{"Affiliation":[{"label":"Affiliation","value":"Applied Science, Faculty of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."},{"label":"Affiliation","value":"Mechanical Engineering, Department of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"AggregatedSourceRepository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Campus":[{"label":"Campus","value":"UBCV","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","classmap":"oc:ThesisDescription","property":"oc:degreeCampus"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the name of the campus from which the graduate completed their degree."}],"Creator":[{"label":"Creator","value":"Zhang, Xun","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"DateAvailable","value":"2009-08-04T19:35:02Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"DateIssued","value":"2001","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Degree":[{"label":"Degree","value":"Master of Applied Science - MASc","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","classmap":"vivo:ThesisDegree","property":"vivo:relatedDegree"},"iri":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","explain":"VIVO-ISF Ontology V1.6 Property; The thesis degree; Extended Property specified by UBC, as per https:\/\/wiki.duraspace.org\/display\/VIVO\/Ontology+Editor%27s+Guide"}],"DegreeGrantor":[{"label":"DegreeGrantor","value":"University of British Columbia","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","classmap":"oc:ThesisDescription","property":"oc:degreeGrantor"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the institution where thesis was granted."}],"Description":[{"label":"Description","value":"The prediction of fiber orientation is a critical parameter for papermakers who wish to\r\ncontrol the quality of their paper products. The wet end processes, especially the headbox\r\nand the drainage stage on the forming wire, play important roles in determining the fiber\r\norientation characteristics. The current thesis is focused on the headbox flow effect on\r\nfiber orientation. It summarizes a mathematical method, which has been developed by\r\nother researchers, for predicting the orientation of rigid fibers in dilute suspensions. This\r\nmethod, composed of a turbulent flow simulation model and a fiber motion model, has\r\nbeen applied to predict fiber motion in a headbox. To validate the method, experiments\r\nhave been conducted by measuring the orientation of dyed nylon fibers moving in a pilot\r\nplexiglass headbox. Comparison of experiments and the present numerical simulations of\r\nthe fiber orientation shows that the simulation method proposed can predict the trend of\r\nthe statistical orientation distribution of dilute suspensions in headboxes, although there\r\nexists obvious deviations between the simulations and experiments. The fibers are seen to\r\nbe more strongly oriented by the predictions than is observed in the experiments. The\r\nanisotropy of the fiber orientation in the headbox flow is caused not only by the mean\r\nflow field characteristics, but also by the turbulence characteristics, and the explicit\r\neffects of the turbulence are not yet included in the predictions. The simulation method is\r\napplied to predict fiber orientations for different headbox geometry, fiber aspect ratio and\r\nflow rate. From the prediction method, using only the mean flow effects, a larger\r\ncontraction ratio is found to produce more concentrated fiber orientation in the flow\r\ndirection at the exit of the headbox. The channel length, the flow velocity and the fiber\r\naspect ratio within the range of study have little influence on the fiber orientation\r\nproperties.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"DigitalResourceOriginalRecord","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/11614?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"Extent":[{"label":"Extent","value":"6377131 bytes","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/extent","classmap":"dpla:SourceResource","property":"dcterms:extent"},"iri":"http:\/\/purl.org\/dc\/terms\/extent","explain":"A Dublin Core Terms Property; The size or duration of the resource."}],"FileFormat":[{"label":"FileFormat","value":"application\/pdf","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/elements\/1.1\/format","classmap":"edm:WebResource","property":"dc:format"},"iri":"http:\/\/purl.org\/dc\/elements\/1.1\/format","explain":"A Dublin Core Elements Property; The file format, physical medium, or dimensions of the resource.; Examples of dimensions include size and duration. Recommended best practice is to use a controlled vocabulary such as the list of Internet Media Types [MIME]."}],"FullText":[{"label":"FullText","value":"F I B E R O R I E N T A T I O N I N A H E A D B O X b y X u n Z h a n g B . E n g . N o r t h w e s t e r n P o l y t e c h n i c a l U n i v e r s i t y , C h i n a , 1985 E n g . B e i j i n g U n i v e r s i t y o f A e r o n a u t i c s a n d A s t r o n a u t i c s , C h i n a , 1 9 8 8 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S O F T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E i n T H E F A C U L T Y O F G R A D U A T E S T U D I E S D E P A R T M E N T O F M E C H A N I C A L E N G I N E E R I N G W e a c c e p t t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d s t a n d a r d T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A J a n u a r y 2 0 0 1 \u00a9 X u n Z h a n g , 2 0 0 1 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l l m e n t o f the r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e that the l i b r a r y s h a l l m a k e it f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e that p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s m a y b e g r a n t e d b y the h e a d o f m y d e p a r t m e n t o r b y h i s o r h e r r e p r e s e n t a t i v e s . It i s u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t m y w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a 2 3 2 4 M a i n M a l l V a n c o u v e r , B C V 6 T 1 Z 4 D a t e : J a n u a r y 2 0 0 1 ABSTRACT The prediction of fiber orientation is a critical parameter for papermakers who wish to control the quality of their paper products. The wet end processes, especially the headbox and the drainage stage on the forming wire, play important roles in determining the fiber orientation characteristics. The current thesis is focused on the headbox flow effect on fiber orientation. It summarizes a mathematical method, which has been developed by other researchers, for predicting the orientation of rigid fibers in dilute suspensions. This method, composed of a turbulent flow simulation model and a fiber motion model, has been applied to predict fiber motion in a headbox. To validate the method, experiments have been conducted by measuring the orientation of dyed nylon fibers moving in a pilot plexiglass headbox. Comparison of experiments and the present numerical simulations of the fiber orientation shows that the simulation method proposed can predict the trend of the statistical orientation distribution of dilute suspensions in headboxes, although there exists obvious deviations between the simulations and experiments. The fibers are seen to be more strongly oriented by the predictions than is observed in the experiments. The anisotropy of the fiber orientation in the headbox flow is caused not only by the mean flow field characteristics, but also by the turbulence characteristics, and the explicit effects of the turbulence are not yet included in the predictions. The simulation method is applied to predict fiber orientations for different headbox geometry, fiber aspect ratio and flow rate. From the prediction method, using only the mean flow effects, a larger contraction ratio is found to produce more concentrated fiber orientation in the flow direction at the exit of the headbox. The channel length, the flow velocity and the fiber aspect ratio within the range of study have little influence on the fiber orientation properties. ii T A B L E O F C O N T E N T S A B S T R A C T i i T A B L E OF CONTENTS i i i LIST OF T A B L E S v LIST OF FIGURES vi A C K N O W L E D G E M E N T S vii i 1. INTRODUCTION 1 2. L I T E R A T U R E REVIEW 3 2.1 Fiber Orientation and Paper Quality 3 2.2 The Definition of Fiber Orientation 4 2.3 Factors Affecting Fiber Orientation 5 2.3.1 Headbox 6 2.3.2 Jet to Wire Speed Difference 8 2.3.3 Forming Wire 8 2.3.4 Fiber Suspension Consistency 9 2.4 Headbox Flow Simulations to Investigate Fiber Orientation 11 2.5 Fiber Suspension Simulation 12 2.6 The Scope of This Thesis Work 15 3. E X P E R I M E N T A L A R R A N G E M E N T S 17 3.1 Objectives of the Experimental Work 17 3.2 Fiber Suspensions 17 3.3 Flow Loop 18 3.4 Image Analysis System 19 i i i 3.5 M e a s u r e m e n t 2 0 4 . C O M P U T E R S I M U L A T I O N O F F L O W A N D F I B E R O R I E N T A T I O N 2 8 4.1 T h e H e a d b o x F l o w M o d e l 2 9 4 . 2 F i b e r M o d e l 3 2 5. R E S U L T S A N D D I S C U S S I O N 3 6 5.1 A n a l y s i s o f the H e a d b o x F l o w F i e l d 3 6 5.2 C o m p a r i s o n o f S i m u l a t i o n a n d E x p e r i m e n t a l R e s u l t s 3 9 5.3 F a c t o r s A f f e c t i n g F i b e r O r i e n t a t i o n 4 4 5.3.1 T h e E f f e c t o f C o n t r a c t i o n R a t i o o n F i b e r O r i e n t a t i o n 4 4 5 .3 .2 T h e E f f e c t o f F l o w R a t e o n F i b e r O r i e n t a t i o n 4 5 5 .3 .3 T h e E f f e c t o f C h a n n e l L e n g t h o n F i b e r O r i e n t a t i o n 4 6 5 .3 .4 T h e E f f e c t o f F i b e r A s p e c t R a t i o o n F i b e r O r i e n t a t i o n 4 7 5 .3 .5 T h e E f f e c t o f F l o w E l o n g a t i o n 4 7 5 .4 S y m m e t r i c C h a n n e l 4 8 5.5 S t a t i s t i c a l E r r o r E s t i m a t i o n 4 9 6. S U M M A R Y A N D C O N C L U S I O N S 6 0 7. R E C O M M E N D A T I O N S F O R F U T U R E W O R K 6 2 8. N O M E N C L A T U R E 6 4 9. R E F E R E N C E S 6 6 i v LIST OF TABLES T a b l e 3.1. T h e G e o m e t r y o f the H e a d b o x C o n v e r g i n g S e c t i o n 18 T a b l e 3.2. T h e S i g n o f the O r i e n t a t i o n A n g l e s 21 T a b l e 3.3. T h e N u m b e r o f F i b e r s at E a c h M e a s u r e m e n t P o i n t 22 T a b l e 5.1. O r i e n t a t i o n P a r a m e t e r s O b t a i n e d f r o m E x p e r i m e n t s a n d S i m u l a t i o n s : 43 T a b l e 5.2. F i b e r O r i e n t a t i o n P a r a m e t e r s f o r D i f f e r e n t Rc (Uo = 0.24 m \/ s , L c = 0.225 m ) 45 T a b l e 5.3. T h e O r i e n t a t i o n P a r a m e t e r s f o r D i f f e r e n t Uo (Rc= 10, L c = 0.225 m ) 46 T a b l e 5.4. F i b e r O r i e n t a t i o n P a r a m e t e r s f o r D i f f e r e n t L c (Rc= 10, Uo-0 .24 m \/ s ) 46 T a b l e 5.5. T h e O r i e n t a t i o n P a r a m e t e r s f o r D i f f e r e n t A r ....47 T a b l e 5.6. T h e E l o n g a t i o n o f F l o w at the C h a n n e l E x i t f o r D i f f e r e n t Rc 48 T a b l e 5.7. O r i e n t a t i o n P a r a m e t e r s at E x i t o f A S y m m e t r i c H e a d b o x f o r D i f f e r e n t U 0 : 48 v L I S T O F F I G U R E S F i g u r e 2 . 1 . F i b e r o r i e n t a t i o n d i s t r i b u t i o n p a t t e r n i n a p i e c e o f p a p e r 16 F i g u r e 3 . 1 . T h e l e n g t h d i s t r i b u t i o n o f n y l o n f i b e r s 23 F i g u r e 3 .2 . I m a g e s o f f i b e r s : (a) d r y d y e d n y l o n f i b e r s , (b) f i b e r s u s p e n s i o n 23 F i g u r e 3 .3 . T h e f l o w l o o p i n the e x p e r i m e n t 2 4 F i g u r e 3 .4 . T h e s c a l e d p l e x i g l a s s h e a d b o x u s e d i n the e x p e r i m e n t 2 4 F i g u r e 3 .5 . C r o s s s e c t i o n a l v i e w o f the s c a l e d h e a d b o x ( d i m e n s i o n s i n c m ) 2 5 F i g u r e 3 .6 . T h e p h o t o g r a p h i c a r r a n g e m e n t f o r (a) s i d e v i e w a n d (b) b o t t o m v i e w 2 5 F i g u r e 3 .7 . T y p i c a l p i c t u r e o f f i b e r s i n the f l o w : (a) b e f o r e a n a l y s i s ; (b) af ter a n a l y s i s . . 2 6 F i g u r e 3 .8 . T h e m e a s u r e m e n t p o i n t s a l o n g the h e a d b o x c h a n n e l 2 7 F i g u r e 4 . 1 . A f i b e r i n t h r e e - d i m e n s i o n a l c o o r d i n a t e s 35 F i g u r e 4 . 2 . T h e i n i t i a l r a n d o m d i s t r i b u t i o n o f 1 0 0 0 f i b e r s 35 F i g u r e 5 .1 . T h e p h y s i c a l m e s h o f the a s y m m e t r i c c o n v e r g i n g s e c t i o n 5 2 F i g u r e 5 .2 . T h e s t r e a m l i n e s o f the f l o w i n the h e a d b o x c o n v e r g e n t c h a n n e l 5 2 F i g u r e 5 .3 . T h e p r e s s u r e a n d u - v e l o c i t y c h a n g e s a l o n g the c e n t r a l s t r e a m l i n e 53 F i g u r e 5 .4 . T h e u - v e l o c i t y c o n t o u r s o n the c e n t r a l s y m m e t r y p l a n e 53 F i g u r e 5 .5 . T h e v - v e l o c i t y c o n t o u r s o n the c e n t r a l s y m m e t r y p l a n e 53 F i g u r e 5 .6 . T h e e l o n g a t i o n o f the f l o w c h a n g e s a l o n g the c e n t r a l s t r e a m l i n e 5 4 F i g u r e 5 .7 . T h e fiber o r i e n t a t i o n d i s t r i b u t i o n at x = 4 .5 c m , 5 4 F i g u r e 5 .8 . T h e fiber o r i e n t a t i o n d i s t r i b u t i o n at x = 12.2 c m , 55 F i g u r e 5 .9 . T h e fiber o r i e n t a t i o n d i s t r i b u t i o n at x = 15 .7 c m , 55 F i g u r e 5 .10 . T h e fiber o r i e n t a t i o n d i s t r i b u t i o n at x = 19.2 c m , 5 6 F i g u r e 5 . 1 1 . T h e f i b e r o r i e n t a t i o n d i s t r i b u t i o n at x = 2 2 . 7 c m , 5 6 F i g u r e 5 .12 . T h e fiber o r i e n t a t i o n d i s t r i b u t i o n at x = 2 6 . 2 c m , 5 7 F i g u r e 5 . 1 3 . T h e fiber o r i e n t a t i o n d i s t r i b u t i o n at the c h a n n e l ex i t , 5 7 F i g u r e 5 .14 . T h e o r i e n t a t i o n p a r a m e t e r s a l o n g the c e n t r a l s t r e a m l i n e , 58 F i g u r e 5 . 1 5 . F i b e r o r i e n t a t i o n d i s t r i b u t i o n s at the c h a n n e l e x i t f o r v a r i o u s C o n t r a c t i o n r a t i o s , (a) i n x - y p l a n e , (b) i n x - z p l a n e 58 v i F i g u r e 5 . 1 6 . C r o s s s e c t i o n a l v i e w o f the s y m m e t r i c h e a d b o x ( d i m e n s i o n s i n m m ) 5 9 F i g u r e 5 . 1 7 . T h e p h y s i c a l m e s h o f the s y m m e t r i c h e a d b o x 5 9 A C K N O W L E D G E M E N T S I e x p r e s s s i n c e r e g r a t i t u d e to m y s u p e r v i s o r s , D r . M a r t h a S a l c u d e a n a n d D r . I a n G a r t s h o r e , f o r t h e i r h e l p f u l a d v i c e a n d s u g g e s t i o n s . I w o u l d a l s o l i k e to t h a n k m y c o l l e a g u e s , M o h a m m a d R . S h a r i a t i a n d S u q i n D o n g . T h e i r e f f o r t a n d h e l p h a s m a d e t h i n g s m u c h e a s i e r b o t h i n m y e x p e r i m e n t a l w o r k a n d m y s i m u l a t i o n w o r k . I a m g r a t e f u l f o r t h e f i n a n c i a l s u p p o r t p r o v i d e d b y F R B C R e s e a r c h A w a r d . F i n a l l y , I w i s h to t h a n k m y w i f e , Y i n g h u i , f o r h e r c o n s t a n t s u p p o r t a n d e n c o u r a g e m e n t d u r i n g the p a s t t w o y e a r s . v i i i 1. I N T R O D U C T I O N Paper is a heterogeneous three-dimensional composite of fibers and other materials. Its mechanical properties are highly dependent on the microstructure characteristics such as fiber properties, and the formation and orientation distribution of the fibers. The demand for high quality paper and paperboard has focussed the attention of papermakers on how to control these critical characteristics in the papermaking processes. The fiber orientation distribution in a piece of paper determines the distribution of strength, permeability and absorbency, and affects the dimensional stability, runability and printability of the paper. The fiber orientation in paper is determined by the processing conditions in the wet-end stage of the headbox and in the forming process. Experimental evidence has shown that fibers have some preferred orientation direction depending on the specific flow field. The headbox has a significant effect on the orientation of fibers leaving the slice. The elongation and shear in the flow leading to the slice tend to orient fibers in the machine direction. If the fiber orientation can be predicted for a given set of processing conditions, manufacturing paper with optimum mechanical properties will become much easier. The general objective of this thesis is to investigate, both numerically and experimentally, the three-dimensional fiber orientation produced by a dilute headbox flow. In the numerical simulations, both symmetric and asymmetric headboxes are studied. The numerical simulation method introduced here provides a quantitative methodology for the prediction of the fiber orientation resulting from the fluid kinematics. It can be used to predict fluid-fiber interactions and provide paper manufacturers a better knowledge of fiber orientation distribution and sheet properties. In this research work, several elements which affect the fiber orientation in a headbox, such as the headbox 1 g e o m e t r y , f l o w c o n d i t i o n s a n d f i b e r p r o p e r t i e s , are i n v e s t i g a t e d w i t h the p r e d i c t i v e a b i l i t y o f t h i s s i m u l a t i o n m e t h o d a n d the r e s u l t s are a n a l y z e d . F o l l o w i n g t h i s c h a p t e r , the r e l e v a n t l i tera ture i s r e v i e w e d i n C h a p t e r 2. T h e d e t a i l e d e x p e r i m e n t a l c o n d i t i o n s a n d m e t h o d s o f m e a s u r i n g the o r i e n t a t i o n d i s t r i b u t i o n o f f i b e r s i n a h e a d b o x f l o w are p r e s e n t e d i n C h a p t e r 3. C h a p t e r 4 d e s c r i b e s the n u m e r i c a l s i m u l a t i o n o f the fiber o r i e n t a t i o n d i s t r i b u t i o n b y a c o m b i n a t i o n o f a f l o w m o d e l a n d a f i b e r m o t i o n m o d e l . C h a p t e r 5 p r e s e n t s the c o m p a r i s o n o f m e a s u r e d a n d n u m e r i c a l l y s i m u l a t e d r e s u l t s . P a r a m e t r i c s t u d i e s , o b t a i n e d u s i n g the n u m e r i c a l m e t h o d , s h o w the i n f l u e n c e o f h e a d b o x g e o m e t r y , f l o w v e l o c i t y a n d fiber p r o p e r t y . C h a p t e r s 6 a n d 7 s u m m a r i z e the m a j o r c o n c l u s i o n s o f t h i s t h e s i s a n d g i v e r e c o m m e n d a t i o n s f o r f u t u r e r e s e a r c h , r e s p e c t i v e l y . 2 2. LITERATURE REVIEW 2.1 Fiber Orientation and Paper Quality A p i e c e o f p a p e r i s c o m p o s e d o f n u m e r o u s f i b e r s w h i c h are l o c a t e d w i t h i n t h e p a p e r p l a n e a n d o r i e n t e d i n d i f f e r e n t d i r e c t i o n s . S t a t i s t i c a l l y , h o w e v e r , m o s t o f the f i b e r s m a y b e a l i g n e d i n o n e d i r e c t i o n . T h i s a n i s o t r o p y o f f i b e r o r i e n t a t i o n i s p r o d u c e d b y t h e p a p e r m a n u f a c t u r e p r o c e s s a n d is c l o s e l y r e l a t e d to s e v e r a l c r i t i c a l p a p e r p r o p e r t i e s . T h e o r i e n t a t i o n p a t t e r n r e t a i n e d i n the final p a p e r c o n t r o l s the m e c h a n i c a l p r o p e r t i e s o f the sheet . N o r d s t r o m a n d N o r m a n [1] i n d i c a t e d that d e p e n d i n g o n the g r a d e , a c e r t a i n d e g r e e o f fiber o r i e n t a t i o n a n i s o t r o p y i n the p a p e r i s d e s i r e d . F o r n e w s p r i n t , a r a t h e r h i g h a n i s o t r o p y i s r e q u i r e d f o r g o o d r u n n a b i l i t y i n the p a p e r m a c h i n e a n d t h e p r i n t i n g p r e s s . B u t f o r w o o d - f r e e sheet g r a d e s , o n the o t h e r h a n d , a l o w e r a n i s o t r o p y is d e s i r e d to e n s u r e i s o t r o p i c d i m e n s i o n a l c h a n g e s w i t h v a r i a t i o n s i n m o i s t u r e a n d t e m p e r a t u r e . N o r d s t r o m a n d N o r m a n a l s o p o i n t e d o u t that the s t r e n g t h i n the p a p e r t h i c k n e s s d i r e c t i o n i s a f f e c t e d p o s i t i v e l y b y the d e g r e e o f f i b e r - t o - f i b e r b o n d i n g a n d a l s o b y the d e g r e e o f fiber o r i e n t a t i o n i n that d i r e c t i o n . T h e s t r e n g t h i n the p a p e r t h i c k n e s s d i r e c t i o n m u s t b e s u f f i c i e n t to a v o i d d e l a m i n a t i o n i n c o l d s e t o f f s e t p r i n t i n g , o r b l i s t e r i n g i n h e a t s e t o f f s e t p r i n t i n g . A s h e e t i s s t r o n g e r a n d s t i f f e r i n the d i r e c t i o n i n w h i c h m o s t f i b e r s are o r i e n t e d , a n d w e a k e r a n d m o r e c o m p l i a n t i n the d i r e c t i o n o f least o r i e n t a t i o n . W e c a n u n d e r s t a n d t h i s b y s t u d y i n g t h e p r o p e r t i e s o f the p r i n c i p a l c o n s t i t u e n t s o f p a p e r , the w o o d fibers, b e c a u s e t h e fiber p r o p e r t i e s a n d p a p e r p r o p e r t i e s are c l o s e l y c o r r e l a t e d [2, 3]. F i b e r d i m e n s i o n s , f l e x i b i l i t y a n d c o a r s e n e s s are c o n n e c t e d w i t h the m e c h a n i c a l p r o p e r t i e s , s t r u c t u r a l v a r i a b l e s a n d f o r m a t i o n o f p a p e r , s u c h as t e n s i l e s t r e n g t h , t e a r i n g s t r e n g t h , b u r s t i n g a n d b o n d i n g s t r e n g t h , p o r o s i t y a n d sheet d e n s i t y . 3 A w o o d f i b e r h a s q u i t e d i f f e r e n t p r o p e r t i e s a l o n g its a x i s c o m p a r e d to t h o s e a c r o s s it . F o r e x a m p l e , the s t r e n g t h o f a f i b e r i s m u c h greater a l o n g the f i b e r a x i s t h a n a c r o s s i t , w h e r e a s the w e t - e x p a n s i v i t y is greater a c r o s s the f i b e r a x i s t h a n a l o n g it [4]. I f t h e m a j o r d i r e c t i o n i s d e f i n e d as the d i r e c t i o n i n the p a p e r s u r f a c e t o w a r d w h i c h m o s t f i b e r s are a l i g n e d a n d the m i n o r d i r e c t i o n as the d i r e c t i o n n o r m a l to the m a j o r d i r e c t i o n , the f o l l o w i n g c o n c l u s i o n s a b o u t p a p e r p r o p e r t y c a n b e i n f e r r e d f r o m the fiber-paper r e l a t i o n s h i p . T h e t e n s i l e s t i f f n e s s , t e n s i l e e n e r g y a b s o r p t i o n , b e n d i n g s t i f f n e s s a n d c r u s h s t r e n g t h are h i g h e r i n the m a j o r d i r e c t i o n , b u t the tear s t r e n g t h a n d w e t e x p a n d i n g t e n d e n c y are h i g h e r i n the m i n o r d i r e c t i o n . D i r e c t i o n a l d i f f e r e n c e s i n m e c h a n i c a l p r o p e r t i e s h a v e b e e n e x p e r i m e n t a l l y c o r r e l a t e d w i t h fiber o r i e n t a t i o n [5, 6, 7]. S i g n i f i c a n t fiber m i s a l i g n m e n t m a y c a u s e s e r i o u s d e f e c t s , l e a d i n g to p o o r d i m e n s i o n a l s t a b i l i t y [8] a n d r e d u c e d s t r e n g t h . L o e w e n [6] s u m m a r i z e d t h e p a p e r q u a l i t y p r o b l e m s that are r e l a t e d to p o o r fiber o r i e n t a t i o n as f o l l o w s : \u2022 T w i s t , w a r p , c u r l a n d s t a c k - l e a n . \u2022 W e b w a n d e r i n g , m i s r e g i s t e r i n g i n m u l t i - p a s s p r i n t i n g a n d c o l o u r p r i n t i n g . \u2022 P a p e r f e e d p a t h j a m m i n g . \u2022 M u l t i - p a r t f o r m s d e b o n d i n g . \u2022 L o w t e n s i l e s t r e n g t h , l o w tear s t r e n g t h a n d w e a k s t i f f n e s s . \u2022 W r i n k l e s o n l o n g l e a d p r e s s e s a n d d r y e r w r i n k l e s . 2.2 The Definition of Fiber Orientation F i b e r o r i e n t a t i o n r e f e r s to the a n g u l a r d i s t r i b u t i o n o f f i b e r s r e l a t i v e to the p a p e r - m a c h i n e d i r e c t i o n ( M D ) . T h i s c a n b e v i s u a l i z e d i n the p o l a r d i a g r a m o f F i g . 2.1. T h e d i s t a n c e f r o m t h e o r i g i n at a g i v e n a n g l e i s p r o p o r t i o n a l to the n u m b e r o f f i b e r s o r i e n t e d i n that d i r e c t i o n . T h e p o l a r d i a g r a m d e s c r i b e s t w o c o m m o n l y u s e d fiber o r i e n t a t i o n t e r m s : t h e fiber o r i e n t a t i o n a n g l e a n d fiber o r i e n t a t i o n i n d e x . T h e fiber o r i e n t a t i o n a n g l e , 9 as s h o w n i n the d i a g r a m , i s the a n g l e f r o m the m a c h i n e d i r e c t i o n i n w h i c h m o s t o f the fibers are o r i e n t e d . T h e f i b e r o r i e n t a t i o n i n d e x is the r a t i o o f the f i b e r s o r i e n t e d i n the M D o v e r t h o s e o r i e n t e d i n the c r o s s m a c h i n e d i r e c t i o n ( C D ) , w h i c h is o f t e n d e f i n e d as t h e r a t i o o f M D to C D s t r e n g t h b a s e d o n the k n o w l e d g e that the f i b e r o r i e n t a t i o n d i s t r i b u t i o n c o r r e s p o n d s to the d i s t r i b u t i o n o f s t r e n g t h . T h e f i b e r o r i e n t a t i o n i n d e x o f F i g . 2.1 i s e q u a l to the r a t i o o f l e n g t h s a \/ b . 2.3 Factors Affecting Fiber Orientation P a p e r i s m a d e i n a c o n t i n u o u s p r o c e s s . T h e s u s p e n s i o n o f f i b e r s a n d f i l l e r s i s d i s c h a r g e d f r o m the s l i c e o f a h e a d b o x a n d d i s t r i b u t e d at h i g h s p e e d o n t o the f o r m i n g w i r e . O n the w i r e a s h e e t i s f o r m e d t h r o u g h d e - w a t e r i n g . T h e sheet t h u s f o r m e d is w e t a n d w e a k a n d n e e d s to b e f u r t h e r p r o c e s s e d i n p r e s s e s a n d d r y e r s . T h e p r i m a r y m e c h a n i s m o f o r i e n t i n g f i b e r s i n the sheet is the h y d r o d y n a m i c s h e a r f l o w s i n t h e e a r l y f o r m i n g s e c t i o n o r w e t e n d o p e r a t i o n s o f the p a p e r m a c h i n e , i . e . , h e a d b o x d i s c h a r g e a n d f o r m a t i o n p r o c e s s . T h e h e a d b o x d e s i g n c a n h a v e a n e f f e c t o n t h e o r i e n t a t i o n o f f i b e r s l e a v i n g the s l i c e . T h e e l o n g a t i o n a n d s h e a r l e a d i n g to t h e s l i c e t e n d to o r i e n t the f i b e r s i n the m a c h i n e d i r e c t i o n . M a n y r e s e a r c h e r s [4, 9 , 10] h a v e a n a l y z e d the f a c t o r s that a f f e c t f i b e r o r i e n t a t i o n a n d h a v e a g r e e d that the p r i m a r y m e c h a n i s m i n the sheet i s the h y d r o d y n a m i c p r o c e s s i n t h e h e a d b o x d i s c h a r g e a n d f o r m a t i o n o p e r a t i o n s o f the p a p e r m a c h i n e . W r i s t [11] s t u d i e d t h e f i b e r o r i e n t a t i o n i n t h e j e t a n d o n the f o r m i n g w i r e a n d c o n c l u d e d that the r e l a t i v e s p a t i a l a r r a n g e m e n t o f the f i b e r s i n a m a c h i n e - m a d e sheet o f p a p e r is v e r y l a r g e l y d e t e r m i n e d b e t w e e n the h e a d b o x a n d the e n d o f the f o r m i n g t a b l e . W i t h i n t h i s s p a c e , the o r i e n t a t i o n o f t h e f i b e r s , t h e d e g r e e o f f l o c c u l a t i o n , the r e l a t i v e d i s t r i b u t i o n o f m a t e r i a l s t h r o u g h t h e t h i c k n e s s o f the sheet a n d the m a c r o - a n d m i c r o - m a s s d i s t r i b u t i o n i n the p l a n e o f t h e s h e e t are a l l l a i d d o w n . S u b s e q u e n t p r o c e s s e s , l i k e p r e s s i n g a n d d r y i n g , h a v e m i n o r e f f e c t s o n f i b e r o r i e n t a t i o n w i t h o n l y s o m e m i c r o - r e a r r a n g e m e n t a n d c o n s o l i d a t i o n o f t h e w e b . N e x t w e w i l l s u m m a r i z e the m a j o r f a c t o r s i n the w e t e n d p r o c e s s e s that l e a d to n o n -5 u n i f o r m i t y o f f i b e r o r i e n t a t i o n . B e c a u s e th is w o r k i s f o c u s e d o n the h e a d b o x , w e w i l l start f i r s t w i t h t h e h e a d b o x e f f e c t o n the fiber o r i e n t a t i o n , t h e n c o n s i d e r r e l a t i v e w i r e s p e e d , w i r e t y p e s a n d fiber c o n s i s t e n c y . 2.3.1 Headbox A f u n d a m e n t a l f u n c t i o n o f a n y h e a d b o x is to e n s u r e the m a c h i n e a n d c r o s s m a c h i n e d i r e c t i o n a l u n i f o r m i t y . T w o areas that are f a c i n g i n c r e a s i n g l y s t r i n g e n t q u a l i t y d e m a n d s are u n i f o r m i t y o f b a s i s w e i g h t p r o f i l e s o n finer s c a l e s a n d the c o n t r o l l a b i l i t y o f fiber o r i e n t a t i o n p r o f i l e s . A h e a d b o x c a n b e d i v i d e d i n t o three s e c t i o n s b y the p r i n c i p a l f l o w p a t t e r n s i n v o l v e d [12] : f l u i d d i s t r i b u t i o n , f l o w r e c t i f i c a t i o n a n d j e t d e v e l o p m e n t . I n the first s e c t i o n , a t a p e r e d h e a d e r is u s e d to a c h i e v e i d e a l l y u n i f o r m f l o w i n t o the d i s t r i b u t o r . T h e n the f l o w f r o m t h e d i s t r i b u t o r i s i m p r o v e d t h r o u g h the r e c t i f i c a t i o n p r o c e s s e s . I n a h y d r a u l i c h e a d b o x , a t u b e b a n k is o f t e n u s e d i n t h e s e p r o c e s s e s . T h e w a l l f r i c t i o n i n t h e t u b e s d a m p e n s f l o w d i s t u r b a n c e s o r i g i n a t i n g i n the s t o c k a p p r o a c h s y s t e m a n d creates t u r b u l e n c e w h i c h i s n e e d e d to p r e v e n t fiber flocculation i n the p a p e r - m a c h i n e f o r m i n g z o n e . T h e p r o c e s s e s i n t h e t u b e b a n k m a y i n c l u d e m i x i n g a n d b l e n d i n g o f separa te f l o w s f r o m a d i s t r i b u t o r , e l i m i n a t i n g u n d e s i r a b l e c r o s s - f l o w a n d e d d i e s , i m p r o v i n g the v e l o c i t y p r o f i l e a n d d e v e l o p i n g t u r b u l e n c e o f d e s i r e d s c a l e a n d i n t e n s i t y [13] . T h e j e t d e v e l o p m e n t p r o c e s s c a n b e d e s c r i b e d as d e l i v e r i n g the s t o c k to the sheet f o r m i n g s e c t i o n . A n i d e a l h e a d b o x s h o u l d p r o d u c e a u n i f o r m a n d s table j e t o v e r the w i d t h o f the m a c h i n e , w i t h o u t l a t e r a l v e l o c i t i e s a n d m a c h i n e - d i r e c t i o n p e r t u r b a t i o n s . I n b r i e f , the h e a d b o x s p r e a d s the f l o w o f p u l p o u t o f the s t o c k a p p r o a c h p i p i n g a l o n g the w i d t h o f the p a p e r m a c h i n e , p r o v i d e s t u r b u l e n c e \" b l e n d i n g \" a n d d e l i v e r s the f u r n i s h to the m a c h i n e f o r m i n g s e c t i o n . K y o s t i et a l . [14] p o i n t e d o u t that i n a h e a d b o x , fiber o r i e n t a t i o n c a n b e i n f l u e n c e d b y the r e c i r c u l a t i o n rate , h e a d e r p r e s s u r e d i s t r i b u t i o n , f l o w d i s t r i b u t i o n u n i t s a n d h e a d b o x t u b e p a t t e r n s . M a n y r e s e a r c h e r s [4, 15, 16, 17] h a v e a g r e e d that the a d j u s t m e n t o f t h e s l i c e l i p 6 p r o f i l e n o t o n l y d o m i n a t e s the b a s i s w e i g h t p r o f i l e o f p a p e r i n the C D d i r e c t i o n , b u t a l s o s i g n i f i c a n t l y a f f e c t s the fiber o r i e n t a t i o n d i s t r i b u t i o n p r o f i l e . I n a c o n v e n t i o n a l h e a d b o x , the s l i c e l i p s h a p e i s g o v e r n e d b y the b a s i s w e i g h t p r o f i l e c o n t r o l l e r , w h i c h k e e p s t h e b a s i s w e i g h t at the r e e l as f la t as p o s s i b l e . H o w e v e r , t h i s d e m a n d f o r a u n i f o r m b a s i s w e i g h t c o m p e t e s w i t h the d e m a n d f o r u n i f o r m i t y o f f i b e r o r i e n t a t i o n p r o f i l e s , b e c a u s e a c h a n g e i n t h e s h a p e o f the s l i c e l i p m a y r e s u l t i n s i g n i f i c a n t c r o s s f l o w , w h i c h l e a d s to a v a r i a t i o n i n f i b e r o r i e n t a t i o n i n the c r o s s m a c h i n e d i r e c t i o n . F o r a c o n v e n t i o n a l h e a d b o x , it i s i m p o s s i b l e to a d j u s t b a s i s w e i g h t a n d c r o s s - m a c h i n e fiber o r i e n t a t i o n p r o f i l e s i n d e p e n d e n t l y o f e a c h o ther . T o s o l v e the p r o b l e m , a r e v o l u t i o n a r y h e a d b o x d e s i g n , w h i c h is c a l l e d the c o n s i s t e n c y p r o f i l e d h e a d b o x o r d i l u t i o n c o n t r o l h e a d b o x , h a s b e e n i n t r o d u c e d [9, 18, 19, 2 0 , 2 1 , 2 2 , 2 3 , 2 4 ] . T h i s h e a d b o x e n a b l e s i n d e p e n d e n t c o n t r o l o f C D b a s i s w e i g h t a n d f i b e r o r i e n t a t i o n p r o f i l e s . T h e b a s i s w e i g h t p r o f i l e is c o n t r o l l e d b y v a r y i n g the s t o c k c o n s i s t e n c y p r o f i l e i n the h e a d b o x a n d t h e s l i c e l i p is t h e n u s e d i n the c o n t r o l o f fiber o r i e n t a t i o n . N o r d s t r o m a n d N o r m a n [ 1 , 7 ] f o u n d that a h i g h h e a d b o x n o z z l e c o n t r a c t i o n r a t i o , w h i c h is the r a t i o b e t w e e n the i n l e t a r e a a n d the o u t l e t a r e a , c a n n o t o n l y g e n e r a t e a h i g h d e g r e e o f a n i s o t r o p y o f fiber o r i e n t a t i o n , b u t c a n a l s o i m p r o v e the f o r m a t i o n . T h e y a t t r i b u t e d t h i s e f f e c t to the e n h a n c e d s t r e n g t h o f the e l o n g a t i o n a l s t r a i n f i e l d i n the n o z z l e a n d the c h a n g e s i n t u r b u l e n c e i n t e n s i t y . T h e a m o u n t o f e d d y d e f o r m a t i o n i s d e p e n d e n t o n the d e g r e e o f c o n t r a c t i o n . U l l m a r a n d N o r m a n [25] i n d i c a t e d that the c o n t r a c t i o n r a t i o o f the j e t d e v e l o p i n g s e c t i o n p l a y s a n i m p o r t a n t r o l e i n fiber o r i e n t a t i o n at the n o z z l e e x i t . T h e i r r e s u l t s i n d i c a t e d that the e f f e c t o f c o n t r a c t i o n r a t i o i s m o r e s i g n i f i c a n t o n t h e fiber o r i e n t a t i o n t h a n that o f the f l o w v e l o c i t y . T h e f i b e r s h a v e b e e n f o u n d to b e m o r e s t r o n g l y o r i e n t e d i n the m a c h i n e d i r e c t i o n f o r h i g h e r c o n t r a c t i o n r a t i o . B a n d h a k a v i a n d A i d u n [26] r e p o r t e d that t h e a c c e l e r a t i n g f l o w i n the c o n v e r g i n g s e c t i o n t e n d s to o r i e n t the f i b e r s i n the m a c h i n e d i r e c t i o n , a n d s t r e t c h a n d r u p t u r e the f l o e s . T h e t u r b u l e n c e i n the f l o w m a y d e c r e a s e fiber o r i e n t a t i o n b u t m a y a l s o i m p r o v e the s u s p e n s i o n d i s p e r s i o n s . 7 L e e a n d P a n t a l e o [17] i n d i c a t e d that b e s i d e s the h e a d b o x , the f o r m i n g p r o c e s s a l s o c o n t r i b u t e s to t h e r e s u l t a n t f i b e r o r i e n t a t i o n d e p e n d i n g o n the t y p e o f f o r m e r , a n d o p e r a t i n g c o n d i t i o n s s u c h as j e t to w i r e s p e e d d i f f e r e n c e , w i r e t e n s i o n a n d d r a i n a g e rate . S e v e r a l o f t h e s e e f f e c t s are s u m m a r i z e d i n the f o l l o w i n g s e c t i o n s . 2.3.2 Jet to Wire Speed Difference T h e m o s t s i g n i f i c a n t f a c t o r d e t e r m i n i n g the f i b e r o r i e n t a t i o n i s u s u a l l y the s p e e d d i f f e r e n c e b e t w e e n the j e t a n d the f o r m i n g w i r e . I d e a l l y , the j e t i s a s s u m e d to b e i n the m a c h i n e d i r e c t i o n , b u t i n p r a c t i c e , there e x i s t s m a l l t r a n s v e r s e f l o w s . T h e m a g n i t u d e o f the c r o s s f l o w s v a r i e s from l a y e r to l a y e r w i t h i n the je t , a n d a l s o v a r i e s a c r o s s the w i d t h o f t h e je t . T h e d i f f e r e n c e b e t w e e n the j e t s p e e d a n d w i r e s p e e d is u s u a l l y s m a l l . B u t e v e n a s m a l l c r o s s f l o w m a y c a u s e a s i g n i f i c a n t c h a n g e i n f i b e r o r i e n t a t i o n a n g l e w h e n t h e s u s p e n s i o n i s d e l i v e r e d o n t o the f o r m i n g w i r e . T h i s i s the r e a s o n w h y , i n the i n d u s t r y , f i b e r o r i e n t a t i o n is p r i m a r i l y c o n t r o l l e d b y c h a n g i n g the j e t to w i r e s p e e d d i f f e r e n c e . A s t h e d i f f e r e n c e b e t w e e n the M D c o m p o n e n t o f j e t v e l o c i t y a n d the w i r e s p e e d i s i n c r e a s e d , t h e a v e r a g e f i b e r o r i e n t a t i o n a n g l e i s r e d u c e d , a n d the f i b e r o r i e n t a t i o n i n d e x i s i n c r e a s e d [4] . 2.3.3 Forming Wire B e c a u s e the j e t d i s c h a r g e d f r o m the s l i c e m a y h a v e a n o n - u n i f o r m v e l o c i t y p r o f i l e d u e to b o u n d a r y e f f e c t s a n d w a k e e f f e c t s , a n d a l s o h a s a n i m p i n g e m e n t a n g l e w h e n the s t o c k i s s p r e a d o n the w i r e , it i s i m p o s s i b l e to e l i m i n a t e the d i f f e r e n c e i n the v e l o c i t y b e t w e e n the j e t a n d the w i r e . T h e v e l o c i t y d i f f e r e n c e m a y c a u s e s h e a r f o r c e s i n the r e g i o n o f t h e s t o c k - w i r e i n t e r f a c e , a n d p r o d u c e f u r t h e r v a r i a t i o n s i n the f i b e r o r i e n t a t i o n . E r i k k i l a et a l . [27] p o i n t e d o u t that the fiber o r i e n t a t i o n f o r e a c h i n d i v i d u a l l a y e r o f the s h e e t i s f i n a l l y s e t t l e d d o w n i n the d r a i n a g e p r o c e s s a n d is a f f e c t e d b y the s h e a r , d e - w a t e r i n g v e l o c i t y o f t h e s u s p e n s i o n , c o n s i s t e n c y a n d the t u r b u l e n c e d u r i n g the p r o c e s s . T h e d i f f e r e n c e i n the 8 m a n n e r o f d e - w a t e r i n g , i n o n e d i r e c t i o n s u c h as i n the F o u r d r i n i e r c a s e o r i n t w o d i r e c t i o n s s u c h as i n g a p f o r m i n g , p r o d u c e s d i f f e r e n t o r i e n t a t i o n t w o - s i d e d n e s s i n the f i b e r o r i e n t a t i o n . I n a d d i t i o n to the h y d r o d y n a m i c e f f e c t o n the f i b e r o r i e n t a t i o n , the t u r b u l e n c e e f f e c t s h o u l d a l s o b e c o n s i d e r e d . T u r b u l e n c e i s g e n e r a t e d i n the h e a d b o x a n d m a i n t a i n e d d u r i n g d r a i n a g e b y t h e d r a i n a g e e l e m e n t s . I n a d d i t i o n , t u r b u l e n c e is i n d u c e d b y t h e s p e e d d i f f e r e n c e b e t w e e n t h e s u s p e n s i o n a n d the w i r e . A s the t u r b u l e n t e n e r g y i s i n c r e a s e d , the a v e r a g e f i b e r o r i e n t a t i o n a n g l e i s n o t c h a n g e d , b u t the i n - p l a n e f i b e r o r i e n t a t i o n a n i s o t r o p y is d e c r e a s e d , a n d the f i b e r o r i e n t a t i o n i n d e x i s r e d u c e d [1]. 2.3.4 Fiber Suspension Consistency T h e o r i e n t a t i o n p r o d u c e d at the s l i c e i s f o u n d to b e c o n s i s t e n c y s e n s i t i v e , a n d to b e a f u n c t i o n o f the f i b e r n e t w o r k s t r e n g t h . F i b e r - f i b e r i n t e r a c t i o n s d e t e r m i n e h o w m a n y i n d i v i d u a l f i b e r s c a n b e r o t a t e d w i t h the o r i e n t e d s h e a r f i e l d . A t h i g h e r c o n c e n t r a t i o n s , f i b e r s are l e s s a l i g n e d i n the f l o w d i r e c t i o n , p r e s u m a b l y as a r e s u l t o f f l o c c u l a t i o n . K e r e k e s a n d S c h e l l [28] d e f i n e d a c r o w d i n g f a c t o r N , w h i c h i s b a s e d o n the v o l u m e c o n c e n t r a t i o n C v , the f i b e r l e n g t h L a n d d i a m e t e r d , to r e p r e s e n t the d e g r e e o f f l o c c u l a t i o n : A s t h e c o n s i s t e n c y i n c r e a s e s , the c r o w d i n g f a c t o r w i l l i n c r e a s e . U l l m a r [29] d i d e x p e r i m e n t s w h i c h s h o w e d that the f i b e r a l i g n m e n t d e c r e a s e s as the c r o w d i n g f a c t o r i n c r e a s e s . C u r l y f i b e r s w e r e a l s o f o u n d to b e less a l i g n e d t h a n s t r a i g h t f i b e r s [29, 3 0 ] . A c c o r d i n g to t h e i r c o n c e n t r a t i o n s , f i b e r s u s p e n s i o n s are u s u a l l y c l a s s i f i e d i n t o t h r e e r e g i m e s : d i l u t e , s e m i - c o n c e n t r a t e d a n d h i g h l y c o n c e n t r a t e d . I f f i b e r s are c o n s i d e r e d to b e N = -Cv 3 (2 .1) 9 r i g i d c y l i n d e r s w i t h l e n g t h L a n d d i a m e t e r d , a n d o c c u p y a f r a c t i o n C v o f the t o t a l v o l u m e o f t h e s u s p e n s i o n , D i n h [31] s h o w s that the d i l u t e r e g i m e i s d e f i n e d w h e n C v < ( d \/ L ) 2 , the s e m i - c o n c e n t r a t e d r e g i m e i s d e f i n e d as ( d \/ L ) 2 < C v < ( d \/ L ) , a n d the h i g h l y c o n c e n t r a t e d r e g i m e i s d e f i n e d as C v > ( d \/ L ) . I n the d i l u t e r e g i m e , t h e d i s t a n c e b e t w e e n a fiber a n d i ts n e a r e s t n e i g h b o r is g r e a t e r t h a n L , s o the f i b e r s are f r e e to rotate , a n d i n t e r a c t i o n s b e t w e e n fibers are rare . I n the s e m i - c o n c e n t r a t e d r e g i m e , the s p a c i n g b e t w e e n fibers i s less t h a n L b u t g r e a t e r t h a n d , a n d i n t e r a c t i o n b e t w e e n fibers are f r e q u e n t . W h e n the s u s p e n s i o n f a l l s i n t o the h i g h l y c o n c e n t r a t e d r e g i m e , the s p a c i n g b e t w e e n fibers i s o n the o r d e r o f fiber d i a m e t e r d . T h r e e r e g i m e s c a n a l s o b e d e f i n e d i n t e r m s o f fiber v o l u m e f r a c t i o n C v a n d fiber a s p e c t r a t i o A r , w h i c h e q u a l s L \/ d [32] : T h e d i l u t e r e g i m e i s w h e n : C \u201e A,2 \u00ab 1 (2 .2) t h e s e m i - c o n c e n t r a t e d r e g i m e is g i v e n b y : A;2 < Cv < V (2 .3) a n d t h e c o n c e n t r a t e d r e g i m e i s d e f i n e d as : CvAr \u00bb 1 (2 .4) I n h e a d b o x e s o f c o n v e n t i o n a l p a p e r m a c h i n e s , the fiber w e i g h t c o n s i s t e n c i e s v a r y b e t w e e n 0.1 a n d 1 .5%, fiber l e n g t h s v a r y b e t w e e n 1 a n d 5 m m a n d a s p e c t r a t i o s v a r y b e t w e e n 3 0 a n d 2 0 0 [33] . F o r e x a m p l e , i f the v o l u m e c o n c e n t r a t i o n o f the fiber s u s p e n s i o n C v is 1 % , f i b e r s h a v e a u n i f o r m l e n g t h o f 3 m m a n d a u n i f o r m d i a m e t e r o f 4 0 u m , t h e n t h e a s p e c t r a t i o A r i s 7 5 . T h e s u s p e n s i o n i s t h e n i n the s e m i - c o n c e n t r a t e d r e g i m e , b e c a u s e A r \" 2 < C v < A r _ 1 (that i s 0 . 0 1 8 % < 1 % < 1 .3%). T h e r e w o u l d t h e n e x i s t 10 f r e q u e n t f i b e r - f i b e r i n t e r a c t i o n s i n the h e a d b o x f l o w . T h e d i l u t e s u s p e n s i o n a s s u m p t i o n i n the c u r r e n t s t u d y is t h e r e f o r e a s i m p l i f i c a t i o n o f the a c t u a l p r o b l e m . 2.4 Headbox Flow Simulations to Investigate Fiber Orientation C o m p u t e r s i m u l a t i o n h a s b e e n w i d e l y u s e d i n the s t u d y o f p r o c e s s e s that o c c u r i n e n g i n e e r i n g e q u i p m e n t . T h e s i m u l a t i o n i n v e s t i g a t i o n s n o t o n l y m e e t the n e e d f o r u n d e r s t a n d i n g a n d p r e d i c t i o n , b u t a l s o h a v e l a r g e e c o n o m i c b e n e f i t s . S e v e r a l r e s e a r c h e r s h a v e c o n d u c t e d h e a d b o x f l o w s i m u l a t i o n s i n o r d e r to i n v e s t i g a t e the f l o w i n d u c e d f i b e r o r i e n t a t i o n . A i d u n [34, 35] s t u d i e d the s e c o n d a r y f l o w s i n the h e a d b o x a n d t h e i r e f f e c t s o n n o n -u n i f o r m f i b e r o r i e n t a t i o n a n d m a s s f o r m a t i o n b y u s i n g a n o n - l i n e a r k - s t u r b u l e n c e m o d e l to i n v e s t i g a t e the c h a r a c t e r i s t i c s o f t u r b u l e n t f l o w i n a l o w c o n s i s t e n c y h e a d b o x . T h e a u t h o r i n d i c a t e d that the c a u s e o f n o n - u n i f o r m i t y i n f i b e r o r i e n t a t i o n i n the c r o s s m a c h i n e d i r e c t i o n i s the s e c o n d a r y f l o w s that are g e n e r a t e d i n s i d e the h e a d b o x i n d u c e d e i t h e r b y t h e g e o m e t r i c e f f e c t s a n d the k i n e m a t i c s , o r b y the a n i s o t r o p y o f t u r b u l e n t f l o w s . L e e a n d P a n t a l e o [17] u s e d a s t a n d a r d k - s t u r b u l e n c e m o d e l to a n a l y z e h e a d b o x f l o w w h e n d i f f e r e n t f l o w c o n t r o l d e v i c e s w e r e e m p l o y e d , s u c h as s l i c e p r o f i l i n g , e d g e v a l v e c o n t r o l , b l e e d c o n t r o l s , t u b e i n s e r t s a n d h e a d e r r e - c i r c u l a t i o n v a l v e s . T h e y e x a m i n e d t h e r e l a t i o n s h i p b e t w e e n the h e a d b o x f l o w c h a r a c t e r i s t i c s a n d the fiber o r i e n t a t i o n , a n d c o r r e l a t e d t h e h e a d b o x f l o w c h a r a c t e r i s t i c s i n t e r m s o f f l o w a n g l e o b t a i n e d f r o m C F D s o l u t i o n s w i t h the m e a s u r e d f i b e r o r i e n t a t i o n . T h e y t r i e d to u s e the f l o w a n g l e [3, w h i c h i s d e f i n e d b y the M D v e l o c i t y , u , a n d C D v e l o c i t y , v , to r e p r e s e n t the a v e r a g e fiber o r i e n t a t i o n a n g l e : P = t a n \" ( -1 (2 .5 ) 11 S h i m i z u a n d W a d a [36] a p p l i e d the k - s t u r b u l e n c e m o d e l a n d a finite d i f f e r e n c e m e t h o d to s t u d y the i n f l u e n c e w h i c h e l e m e n t s o f a n i m a g i n a r y h e a d b o x , s u c h as a t a p e r e d h e a d e r , s i d e w a l l , c o n t r a c t i n g p a r t a n d s l i c e l i p , h a v e o n p a p e r q u a l i t y , e s p e c i a l l y t h e u n e v e n b a s i s w e i g h t p r o f i l e s a n d fiber o r i e n t a t i o n . T h e r e s e a r c h e r s m e n t i o n e d a b o v e h a v e the c o m m o n p r o b l e m that t h e y t r i e d to s t u d y fiber o r i e n t a t i o n i n the f l o w w i t h o u t a s p e c i f i c s i m u l a t i o n o f fiber b e h a v i o r . 2 . 5 F i b e r S u s p e n s i o n S i m u l a t i o n T h e first f u n d a m e n t a l s t u d y o f the o r i e n t a t i o n o f a r i g i d e l l i p s o i d a l p a r t i c l e i n a d i l u t e v i s c o u s N e w t o n i a n l i q u i d w a s c o n d u c t e d b y J e f f e r y [37] . H e s o l v e d the f l o w field a r o u n d a r o t a t i n g e l l i p s o i d b y s o l v i n g S t o k e s e q u a t i o n s , u s i n g a n o - s l i p b o u n d a r y c o n d i t i o n at the s u r f a c e o f the p a r t i c l e . T h e a n g u l a r v e l o c i t y v e c t o r o f the p a r t i c l e w a s t h e n f o u n d f r o m the r e q u i r e m e n t that the to ta l t o r q u e a c t i n g o n the p a r t i c l e b e z e r o . T h e f o l l o w i n g J e f f r e y ' s e q u a t i o n d e s c r i b e s a s i m p l i f i e d c a s e o f a fiber l y i n g i n a t w o - d i m e n s i o n a l f l o w field [38] . . _ . 2 du 2 dv -smtpcostp s i n tp\u2014 + c o s (p\u2014 + s i n ^ c o s ^ du dx dy dx dv_ dy, ( 1 ^ (2 .6) . , i , du . i ,dv . , , - s i n ^ c o s ^ \u2014 + c o s
focus point 0.04 0.02 - --0 -0.02 , , i , , , , i , 1 1 , , , , 1 , 0 0.05 0.1 0.15 0.2 0.25 0.3 X Figure 3.8. The measurement points along the headbox channel. 27 4. C O M P U T E R S I M U L A T I O N O F F L O W A N D F I B E R O R I E N T A T I O N T h e f i b e r o r i e n t a t i o n i n a p i e c e o f p a p e r i s d e t e r m i n e d b y the p a p e r m a k i n g p r o c e s s , e s p e c i a l l y i n the h e a d b o x a n d o n the f o r m i n g w i r e . E f f o r t s m u s t b e m a d e to d e r i v e q u a n t i t a t i v e r e l a t i o n s h i p s b e t w e e n p r o c e s s i n g c o n d i t i o n s a n d f i b e r o r i e n t a t i o n s . T h e i n t e n t i s to l e a r n h o w to d e s i g n a n d c o n t r o l m a n u f a c t u r i n g p r o c e s s e s to g e n e r a t e f a v o r a b l e o r i e n t a t i o n states, s o as to o b t a i n the b e s t p o s s i b l e p a p e r p r o d u c t s . T o p e r f o r m t h e p r e d i c t i o n o f f i b e r o r i e n t a t i o n that i s r e q u i r e d f o r the d e s i g n a n d p r o c e s s c o n t r o l , o n e m u s t h a v e a n a c c u r a t e q u a n t i t a t i v e m o d e l o f the w a y f i b e r s c h a n g e o r i e n t a t i o n as t h e y m o v e i n the f l o w . T o s i m u l a t e f i b e r m o t i o n , t w o m o d e l s n e e d to b e d e v e l o p e d a n d e f f e c t i v e l y c o m b i n e d t o g e t h e r . T h e f i r s t m o d e l is u s e d to d e s c r i b e the f l u i d m o t i o n i n a 3 - d i m e n s i o n a l d o m a i n , as c o n s t r a i n e d b y the s p e c i f i c b o u n d a r y c o n d i t i o n s . T h e s e c o n d m o d e l d e s c r i b e s f i b e r m o t i o n a n d o r i e n t a t i o n i n the f l o w f i e l d . T h e i m p o r t a n t p a r t o f the m e t h o d is to c o m b i n e t h e s e t w o m o d e l s . T h e s i m u l a t i o n m e t h o d is u s e d h e r e f o r the s o l u t i o n o f f i b e r o r i e n t a t i o n i n a f l o w f i e l d o f a N e w t o n i a n f l u i d w h e r e the f i b e r s d o n o t a l ter the f l o w . F o r s u s p e n s i o n s w i t h h i g h e r v o l u m e f r a c t i o n s , these s o l u t i o n t e c h n i q u e s c a n b e u t i l i z e d w i t h s o m e m o d i f i c a t i o n s . C u r r e n t l y , t h e a b o v e t w o m o d e l s are u n c o u p l e d i n that the f i b e r o r i e n t a t i o n state w i l l n o t a l ter the g o v e r n i n g e q u a t i o n s f o r the f l o w . F i b e r o r i e n t a t i o n s are c a l c u l a t e d s u b s e q u e n t to t h e v e l o c i t y f i e l d d e t e r m i n a t i o n , h e n c e , the t w o m o d e l s m a y b e s o l v e d c o n s e c u t i v e l y . T h e d e t a i l e d a p p r o a c h c a n b e d e s c r i b e d as f o l l o w s . F i r s t l y , the f l o w f i e l d i s p r e d i c t e d b y t h e s o l u t i o n o f the R e y n o l d s a v e r a g e d N a v i e r - S t o k e s e q u a t i o n s . T h e n t h e t r a n s l a t i o n a n d r o t a t i o n o f a r i g i d f i b e r i s d e s c r i b e d b a s e d o n N e w t o n ' s S e c o n d L a w a n d t h e l a w o f a n g u l a r m o m e n t u m . T h e a n g u l a r v e l o c i t y o f a f i b e r d e p e n d s u p o n the l o c a l f l o w c o n d i t i o n s , s u c h as v o r t i c i t y a n d the c o m p o n e n t s o f the rate o f d e f o r m a t i o n t e n s o r . 28 4.1 T h e H e a d b o x F l o w M o d e l I n the s i m u l a t i o n s t u d y , the l i q u i d is a s s u m e d to b e p u r e w a t e r o r a d i l u t e f i b e r s u s p e n s i o n . T h e c o n s i s t e n c y o f the s u s p e n s i o n is v e r y l o w , s o t h e r e i s n o i n t e r a c t i o n b e t w e e n f i b e r s , a n d the f i b e r s d o n o t a f f e c t the f l o w f i e l d . T h e f i b e r s are u n i f o r m a n d l o n g e n o u g h s o that the B r o w n i a n m o t i o n c a n b e i g n o r e d [51] . T h e s u s p e n s i o n c a n t h e r e f o r e b e v i e w e d as a u n i f o r m i n c o m p r e s s i b l e N e w t o n i a n f l u i d . B a s e d o n t h e a b o v e a s s u m p t i o n s , t h e a v a i l a b l e c o n t i n u u m t h e o r i e s c a n b e u s e d f o r t h e d i l u t e s u s p e n s i o n [32 ] . T h e n u m e r i c a l s i m u l a t i o n o f the f l o w h a s b e e n c a r r i e d o u t b y s o l v i n g t h e t h r e e -d i m e n s i o n a l i n c o m p r e s s i b l e R e y n o l d s a v e r a g e d N a v i e r - S t o k e s e q u a t i o n s . T u r b u l e n c e c l o s u r e i s o b t a i n e d b y the u s e o f the s t a n d a r d k - s m o d e l w i t h the w a l l f u n c t i o n t r e a t m e n t . W e c a n w r i t e t h e c o n t i n u i t y e q u a t i o n i n the f o r m o f : w h e r e : u = i n s t a n t a n e o u s f l u i d v e l o c i t y v e c t o r p = m o d i f i e d p r e s s u r e i n c l u d i n g the g r a v i t a t i o n a l f o r c e s p = d e n s i t y x = f l u i d stress t e n s o r . F o r a N e w t o n i a n f l u i d w i t h c o n s t a n t v i s c o s i t y , V u = 0 (4 .1) T h e e q u a t i o n o f c o n s e r v a t i o n o f m o m e n t u m i s : u-Vu = -Vpl p + V -r I p (4 .2 ) V - T = \/ \/ V 2 u (4 .3) w h e r e : 2 9 ^ = d y n a m i c v i s c o s i t y o f the f l u i d . I n t u r b u l e n t f l o w , the v e l o c i t y a n d p r e s s u r e c a n b e e x p r e s s e d as a m e a n a n d a f l u c t u a t i n g p a r t : u = u + u' (4-4) p = p + p' (4-5) I n t h e e q u a t i o n s , the o v e r - b a r d e n o t e s the m e a n , a n d the p r i m e i n d i c a t e s the f l u c t u a t i n g c o m p o n e n t . A f t e r s u b s t i t u t i n g E q u a t i o n s (4 .3) , (4 .4) a n d (4 .5) i n t o E q u a t i o n s (4 .1 ) a n d (4 .2 ) , a n d t a k i n g a t i m e a v e r a g e , the g o v e r n i n g e q u a t i o n s o f the t u r b u l e n t f l o w b e c o m e : V - u = 0 (4-6) u V u = -Vp\/p + V-r\/p (4-7) N o w the stress t e n s o r x i n c l u d e s b o t h the v i s c o u s a n d t u r b u l e n t R e y n o l d s stress t e n s o r s : V T = \/J V 2 u + V - ( - p u\\u'j ) (4-8) w h e r e : r , = uTV; ( i , j = l , 2 , 3 ) (4 .9 ) c a n b e u s e d to s i m p l i f y E q u a t i o n (4 .8) . T h e R e y n o l d s stress t e n s o r T . . i n t r o d u c e s a d d i t i o n a l u n k n o w n s f o r the t u r b u l e n t f l o w . I n o r d e r to d e s c r i b e the m e a n v e l o c i t y a n d p r e s s u r e f i e l d s , a c l o s u r e f o r m u l a t i o n is n e c e s s a r y to re la te the c o m p o n e n t s o f the R e y n o l d s stress t e n s o r to the m e a n f l o w v e l o c i t y o r v e l o c i t y g r a d i e n t s . T h e s t a n d a r d l i n e a r k - s m o d e l [52] i s e m p l o y e d to s o l v e the c l o s u r e p r o b l e m . 3 0 T h e R e y n o l d s stress t e n s o r c a n t h e n b e e x p r e s s e d as : T,J = v t S u - - k S v w h e r e : du, dui + dx, dx, ( 4 . 1 0 ) ( 4 . 1 1 ) k = \u2014 u'u' 2 ' ' ( 4 . 1 2 ) k i s t h e t u r b u l e n t k i n e t i c e n e r g y , 5.. i s the K r o n e c k e r D e l t a , a n d V t i s t h e t u r b u l e n t k i n e m a t i c v i s c o s i t y w h i c h , u n l i k e its l a m i n a r c o u n t e r p a r t , v a r i e s s p a t i a l l y a n d is n o t a p r o p e r t y o f t h e f l u i d . T h e t r a n s p o r t e q u a t i o n f o r k i s : w h e r e : a n d 5 lr- 9 ku, = dx dk + G-E G = -u] Uj Sa (4 .13 ) ( 4 . 1 4 ) E = VS'iS'g ( 4 . 1 5 ) G a n d E a r e the rates o f k i n e t i c e n e r g y p r o d u c t i o n a n d d i s s i p a t i o n p e r u n i t m a s s , r e s p e c t i v e l y . T h e t r a n s p o r t e q u a t i o n f o r the k i n e t i c e n e r g y d i s s i p a t i o n E i s g i v e n i n t h e f o r m o f : 5 z r - 8 EU: = dx, 1 dx v + - ^ + ( C l G - c 2 E ) ^ (4 -16) dx, K 31 A f i n a l c o r r e l a t i o n , b a s e d o n a n i s o t r o p i c v i s c o s i t y a s s u m p t i o n f o r the t u r b u l e n t v i s c o s i t y i n t e r m s o f k a n d E , as g i v e n b y V { = k 2 \/ E , c l o s e s the s y s t e m o f e q u a t i o n s . T h e u s u a l v a l u e s o f the c o n s t a n t s are : = 0 .09 , C j = 1.44, C 2 = 1 .92, a k = 1.0, a E = K2 \/ [ ( C 2 - C , ) Cm], w h e r e K = 0.41 i s the V o n K a r m a n c o n s t a n t . A f i n i t e v o l u m e m e t h o d i n c o n j u n c t i o n w i t h g e n e r a l c u r v i l i n e a r g r i d s i s u s e d i n t h e c o m p u t a t i o n a l c o d e , w h i c h w a s d e v e l o p e d i n o u r r e s e a r c h g r o u p b y N o w a k [53] . U s e a n d v a l i d a t i o n o f t h i s c o d e f o r h e a d b o x f l o w s h a s b e e n r e p o r t e d i n the w o r k o f S h a r i a t i et a l . [49] a n d H u a e t a l . [50] . 4 .2 F i b e r M o d e l T h e m a i n c o n c e r n o f t h i s w o r k i s the p r e d i c t i o n o f f i b e r o r i e n t a t i o n i n the h e a d b o x f l o w f i e l d . I n t h i s w o r k , the f i b e r o r i e n t a t i o n i s c a l c u l a t e d f o r a g i v e n v e l o c i t y f i e l d , d e c o u p l i n g t h e f l o w a n d f i b e r o r i e n t a t i o n c a l c u l a t i o n s . T h e o r e t i c a l l y , the s o l u t i o n s are o n l y v a l i d f o r z e r o fiber c o n s i s t e n c y , b e c a u s e t h e fibers i n f l u e n c e t h e f l o w . H o w e v e r , f o r d i l u t e s o l u t i o n s , t h i s m o d e l s h o u l d n o t g i v e s i g n i f i c a n t e r r o r s . A t fiber l o c a t i o n s , the v e l o c i t y a n d v e l o c i t y g r a d i e n t s are c a l c u l a t e d b y i n t e r p o l a t i n g the v a l u e s at n e i g h b o r i n g n o d e s a n d are u s e d to d e t e r m i n e the t r a n s l a t i o n a n d r o t a t i o n o f the fiber. T h e c a l c u l a t e d fiber p o s i t i o n a n d o r i e n t a t i o n a r e u s e d as i n i t i a l c o n d i t i o n s f o r t h e c a l c u l a t i o n o f t h e fiber's n e w l o c a t i o n a n d o r i e n t a t i o n at the n e x t t i m e step (t + A t ) . T h e fiber m o t i o n m o d e l u s e d i n t h i s w o r k w a s first d e v e l o p e d b y R o s s a n d K l i n g e n b e r g [46 , 5 4 ] a n d a d a p t e d b y D o n g [48] . J e f f r e y ' s e q u a t i o n [37] i s u s e d f o r t h e v e r i f i c a t i o n o f t h i s m o d e l . D o n g s h o w e d the i d e n t i t y o f the r e s u l t s f r o m b o t h a p p r o a c h e s . A l t h o u g h f l e x i b l e f i b e r s c a n b e s i m u l a t e d w i t h t h i s m o d e l , o n l y r i g i d f i b e r s are s i m u l a t e d i n t h i s t h e s i s . A s d e s c r i b e d b y D o n g , a fiber i s r e p r e s e n t e d b y o n e o r m o r e p r o l a t e s p h e r o i d s . I n t h i s t h e s i s r e s e a r c h , a r i g i d fiber i s r e p r e s e n t e d b y o n e p r o l a t e s p h e r o i d w i t h u n i f o r m l e n g t h L a n d d i a m e t e r d . T h e d e n s i t y o f the fiber is the s a m e as the f l u i d . T h e m o t i o n o f a 3 2 fiber i s d e t e r m i n e d b y s o l v i n g the t r a n s l a t i o n a n d r o t a t i o n e q u a t i o n s w h i c h are b a s e d o n J e f f e r y ' s o r i g i n a l w o r k [37]. T h e o r i e n t a t i o n o f a fiber is t h r e e - d i m e n s i o n a l a n d c a n b e d e t e r m i n e d b y t w o a n g l e s as e x p r e s s e d i n F i g u r e 4.1. T h e a z i m u t h a l a n g l e