Modelling Vacuum Infusion

University of Pretoria School ofEngineering, the Built Env ironment and Informat ion Technology Department of Mechanical and Aeronautical Engineering MSC 422 2011 Modelling the Vacuum Infusion Process Final Report Grant Stephens Student Number 27040713 Supervisor: Dr N Wilke

Modelling the Vacuum Infusion Process

Abstract

Abstract

The purpose of this project was to model the vacuum infusion process mathematically and compare this to the real world solution. The process is derived for one and a half dimensions, thus it shows the flow as well as height from which other factors like fibre volume fraction can be found. This is needed to determine the strength of a composite. The presented model uses the finite element method with a backwards difference approximation for time to calculate the height in the preform. This has been implemented in a mathematical solver and the height is then compared to the actual results obtained in experiments. The comparison shows some difference in the results gained experimentally and from the model. These differences are explained and possible changes to the experiments are suggested to gain better results.

University of Pretoria - MSC 422

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Abstract

Table of Contents Abstract ..................................................................... ...................................................................... .........i List of Tables ............................................................ ................................................................... ........... v List of Figures .................................................................................. ...................................................... vi List of Code Extracts ...................................................................... ..................................................... vii List of Symbols ......................................................... ................................................................... ........ viii Glossary of Terminologies ............................................................ ........................................................ x 1.

Introduction............................................................... ...................................................................1

2.

Scope of Work ........................................................... ................................................................... 2

3.

2.1.

Theoretical Aspect ...............................................................................................................2

2.2.

Practical Aspect ...................................................................................................................2

Literature Study..................................................................... .......................................................3

3.1.

Background ..........................................................................................................................3

3.2.

Process Description .............................................................................................................3

3.3.

History ..................................................................................................................................4

3.4.

Model Constants ..................................................................................................................5 3.4.1. Permeability ...............................................................................................................5 3.4.2. Viscosity.....................................................................................................................6 3.4.3. Fibre Compaction ......................................................................................................6 3.4.4. Relaxation ..................................................................................................................7 3.4.5. Resin..........................................................................................................................7

3.5.

Boundary Conditions............................................................................................................8

3.6.

Part Thickness .....................................................................................................................8

3.7.

Finite Element Methods .......................................................................................................8

3.8.

Other Models .......................................................................................................................9

3.9.

CFD Software Research ....................................................................................................10

3.10. General Notes on Available Literature ...............................................................................10 4.

Theoretical Investigation...........................................................................................................11

4.1.

Compaction Behaviour.......................................................................................................11

4.2.

Permeability ....................................................................................................................... 11

4.3.

Flow Modelling ...................................................................................................................12


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Abstract

4.3.1. Prefilling ...................................................................................................................12 4.3.2. Filling Model.............................................................................................................13 4.3.2.1. Continuity Equation ........................................................................ 13 4.3.2.2. Implementing Galerkin ...................................................................14 4.3.2.3. Flow Front Velocity Derivation .......................................................16 4.3.2.4. Smaller Derivations ........................................................................ 18 4.3.2.5. Variable Naming ............................................................................19 4.3.2.6. Program Flow Chart .......................................................................20 4.3.2.7. Filling Program Code Extracts .......................................................21 4.3.2.8. Boundary Conditions ......................................................................27 4.3.3. Post-filling ................................................................................................................ 27 4.3.3.1. Model .............................................................................................27 4.3.3.2. Boundary Conditions ......................................................................28 5.

6.

Program........................................................... ................................................................... .........29

5.1.

Verification ......................................................................................................................... 29

5.2.

Validation ........................................................................................................................... 30

5.3.

General Program Notes .....................................................................................................31

Practical Investigation......................................................... ...................................................... 35

6.1.

General Practical Information ............................................................................................35 6.1.1. Composite Laboratory Setup ...................................................................................35 6.1.2. General Experimental Constants .............................................................................36 6.1.3. Stereophotogrammetry ............................................................................................37

6.2.

Model Parameter Tests......................................................................................................38 6.2.1. Compaction Tests ....................................................................................................38 6.2.1.1. Compaction Test Method ...............................................................38 6.2.1.2. Compaction Test Results ...............................................................40 6.2.2. Permeability Tests ...................................................................................................41 6.2.2.1. Permeability Test Method ..............................................................41 6.2.2.2. Permeability Test Results ..............................................................43

6.3.

Infusion Experiments .........................................................................................................45 6.3.1. Infusion Test Procedure ..........................................................................................45 6.3.2. Infusion Test Parameters ........................................................................................46 6.3.3. Infusion Results .......................................................................................................47

7.

8.

Comparison of Ex periments and Model..................................................................................50

7.1.

Comparison Using Exact Experimental Values .................................................................50

7.2.

Fitting Model to Improve Results .......................................................................................50

Conclusionand Future Work ............................................... ..................................................... 53


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Abstract

8.1. Conclusion .................................................................... ..................................................... 53 8.2. Future Work.................................................................. ..................................................... 53 9.

Bibliogra phy .............................................................. .................................................................54

Appendix A- Protocol ............................................................................................ ............................... 6 5 Appendix B- Progress Report 1 ......................................... ................................................................. 57 Appendix C- Progress Report 2 ......................................... ................................................................. 58

Appendix D- Report Card .............................................................. ...................................................... 59 Appendix E- Plaigarism Sheet ............................................................................................................ 60 Appendix F- Least Squares Fit Code................................................................... ............................... 61


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List of Tables

List of Tables Table 4.1. Variable Naming ............................................................................................................................. 19 Table 6.1. Material Constants. ........................................................................................................................ 36 Table 6.2 . Compaction Factors ........................................................................................................................40 Table 6.3. Modified Carman-Korzeny Constants ............................................................................................. 44 Table 6 .4. Infusion Experiemental Parameters ................................................................................................ 46 Table 7.1. Fitted Constants ............................................................................................................................. 51


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List of Figures

List of Figures Figure 4.1. Program Flow Chart ....................................................................................................................... 20 Figure 5.1. Thickness Comparison (Govignon on left, student on right) .......................................................... 29 Figure 5.2. Pr essure Comparison (Govignon on left, student on right) ............................................................ 30 Figure 5.3. Experimental and Theoretical Compar ison ....................................................................................31 Figure 5.4. Newton-R aphson Iterations .......................................................................................................... 32 Figure 5.5. Change in dt as flow progresses .................................................................................................... 32 Figure 5.6. Newton-Raphson Itera tions- Post Filling ....................................................................................... 33 Figure 5.7. Cumula tive Time Passed per Ti me Step ......................................................................................... 34 Figure 6.1. New Composite Laboratory ...........................................................................................................35 Figure 6.2. Vacuum Gauge Pressure Correction .............................................................................................. 36 Figure 6.3. Typical Stere ophotogrammetry Image- Left Camera ..................................................................... 37 Figure 6.4. Typical Stereophotogrammetry Image- Right camera .................................................................... 37 Figure 6.5. Stereophotogrammetry setup ....................................................................................................... 38 Figure 6.6. Stere ophotogrammtry model of compaction ................................................................................ 39 Figure 6.7. Compaction Response. .................................................................................................................. 40 Figure 6.8. Compacti on Comparison ............................................................................................................... 40 Figure 6.9. Per meability Test Setup................................................................................................................. 42 Figure 6.10. Experime ntal Permeability .......................................................................................................... 43 Figure 6.11. Modified Carman -Korzeny Permeability ...................................................................................... 44 Figure 6.12. R esin Inlet.................................................................................................................................... 45 Figure 6.13. T ypical Stereophotogrammetry Layup Image .............................................................................. 46 Figure 6.14. Infusion Calculated Solution Example ..........................................................................................47 Figure 6.15. Effect of Data smoothing ............................................................................................................. 47 Figure 6.16. Cha nge in Height over Preform with Time ................................................................................... 48 Figure 6.17. Point Heights with Time .............................................................................................................. 48 Figure 6.18. P oint Heights wit h Time- Single Point ..........................................................................................49 Figure 7.1. Exact Experimental Values Comparison .........................................................................................50 Figure 7.2. Fitted Compa rison ......................................................................................................................... 51 Figure 7.3. Full Field of Model .........................................................................................................................52


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List of Code Extracts

List of Code Extracts Code Extract 4.1. Variable Initia lization .......................................................................................................... 21 Code Extract 4.2. Function Declarations ..........................................................................................................23 Code Extract 4.3. Meshing Domain ................................................................................................................. 23 Code Extract 4.4. Full Vacuum Initi alization .................................................................................................... 23 Code Extract 4.5. Conditions for full first element ........................................................................................... 23 Code Extract 4.6. Time to fill first element iterating loop. ............................................................................... 24 Code Extract 4.7. Ti me Step Loop .................................................................................................................... 25 Code Extract 4.8. Newton-R aphson Do-Untill Loop ......................................................................................... 26 Code Extract 4.9. vi_solve.m Procedure ..........................................................................................................26 Code Extract 4.10. Changes in B oundary Conditions ....................................................................................... 28


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List of Symbols

List of Symbols Symbol

 ̅  ̅ ̅  ̅()  ̅ ̅                                    ̅   

Name

Unit

Unit Symbol

Capacitance matrix

Meters

m

New iterated height vector

Meters

m

Previous height vector

Meters

m

Mass flow rate

Kilograms per second

kg/s

Stiffness matrix

Complex

Volumetric Flow Rate (Area due to 1D)

Meters squared per

Tangent of stiffness matrix

m /s

second Residual matrix Volume of an element

Meters cubed

Fibre volume fraction

Unit less

Volume of the fibre present in element

Meters cubed

Volume fraction of the compaction test piece

Unit less

Fibre volume fraction under zero compaction

Unit less

m

m

stress The fibre volume fraction of the layup

Unit less

The volume of 10% of the fibre being modelled

Meters cubed

m

The volume of 10% of the layup

Meters cubed

m

Thickness of the element

Meters

m

The height of the fibre being modelled

Meters

m

Preform height under zero compaction stress

Unit less

Length of an element

Meters

m

The length of the part being modelled

Meters

m

Mass of the fibre in an element

Kilograms

kg

Distance between two markers on test setup

Meters

m

Time taken for flow between two markers

Time

s

Volume averaged flow velocity in x direction

Meters per second

m/s

Speed of flow in permeability test

Meters per second

m/s

Velocity of flow in preform

Meters per second

m/s

The width of the part being modelled

Meters

m

Width of the compaction test piece

Meters

m

Value about which Taylor series is cantered

Meters

m

Change in preform height vector

Meters

m

Oil Density

Kilgrams per meters

kg/ m

cubed Area density of the fibre


Kilograms per meter

kg/ m

cubed

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Modelling the Vacuum Infusion Process Symbol

                

List of Symbols

Name

Unit

Unit Symbol

Density of the material from which the fibre is

Kilograms per meter

made

cubed

Compaction stress

Pascal

Porosity

Unit less

Change in porous volume

Meters cubed

m

Permeability

Meters squared

m

Carman-Kozeny Constant

Unit less

Carman-Kozeny Constant

Meters squared

m

Length of element in preform

Meters

m

Pressure

Pascal

Pa

Number of layers

Unit less

Function used in calculation of Local layup thickness

̅ 

kg/ m

Pa

Complex Meters

m

Time

Seconds

s

Cartesian position of length

Meters

m

Cartesian position of width

Meters

m

Cartesian position of height

Meters

m

Resin Viscosity

Pa per second

Pa/s


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Glossary of Terminologies

Glossary o f Terminologies 

CSM

Chopped Strand Mat



RIFT

Resin Infusion under flexible tooling



RTM

Resin Transfer moulding



SCRIMP™

Seeman Composites Resin Infusion Process



VI

Vacuum Infusion



VM

Vacuum Moulding



CFD

Computational Fluid Dynamics



C-K

Carman-Kozeny



N-R

Newton-Raphson


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Modelling the Vacuum Infusion Process 1.

Introduction

INTRODUCTION

Vacuum infusion (VI) is a process by which composites can be manufactured. A vacuum is drawn over the mould and this is the driving force for the resin that is drawn through the mould to the vacuum point. Critical to the success of the mould is deciding the inlet points for the resin and outlet point where the vacuum is drawn. This process is difficult to model as there are many changes, such as part thickness variations, compaction and relaxation, as infusion takes place. The strength of the composite depends largely on the fibre volume fraction in the part and thus a critical outcome of the model is the volume fraction of the part after infusion. There have been numerous other studies and investigations into this field. These studies include specific ones relating only to the resin properties or fibre compaction. There are a number of studies that develop the governing equations for the flow through the preform. This report will show how these equations are implemented in a finite element method to solve the flow and volume fraction in the vacuum infusion process. The model will then be verified using the physical process that is being modelled to determine the accuracy thereof. The purpose of this process is to accurately determine the final part thickness of the mould as this directly influences the strength of the product. With accurate data for the part thickness and an exact flow model, the strength can be calculated and repeatability can be ensured. The report also aims to show that the student has independently learnt about the process and has been able to make decisions using this knowledge about the planned method of solving the problem. Appendix A to E contains all the administrative aspects of the project including the plagiarism form, protocol and progress reports. The attached compact disc contains a PDF version of this report as well as all the other data obtained that has been used in this report.


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SCOPE OF WORK

2.1.

Theoretical Aspect

Scope of Work

The theoretical aspect of this project is to develop and implement a numerical model of the vacuum infusion process. This has been done using a combination of models developed in previous studies that are then be derived into analytical equations that are programmed into a mathematical solver in this case Octave. Existing CFD software has not been used. The program solves for the part thickness and other variables such as volume fraction are then obtained from the height. The program only works for flow in one direction, essentially making the problem 1D, even though the part thickness is perpendicular to this. In literature, this is known as 1½D. 2.2.

Practical Aspect

The practical aspect of the project can be divided into two parts. The first is to determine the constants that will be needed by the theoretical part. These include the permeability, viscosity and any other variables needed to determine them. Other information was also needed such as information on how the fibres compact under the vacuum as well as how much they then expand when the resin flows through them. Using data obtained from the experiments or data found in previous studies relationships between these variables have been set up. The second part of the practical aspect is to validate the program that has been written. This consisted of setting up the process that is being modelled and comparing the results of the theoretical solution to these practical results.


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LITERATU RE STUDY

3.1.

Background

Literature Study

Composite structures are manufactured in various ways, one of these being the vacuum infusion process. Vacuum infusion (VI) uses a vacuum to draw the resin through the laminate; however, it is described in more detail in 3.2 below. Vacuum infusion is known by various names, these include vacuum assisted resin transfer moulding (VARTM), resin infusion under flexible tooling (RIFT), vacuum moulding (VM), vacuum bag moulding and SCRIMP™ (Seeman Composites Resin Infusion Process) (Correia et al., 2004). RTM (Resin Transfer moulding) is the process whereby the resin is driven through the mould by pressure that is applied to the resin. RTM uses a solid mould on both sides of the part whereas vacuum infusion uses a flexible bag over one side of the mould that is pulled onto the fibres because of the vacuum. The advantages of vacuum infusion are numerous and include; high fibre content (up to 70% (by weight) compared to hand-layup of 45%), low void content, increased mechanical strength, fume free, cheaper and complicated structures can be manufactured (Hammami and Gebart, 2000). A number of disadvantages also exist for vacuum infusion moulding. Yenilmez et al (2009) states disadvantages as being thickness variation due to non-uniform compaction pressure and limited ability to achieve high fibre content. The problem of certain sections of the mould being un-wetted or only partially wetted is very prominent, especially in new products where the process is not fully optimized yet. At this point in time, many vacuum infusion processes are set up via trial and error. The resin inlets and vacuum points are often selected by a person with experience in the field. A number of software tools exist to model this flow and thus most of the guesswork has been eliminated. Most components that are manufactured using VI are purely cosmetic due to the variations in part thickness and volume fractions. This results in the properties such as strength not being constant over a number of parts. A model that could accurately represent the VI process would thus make it possible to fully define all the part variables and thus make the process repeatable and possibly usable in structurally significant components. The accuracy of the model is dependent on a number of factors. Each of these is discussed in more detail in sections 3.4-3.4.4 A simple model of the flow through the fibre layup could easily be created; however, accurately defining the process requires these factors must be included in the model. There have been a number of attempts at developing models for the vacuum infusion process, each of these with varying degrees of success. Some of these attempts are discussed in section 3.7. The focus of these models often varies greatly; this is intentional as the model developed in this project hopes to include all the different phenomenon associated with the process. 3.2.

Process Description

Vacuum infusion processes start with laying the fibre on the mould that will form the part. Unlike process such as RTM, VI uses a single sided mould instead of a positive and a negative mould. A large portion of the cost saving occurs because of this fact. Once the fibre has been laid on the mould, it is covered with a layer of peel ply. The peel ply is then covered by a flexible vacuum bag. The peel ply ensures that the reusable parts are easily separated from the consumable ones. The inlet and outlet are selected in such a way that the entire mould will be fully permeated by the resin. They are often made into a line inlet or outlet by a pipe with holes drilled along the length or using a highly permeable substance such as resin distribution tape. The entire layup us surrounded by tacky tape to ensure a good seal with the mould. The outlet usually contains a resin trap before the vacuum pump to ensure that excess resin that goes through the entire mould does not enter the vacuum pump.


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Literature Study

The inlet is then closed and the vacuum switched on. The part of the process will be called pre-filling from hereon. This is to check for leaks in the system before the mould is affected by the resin. An effect of this vacuum being applied to the layup is that it is compressed. This compression is an important factor that affects the permeability of the system. The compression during the pre-filling will be called dry compression from hereon. The compression of the fibres is discussed in section 3.4.3. Once all the leaks have been found and attended to the resin can be allowed to enter the system. This process will be called filling. The resin flows through the layup and is allowed to permeate all the fibres. A number of other processes occur during filling. There is a change in the compaction pressure (3.4.3) as well as a phenomenon called relaxation, which is detailed in section 3.4.4. The flow is modelled successfully by a number of studies (Govignon et al (2010) and Correia et al (2004) for example) using a combination D’Arcy law and the continuity equation. A number of other variations on this method are used (Walsh and Freese, 2005); however, the fundamentals behind the model remain the same. The second last step of the process, which will be called post-filling, is when the resin is once again closed and the vacuum is still applied. The point at which the resin is closed depends on many factors. The resin can be closed before the infusion is complete, the idea being that no resin will be wasted and the resin already in the mould will permeate the entire mould. The other option is to leave the resin on until the entire mould has been permeated before closing the inlet. These two methods are easily solved using the same model as shown by Govignon (2010) and resultant parts vary slightly in thickness. During the post-filling process the compaction stress changes once again (3.4.3) as the excess resin is sucked out of the layup and the final part thickness is established. The final part of the process is waiting for the resin to cure (solidify). To ensure that the part thickness does not change again the vacuum is usually left on the preform. This step is essentially an extension of post filling and all details are covered in post filling. It must however be noted that it is very important that the resin curing time is not shorter than the port filling process as the viscosity of the resin is assumed to be constant throughout the process. 3.3.

History

Williams et al (1996) states that VI has been around since the 1950’s, however a recent interest due to new environmental, health and safety restraints has prompted a renewed interest in the process (Williams, Summerscalest and Grove, 1996). The Marco method (Patented) is considered the first clearly defined method for manufacturing composited by vacuum. The Marco method was initially developed for use in the boat manufacturing process; however, the Group Lotus Car Ltd patented a similar method in 1972. Over time, the process has been renamed and patents have been applied for, however the general principle behind the process has remained the same. In 1994, a slightly different method was developed by DSM Brittles (Williams, Summerscalest and Grove, 1996). This method used two bags on top of each other. The outer bag used a vacuum to apply a compaction pressure to the fibres and the inner bag was used to pull the resin through the layup. This resulted in the ability to compact the layup by different amounts. A number of companies have used female moulds; however, this is dependent on the geometry of the part. Despite this advancements are slow in this process when compared RTM and other resin transfer moulding (Williams, Summerscalest and Grove, 1996).


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Literature Study

There have also been a number of patent applications for parts associated with the process (Williams, Summerscalest and Grove, 1996). These include piping for the resin into and out of the bag, the bag as well as materials to enhance flow through the layup. A number of patented parts that are available to ensure line infusion at the inlet of the system; however, most of the studies simply use pipes with holes drilled along the length or coil wire holders. 3.4.

Model Constants

3.4.1.

Permeability

A major factor affecting the numerical model is the permeability medium in which there is transfusion. Permeability measurement in the vacuum infusion process is not the same as other processes such as the resin transfer process; in fact, it is even more of a problem as opposed to other processes (Hammami, 2002). The obvious factors that affect the permeability are the type of fibre being used, the number of layers in the mould as well as the edge conditions. The permeability of a substance can be defined as the ability of the fibres to transmit fluids. Research into different fibre architectures is another project altogether. There are many different types, ranging from weaves to mats that are made of many different materials. Most of the studies that are referenced in this project use any readily available fibre and do experiments on it to determine constants for that fibre. It is envisaged that eventually standard characteristics for standard fibres would exist, however standards still need to be defined and agreed upon by relevant authorities. Hammami (2002) also notes that a big factor in the permeability measurements is whether it is a point or line infusion. Point infusion means that the resin is introduced via a single point in the mould while line infusion process makes use of a spiral tubing or similar device to introduce resin into the mould along a line across an edge of a mould. Usually the permeability of a substance is determined experimentally. There are a number of problems with this method. The one problem is that the permeability does not vary linearly with the number of layers in the preform as the resin pressure separates the layers slightly and pushes the plastic bag up creating thickness variations. These are discussed in 3.6. The other problem is that the permeability of the resin changes once it is wetted (Hammami, 2002). This would result in a step function for the permeability dependent on whether it is wetter or not. To account for the change in the permeability certain studies (Li et al., 2008) proposed that the change in the permeability was due to a pressure change and hence their relationship was related to the pressure acting on the fibres at different time intervals. Other studies (Govignon, Bickerton and Kelly, 2010) developed equations which accounted for the change in the permeability once the fibre had been wetted by arguing that the volume fraction of fibre had changed hence a change in the permeability. The change in the volume fraction is once again related to the compaction (3.4.3) and thickness variations (3.6). Many studies use the modified Carman-Kozeny (C-K) equation, which is actually for the permeability of a spherical cluster, to establish a relationship between the volume fraction and permeability. D’Ar cy is used to relate the flow velocity to the permeability and pressure. The pressure is related to the fibre volume fraction using the compaction model and thus the volume fraction determines the permeability. This derivation and method is described in detail in section 4.2.


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Literature Study

A completely different approach (Chohra et al., 2006) used micro models of the fibre to determine the permeability. Most fibre arrangements are very complex and thus method would be very expensive in terms of computing time for such models. There is also always an unknown in the system, as two layers of fibre are never perfectly aligned when placed on top of each other so a certain amount of variability is inherent for multiple layer layups. This method could however be very effective in the future when computing power is no longer a limiting factor. This method is also limited to fibre arrangements that are repetitive and not random such as chopped stand mat (CSM) Research into methods of determining the permeability of dry composite layups has increased during recent years however, in some cases results were conflicting (Hammami, 2002). Studies directly contradict each other on whether or not the fluid used to determine the permeability has an influence on the results obtained. It would seem that the acceptable method is to use the actual resin in the permeability test or a substance with a similar viscosity to resin such as corn syrup or certain motor oils (Ma and Shishoo, 1999) as this is what various studies have done and achieved good results. 3.4.2.

Viscosity

“Viscosity is a quantitative measure of a fluid’s resistance to flow” (White, 2008). It determines the generated strain rate by applying a shear stress. Simply put it is the ability of a liquid to resist flow. The viscosity of the resin is an important factor in the VI process, as a higher viscosity will result in a slower rate of infusion. Viscosities of fluids vary by large amounts if one compares air and molasses. The Brookfield viscometer was used previously (Ma and Shishoo, 1999) to determine the viscosity of the resin. It is important to note that the resin must not start curing during infusion as this means that the viscosity will start to change. This would complicate the model and ideally, the filling stage should be completed before curing starts to ensure the entire preform is wet and then the resin can start curing. Many resins have the Brookfield viscosity listed in their specifications sheets and thus no viscosity experiments need to be done on the resin, however the gelation time must be accurately determined to ensure the viscosity does not change before the infusion has been completed. 3.4.3.

Fibre Compaction

Dry moulds under vacuum are essentially being compressed and thus they compact. The amount by which it compacts is dependent on the fibre being used. A number of different models have been developed for this phenomenon, for example, Anderson et al (2003) related the compaction stress to the volume fraction. The compaction of the fibres influences the permeability of the layup. It was also found by Govignon (2010) and others that the compaction varies depending on the fibre state, being dry, wetted or even undergoing a couple of compaction cycles. The compaction of the layup also influences the final part thickness. One study focussed purely on the compressibility of the fabric (Pearce and Summerscales, 1995) and found that compaction only occurs in the thickness and does not result in lateral spreading. It also found that reloading of the compaction force could result in higher volume fraction rates. This study also found that the compression of the fibres could be described by a viscoelastic deformation; however, Govignon et al (2010) stated that because of the relatively slow deformation this effect could be neglected. Williams et al (1998) presented experimental results that give a very clear indication of the compression response and part thickness in the VI process. This study also provided all the important constants and experimental data that could be used as verification of this project at a later stage. Both Song (2009) and Govignon (2010) develop equations that describe the compaction and part thickness variables.


Page 6

Modelling the Vacuum Infusion Process 3.4.4.

Literature Study

Relaxation

A study (Walsh and Freese, 2005) provides a numerical model for the variation in part thickness in the post infusion process; however, it includes a relaxation factor. During the VI process, some of the fibres can experience some level of relaxation, which this study accounts for. The study then offers an implicit formulation of the model that includes the relaxation phenomenon. After more investigation it was found that this study does not account for any compaction effects in whole process; however to account for the increase in the part thickness the decrease in the compaction described by other models is modelled as relaxation in this one. 3.4.5.

Resin

Resin has developed over the years to satisfy the needs that have arisen because of VI in this case. Environmental and health regulations have been tightened significantly over the last few years. Restrictions have been imposed on worker exposure to volatile organic compounds (Hammami and Gebart, 2000). Hammami (2000) also stated that most widely used process is still open moulding such as hand layup. Open moulding use resins that contain 30-45% styrene that is identified as the main harmful substance (Hammami and Gebart, 2000). By using a vacuum infusion process the exposure to these harmful substances can be avoided as the process can operate on a closed system, thus exposure to the harmful substances are very limited. Another development that has taken place in resins is that the gelation times and viscosities have been reduced. This enables manufacturers to produce larger and more complicated parts. According to Williams et al. (1996) the ideal viscosity for an injection resin is between

   and

. In comparison, the viscosity of

water is around 1mPa.s, thus the resins are generally more viscous than water.

The US Navy has also been investigating the use of UV lights to cure the resin. This enables certain areas to be cured first or faster. The used of the UV light is not easy to control and expensive to operate. A special bag was also developed to allow the UV light through so that it can be cured (Williams, Summerscalest and Grove, 1996). A problem that can be encountered when using resins containing styrenes is that the vacuum can cause them to boil off the mould while curing. Williams et al. (1996) however showed that this is unlikely due to the boiling point of the styrenes increasing under vacuum. It was however found (Govignon, Bickerton and Kelly, 2010) that this only happens if the decrease in pressure to a very low level is sudden such as when the inlet is clamped early. The styrenes boiling off create gasses in the mould, which can influence the porosity of the final product. The two main types of resins used in composite manufacturing are epoxies and polyester. Both resins exist for use in VI; however, epoxy resin does not work well with CSM. This is because the epoxy reacts with the binding agent in the CSM and causes it to disintegrate. The choice of resin is very dependent on the type of application for which the part is intended. Previous studies have not placed a lot of emphasis on the resin choice; they did however have exact specifications for the resin. The model developed in this project is not specifically designed for one resin.


Page 7

Modelling the Vacuum Infusion Process 3.5.

Literature Study

Boundary Conditions

There are a number of ways to deal with the boundary conditions and the effects thereof. Most studies however try to solve the problem with little influence from the boundaries as this simplifies the problem greatly. The layup is simplified by making it wide enough so that the edge does not play a part in the infusion process, thus ensuring a 1D model. The resin is introduced by line infusion (Mathur et al., 2001) and the vacuum is applied along a whole edge of the mould as this means that the flow is kept in the two dimensional plane, being from inlet to outlet and in the thickness of the part direction. Some studies (Govignon, Bickerton and Kelly, 2010) use resin distribution tape at the inlet and outlet to ensure that the resin is evenly distributed at these points. The bag surface has been modelled as a free surface (Li et al., 2008) and as a fixed surface (Correia et al., 2004). The boundary condition for the bag depends on what the desired output of the problem is. If it is part thickness then the bag should be modelled as a free surface, however if the output must just be the flow path or to determine the permeability of the preform it can be modelled as a wall. The bottom surface is always a ridged wall boundary condition. 3.6.

Part Thickness

The vacuum bag being the top surface of the mould the makes it possible for the final part to have variations in the thickness. This in turn affects the strength of the part and thus certain parts could be rejected due to them not being strong enough. There are also two possible variations. The first is during infusion where one part will receive more resin than another is, thus resulting in a possibility of certain parts not being fully wetter while others are. The second variation is when the resin inlet is closed and the part is said to be in post infusion where the vacuum is merely removing excess resin from the mould. Li et al (2008) noted that the part is generally thickest at the resin inlet and thinnest at the resin outlet. The variation in the part thickness and the compaction pressure are closely related and a number of studies solve the part thickness variation by using the data obtained from the compaction pressure. Relating the part thickness directly to the strength is however not advisable as there are a number of different scenarios whereby a thick part could actually be quite strong. This could be because of all the fibre being at the bottom and the thickness of the part is merely a resin pool on top of the fibres. This would cause endless modelling problems as well as unknown strengths for similar parts. It is therefore desirable to keep the part thickness to a minimum to ensure constant and reliable part strength. 3.7.

Finite Element Methods

Research into finite element methods for flow in the VI process proved difficult. The student attributes this to it not having been applied before except in one case (Govignon, Bickerton and Kelly, 2010). This study used a combination of the Galerkin method, implicit method and the Newton-Raphson algorithm to solve the problem. Govignon (2010) does not show any working out of the method and merely provides results, making this study very difficult to apply to the problem. Two other studies were found (Zabaras and Samanta, 2004) & (Juanes, 2005) which focussed purely on modelling flow in porous media. These studies were done in the general case, however are slightly more suited to the flow of groundwater. The mathematics in these reports is often very complex and difficult for the student to understand.


Page 8


Literature Study

Other Models

A number of previous studies are outlined below with the focus being on representing a variety of different models. Anderson et al (2005) showed that it is possible to use software to model the vacuum infusion process. They modelled a complex 3D geometry with moving boundaries as well as irregularities in the fibres. The results achieved were positive and showed that the equations are solved in a proper way using the CFD software, CFX-4. However problems they encountered were variations in part thickness due to the flexible bag as well as pressure variations, also because of the flexible bag. These problems have yet to be properly investigated and hence have not been solved yet. Correia et al. (2004) used a slightly different approach to simulate the flow in the vacuum infusion process. By using the RTM simulation to predict the flow, saturation and compaction of the vacuum infusion process they were able to validate their model. They found the flow patterns to be similar and attributed this to the model having a non-dimensional pressure field. The RTM model must however be modified slightly to account for fibre compaction as well as permeability. According to them, this model can then be used to estimate the mould filling time and distribution of the fibre volume fraction. Song et al (2009) performed and investigation into the laminate thickness variation. They were able to establish a model, which can analyse the post-infusion process, which ultimately determined the thickness variation. This variation is due to a number of factors, one of which being the flexible nature of the bag. Their results show that a stiffer fabric reduces the thickness variation. Li et al (2008) also performed a study into the thickness variation. Their study included the entire process and not just post-infusion as Song et al did. Li et al. concluded that a number of potential methods exist to reduce part thickness variations. One of these is to provide an extra relaxing force close to the vacuum source during infusion as well as pushing resin located near inlets down (Li et al., 2008). Govignon et al (2010) also did a study into the complete process and developed a numerical model to describe the flow in both the pre and post infusion times. Another approach (Chohra et al., 2006) uses micro models of the fibres as discussed in 3.4 above. In the future, this could well be a very good solution when computing power is no longer a limitation. This model is however useful for a different reason in that sometimes particles are added to the resin to introduce certain properties in the composite. The fibres then act as a filtration device and this cannot be modelled in a continuous method. Some studies (Mekic, Akhtov and Ulven, 2009) define a model for the radial infusion scenario. This is particularly useful in large-scale models where resin inlet points are needed in the middle of the part to ensure complete wetting of the product. Most derivations of the flow equations are in the 1D case for cartesian coordinates, not cylindrical. A number of studies merely focus on a single aspect of the process, being permeability (Hammami, 2002) or even the flow front (Mathur et al., 2001). The latter study does in depth measurements on the flow front and the form thereof. The drawback to many of these studies is that they use a flow enhancement layer to increase the permeability of the layup. This is a drawback because this study specifically excludes the use of these layers in the process; however, they may be used at the inlet and outlets to ensure an even distribution of resin and vacuum along the width of the preform.


Page 9


Literature Study

CFD Software Research

The initial thought behind the project was to use an existing computational fluid dynamics (CFD) package such as FLUENT or STAR CCM+ to model the flow process as well as get values for the volume fraction at different points in the layup. After discussing the problem with representatives of the software, it was found that it would be possible to model the basic flow through the layup, which would be modelled as a porous medium; however, this would not include any information about the part thickness or subsequent volume fraction. In other words it would be possible to model the RTM method. The difficulty lies in the flexible vacuum bag. This could be modelled as a free surface however then the driving force behind the infusion is lost, as the vacuum does not act on the resin inlet, but just to atmosphere. Modelling of the vacuum bag would require a dynamic mesh that results high computing time requirements as the mesh would change with every time iteration. Modelling of the bag would also require many parameters such as the stiffness of the bag. This method work for one layer of fibre; however, two or more layers of fibre become difficult to model, as the amount of resin flowing between the layers is not known. Another difficult is that there is no information available about the interaction of fibre layers. There are a number of software packages available on the market that caters specifically to composite moulding simulations. Polyworx is an example of such software. A little research was done on the Polyworx software and it was found that it establishes flow paths for the infusion process to eliminate guesswork from parts. It would seem that the volume fraction required for detailed part specification does not yet exist as most of the software deals with the resin distribution during infusion and not post-infusion which is essentially the process that determined the part thickness and subsequent volume fraction. In many of the existing software packages, it is possible to modify the fundamental equations by which they operate. It would therefore be possible to use any model that has been developed in the software and solve the problem using it. The first problem with this is than an extensive knowledge of the working of the program is needed to modify the equations on which it operates. The second problem is that the model would have to be derived in 2D and possible even 3D. 3.10.

General Notes on Available Literature

Many studies have been done in this subject field, of which most picked a certain aspect and concentrated solely on that. Very few studies try to combine all the best studies for each individual section of the process. There are also many different methods for determining values for permeability for example. This creates a problem as to choosing a method to use. As a result of many studies only focussing on one aspect of the process the results of studies and methods used are often difficult to compare. An example would be two studies focussing on the post-filling process and using different data for the filling process which acts as the starting point for their study.


Page 10


Theoretical Investigation

4.

THEORETICAL INVESTIGATION

4.1.

Compaction Behaviour

The data that will be obtained from the practical experiments for the compaction behaviour, as described in section 6.2.1 below, will have the compaction stress against fibre volume output, as found in most studies. The compaction stress is then compared to the pressure being applied to that part of the preform, thus the stress is another way of saying the pressure applied to the fibres. Using the experimental data a power law model can be applied to that is similar to the data. Govignon et al took this a step further by interpolating the data and applying three overlapping power laws to generate a better fit. Initially it was thought that this compaction data would be relatively easy to find, however with the available equipment it was found that this data is very difficult to obtain, especially at the low compaction stresses. The exact experimental procedure is described in 6.2.1 below. With a full set of accurate data, it was thought that a different model could be set up using a function such as polyfit in Octave, however with the limited data, this was not possible and a power law model has been used. The following equation represents the relationship that has been obtained:

 

(4.1)

Two different functions have been determined for the following cases: Dry compaction and wet compaction. Dry compaction occurs when the fibres are compacted due to the vacuum without resin being present. Finally, wet compaction is the process that occurs when the resin inlet is closed and the part thickness decreases to its final value. The experiments for each of these are defined in section 6.2.1. It was also thought that a wet unloading factor could be determined but due to time and equipment constraints, this proved very difficult. Initially it was also thought to investigate the number of layers and the influence they have on the compaction factor. It was found that with the available equipment, no measurable difference could be detected with different number of layers and thus the idea was also omitted. The student also noticed that the current model starts at the srcin. This means that the fibre has a zero volume fraction for no compaction stress whereas in reality the fibre will always have thickness. A slightly different model is presented in section 7.2 however due to the inaccurate experimental data the model lacks credibility. 4.2.

Permeability

Micro model have been excluded from this project, this leaves one method of defining the permeability of the layup. Most recent studies have used this method, which is a combination of D’ Arcy and the modified Carman-Kozeny (C-K). The modified C-K equation stated by Govignon (2010) and others is represented by equation 1 below.

Here



is the permeability,

  and

 

are constants determined from the experiments and

volume fraction. The experiments that will be used to determine given by Correia et al (2004) and others by:


(4.2)

   

  and



is the fibre

are detailed in section 6.2.2. D’Arcy is

(4.3)

Page 11

Modelling the Vacuum Infusion Process Where

and



is the volume averaged velocity of the flow in the



direction,



Theoretical Investigation is the viscosity of the resin

 is the change in the pressure in the direction  direction. Equation (4.3) can be rewritten as follows:     



(4.4)

Using equation (4.4) a value for the permeability can be obtained. Using a number of different volume fractions the constants for equation (4.2) can be defined and thus permeability can be obtained for any fibre volume fraction. The permeability experiments have been performed at a number of different volume fractions and thus a number of different values for the constants have been obtained. The change in the permeability for wetted and non-wetted layups is accounted for using the approach described in the literature study that was implemented by Govignon et al (2010). This study neglected the dry permeability of the preform stating that the pressure in the preform would be constant when dry. The permeability is linked to the volume fraction and thus as the resin flows into the preform the permeability in that part of it changes. A factor that has not been investigated yet is the influence in the number of layers present in the preform. The student aimed to consider this but found that the experiments were difficult to perform for high numbers of layers and thus no conclusive data could be obtained. It was thought that the

  and

constants would

be adpated to have a factor in them that contained the number of layers, thus changing the permeability of the preform depending not only on the volume fraction but also on the number of layers. The student feels that this could influence the flow greatly as the amount of flow between the layers is something that is otherwise not accounted for. The experimental procedure and results are given in section 6.2.2 below. 4.3.

Flow Modelling

As discussed in 3.2 the flow can be split into three parts. The modelling of each of these three is discussed in detail in the next three sections. 4.3.1.

Prefilling

Prefilling is when the resin inlet is closed and the vacuum is applied. Due to the low viscosity of air (approximately 50 times less than the resin (White, 2008)) the compaction of the mould is not very time dependant. This means that the vacuum will be applied to all areas of the layup relatively quickly (within a few seconds depending on the mould). The result of this is that the layup is compressed in all areas. Another result of the low viscosity of the air is that there is a negligible pressure difference over the layup. This causes the compaction pressure over the layup to be uniform and thus the layup has a uniform part thickness during prefilling. It is important to remember that over larger models the compaction could take a while to be completed; however it is expected that the vacuum bag will show where it is applying pressure to the mould and hence if some sections have not been evacuated it would be visible. To be entirely sure the part thickness could be measured at different sections. For the purpose of this project, the pre-filling stage will be neglected and a uniform volume fraction will be calculated using the applied pressure and the compaction model developed in section 4.1. The same approach was taken by a couple of studies such as Govignon et al (2010). It was also found using experimental measurements that the preform has a constant height when the vacuum has been drawn, making this assumption valid.


Page 12



FillingModel

The purpose of this project is not to derive a new method of determining the flow in the preform, but the implementing into a numerical solution is important. For this reason, the flow model that is going to be used is well defined and has been used successfully in a number of studies. This particular derivation thereof is taken from Govignon et al (2010) as it is derived in such a way that it can be implemented in a numerical model. 4.3.2.1.

Continuity Equation

Porosity is the ratio of the volume of the voids to the total volume and defined as such in equation (4.5) below.

     

(4.5)

The fibre volume fraction is given by equation (4.6). (4.6)

A relationship can then be obtained for porosity and fibre volume fraction and given in equation (4.7) below.

 

(4.7)

With the assumption that the fibres in the preform are incompressible and that compaction of the preform only causes strain in the height direction the following relationship can be obtained.

      In this equation the

  and

(4.8)

are for the preform under a zero compation stress. The

density of the fibre. Equation (4.8) can then be represented as:

    



term is the

(4.9)

Equation (4.9) represents the conservation of solid mass in the system. The fluid mass in the system is more difficult to calculate as it changes while the resin is flowing. The fluid is assumed to be incompressible for the problem. averaged velocity and is defined as follows:



is the D’Arcy velocity or volume-

 

Here

is the volume flow rate in the medium, however to the model being 1D the volume flow

 

rate is actually area volume flow rate obtained by dividing by the width and having units of the



(4.10)

    

factor having the correct units of



. This also results in

. Using the incompressibility of the fluid as well as the conservation of

fluid mass the following relationship can be derived:

Where



(4.11)

is the change in the porous volume of the preform.


Page 13


       

Expanding and taking the limits as

and

Theoretical Investigation gives the initial continuity equation: (4.12)

This can be further simplified using equation (4.9) and (4.11) to get equation (4.13)

    It is worth noting that very few publications take the 4.3.2.2.

(4.13)

 term into account and generally it is set to zero. 

Implementing Galerkin

By combining equation (4.13) and D’Arcy’s law stated in equation (4.3), equation (4.14) can be obtained, stated as:

    

(4.14)

This is a very important equation as it is the starting point for the implementation of the Galerkin finite element method as well as the velocity at the flow front, shown in 4.3.2.3. It should also be noted that using D'Arcy intrinsically implies that flow is laminar as well as the resin is a Newtonian fluid. Govignon et al (2010) modified the D’Arcy equation with an empirical type correction factor to try to get a better fit to the experimental values. The effect of this factor was not seen to have much effect on the final outputs of the program and good results were obtained without it, thus it has been omitted. The strong formulation of equation (4.14) gives:

 ∫       

(4.15)

Transforming this to the weak formulation gives:

∫          

(4.16)

Using one-dimensional linear elements one would approximate each variable using a linear shape function over each element. This would mean that each variable is expressed using trial functions as given below for the height as an example:

  

(4.17)

The trial functions, given in local coordinates, are:

     and

(4.18)

Transformation from local to global coordinates is as follows:

    

(4.19)

The derivative of this is also required for the implementation of the Galerkin method and is given below.

Here the



    

(4.20)

term is the length of an element and not the complete preform length.


Page 14



Equation (4.14) can now be discretized using these trial functions that give:

∫                    

(4.21)

Converting this to local coordinates:

j=1:

              ∫∫             

(4.22)

j=2:

 ∫         ∫      Completing the integration on the left hand side gives: j=1:

             |

(4.23) j=2:

          |



This can then be written in matrix form which is easier to understand and will be used further in the report. The matrix form is thus:

̅(̅)   ̅ (̅ ̅)

̅(̅)     ̅(̅)   [    ]      

The stiffness matrix,

The capacitance matrix,


(4.24)

, can then be represented by:

(4.25)

, can be represented as:

(4.26)

Page 15

Modelling the Vacuum Infusion Process The

̅(̅)


term cancels, as the only values that it would represent are those at the inlet and outlet

however, those are replaced by the boundary conditions hence the term falls away. The using a backward difference approximation as follows:

 term is dealt with by 

    ̅  ̅  ̅ ̅  ̿   ̅ ̅  ̅ ̅ ̅  ̅  ̅ ) ̅   ̿ (

(4.27)

Thus changing equation (4.22) to the following:

(4.28)

An iterative approach must thus be used to get the solution due to the height estimates being used from a previous time step as the initial guess. The error or residual, Raphson algorithm. It is given by:

, is thus required to apply the Newton-

(4.29)

Applying the Newton-Raphson algorithm:

The matrix

̅ 

* ̅ +̅  ̅ ̅ 

(4.30)

̅ ̅  * ̅ +  ̅ ̅

(4.31)

̅ ̅  ̅ 

(4.32)

is the tangent matrix of the residual and is given below:

               [          Where







* ̅ +                          

(4.33)

is given as:

     

In all the above equations the subscripts



 ]

(4.34)

denote the element number in the preform where as the

superscripts, denote the iteration number in the Newton-Raphson algorithm. 4.3.2.3.

Flow Front Velocity Derivation

The resin flow through the layup is described by D’Arcy’s law , which for 1D flow in the x direction is stated in equation (4.3) and restated here for convenience.

     University of Pretoria - MSC 422

(4.3)

Page 16



It should be noted that the variable names have been changed to follow on from previous ones defined in the report. It is also assumed that the permeability of the fibre is constant in the layup, direction of flow) and





direction (length of

direction (width of the layup) as well as flow in the in plane direction,



(thickness of

layup), being neglected due to the in plane flow being neglected. The assumption that the resin and the fibre are incompressible can be made since the fibre is made of a solid and the compaction of the fibre structure is described in section 4.1. The resin is also assumed to be incompressible as a condition of applying D’Arcy however due to it being a liquid this is a good assumption. The continuity equation for the conservation of mass can then be stated as:

          

(4.35)

This equation is derived in section 4.3.2.1 above. By combining equations (4.3) and (4.5), equation (4.36) is found:

The flow



(4.36)

needs to be determined at the flow front. This is done using a non-mixed method with

conservative elements. By applying linear finite elements, the first derivative of the pressure is constant over an element. A Taylor series about the centre of the element can then be used and one finds that:



is the value



         

(4.37)

value about which the Taylor series is centred. Equation (4.37) would prove difficult

 to solve due to the  in the expression for . It is simplified as follows. As the thickness and hence, permeability  in the  direction, the gradient varies along the layup  of  can be expressed as:             (4.38) Equation (4.14) can thus be expanded to the following:

            By combining Equations (4.38) and (4.39), an expression for

         

(4.39)

 can be obtained.  (4.40)

Substituting Equation (4.40) into equation (4.37) yields the volume averaged flow velocity at the flow front.

As



              

(4.41)

is the volume avergae velocity, the velocity of the flow in the preform can then be calculated

using the porosity as follows:

   University of Pretoria - MSC 422

(4.42)

Page 17

Modelling the Vacuum Infusion Process 4.3.2.4.


Smaller Derivations

The two main derivations of the equations have now been completed. It was found that a number of other equations are needed to implement the code. These derivations are just linking variables. The first two variables that are linked are the height and the volume fraction. They are linked using the bulk density of the fibre as well as the area density of the fibre.

 

(4.43)

      

(4.44)

This is the volume of entire layup.

          

(4.45)

    

(4.46)

    

(4.47)

The next linking that has to occur is that of the pressure to the compaction stress. The compaction stress is defined as follows:

   

(4.48)

 

(4.1)

The compaction model given in section 4.1 above links the volume fraction to the compaction stress as given in equation (4.1) shown here again:

The variables

  and

are determined experimentally in section 6.2.1.

The last link that has to occur is that between the permeability and the fibre volume fraction. This has already been stated in equation (4.2) but is restated here for convenience:

   The variables

  and

(4.2)

here will also be determined from experiemental values in section 6.2.2.


Page 18



Variable Naming

Due to certain variables being Greek characters and other reasons the following table has been added to draw a comparison between the variable names used in the report and in the program. ReportName

     ̅ ̅ ̅  ̅   

Program Name

ShortDescription

vf

Fibre volume fraction

p_glass

Area density of fibre

bulkd

Bulk Density of fibre

of

Compaction stress

layers

Number of layers in the preform

poro

Porosity

dh

Change in h per N-R iteration.

Ks

Stiffness Matrix

Kt

Tangent Matrix

C

Capacitance matrix

b

Compaction factor constant

Table 4.1. Variable Naming

Variables not given in Table 4.1 have the same name in both the report and the program.


Page 19



Program Flow Chart

0. Start Up 0.1 Initialize Variables 0.2 Declare functions 0.3 Mesh Domain 0.4 Initialize domain for full vacuum

1. Fill First Element 1.1 Fill first element st 1.2 Calculate , , ,  and  with 1 element full. 1.3 Iterate to find ,  and  to fill first element.



2. Increment time step 2.1 Use height profile from previous time step

3. Newton-Raphson Starts 3.1 Calculate  , , ,  for current iteration. 3.2 Set  and at flow front to vacuum and respective . 3.3 Iterate to get  to fill next element. Solve to get new profile.





No



Is  within rnge?

No Yes

Has flow reached end of preform?

Yes

3. Start Post filling phase

Figure 4.1. Program Flow Chart

This program flow chart gives a very basic overview of the procedure which the program follows in the implementing the model. Each part is explained in more detail in the following section which includes extracts from the code to show how each part is programmed.


Page 20



Filling Program Code Extracts

Following the number scheme from the program flow chart above pieces of code will now be shown and explained briefly. 0.) Initializing Variables. This is done to set all the variables to zero and introduce all the constants into the problem. The constants’ values shown in this case are those used by Govignon et al (2010). width =0.2;

%m

l=0.38;

%m

visc=0.227;

%pa.s

p_inlet =99000;

%pa

p_vac =470;

%pa

p_atm =101325 ;

%pa- atm

layers =10;

%number

inicompvar =[0.1447 0.1042 ];

%gov

wetunvar =[0.286561 0.046089 ]; %gov c_perm =9.5e-11 ; n_perm =2.6; bulkd =.45;

%bulk fibre density kg/m^2

p_glass =2500;

%glass density kg/m^3

ele=100;

%Number of elements for mesh

t_max =10;

w=(bulkd*layers)/p_glass; %Ini Fields h=zeros (ele+4,1); %Height profile p=zeros (ele+4,1); %Fluid Pressure vf=zeros(ele+4,1);

%Volume fraction

k=zeros (ele+4,1); %Permeability of=zeros(ele+4,1);

%Compaction Stress

fact=1; newcon =10^-6; %std 10-^-6 t=0;

dtruntime=0; tsit(3)=0; ts=3; saturated =0; y=0; dh=0; Code Extract 4.1. Variable Initialization


Page 21



0.2.) This process declares the functions that will be used in the program, as there are numerous functions that are used repeatedly. %vi functions declarations vf_func =@(vf0,of,b) vf0.*of.^b; k_func =@(vf) c_perm .*((1-vf).^(n_perm +1)./(vf.^n_perm )); poro=@(vf) 1-vf; h_func =@(vf) bulkd ./(p_glass *vf)*layers; of_func =@(vf,b,vf0) (vf./vf0).^(1./b); vfh_func =@(h) bulkd./(p_glass .*h).*layers; h_qfunc =@(h,ts,q,dt,incre) (((q(ts)-q(ts1)).*h(ts,ts))+(h(ts,ts).*q(ts))+(h(ts,ts).*incre./dt(ts)))./((in cre+(q(ts).*dt(ts)))./dt(ts));

kt_func =@(i,h,k,ts,mesh) (2.*k(i,ts).*h(i,ts)+k(i,ts).*h(i+1,ts)+k(i+1,ts).*h(i,ts)+2.*k(i +1,ts).*h(i+1,ts))./(6.*visc*(mesh (i+1,2)-mesh (i,2)));

dp=@(i,h,ts,b,vf0,p) (p(i+1,ts)-p(i,ts))/(h(i+1,ts)-h(i,ts)); dk=@(i,h,k,ts) c_perm *(((w/h(i,ts))^n_perm *(1w/h(i,ts))^n_perm *(n_perm +1)*(w/h(i,ts)^2))+((1w/h(i,ts))^(n_perm +1)*(w^n_perm /h(i,ts)^(n_perm 1))*n_perm ))/(w/h(i,ts))^n_perm ; k_stiffvec =@(z,p,h,k,ts,mesh) [... (p(z,ts)-p(z+1,ts))*kt_func (z,h,k,ts,mesh ); (p(z+1,ts)-p(z,ts))*kt_func (z,h,k,ts,mesh )];

c_capmat =@(mesh,z) [(mesh(z+1,2)-mesh(z,2))/3 (mesh(z+1,2)mesh(z,2))/6;(mesh(z+1,2)-mesh(z,2))/6 (mesh(z+1,2)mesh(z,2))/3]; k_tanmat =@(z,p,h,k,ts,b,vf0,mesh) [... (((p(z,ts)-p(z+1,ts))./(6.*visc .*(mesh (z+1,2)-

mesh(z,2)))).*(2.*k(z,ts)+2.*h(z,ts).*dk(z,h,k,ts)+h(z+1,ts).*dk(

z,h,k,ts)+k(z+1,ts)))+... kt_func (z,h,k,ts,mesh).*dp(z,h,ts,b,vf0,p) ... (((p(z,ts)-p(z+1,ts))./(6.*visc .*(mesh (z+1,2)-

mesh(z,2)))).*(2.*k(z+1,ts)+2.*h(z+1,ts).*dk(z+1,h,k,ts)+h(z,ts). *dk(z+1,h,k,ts)+k(z,ts)))-...

kt_func (z,h,k,ts,mesh).*dp(z+1,h,ts,b,vf0,p);... (((p(z+1,ts)-p(z,ts))./(6.*visc .*(mesh (z+1,2)-

mesh(z,2)))).*(2.*k(z,ts)+2.*h(z,ts).*dk(z,h,k,ts)+h(z+1,ts).*dk( z,h,k,ts)+k(z+1,ts)))-... kt_func (z,h,k,ts,mesh).*dp(z,h,ts,b,vf0,p) ... (((p(z+1,ts)-p(z,ts))./(6.*visc.*(mesh(z+1,2)-

mesh(z,2)))).*(2.*k(z+1,ts)+2.*h(z+1,ts).*dk(z+1,h,k,ts)+h(z,ts). *dk(z+1,h,k,ts)+k(z,ts)))+...

kt_func (z,h,k,ts,mesh).*dp(z+1,h,ts,b,vf0,p)];


Page 22



Code Extract 4.2. Function Decla rations

0.3.) This process of meshing the domain divides the length into the required number of elements and then calculated the increment to each one and adds the node numbers. incre =(l)/ele; mesh=[[ 0 1:ele+2]' [0 0:incre:l+incre]' [0 0:incre:l+incre ]']; mesh(2,2:3)=10e-15 ; Code Extract 4.3. Meshing Domain

0.4.) Initializing the domain is applying all the conditions that would exists if there was no resin present and a full vacuum had been drawn. vf0=inicompvar (1); for dry

%Initial

b=inicompvar (2); of(:,:)=p_atm-p_vac; vf_dry =vf_func (vf0,of(1,1),b); h(:,2:3)=h_func (vf_dry );%Initial prop of dry preform from pre filling p(:,2:3)=p_vac ; of(:,2:3)=p_atm-p_vac;

%No fluid pressure

vf(:,2:3)=vf_dry ; k(:,2:3)=k_func (vf(1,1)); Code Extract 4.4. Full Vacuum Initialization

In Code Extract 4.4 is can be seen that the compaction constants that are used are that of the dry preform. In the next piece of code the wet compaction constants are used for the then wet part of the preform. 1.1-2.) Here the first element is filled with resin and properties for the preform in that region are calculated. vf0=wetunvar (1); b=wetunvar (2); p(1:2,3)=p_inlet ; p(3,3)=p_vac; of(1:3,3)=p_atm-p(1:3,3); of(3:end,3)=of(3:end,1); h(1:3,3)=h_func (vf_func (vf0,of(1:3,3),b)); k(1:3,3)=k_func (vf_func (vf0,of(1:3,3),b)); vf(:,3)=vfh_func (h(:,3)); Code Extract 4.5. Conditions for full first element


Page 23



1.3.) This is where a few iterations take place to determine the time required to fill the first element and then calculate the flow rate and velocity through the first element. dt(3)=0.21677 ; %initial guess do

dtstart =cputime ; if incre >l/ele

dt(ts)=dt(ts)*0.9999 ; end if incre
dt(ts)=dt(ts)*1.001 ; end q(ts)=-(k(ts,ts)/visc*((p(ts,ts)-p(ts-1,ts))/(mesh(ts,2)-

mesh(ts-1,2))))... %NB Trial q- check- other one in scratch +(((mesh (ts,2)-

incre /2))/h(ts,ts))*(k(ts,ts)/visc*((p(ts,ts)-p(ts1,ts))/incre)*(h(ts,ts)-h(ts-1,ts))/(mesh(ts,2)-mesh(ts-1,2))((h(ts,ts)-h(ts-1,ts))/(dt(ts))));

v=q(ts)/poro(vf(ts,ts)); incre=v*dt(ts); y++; dtruntime =dtruntime +cputime -dtstart ; until ((l/ele-10e-10 ) < incre && incre < (l/ele+10e-

10))|y==100000 ; if y>30000 %| dt(ts)>dt(ts-1)%Warning

beep ts j y tsit(ts) disp("Warning- high dt count")

fflush(stdout) end

mesh(ts,2)=incre ; Code Extract 4.6. Time to fill first element iterating loop.

From Code Extract 4.6 the iteration scheme to find the initial time can be seen. The scheme is given an initial guess and then calculates the distance the flow would travel using the flow speed at the flow front, this is then compare to the mesh incremental value and the time is then either increased or decreased. A similar code is used for each time step for the filling procedure. This scheme is accurate to 10

-10

for the first element and 10

-6

for

the other nodes in the preform. It was found that by running this code for greater accuracies greatly increased the computing time.


Page 24



2.1.) The setup of the domain is now complete and the filling iterations can be started. The first is the time step iteration. This is given including the code for using the previous time step’s height profile. for ts=4:103

%103 for node of fixed height to reach end+1

and calc incre to last node %ts++ tsit(ts)=0; dt(ts)=dt(ts-1); j=0; h(1:end,ts)=h(1:end,ts-1); %Using height profile of previous time h(2:ts-1,ts)=h(2:ts-1,ts)+1e-16 ; %Prevent non zero div if (tsit(ts)>(tsit(ts-1)) && (ts>6) && (factboo=1) && tsit (ts-1)>=(tsit(ts-2)))%rem(ts,5)==0 fact=fact+1; factboo =2; end; do

Newton-Raphson goes here...... until ((dh(:,ts,j)-newcon )) |(tsit (ts)>300 ); if (tsit (ts)<(tsit (ts-1)) && fact>2 && tsit (ts-1)<(tsit (ts-

2))) fact=fact-1; factboo =2; end; if j>250 %Warning

beep ts tsit(ts) disp("Warning- high iterations")

fflush(stdout) end if rem (ts,10)==0

ts fflush (stdout ); end;

end Code Extract 4.7. Time Step Loop

From this piece of code, it can be seen that the program goes through the for-loop for each element as the flow is at a node after every iteration due to the time iteration scheme shown in Code Extract 4.6. It can also be seen that there are warning systems built into the code to warn the user if a high number of iterations occur which is usually a good indication that something is not running properly. The increasing and decreasing of the factor is visible here and is done with an if-statement in both cases.


Page 25



3.) This is where the Newton-Raphson algorithm is looped in a do statement, as shown below: do

j++; vf(:,ts)=vfh_func (h(:,ts)); k(1:end,ts)=k_func (vf(1:end,ts)); p(2:ts-1,ts)=p_atm -of_func (vf(2:ts-1,ts),b,vf0); p(ts:end,ts)=p(ts:end,ts-1); of(:,ts)=p_atm -p(:,ts); p(1,ts)=p_inlet ; y=0; h(ts,ts)=h_func (vf_func (vf0,of(ts,ts),b)); dt_func; %find dt for filling next node and incre h(ts,ts)=h_func (vf_func (vf0,of(ts,ts),b)); mesh(ts,2)=mesh(ts-1,2)+incre ; vi_solve ; tsit(ts)=j; until ((dh(:,ts,j)-newcon )) |(tsit (ts)>300 );

Code Extract 4.8. Newton-Raphson Do-Untill Loop

The extract does not actually show the implementation of the formulas listed in 4.3.2.2. The implementation of these formulas is shown in Code Extract 4.9. This piece of code does however show how each variable is recalculated for the new h value that is obtained in the vi_solve procedure. The dt_func is responsible for calculating the time to fill an element and is similar to the one given in Code Extract 4.6. %Construction and solving of VI matrices C=zeros (ts+3);Ks=zeros (ts+3,1);Kt=zeros(ts+3); for z=1:ts-1

C(z:z+1,z:z+1)=C(z:z+1,z:z+1)+c_capmat (mesh,z); Ks(z:z+1)=Ks(z:z+1)+k_stiffvec (z,p,h,k,ts,mesh); Kt(z:z+1,z:z+1)=Kt(z:z+1,z:z+1)+k_tanmat (z,p,h,k,ts,b,vf0,m

esh); end

hh=zeros(ts,1); hh(2:ts-1)=h(2:ts-1,ts)-h(2:ts-1,ts-1); R=-((C(2:ts-1,2:ts-1)*hh(2:ts-1))+(dt(ts)*Ks(2:ts-1))); dh(2:ts-1,ts,j)=(Kt(2:ts-1,2:ts-1))\R(1:ts-2); h(2:ts-1,ts)=h(2:ts-1,ts)+dh(2:ts-1,ts,j)./fact; return

hh=zeros(ts,1); hh(1:ts-1)=h(1:ts-1,ts)-h(1:ts-1,ts-1);

R=-((C(1:ts-1,1:ts-1)*hh(1:ts-1))+(dt(ts)*Ks(1:ts-1))); dh(1:ts-1,ts,j)=(Kt(1:ts-1,1:ts-1))\R(1:ts-1); h(2:ts,ts)=h(2:ts,ts)+dh(1:ts-1,ts,j)./fact; Code Extra ct 4.9. vi_solve.m Proce dure


Page 26



This code extract shows how the Newton-Raphson algorithm and Galerkin finite element method are combined and implemented. The matrices given in equations (4.24) to (4.34) are assembled and solved in this code. hh is equivalent to the equivalent to the

̅

̅

given in equation (4.32). R is the calculated using equation (4.29). The dh term is

term given in equation (4.30) and solved using octave’s backslash operator which uses a LU

decomposition type method to solve the matrix. 4.3.2.8.

Boundary Conditions

Due to the fact that a 1D model is being used, the boundary conditions that have to be applied are relatively simple. During the filling stage, the inlet will be assigned a fluid pressure. The losses from the piping of the resin is assumed to be very small after a calculation similar to that performed by Govignon et al (2010) showed that the loss was only a couple of pascals. The flow front node will be assigned a pressure (Equal to that of the vacuum) (Shown in Code Extract 4.5) as the layup contains air ahead and the air pressure is constant in the layup as discussed in 4.3.1. The end conditions have been simulated using additional elements that will simulate the line inlet and outlet. The bag is modelled as a free surface and the thus can displace in the z direction whereas the bottom is a solid surface and has no displacement. Due the problem being simplified to 1D the velocity is also assumed to be constant over the height of the preform, meaning that neither the bag nor the bottom surface provide resistance to the flow. This will be discussed further in the results section 7.2. The 1D simplification also means that no boundary conditions need to be applied to the sides of the preform. This was proved to be a good assumption when the results from the stereophotogrammetry device showed nearly no variance in the part thickness in the y direction. 4.3.3.

Post-filling

4.3.3.1.

Model

The model that will be used in the post-filling process will be the same as that in the filling process. This is because the governing equations do not change between the processes. The change occurs in the boundary conditions. These are discussed in section 4.3.3.2 below. The amount of time that this process will be run for is dependent on the part thickness. The idea is that the process will be run until the part thickness stabilizes and changes in it reduce to below a certain limit. The process would not be left to run for the time that the resin would take to cure as the problem is defined as being completed before the curing of the resin would start. An improvement to the program would be a time dependent viscosity field and thus the flow would ultimately stop when the viscosity reaches a certain amount. From the experience gained whilst doing some experiments it was seen that the resin viscosity does not remain constant for the current model to be applied. This obviously depends a lot on the type of resin that is being used. It was noted that the resin might take 24 hours to set however, the viscosity increases from the pot-life time, which is approximately an hour. To include a time dependence on the viscosity a number of experiments would have to be performed on the resin to find the exact viscosity response with regard to time.


Page 27



Boundary Conditions

The inlet boundary condition of the post-filling process is set to a zero pressure gradient as the resin inlet is closed off. This zero pressure gradient results in the first two nodes having an equal height. The outlet boundary condition is set to the last node in the system to which a vacuum is assigned again. These changes are shown in the following code extract: h(2,ts)=h(3,ts)+0.0000001 ; p(103,ts)=p_vac; Code Extract 4.10. Changes in Boundary Conditions

As can be seen in the code the height difference is not set to be exactly zero as this results in some division by zero in the solving procedure, hence a very small height difference is assumed. The vacuum pressure is also reapplied to the last node.


Page 28


PROGRAM

5.1.

Verification

Program

Verification is checking whether the implementation accurately represents the mathematical basis behind the model. In this case it is done by comparing the outputs student’s and Govignon’s program. The exact data obtained from Govignon’s program is not available and thus most of the comparison is done graphically, using the graphs in Govignon’s report and the graphs generated by this project’s program The fact that this comparison has to be done graphically makes it rather difficult and thus the quality of the graphs is not good as they are copies from Govignon’s report. Other factors that make the comparison difficult are that this project’s program does not model exactly the same process as that of Govignon. This project only uses a single power law to relate the compaction stress to the volume fraction whereas Govignon used a multipower law. It is suspected that this has resulted in the heights of the preform not matching. Govignon also makes use of the modified D’Arcy equation and this results in the pressure during post filling not dropping off so quickly, however the two implementations seem to match closely here. It was because of this that the modified D’Arcy law was not implemented in this project. The following two figures represent the two height outputs of the implementations. The comparison graphs shown are in the same units and each line represents a point along the preform for which the desired property is plotted. The red lines show a point closest to the inlet and the purple line closest to the outlet. The exact point for which the line is drawn is not given by Govignon and hence the student has to guesstimate the points that are being plotted. The black line represents the point at which the inlet is clamped.

Figure 5.1. Thickness Comparison (Govignon on left, student on right)

From Figure 5.1the following comparisons can be drawn: The shape of the curves is very similar. 



The time at which the flow reaches the end of the preform and subsequently clamped is about 1000s in both cases.



The time at which the preform regains uniform height is also very similar at around 1500s.


Page 29

Modelling the Vacuum Infusion Process 

Program

The height values do not match exactly. This is attributed to this project using a single power law and Govignon using a multi power law. Govignon also never states what pressure is used as atmospheric and the student had to assume that it was standard. The student experimented using different values in the power laws and the model was able to capture the same heights as Govignon. The problem is that the bottom height would be correct and the top one would not be accurate and vice versa.



The student’s graph has a dip in it as the resin reaches it, whereas Govignon does not. It is assumed that Govignon has not plotted this dip in his results because the compaction factors clearly account for a lower preform once wetted.



Some of the lines’ gradients are not exactly the same, especially during filling. This could be due to a number of factors. The first is that Govignon does not state at which points each of these lines is obtained from and thus the student had to guess whilst plotting his graph. These differences, especially with regard to the red line could be attributed to Govignon using the modified D’Arcy law and the student using the standard one.

The next comparison is that of the pressures.

Figure 5.2 . Pressure Comparison (Govi gnon onleft, student on right)

Figure 5.2 shows the different pressure distributions of the two implementations. The comparisons that can be drawn between the graphs are the same as those of Figure 5.1. This is correct as the pressure in the preform and all the other variables are a function of the height. This section shows that the student’s implementation can be verified, although not a numerical comparison, the student feels that the comparison given provides enough evidence that the model is correct, taking the differences between the two models into account. 5.2.

Validation

Validation is checking if the implementation accurately represents what is being modelled in reality. The following section aims to show how the program written by the student compares to the experimental results obtained by Govignon et al (2010). As the report that the program is being compared to does not contain the actual data obtained in the experiments the comparison will once again have to be made using the graphs presented in the report. This comparison is between the results obtained from experiments by Govignon and program written by the student. University of Pretoria - MSC 422

Page 30


Program

Figure 5.3. Experimental and Theoretical Comparison

The figure above shows vast differences between the theoretical model and the experimental data obtained by Govignon. These are explained in section 7.2. Once again the time seems accurate, however the shape of the graphs differ vastly. There is large difference in the height of the preform at the inlet (the red line). The post filling process is not modelled accurately at all, as the experimental values take a lot longer to compress after the inlet is clamped. A factor, which is relatively unknown in all these processes, is the effect that the bag has on the process. Due to the high value given by the red line it is suspected that the bag was lifted off the preform by the resin. This is discussed in more detail when the student compares the model to his own experimental data. 5.3.

General Pro gram Note s

This section details some of the program specific parts of implementing the model. The program was written for use in GNU Octave, developed to do many different numerical problems. It is used as a replacement to the expensive MATLAB. The student found that Octave ran much better in the OS X environment as opposed to Windows. The computer for which the computational statistics are given here is a 2.3 GHz Intel i5 Processor, 4 GB RAM and Apple’s OS X 10.7.2. The Octave version used was 3.4.0 with the optin, misc and struct packages added on. The first item is that of the factor used in the Newton-Raphson implementation. This factor decreases the amount that



changes for each iteration of the algorithm. This factor is increased when trend of the number of

iterations increases and is decreased if the number of iterations decreases. Theoretically, Newton-Raphson should be quadratically convergent however; it is suspected that due to the manner in which the time increment is calculated the quadratic convergence is lost. It was also suspected that the tangent matrix or one of the other large complex matrices was not being correctly calculated. This was disproved when using certain constants in the model a quadratic convergence for all time steps was obtained, the dt was also set to a constant calculated amount, this neglecting the time factor from the problem. Figure 5.4 below shows the number of iterations that the loop performs for every loop. This factor is not increased for the post filling process, thus is merely constant.


Page 31


Program

Number of Newton-Raphson Iterations 14 12 10 s n8 io t a r6 te I

4 2 0 1

11

21

31

41

51

61

71

81

91

Flow Front Position Figure 5.4. Newton-Raphson Iterations

From Figure 5.4 it can be seen that the number of iterations seem stabilize at around seven per time step. This includes the factor, which then implies that the error that the factor is accounting for seems to get worse as the time step increases. From this is can also be seen that the problem does converge quadratically at points, such as number 6 in this case. The calculation of the time interval is another point of interest in the program. It is expected that the time interval should increase to fill an element as the flow is slowing down. Figure 5.5 shows how the dt changes for each element.

Change in dt as flow progresses 25 y = 0.1984x - 0.1825 R² = 1

20

) (s e m 15 ti n i e g 10 n a h C

5 0

1

11

21

31

41

51

61

71

81

91

101

Element Number

Figure 5.5. Change in dt as flow progresses


Page 32


Program

From this it can seen that the relationship is linear and can be accurately described by an equation of a straight line. Once this relationship is known it could be pre-programmed and thus eliminate the need to calculate the value each time, however this would only be applicable to a very specific layup. The slight variances in the dark line is explained by the convergence criteria of the dt_func calculation. These variances can be eradicated with higher convergence criteria. This penalised heavily on the computational time and was found to have little influence on the final solution. A possible addition to the program would be to accurately determine the change in the time for the first three intervals and then extrapolate to get the following time values. This would of course require the assumption to be made that the change is in time increases linearly for the entire filling process. The mesh of the program is not a standard linear mesh. The first element is considered as the inlet element and thus is assigned a very small size. It was found that this was the easiest way to approximate the boundary conditions. The last element in the mesh is considered as the outlet and thus assigned a vacuum pressure. During all the calculations, the mesh is thus solved from 2 to 101 instead of the usual 1 to 100. Whilst the flow has not reached the end of the preform the mesh is only solved to the point where the flow has reached, thus decreasing the computational requirements. The convergence criteria of the program were chosen whilst considering many factors. The NewtonRaphson criteria requires the change in height to be smaller than 10e-6. This is equivalent to 1 micron and thus deemed to be acceptable the measurement equipment is not this accurate. This resulted in the filling part of the process being computed in approximately 2 minutes. The post-filling program runs for approximately 12 minutes. The exact reason for the post program running for such a relatively long time is not known, however a number of factors could contribute. The first is that the post-filling program iterates many more times.

Number of Newton-Raphson Iterations 160 140 120 s100 n io t 80 a r e tI 60

40 20 0 1

21

41

61

81

101

121

141

Time Step Figure 5.6. Newton-Raphson Iterations- Post Filling

Figure 5.6 shows how the number of iterations increases drastically as the boundary conditions are changed to that of post filling at the 101 mark. They then steadily decrease until the flow has equalized at around the 160 mark. It is suspected that the reason for all these iterations is the steepness of the post filling height gradient. The post-filling program was tested without a factor being used but this caused the program to crash so the same factor is kept for the filling and post filling processes, however the factor is not increases or decreased for the post filling procedure. It should be noted that the time step is not constant for the filling process, however for the post filling process it is fixed at whatever the last value was that was obtained in the filling process. Thus, the dt graph becomes a straight line and the time passed for each iteration and looks as follows. University of Pretoria - MSC 422

Page 33


Program

Cumulative Time Passed per Time Step

2500 2000

) (s

d e1500 s s a P e1000 m i T

500 0 1

21

41

61

81 Time Step

101

121

141

Figure 5.7. Cumulative Time Passed per Time Step

As can be seen in Figure 5.7 the time passed becomes linear as soon as the post filling process it started at the 101 position. The integral of Figure 5.5 would give the first part of this graph, which shows exponential growth.


Page 34


PRACTICALINVESTIGATION

6.1.

General Pr actical Information

6.1.1.

Composite Laboratory Setup

Practical Investigation

One of the biggest headaches in this project was the composites laboratory. This new facility has been commissioned in the Thermo-Flow labs. The room was cleared out, washed, the fan vent was cleaned and some old furniture was arranged from the technical department. The lab it fitted with an extraction fan as it used to be a combustion engine dyno room. Some safety equipment was also bought for the lab such as gloves, an apron and gas masks. Safety signage was installed to inform people of the necessary measures required for safe working in the lab. A composite company was asked about proper procedures with regard to working with composites and if was found that no standards exist at this point. The safety instructions that accompanied the products were then used.

Figure 6.1. New Composite Laboratory

After a struggle between the University and the supplier, the equipment for the lab was eventually delivered on the 9

th

of September 2011. This meant that there was about a month to perform all the needed

experiments. This was a large learning curve for the student. There are a number of items that could be improved upon in the labs. The first is the gauge of the vacuum pump. The gauge needs to be calibrated. A gauge was borrowed from the chemical engineering department to see what the current gauge is set relative to. The following graph represents the comparison between the two gauges. It is suspected that the borrowed gauge is also not correctly calibrated but it is trusted more than the one on the pump. From this test the pressure of -65kPa relative to the atmospheric pressure was used in the future experiments for full vacuum as this is where the pump turns off automatically. The South African weather service quotes the atmospheric pressure in Pretoria to be 87.7kPa (Absolute). This means that the absolute pressure that has been used for infusion is 22.7kPa.


Page 35



Vacuum Gauge Pressure Correction

0.00 ) a P-10.00 (k ) m t -20.00 a o t l -30.00 e R ( e r -40.00 u s s e r

y = 0.1x - 95 R² = 1

lp-50.00 a u t c-60.00 A

-70.00 0

200

400

600

800

1000

Gauge pressure (mBar)

Figure 6.2. Vacuum Gauge Pressure Correction

It would also help a lot if the vacuum pump could be set to turn off at different pressures. It is suspected that the pressure switch located on the pump could be adjusted however, the student did not have time to start fiddling with the pump. Different pressures would have been especially useful in the compaction tests, as the tests had to be done a numerous different pressures to generate useful data. These tests were done for different pressures by opening a valve a set amount and letting the pressure stabilize however this resulted in the pump running continuously for long periods. 6.1.2.

General Experimenta l Constants

The following constants were obtained from the product manufacturers or other literature: Materialand Property

Value

SAE 30 Oil Viscosity (20°C)

0.2 Pa.s

SAE 30 Oil Density (20°C)

876 kg/m

SAERTEX Bi-Diagonal Glass (45°-45°)

0.409 kg/m

Area Density E-glass bulk density

2550 kg/m

Table 6.1. Material Constants.

Notes on the table above: 



E-Glass is the material used to manufacture the fibres that are used which is basically standard fibre glass. SAE 30 was chosen due the viscosity being close to that used by Govignon and resins are available in this range too.



The Bi-diagonal glass was chosen due to it having uniform construction and thus every piece will be very similar as opposed to CSM, which is not 100% uniform as it is possible to have thicker pieces and thinner pieces at random. This could result in certain areas having a higher volume fraction than others in the same preform, thus disrupting the linear flow.


Page 36



Stereophotogrammetry

For all the experiments requiring a measured height the stereophotogrammetry device was used. This device uses two cameras mounted at a specific distance and angle to each other to triangulate points relative to each other. The machine is made by GOM optical measurement devices and the software used was Aramis 4.7 running on KDE. The measurements are accurate to a couple of micron. The item that must be measured must be painted using matt black and white paint to create a speckle pattern. The software uses the differential on the surface to calculate many things, including stress strain and displacement. For this project on the displacement, part of the program was used. A reference point was also set on a piece of the bag so that the initial height difference could be obtained and thus points could be generated for Z on XY. Photos can be taken at extremely quick intervals but for this project, they were taken every 1 or 10 seconds depending on the experiment. For the flow experiments, this resulted in more than 600 sets of photos over 100 minutes. Figure 6.3 and Figure 6.4 are images captured from the two cameras, which are at approximately 15 ° relative to each other.

Figure 6.3. Typi cal Stere ophotogramm etry Image- Left Came ra

Figure 6.4. Typical Stereophotogrammetry Image- Right camera

The machine was only available for a week to run tests with and this is another reason why all of the initially thought out experiments and factors that the student wanted to test for could not be completed. The following figure shows the setup over a layup.


Page 37



Figure 6.5. S tereophotogramme try setup 6.2.

Model Parameter Tests

Both the compression response of the fibre and the permeability of the fibre layup need to be determined which are then be used in the model. The method and results of these tests are shown in the next two sections. 6.2.1.

Compaction Tests

The aim of these tests is to determine the constants here for convenience:

  and

represented by equation (4.1), restated

  6.2.1.1.

(4.1)

Compaction Test Method

The following method was used for doing the compaction tests: 1.

Ten layers of dry and ten layers of wet fibre are laid next to each other on the table. The wet fibre was obtained from a previous flow experiment and was assumed to be fully wetted.

2.

The layups are then sealed using a vacuum bag and tacky tape and each given its own vacuum point.


Page 38



3.

The vacuum pump is turned on and the seal is checked.

4.

The layup is sprayed with speckle paint so that the stereophotogrammetry machine can be used. Figure 6.4 shows the setup with two sets of fibre and the green blocks are the areas in which the stereophotogrammetry machine calculates the heights.

5.

The vacuum is released and the system is allowed to return to atmospheric pressure.

6.

The vacuum pump is then run continuously with a valve that is controlled to hold a specific pressure. This pressure was varied from atmospheric through 10 steps to the maximum vacuum that the pump could pull.

7.

Whilst the pressure was set at a constant, the cameras were triggered to take five photos at 1Hz.

The output of these experiments was thus the height against the different pressures. The heights are obtained from the stereophotogrammetry device via a couple of points on the surface and their respective z coordinate. These were then averaged over the values for a specific pressure as well as over the five different points on that specific layup. By using a number of different points per layup, one ensures that the layup is uniform. This was also confirmed by Figure 6.6 shown below:

Figure 6.6. Stereophotogrammtry model of compaction

One can see some slight variation in the thickness on the top of the layups and this is what the five points aimed to average out. Figure 6.6 also shows the difference in the dry and the wet compaction as the green blocks are the dry layups and the cyan ones are the wet layups and thus the wet layups are compacted more than the dry ones. The stereophotogrammetry device’s values were also checked using a dial gauge to see if the values that it calculated were realistic and they were found to accurate. The height was then converted to a volume fraction using the equation derived in equation (4.47), given below again:


    

(4.47)

Page 39



Compact ion Test Results

The pressures from the gauge were converted to the correct values obtained in 6.1.1. Figure 6.7 below represents the graphs of these values.

Compaction Response 0.6 n0.5 io t c a r F0.4 e m lu o V0.3

Wet Dry Power (Wet) Power (Dry)

0.2 0.00

20000.00

40000.00

60000.00

80000.00

Compaction Stress (Pa)

Figure 6.7. Compaction Response.

From the figure above, the following values for Dry

  

  and

were obtained:

Wet

0.3432

0.3326

0.0218

0.0352

0.9424

0.9371

Table 6.2. Compaction Factors

In the table above the

  nd

value were obtained using the trendline function in Excel. The



is the

square of the residuals and the closer it is to unity the better fit the line is. These lines are shown in Figure 6.7 as the dotted lines. These values were then compared to those of Govignon and the following figure shows all these lines together:

Compac tion Comparison 0.6 0.5 n o ti 0.4 c a r F e0.3 m u l 0.2 o V 0.1

Wet Dry Wet (Gov.) Dry (Gov.)

0.0 0

20000

40000

60000

80000

100000

Compact ion Stress

Figure 6.8. Compaction Comparison


Page 40



From this figure, it can be seen that the Bi-Axial mat that this project is using compacts more than the CSM, especially when wetted. The shape of the graphs is not the same though, especially at lower compaction stresses. This is attributed to the vacuum pump not being able to keep a lower pressure as easily. This problem is also compounded by the fact that Govignon specifically used a combination of power laws to get a rounder shape at the lower compaction stresses. Another point is that the two graphs do not come close to each other at the higher compaction stress. This is attributed to the low



values of the fitted lines.

It is felt that with better equipment, a more suitable relationship could be obtained and this would provide better results in section 7. It would seem that this is also the first time that the relationship has been obtained using this method and with a few modifications, specifically to the vacuum pump, it is expected that accurate data could be obtained. 6.2.2.

Perme abilityTests

It was initially thought that the permeability could be measured by simply changing the vacuum pressure and thereby changing the volume fraction. This proved to be problematic as the vacuum pump was not adjustable. The following method was then formulated which relates the compaction stress to the volume fraction via equation (4.2), given below again:

   6.2.2.1.

(4.2)

Permeability Test Method

The constants

  and

needed to be determined and thus the experiment needed to be done for a

number of different volume fractions. The experiment was conducted as follows: 1.

The layers are cut very accurately and place on top of each other. Care was taken to ensure that the sides lined up nicely. This is to ensure that all the oil would flow through the fibre and not around the side, called fast tracking.

2.

The preform was sealed with tacky tape around the sides, ensuring that there were no gaps between the fibre and the tape on the sides. A piece of glass was used as the top surface.

3.

Spacers were placed under the glass to ensure that a very specific volume fraction was maintained in the preform by controlling the height.

4.

Oil was allowed to flow in from the one side whilst a vacuum were drawn on the other that draws the oil through the preform.


Page 41



The oil was placed on a mass balance and the amount of oil as a function of time was recorded for five minutes once oil had completely wetted the preform. The following figure shows the setup:

Figure 6.9. Permeability Test Setup

The output from this experiment is the change in mass relative to time. The first thing that needs to be calculated is the permeability of the preform. By rearranging equation (4.2) the following relationship is obtained:

   



(6.1)



The and are the change in pressure over the length in the preform and the oil viscosity respectively, all of which are know and shown in section 6.1.2. The needed term is thus the and is calculated as



follows: The mass flow is easily calculated as follows:

Where balance and





is the mass flow in

  ,

̇  

(6.2)

is the change in mass (in



) which is obtained from the mass

(In seconds) is the change in time between each mass balance reading. The volumetric flow rate

can then be calculated using the following equation:

In equation (6.3), 6.1.2 and



  ̇         

is the volumetric flow rate in

,

(6.3) is the density of the oil, given in section

is the width of the preform. The volumetric flow rate is actually an area flow rate due to the



problem being in 1D. The final step is thus to convert the


to

:

(6.4)

Page 42



The permeability of the preform can then be calculated as shown in equation (6.1). The fibre volume fraction is easily calculated using equation (4.47). Ideally, this process would be done for numerous volume fractions. This proved to be difficult, as the sealant tape would be sucked into the preform if it was too thick. It was also difficult if volume fraction became too large as the fibre lift the glass up. A proper test table that could set an exact height for the preform would solve this problem and a method of sealing the sides of the preform would then make this method a viable option. Another factor that could have influenced the data is the fact that the tests were done on 5 layers of fibre and the this data is then being used for a 10 layer model. The effect that the number of layers has on the preform is unknown and could be a separate investigation altogether. 6.2.2.2.

Perme abilityTest Resul ts

Eventually the best results were obtained using five layers and three different volume fractions were used. These tests resulted in the following figure, please note the logarithmic y-axis scaling:

Experimental Permeability 1.E-08 ) 2 ^ (m y ti li b a e m r e P

Govingnon

1.E-09

Experimental Values 1.E-10

1.E-11 0.25

0.35

0.45

0.55

Fibre Volume Fraction

Figure 6.10. Experimenta l Perme ability

The figure also shows the modified C-K fit of Govignon. As can be seen the values are in the same range and the line seems to have a slightly different gradients. The next step was to find the coefficients of the modified C-K equation (4.2), being

 

and . This proved to be slightly problematic and it is expected that the fibre

volume fraction values that were used were not far enough apart and this caused the discrepancy. The were calculated as follows:

The



⁄( )     ( )( )( )   

values

(6.5)

value was then simply obtained by subsititution. Due to three experimental points being

calculated it was possible to find three different sets of line in Figure 6.11.




and

values. These were then averaged to generate the

Page 43



The values that were obtained using the three points were not close to those of Govignon and did not provide a good fit to the calculated points. By applying the Levenberg-Marquardt non-linear regression least squares algorithm in Octave constants were calculated with an accuracy of 10e-23. The following figure shows both the line with the calculated points and one that had been fitted by least squares. Please note that the y-axis is logarithmically scaled again:

Carman-Korzeny Permeability 1.E-08 Calculated Line

) 2 ^ ( 1.E-09 m ty lii b a e rm 1.E-10 e P

Govignon Fitted Line Experimental Line

1.E-11 0.25

0.35

0.45

0.55

Fibre Volume Fraction Figure 6.11. Modified Carman-Korzeny Permeability

As can be seen from Figure 6.11 the calculated line has a completely different gradient to that of Govignon and the experimental points. The figure also shows how this project has a lower permeability at lower fibre volume fractions and a higher permeability at higher fibre volume fractions. The following table represents the values of

 

and :





Calculated line

2.37E-11

5.22

Least Squares Fit

1.73E-10

0.8374

Govignon

9.50E-11

2.60

Table 6.3. Modified Carman-Korzeny Constants

It was seen that the



constant controls the intercept of the graphs whilst the

gradient of the line. This explains the large difference in the





constant controls the

value of the fitted line and the Govignon line.

In section 7.1 below, the fitted line is used for comparison to the experimental data. The code for calculating the least squares fit is in Appendix F- Least Squares Fit Code.


Page 44



Infusion Experiments

The services of the stereophotogrammetry machine were once again called upon to measure the height of the preform during the infusion process. The following procedure details the process that was followed. 6.3.1.

Infusion Test Procedure

First, it must be mentioned that the stereophotogrammetry machine was in position whilst the layup was being setup. It proved to be very sensitive to bumps and had to be recalibrated a number of times which not only took precious time but also wasted that infusion experiment as the results obtained could not be calculated and this was only discovered after all the pictures had been taken. This resulted in less than the desired number of tests being completed. The following procedure was followed: 1.

The required layers were cut to the correct size and placed on the table. It was important to ensure that the layup was in the middle of the range of the cameras as there was not a lot of room to spare in terms of the limits of the recordable size of the cameras. This can be seen in Figure 6.5.

2.

The inlet was made using a piece Rovichord with resin distribution tape under it. This created a good line inlet for the infusion, ensuring the 1D simplification is valid. Figure 6.12 shows this below:

Figure 6.12. Resin Inlet

3.

The outlet was made in a similar manner however, the distribution mesh was neglected. It was ensured that the Rovichord was in contact with the full width of the layup to make sure the vacuum is applied equally over the entire preform.

4.

Tacky tape was then placed around the sides of the preform, however a gap was left between the side of the layup and the tape to ensure that the bag would touch the glass and thus prevent fast tracking of the resin. This is also shown in Figure 6.12.

5.

The bag was the stuck down. It was pulled slightly tight; this ensured no folds along the layup and thus a good surface for the stereophotogrammetry machine take measurements off.

6.

The vacuum was then turned on and the layup was checked for leaks.

7.

The speckle paint was then applied and a test measurement was done with the cameras to ensure they were still correctly calibrated and working.


Page 45



The infusion was started by allowing the oil into the preform. The stereophotogrammetry machine was also triggered to take 600 pictures at 10-second intervals. Figure 6.13 shows a typical picture captured by one of the cameras. The large green section is the calculated area of the layup and the smaller one is on the gap between the fibres and the tape, this is to get a reference point for the zero of the z-axis.

Figure 6.13. Typical Stereophotogramme try Layup Image

9.

The resin flow was then monitored until it reached the outlet at which point the resin inlet was clamped and the post filling process was left to continue.

Once all the photos had been captured, the processing of them started. A mask was defined over the preform and one just next to it. This decreased the amount of computational time required dramatically. Starting points for the calculations also had to be defined and the computational process was started. With 600 pictures from each camera, this took approximately 30min. The test was done twice and the two results nearly identical. 6.3.2.

Infusion Test Parameters

The following table shows the parameters decided upon for the experiments: Parameter

 

Value

Length-

400mm

Width-

130mm

Layers

10

Atmospheric Pressure

87700 Pa

Vacuum Pressure

22700 Pa

Table 6.4. Infusion Experiemental Parameters

The seeming random width was chosen as this created the least waste over the roll width that the fibre came on whilst ensuring that the edges do not affect the flow.


Page 46



Infusion R esults

Figure 6.14 shows an image of the calculated results gained from the infusion experiments.

Figure 6.14. Infusion Calculated Solution Example

From this is can be seen that the edges do not influence the flow in the preform and that the preform is uniform in the y direction. The two lines of small dots along the length of the preform are the points at which data was extracted from the model. Thus, there were two points over the width that gave very similar results and thus were averaged. There were spaced at the following intervals along the length of the preform: 0, 10, 20, 40, 80, 12, 160, 200, 240, 280 and 320mm. The reason for this not going all the way to 400mm, which is the preform length, is that the cameras struggled to pick up enough differential on the edges of the layup as a result of the Rovichord placed on the ends and hence the mask was applied to the layup for 320mm in the middle of the 400mm length. These points are now known and thus it will be easy to compare to the same points in the model at a later stage. Due to the sensitivity of the stereophotogrammetry machine, the data obtained contained some noise. This was smoothed using a function in Octave that uses Tikhonov regularization to smooth the data. Figure 6.15 shows the effect the smoothing algorithm has on the data.

Effect of Data Smoothing 3.30 3.28 3.26 ) 3.24 m 3.22 m ( t 3.20 h g i 3.18 e H3.16 3.14 3.12 3.10

Raw Data Smoothed

0

1000

2000

3000

4000

5000

6000

Time (s)

Figure 6.15. Effect of Data smoothing


Page 47



After this smoothing was applied to the entire field of data, the following plot was obtained using the surf function in Octave.

Figure 6.16. Change in Height over Preform with Time

Figure 6.16 above a good general view of the process, however there is little detail on factors such as the compaction change when the fibre is wetter. Figure 6.17 and Figure 6.18 shows these changes more clearly.

Point Heights with Time 5.50 5.00 e tli 4.50 T s i x4.00 A

Point 30mm

3.50

Point 350mm

Point 50mm Point 110mm Point 250mm

Clamping Time

3.00 0

2000

4000

6000

Axis Title Figure 6.17. Point Heights with Time

Form this figure it can be seen how the height increases and then almost immediately drops off once the inlet has been closed and that effect seems to lag behind slightly for the points further down the preform. One can also see how the change in the height is greater the closer the point is to the inlet to very little for points closer to the outlet.


Page 48



Point Heights with Time- Single Point 3.29 3.27 ) m3.25 m ( 3.23 t h g i 3.21 e H3.19

Point 320mm Clamping Time

3.17 3.15 0

2000

4000

6000

Time (s)

Figure 6.18. Point Heights with Time- Single Point

This graph shows how the height varies for a point that is close to the outlet. Something that is noticeable is the decrease in the height between 2000 and 3000 seconds. This is attributed to the change in the compaction factors and fibres now compacting more because they are wet. There is also a slight increase leading up to this point. The reason for this is not exactly known, as the model would have this represented as a straight line as it is just a preform under vacuum. A number of factors could cause this increase to occur, one of them being the fact that the bag is not being modelled. Before this point in the preform, the bag is moving due to the flow and this could influence the height of this point but it could also cause a slight disturbance on the bag and this would be interpreted as a change in height by the stereophotogrammetry machine. It is also noteworthy that this point does not experience the drop in pressure due to the clamping of the inlet. This indicates that the pressure distribution takes time to equalize after clamping and the excess oil that is being sucked out also still flows past this point. Due to the fine scale on y-axis in Figure 6.18 some of the data could be slightly skewed due to the smoothing. This is particularly evident when comparing it to Figure 6.17 where it is represented as a straight line. There are also many other factors that have not been considered such as keeping a constant temperature in the room as well as and wind that could be causing slight vibrations. Depending on the sensitivity of the measurements, even walking on the floor next to the tripods of the cameras could have influenced the results.


Page 49


Comparison of Experiments and Model

COMPARISON OF EXPERIMENTS AND MODEL

The following section aims to compare the experimental values obtained for the flow and the values calculated by the model. Due to the fact that the height value is the only one that is being solved and it was the only one measured in section 6.3 all the comparisons will only be comparing these values. 7.1.

Comparison Using Exact Experimental Values

This comparison is to the model using the exact values calculated in section 6.2. The results are not expected to be very accurate due to the inaccuracies in determining experimental constants. The dashed lines are generated by the model and the solid lines are experimental line. For all of the comparison figures the same points in the preform are compared and the bottom most line is the point closest to the outlet and the highest line is that closest to the inlet. The lines in-between these are thus scaled between these two.

Comparison Using Exact Experimental Values 5.50 5.00 ) 4.50 m m ( 4.00 t h 3.50 g i e H3.00

2.50 2.00 0.00

1000.00

2000.00

3000.00

4000.00

5000.00

6000.00

7000.00

Time (s)

Figure 7.1. Exact Experimental Values Comparison

From the figure above a number of things must be pointed out. The first is that the time to complete the infusion process is approximately half of what it should be in the model. It was found that the permeability of the layup controlled this aspect of the infusion. The conclusion is thus that the volume fractions for which the permeability tests were done for were not far enough apart. The reasons for this were discussed in section 6.2.2.2. It is also seen that the two preforms start at different heights and this because of the compaction model not being accurate. The models also do not have a similar change in height. This is once again attributed to the compaction model that has been set up. 7.2.

Fitting Model to Improve Results

This section aims to fit the results of the model to those gained experimentally. The supervisor suggested that this be done using the least squares method. A number of problems were encountered when applying this to the model. The first was that of running time. It took approximately 23 hours to do 20 iterations of the least squares method on the model and this did not provide convergence. This method only started a week before the due date of the project and it would not doubt be possible with slightly more time.

the



It was found that the time to complete the infusion could easily be adjusted to the right value by using value in the permeability equation. By changing this value to 4.9e-11 the time to complete the infusion would

be correct at 3200 seconds. This value does not change the gradient of the line, merely the intercept, meaning that the permeability is lower that the experimentally found value.


Page 50



The remaining adjustments were done to the compaction constants. These were done by taking the initial height values to find the needed compaction constants, the idea being that the initial values will be the same for the model and the experiment. It was also decided to adjust the model slightly. Due to the current model being a power law the volume fraction at zero compaction stress is zero, whereas in reality this is not the case as the fibre under no compaction will still have thickness. The power law equation was thus adjusted to give the fibre a thickness at zero stress. This is represented by the following equation:

  

(4.1)

Using the experimental data for the compaction the following values were obtained using the least squares method describes earlier:

  

Dry

Wet

0.01501

0.02088

0.25813

0.21113

0.2097

0.29699

Table 7.1. Fitted Constants

It should be noted that the highest point in the experiment is not necessarily accurate and it is expected that this values are so large as a result of the Rovichord which pushes the inlet side of the preform higher due to the stress it places on the bag. This hypothesis could easily be tested by using a different method of introducing the resin to the system that did not lift the bag up. The following figure shows the model in dashed lines and the experimental data in with solid lines.

Fitted Comparison 5.50 5.00 ) m4.50 (m t h g i 4.00 e H

3.50 3.00 0.00

1000.00

2000.00

3000.00

4000.00

5000.00

6000.00

7000.00

Time (s)

Figure 7.2. Fitted Comparison



Figure 7.2 shows that the time estimate is now accurate using the adapted value for permeability. The problem is however in the height of the preform. This is expected to be both as a result of the compaction model that has been used as well as the Rovichord problem mentioned earlier. The other difference is the change in the gradient once the model has been clamped. The model tends to drop off much quicker than the experimental values. The reason for this phenomenon is not exactly known and it was a problem that was experienced by Govignon et al (2010) as well. It would appear that the permeability of the layup is increased in the post-filling process and therefor the time taken to remove the excess oil is more than predicted. The other factor that must be considered is the vacuum bag. This could be playing a role in the process and the role is unknown and would be difficult to model. University of Pretoria - MSC 422

Page 51



The following figure shows the complete field of the process and is the model equivalent to that given in Figure 6.16. Change in Height over preform with time

0.0044 0.0042 0.004 0.0038 0.0036 0.0034 0

0.0032 0.003

1000 0 2000

20 3000

40 4000

60 Preform length (x-mm)

Time (s)

5000

80 6000

100 120 7000

Figure 7.3 . Full Field of Model


Page 52


CONCLUSION AND FUTURE WORK

8.1.

Conclusion

Conclusion and Future Work

A literature review was done and a number of similar studies were found. The student studied these and came to a number of conclusions, which resulted in decisions being taken as to which models to use and what equations to apply. The data from these literature studies was also used in this report for comparison purposes. This report presents a model for the vacuum infusion process that has been implemented in Octave and applied to a certain preform. The model and the experiments are discussed separately and then a discussion on the comparison between them will follow. The model that has been presented is a simplified version of that presented by Govignon et al (2010). It has been verified and validated to the best of the student’s ability using the available data and found that results from the student’s model and that of Govignon are very similar, however both vary when compared to reality. The experiments performed to determine the experimental constants did not give conclusive results and this is evident in the comparison. These experiments proved difficult to complete and would be easier using more specialized equipment, however with some refinement the experiments used here could be applied successfully. The use of the stereophotogrammetry equipment provided a very accurate representation of the physical process. Due to the constants that were determined not being accurate the comparison proved very difficult. The filling process would seem to have the correct shape whereas the post filling process seems to be a lot slower in reality. This is attributed to a number of factors including the bag. The lifting of the preform to a higher-thanpredicted point can be attributed to the Rovichord or possibly flow between the layers of the preform, which is not accounted for in the model. The model and the experimental work do thus not correspond directly however it is believed that with accurate constants in the model this could be corrected. The model was found to be very robust and able to model many different sets of constants. The attached compact disc contains the code for this model as well as all the experimental data obtained and a PDF version of this report. 8.2.

Future Work

The biggest problem in this project was the determining of the constants that were used in the model. The student believes that an entire project could be dedicated to determining an accurate compaction model and permeability model. Once these models have been accurately set up, the model presented here could be applied and thus the entire process could be accurately modelled. Naturally the fibre that is being used plays a role in model as well as the number of layers and each of these would need to be investigated in these projects. Once accurate models exist for these properties of the process the model could be tested again and it is believed that accurate results would be obtained. This model could also be changes and applied in 2D. A 2D model is something that has never been done before using the fundamental equations presented in this report and would be the next logical step in the process.


Page 53


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Mekic, S., Akhtov, I. and Ulven, C. (2009) 'A Radial Infusion Model for Transverse Permeability Measurements of Fiber Reinforcement in Composite Materials', Polymer Composites , pp. 907-917.



Pearce, N. and Summerscales, J. (1995) 'The Compressibility of a Reinforcement Fabric', Composites Manufact uring , vol. 6, no. 1, pp. 15-21.



st

Schafer, M. (2006) Computational Engineering , 1 edition, Berlin: Springer.


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Modelling the Vacuum Infusion Process 

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Song, Y.S. and Youn, J.R. (2009) 'Numerical Investigation on Flow through Porous Media in the Post-infusion Process', Polymer Composites , pp. 1125-1131.

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Walsh, S.M. and Freese, C.E. (2005) 'Numerical Model of Relaxation During VacuumAssisted Resin Transfer Molding (VARTM)', Polymer Composites , pp. 628-635. th

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White, F.M. (2008) Fluid Mechnic s, 6 edition, New York: McGraw-Hill Companies Inc.

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Williams, C.D., Grove, S.M. and Summerscales, J. (1998) 'The compression response of fibre-reinforces plastic plates during manufacture by the resin infusion under flexible tooling ethod', Composites Part , vol. A 29, no. A, pp. 111-114.

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Williams, C., Summerscalest, J. and Grove, S. (1996) 'Resin Infusion under Flexible Tooling (Rift): A Review', Composites , vol. A, no. 27, pp. 517-524.

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Yenilmez, B., Senan, M. and Murat Sozer, E. (2009) 'Variation of part thickness and compaction pressure in vacuum infusion process', Compositescienc S e and Te chnology , vol. 69, pp. 1710-1719.

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Zabaras, N. and Samanta, D. (2004) 'A stabilized volume-averaging finite element method for flow in porous medis and binary alloy solidification', Internat ionalJournal for Numeric al , vol. 60, no. 5, pp. 1-38. Methods in Engineering

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Appendix A- Protocol

APPENDIX A- PROTOCOL


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Appendix B- Progress Report 1

APPENDIX B- PROGRESS REPORT 1

MSC Progress Report 1- 22/03/2011

Student: Grant Stephens (27040713)

Supervisor: Dr Wilke

Modellingthe Va cuum Infusion Process without Flow Media

This report aims to give a brief overview of the progress that the student has made with the above mentioned project. The updated gantt chart is attached as well as the literature review to date. The student has made some progress in the literature review however this was slow due to the technical nature of many articles. The attached literature review shows what the student considers a good general background into the process as well as the history of the process. Most of this information was easy to obtain thanks to the review on the history by Williams in 1996. The process has existed for a long time and hence the history portion could be considerably larger, however the student believes that this is not necessary in the project as it has little influence. Research into the permeability of the fibres was relatively easy and a number of studies were found that contained useful information. The formulas listed is purely from one source and the student feels that the next step would be to verify these formulas by either finding more studies using the same method or doing experiments to verify them. The problem with finding the permeability in this manner is that the viscosity of the resin (or similar testing substance) must be known as well as it being a destructive test in that the fibres cannot be used again after finding their permeability. The student feels that a method should be found that does not destroy the fibres when the experiment is done. A brief overview of some different resins is given however not completed. Once this is completed a resin can be selected and then the viscosity can be investigated. An important point is the danger that some resins pose as opposed to other safe resins. This would be a big factor to consider when selecting a resin for the model. An ASTM code has been found which can be used to determine the viscosity of the resin, however acquiring this code and checking if it is applicable must still be attempted. A number of other studies were found that are similar to this project. These studies were very specific in their scope and cannot be applied universally. There is also often very little information about how they went about determining constants and boundary conditions. A CFD package that can model the process was used in one of the studies which proved to have good results. This CFD package must be investigated further and especially when choosing one to do the simulations on. A number of studies stated the flexible nag as being one of the problems they encountered. This is another factor which must carefully be chosen when doing the experimental process. The CFD packages in the labs are proving to be a problem as there seems to be issues with the licences. In conclusion, the student feels that the background and history aspects of the literature study are dealt with; however a large amount of work is still needed in the viscosity and permeability departments. The boundary conditions are one area of concern as very little was found about them is the literature. A meeting with the student doing a similar project with flow media will be scheduled to compare findings and possible collaborate in certain areas.


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Appendix C- Progress Report 2

APPENDIX C- PROGRESS REPORT 2

MSC Progress Report 2- 29/08/2011

Student: Grant Stephens (27040713)

Supervisor: Dr Wilke

Modellingthe Va cuum Infusion Process without Flow Media

This report aims to give a brief overview of the progress that the student has made with the above mentioned project. The updated Gantt chart is attached to provide a graphical view of the current progress. The student has made good progress with regard to implementing a mathematical model, however progress on the experiments has not started yet and is explained in this report. The implementation of the model as presented by Govignon et al has progressed well and can now replicate the results that were obtained by his model, however the model fails to accurately represent the post filling flow in the preform as well as the final height profile as obtained by his experiments. Reasons for this are currently being investigated and different constants for the relationship between the permeability and the volume fraction are being tested. There is also a slight problem with an instability that perturbs the post filling solution, however it is expected that this is merely a programming error and should not prove to be a problem. The model behaves well when using different constants, however the real test lies in using it with the student’s own set of experimental results. The experimental side of the project has been very slow up to this point due to problems aquireing equipment for the labs, however it has now been ordered and should arrive in about a week. If for some reason the lab equipment does not arrive in the next week as backup plan has been devised and researched which will make use of a venturi system to draw a vacuum. Once the equipment has arrived the lab can be set up and experimentation can begin. The student has also been able to obtain the use of the stereophotogrammetry measurement equipment in the labs and this will be used to obtain a very accurate representation of the flow in the preform (Up to a few microns in displacement). The only concern is that this equipment is only available for the last week before the labs close and hence time is limited after this to finish the report. It has thus been decided that the results obtained from this equipment will be used for an accurate representation of the problem and a simpler method of using micrometers will be used for the validation of the model. Overall progress has been good however a lot of work lies ahead in the next few weeks. The Gantt chart has had to be adjusted slightly to account for the labs not being available. This also means that the writing of the final report will be starting later. There was a initially lot of time allocated to this and therefor it is not seen as a problem at this stage.


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Appendix D- Report Card

APPENDIX D- REPORT CARD


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Appendix E- Plaigarism Sheet

APPENDIX E- PLAIGARISM SHEET

MECHANICAL AND AERONAUTICAL ENGINEERING MEGANIESE EN LUGVAARTKUNDIGE INGENIEURSWESE INDIVIDUAL ASSIGNM ENT COVER P AGE /INDIVIDUELE OPDRAG DEKBLAD

Name of Student / Naam van Student

Grant Stephens

Student numberStudente / nomme r

27040713

Name of Module / Naam van Module

Project

Module Code / Modulekode

MSC 422

Name of Lecturer / Naam van Dosent

Dr Wilke

Date of Submission / Datum van Inhandiging 23/10/2011 Declaration:

Verklaring:

1. I understand what plagiarism is and am aware of

1. Ek begryp wat plagiaat is en is bewus van die

the University’s policy in this regard.

Universiteitsbeleid in hierdie verband.

2. I declare that this half report is my own, srcinal

2. Ek verklaar dat hierdie verslag my eie,

work. 3. I did not refer to work of current or previous

oorspronklike werk is. 3. Ek het nie gebruik gemaak van huidige of vsrce

students, memoranda, solution manuals or any other

studente se werk, memoranda, antwoord-bundels of

material containing complete or partial solutions to

enige ander materiaal wat volledige of gedeeltelike

this assignment.

oplossings van hierdie werkstuk bevat nie.

4. Where other people’s work has been used (either

4. In gevalle waar iemand anders se werk gebruik is

from a printed source, Internet, or any other source),

(hetsy uit ´n gedrukte bron, die Internet, of enige

this has been properly acknowledged and referenced.

ander bron), is dit behoorlik erken en die korrekte

5. I have not allowed anyone to copy my assignment.

verwysings is gebruik. 5. Ek het niemand toegelaat om my werkopdrag te kopieër nie.

Signature of Student / Handtekening van Student


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Appendix F- Least Squares Fit Code

APPENDIX F- LEAST SQUARES FIT CODE function [kout ] = fperm (vf,guess )

c_perm =guess(1) n_perm =guess(2) for i=1:length (vf)

kout(i)=c_perm .*((1-vf(i)).^(n_perm+1)./(vf(i).^n_perm )); end;

%perm least squares guess (1)=1.8e-10 guess (2)=0.78 vf=[0.34 0.4 0.44] y(1)=2.02e-10 ; y(2)=1.40e-10 ; y(3)=1.21e-10 ; [f,p,cvg,iter ,corp ,covp ,covr,stdresid ,Z,r2]=leasqr (vf,y,guess ,'fp

erm')


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Modelling Vacuum Infusion

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