further research.

5.2 Wind Tunnel Testing

Unfortunately, wind tunnel testing cannot be done; it is because a non-popular reasons

that the technician and specific tools are not available during the period time. Those models

promised to test in wind tunnel at that time, then such as a problem came up before testing.

1:1000 scale model was already constructed, however it doesn’t complete with the requirement of

model such as maintaining the pressure taps. The technician was not available is a real problem to

avoid testing. Fortunately, published data available led to a number of observations regarding the

behaviour of wind load to these structures. In this particular case, data of wind tunnel test has

completely been replaced and the published data available represented wind tunnel study.

5.3 Wind loading test by CFD method The numerical investigation of wind load testing on CDF method indicated that the

general nature of the pressure and suction distributions on the model were obtained. In this

particular case, the advantages of CFD method applied wind load to fabric membrane structure

rather than to solve the dynamic fluid behaviour of wind problems.

However, various flow model problems have been tried such as laminar and turbulence to

the model structures. These current statuses of flow model applied in order to recognise a better

result can be obtained. Laminar flow problem has been applied to the all model structures as a

default in Fluent or solver CFD. Reynolds Number simulation (RANS) has been tried in sphere

model only in order to compare to other simulation model. The latest model simulation has been

tried is the dynamic Large Eddy simulation (LES).



5.3.1 Comparison reliability between Laminar and Turbulent problem flow model in

CFD method

The results of these methods are more concern in predicting pressure coefficient, which is

useful for the wind load to the structure. Eventually, many parameters can be observed in this

area related to the result of CFD method such as velocity, dynamic and static pressure, and other

behaviour of wind load to the structures.

The result has been compared between the laminar and the turbulent model. More specific

comparison has been done to the laminar simulation model, RANS model and the LES model.

From the three models simulation involved, the dynamic Large Eddy simulation (LES by

Smagorinsky & Lilly’s) model indicated has a better result obtained. The laminar model offered

the worst result in every stage investigation, however there is not take for along time to get the

result when it running the iteration. On average, RANS and LES model need time consumed

longer than in laminar model. It is depend on the capacity of computer has been used. This result

can be proofed and observed in many other area studies. The results are indicated have agreement

to earlier studies and indeed are supported by the researcher whom concerned to this problem.

5.3.2 Comparison between published data and CFD method study of wind loading to

fabric membrane structure.

Fabric membrane structures model has been developed in several shape model that are

sphere, shape model as a cooling tower and tandem model or combination on each the basic

model. The single sphere and single cooling tower shape model are similar to the model

developed on the earlier study. Published data by Maher on domes model and ASCE 1987 on

cooling tower replaced data wind tunnel testing on model fabric membrane structure.

The numerical experiment on CFD method gives good opportunity to predict pressure

distribution of wind loading to fabric structure and other parameter required. It is because wide

range capabilities belong to the CFD and it is quite easy to develop model desired. It is also more

application programme has already link with the CFD such as AutoCAD program, in order to

make it easy to develop model.

The pressure coefficient distribution that obtained from the CFD methods has agreed to

the published data available, particularly on domes and cooling tower model. Very close value of

maximum positive Cp = + 0.621 by dynamic LES turbulent method to the Cp = +0.6 (Maher’s



dome study of h/D =½). Maximum Cp at the centre of dome of by CFD is Cp = –1.2 and Maher

has Cp = -1. Pressure coefficient on various h/D values such as ¼ and 1/6 has also been observed

that indicated similar argue to the published data.

Mean and fluctuating pressure distribution on cooling tower by the CFD has also

indicated good agreement to the ASCE published. The maximum value of pressure coefficient

(positive Cp = + 0.965) occurred around the throat of cooling tower compare favourably to the

ASCE at Cp =+1.0. The maximum negative Cp=- 1.4 to –1.7 were obtained by CFD that

compared to the Cp = -1.5 by ASCE. This result has smoothly promised prediction on the study,

which led to a number of observations regarding the behaviour of fabric membrane structures.

5.4 General Conclusion and Recommendations

It was good opportunity of CFD method to predict wind loading to the fabric membrane

structures. The result is promised to solve a problem such as wind load acting to the fabric

structure or to other structures. The model developed in CFD is more flexible depend on the

ability of user to make it. Many kinds model structure can be developed easily regarding to the

aims of research study. All of them are such as the advantage of CFD methods presented,

however it is depend on the capability and availability of computer hardware and the software.

As an individual conclusion that this study would probably be replaced the wind tunnel testing to

predict pressure coefficient and other parameters intended. It also may be concluded that many

advantages can be used for other study related to structural engineering.

This investigations have been conducted indicate that additional study of this type needs

to be executed in order to obtain a better understanding to fabric membrane structures. One

aspect that future research should address is the real wind tunnel testing to this type model

structure. It is belief that more confidence study will be presented when wind tunnel studies can

be established.

Appendix 1 In general, fundamental aspect cable mechanics can be illustrated by the treatment of a

weightless string supported at A and B and loaded as shown in figure 1. The moment at a point X in

the cable is given by:

HzMeMxx

−= 1



T5

T1

P3P2

P1

P4

SB

HB

SA

HA

X

Fig. A1.1Funicular curve of a cable loaded with point loads

Moment at any point on cable = 0

H

Mez x= 2

where Mex is the simple bending moment at x.

Consider a string stretched between A and B figure A1. 2. a When load P to a central , it deflects

P

P + P

Fig. A1.2 Load vs. deflection for a taut string

By an amount W1, and the value of the tension in it changes from T1 to

T1+∆ T1.

For the equilibrium of the deflected string,

L

WTTP

1)(4

11∆+= 3

or

24

1T

PLW = 4

where T2 = T1+ ∆ T1

Further loaded with an additional load P, it undergoes a change in tension equal to ∆T2 and a deflection W2 as shown in figure A1.2 b. For the equilibrium of final deflected shape.

L

WWTTP1

)21)((4222

+∆+= 5

or, on substitution of the value of W1 from Eq. 3-4 and rearranging,

)(4

142

22

2

TT

WTPLW

∆+

∆−= 6



Appendix 2

1. Differential Equations of equilibrium

Initial consideration to the equilibrium of a plane element subjected to normal stresses xσ and

yσ , in plane shear stress xyτ (in unit of force per unit volume), and body forces Xb and Yb (in units

of force per unit volume), as shown in figure A2.1

στ

σ

τ

σ σ

σ σ

τ τ

τ τ

Fig.A2.1 Plane differential element subjected to stresses, by

Logan

Firstly, the stresses are assumed to

be constant as they act on the width

of each face, however the stresses

are assumed to vary from one face

to the opposite. xσ acting on the

left vertical face, whereas

dxx

x

x

∂

∂+

σσ act on the right.

Summing forces in the x direction,

0)1()1(

)1()1()1(0

=−

∂

∂+

++−

∂

∂+∂==∑

dxdxdyy

dydxXbxdydydxx

xxFx

yx

yx

yxτ

ττ

σσ

1

Simplifying and canceling term in Eq. 1, obtained

0=+∂

∂+

∂

∂Xb

yx

yxxτσ

2

Summing forces in the y direction

0=+∂

∂+

∂

∂Yb

xy

xyy τσ 3

Three equilibrium equations must be satisfied, when considering only planar element. The third

equation is equilibrium of moments about an axis normal to the x-y plane; taking moment about point

C in figure A2.1.



2

2)1(

22)1(0

dydy

y

dydx

dxdx

x

dxdyMx

yx

yx

yx

xy

xyxy

∂

∂+

−−

∂

∂++==∑

ττ

ττ

ττ 4

Simplifying Eq.4 and neglecting higher –order term yields

yxxy ττ = 5

Considering the three-dimensional state of stress (figure A2.2), which shows the additional stresses

zσ , xzτ and yzτ .

Extended the two dimensional equations 2, 3 and 5 to three dimensions, esulting total set of

equilibrium equations is

0=+∂

∂+

∂

∂+

∂

∂b

xzxyx Xzyx

ττσ

0=+∂

∂+

∂

∂+

∂

∂b

yzyxyY

zyx

τστ

0=+∂

∂+

∂

∂+

∂

∂b

zyzxz Zzyx

σττ 6

σ

ττ

σσ

τ

ττ

τ

Fig.A2.2 Three-dimensional stress element, by Logan

The simplified equation is

yxxy ττ =

zxxz ττ = 7

zyyz ττ =



2. Strain/Displacement and Compatibility Equations

Fig.A2.3 Differential element before and after deformation, by Logan

Considering the differential element shown

in figure A2.3, the un-deformed state is

represented by the dotted lines and

deformed shape is represented by the solid

lines. Considering line element AB in the x

direction, and A’B’ after deformation,

where u an v represented the displacement

in the x and y directions.

AB

ABBAx

−=

''ε 1.1 AB = dx

1.2

22

2)''(

∂

∂+

∂

∂+= dx

x

vdx

x

udxBA 1.3

Evaluating A’B’ using the binomial theorem and neglecting the higher-order term

22

∂

∂

∂

∂

x

vand

x

u, it has

dxx

udxBA

∂

∂+='' 1.4

Using Eqs. 1.2 and 1.4 in Eqs. 1.1, obtained

x

ux

∂

∂=ε 1.5

Similarly, line element AD in y direction is

y

uy

∂

∂=ε 1.6

The shear strain is defined to be the changed in the angle between two lines, such as AB and AD.

From figure A2.2 that the shear strain xyγ is the sum of two angles and is given by

x

v

y

uxy

∂

∂+

∂

∂=γ 1.7



Equations 1.5, 1.6 and 1.7 represent the strain/displacement relationship for in-plane behaviour. For

the three dimensional, a displacement w in the z direction, than becomes straightforward the

additional strain/displacement equation as

z

wz

∂

∂=ε 1.8

x

w

z

uxz

∂

∂+

∂

∂=γ 1.9

y

w

z

vyz

∂

∂+

∂

∂=γ 1.10

For the planar-elastic case, the compatibility equation by differentiating xyγ with respect to both x

and y, and then using the definitions for xε and yε given by Eqs. 1.5 and 1.6 so that:

2

2

2

2222

xyx

v

yxy

u

yxyx

yxxy

∂

∂+

∂

∂=

∂

∂

∂∂

∂+

∂

∂

∂∂

∂=

∂∂

∂ εεγ 1.11

This equation is called the condition of compatibility.

Appendix 3

1. The result of simulation models under laminar flows problem A. Single Cooling Tower (4Wall)

111841 mesh volume Fig. A3.1. a Pressure coefficient contour of the whole body from the top of plan (Coded De1)



23758 nodes element Fig. A3.1. b Pressure coefficient contour of the whole body from side elevation

Fig. A3.1. c Diagram pressure coefficient in distance position of the model to the sources



Fig. A3.1.d Pressure coefficient contour occurred at z = 0.2 H ~ 32 m (Plane-5)

Fig. A3.1.e Diagram pressure coefficient at z =0.2 H ~ 32 m (Plane-5)



Fig. A3.1.f Pressure coefficient contour occurred at z = 0.45 H ~ 72 m (Plane-6)

Fig. A3.1.g Diagram pressure coefficient at z =0.45 H ~ 72 m (Plane-6)



Fig. A3.1.h Pressure coefficient contour occurred at z = 0.7 H ~ 112 m (Plane-7)

Fig. A3.1.i Diagram pressure coefficient at z =0.7 H ~ 112 m (Plane-7)



B. Single Sphere h/D = ¼ (4Wall)

86506 mesh volume

Fig. A3.2.a Pressure coefficient contour of the whole body from the top of plan (Coded De2)

18603 nodes element Fig. A3.2.b Pressure coefficient contour of the whole body from side elevation



Fig. A3.2.c Diagram pressure coefficient in distance position of the model to the sources.

C. Single Sphere h/D = ½ (4Wall)

120838 mesh volume






D. Multiple Sphere (4Wall)

163452 mesh volume




163452 mesh volume






E. Multiple Cooling Tower (4Wall)

229257 mesh volume Fig. A3.5. a Pressure coefficient contour of the whole body from the top of plan (Coded De5)





Fig. A3.5.f Pressure coefficient contour occurred at z = 0.45 H ~ 58.5 m (Plane-6)



Fig. A3.5.g Diagram pressure coefficient at z =0.45 H ~ 58.5 m (Plane-6)





F. Single Sphere h/D = 1/6 (4Wall)

93135 mesh volume






2. The result of simulation models under turbulent flows problem (LES-

Smagorinsky &Lilly) A. Multiple Cooling Tower (3Wall)



112827 meshes volume Fig. A31.1. a Pressure coefficient contour of the whole body from the top of plan (Coded LESDe11)






Fig. A31.1.f Pressure coefficient contour occurred at z = 0.45 H ~ 72 m (Plane-6)



Fig. A31.1.g Diagram pressure coefficient at z =0.45 H ~ 72 m (Plane-6)





B. Single Sphere h/D = ¼ (3Wall)

85392 meshes volume

Fig. A31.2.a Pressure coefficient contour of the whole body from the top of plan (Coded LESDe21)





C. Single Sphere h/D = ½ (3Wall)



120909 meshes volume







E. Multiple Cooling Tower (3Wall)



29765 mesh volume Fig. A31.5. a Pressure coefficient contour of the whole body from the top of plan (Coded LESDe51)





Fig. A31.5.f Pressure coefficient contour occurred at z = 0.45 H ~ 58.5 m (Plane-6)

Fig. A31.5.g Diagram pressure coefficient at z =0.45 H ~ 58.5 m (Plane-6)



F. Single Sphere h/D = 1/6 (3Wall)

92894 meshes volume






3. The result of simulation models under turbulent flows problem (LES-

RANS) A. Single Sphere h/D = ½ (3Wall)


Fig. A32.3.a Pressure coefficient contour of the whole body from the top of plan (Coded RANSDe31)





Diagram Pressure Coefficient of Single sphere h/D=1/2 Model



Pressure Coefficient of Single sphere h/D=1/2 Model Convert to Angle Data



Diagram Pressure Distribution of Single Cooling Tower Model



Pressure Coefficient of Single Cooling Tower Model Convert to Angle Data



Diagram Pressure Distribution of Single Cooling Tower Model around throat of Plane 5 =Z1/H=0.2 =32m



Pressure Coefficient of Single Cooling Tower around throat of Plane 5 =Z1/H=0.2 =32m Convert to Angle

Data



Pressure Coefficient of Single Cooling Tower around throat of Plane 6 =Z2/H=045 =72m Convert to Angle

Data

Predicting Pressure Distributions Using CFD

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