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Effect of aperture geometry on the steady flow through the narrow apertures in a pulp screen : numerical… Mokamati, Satyanarayana V. 2007

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EFFECT OF APERTURE GEOMETRY ON T H E STEADY FLOW THROUGH T H E NARROW APERTURES IN A PULP SCREEN: NUMERICAL AND EXPERIMENTAL STUDY by SATYANARAYANA V. MOKAMATI B.Tech, Ranchi University, 1998 M.A.Sc.E, The University of New Brunswick, 2002  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA September, 2007 © Satyanarayana V. Mokamati, 2007  ABSTRACT This investigation examines turbulent flow across a contoured wall with evenly-spaced slots and a series of flow bifurcations, as found in industrial pulp screening. The contoured wall and slotted apertures are formed from an array of 'wires', with cross-sectional geometry characterized by contour height and wire width. Four complementary studies were conducted to examine the velocity and turbulence characteristics of this complex flow. In the first study, a Computational Fluid Dynamics (CFD) model was developed to theoretically examine the effect of wire cross-sectional geometry on the flow field. The model shows that separation of the viscous layer occurs upstream of the aperture, and a vortex occupies the slot entry. As contour height increased, turbulence intensity near the wall increased. Further, turbulence intensity near the wall increased with decreasing wire width. It was shown that the ratio of contour height to wire width controls the boundary layer thickness and turbulence intensity near the wall. In the second study, the velocity field near the slot entry was experimentally measured using Particle Image Velocimetry (PIV) and was compared with theoretical predictions. In general, the vortex size and shape were similar to that predicted by CFD. In the third study, the velocity and turbulence intensity distributions above the wall were experimentally measured using Laser Doppler Velocimetry (LDV). The velocity near the wall was shown to decrease with contour height and increase with wire width. Further, the velocity near the wall was shown to increase as the flow through the slots increased. A correlation for velocity above the wall was determined as a function of the ratio of contour height to wire width, upstream velocity and flow through the slotted apertures. The correlation can be used to estimate shear stress at the wall. The maximum turbulence intensity near the wall was shown to increase with contour height and decrease with wire width. In the fourth study, the motion of 2 mm long nylon fibres moving near the apertures was experimentally observed using High-speed Video (HSV). Fibres were shown to interact with both the wires and the vortices during passage. It was observed that fibres only passed through the slots after impacting the wire and being pulled back into the slot by the vortex. Further, fibres were shown to pass through the slots with high contour wires more readily.  ii  Table of Contents ABSTRACT  u  TABLE OF CONTENTS  m  LIST OF TABLES  ' ' v  LIST OF FIGURES  v i  LIST OF SYMBOLS  x i i  ACKNOWLEDGEMENTS  xiv  1  INTRODUCTION  1  2  LITERATURE REVIEW  6  2.1  F U N D A M E N T A L SCREENING HYDRODYNAMICS  6  2.2  P U L P SUSPENSIONS F L O W WITH T U R B U L E N C E  9  2.3  FIBRE M O T I O N  11  2.4  ROTOR HYDRODYNAMICS  13  2.5  S C R E E N C A P A C I T Y A N D EFFICIENCY  15  2.6  F L O W O V E R R O U G H S U R F A C E S WITH SUCTION OR B L O W I N G  16  3  PROBLEM STATEMENT  21  4  NUMERICAL SIMULATION  23  4.1  T U R B U L E N C E M O D E L SELECTION  4.1.1  25  Realizable k-s model  26  4.2  B O U N D A R Y CONDITIONS  27  4.3  D O M A I N DISCRITIZATION  27  4.4  R E S U L T S A N D DISCUSSION  4.4.1 4.4.2 4.4.3  27  Solution sensitivity Effect of contour height Effect of wire width  29 30 37  4.5  C O M B I N E D E F F E C T OF C O N T O U R H E I G H T A N D W I R E W I D T H  42  4.6  SUMMARY  45  5  EXPERIMENTAL MEASUREMENT OF FLOW FIELD  46  5.1  FLOW CHANNEL  46  5.2  TEST COUPONS  47  5.3  FLOW LOOP  48  5.4  PIV M E A S U R I N G S Y S T E M  49  5.4.1 5.4.2 5.4.3 5.4.4 5.4.5 5.5  5.5.1 5.5.2 5.5.3 5.5.4  Laser source and light sheet optics Camera and image grabber Light scattering considerations Flow seeding Results and discussion  50 51 52 53 53  LDV M E A S U R I N G S Y S T E M  59  Measuring principle Parameter adjustment Experimental procedure Uncertainty of LDV measurements  59 63 63 64 iii  5.5.5 6  Results and discussion  66  EXPERIMENTAL MEASUREMENT OF FIBRE MOTION  88  6.1  EXPERIMENTAL APPARATUS  88  6.2  FIBRE M O T I O N A N A L Y S I S  90  Low contour height High contour height  91 93  6.2.1 6.2.2 7  CONCLUSIONS  8  RECOMMENDATIONS  9  REFERENCES  97 100 .'  101  APPENDIX 1 Streamline plots for all wire geometries showing details in the relief of the slot 107 APPENDIX 2 Details of flow channel Ill APPENDIX 3 Hardware and software specifications of the PIV system 112 APPENDIX 4 Timing diagram, camera and laser synchronization 113 APPENDIX 5 Hardware and software specifications of the LDV system 115 APPENDIX 6 Properties of pulp and nylon fibres 116  iv  LIST OF T A B L E S Table 4.1 Variables tested in CFD simulations  28  Table 4.2 Comparison of vortex location data with previous study  31  Table 5.1 Experimental variables for PIV measurements  56  Table 5.2 Comparison of CFD and PIV data  57  Table 5.3 Experimental variables for LDV measurements  64  Table 6.1 Experimental variables for fibre motion measurements  89  v  LIST OF FIGURES Figure 1.1 Schematic of the principal flows through a pressure screen  4  Figure 1.2 Typical cross-section of the wires banded together to form narrow apertures  5  Figure 1.3 Close-up of the wire cross-section near the feed surface showing wire width, slot width.and contour height  5  Figure 3.1 Flow over a periodic array of narrowly-spaced wires under steady cross-flow  22  Figure 4.1 Schematic of the two-dimensional slice across the pulp screen cylinder showing the periodicity of rotor foils  24  Figure 4.2 Schematic showing the single slot domain considered for CFD calculations (not to scale)  24  Figure 4.3 Geometry of the pulp screen slot showing the boundary conditions and mesh near the slot  25  Figure 4.4 Flow field near a screen slot outlining the flow features schematically  28  Figure 4.5. Sensitivity of the solution to the number of iterations and grid size (distance is normalized by the wire width of 3.2 mm)  29  Figure 4.6 Fluid streamlines at the aperture entry for contour heights equal to (a) 0.3, (b) 0.6, (c) 0.9 and (d) 1.2 mm for a 3.2 mm wide wire showing how the vortex size and location vary  31  Figure 4.7 Acceleration contours and streamlines at the aperture entry for contour heights equal to (a) 0.3, (b) 0.6, (c) 0.9 and (d) 1.2 mm for a 3.2 mm wide wire showing strong acceleration on the top of the contour and near the re-attachment point Figure 4.8 Origin for comparing the velocity and turbulence properties Figure 4.9 The upstream velocity profiles of the flow approaching the slot for contour heights equal to 0.3, 0.6, 0.9 and 1.2 mm. The velocity profile is taken at the top of the vortex  vi  32 33  center, and the distance is normalized by the wire height of 10 mm, upstream velocity is normalized by the velocity specified at the inlet boundary condition  34  Figure 4.10 Turbulence intensity profile above the screen surface showing the slight increase in turbulence with contour height at the screen surface. The turbulence velocity profile is taken at the top of the vortex center, and the distance is normalized by the wire height of 10 mm  35  Figure 4.11 Contour plots of turbulence kinetic energy near the screen surface for contour heights equal to (a) 0.3, (b) 0.6, (c) 0.9 and (d) 1.2 mm  36  Figure 4.12 Fluid streamlines at the aperture entry for wire widths of (a) 2.6, (b) 3.2, and (c) 4.0 mm  38  Figure 4.13 Velocity profiles of the flow approaching the slot for wire widths of 2.6, 3.2, and 4.0 mm. The velocity profile is taken at the top of the vortex center, and the distance is normalized by the wire height of 10 mm, upstream velocity is normalized by the velocity specified at the inlet boundary condition  39  Figure 4.14 Turbulence intensity near the screen surface for wire widths of 2.6, 3.2, and 4.0 mm showing the increase in turbulence intensity with decreasing wire width The turbulence profile is taken at the top of the vortex center, and the distance is normalized by the wire height of 10 mm  40  Figure 4.15 Contour plots of turbulence kinetic energy near the screen surface for wire widths of (a) 2.6, (b) 3.2 and (c) 4.0 mm showing the increase in turbulence kinetic energy with decreasing wire width  41  Figure 4.16 The effect of aperture geometry on average boundary layer thickness  43  Figure 4.17 A sample streamlines plot overlaid with velocity profiles showing the seven locations along the wire where the boundary layer thickness was estimated  43  Figure 4.18 The effect of aperture geometry on average turbulence kinetic energy  44  Figure 4.19 The effect of aperture geometry on skin friction coefficient  45  Figure 5.1 Exploded view of the experimental flow channel.  47  vii  Figure 5.2 Orthogonal views of a test coupon used in the experiments. Dimensions are in inches unless stated otherwise  48  Figure 5.3 Schematic of the flow loop used for PIV experiments  49  Figure 5.4 Overview of the PIV measuring system  50  Figure 5.5 Schematic showing the measuring area near the aperture (4.5 x 4.5 mm)  55  Figure 5.6 A sample PIV raw image of a contour with h = 1.2 and w = 3.2 mm  55  Figure 5.7 A sample PIV raw image overlaid with cross-correlated vectors for a contour with h = 1.2 mm and w = 3.2 mm  56  Figure 5.8 Flow field near the aperture entry for contour heights equal to (a) 1.2, (b) 0.9, and (c) 0.6 mm for a 3.2 mm wide wire  58  Figure 5.9 Schematic of a single-component dual-beam LDV system in back-scatter mode  61  Figure 5.10 Schematic detail of the measurement volume showing the formation of fringes. Lines represent the peaks of the light  61  Figure 5.11 Schematic detail showing the relationships between fringe spacing, light wavelength, and the angle between beams  61  Figure 5.12 A typical LDV signal burst generated when a particle passes through the measurement volume  62  Figure 5.13 Detail showing the origin of the measurement plane where the horizontal laser beams just touch the wire top surface  66  Figure 5.14 Comparison of experimental velocity profiles for a smooth wall with classical loglaw of the wall  67  Figure 5.15 Position of velocity profiles measured along the coupon to test the sensitivity of the measurements with position  68  Figure 5.16 Position of velocity profiles measured along a single wire to test the sensitivity of the measurements with location  68 viii  Figure 5.17 Upstream velocity variation at three different positions along the coupon. The distance is normalized by the wire height of 10 mm and the upstream velocity is normalized by the mean velocity in the free stream of channel  69  Figure 5.18 Upstream velocity variation at three different positions over a single wire. The distance is normalized by the wire height of 10 mm and the upstream velocity is normalized by the mean velocity in the free stream of channel  70  Figure 5.19 Velocity profiles for boundary layers with V = 1 m/s and V = 10 m/s for three s  u  different contour heights. The distance is normalized by the wire height of 10 mm and the upstream velocity is normalized by the mean velocity in the free stream of channel  73  Figure 5.20 Velocity profiles for boundary layers with, V = 1 m/s and V = 10 m/s for two s  u  different wire widths (4.0 and 3.2 mm) and a wire height of 0.9 mm. The distance is normalized by the wire height of 10 mm and the upstream velocity is normalized by the mean velocity in the free stream of channel  74  Figure 5.21 Velocity profiles for boundary layers with V = 1 m/s and V = 10 m/s for two s  u  different wire widths (3.2 mm and 2.6 mm) and a wire height of 0.6 mm. The distance is normalized by the wire height of 10 mm and the upstream velocity is normalized by the mean velocity in the free stream of channel  75  Figure 5.22 Variation of upstream turbulence for three contour heights (0.6, 0.9 and 1.2 mm) in wall coordinates at V =10 m/s and V = 1 m/s u  76  s  Figure 5.23 Variation of upstream turbulence level for two wire widths (4.0 mm and 3.2 mm) with a contour height of 0.9 mm in wall coordinates at V =10 m/s and V = 1 m/s u  s  77  Figure 5.24 Variation of upstream turbulence for two wire widths (3.2 mm and 2.6 mm) with a contour height of 0.6 mm in wall coordinates at V =10 m/s and V = 1 m/s u  s  77  Figure 5.25 Effect of wall suction on the wall normal distribution of the velocity profiles in wall coordinates for h = 1.2 mm, w = 3.2 mm; (h/w = 0.375): V / V = 2.5, 10 ,25, and 45%. 79 s  u  Figure 5.26 Effect of wall suction on the wall normal distribution of the velocity profiles in wall coordinates for h = 0.9 mm, w = 3.2 mm; (h/w = 0.281): V / V = 2.5, 10, 25, and 45%. 79 s  IX  u  Figure 5.27 Effect of wall suction on the wall normal distribution of the velocity profiles in wall coordinates for h = 0.6 mm, w = 3.2 mm; (h/w = 0.188): V / V = 2.5, 10, 13, 22, and 50% s  u  80 Figure 5.28 Effect of wall suction on the wall normal distribution of the velocity profiles in wall coordinates for h = 0.9 mm, w = 4.0 mm; (h/w = 0.225): V / V = 2.5, 10, 25, 50 and s  u  100%  80  Figure 5.29 Effect of wall suction on the wall normal distribution of the velocity profiles in wall coordinates for h = 0.6 mm, w = 2.6 mm, (h/w = 0.231): V / V = 2.5, 10, 25, and 50%. 81 s  u  Figure 5.30 Effect of wall suction on the wall normal distribution of the turbulence intensity in wall coordinates for h = 1.2 mm, w = 3.2,mm (h/w = 0.375): V / V = 2.5, 10, 25, and s  u  44%  82  Figure 5.31 Effect of wall suction on the wall normal distribution of the turbulence intensity in wall coordinates for h = 0.9 mm, w = 3.2 mm, (h/w = 0.281): V / V = 2.5, 10, 25, and u  44%  82  Figure 5.32 Effect of wall suction on the wall normal distribution of the turbulence intensity in wall coordinates for h = 0.6 mm, w = 3.2 mm, (h/w = 0.188): V / V = 2.5, 10, 13, 22, and s  u  50%  83  Figure 5.33 Effect of wall suction on the wall normal distribution of the turbulence intensity in wall coordinates for h = 0.9 mm, w = 4.0 mm, (h/w = 0.225): V / V = 2.5, 10, 25, 50 and s  u  100%  83  Figure 5.34 Effect of wall suction on the wall normal distribution of the turbulence intensity in wall coordinates for h = 0.6 mm, w = 2.6 mm, (h/w = 0.231): V / V = 2.5, 10, 25, and s  u  50%  84  Figure 5.35 Effect of contour height and wire width on the roughness function AB for a range of slot velocities  86  Figure 5.36 Relation between shear velocity and roughness function for different contour geometries and a range of slot velocities  86  x  Figure 6.1. Schematic diagram of a cross-sectional screen and photo showing the rotor, screen plate coupon and plexiglass cover  88  Figure 6.2 Sample image of a nylon fibre trajectory (arrow is pointed to the nylon fibre image). 90 Figure 6.3 Trajectory of a 2 mm long nylon fibre above the screen with a 0.3 mm contour height showing how the fibre orients itself along the slot length  91  Figure 6.4 Trajectory of a 2 mm long nylon fibre above the screen with a 0.6 mm contour height showing the "surfing" action of the fibre along the wall shear layer  92  Figure 6.5 Trajectory of a 2 mm long nylon fibre above the screen with a 0.6 mm contour height showing the "vaulting" motion of the fibre  92  Figure 6.6 Trajectory of a 2 mm long nylon fibre above the screen with a 0.9 mm contour height showing the fibre falling into a slot in a backward motion  93  Figure 6.7 Trajectory of a 2 mm long nylon fibre above the screen with a 1.2 mm contour height showing the fibre caught in a vortex before it slides into a slot  94  Figure 6.8 Trajectory of a 2 mm long nylon fibre above the screen with a 0.9 mm contour height showing the "vaulting" motion of the fibre  xi  94  LIST OF SYMBOLS B  a constant in log-law for smooth wall  AB  roughness constant  C  a constant in turbulence model  M  Cie  a constant in turbulence model  C2  a constant in turbulence model  d  fringe spacing  f  Doppler frequency  h  height of the wire contour  H  height of the wire  k  roughness height or turbulence kinetic energy  N  number of data samples  s  standard deviation  S  slip factor  Td  blinking time period  u  local mean upstream velocity  u'  fluctuating component of x-velocity  u  non-dimensional upstream velocity (= u/u*)  d  +  u*  shear velocity, (  V  s  slot velocity  V  t  tip speed  V  u  mean upstream velocity specified at the inlet boundary/mean upstream velocity at the  =  fijp~)  core of the flow channel.  Vw  wall suction velocity  V*  non-dimensional wall suction velocity  w  wire width  W  CFD domain width  y  distance from wall  y  +  non dimensional distance from wall (= yu*/ v)  xii  Greek Symbols a  half angle between the laser beams  8  boundary layer thickness  e  turbulence kinetic energy dissipation  X  wavelength  |i  dynamic viscosity  [i  turbulence viscosity  v  kinematic viscosity  p  density of fluid  t  o  2  a constant in turbulence model  a  e  a constant in turbulence model  oi<  a constant in turbulence model  x  shear stress at wall  w  ACKNOWLEDGEMENTS  I would like to thank all those who offered me support and assistance throughout the duration of this work. In particular, I sincerely thank my supervisor Dr. James A. Olson for his guidance, kind support, encouragement and valuable discussions. I would also sincerely thank my research committee members Dr. Carl F. Ollivier-Gooch, Dr. D. Mark Martinez, and Dr. Robert W. Gooding for their continuous support and assistance. The time they have invested and the ideas they contributed over many fruitful discussions were greatly appreciated. I would also like to thank Dr. Daniel Ouellet for his useful discussions, help with the high-speed video study and being my research committee member for the first two years of my study. The staff at the Pulp and Paper Center and Mechanical Engineering Department deserves special thanks for their frequent and valuable help and ever-present friendliness. Thanks to Mr. Tim Paterson, Mr. Glenn Jolly, and Mr. Dan Miner for their help with the experimental set up, and to Mr. Ken Wong and Ms. Lisa Hudson for their administrative assistance. Thanks also to Dr. Alan Steeves and Dr. Jay Zhao for their help and technical support in using computer facilities in the Mechanical Engineering department. My fellow students at the Pulp and Paper Center and Mechanical Engineering department deserve special thanks for their frequent and valuable help. My friends Chuntao, Edmund, Yubing, Jacky, Payam, Shiva, Quak, Antti, George, Sean, Jens, Cameron, and Stefan deserve great thanks for being very supportive. Many thanks go to Albert Young for conducting the highspeed video experiments. Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), Advanced Fiber Technologies, and the Advanced Paper Making Initiative (API) is greatly acknowledged. Most of all, I would like to thank my parents, my wife Vipanchi, my sisters and their families for their unconditional love, understanding, support and help throughout this work.  xiv  1  INTRODUCTION  Pulping is the means by which papermaking fibres are separated from the wood structure. Pulping can be accomplished mechanically or chemically or by a combination of both. Commercial pulping processes are broadly classified as "mechanical pulping" or "chemical pulping". In chemical pulping, the lignin, a natural bio-polymer holding the fibres together, is dissolved and the fibres are separated from each other with little damage. In mechanical pulping, the fibres are mechanically separated by passing wood chips between two narrowly-spaced, rotating discs equipped with bars and grooves that comminute the wood into individual fibres.  Both chemical and mechanical pulping processes produce small quantities of shives, which are bundles of unseparated fibres. Shives lower the strength and optical quality of the paper and must be removed in order to produce high-quality paper. Pulp screening is the principal means of removing shives from pulp. In addition to shive removal, screens are used to remove various other oversized contaminants from the pulp and are especially important in the processing of recycled pulps. Further, pulp screens are capable of separating fibres by length to enable the targeted processing of long and short fibre fractions, or for the production of specialty pulp and paper products.  In mechanical pulping, screening is located after high consistency refining, as shown in Figure 1.1. The screens are connected together either in series or in a cascade arrangement according to the required pulp quality and process limitations. High quality pulp^ and paper typically require screens with very narrow slotted apertures with slot widths of approximately 0.15 mm. Screening is also very important unit operation in kraft, OCC (old corrugated container) and de-ink pulping processes. Figure 1.1 shows a schematic of a typical pressure screen. The pulp and contaminants enter tangentially through the feed port at the top of the screen cylinder and pass through a narrow annular zone between the slotted screen cylinder and a rotor. The fibres pass through the slots in the screen cylinder and exit the screen through the accept port. The oversized contaminants and reject pulp are retained by the cylinder and exit the screen through the reject port. To prevent the fibres from plugging the narrow slots, a rotor is used to generate negative pressure pulses that  1  fibres from plugging the narrow slots, a rotor is used to generate negative pressure pulses that periodically backflush the flow through the slots, thus clearing any fibre accumulations.  The main flows inside a pressure screen are: the tangential flow induced by the rotor, the axial flow induced by rejects removal and the radial pulsating flow through the slots created by the flow of the accept pulp and the pressure pulses generated by the rotor. The rotor tip speed that induces tangential velocity is typically 10 to 20 m/s. The axial flow in the screen is approximately 0.5 m/s, and the mean, time-averaged, flow through the apertures is in the range of 0.8 to 3 m/s. The fluid velocity through the slots is commonly referred to as the "slot velocity" in industry. This term will be used throughout this thesis. In the classical problem of flow over permeable walls with suction, the fluid velocity through the wall is commonly referred to as "suction velocity" in the literature.  The critical performance component of a pulp pressure screen is the screen cylinder. The screen cylinder may have apertures that are either drilled or slotted. Screen cylinders with slots are typically constructed by banding together specially shaped wires, as shown in Figure 1.2. In cross-section, the wires are in the range of 2 to 4 mm wide and are approximately 10 mm high. The cross-sectional shape of the wires is characterized by the contour height and the wire width, as shown in Figure 1.3. The wire height above the slotted aperture is called the contour height and is a measure of the roughness of the cylinder surface. The cross-sectional shape of the wire is designed to provide three effects: 1) to generate turbulence at the wall and ensure the pulp suspension is sufficiently fluidized. 2) to reduce the hydraulic resistance of the flow that turns into the slot and 3) to redirect the fibres in suspension into the slot to facilitate fibre passage.  The contour height and wire width are specified depending on the application. Higher contours create a rougher wall which in turn creates a higher level of turbulence near the wall. The increased turbulence results in more mixing and enhances the passage of long fibres through the slots, increasing the pulp concentration in the accept stream and the mass flow rate through the screen. However, increased turbulence at the wall is also known to increase the passage of small contaminants, lowering the contaminant removal efficiency of the screen. Wider wires reduce the number of slots in the wall and directly affect the volumetric and mass flow rates through the cylinder. Wire width is thus used to set the slot velocity. Higher slot velocities facilitate the passage of fibres through the screen, increasing accept fibre concentration and 2  increasing mass flow rate (capacity). Narrower wires will lead to an increased maximum flow rate through the cylinder. However, if the wires are too small, fibres will "staple" across the wires and plug the screen. The effect of wire shape on the flow behavior and turbulence properties near the surface of the cylinder is the subject of this thesis. The effect of wire shape on the flow at the cylinder surface is not well understood for industrially-relevant geometries. Therefore, four complementary studies were conducted to examine the effect of contour height and wire width on the velocity and turbulence characteristics of the flow. In the following thesis, Chapter 2 reviews the scientific literature relevant to fundamental screening hydrodynamics, pulp suspension flow with turbulence, fibre motion studies, rotor hydrodynamics, screen capacity and efficiency, and flow over rough surfaces with suction or blowing. Chapter 3 summarizes the literature and states the problem in detail with the research objectives and approach. Chapter 4 describes a computational Fluid Dynamic (CFD) model developed to theoretically examine the effect of the aperture geometry. Chapter 5 presents experimental measurements of the velocity field near the aperture entry using Particle Image Velocimetry (PIV) and experimental measurements of the velocity and turbulence intensity profiles above the wall. Chapter 6 describes experimental measurements of fibre motion in the flow over the wall and through the slotted apertures. Chapter 7 presents the summary and conclusions of this work and Chapter 8 presents recommendations for future work.  3  Cross-sdction A-A Figure 1.1 Schematic of the principal flows through a pressure screen. 4  Figure 1.2 Typical cross-section of the wires banded together to form narrow apertures. Wire width, w  •4  •  Contour height, h  Slot width, s Figure 1.3 Close-up of the wire cross-section near the feed surface showing wire width, slot width and contour height.  5  2  LITERATURE REVIEW  The scientific literature relevant to pulp screening is divided into the following subcategories: 1) fundamental screening hydrodynamics, 2) fibre motion studies, 3) Pulp suspension flow with turbulence 4) rotor hydrodynamics, 5) screen capacity and efficiency, and 6) flow over rough surfaces with blowing or suction. 2.1  Fundamental Screening Hydrodynamics Early investigations of the flow over slotted screen plates were done by Halonen et al.  (1989) using CFD to obtain the turbulence properties and flow patterns near the aperture entry. In this study, the smooth slot has a vortex partially occupying the slot opening (about half of the slot size) and the contour moves the vortex to the region above the slot entry. The shape of the contour also caused the flow to bend more smoothly towards the slot. The ability to move the vortex out of the slot significantly decreased the hydraulic resistance of contoured screen cylinder by 20 to 50% in comparison to conventional screen cylinders. They found that, the turbulence kinetic energy increased by approximately seven times near the slot due to the presence of the contour. The maximum turbulence kinetic energy was spread across the downstream slope of the contour. The results obtained using the CFD model were verified with velocity measurements taken from Laser Doppler Velocimetry (LDV) experiments. They measured about 0.1 m/s velocity fluctuations near the wall for the smooth slot. For the contoured slot the velocity fluctuations near the wall were increased by 15%. This study did not include the necessary detailed information about LDV experiments and CFD simulations to allow the comparison at the flow conditions used in this thesis. Their work focused on comparing smooth apertures to a particular contour geometry rather than on the detailed understanding of the effect of contour geometry on the flow field.  Oosthuizen et al. (1994) investigated the flow of a dilute mixture of water and fibres in the vicinity of a 1 mm wall slot under laminar flow conditions. Fibre motion was studied by injecting dyed fibres into the flow. Their study of fibre motion indicated that fibres did not separate from the curved streamline flows near the slot. 6  Yu and DeFoe (1994a) studied the flow patterns at the surface of different types of model screen cylinders under steady flow conditions. Their experimental observation showed that a "fiber mat", which was a collection of fibres, floes and contaminants, builds up randomly around the screen opening. They explained how thefibremat is remixed and diluted during screening. In further work (1994b), they examined fibre motion at the feed-side surface of smooth and contoured screen baskets. They showed thatfibrepassage depended on fibre orientation, which in turn, strongly depended on the flow velocity and distance from the screen surface. These authors developed a framework for a model that can estimate the "effective open area" of a screen cylinder, i.e. the area remaining after the total open area is partially obstructed with fibres as it would be in normal operation. The factors used in this model are based on the rotor, furnish and screen cylinder geometries. These factors need to be measured experimentally. Note that, industrial practice is to calculate the slot velocity as the accept flow rate divided by the total open area of the screen cylinder (1994).  Gooding (1996) examined the flow patterns and turbulence levels of various smooth and contour screen slots in a steady cross-flow to obtain a mechanistic understanding of what determines slot resistance and the conditions that lead to minimum values of slot resistance. He found that for a smooth slot the vortex occupied more than 60% of the slot size (at V = 7.5 m/s u  and V = 1.5 m/s) and he found that the vortex size decreased (less than 30 % of slot width at V s  s  = 9.3 m/s) with increasing slot velocity. For the contour slot, two vortices existed (at V = 1.3 s  m/s) - one inside the slot and the other one above the slot. He found that two vortices existed at lower slot velocities (less than 1.3 m/s) and the vortex inside the slot was completely eliminated at higher slot velocities. His work estimated the pressure drop coefficient for screen cylinders in pulp screens and confirmed that contoured screens generally reduce hydraulic resistance. The effect of contour shape is dependent on slot upstream and slot velocity, however, and simply the presence of contours is not sufficient. Gooding's slot resistance analysis was based on step-step and step-slope contours which represent generic descriptions of industrial contours. His findings did not include the details in the relief of the slot. Maximum upstream velocity in his study was 10 m/s. This was estimated to be representative of the mean velocity in the wake of a rotor element.  7  In the modern industrial pressure screen, wires with various cross-sectional shapes are assembled to form a screen cylinder with narrow slots with prescribed entry geometry. The aperture entry geometry is known to significantly affect screen performance. Gregoire (2000) modeled the flow through screen slots under steady-state and unsteady conditions. In the unsteady case, the effect of the rotor was taken into account by imposing an experimentallymeasured pressure pulse as a boundary condition at the slot inlet. The pressure pulse obtained from the experiments was fitted with a piecewise function and used as a boundary condition. Steady flow through the screen apertures was modeled using a Two-Layer-Zonal-Model (TLZM). Gregoire proposed a logarithmic law for permeable and impermeable rough walls by treating screen contours as two-dimensional roughness. The results justify that the wall function approach gives a good approximation of the flow field compared to the detailed numerical simulation of flow around screen contours. The origin of the wall was located at the crest of the contours. Gregoire used the roughness function determined for sand grains found in the literature. The concept of equivalent sand grain roughness for a wire contour height may not be a good approximation as the sand grains do not represent the complex details of the contour geometry. This thesis focuses on developing roughness functions for various contour geometries. From the steady flow CFD simulations for the flow pattern over a contour screen surface (contour height =1.2 mm and slot separation distance = 3.2 mm) with upstream velocity equal to three times slot velocity, he found that the back-facing steps produced flow separation with vortices forming at the entrance of the slots between two successive contours. The flow separated at the top of the contour and re-attached ahead of the next contour at a distance of about 1.9 times contour height from upstream edge of the slot. The vortex center was formed at a distance of about 0.46 times the contour height from the upstream edge of the slot. Between the vortex and re-attachment point there was a stream tunnel that leads the upstream flow through the slot.  Dong (2002) examined the flow field through different slots with several contour shapes of screen cylinder using CFD. From the steady flow CFD simulations for the flow over two different slope-slope contours with contour heights equal to 0.5 mm and 1.3 mm (V = 6.5 m/s u  and V = 2.4 m/s), she found that both the contours a vortex formed at the entrance of the slot. s  For lower contour height (0.5 mm) the vortex partially covered the top of the slot and the upstream flow smoothly bent over the vortex to enter the slot. The separated flow at the top of the contour was re-attached at a very shorter distance, approximately 1.5 times contour height 8  (Note the smaller height of contour) very close to the down stream edge of the slot because of smaller vortex size created by the lower contour height. For higher contour height (1.3 mm), the vortex size was relatively larger and completely covered the top of the slot width creating a tunnel between the vortex and the slope for the upstream flow to enter the slot. The separated flow was re-attached at a distance of 1.8 times the contour height from the down stream edge of the slot. With increased slot velocities, the vortex size decreased for both the contour heights. In summary, previous studies showed that cross-flow and slot velocities, and aperture geometry affect the flow field near the wall. These studies included generic industrial contours. These studies either focused on hydraulic resistance offered by apertures or detailed fibre motion near the aperture. These studies did not provide detailed turbulence and velocity profiles upstream of apertures. Gregoire (2000) determined the velocity profiles near the aperture but his work was focused on developing a mathematical model to simulate the unsteady flow behavior in a pulp screen using CFD. Still, it is not clear about how aperture geometry differs from each other. Unsteady-state CFD modeling done by Gregoire (2000) is a big leap towards modeling more realistic pulp screening conditions, however, there is still more work that needs to be done in the area of steady flow modeling near industrial screen contours. 2.2  Pulp Suspensions Flow with Turbulence  The flow of pulp suspensions is fundamental in most of the unit operations in pulp and paper production including pulp screening. Pulp suspensions constitute complex multi-phase systems which contain fibres, contaminants/debris, air and chemicals in water. Above certain consistency, fibres in the pulp suspension entangle with other fibres to form floes (Kerekes and Schell (1992 and floes form more easily with increasing pulp consistencies. Kerekes and Schell (1992) have also shown that the fibre flocculation mainly deepens on mechanical forces between fibres rather than on chemical factors. Floes are dispersed or fluidized when enough turbulence is introduced into the pulp suspension. However, when turbulence decays fibres tend to refloculate within milli-seconds (Kerekes (1983)). Kerekes and Schell (1992) introduced the crowding number, which represents the number of fibres inside a sphere with a diameter equal to the average length of the fibres in the suspension. The crowding number has shown to indicate the tendency to form floes.  9  According to Robertson and Manson (1957), and Lee and Duffy (1976), three different types of pulp suspension flows exist in pipes: plug, mixed and turbulent flows. At low Reynolds numbers, the fluid stress is not enough to disrupt the fibre network and the suspension flows as a plug. Increasing mean flow velocity results in a hollow cylindrical layer of water in the proximity of the pipe wall where the fluid shear is a maximum. The core region is however occupied by an intact plug of networked fibres. This type of flow is referred to as mixed flow. At high mean flow velocity the core plug would vanish as the fluid shear stress becomes higher than the fibre network yield stress, and fibres in the suspension move randomly giving rise to a turbulent flow condition. In this regime, the equilibrium size of floes was observed to diminish with increasing flow velocity (and hence increasing turbulence). In pipe flows, fluidization of pulp suspension occurs in the turbulent regime because of the increased level of shear required to rupture the fibre networks. Gullischen and Harkonen (1981) defined fluidization as the point where the entire pulp suspension becomes fully turbulent. This definition is similar to that in pipe flow, and they found that the pulp suspension has similar flow properties as water in the fluidized state under the similar conditions. Many researchers (Lee and Duffy (1975), Jasberg (2007), Robertson and Manson (1957)) showed that pulp suspensions present a greater friction resistance than that of water at low flow velocities and as the velocity increases the friction resistance becomes less than that of water. Lee and Duffy (1975), Jasberg (2007), Xu and Aidun (2005) showed that the fibres in the turbulent annulus of pulp suspensions modified the momentum transfer and Lee and Duffy (1976) found that in the low flow rate turbulent regime, the von Karman constant (=0.41 for water) decreases with flow rate, while at a higher flow rate turbulent regime the behavior is reversed.  Jasberg (2007) speculated that drag reduction in the mixed and turbulent regimes is  due to the existence of yield region in these regimes and is most likely related to quenching of wall induced turbulence due to the presence of fibres. As a consequence, the rate of turbulent transfer of longitudinal momentum from the core region towards the wall is reduced. The turbulence friction near the wall is attenuated leading to the yield layer characterized by increasing velocity gradient. These conclusions were based on the assumption that the friction is dominated by the turbulence. Andersson and Ramuson (2000) studied the transition of fibre suspension to turbulent flow in a rotary shear device and found that the fluctuation velocity approaches that of water with increasing rotational speed. Xu and Aidun (2005) measured velocity profiles for a range of pulp consistencies (0 - 1.0%) and found that if the flow rate is high enough ( R e » 37,000), the presence of fibres in the flow has so small effect that there is 10  virtually no difference between the velocity profiles of water and pulp suspension. The presence of fibres or fibre floes in the pulp suspension will reduce the turbulence intensity. This will decrease gradually when the flow rate increases.  If the flow rate is high enough, the fibre  concentration has no effect on turbulence intensity. Although the pulp suspension is a multi-phase fluid, Wikstrom (2002) treated the flow of pulp suspensions as a single homogeneous fluid flow exhibiting non-Newtonian flow behaviour. This treatment ignores the individual treatment of the fibres and considers the effect of fibre suspension rheology as a whole. The rheology of the pulp suspensions relates the shear rate to the shear stress of the suspension. Wikstrom (2002) modeled the contribution of the pulp suspensions on fluid flow by a non-Newtonian model while solving the coupled momentum equation for a turbulent flow. The most widely used non-Newtonian model to represent pulp suspensions is the Bingham plastic model.  2.3  Fibre Motion Early investigations of fibre passage during screening were mostly based on statistical  and empirical analysis of fibre passage through apertures. Tirado (1958) related the length of a fibre relative to the screen cylinder hole diameter and the effect it has on the probability of passage through the screen. Estridge (1962) analyzed fibre retention by screens using a statistical model that was verified experimentally. The analysis was simplified by assuming that all the fibres act independently and that flow conditions do not affect the retention process. Reise et al. (1969) experimentally studied stiff nylon fibres approaching a screen plate at a normal angle of incidence. They also developed a numerical model to calculate the trajectory and orientation of fibres as they approached the screen in order to determine the probability of a fibre passing through an aperture. The experimental conditions used in these studies, however, were significantly different from the conditions that exist inside pressure screens. Several fundamental studies have examined the motion of fibres and fluid flow through a narrow aperture in a steady cross-flow, which serves as a model pulp screen. Gooding and Kerekes (1986, 1989) used high-speed cinematography to capture the trajectories of fibres as they approached a single aperture in a cross-flow. They showed that fibre concentration near the wall was lower than in the main-stream flow. As a consequence of this gradient, the thin fluid near the wall entering the slot has less fibres than the average. This alone (called "wall effect") 11  created a screening effect. The "turning effect" referred to the effect of upstream velocity on fibre passage. For example, long stiff fibres were not always able to turn at the aperture entry to enter the slot before being swept downstream. Long flexible fibres tend to bend and enter the slot, and short rigid fibres tend to rotate and swept back into upstream flow. The effect of fibre length, slot width, slot velocity and upstream velocity on the probability of fibre passage was experimentally determined for a single slot in a cross-flow by Kumar (1991). He found that fibre passage varied significantly with the ratio of fibre length to slot width. He also observed an exponential increase in fibre passage with increasing V / V when the ratio of fibre length to slot s  u  width is < 2. The concentration and orientation of fibres in a turbulent flow near a smooth wall was determined by Olson (1996) and the fibre concentration near the wall was found to be a function of fibre length. High-speed video of fibres moving near a wall in turbulent near-wall flow showed the fibres would "pole-vault" away from the wall as they rotated in the wall shear layer, thus decreasing fibre concentration at the wall. This resulted in a lower concentration of fibres passing through the apertures. Yu and DeFoe (1994) also used high-speed video of fibres moving through a slot in a steady cross-flow to understand the factors affecting fibre passage. Fibre passage was shown to depend on the approachingfibreorientation, upstream velocity and distance of the fibre from the screen cylinder wall. This study did not investigate the effect of contour geometry on fibre motion. CFD studies of the steady flow near the aperture (Gregoire, 2000) have been conducted, including computer simulation of flexible fibres passing through narrow-contoured apertures (Lawryshyn 1996, Dong et al. 2000). Despite the large number of fundamental studies, the mechanisms of fibre passage through narrow, contoured apertures remain unclear, especially under the conditions of pulsed flow imposed by the rotor. JulienSaint-Amand (2001) hypothesized that contours increase fibre passage by decelerating the flow at the aperture entry, turning the fibres to align their length with the slot and thus promoting passage. Dong (2003) developed a simulation tool to examine the flow and fibre behavior near a single slot of any reasonable slot shape. This tool includes a three-dimensional flexible fibre model which can model both rigid and flexible fibres. However, this model ignored fibre-fibre interaction and the effects of the fibres on the flow. Dong applied this model to study the effect of slot shape on pulp screen performance. She found that among slot shapes tested, a slot with sloping sides upstream and downstream provided the highest passage of fibres for the same flow conditions and the same overall slot width. In summary, early investigations onfibremotion were conducted under ideal conditions and are very different from real industrial pressure screen conditions. Recent studies have 12  examined fibre motion as it occurs in a model pulp screen with model fibres and numerical simulations. The studies showed that the fibre passage was dependent on flow conditions near the aperture and aperture geometry. However, these studies were conducted for generic contour shapes. Knowledge gained from these studies needs to be extended to apertures with industrial contours by conducting fibre motion studies near an industrial screen contour.  2.4  Rotor Hydrodynamics  Previous researchers (Yu et al. (1994), Pinon et al. (2002), Gonzalez (2002), Wikstrom (2002), Feng (2003)) studied the effect of the key design and operating variables including the tip speed on pressure pulses produced by the rotor. According to them, the magnitude of the pressure pulse dependent on the tip speed of the rotor. Apart from producing pressure pulses, the rotor (tip speed) also induces tangential velocity to the flow approaching the screen apertures. In this thesis we refer the tangential velocity as the "upstream velocity". The upstream velocity of the pulp suspension is an important variable for the fiber passage (Gooding (1986, 1996), Kumar (1991) and Olson (1996)).  The relationship between tip speed of the rotor and upstream velocity of flow approaching the apertures was examined by Gooding (1986, 1993). It was found that the upstream velocity was less than tip speed by a factor. The upstream velocity (V ) expressed in u  terms of the tip speed (V ), and a slip factor (S), with Equation 2.1 (Gooding (1986)). t  V = (l-S)V u  t  Equation 2.1  Gooding (1986) estimated the slip factor and it was approximately 85% based on the analysis of the velocity profile in the wake of a cylinder. This slip factor was developed for a bump rotor. The slip factor is expected to vary depending on the rotor design, gap, pulp consistency, etc.  Rotor designs vary among manufacturers depending on the application. A drum-type rotor having hemispherical bumps (bumps are also known as "lugs") on its outer surface facing the screen cylinder as shown in Figure 1.1. The drum-type rotor fills up the most of the space within the screen cylinder, and the screening zone (i.e. the zone between the cylinder and rotor) 13  takes the form of a narrow annular gap. In a foil type rotor, there is a central rotor shaft (significantly smaller in diameter than the core of the drum-type rotor) and vertical foils are held by radial supports. The upstream velocity varies with location in the wake of the lug/foil, thickness of annular zone, and the clearance between rotor and cylinder. The tip speed of the drum-type rotors is about 25 to 30 m/s and the tip speed of foil type rotors is 20 to 25 m/s (Plueger et al. (2007)). At these tip speeds the lugs/foils interacts with the wake of leading lugs/foils as they rotate. The frequency of the interaction of the wakes depends on the number of lugs/foils and its placement along the circumference of the rotor. The upstream velocity also varies with location from the wall due to the presence of a boundary layer. The boundary layer thickness depends on the screen cylinder design. Julien-Saint-Amand (1997) reported an increase in pressure pulse magnitude when a contoured screen cylinder was used. He proposed that the average upstream velocity of the pulp suspension decreased in the annulus (which would increase the relative velocity) due to a large breaking force exerted by a contoured screen surface. For a drum-type rotor, the thickness of annular zone is approximately 20 mm and the clearance between the tip of rotor and the screen surface is about 2 mm. For a foil rotor, the thickness of annular zone is much less than drum-type rotor and the clearance between the foils and screen surface is 1 to 3 mm. The rotor element (lug, foil or any other shape depending on the rotor design) causes a "venturi effect" in the clearance between the rotor element and screen wall, which causes the pressure and also the upstream velocity to vary in the annulus (Karvinen and Halonen, (1984)).  Gooding (1993) measured upstream velocities in a pulp screen with a rotor tip speed of 11.7 to 21.8 m/s. He determined that for a tip speed of 12 m/s, the velocity in the wake of the foil was approximately 8.5 m/s (which suggest a slip factor of approximately 30 %). The slip factor varies depending on the rotor type, the size of annular gap, and interaction of wakes. It is beyond the scope of this thesis to estimate the upstream velocity in the wake of a rotor element due to the complexity of the flow field induced by the rotor. We will use the previous studies to guide the selection of upstream velocities representing industrial values.  In spite of the differences in shape, any rotor serves a similar function. They accelerate the pulp suspensions to a high tangential velocity and along with axial flow, establish necessary flow field adjacent to the screen surface. Also, the lugs/foils on the rotor produce pulses and turbulence that prevent apertures from plugging. 14  2.5  Screen Capacity and Efficiency A typical challenge for pressure screen manufacturers is to design pressure screens that  provide adequate capacity while consuming minimal energy and providing the required level of contaminant removal efficiency. Capacity and efficiency are inter-related. In general, changes in parameters, such as, screen cylinder design, rotor design, upstream velocity, slot velocity and furnish characteristics, which cause an increase in capacity will reduce efficiency - and viceversa. The choice of screen cylinder is therefore a trade-off between the efficiency and capacity. The challenge of the current screen cylinder design is to keep the aperture size small and at the same time to increase capacity. Wire screen basket technology has been developed to address these issues. Kumar et al. (1998) proposed that for smooth-surface holed screen cylinders, the aperture size should be less than half of the target fibre length, and aperture velocity should be less than 30% of tangential velocity just above the screen wall in order to achieve efficient separation. Sloane (2000) found that long fibre fractionation efficiency increased with decreasing aperture size for smooth surface cylinder. She also concluded that the rotor shape had a great effect on the screening efficiency, while the rotor speed did not. However, other research (Repo and Sundholm (2001), Heise (1992)) reported that lower rotational speed (which is referred to upstream velocity in this thesis) would increase the separation efficiency by controlling the intensity of mixing at the screen wall. Similarly, the slot velocity has a contradictory result on the contaminant removal efficiency. The screen plate profile has a significant effect on screening efficiency. Contoured screen cylinders are reported to increase the contaminant removal efficiency while decreasing the fractionation efficiency because long fibres tend to go through the apertures more easily (Frejborg et al. (1989), Halonen et al. (1990)). However, the right choice of contour design is an important decision, since one design is not necessarily always the best for every application. For example, low contours could be used to separate long fibres from short fibres which increase the short fibre fractionation efficiency. Ninimaki et al. (1998) reported that the efficiency of probability screening is more dependent on contour height rather than slot width, where as slot width was more important in relation to the screen capacity. Increased contour height led to a decline in screening efficiency and an improvement in the maximum capacity of the screen which has been speculated to be due to an increase in turbulence with increasing contour height. However, these speculations need to be supported by turbulence data near a screen cylinder wall. 15  One of the objectives of this thesis is to determine how much turbulence is generated by different contour geometries. This knowledge would help in choosing a geometry for a particular application. Ninimaki et al. (1998) found that for screening ground wood pulp which typically contains short and stiff fibres, low contour heights (0.6 mm) gave better screening efficiency. The open area of the screen plate has a dominant influence on capacity: the larger the open area, the greater the capacity. But, as the open area increases, aperture spacing may decrease. Gooding and Craig (1992) found that if 30% of the fibres are longer than the slot spacing, severe blinding will occur due to fibre stapling between adjacent slots. Martinez et al. (1999) developed a mathematical model to identify the factors that determine the pulp screen capacity. They demonstrated the importance of aperture geometry on capacity.  2.6  Flow Over Rough Surfaces with Suction or Blowing Flow over smooth surfaces with suction/blowing has been studied in great detail by the  aeronautics community for boundary layer control, either to reduce aircraft drag or prevent separation and stall. A review of the relevant studies indicates that most of the experimental and numerical work in this area has been focused on skin friction reduction. Typically, the concept of reducing drag is implemented by using wall suction through an array of small circular holes drilled in the wing surface. This is similar to the flow in a pressure screen cylinder surface, where the rotor induces a cross-flow which is pulled through drilled or slotted apertures. As described previously, the entry of the screen aperture can be either smooth or contoured to improve fibre passage and reduce hydraulic resistance. Therefore, the flow of interest to this investigation generally resembles the case of flow over a rough surface with suction.  Thomas and Cornelius (1981) examined the suction of laminar boundary layer into a slot in a smooth wall. They observed a vortex bubble in the slot and the size of this bubble increased with increased upstream fluid velocity or reduced slot velocity. They also noted that the slot resistance increased due to the presence of vortex bubbles in the slot. Sano and Hirayama (1985) examined the effect of steady suction or blowing through a span-wise slit in a turbulent boundary layer. They found that steady suction decreases skin friction and turbulence intensity behind the slit. Antonio et al. (1985) demonstrated that the turbulent boundary layer can be re-laminarized by an intensive local suction with skin friction being reduced during the relaminarization. In this 16  study, the suction effect is applied through a short porous wall strip. Yoshioka et al. (2004) performed an experimental investigation of free stream turbulence-induced disturbances in boundary layers with wall suction. The experiments showed that wall suction suppresses the disturbances' growth and significantly delays or inhibits the breakdown to turbulence. The introduction of a permeable boundary causes significant change in the flow structure. Studies on flow over a permeable bed (Zagni and Smith (1976), Gupta and Paudyal (1985)) found that the velocity was not zero near the bed surface but at some distance below it. Therefore, the no-slip boundary condition cannot be applied. Chen (2004) et al. investigated the velocity distribution of turbulent flow in an open channel with bed suction theoretically and experimentally. The author proposed a velocity profile with a slip velocity at the bed surface and an origin displacement under the bed surface. The values of the origin displacement, slip velocity, and shear velocity were found to increase with increasing relative suction.  The aforementioned studies in this section focused on the flow over smooth wall, and did not consider the effect of wall roughness. Some studies related to flow over rough walls with suction are relevant to pulp screening, such as, Gooding (1996), Olson (1996), Halonen and Ljokkoi (1989), Gregoire (2000), Dong (2002). These studies were discussed in the previous section.  Flow over impermeable rough surfaces has been studied for more than a century and there is an extensive literature available, notably, White (1991) and Schiltching (1979). Much of the literature before 1990 is concerned with the universal aspects of flow over rough walls. More recent research has emphasized differences between different types of roughness ((Jimenez, (2004)). Perry et al. (1969) classified roughness into k-type and d-type. When flow characteristics such as the roughness function depend on the roughness height, "k" it is called "ktype". In contrast, when the cavities between the roughness elements are narrow, the flow depends on outer scales such as pipe diameter and the roughness is called "d-type". In k-type roughness, the roughness height alone is not sufficient to characterize the wall roughness (Patel and Yoon, (1995)) and several attempts have been made to express the roughness in terms of other parameters. Simpson (1973) defined a roughness density as the ratio of the total surface area to the total roughness frontal area normal to the flow direction. Walls with grooves wider than 3 to 4 times roughness height behave like k-type surfaces and also have recirculation bubbles that re-attach ahead of the next rib exposing the rib to the outer flow. Tani (1987) 17  suggested that the demarcation between k-type and d-type roughness can be made at the ratio of pitch between roughness elements to roughness height equal to 4. Walls with grooves shorter than 4 times roughness height behave like d-type surfaces and stable vortices are set up in the grooves and the outer flow is relatively undisturbed by the roughness elements. In flows with a ratio of boundary layer thickness to roughness height, lesser than or equal to 50(8/k < 50), the effect of the roughness extends across the boundary layer (Jimenez (2004)). In such a case, wall functions may not apply and the flow is better described as flow over obstacles. It is also dependent on roughness geometry. The boundary layer is attached or separated from these obstacles depending on the type of geometry.  Flow over obstacles which are complex in shape require a detailed description of the flow pattern, vortex size and shape, boundary layer separation point and reattachment point. The size and shape of the obstacles have tremendous effect on the flow details cited above. Therefore, it is important to model the flow over the screen surface by treating the wire contour as an obstacle rather than as roughness. The roughness function AB in the log-law velocity profile will depend on the size and shape of the roughness and the effective location of the fictitious wall from which the distance is measured (Patel, (1998)). Flow in the near-wall region can be modeled using twolayer zonal turbulence models (TLZM) and large eddy simulation (LES). Application of LES techniques to solve flow over complex rough-walled surfaces takes tremendous computational time and these techniques are under development. The TLZM approach can assist in solving the flow near-wall region with the present computational resources available; however, it is known to be less accurate.  To save computational time and resources, a near wall treatment can be used instead of solving the detailed flow over rough surfaces. In this, roughness functions are introduced into the logarithmic law of the wall which is used to match the velocity profile near the wall. In this case, the velocity profile is characterized by the same slope as a smooth surface, but with a different integration constant, AB.  In near-rough-wall modeling, a two-equation turbulence model is employed in the outer core flow and modified wall functions are used to bridge the roughness sub-layer. Here, the nearwall model is based on the introduction of the surface roughness length scale k  + s  (non  dimensional roughness height, = k u 7 v ) and the roughness function AB. The surfaces roughness 18  effect is taken into account through the inclusion of a sink term in the momentum equation and a source term in the turbulent kinetic energy equation (Lakehal (1999)).  The properties of the flow over a rough surface have been intensively studied using experiments since the early works of Nikuradse (1933), focusing on densely-packed uniform sand grain roughness (Lakehal (1999)). From all these investigations, various correlations between skin friction and roughness type were established. Schlichting (1979) gives the following relation (Equation 2.2) for turbulent velocity profiles over smooth walls in the region of the viscous wall layer. This relation applies in the overlap region, 35 <y > 350.  u 1 , yu^ — = — In f  U  K  \  v  +B  Equation 2.2  J  The presence of roughness displaces the velocity profile by a shift, often referred to as the roughness function AB. yu U  K  v  v  + B-AB  Equation 2.3  J  The non-dimensional variables u (= u/u* and y ( = yu*/v) are defined as the non-dimensional +  }  +  upstream velocity and non-dimensional distance from the wall respectively.  The Karman constant K = 0.41 does not change with roughness (White, 1991). The roughness function which shifts the log-layer from the smooth wall with a correspondingly large friction increase is a function of the type of roughness which has been traditionally measured for objects such as sand, rivets, threads, and spheres.  For flow over rough walls with suction or blowing, the stream-wise velocity profile changes significantly and the law of the wall needs to be modified to accommodate the suction or blowing. Schlichting (1979) has conducted studies on suction and blowing effects on the boundary layer under conditions of zero pressure gradient. Stevenson (1963) and Schlichting (1979) derived the following modification of the logarithmic law of the wall where either suction or blowing is present:  i In yu^ f  i  K  \  v  +B  Equation 2.4  J  19  Equation 2.4 reduces to the impermeable wall law (Equation. 2.2) when V = 0. A shift w  constant AB is included in Equation. 2.4 to consider the effect of roughness. Gregoire (2003) modified Equation 2.4 and implemented it into his CFD computations to calculate the flow field near the wall of a pulp screen. In summary, the flow over the screen surface generally resembles the case of flow over a rough surface with suction. Similar flow physics has been studied in a great detail by the aeronautics community but these studies were limited to skin friction reduction. Most of the studies related to flow over a wall with suction were limited to smooth walls and did not include the effect of wall roughness. In the case most relevant to our work, Nikuradse (1933) developed a log-law for the velocity profile near the smooth wall which was modified to include the effect of wall roughness by introducing roughness function, AB. Previous work showed that AB is a function of roughness height (or type of roughness) and wall suction. However, geometry considered in this study has two length scales, "h" and "w", and also wall suction. Therefore, AB is a function of h, w, and V . The flow near the screen wall can be modeled in CFD using wall s  functions. However, there is no correlation available in the literature for AB relevant to pulp screen geometry. The concept of equivalent sand grain roughness used by Gregoire (2003) for a wire contour height may not be a best approximation. Therefore, there is a need to develop a correlation for AB to include both the effects of h, w, and V . s  20  3  PROBLEM STATEMENT  The flow near the surface of a pulp screen is similar to the flow over a rough wall with suction. Previous studies showed that the upstream velocity, the slot velocity and the aperture shape will dramatically affect the fluid flow near the wall which, in turn, controls fibre passage and screen performance. These studies were done for generic industrial contours and either focused on the hydraulic resistance of a screen aperture or detailed fibre motion near the aperture. These studies did not provide detailed turbulence and velocity profiles upstream of apertures. Even though previous work determined the velocity profiles near the aperture upstream, much of the work focused on developing mathematical models to simulate the pulp screen using CFD and to model the unsteady flow behavior. Still, it is not clear about how aperture geometry affects the flow near the wall. Unsteady-state CFD modeling is a big leap towards modeling more realistic pulp screening conditions and we still need to gain more understanding in the area of steady flow modeling near industrial screen contours. Also, the unsteady phenomenon is localized during the passage of the rotor and we can disregard the unsteady flow during the rest of the time. For industrially-relevant screen cylinder geometries, the flow is complex and there have been limited investigation of the effect of aperture geometry on the flow field and turbulence properties near the surface.  The objective of this thesis is to experimentally and theoretically determine the detailed flow behavior of steady flow through a periodic array of narrowly-spaced wires in a cross-flow as shown in Figure 3.1. The approach to accomplish this objective is to:  1. Develop a CFD model to investigate the detailed flow behavior in a simplified screen geometry. Specifically, the model will be used to determine the velocity and turbulence fields. The model will be used to investigate the effect of wire geometry on the key flow features, such as vortex size and reattachment locations. 2. Experimentally measure the flow behavior and compare with CFD results. Specifically, Particle Image Velocimetry (PIV) will be used to measure the velocity field near the aperture to determine vortex size and re-attachment. Laser Doppler Velocimetry (LDV) 21  will be used to measure the velocity profiles and turbulence properties above the screen surface. 3. Experimentally measure the fibre trajectories inside a laboratory pulp screen using HighSpeed Video (HSV) and link the results of computational and experimental investigations to fibre motion in a cross-sectional pulp screen. In particular, the influence of wire geometry on vortex size and fibre motion will be examined using model nylon fibres.  We will consider water as the working fluid for CFD, PIV and LDV experiments. At low consistency and high shear rates found in an industrial pulp screen, the pulp suspensions have the same properties as water (Xu and Aidun (2005)). Therefore, the insights gained from water as the working medium can be related to low consistency pulp suspensions, typically used in screening.  Upstream velocity, V m/s u  WCKKKKKKKKK) T  -*• -#• -*• -*•  ~  yf  ^  yf  Slot velocity, V m/s s  Figure 3.1 Flow over a periodic array of narrowly-spaced wires under steady cross-flow.  22  4  NUMERICAL SIMULATION  CFD simulations were carried out on a simplified model of a pulp screen cylinder under steady cross-flow conditions to investigate the detailed flow behavior. The principal flows inside a pulp screen were described in Chapter 1. In studying the flow at an aperture, the variations in the axial screen flow are secondary compared to tangential flow induced by the rotor. Therefore, a three-dimensional pulp screen cylinder flow can be reduced to a slice across the cylinder as shown in Figure 4.1. (Note: We have considered a foil rotor in this study). The flow is periodic in nature from foil to foil. This allows a further simplification in being able to consider only a sector of the two-dimensional section of pulp screen. The problem is furthered simplified by assuming that the unsteady phenomena associated with the rotor pulsations are localized during the passage of the foils and may be disregarded during the rest of the time. With that simplification, we can neglect the presence of the rotor and the pressure pulses produced by the rotor. As a result, the wall region is modeled as flow over a periodic array of wires under steady cross-flow as show in Figure 4.2. In addition to the above simplifications, we considered water as the working fluid and did not include the non-Newtonian effect of pulp suspensions which is beyond the scope of this thesis. The low consistency pulp suspensions (<1%) have the same flow properties as water in a fully turbulent state (Gullischen and Harkonen (1981)). Therefore the insights gained from using water as the working medium can be related to the low consistency pulp suspension used in an industrial screen.  The tangential velocity (referred in this thesis as the "upstream velocity") is induced by the rotor foils moving close to the wall with typical foil clearances of 5 to 10 mm. The upstream velocity is less than the tip speed by approximately 30% in the wake of the foil (Gooding (1993)). A typical height of the wires is 10 mm. The separation distance between the slots and the height of the contour are parameters of this study.  To provide a CFD solution for the flow field at a screen slot, the Navier-Stokes equations were solved using the commercial CFD program Fluent (version 6.1) and its segregated solution method. This method solves the continuity, momentum and turbulence equations sequentially. The SIMPLEC algorithm is used to couple the pressure and velocity, and a second-order spatial 23  interpolation method was employed. The flow inside a screen basket is periodic in nature, thus the domain consists of a single slot with periodic boundary conditions, as shown in Figure 4.3.  Figure 4.1 Schematic of the two-dimensional slice across the pulp screen cylinder showing the periodicity of rotor foils.  Figure 4.2 Schematic showing the single slot domain considered for CFD calculations (not to scale).  24  Velocity inlet Periodic  £  • Mesh near the slot entry  Pressure outlet  Figure 4.3 Geometry of the pulp screen slot showing the boundary conditions and mesh near the slot.  4.1  Turbulence Model Selection Most of the studies on flow over a backward-facing step were focused on improving the  turbulence models to better simulate the resulting turbulence, see for example, Acharya et al, (1994), Durst and Rastogi (1979) and Benodekar et al. (1983). Wall function approximations were used in these studies to account for the near wall effect. Predicted results indicated that all models under-predicted the magnitude of turbulence. In consideration of wall bounded flows, the use of the wall functions for near wall treatment is correct only for simple shear flows. Flow over obstacles involves strongly separated flows around them. The flow near the pulp screen apertures is similar to both the flow over a rough wall with suction through small slots, and flow over a backward facing step. This requires modeling the flow up to the wall. An ultra-fine grid near the wall is required because the spatial variations in the near-wall turbulence structure are very large due to the combined influence of viscosity and wall-induced anisotropy. An alternative to the use of wall functions is to use turbulence models that are valid all the way to the wall. Therefore, an  25  enhanced wall treatment with two-layer zonal model (TLZM) was used in the present study. In this approach, the solution is integrated numerically through the entire wall region including the viscous sub-layer up to the wall where the no-slip boundary condition is applied. The flow domain is divided into two regions. A one-equation model is applied in the region close to the wall to account for wall proximity affects. In the region beyond the near-wall layer, the Realizable k-£ model was used to model eddy viscosity. The complete details of Realizable k-£ model and TLZM can be found in the FLUENT User Manual (FLUENT, (2001)); however the salient features of this model are described here. Another alternative to TLZM would be to use Large Eddy Simulation (LES) but this approach demands tremendous computer resources. 4.1.1  Realizable k-£ model This turbulence model ensures that normal stresses are positive to be consistent with the  physics of the turbulent flows. Normal stresses are, by definition, positive quantities, but they become negative (i.e. non realizable) when the strain rate is large (Shih et al. (1995)). Like all other turbulence models, the turbulence viscosity is computed from Equation 4.1. k  2  //, = pC —  Equation 4.1  e where, /u = turbulent viscosity t  C = model constant k = turbulence kinetic energy E = turbulence kinetic energy dissipation The realizable k-£ model differs from other k-e models by not having a constant value for C , e.g. C is equal to a constant value of 0.09 which it does for the other models. To ensure the A  realizability (i.e. positive normal stresses) the constant C is made variable by sensitizing it to the mean flow and the turbulence quantities, k, £. C thus becomes a function of the mean strain fl  and rotation rates, the angular velocity of the system rotation and the turbulence quantities. The modeling coefficients used in this study for the realizable k-£ model are as follows: C =0.09, CT =1.9,o- =1.2,or* =1.0, C = 1.44 2  2  ff  u  26  4.2  Boundary Conditions Periodic boundary conditions are applied on the left and right faces of the domain  because the flows across these two opposite faces in the computational model are identical. The inlet velocity boundary condition is applied at the top of the domain by specifying the x-velocity component and the y-velocity component. The x-velocity component is chosen to be equivalent to the upstream velocity of 15 m/s. This value represents a tip speed of about 21 m/s which is based on 30% slip factor from Gooding's (1993) measurements. The tip speed could be higher than estimated because, with increasing tip speed the momentum transfer between the rotor and fluid increases. Nevertheless, the estimated tip speed is in the range of operating tip speeds used in a pulp screen (Pflueger et al. (2007). The y-component is chosen to yield a slot velocity of 1 m/s. We kept the upstream velocity and the slot velocity constant for all the simulations. A pressure outlet boundary condition is applied at the bottom of the domain by setting the pressure equal to zero. By specifying the y-velocity component at the inlet velocity drives the flow across the cylinder. The inlet pressure would then vary to give the correct pressure drop across the cylinder. A no slip boundary condition is assigned to the walls of the wires. 4.3  Domain Discritization A TLZM model demands a y (= yu*/v) value approximately equal to 1 which requires a +  very fine mesh close to the wall. A structured grid is generated close to the wall and the grid is unstructured away from the wall. For the entire domain a minimum of 900,000 cells were required to get an aspect ratio of cell approximately equal to one. 4.4  Results and Discussion CFD simulations were carried out on six screen surfaces with different contour heights and  wire widths (Table 4.1). The results are grouped into two categories: 1) the effect of contour height, and 2) the effect of wire width. For all the simulations, the upstream velocity and slot velocity are kept constant at V = 15 m/s and V = 1.0 m/s respectively. Figure 4.4 shows the u  s  flow field near a screen slot outlining the flow features: vortex center, re-attachment point, exit layer and stream tunnel.  27  Table 4.1 Variables tested in CFD simulations Working fluid: Water Upstream velocity: 15 m/s Slot velocity: 1.0 m/s Dimensions coupon # of test coupons: 1 2 3 4 6 6  contour height (mm) wire width (mm) 1.2 3.2 0.9 3.2 0.6 3.2 0.3 3.2 0.9 2.6 0.9 4.0  slot width (mm) 0.15 0.15 0.15 0.15 0.15 0.15  Exit layer height Stream tunnel  Re-attachment point  Figure 4.4 Flow field near a screen slot outlining the flow features schematically.  28  4.4.1  Solution sensitivity  In order to test the sensitivity of the solution to grid size, cases with three different grid sizes were considered: Case 1 with 900,000 cells, Case 2 with 1.1 million cells, and Case 3 with 1.4 million cells. The mesh was refined in the region of wall, vortex center, re-attachment point and in the shear layer which develops in the downstream of flow separation. The solution is sensitive to the iteration number and grid size. The sensitivity is checked by comparing the size and position of the vortex formed at the entrance of the slot (see Figure 4.4). The vortex size at the slot entrance is increased with increasing number of iterations. As shown in Figure 4.5, the vortex center and re-attachment point move away from the slot as the solution progresses and remain at the same position after 75,000 iterations. Case 2 with 1.1 million elements is considered as the optimum case for the present study as the change in flow features is less than 4% compared to the most refined mesh. It took minimum three weeks to run one simulation case on a Pentium IV desktop PC with 3 GHz processor and 3 GB RAM.  0.6  -i  •©— Vortex Center: Case 1 Vortex Center: Case 2 G— Vortex Center: Case 3 Re-attachment Point: Case 1 Re-attachment Point: Case 2 Re-attachment Point: Case 3  Casel: 913,000 cells Case 2: 1,134,000 cells Case 3: 1,386,000 cells 0 5000  25000  45000  65000  85000  Iterations  Figure 4.5 Sensitivity of the solution to the number of iterations and grid size (distance is normalized by the wire width of 3.2 mm). 29  4.4.2  Effect of contour height Four contour heights were studied: 0.3 mm, 0.6 mm, 0.9 mm, and 1.2 mm. Figure 4.6  shows the streamline plots of flow approaching a slot for a slot velocity of 1.0 m/s and upstream velocity at the inlet equal to 15 m/s. The figure shows that as contour height increases, the vortex size increases and the center of the vortex moves away from the slot. The vortex dominates the entry region of the slot. This agrees with previous studies (Gooding (1996), Gregoire (2003) and Dong (2002)) who also observed the presence of vortex at the slot entrance and its changing shape with changing contour height. One of the key features of the flow is the exit layer which turns from the upstream of the slot entry and passes into the slot. The slot flow passes around the vortex creating a tunnel between the vortex and re-attachment point. While streamlines far away from the contours are nearly parallel, in the vicinity of the wall, they curve in response to the contour geometry. The flow separated from the top of the contour is re-attached ahead of the next contour at 0.19, 0.39, 0.48, and 0.68 times wire width (from upstream edge of the slot) for contour heights equal to 0.3, 0.6, 0.9 and 1.2 mm respectively. With increasing contour height vortex center moved away from the upstream edge of the slot to a distance of 0.04, 0.16, 0.2, and 0.22 times wire width for contour heights equal to 0.3, 0.6, 0.9 and 1.2 mm respectively. The vortex center and re-attachment locations are compared in Table 4.2 for a similar geometry (shown in Figure 2.5; h= 1.2 mm and w = 3.2 mm) with the findings from Gregoire (2003) which shows a good agreement. The differences between the two studies might be attributed to the differences in the ratio of upstream velocity to slot velocity (4.7 times higher than the current study) and slot width (two times higher than the current study).  30  Table 4.2 Comparison of vortex location data with previous study  Current study  Gregoire (2003)  Re-attachment point distance (from upstream edge of slot)  Contour geometry  V /Vu  Vortex center distance (from upstream edge of slot)  h = 1.2 mm, w = 3.2 mm and slot width = 0.15 mm  0.07  0.47 x h  1.9 xh  h = 1.2 and w = 3.2 mm and slot width = 0.30 mm  0.33  0.46 x h  1.7xh  s  31  Figure 4.7 Acceleration contours and streamlines at the aperture entry for contour heights equal to (a) 0.3, (b) 0.6, (c) 0.9 and (d) 1.2 mm for a 3.2 mm wide wire showing strong acceleration on the top of the contour and near the re-attachment point.  32  As shown in Figure 4.7, the flow experiences a strong acceleration and deceleration. The flow accelerates after re-attachment where the streamlines come together. The flow then goes through a sudden deceleration at the top of the contour where the flow separates. A second deceleration occurs in the region approaching the re-attachment point where the flow splits to continue over the next contour or to pass into the aperture. We speculate that the deceleration near the re-attachment point is critical for fibre passage. The fibre would slow down near the reattachment point and it would either turn to follow the flow towards the slot or be carried away by the upstream flow. The probability of occurrence of one of these two events depends on the fibre length and its flexibility. We also speculate that the periodic acceleration / deceleration could also contribute to flow disruption at the screen surface, which would break apart fibre bundles. Further, this figure indicates that the velocity and turbulence intensity profiles above the surface vary significantly depending on the point where the data for velocity profile is taken. In order to compare the velocity and turbulence properties, the origin is taken above the vortex center at the contour surface level as shown in Figure 4.8. Therefore, the origin will change with geometry because the vortex centre position changes with geometry. The distance from the wall is normalized by the wire height (H = 10 mm) which is the same for all six geometries considered in this study. Local mean upstream velocity is normalized by the mean velocity specified at the inlet boundary condition (V =15 m/s). u  Figure 4.9 shows the upstream velocity profile immediately upstream of the slot at the top of the vortex center of the wire for the four contour heights. A low contour height generates stronger vortices. Local expansion and wall friction slows the flow near the wall for the higher (0.9 and 1.2 mm) contours. y  Figure 4.8 Origin for comparing the velocity and turbulence properties.  33  h • •- - 1.2 •x -0.9 • - • 0.6 0.3  0.6  5  w 3.2 3.2 3.2 3.2  h/w 0.375 0.281 0.188 0.094  0.4  o o c  0.2 o z 0.5  0.6  0.7  0.8  0.9  1.1  Normalised upstream velocity  Figure 4.9 The upstream velocity profiles of the flow approaching the slot for contour heights equal to 0.3, 0.6, 0.9 and 1.2 mm. The velocity profile is taken at the top of the vortex center, and the distance is normalized by the wire height of 10 mm, upstream velocity is normalized by the velocity specified at the inlet boundary condition.  34  h  0  5  w  10  h/w  15  20  Turbulence Intensity, %  Figure 4.10 Turbulence intensity profile above the screen surface showing the slight increase in turbulence with contour height at the screen surface. The turbulence velocity profile is taken at the top of the vortex center, and the. distance is normalized by the wire height of 10 mm.  35  (c)  (d)  Turbulence Kinetic Energy  3 2 10  Figure 4.11 Contour plots of turbulence kinetic energy near the screen surface for contour heights equal to (a) 0.3, (b) 0.6, (c) 0.9 and (d) 1.2 mm  Figure 4.10 shows the turbulence intensity profile as a function of distance above the screen surface, and the modest increase in intensity with increasing contour height. The highly turbulent region is concentrated in the vicinity of the screen cylinder wall where it is most needed for disrupting the floes. Figure 4.11 shows the turbulent kinetic energy near the screen surface for all contour heights. Higher turbulence levels (equal to 5 m /s ) are found near the location where the flow is re-attached to the contour. The same phenomenon was observed by Halonen et al. (1989) but the magnitude of turbulence kinetic energy is about 4 times higher. However, the flow conditions and geometry are different from the current study.  36  Turbulence kinetic energy is due to the Reynolds stresses. Turbulence kinetic energy is high in the shear layer near the wall because of high Reynolds stresses (Panigrahi (2001)). Contours enhanced mixing in the separated shear layer behind the wire. With the higher contours, greater mixing is possible and leads to shear layer growth. Increased turbulence is the result of a thick separated shear layer downstream of the contour that persists from aperture to aperture. With decreasing contour height, mixing levels were decreased. The shear layer becomes thinner. Low contour heights produced high levels of turbulence only at the reattachment point. We speculate that the local mixing provided by the turbulence near the wall increases the concentration of fibres near the aperture entry, and thus the concentration of fibres passing through the aperture. This results in a reduced amount of good fibres exiting the reject outlet of the pulp screen. The increased turbulence also disrupts fibre floes so individual fibres can move freely. The increased mixing due to increased turbulence at the screen surface may also lead to a decrease in fractionation and contamination removal efficiency. This is consistent with industrial screening practice that uses low contours for increased fractionation and increased contaminant removal.  4.4.3  Effect of wire width  The capacity of the screen is related to the open area of the cylinder which is proportional to the wire width and hence the number of slots in the cylinder. Increasing the number of slots in the screen will generally increase the capacity of the screen. However, the screen cylinder can blind over by having the screen slots spaced so closely together that fibres staple from one slot to the next (Gooding and Craig (1992)). For this reason wire width is an important design parameter when optimizing screens for different applications.  37  (a)  (b)  Figure 4.12 Fluid streamlines at the aperture entry for wire widths of (a) 2.6, (b) 3.2, and (c) 4.0 mm.  Three cases, with wire widths equal to 2.6, 3.2 and 4.0 mm were studied. For this comparison, the contour height was set at 0.9 mm and the slot width was 0.15 mm. The upstream velocity and slot velocity were set to 15 m/s and 1 m/s, respectively. Figure 4.12 shows the streamline plots for the three cases. As shown in Figure 4.12, the vortex size increased and stretched with increasing wire width and became shallower. The wider vortex provides a much larger region for fibres to interact with the vortex. For screens with a low contour height and wire width, the vortex is too small for the fibres to interact with the vortex. We speculate that the large vortex region would give more chance for fibres to interact with and enter the vortex and eventually pass through the slot. As expected the center of the vortex moves away from the slot with increasing wire width. Figure 4.13 shows the velocity profile immediately upstream of the slot at the top of the vortex center for the three wire widths. In this study, the contour height is 38  considered as roughness element. In the previous studies, Gregoire (2003) also considered contour height as roughness. For narrower wires the roughness increases and the flow near the wall decreases. Roughness increases for narrower wires as there are more contours per unit length. As shown in Figure 4.14, the turbulence intensity near the screen surface increases with decreasing wire width. This increase is due to the increase in number of contours for a given distance, which effectively makes the wall rougher. However, the effect of wire width on the turbulence intensity is considerably less than that resulting from changes in contour height.  Figure 4.13 Velocity profiles of the flow approaching the slot for wire widths of 2.6, 3.2, and 4.0 mm. The velocity profile is taken at the top of the vortex center, and the distance is normalized by the wire height of 10 mm, upstream velocity is normalized by the velocity specified at the inlet boundary condition.  39  Turbulence Intensity, % Figure 4.14 Turbulence intensity near the screen surface for wire widths of 2.6, 3.2, and 4.0 mm showing the increase in turbulence intensity with decreasing wire width The turbulence profile is taken at the top of the vortex center, and the distance is normalized by the wire height of 10 mm.  40  (c)  Figure 4.15 Contour plots of turbulence kinetic energy near the screen surface for wire widths of (a) 2.6, (b) 3.2 and (c) 4.0 mm showing the increase in turbulence kinetic energy with decreasing wire width.  Figure 4.15 shows contour plots of turbulent kinetic energy near the screen surface for varying wire width. For narrow wires, the turbulence generated spans from one aperture to the next creating a layer of intense turbulent kinetic energy. The result is that narrow wire cylinders are effectively rougher than wide wires.  41  4.5  Combined Effect of Contour Height and Wire Width  Contours are characterized by various groups in industry in terms of contour height, contour angle, or contour volume. It is thus interesting to see the effect of contour slope on boundary layer thickness, wall shear stress, and turbulence kinetic energy. The ratio of contour height to wire width, h/w, constitutes the slope of the contour. The results obtained in the previous sections for the individual effects of the contour height and wire width are considered in this section in terms of the contour slope (i.e. h/w). Figure 4.16 shows the effect of contour slope on the average boundary layer thickness near the wall. The boundary layer thickness is estimated at seven locations along the wire as shown in Figure 4.17. The distance from wall to the point where the upstream flow approaches 99% of mean flow is measured at each location along the wire. In the region of flow separation, the distance was measured from the point of inflection instead of the wall. The boundary layer thickness is an average for all seven points. The boundary layer thickness is increased with increasing slope. The boundary layer thickness increases approximately linearly with the contour slope. From this linear relationship, we can estimate average boundary layer thickness for the slopes in the range (0.094 to 0.375) tested. If we increase the contour height, by keeping the wire width constant, the slope increases - the average boundary layer thickness increases. If we increase the wire width, by keeping the same contour height, the slope decreases - the average boundary layer thickness decreases. When the contour slope approaches zero (i.e. h = 0), the screen surface behaves like a "smooth wall" with slots. There still exists a thin boundary layer for a smooth wall. This smooth wall has slots with a flow bifurcation. The intercept in Figure 4.16 corresponds to boundary layer thickness of a smooth wall with flow going through the slots separated by a certain distance. If the groove width (width of open space between two contours or slot separation distance) is less than a threshold value, the screen surface would behave like a d-type surface. In the case of a ribbed impermeable wall, the threshold value for rib spacing is four times the rib height (Tani (1997). The threshold value for the screen surface would be less than four because of the existence of flow through the slots. If the slope reaches this threshold value, the vortex would completely occupy the grove and it would not expose the slot to the upstream flow. The upstream flow will be relatively undisturbed by the contour height.  42  Figure 4.17 A sample streamlines plot overlaid with velocity profiles showing the seven locations along the wire where the boundary layer thickness was estimated. 43  Figure 4.18 shows the effect of contour slope on the average turbulence intensity near the wall. The average turbulence intensity is calculated from the average turbulence kinetic energy. The average turbulence kinetic energy is calculated by integrating throughout the boundary layer over the entire surface. The normalized average turbulence intensity varies approximately linearly with the slope. The intercept at zero slope provides an estimate of turbulence over a smooth wall with flow going through the slots. This quantity increases with increasing slope. This is likely because; the deeper contour slope leads to increased velocity fluctuations which lead to increased turbulence. As shown in previous sections, the turbulence kinetic energy increased with increasing contour height and decreasing wire width, which directly relates to increased slope.  0.16 n 0.14 0.12 urbulence in1  d  0.1 •  0.08 0.06 0.04 0.02 00  0.1  0.2  0.3  0.4  h/w  Figure 4.18 The effect of aperture geometry on average turbulence kinetic energy.  Figure 4.19 shows the effect of contour slope on the skin friction coefficient. The skin friction coefficient is calculated from the wall shear stress, mean upstream velocity and fluid density. The average wall shear stress is calculated by taking the average of the shear stress on the wall (the wall shear stress below the slot entry is very small in magnitude compared to the shear stress of the wall exposed to the upstream flow). Figure 4.19 shows an approximately linear increase in skin friction coefficient with slope. The intercept at zero slope provides an estimate of skin friction coefficient for a smooth wall with flow going through the slots. The wall shear stress is 120 to 150 N/m for the contour slopes tested. From the wall shear stress, we 2  44  can estimate the drag force due to skin friction on the screen cylinder wall under ideal conditions stated at the beginning of this chapter. The drag force could be used to evaluate the failure modes of screen cylinder during operation.  o  0.0014 -I  c  0.0012 -  o  0.001 -  •  o 1  c  CO  0.0008 -  o  0.0006 -  CD  0.0004 -  —'  o  £  Q) 0.0002 -  O  o  0 0  0.05  0.1  0.15  0.2  0.25  0.3  0.35  0.4  h/w  Figure 4.19 The effect of aperture geometry on skin friction coefficient. 4.6  Summary  CFD simulations were carried out on six screen geometries with a range of wire widths and contour heights. The upstream velocity, slot velocity and slot width were constant. Analysis of the flow patterns showed that the slot entry region is dominated by a stationary vortex. This study documented the sensitivity of the vortex size and shape to changes in contour height and wire width. The effect was substantial. This study also documented the effect of aperture geometry on turbulence properties and velocity profiles. Turbulence intensity was found to increase with increasing contour height and decreasing wire width. The upstream velocity near the wall increased with decreasing contour height and decreasing wire width. It was also found that there is a significant importance of cumulative effect of contour height and wire width both of which constitute the contour slope (h/w).  45  5 E X P E R I M E N T A L M E A S U R E M E N T OF F L O W FIELD Experimental apparatus and procedures were developed to measure the velocity field and turbulence properties near a rough wall in steady cross-flow with suction. The experimental flow field is a model pulp screen and has similar simplifying assumptions found in the CFD analyses, that is, a steady flow screen with water. The range of the experiments was extended beyond the CFD study to include the effect of various slot velocities. This chapter describes the experimental set up used for both LDV and PIV measurements and then presents the methodology for determining the mean flow features using PIV, and the velocity and turbulence profiles using LDV. 5.1  Flow Channel The experiments were carried out on a laboratory flow channel. The channel is intended to  simulate the flow through a section of the screen cylinder under steady flow conditions. The channel is made from plexiglas with 12.5 mm wall thickness. The channel is 1.244 m long and has 38.1 mm x 38.1 mm square cross-section. The detailed dimensions are given in Appendix 2. The flow is from the left to right of the channel and the upstream flow bifurcates through the slots of the coupon and enters the plenum at the bottom as shown in Figure 5.1. Using a very similar apparatus, Gooding (1986, 1996), Kumar (1991), and Olson (1996) observed the fiber motion near the slot. The flow channel used in this study differs from previous studies in size which is 1.9 times bigger in cross-section and 3.5 times longer. The flow measurement techniques which are explained in the later sections require that the plexiglas surface is scratch free to minimize the deviations and attenuation of the laser beam. The entry to the channel was an abrupt contraction from a circular pipe of 76 mm diameter. The developing flow downstream created a flow field, which could be estimated from similar flows reported in the literature. Lissenburg el al. (1975) investigated the effect of a constriction on turbulent pipe flow. They found that, after 10 pipe diameters distance downstream from the constriction an almost complete recovery of the disturbed turbulent flow was obtained. The Reynolds number in their study was kept at 5000. Even shorter distances are sufficient for higher Reynolds numbers (Diessler, (1953)). In our channel, the test coupon was located at 14 equivalent diameters from the channel entry. The Reynolds number in the channel based on the equivalent diameter of the channel was about 546,000.  46  Figure 5.1 Exploded view of the experimental flow channel.  5.2  Test Coupons The primary component of the experimental system is the test coupon. All the test coupons  were 152.4 mm long and 38.1 mm wide. Five coupons with different geometries were used (Table 5.2). The geometry of the slots used in this study was taken from commercial pulp screens whereas the previous studies (Gooding (1986, 1996), Kumar (1991) and Olson (1996)) used a generic slot geometry. A detailed drawing of a coupon is shown in Figure 5.2. A plexiglas flow channel which houses the test coupons was designed using a CAD (Unigraphics NX) modeling software. The design of the flow channel is modular so that the test coupons can be flush mounted horizontally inside of it and can be replaced very quickly and easily.  47  6.000  L 3 ) ..620_  4.798  45--J  Figure 5.2 Orthogonal views of a test coupon used in the experiments. Dimensions are in inches unless stated otherwise.  5.3  Flow Loop As shown in Figure 5.3, the flow loop comprised a circulation pump, two magnetic flow  meters, a 0.2 m tank and the flow channel. In an industrial pulp screen, as explained in the 3  introduction chapter, the upstream velocities are in the order of 10 to 20 m/s and the slot flow velocities are in the order of 0.8 to 5.0 m/s.  Because of the limited capacity of the pump only 10 m/s average upstream velocity could be achieved in a 38 x 38 mm square channel. The flow rate was controlled by a pump with a variable frequency drive. The flow channel was connected to an industrial pump (20 HP) with 76 mm diameter schedule 80 PVC pipe. The flow from the channel was diverted back to a 0.2 m tank. The flow from the plenum at the bottom of the coupon was also diverted back to the tank with 25 mm diameter schedule 80 PVC pipe. The flow through the slots can be controlled from 0.25 to 10 m/s using a ball valve. The upstream velocity was measured using a 76 mm diameter magnetic flow meter whereas the slot velocity was measured with a 25 mm diameter magnetic flow meter. 48  Flow channel  Flow meter Tank Flow meter Pump Figure 5.3 Schematic of the flow loop used for PIV experiments  5.4  PIV Measuring System PIV was chosen as a measurement method because it is capable of giving a complete  snapshot of the flow field over the region of interest. Although PIV can be used to determine ensemble mean velocities, the metal reflections from the wall made PTV inadequate for finding turbulence properties and velocity profiles close to the wall. As a result, LDV was used as a complementary flow measurement technique to determine the turbulence profiles above the coupon. LDV is described in a later section.  The PTV system works by pulsing a thin laser sheet twice through the transparent test section. The sheet, which was approximately 1 mm thick, was aligned perpendicular to the middle of the test coupon. The pulse separation time was 5 microseconds. The double pulsing sequence was initiated by triggering a signal from the pulse generator which in turn send timed pulses to the laser unit. Microscopic particles (hallow glass spheres with nominal diameter 10 um, density 1.1 g/cm ) that were seeded into the flow loop that followed local flow inside it were 3  illuminated each time the laser pulsed. For each of two laser pulses, a synchronized digital camera recorded an image of the illuminated particles. The resulting image pair was later analyzed using the PIV image processing software Flow Manager® (see Appendix 3 for details) which tracks the displacement of small groups of particles. From the known time difference between pulses and the displacement of the particles obtainedfromcross correlation, the velocity vectors are obtained from each interrogation area. The outcome is a velocity field map of the 49  flow parallel to and inside the laser sheet. Figure 5.4 shows the overview of the P I V system. The hardware and software specifications of the system can be found in Appendix 3.  Figure 5.4 Overview of the P I V measuring system  5.4.1  Laser source and light sheet optics A double-pulsed laser supplied by New Wave Inc. was used for the P I V applications as  the illumination source for the laser light sheet. It has two N d - Y A G infrared laser heads, each of which emits a beam with a 1064 nm wavelength. The beam from the laser head entered a second harmonic generator to produce visible green light of wave length 532 nm. Dichoric mirrors separated the visible light from the residual infrared light and directed the beam to a 45° angled mirror. The mirror angle was adjusted to deflect the incident laser beam by 90°.  The laser sheet was formed by two lenses that were mounted between a mirror and the test section. The mirror and optics were mounted exclusively on a steel tower secured to the ground to alleviate the vibrations created by the pump. The pulse laser output was a collimated beam with a nominal diameter of 4.5 mm. The mirror diverted the beam from laser source at 90° 50  to positive cylindrical lens that caused the beam to converge. The converged beam entered a negative spherical lens which formed a thin sheet of light with a thickness of 1 - 2 mm. The thinner laser sheet would minimize the out-of-plane motion of seeding particles by minimizing the lateral extent of the measurement volume. The out-of-plane motion of particles caused by cross-flow increases the chance of local velocity errors.  The pulse was triggered manually from a pulse generator which can be programmed to control the delay between the two pulses. The energy of the laser delivered from each head was 120 mJ per pulse. The pulse width was approximately 5 ns. The mean light power during illumination was 24 MW. With upstream velocity of 10 m/s, the 5 ns pulse was short enough to freeze the particle locations to within 0.05 pm. This represents less than 1% of particle diameter. During the experiments, complete pulse energy was not used. It was adjusted for each laser head to provide ample contrast in each of the two images. The contrast ensured that particles were distinguishable for PIV analyses.  The laser pulse separation time was 5 ps for all the experiments (timing diagram for camera and laser synchronization is given Appendix 4). This pulse separation period was chosen such that adequate particle movement occurred between two subsequent images. Excessively large separation times allow particle groups to lose their unique pattern, thus lessening the chance of calculating the true particle displacements. Conversely, very short separation times produce particle displacement approaching the spatial resolution of the images, which makes it difficult in determining the displacements. The maximum displacement allowed by a particle within an interrogation area is 1/3 of the window size (i.e. 10 pixels for a 32x32 interrogation area window size). In order to reduce the variability due to out-of-plane motions, we selected a camera with 9 mm spacer tube to limit the depth offieldto less than 2 mm (less than laser sheet thickness).  5.4.2 Camera and image grabber A CCD digital camera (Roper Scientific ES 1.0) was used to record the light scattered from the particles illuminated by the laser. The monochrome camera was fitted with a 35 mm Yashica lens. Five spacer rings which will add up to 9 mm were used between the lens and 51  camera to focus at a very small field of view (4.5 mm x 4.5 mm). With the insertion of spacer rings, the magnification increased and the field of view decreased. The drawback of using a spacer ring was that the depth of field was reduced to the order of 2 mm. On the other hand, the advantage of shorter depth of field was that it would freeze the motion of seeding particles within a thin measurement volume and it would minimize the out-of-plane motion of seeding particles. The camera was focused on a single slot. The camera was mounted on a two axis (Y-Z) traverse which gave a very precise movement. The images were 1008 pixel widths across and 1018 pixels widths along with each square pixel having 256 possible grey scale levels.  The camera was set to dual exposure and was triggered by the frame grabber that resided in a dedicated PC. The exposure mode and exposure times were set by the commands sent in RS -232 protocols from a serial port of the PC to the camera. The frame grabber (Matrox Meteor II digital) was triggered by a pulse generator that synchronized the camera with the laser pulses. When the frame grabber received the trigger from the pulse generator it did send a trigger to the camera to capture PIV image pair and at the same it also initiated a custom computer code to grab the two separate images from the camera. These image pairs were saved for later processing in Flow Manager software.  5.4.3 Light scattering considerations The major problem in PIV measurements was glare from the walls. The test coupons are manufactured by Advanced Fibre Technologies Inc. out of stainless steal with very narrow slots with high tolerances. Stainless steel cannot be anodized. Also, it cannot be coated using the Black Oxide process because the coating won't stick to the stainless steel surface. We cannot spray the black paint as it will clog the slots. However, a black pen was used to paint the surface of the coupon. The thickness of the coating is very small compared to the slot width, which is 0.15 mm. All the coupons were coated before each experiment. However, the black ink coating did not completely eliminate the reflections, making it extremely difficult to make accurate measurements in the proximity of 0.2 mm close to the wall.  52  5.4.4 Flow seeding The flow was seeded with 10 um hollow glass spheres (HGS) supplied by Dantec Dynamics. There particles are small enough to follow the flow which has a range of 1 to 10 m/s. Also they are large enough to dampen Brownian motion effects. The scattered image of the particles was in the range of 4 to 6 pixels. As a general rule, there should be a minimum of five particles per interrogation window to get a good correlation. Given the interrogation window size of 32 x 32 pixels, light sheet thickness of 1 mm, an imaging area of 4.5 x 4.5 mm, and an image density of 5 particles per region corresponds to particle density in the flow loop. In order to achieve this density in the test section, the mass of particles needed was 83 grams (volume of fluid in the system was 0.141 m ). 3  5.4.5 Results and discussion Experiments were performed on three different test coupons (Table 5.1) to measure flow features near the slot. For all the experiments, the upstream velocity and the slot velocity were kept constant at V = 10 m/s and V = 1.0 m/s respectively. PIV measurements were always taken u  s  in the plane bisecting the test coupon with the imaging region arranged as shown in Figure 5.5. The image size in all the tests was 4.5 x 4.5 mm giving a resolution of 4.45 micron/pixel.  The raw PIV images were processed using commercially available software, Flow Manager® (details in Appendix 3). The image pair was imported into the software and the images' real size and laser pulse duration were given as inputs. The image real size is calculated using resolution target tests (details in Appendix 3) at the corresponding focal length. Using the masking feature available in the software, wall regions in the PIV images were selected to be ignored in the image processing.  Images were processed using an adaptive correlation technique to obtain velocity vector maps. Adaptive correlation is an iterative form of cross-correlation in which the interrogation area shrinks, thus providing more velocity vectors per unit area of images. Each time the window is shrunk, the velocity information from the larger window is used to place a refined search boundary for the shrunken window. This feature is extremely useful for velocity determination in the parts of the image where the particle distribution is relatively scant. The vectors obtained 53  from the adaptive correlation were validated to remove any false measurements. A moving average method validates or rejects vectors based on comparison between neighboring vectors. The rejected vectors were replaced by vectors estimated from surrounding values. Figure 5.6 shows a sample PIV raw image. In this image, reflections from the wall are visible very clearly. The dark shaded area represent stainless steel contour coated with black ink. Figure 5.7 shows a sample PIV raw image overlaid with cross-correlated vectors. From the Figure 5.7, we notice that the flow filed in the slot and near-wall regions could not be captured by PIV due to light reflections.  To reduce the statistical uncertainty in the average measurement, 71 PIV images were averaged (it required minimum 71 images for averaging in order to reduce the standard error). The ensemble velocity vector at a point in the measurement plane (in-plane of image) was calculated by averaging the velocities at the same point from all the tests. The cross-flow velocity (equal to 10 m/s) would act as a large in-plane velocity component compared to out-ofplane velocity component which would not cause significant error in the measurements. Therefore, in-plane velocity components should dominate the instantaneous velocity filed. The 90% confidence interval for the measured velocity was calculated using the following equation;  rms  (7,  For N values greater than 30, r  005  Equation 5.1  is considered independent of N and is approximated as  1.96. The maximum uncertainty of time averaged velocities was estimated to be ± 9.9 % for cases with high contours. The maximum uncertainty for low contours was ± 18% which is much higher than the other two cases, because with the low contour height, there are many more spurious vectors close to the wall. The total error constitutes the error due to particle tracking and statistical uncertainty. The software interpolation accuracy was expected to be 0.1 pixel which gave a relative uncertainty of ± 4.43 % at 1 m/s based on pulse separation time and the length conversion factor. The flow meter has an accuracy of ± 0.02% of full scale. The dimensions of the test coupon were accurate within ± 0.02 mm. The error in locating the origin at the wall was ± 0.1 mm  54  55  . 0 W F I 0 W 6 2 * 6 2 v e c t o r s (3 >44) IIMIIM 11 1 l | ' i > l i | H U M 1 Mil t' 1 • 1 > lioo |«o [Soo |.-so 1  M j t ' I M M ' l j l t l M ' l M|i>iiii ' 1 j 11| |350 1<00 Isoo  '1 j l ' J M ' 11' |550  M j l ' I U i "IMM'M '•|*50  • I TOO  |r50  "111 MM* !•! jl 'I'M HI IM'M l | | | l | ' l ' M I | (800 |»« i * !  Figure 5.7 A sample PIV raw image overlaid with cross-correlated vectors for a contour with h = 1.2 mm and w = 3.2 mm. Table 5.1 Experimental variables for PIV measurements Working fluid: Water Upstream velocity: 10 m/s Slot velocity: 1.0 m/s Dimensions Coupon # of test coupons: 1 2 3  contour height (mm) wire width (mm) 1.2 3.2 0.9 3.2 0.6 3.2  slot width (mm) 0.15 0.15 0.15  A comparison of the predicted results and the experimental data are shown in Figure 5.8. In order to compare the CFD results with the PIV measurements, the simulations were run with the identical conditions used in the PIV experiments. The boundary conditions were changed to get upstream velocity equal to 10 m/s and slot velocity equal tol m/s. (Note: The vectors plotted from CFD overlap on each other and do not look clear. We were not able to get streamline plots 56  for PIV results because of very coarse sized interrogation windows and poor resolution near the wall). Vector plots indicate that the basic structure of the flow field was modeled quite well by CFD and all the features including vortex center and flow re-attachment point were well captured. For all contours, the experimental measurements confirmed that a stable, stationary vortex existed above the slot. For the large contours, both CFD and the experimental velocity field indicated that the vortex occupied most of the contour volume and that the reattachment point was approximately two thirds of the distance from the slot to the top of the contour. Experimental results also confirmed that as the contour height decreased, the size of the vortex decreased and the re-attachment point moved closer to the slot. The smallest contour height yields the smallest vortex with the re-attachment point closest to the slot. A quantitative comparison of the CFD and the PTV data is done by comparing the horizontal distance between the vortex center and reattachment point. The results are summarized in Table 5.2. The percentage difference between the PIV data and CFD data increased with decreasing contour height. This is because the PIV measurements are not very good close to the wall. The smaller the vortex size, the closer it is to the wall.  Table 5.2 Comparison of CFD and PIV data. Coupon #  Horizontal distance between vortex center and re-attachment point, mm CFD PTV  Difference (%)  1  1.0  1.13  13.0  2  1-2  0.88  26.6  3  0.8  0.5  37.5  It is, unfortunately, not possible to clearly visualize the flow in the slot and in the boundary layer as the experimental results very close to the wall have relatively large error attributed to wall glare. In addition, because of the sharp velocity gradients close to the wall, it was not possible to track the particles very near the wall using the camera with limited field of view (4.5 x 4.5 mm). The PIV imaging was optimized for the 10 m/s flow rate. However, the flow rate near the slot was 1 m/s. Although the PTV qualitatively confirmed the large scale flow features, it did not provide accurate velocity profile measurements in the region close to the wall and in the contour.  57  (a)  (c)  Experimental results (PIV)  Predicted Results (CFD)  Figure 5.8 Flow field near the aperture entry for contour heights equal to (a) 1.2, (b) 0.9, and (c) 0.6 mm for a 3.2 mm wide wire  58  5.5  LDV Measuring System A Laser Doppler Velocimeter (LDV) system was used to determine the velocity and  turbulence property profiles above the wall. 5.5.1  Measuring principle  The LDV used in this study was a commercially-available system: MiniLDV® (details in Appendix 5). Figure 5.9 shows the schematic of a single-component dual-beam LDV system in back scatter mode. The LDV system works by using a convex lens to focus two parallel monochromatic and coherent laser beams of similar thickness and intensity so that they cross at the point where the beams were focused. The region where the beams intersect is called the measurement volume and is 100 microns wide. The interference of light beams in the measurement volume created a set of equally spaced fringes that are parallel to the bisector of those fringes. Figure 5.10 shows the details of the measurement volume showing the formation of fringes. Lines represent the peaks of the light. When a particle crosses the probe volume, the light it scatters back toward the photo multiplier from each beam is Doppler shifted by an amount depending on the particle velocity and the beams' incidence angle. The photo multiplier is then exposed to the sum of the two Doppler shifted frequencies. The summed frequencies produce a beat frequency that is proportional to the speed of the particle in a certain direction. This direction is normal to the line bisecting the two beams and in the common plane of the two beams. It follows that if the beams are placed in the vertical plane, the vertical speed is detected by the photo multiplier. Figure 5.11 shows the details of the relationships between fringe spacing, light wavelength, and the angle between beams. The fringe separation, 'd' is given by d=  X 2 sin  Equation 5.2 a  where A, = wavelength of laser beams a = half-angle between the beams The speed of the component normal to the fringes (V ) is given by, n  Equation 5.3  59  where T is the blinking period. The short period of pulsing light is often called a "Doppler d  burst".  The photo detector amplifies the weak back-scattered burst and converts it into an electrical signal whose amplitude is proportional to the intensity of the light signal. The LDV system uses a photo detector which is a photo diode. Figures 5.12(a) shows an example of a raw signal and Figure 5.12 (b) shows a filtered signal obtained during a preliminary test. The raw signal from the photo detector can be split into two parts: a low-frequency component called the pedestal and a high-frequency component that contains the Doppler signal. The LDV system used for this study comes with a signal processing software called a Burst Processor (details in Appendix 5) and VioFilter which contains a bandpass filter. The bandpass filter was used to remove the pedestal as well as very high frequency noise in the desired signal. The bandpass filter consists of a high pass filter that removes signals with a frequency lower than the desired frequency- a lowpass filter that removes signals with a higher frequency than the desired signal. The filtered signal was digitized using an analog-to-digital converter. By filtering the analog signal before digitizing it, the maximum resolution of the signal was obtained from the digitizer.  The basic LDV set up suffers from a directional ambiguity problem: it cannot distinguish between particle motions in the forward or reverse direction since both will create the same intensity fluctuation at the detector. This is resolved by shifting the frequency of the one of the two beams of a beam pair. The LDV system uses a rotating diffraction grating. With one beam frequency shifted, the interference patterns will appear to move at the shift frequency. Particles moving in the direction of the apparent interference pattern motion will produce a lower Doppler frequency shift and particles moving against this motion will produce a higher Doppler frequency shift. This allows negative velocities to be distinguished. This feature was not used in this study, however, because negative velocities are not expected in the region of measurement.  60  Beam Splitter  Sending lens  Laser •:  Mirror  Receiving lens Photo detector Figure 5.9 Schematic of a single-component dual-beam LDV system in back-scatter mode  Figure 5.10 Schematic detail of the measurement volume showing the formation of fringes. Lines represent the peaks of the light.  Fringe spacing  Figure 5.11 Schematic detail showing the relationships between fringe spacing, light wavelength, and the angle between beams.  61  0.12 n  o £  I  -0.02 -0.04 -I 0.00E+00  1  1  1  1  1  5.00E-06  1.00E-05  1.50E-05  2.00E-05  2.50E-05  Time, sec (a) A raw LDV signal obtained from the photomultiplier showing the pedestal.  0.00E+00  5.00E-06  1.00E-05  1.50E-05  2.00E-05  2.50E-05  Time, sec (b) A bandpass filtered LDV signal  Figure 5.12 A typical LDV signal burst generated when a particle passes through the measurement volume.  62  5.5.2 Parameter adjustment The LDV system is controlled through the software (VioBP software, details are given in Appendix 5) supplied by the manufacturer. This software also manages data acquisition and performs signal processing. The LDV probe is mounted on an automated traverse which makes it easy to align the LDV probe so that the probe volume can be located at the desired location over the screen coupon. The traverse system can be controlled from the software to make a single point measurement or velocity profile acquisition.  Due to the nature of the flow channel and test coupon, it is difficult to measure the vertical velocity component. In these experiments, only the horizontal (x-velocity) component was measured. The frequency shifting was not used because the reverse flow was not expected in the region of measurement above the contour.  Before taking measurements, it is very important to make a good estimate of the speed of the fluid and adjust the bandpass filter settings. "Timeout" is another important parameter that needs to be adjusted. Timeout is the maximum time allocated for acquisition, after which the program will proceed to the next data point. For all the experiments, timeout was set to 30 seconds, which gave a sufficient number of samples required to calculate statistics. The seeding particles used for LDV measurements were Titanium Dioxide (TiC^) particles. These particles had a nominal diameter of 100 nm and specific gravity of 3.5. The particles were small enough to track the turbulent flow, yet just large enough to scatter a noticeable amount of light for the photomultiplier. Particle density was controlled to achieve a strong photo detector signal.  5.5.3 Experimental procedure The velocity profile and turbulence measurements were made for five different test coupons (Table 5.3). Each experiment began by filling the reservoir with water at room temperature. Water was circulated through the system and air was purged from the flow channel. The frequency of the variable frequency drive of the pump was adjusted to achieve the specified flow rate. The control valve on the plenum side of the coupon was adjusted to a flow rate that gave the specified slot velocity. The laser and bandpass filters were turned on. Bandpass filters 63  were adjusted until a strong burst signai was found. Start and end positions of the velocity profile and number of data points along that profile was specified. One of the most important procedures when setting up the LDV was to ensure that the beams crossed with the maximum overlap near the wall. This ensured the formation of many fringes and provided a strong photo detector signal when a particle traversed them. Due to the rugged nature of the coupon wall, the overlap of the beams has to stay at the contour surface level. As the contour geometry and beam width are extremely small, a magnifying lens was used to aid alignment. When the acquisition started, the traverse moved to the next position automatically where the next set of measurements were taken. The data acquisition software would optimize the velocity profile data recording and adapt thefiltersettings and data acquisition for each data point. The system was needed to be set up for the first point only. In this manner, the system was able to make the complete survey without user intervention.  Output statistics, speed histogram, and velocity profile were recorded. A file was generated which compiled statistics for all positions of the velocity profile. The data files consisted of mean velocity and standard deviation of velocity measurements which were used in the data evaluation.  Table 5.3 Experimental variables for LDV measurements Working fluid: Water Upstream velocity: 10 m/s Slot velocity: 0.25 - 10 m/s Dimensions coupon # contour height (mm) wire width (mm) of test coupons: 1 1.2 3.2 2 0.9 3.2 3 0.6 3.2 4 0.9 2.6 5 0.9 4.0  slot width (mm) 0.15 0.15 0.15 0.15 0.15  5.5.4 Uncertainty of L D V measurements The uncertainties in the LDV measurements are dependent on the accuracy of the LDV system, the accuracy in locating the measurement plane, and the statistical uncertainty of the measurements. Error would come from the resolution of frequency determined by FFT analysis 64  and/or uncertainty in the beam convergence angle. Thus, the total uncertainty/accuracy of the LDV signal specified by the manufacturer is -7 mm/s to 8 mm/s. These values were obtained by measuring the signal against a stationary target. The statistical uncertainty for the velocity is estimated from the student t-distribution. The 90% confidence interval for the velocity was calculated using Equation 5.1. Since the standard deviation of the velocity measurements was at most 1.75 m/s (near the wall), the maximum statistical uncertainty in the ensemble averaged velocity was 0.34 m/s. This gives maximum uncertainty in the velocity near the wall to be ± 7% and away from the wall in the free stream ± 5%. The uncertainty in the RMS velocity is found using Chi-squared distribution. The 95% confidence interval for the rms velocity can be expressed as (Benson and Eaton (2003)):  Pr  r  S  1  <<J  = 95%  <S  Zo05  Equation 5.4  %0.'..95  For large values of N (N>100), the chi-squared distribution is approximated by Equation 5.5 as follows (Benson and Eaton (2003)):  9(N-\)  l  (N-l)9  Equation 5.5  where z is a function of the confidence level for chi-squared distribution (z = 1.96 for 95% confidence level as N —» oo)  At least 100 samples were taken for each data point and the standard deviation (s) was 1.75 m/s. This gives an estimated maximum fractional uncertainty in the rms velocity of 12%. There was also error in accurately locating the reference point (zero location) at the wall of the screen plate due to the blockage of the laser beams by contours. This error is estimated to be ± 0.1 mm (half the size of the measurement volume). Accuracy of the traverse system is ± 0.01 j mm. Therefore, total error in locating the y-ordinate is ± 0.11 mm. As Equation 5.1 and 5.4 show, the statistical uncertainty depends on the rms fluctuations which vary from wall to the upstream of the flow. Therefore, the error along with the statistical uncertainty is reported in the plots. 65  5.5.5  Results and discussion Experiments were performed on five test coupons to measure the velocity and turbulence  intensity profiles. Only one dimensional measurement (horizontal velocity component) was performed in the experiments. The origin is defined as the plane where the horizontal laser beam just passes the coupon top surface as shown in Figure 5.13. There is no data in the boundary layer due to blockage of the laser beams by the contours of the coupon. Flow direction  Origin is located above the vortex center  Figure 5.13 Detail showing the origin of the measurement plane where the horizontal laser beams just touch the wire top surface.  In order to test the reliability of the experimental system, measurements were performed over an impermeable smooth wall to validate the data with well-established experimental data. The measurements were compared with logarithmic law of the wall. Figure 5.14 shows that the measured profile follows the log-law. The shear velocity is determined using curve fitting technique similar to the procedure outlined in section 5.5.5.1.  66  30 u+=2.5*ln (y+)+5.5  25 20 u 15  • Smooth Wall Data — Log Law  +  10  0 10  100  1000  10000  + Figure 5.14 Comparison of experimental velocity profiles for a smooth wall with classical loglaw of the wall.  The sensitivity of the measurements along the coupon is tested by comparing the velocity profiles at three different positions as shown in Figure 5.15. Figure 5.17 shows that three profiles associated with three different positions collapse on to a single curve, within error of measurement. This indicates that the turbulence properties, near the wall, are fully developed at the measurement point. Velocity profiles at three different positions (see Figure 5.16) over a wire are shown in Figure 5.18 and are found to be similar. However, very close to the wall, at the upstream of the slot, there is a small but significant difference compared to other two velocity profiles measured. This difference is due to the flow acceleration that occurs when it approaches the top of the contour, as predicted by the CFD simulations. Therefore, the velocity profiles were measured above the vortex center and reported in all the subsequent plots. The approximate location of the vortex center was obtained from the CFD simulations.  67  0 ,/whm mum mmmi\  x  \  @  Upstream  i  (g)  Measurement location  i  (c)  Downstream  Figure 5.15 Position of velocity profiles measured along the coupon to test the sensitivity of the measurements with position.  ©  g ) (?)  Reference plane for measurements  ( D ) Upstream of the slot ( E ) Above the slot ( F ) Above the vortex center Figure 5.16 Position of velocity profiles measured along a single wire to test the sensitivity of the measurements with location.  68  0.7 • 0.6 o Measurement Location  5 0.5 4  • Down Stream  + 5  X Up Stream  I 0.4 O  + 3  0.3 T3  2 *  0.2 o £ 0.1  0.2  0.4  0.6  0.8  1.2  Normalised Upstream x-Velocity Figure 5.17 Upstream velocity variation at three different positions along the coupon. The distance is normalized by the wire height of 10 mm and the upstream velocity is normalized by the mean velocity in the free stream of channel.  69  0.7 0.6  x Above the vortex center • Upstream of the slot  0.5 o o 03  T3  A Above the slot  0.4 i  0.3  m  4 =3 i  \u >  i rn i  i  0.2  + 2 i  • JSP*  i H j  I UJ I  o  0.1  l2Ll  0 0.2  0.4  0.6  0.8  1.2  Normalised Upstream x-Velocity Figure 5.18 Upstream velocity variation at three different positions over a single wire. The distance is normalized by the wire height of 10 mm and the upstream velocity is normalized by the mean velocity in the free stream of channel.  The experimental results obtained for all five coupons can be broadly grouped into two categories: 1) effect of wire geometry, characterized by contour height and wire width and 2) the effect of slot velocity. In the first category of experiments, measurements were made by keeping the slot velocity and upstream velocity constant (V = 1 m/s, V = 10 m/s). In the s  u  second category, the upstream stream velocity was kept constant at V = 10 m/s and the slot u  velocity were varied between 0.25 m/s and 10 m/s. In order to compare the CFD results with the LDV measurements, the simulations were run with the identical conditions used in the LDV experiments. The boundary conditions were changed to provide an upstream velocity equal to 10 m/s and slot velocity equal to 1 m/s. The turbulence and velocity profiles obtained from CFD were taken above the vortex center with origin located at the reference plane as shown in Figure 5.16.  Figure 5.19 shows the velocity distribution for three contour heights (0.6, 0.9 and 1.2 mm) and the same wire width. The local velocities increased with decreasing contour height near 70  the wall. Figures 5.20 and 5.21 shows the velocity distribution for three different wire widths equal to 4.0 mm, 3.2 mm and 2.6 mm. The local velocities have decreased with decreasing wire width. The increased roughness (more contours per unit length of screen surface) decreased the mean fluid velocity near the screen surface. It is hypothesized that the higher local velocities found with low contours (h = 0.6, w = 2.6, (h/w = 0.231); h = 0.6, w = 3.2, (h/w = 0.188)) make the particles more difficult to turn into the slot which improves debris removal and fibre fractionation efficiency. It will also increase the reject thickening. Conversely, the decreased upstream velocity with high contours allows more time for the fibres to be pass into the aperture and results in higher accept consistency and less reject thickening. A comparison of CFD and experimental results is seen in Figures 5.19 to 5.21 for all the five wire geometries. A similar trend is obtained for numerical and experimental measurements; however CFD predicted shallower velocity gradients. The increased velocity near the wall that was predicted by CFD for shallower contours was not seen in the LDV measurements. The vorticity predicted by the CFD model of the re-circulating flow near the contour height may have a large role in causing the above discrepancy. It is possible that CFD predicts stronger vortices than in reality, thus causing more prominent velocity gradients near the wall. Another reason for differences between CFD and experimental results is the way the boundary conditions were imposed in the CFD simulations. In the CFD simulations, the suction through the slots is applied by imposing a uniform downward velocity through the upper boundary. The flow coming down from the upper boundary is balanced by the outflow through the slots. Therefore, the flow is periodic from left to right of the domain. In the LDV experiments, however, the out flow through the slots was not compensated by the downward velocity through the upper wall. Therefore, there will be a loss of flow over the slots. It is estimated that this decrease in velocity is not significant compared to upstream flow rate. Even though, the experimental set up could not mimic the CFD simulations exactly, the results obtainedfromthe experiments reveal the similar trends with the CFD results. Figure 5.22 shows the turbulence intensity profiles distribution for three different contour heights (0.6, 0.9 and 1.2 mm) with the same wire width (3.2 mm). This figure shows that the experimental turbulence intensity decreases with distance away from the screen cylinder with a high of nearly 15% to the free stream turbulence level of approximately 4%. The maximum turbulence intensity near the wall corresponds to 1.5 m/s fluctuating component of x-velocity (u') which is less than 1% agreement with the LDV measurements done by Halonen and Ljokkoi (1989) over a contoured screen coupon. Turbulence measurements were available only above y  +  71  ~ 100 because it was not possible to get the LDV data very close to wall. Further, the figure shows that turbulence intensity slightly increases with increasing contour height. The turbulence values predicted by CFD were about half that measured with LDV. Another cause for the differences between the CFD and experimental results may be due to the turbulence model. The k-e turbulence model assumes isotropic Reynolds stresses and linear eddy viscosity. There might be a need to adjust any closure constants since default values are. used for all closure constants in this thesis. This turbulence model may not have captured the Reynolds stress anisotropy which occurs in the near-wall region. The normal stress anisotropy is responsible for the production of shear stresses. Hence, a reduction in normal shear stress anisotropy would have lead to an under estimation of shear stress, which in turn would have lead to reduced shear stress production. A significant discrepancy in results might also be attributed to three dimensional effects of the flow.  Figures 5.23 and 5.24 show the turbulence profile for wire widths of 4.0, 3.2 and 2.6 mm. The turbulence intensity increases slightly with decreasing wire width. As wire width decreases, the apparent roughness of the surface increases (the number of contours per unit length) which could well be responsible for the increase in turbulent intensity. It should be noted that the impact of width changes on the turbulence is less than that of contour changes. Wire width is chosen in industry to be as narrow as possible to increase the open area of the cylinder and the capacity of the screen. Wire width must, however, be sufficiently large to avoid the case where fibres are stapled from one slot to the next, leading to screen plugging. The minimum wire width for reliable operation is thus a strong function offibrelength (Gooding and Craig, 1992). The increased mixing levels at the screen surface caused by increased turbulence are thought to bring the long fibres closer to the surface and increase their passage through the apertures. This results in a decreasedfractionationefficiency and increased accept consistency (Julinet-Saint-Amand and Perring (1998)). Low contour heights and wider wires constitute shallower sloped contours which gave higher local velocities and lower mixing levels near the wall compared to higher sloped contours. The low turbulent intensity generated by wires with shallow contour slope minimizes mixing and enhances fractionation.  72  Normalised Upstream x-Velocity, u/V  u  gure 5.19 Velocity profiles for boundary layers with V = 1 m/s and V = 10 m/s for three s  u  different contour heights. The distance is normalized by the wire height of 10 mm and the upstream velocity is normalized by the mean velocity in the free stream of channel.  73  0.7  T  LDV  ' 0.6  a  •  h  w  h/w  0.9  4.0  0.225  0.9  3.2  0.281  7  —0.9  CFD  *- - 0.9  s o  I  0.3  T3 w 0.2  0.2  0.4  0.6  1.2  0.8  Normalised Upstream x-Velocity Figure 5.20 Velocity profiles for boundary layers with, V = 1 m/s and V = 10 m/s for two s  u  different wire widths (4.0 and 3.2 mm) and a wire height of 0.9 mm. The distance is normalized by the wire height of 10 mm and the upstream velocity is normalized by the mean velocity in the free stream of channel.  74  if  0.7  h  0.6  O0.6 A 0.6  w 2.6 3.2  h/w 0.231 0.188  T  7  0.5  e & 0.4 <D O l>  0.3  ffi  T3  1  ffi  «  2  O ^ 0.1  Q  l7T\1  0.2  0.4  0.6  1.2  0.8  Normalised Upstream x- Velocity gure 5.21 Velocity profiles for boundary layers with V = 1 m/s and V = 10 m/s for two s  u  different wire widths (3.2 mm and 2.6 mm) and a wire height of 0.6 mm. The distance is normalized by the wire height of 10 mm and the upstream velocity is normalized by the mean velocity in the free stream of channel.  75  Figure 5.22 Variation of upstream turbulence for three contour heights (0.6, 0.9 and 1.2 mm) in wall coordinates at V =10 m/s and V = 1 m/s. u  s  76  h/w 0.225 0.281 0.225 0.28.1  4.0 3.2 4.0 3.2  10000  1000  100  5  0  20  10 15 Turbulence Intensity, %  Figure 5.23 Variation of upstream turbulence level for two wire widths (4.0 mm and 3.2 mm) with a contour height of 0.9 mm in wall coordinates at V =10 m/s and V = 1 m/s. u  10000  s  h O0.6  w 2.6  h/w 0.231  A0.6  3.2  0.188  1000 o +  A 100 AO  10 5  10  20  15  Turbulence Intensity, %  Figure 5.24 Variation of upstream turbulence for two wire widths (3.2 mm and 2.6 mm) with a contour height of 0.6 mm in wall coordinates at V =10 m/s and V = 1 m/s. u  s  77  Figure 5.25 to 5.29 shows the velocity distribution for all five geometries at varying slot velocities and constant upstream velocity. For all geometries, the velocity profile is approximately log-linear and u increases with slot velocity. The increase in velocity is due to +  the reduction in boundary layer height with increasing slot velocity, that is, high velocity flow is pulled closer to the screen surface as more fluid is pulled through the apertures. At low slot velocities, the differences in shear velocity are very small compared to that at high slot velocities. It is unclear how the increase in upstream velocity with increased slot velocity affects screen performance - though it has been hypothesized that increasing upstream velocity increases contaminant removal and fractionation. Slot velocity, however, is clearly recognized as being a critical factor affecting screen performance. At high slot velocities, the efficiency of the screen decreases, reject consistency decreases and the fractionation efficiency decreases. One possible explanation is the increased hydrodynamic drag on the contaminants and fibres causes them to pass through the narrow apertures in the cylinder. This is particularly true for deformable contaminants such as adhesive particles found in recycled pulp. In addition to increasing the drag on the debris particles, increasing the fluid velocity through the aperture is also thought to change the flow direction at the aperture entry, making it easier for contaminants and long fibres to pass into the accept stream.  78  Figure 5.25 Effect of wall suction on the wall normal distribution of the velocity profiles in wall coordinates for h = 1.2 mm, w = 3.2 mm; (h/w = 0.375): V / V = 2.5, 10 ,25, and 45%. s  u  16 14 ^  v 0 0.25 m/s • 1.0 m/s A 2.5 m/s 04.5 m/s s  12 10 +  3  8 6 4 2 0 1000  100000  10000 y+  Figure 5.26 Effect of wall suction on the wall normal distribution of the velocity profiles in wall coordinates for h = 0.9 mm, w = 3.2 mm; (h/w = 0.281): V / V = 2.5, 10, 25, and 45%. s  u  79  4 2 0 -I 1000  1  1  1  —  1  I  1  1  —  I  10000  100000  +  y  Figure 5.27 Effect of wall suction on the wall normal distribution of the velocity profiles in wall coordinates for h = 0.6 mm, w = 3.2 mm; (h/w = 0.188): V / V = 2.5, 10, 13, 22, and u  50%  V o 0.25 m/s  16  s  14  • 1.0 m/s  12  A 2.5 m/s  10  o 5.0 m/s  8  • 10.0 m/s  6 4 2 0 1000  10000 y  100000  +  Figure 5.28 Effect of wall suction on the wall normal distribution of the velocity profiles in wall coordinates for h = 0.9 mm, w = 4.0 mm; (h/w = 0.225): V / V = 2.5, 10, 25, 50 and s  u  100%. 80  V  16  s  o 0.25 m/s • 1.0 m/s A 2.5 m/s o 5.0 m/s  14 12 H 10 ^ 8 6 4 2 0 100  1000  10000  y+  Figure 5.29 Effect of wall suction on the wall normal distribution of the velocity profiles in wall coordinates for h = 0.6 mm, w = 2.6 mm, (h/w = 0.231): V / V = 2.5, 10, 25, and 50%. s  u  Figure 5.30 to 5.34 shows the turbulence intensity above the screen surface for all geometries at various slot velocities and an upstream velocity of 10 m/s. The turbulent intensities are at a maximum near the wall and decrease to the upstream turbulence of approximately 4%. The near-wall turbulence intensity decreases slightly with increased slot velocities, as the turbulent kinetic energy is convected from the screen surface through the apertures. The decrease in turbulent intensity at high slot velocities may affect the ability of the contours to break up any floes above the screen.  81  10000  O 0.25 m/s a 1.0 m/s A 2.5 m/s o 4.4 m/s  •O O  A  o •  o O  A °  A O  o  M000  • A  100 10  15  20  Turbulence Intensity, % Figure 5.30 Effect of wall suction on the wall normal distribution of the turbulence intensity in wall coordinates for h = 1.2 mm, w = 3.2,mm (h/w = 0.375): V / V = 2.5, 10, 25, and s  u  44%. 10000  V  o a o O  A  o  o  O 0.25 m/s • 1.0 m/s A 2.5 m/s o 4.4 m/s  o  • ^  B  ° A  O  A O  « •  s  °  • O A O D  o /  o  1000  • A  100 5  10  Turbulence Intensity, %  15  20  Figure 5.31 Effect of wall suction on the wall normal distribution of the turbulence intensity in wall coordinates for h = 0.9 mm, w = 3.2 mm, (h/w = 0.281): V / V = 2.5, 10, 25, and s  u  44%. 82  10000  V  T  s  O 0.25 m/s O  • 1.0 m/s  o  A° A  •=>  O  o  i 8  A  2.2 m/s  o 5.0 m/s  •  T000  o  A  a.  o  oo  D  100 10  15  20  Turbulence Intensity, % Figure 5.32 Effect of wall suction on the wall normal distribution of the turbulence intensity in wall coordinates for h = 0.6 mm, w = 3.2 mm, (h/w = 0.188): V / V = 2.5, 10, 13, 22, s  u  and 50%. V o 0.25 m/s • 1.0 m/s A 2.5 m/s o 5.0 m/s A 10.0 m/s s  10000 o  •O A  A  A ° A  Q  A O  A  n o DQ  O A  O  A  A + y  1000  •  C  O AD  A  100 10 Turbulence Intensity, %  15  20  Figure 5.33 Effect of wall suction on the wall normal distribution of the turbulence intensity in wall coordinates for h = 0.9 mm, w = 4.0 mm, (h/w = 0.225): V / V = 2.5, 10, 25, 50 s  u  and 100%. 83  V o 0.25 m/s s  10000 Oo  O  A  a 1.0 m/s  an  o o  A  A  9 °  o  z  2.5 m/s  o 5.0 m/s  a o OA A°0 . A G D  1000  • £  100  -I— — — —'—I— — — — —I— — — —'—i—'—'— — —l 1  1  1  1  0  1  1  5  1  1  1  1  1  10  15  1  20  Turbulence Intensity, %  Figure 5.34 Effect of wall suction on the wall normal distribution of the turbulence intensity in wall coordinates for h = 0.6 mm, w = 2.6 mm, (h/w = 0.231): V / V = 2.5, 10, 25, and s  u  50%.  5.5.5.1 Roughness function determination  The mean velocity profiles obtained for five test coupons at various slot velocities can be used to obtain a roughness function, AB. In the present study the shear velocity required to calculate AB is determined by fitting the experimental data in the following way. The logarithmic law is modified from its original form to include the effects of both the dimensions of contour (h and w) as well as slot velocity with AB(h, w, V ) so that, s  u =-ln(y )+B-AB(h,w,V ) +  +  s  Equation 5.8  The last two terms in equation 5.8 are combined so that, 84  w = - ln(y ) +  +  - -ln(c )  Equation 5.9  +  K  K  where - - ln(c ) = B - AB{h, w, V ) +  s  Now the equation 5.8 becomes, u ( V„ = —In 2i  A:  or  F„ = — ln(y) - — ln(c)  Equation 5.10  When the experimental data of the each mean-velocity profile is fitted with a linear regression and matched with equation 5.10, the slope of the curve is— and intercept K *  is  ln(c) • The shear velocity for each velocity profile can calculated from the slope of the K  fitted linear regression curve. The roughness function is a measure of how much a velocity profile (of a wall with different roughness geometries and suction velocities) is shifted downwards from a smooth wall velocity profile in a semi-log plot. The roughness function, AB is a function of wire width, contour height and slot velocity (i.e AB = f (h, w, V )). The roughness function, AB was obtained s  for each velocity profile by determining its downward shift from the smooth wall velocity profile. Figure 5.35 shows the roughness function, AB, for all contour heights, wire widths and flow velocities tested. The figure indicates that AB increases with contour height and decreases with wire width. Further, it suggests that the velocity profile is the same for wire geometries with similar ratios of contour height to wire width (contour slope). This is industrially-significant, since it helps to resolve debate on whether comparisons between different contours should be made on the basis of contour height or angle. As slot velocity increases, the roughness decreases. The effect of aperture geometry at high slot velocities is less than at low slot velocities. A correlation for the data shown in Figure 5.35 was developed and is given by Equation 5.8. 0 6 1  AB = -20.64 f - 1  (y  \  0.39  + 28.95 (-)  (R = 0.94) 2  Equation 5.11  85  25  20  AB 15  •  •  8  I  •  h • 1.2  w h/w 3.2 0.375  • 0.9  3.2  0.281  A 0.6 2.6  0.231  • 0.9  4.0  0.225  • 0.6  3.2  0.188  • 8  10  0.2  0.4  0.6  0.8  1.2  V /V v  s' u v  Figure 5.35 Effect of contour height and wire width on the roughness function AB for a range of slot velocities. 0.14 0.12 0.1 u*/V,  w  0.08  h/w  0.375 0.281 0.231 0.225 0.188 Equation 5.12  0.06 0.04 0.02 0 10  15  20  25  AB  Figure 5.36 Relation between shear velocity and roughness function for different contour geometries and a range of slot velocities  86  Figure 5.36 shows the relation between shear velocity and AB for all contour geometries and slot velocities tested. It indicates that the shear velocity varies linearly with AB as indicated by the correlation given by Equation 5.9. *  — = 0.00584 AB  (R = 0.937) 2  Equation 5.12  These correlations can be used to calculate the near-wall velocity for a range of conditions. One application could be to minimize the computation required in computational fluid dynamics modeling of the flow through slots in pulp screens where this correlation can be implemented for AB in the log-law region. The correlation for shear velocity also enables the prediction of wall shear stress on the cylinder for a wide range of design and operating conditions. The wall shear stress on the cylinder is one of the key parameters in determining the power consumption of the rotor.  87  6  E X P E R I M E N T A L M E A S U R E M E N T O F FIBRE MOTION  CFD simulations and PIV measurements described a stationery vortex at the entrance of the slot region. In this chapter, fiber motion is studied relative to wire geometry and vortex size.  6.1  Experimental Apparatus Visualization experiments were carried out using a cross-sectional screen (CSS) (Pinon et al.  (2002) and Feng et al. (2004)) and a high-speed video camera. The CSS is a laboratory screen modeled after a cross-section of a Hooper PSV 2100 pressure screen. As shown in Figure 6.1, a small screen plate was positioned at the bottom of the CSS. A removable transparent plexiglas plate covered the CSS to get clear images of the fibre motion near the screen plate.  Figure 6.1. Schematic diagram of a cross-sectional screen and photo showing the rotor, screen plate coupon and plexiglass cover. The CSS has a diameter of 279 mm and depth of 50 mm. Different types of airfoils can be attached to the each end of the rotor. The rotor used for this project was a foil rotor with zero angle of attack. The feed flow is pumped from the reservoir into the screening zone through the feed port. The nylon suspensions either flow out the reject port or through the screen plate is returned to the reservoir. The amount of nylon pulp accepted through the screen plate is small in 88  comparison to the feed flow. Thus an assumption of constant consistency and the fibre length distribution may be made for the screening zone. Four wire screen coupons were used in this experiment (Table 6.1). Each coupon has 10 slots with 0.15 mm slot width and 3.2 mm wire width. The fibres used in this study were 2 mm long nylon fibres. Their properties in comparison to pulp fibres are given in Appendix 6. The nylon fibres selected for this study are thicker and stiffer than pulp fibres. The apparent density of nylon fibres is quite close to that of pulp fibres. The experiments were conducted at a slot velocity of 1 m/s and the rotor tip speed was set to 5 m/s throughout the whole experiment. The upstream velocity of the suspensions induced by 5 m/s tip speed would be about 3.5 m/s based on Gooding (1993) measurements. The upstream velocity would be less than expected because, the momentum transferred between the rotor and the suspension is less at lower tip speeds. The relatively low rotor speed was used to ensure enough images were collected to track the fibre through the small field of view.  The NAC color high-speed video 1000 FPS system was used to capture the fibre motion. The system consists of the High-speed Video Capture software, which converts analogue images to digital and controls the camera and videocassette recorder. For this experiment, the shutter speed was set to 1/5000 sec due to limited light source. The maximum recording speed of 1000 frames per second was used. The test coupon was illuminated by a ring lamp, which produced 1200 watts. The Nikon Micro-NIKKOR 105 mm lens was used in this experiment. The aperture size was set to f/8. Table 6.1 Experimental variables for fibre motion measurements Working fluid: water diluted with rigid 2 mm long nylon fibres. Tip speed: 5 m/s Slot velocity: 1.0 m/s Dimensions coupon # contour height (mm) wire width (mm) slot width (mm) 0.15 of test coupons: 1 1.2 3.2 0.15 2 0.9 3.2 0.15 3 0.6 3.2 0.15 4 0.3 3.2  89  6.2  Fibre Motion Analysis  The video images were electronically captured and analyzed frame by frame to determine the fibre trajectories. Several hundred fibre trajectories were analyzed. Nearly all the fibres passed by the apertures without passing through the slot or interacting with the contour. The fibres that did interact with the screen coupon are analyzed in detail and discussed in terms of contour height.  The images of objects moving at higher speeds produce blur and the image blur in visual analysis should be kept below 0.05 mm to avoid noticeable blur (Nissen (1993)). The expected blur of the images with 1/5000 seconds shutter speed and 3.5 m/s upstream velocity of the nylon fibre suspensions is about 0.7 mm. It is not possible to obtain crisp images with the maximum available shutter speeds of the camera which generate a blur of 15 times acceptable limit. A sample image of nylon fibre trajectory is shown in Figure 6.2. Thefibrepositions were overlaid with precisely hand drawn lines to visualise more crisp images of trajectories.  Figure 6.2 Sample image of a nylon fibre trajectory (arrow is pointed to the nylon fibre image).  90  6.2.1 Low contour height  For low contour height wires (0.3 mm and 0.6 mm), all the fibres passed by the slot without passing through. This held true even when the fibres were close enough to the exit layer to interact with the contour. As shown in Figure 4.6, the low contour height generate a small but stronger vortex at the slot entry. The re-attachment point is also relatively close to the slot entry.  Flow direction ,B  Figure 6.3 Trajectory of a 2 mm long nylon fibre above the screen with a 0.3 mm contour height showing how the fibre orients itself along the slot length.  As shown in Figure 6.3, the fibre is initially close to the screen surface. It moves over the slot entry and is pulled down toward the wire but it comes in contact too late to be captured by the vortex. There is some indication, observed by the decrease in projected fibre length, that the fibre becomes partially oriented parallel to the slot length in the decelerating flow near the reattachment point (arrow A). Similar behaviour is also observed as the fibre passes over the third (arrow B) slot entry, with the fibre becoming even more aligned parallel to the slot. The fibre does not enter any of the apertures, despite interacting with several contours. For afibreto enter an aperture it has to first enter the vortex. For the low contour screens, the vortex is too small for the fibres to enter, even though the thickness of the exit layer is the same for all contours. Near the end of the trajectory in Figure 6.3 the fibres moves away from the screen surface — most likely because it has been caught up in a relatively large turbulent eddy.  91  Figure 6.4 Trajectory of a 2 mm long nylon fibre above the screen with a 0.6 mm contour height showing the "surfing" action of the fibre along the wall shear layer.  As shown in Figure 6.4, the fibre approaches the first contour horizontally. The fibre comes close to the vortex and it appears that the trailing edge of the fibre enters the vortex near the re-attachment point. The fibre impacts the contour slope downstream of the reattachment point. The point of impact is too far downstream of the reattachment point to allow the fibre to be pulled back into the slot by the vortex and the fibre continues over the next slot. The fibre does not pass through the slot and impacts the slope of the contour too far away from the reattachment point and vortex to be pulled in. The fibre then moves away from the screen surface and into the main flow.  Figure 6.5 Trajectory of a 2 mm long nylon fibre above the screen with a 0.6 mm contour height showing the "vaulting" motion of the fibre.  92  Figure 6.5 shows a fibre oriented such that it is closer to vertical (perpendicular to the screen surface) than the first two fibres. The fibre misses the first contour and impacts the slope of the contour with its leading edge. The fibre then "pole vaults" over the next slot, rotates without further impacting the slope of the contour and moves away from the screen surface. 6.2.2  High contour height  For higher contour heights, several nylon fibres were seen entering the slot. The modes of passage observed are typified in the figures below. The C F D results in Figure 4.6 showed that there is a substantially larger vortex over the slot entry. Also, the re-attachment point is much farther downstream on the contour slope. Together, these create a much larger region for the fibre to interact with the vortex.  Flow direction Re-attachment point  Exit layer thickness ~ 0.1 mm  Figure 6.6 Trajectory of a 2 mm long nylon fibre above the screen with a 0.9 mm contour height showing the fibre falling into a slot in a backward motion.  Figure 6.6 shows a fibre approaching the slot and is initially nearly horizontal to the screen surface upstream of the aperture. At this point the fibre is either within or very near the "exit layer". The thickness of exit layer in Figure 6.6 is approximately 0.1 mm and in industry it might be about 0.02 mm. The fibre is pulled down and the leading tip of the fibre impacts the  93  contour slope very near the reattachment point. At this point, the fibre slows down in the decelerating flow and is pulled backwards along the slope of the contour and into the slot.  Figure 6.7 Trajectory of a 2 mm long nylon fibre above the screen with a 1.2 mm contour height showing thefibrecaught in a vortex before it slides into a slot.  In Figure 6.7, the fibre is aligned more to be parallel to the slot. Similar to the trajectory captured in Figure 6.6, the fibre enters the exit layer upstream of the slot entry, passes over the slot and impacts the contour slope near the re-attachment point. The fibre then rotates within the vortex for two rotations and then it is pulled back into the slot by the vortex.  Figure 6.8 Trajectory of a 2 mm long nylonfibreabove the screen with a 0.9 mm contour height showing the "vaulting" motion of the fibre. 94  In Figure 6.8 the fibre approaches the screen surface then it rotates in the shear near the surface and aligns itself to be nearly horizontal to the screen surface (arrow C) just upstream of the slot. One end of the fibre is then pulled deep into the centre of the vortex and rotates rapidly due to the extreme shear. The rapid rotation moves the fibre such that the leading tip of the fibre does not contact the contour slope near the re-attachment point. Fibres that do not impact the contour with their leading tip first, may not pass through the slot. A nearly identical trajectory over the next slot is observed with the fibre rotating and not passing through the slot. However, fibre moving with length aligned along slot can drop through easily. The difference between the nylon fibre trajectories observed for low and high contours have several implications on fractionation efficiency and contaminant removal efficiency. With low contour screens, all the short fibres and fines can be easily directed by the favourable fluid streamlines into the accept side of the screen. That means higher fibre passage ratio is possible for short fibres (and fines) which gives high fractionation efficiency. Similarly, the long fibres and shives that were not able to pass through the slots pass to the reject port. Short fibres would have a higher probability of passing through the slots because, when a short fibre tips in to the vortex, less of the fibre is exposed to drag forces in the main-stream which could pull the fibre from the vortex. In the case of high contour screens, the fibre may land on the slope of the contour with its leading edge, and be pulled in to the slot by the vortex. We attempted to simulate mechanisms found in industrial screening. However, the trajectories found in this study may slightly differ from actual industrial screening scenario because of the following main reasons: 1) Model fibres: The synthetic fibres used in this study are thicker and stiffer than pulp fibres. The nylon fibre suspension is very dilute. In industrial screening pulp concentrations exist in the range of 1 to 1.5 %, which would contribute to significant fibre-fibre interactions. 2) Very low tip speed: The operating tip speed was 5 m/s. This tip speed is not representative of industrial values, which are in the range of 15 to 25 m/s (Pflueger et al. (2002). Also because of low tip speed the foil rotor generates pressure pulses with a very low magnitude.  95  Nevertheless, the results are informative and interesting and can be applied to industrial screens. The observation ofrigid2 mm long fibre trajectories found can be summarized as follows: •  Fibres that entered the aperture landed on the slope of the contour with its leading edge to be pulled in by the vortex.  •  Low contours generate a vortex that is small which limited the fibres from entering the slot. Passage through these contours was only observed when fibres were oriented to be parallel with the slot length.  •  High contours generate a large vortex with a re-attachment point much farther downstream, on the contour slope compared to low contours. Together, these create a much larger region for the fibre to interact with vortex and lead to a greater probability of fibre passage. In general, these observations support industry experience that low contour screens give  high fractionation efficiency by separating short fibres and fines from long fibres. Whereas, high contour screens give high throughput by enhancing long fibre passage.  96  7  CONCLUSIONS  The detailed flow behavior near a rough wall with equal spaced slots in a steady cross-flow with "a series of flow bifurcations" was determined through numerical and experimental studies. As a result, a greater understanding of the complex flow near the screen surface was gained. A Computational Fluid Dynamics (CFD) model of the flow through the slotted apertures in a steady was developed. Experimental studies included Particle Image Velocimetry (PIV) to determine the velocity field near the aperture entry, Laser Doppler Velocimetry (LDV) to determine the velocity and turbulent intensity profiles above the screen surface and High-speed Video (HSV) to capture thefibremotion near the aperture entry.  The CFD model theoretically determined the effect of aperture entry geometry, characterized by contour height and wire width, on the flow field. From the computational study it was shown that: 1. A vortex forms over the aperture entry due to separation at the trailing edge of the wire and the size, shape and strength of the vortex that forms over the aperture entry is strongly dependent on aperture contour height and wire width. 2. The vorticity at the aperture entry increases with decreasing aperture contour height and that for the smallest contour heights the high vorticity and associated pressure gradient creates a local acceleration upstream of the aperture entry. 3. The turbulence intensity increases with increasing contour height and decreasing wire width. The turbulence intensity at the cylinder surface increased by approximately 40% for each 0.3 mm increment of profile height. In contrast, turbulence intensity decreases by approximately 14% for each 0.8 mm increment in wire width. 4. The main parameter controlling boundary layer thickness and turbulent intensity near the wall was determined to be the ratio of contour height to wire width, h/w. The ensemble mean velocities and turbulence intensities that were measured over a screen plate were compared with corresponding values from CFD. Measurements were made by Particle Image Velocimeter (PIV) and Laser Doppler Velocimeter (LDV) and in order to reproduce the initial and boundary conditions set in the CFD simulations, a novel test loop was 97  developed. PIV gave a complete view of flow field near the contour region, while LDV produced single point velocity data that were used to more accurately determine rms velocity fluctuations.  The mean flow features (including vortex center and reattachment point) measured by PIV near the apertures of various wire geometries were reasonably predicted by CFD. The main discrepancies between CFD and PIV measurements of velocity occurred at the wall. These discrepancies were attributed to experimental error due to the unwanted light reflections from the wall and the use of isotropic turbulence model in the CFD. The maximum statistical uncertainty in PIV measurements is estimated to be ± 9.9 % near high contours and ± 18 % near low contours.  The velocity and turbulent intensity profiles above a contoured surface in a steady crossflow with suction were determined by LDV for a range of contour geometries and flow velocities. The velocity profiles were shown to be log-linear with an offset from the classical flow over a smooth plate. The offset was shown to be a function of contour height, wire width, slot velocity and upstream velocity. Local velocity decreased with contour height and increased with wire width. Wires with similar ratios of contour height and wire width had similar velocity profiles. Local velocity increased as slot velocity increased and the boundary layer was pulled through the apertures. A correlation for velocity profile was determined as a function of contour height to wire width, h/w, and the ratio of slot velocity to upstream velocity, V /V . The turbulent s  u  intensity profile in the cross-flow direction was also determined. The near-wall turbulence was a strong function of contour geometry and slot velocity. The maximum intensity near the wall was shown to increase with contour height and decrease with wire width. The maximum turbulent intensity decreased with increasing slot velocity.  One significant finding of this study is that the ratio of contour height to slot width (known as contour slope) is an important design parameter. This study recommends that wire geometries should be compared on the basis of contour slope instead of either wire width or contour height, alone.  The interplay of wire geometry with flow field andfibremotion is examined by experimental observation offibretrajectories using high-speed video. The observation of 2 mm  98  long fibres that have the rigidity of shives moving near the screen wall can be summarized as follows: •  Low contours generate a small vortex that that tends to prevent fibres from entering the slot. Passage through these contours was only observed when fibres are oriented to be parallel with the slot length.  •  High contours generate a large vortex with a re-attachment point much farther downstream on the contour slope compared to low contours. There is a much larger region for the fibres to interact with the vortex, which leads to a greater probability of fibre passage.  Although the CFD simulations well predicted the flow features and general trends compared to experiments, the turbulence properties were under predicted and the mean velocities are over predicted. These discrepancies in turbulent and mean flow quantities are believed to be due to limitations in the k-s turbulence model, in particular, the assumption of isotropy and linear eddy viscosity. However, the experimental and numerical study showed the effectiveness of wire geometry in controlling the mean and fluctuating components of the near wall flow. This improved understanding of the complex fluid flow near the screen surface will lead to improved understanding of pulp and contaminant transport through the screen, improved screen cylinder design and improved separation performance.  99  8  RECOMMENDATIONS  Although the general flow trends predicted follow the experimental observations, there is potential for CFD to more closely match the measurements by improving the models used. Since the k-e turbulence model is relatively lenient on computer resources, this model is preferred even though it does not resolve turbulent anisotropy. In order to resolve the anisotropy, it is recommended to use Reynolds stress model, if the computer resources permit. Simultaneous measurements of the two orthogonal velocity components could be done to reveal the flow structure (such as vortex, and flow separation) and check the anisotropy of the turbulence. Improved PIV measurements require improved anti reflective coatings need to be applied or have the screen coupons made of a different material. A successful coating would significantly reduce the local error in PIV velocity measurements. To make this work more relevant to the papermaking industry, the effect of pulp suspensions can be included in the CFD by using Non-Newtonian fluid models such Bingham plastic model. These methods do not exactly model the real fibre suspension. This method ignores the individual treatment of the fibres and considers the effect of fibre suspension rheology as a whole. The rheology of the pulp suspensions relates the shear rate to the shear stress of the suspension. Finally, this work needs to be extended to simulate the unsteady flow behavior at a screen slot in a pulp screen cylinder. This could be achieved by using the sliding mesh technique available in CFD. Fiber motion studies need to be repeated using more realistic fibres and flow velocities.  100  9  REFERENCES  Acharya, S, Dutta, S, Nyrum, T.A, and Baker, R.S, Turbulent flow past a surface-mounted two-dimensional rib, Trans, of the A S M E , J. Fluids Eng., 116 (2): 238-46 June 1994. Antonia, R.A, Zhu, Y,and Sokolov, M , Effect of concentrated wall suction on a turbulent boundary layer, Physics of Fluids, 7(10):2465-74,1995. Andersson, S. R , and Rasmuson, A , Flow measurements on a turbulent fibre suspension by laser doppler anemometry, AIChE J , 46(6): 1106-1119, 2000. Benodekar, R.W, Goddard, A.J.H, Gosman, A. D , and Issa, R. I, Numerical prediction of turbulent flow over surface-mounted ribs, AIAA J , 359-366, 1983. Benson M. J , and Eaton J. K , The Effects of Wall Roughness on the Particle Velocity Field in a Fully Developed Channel Flow, Report No. TSD-150, Thermosciences Division, Dept. of Mech. Eng., Stanford University, Stanford, May 2003. Chen, X , and Chiew, Y - M , Velocity distribution of turbulent open-channel flow with bed suction, J. Hydraulics Eng., 130(2), 140-148, 2004. Cui, J , Patel, V. C , and Lin, C - L , Large eddy simulation of turbulent flow in a channel with rib roughness, Intl. J. Heat and Fluid Flow, 24, 372-388, 2003. Deissler, R.G, NACA TN 3016, 1953. Durst, F , and Rastogi, A . K , Turbulent flow over two-dimensional fences, Turbulent Shear Flows, 2, 218-232, 1979. Dong, S, Salcudean, M , and Gartshore, I, Fibre motion in single and multiple screen slots, 2000 TAPPI Papermakers Conf. and Trade Fair Proc, 597-602, Vancouver, 16-19 April 2000. Dong, S, Modeling fiber motion in pulp and paper equipment, PhD Thesis, University of British Columbia, Canada, 2002. Estridge, E , The initial retention of fibres by wire grids, TAPPI J , 45(1): 285-289,1962. Frejborg, F , Giambrone, J , Improvements of new and old screens in cleaning efficiency at maintained or increased capacity, TAPPI pulping Conf. Proc, 529-532, 1989. Julien-Saint-Amand, F , Principles and technology of screening, Centre Technique du Papier, Grenoble, France, 1997. Julien-Saint-Amand, F , Stock preparation Part 2 - Particle peparation processes, Fundamental Research Symposiom, 2001 Feng, M , Numerical simulation of pressure pulses produced by a pressure screen foiled rotor, M.A.Sc. thesis, University of British Columbia, Canada, 2003. 101  FLUENT 6.2 User's Guide, Fluent Inc., Lebanon, NH, 2001. Gonzalez, J. A., Characterization of design parameters for a free foil rotor in a pressure screen, M.A.Sc. thesis, University of British Columbia, Canada, 2002. Gooding, R. W., The passage of fibres through slots in pulp screening, M.A.Sc. thesis, University of British Columbia, Canada, 1986. Gooding, R. W., and Kerekes, R. J., Derivation of performance equations for solid-solid screens, The Canadian Journal of Chemical Engineering, 67: 801-805, 1989. Gooding, R. W., and Kerekes, R. J., The motion of fibres near a screen slot, JPPS, 15(2): 5962, 1989. Gooding, R. W, and Craig, D. F., The effect of slot spacing on pulp screen capacity, TAPPI J., 75(2):12-16, 1992. Gooding, R. W., Measurements of tangential velocity inside a pulp screen, Paprican internal report, Feb. 1993. Gooding, R. W., Flow resistance of screen plate apertures, PhD Thesis, University of British Columbia, Canada, 1996. Green, A.E., The two-dimensional aerofoil in abounded stream, Quarterly J. of Mathematics, 18, 1947. Gregoire, G., Study and modeling of the flows in a screen in order to optimize the recycling of the paper pulp through slotted basket, Institut national polytechnique de Grenoble, Grenoble, France, 2000. Gregoire, G., Favre-Marinet, M., and Julien-Saint-Amand, F., Modeling of turbulent fluid flow over a rough wall with or with out suction, J. Fluids Eng., 125:636-642, 2003. Gupta, A.D., and Paudyal, G. N., Characteristics of free surface flow over a gravel bed, J. Irrigation Drainage Eng., 111(4), 299-318, 1985. Gullichsen J, and Harkonen, E. J., Medium consistency technology I: Fundamental data, TAPPI J., 1981; 64(6): 69v'71. Halonen, L., and Ljokkoi, R., Improved screening concepts, TAPPI Pulping Conf, 61-66, 1989. Halonen, L., and Ljokkoi, R., Peltonen, K., Improved screening concepts, TAPPI Conf. Proc. 207-212, 1990. Heise, O., Slotted headbox screening for fine, publication, and news print grades, TAPPI J. 78(2): 117-119, 1992.  102  Jasberg, A , Flowbehaviour of fibre suspensions in straight tubes: new experimental techniques and multiphase modeling, PhD Thesis, University of Jyvaskyla, Jyvaskyla, Finland, 2007. Jimenez, J , Turbulent Flows Over Rough Wall, Ann. Rev. Fluid Mech, 36:173-96, 2004. Julien-Saint-Amand, F , Principles and technology of screening, Center Technique du Papier, Grenoble, France, 1997. Julien-Saint-Amand, F and Perrien, B , Fundamentals of screening: Experimental approach and modeling, TAPPI Pulping Conf. Proc, 1019-1031, Montreal, 1998. Julien-Saint-Amand. F, and Perring, B , Fundamentals of screening: effect of rotor design and fibre properties, TAPPI Pulping Conf, 1999. Julien-Saint-Amand, F„ Stock preparation: Part 2 - Particle Separation processes", Fundamental research symposium, 2001. Kerekes, R. J , and Garner, R. G , Measurement of turbulence in pulp suspensions by laser anemometry, JPPS, 8(3):53-59, 1982. Kerekes, R.J, and Schell, C.J,. Characterization offiberflocculation by a crowding factor, JPPS, 18,32-38, 1992. Kerekes, R.J , Pulp flocculation in decaying turbulence: a literature review, JPPS, 9(3):86-91, 1983. Kumar, A , Passage of fibres through screen apertures, PhD thesis, University of British Columbia, Canada, 1991. Kumar, A , Gooding R.W, and Kerekes, R.J, Factors controlling the passage of fibres through slots, TAPPI J , 81(5): 247-254, 1998. Karvinen, R , and Halonen, L , The effect of various factors on pressure pulsation of screen, Paperi jaPuu, 2, 1984. Lissenburg, R. C. D , Hinze, J. O , and Leijdens, H , An of experimental investigation the effect of a constriction on turbulent pipe flow, App. Sci. Res, 31:343-362, 1975. Lawryshyn, Y . A , and Kuhn, D.C.S, "Large deflection analysis of wet fibre flexibility measurement technique", JPPS, 22(11): 423-431, November 1996. Lakehal, D , Computation of turbulent shear flows over rough-walled circular cylinders, J. Wind Eng. and Industrial Aerodynamics, 80:47-68, 1999. Lee, P.F.W, Duffy, G . G , Velocity profiles in the drag reducing regime of pulp suspension flow, APPITA, 30, 219-226, 1976. Lee, P.F.W. and Duffy, G . G , Analysis of the drag reducing regime of pulp suspension flow, TAPPI J,59(8):l 19-122, 1976. 103  Li, Z., Pipe flow behavior of hardwood pulp suspensions studied by NMRI, JPPS, 21(12), 1995. Martinez, D. M., Gooding, R. W., and Roberts, N., A force balance model of pulp screen capacity, TAPPI J., 82(4): 181-187, 1999. Nissen, M. R., Image blur, DOE's Office of Scientific and Technical Information (OSTI), Technical report: SAND93-0644, Sandia National Labs., Albuquerque, NM (United States), 1993. Nikuradse, J., Stroemungsgesetze in rauhen rohren, VDI-Forsch. 361 (English translation 1950. Laws of flow in rough pipes,. NACA TM 1292). Oosthuizen, P. H., Chen, S., Kuhn, D.C.S., and Whiting, P., Fluid and fibre flow near a wall slot in a channel, Pulp and Paper Canada, 95(4): 27-30, 1994. Olson, J. A., The effect of fibre length on passage through a single screen apertures, PhD thesis, University of British Columbia, Canada, 1996. Olson, J., Roberts, N., Allison, B., and Gooding, R., Fibre length fractionation caused by pulp screening, JPPS, 24(12): 393-397, 1998. Olson, J., Fibre length fractionation caused by pulp screening: slotted screen plates, JPPS, 27(8): 255-261,2001. Patel, V.C., Perspective: flow at high reynolds number and over rough surfacesAchilles heals of CFD, ASME J. Fluids Eng., 120:434-444, 1998. Patel, V.C., and Yoon, J. Y., Application of turbulence models to separated flow over rough surfaces, J. Fluids Eng., 117:234-241, 1995. Perry, A.E., Schofield, W. H., and Joubert, P. N., Rough-wall turbulent boundary layers, J. Fluid Mech., 37:383-413, 1969. Pinion, V., Gooding, R. W., and Olson, J., Measurements of pressure pulses from solid core screen rotor, TAPPI J., 2002. Pflueger, C. D., Olson, J., and Gooding, R. W., The performance of the EP Rotor in de-ink pulp screening, APPITA Conf, Australia, 2007. Riese, J. W., Spiegelberg, H. L., and Kellenberger, S. R, Mechanism of screening: Dilute suspesionsof stiff fibres at normal incidence, TAPPI J., 62(5); 895-903, 1969. Repo, K and Sundholm, J., The effect of rotor speed on the separation of coarse fibres in pressure screening with narrow slots, Pulp and Paper Canada J., 97(7):67-71, 1996. Robertson, A.A., Mason, S.G., Flocculation in flowing pulp suspensions. Pulp and Paper Magazine of Canada, Convention Issue, 264-269, 1954.  104  Sano, M , and Hirayama, M , Turbulent boundary layers with injection and suction through a slit, JSME,28: 807-814,1985. Schlichting, H , Boundary layer theory. New York: McGraw-Hill, 6 ed, 1979. th  Shih, T - H , Liou, W . M , Shabbir, A , Yang, Z , and Zhu, J , A new k-e eddy viscosity model for high Reynolds number turbulent flows, Computer and Fluids, 24(3): 227-238, 1995. Simpson, R.L, A generalized correlation of roughness density effects on the turbulent boundary layer, AIAA J , 11:242-244, 1973. Sloane, C. M , Kraft pulp processing - pressure screen fractionation, APPITA J , 53(3): 220-226, 2000. Soszynski, R. M , The formation and properties of coherent floes in fiber suspensions, PhD thesis, Dept. of Chemical Engineering, University of British Columbia, Vancouver, BC, 1987. Stevenson, T. N , A law of the wall for turbulent boundary layers with suction or injection, Cranfield College, Aero. Report 166, 1963. Sundholm, J , Paper making science and technology: Mechanical pulping, Book 5, Fapet Oy, Helsinki, Finland, 1999. Tani, J , Turbulent boundary layer development over rough surfaces, Perspectives in turbulence studies, Springer, 1987. Thomas, A. S. W , and Cornelius, K . C , Investigation of a laminar boundary layer suction in a slot, AIAA J , 20 (6): 790-796, 1981. Tirado, A , Theory of screening, TAPPI J , 41(5): 237-245, 1958. White, F. M , Viscous fluid flow, New York: McGraw-Hill, 2  nd  ed, 1991.  Wikstrom, T , Flow and rheology of pulp suspensions at medium consistency, PhD thesis, Chalmers University of Technology, Sweden, 2002. Xu, H. and Aidun, C. K , Characteristics of fiber suspension flow in a rectangular channel Intl. J. Multiphase Flow, 31(3):318-336, 2005. Yoshioka, S, Fransson, J.H.M, and Alfredsson, P.H, Free stream turbulence induced disturbances in boundary layers with wall suction, Physics of Fluids, 16(10):3530-3539, 2004. Yu, C. J , Pulsation measurement in a screen, TAPPI Eng. Conf, 1994. Yu, C. J , and DeFoe, R. J , Fundamental study of screening hydraulics-1, TAPPI J , 77(8): 219225, 1994 a. Yu, C. J , and DeFoe, R. J , Fundamental study of screening hydraulics-2, TAPPI J , 77(9): 119124, 1994 b. 105  Yu, C. J., Crossley, B. R., and Silveri, L., Fundamental study of screening hydraulics-3, TAPPI J., 77(9): 125-131, 1994. Zagni, A. F. E., and Smith, K. V. H., Channel flow over permeable beds of graded spheres, J. Hydraulics, ASCE div., 102(2), 207-222, 1976.  106  APPENDIX 1 Streamline plots for all wire geometries showing details in the relief of the slot. In this study we focused on the flow approaching the slot and it has been proved to be very important factor effecting the fiber passage (Gooding (1986), Kumar (1991, Olson (1996)). Streamline plots for all six geometries in the relief of the slot (i.e. the flow after the slot) obtained from the CFD simulations explained in section 3 are shown in this appendix. The bulk velocity of the flow in the slot is about 1 m/s. We notice a series of vortices in the slot relief for all five geometries. These vortices formed a tunnel for the slot flow to reach the accept side. At the end of the slot relief, the vortex occupied more than 95% of the relief width. The bulk flow velocity in the accept side is about 4 to 7 m/s. The pressure outlet boundary condition was applied at the outlet allowed the flow driving from the feed side to the accept side. However, the boundary condition applied at the outlet is not realistic. The strong cross-flow initial condition applied on the accept side of the slot helped in convergence. But the strong cross-flow prevents the jet from emerging from slot relief. This would have much impact on the accept side of the flow.  107  h = 0.9,w = 3.2; (h/w = 0.281)  h = 1.2, w = 3.2; (h/w = 0.375)  109  110  APPENDIX 2 Details of flow channel  APPENDIX 3 Hardware and software specifications of the PIV system Hardware: Laser  Gemini PIV 120-15  Wave length  532 nm  Max. pulse energy  120 mJ  Beam diameter  4.5 mm  Pulse width  3-5 ns  Beam divergence  < 2 degree  Signal generator  Beckley Nucleonics model 500D  Number of channels  8  External trigger  1  Time accuracy  25 ns  Time resolution  0.2 micro seconds  Frame grabber  Matrox Meteor II - Digital  Camera  Roper Scientific ES 1.0  PIV processing software: Name: Dantec Flow manager, Version 3.62 Supplier: Dantec Dynamics A/S Year: 2001 Resolution test targets: Supplier: Melels Griot Make: USAF 1951 Chromium Negative Resolution Test Target  112  APPENDIX 4 Timing diagram, camera and laser synchronization A synchronized activation sequence for the laser and camera was initiated by a manual trigger from the pulse generator. The activation sequence came in the form of five carefully timed pulses (5V) sent from the pulse generator. Two of the pulses were delivered to laser 1 and two other pulses were sent to laser 2, the fifth pulse went to a frame grabber. The only input to the pulse generator was the manual trigger signal. Each laser required two pulses. The first pulse was for triggering flash lamp while the second pulse triggered the Q-switch which fired the laser. The time delay between flash lamp firing and q-switch triggering was set to 200 ms for both the lasers. The laser pulse separation time was 5 ps for all the experiments. This pulse separation period was chosen such that adequate particle movement occurred between two subsequent images. Excessively large separation times allow particle groups to lose their unique pattern, thus lessening the chance of calculating the true particle displacements. Conversely, very short separation times produce particle displacement approaching the spatial resolution of the images, which makes it difficult in determining the displacements. As a rule of thumb, maximum displacement allowed by a particle within an interrogation area is 1/3 of the window size (i.e. 10 pixels for a 32x32 interrogation area window size). Therefore, in order to get 5 ps time separation between two laser pulses, the time difference between Q-switches of two lasers is set accordingly. There was no delay for the pulse of the frame grabber. The width of the pulse was set to 4 ns which is the requirement for the camera. Figure A-4.1 shows the timing diagram used to synchronize the camera and the laser source.  113  Delay Os  Camera Trigger  4 ns  33 ms (camera default for PIV mode)  Camera Exposure  Delay 29.78 s  Flash Lamp 1  n  1st image exposure  2nd image exposure  1 200 ps  ^  p  Delay 29.98 s  Q - Switch 1 i  r  AT = 5 ps •* Delay 29.785 s  Flash Lamp 2  200 ps Q - Switch 2  Delay 29.985 s  Figure A-4.1 Timing diagram showing a synchronized activation sequence for the camera and laser source.  114  APPENDIX 5 Hardware and software specifications of the LDV system Hardware: Supplier: Meaurement Science Enterprise, Inc. (formerly owned by VioSence Corporation, Inc.) 123 W. Bellevue Dr., Suite 1 Pasadena, CA 91105-2549 Phone: (626) 577-0566 Fax: (626) 577-0565  Laser probe type  MiniLDV-2D system  Laser wave length  660 nm and 785 nm  Laser power  Below 20 mW in probe volume  Probe volume distance  500 mm  Speed range  -4 to 40 m/s  Resolution  0.3 % full scale  Operating temperature  0 to 40° C  Measurement  UandV  Traverse travel  500 mm  Traverse accuracy  250 um  LDV data processing software: Name: Burst Processor (VioBP-S3), National Instruements Lab VIEW based software, Version 2.16, year 2004. Supplier: Meaurement Science Enterprise, Inc. (formerly owned by VioSence Corporation, Inc.)  115  APPENDIX 6 Properties of pulp and nylon fibres  Density (kg/m )  Apparent Density (kg/m )  Average fiber diameter (mm)  Stiffness (N.m xl0 )  Nylon Fiber 15Denier  1140  1130  0.02  329  Wood pulp fibres (Western red Cedar kraft)  1500  1123  0.03  3.5  Fibre type  3  3  a  2  Reference: Soszynski, R . M , 1987. a - calculated from denier and fiber density  116  12  

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