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Modeling the maximum capacity of a pulp pressure screen Salem, Hayder Jabber 2013

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Modelling the MaximumCapacity of a Pulp PressureScreenbyHayder Jabber SalemB.Sc. University of Baghdad, 1993M.Sc. University of Baghdad, 1997M.Sc. American University of Sharjah, 2006A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Mechanical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)September 2013c? Hayder Jabber Salem 2013AbstractPressure screens are used as a means of separating pulp fibres from contaminants.They are also used to improve pulp quality by fractionating fibres by length. Bothfunctions are limited by the capacity of the device. Three studies were conducted inthis thesis to understand the factors that affect maximum capacity.Capacity is determined by the complex hydrodynamics in the region between thescreen rotor and the screen wall. To better understand this flow, the stream-wisevelocity and aperture velocities were measured using particle image velocimetry. Thevortex generated above the aperture and its size is shown to be strongly dependenton the aperture velocity, wall roughness and, to some extent, on the rotor speed.The vortex diminishes in size at higher aperture velocities that increase the exit layerheight. The experiments also show that the reversal flow through the slot decreasedwith lower rotor speeds and increased slot velocities. This observation challengesthe existing models of apertures being cleared simply by flow reversal driven by asuction pulse caused by flow acceleration between the foil and cylinder. In its place,this study identifies elements of a more sophisticated flow model that considers suchfactors as the depletion of the zone below the rotor and flow disturbances in the wakeof the foil. The effects of screen cylinder geometry, pulp type, rotor and flow velocitieson capacity were also investigated. Five types of screen cylinders were tested usingdifferent ratios of softwood/hardwood kraft pulp and different reject rates. It wasfound that the average fibre length has a significant impact on capacity.iiAbstractA comprehensive understanding of pulp screen capacity remains elusive. Thepresent research has, however, provided insights which move away from the simplistic?backflush? models used in the past and supports a more sophisticated model thatalso considers: 1) the dynamics of fibre accumulation and removal rates of the slotentry, 2) the importance of a small-scale perturbations created by turbulent flowfor fibre removal, and 3) the mechanics of fibre trapping on the downstream edgeof the slot. These advancements also provide some direction for future equipmentdevelopments.iiiPrefaceIn this work, I was responsible for conducting all parts of the research and all ofthe simulations and analysis of the data presented. Dr. Olson and Dr. Martinezsupervised the research and provided feedback and reviewed the manuscript. Dr.Robert Gooding from AFT also provided valuable feedback and reviewed the workpresented.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1 Flow of Fibres Near a Screen Wall . . . . . . . . . . . . . . . . . . . . 42.2 Effect of Wall Geometry, Local Flows and Flocculation on Fibre Screening 52.3 Effect of Rotor on Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 7vTable of Contents3 Experimental Study of Flow Fields Near Screen Cylinder Surface 93.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 143.3.1 Steady State Flow Analysis . . . . . . . . . . . . . . . . . . . 143.3.2 Time-Varying Flow Analysis . . . . . . . . . . . . . . . . . . . 193.3.3 Fibre Concentration Analysis . . . . . . . . . . . . . . . . . . 333.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 374 Maximum Capacity of a Pilot Pressure Screen . . . . . . . . . . . 394.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.1 Effect of Consistency on Capacity . . . . . . . . . . . . . . . . 444.3.2 Effect of Feed Flow Rate on Capacity . . . . . . . . . . . . . . 484.3.3 Effect of Pulp Properties and Contaminants on Capacity . . . 494.3.4 Effect of Cylinder Geometry on Capacity . . . . . . . . . . . . 504.3.5 Effect of Rotor and Slot Velocity on Reject Thickening . . . . 564.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 565 New Model for Pressure Screen Capacity . . . . . . . . . . . . . . . 595.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.1.1 Visual Observation of Fibre Motion Near the Screen Surface . 605.2 Mathematical Model Details . . . . . . . . . . . . . . . . . . . . . . . 605.3 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 74viTable of Contents6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 766.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.1.1 Flow Field Study (Chapter 3) . . . . . . . . . . . . . . . . . . 766.1.2 Pilot Pulp Screen Capacity (Chapter 4) . . . . . . . . . . . . . 776.1.3 Model of Pulp Screen Capacity (Chapter 5) . . . . . . . . . . 786.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87A Flow and Wire Geometry Effects on Fibre Fractionation . . . . . . . 87B PIV Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . . 93C Characterization of Fibres Used for Capacity Trials . . . . . . . . . . 96viiList of Tables3.1 Coupon geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Experimental test conditions . . . . . . . . . . . . . . . . . . . . . . . 134.1 Screen wire geometries . . . . . . . . . . . . . . . . . . . . . . . . . . 43B.1 Principal dimensions for PIV measurment . . . . . . . . . . . . . . . 94B.2 Uncertainties for velocity . . . . . . . . . . . . . . . . . . . . . . . . . 95B.3 Uncertainties for position . . . . . . . . . . . . . . . . . . . . . . . . . 95viiiList of Figures1.1 Schematic of the principal flows through a pulp screen. . . . . . . . . 23.1 Flow geometry studied experimentally. . . . . . . . . . . . . . . . . . 103.2 Schematic diagram of the Cross-Sectional Screen apparatus (CSS). . . 123.3 Close-up of the wire cross-section at the entry to the slot showingcharacteristic wire dimensions . . . . . . . . . . . . . . . . . . . . . . 133.4 Smooth rotor-wall flow geometry. . . . . . . . . . . . . . . . . . . . . 153.5 Slot-entry vortex for a high contour at (a) Vt = 10 m/s, Vs = 1 m/s,(b) Vt = 10 m/s, Vs = 4 m/s, (c) Vt = 20 m/s, Vs = 1 m/s, (d) Vt =20 m/s, Vs = 4 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.6 Slot-entry vortex for a low contour at (a) Vt = 10 m/s, Vs = 1 m/s,(b) Vt = 10 m/s, Vs = 4 m/s, (c) Vt = 20 m/s, Vs = 1 m/s, (d) Vt =20 m/s, Vs = 4 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.7 Vortex stagnation point length. . . . . . . . . . . . . . . . . . . . . . 173.8 Exit layer height (normalized by slot width) versus the ratio of slotvelocity and upstream velocity. . . . . . . . . . . . . . . . . . . . . . 173.9 High contour circulation within the vortex as a function of flow ratio. 183.10 Low contour circulation within the vortex as a function of flow ratio. 183.11 Foil rotor-wall geometry. . . . . . . . . . . . . . . . . . . . . . . . . . 193.12 ROI?s for u and v components. . . . . . . . . . . . . . . . . . . . . . . 20ixList of Figures3.13 The flow between the foil and cylinders surface are examined for twoalternate frames of reference: (a) a steady flow problem follows fromfixing the frame of reference on the foil, which is moving at u1. The flowbetween the foil and cylinder surface increases by an amount ?u. (b)An unsteady flow situation results from fixing the frame of reference tothe screen cylinder. The apparent velocity under the rotor is decreasedby an amount ?u relative to the general flow velocity. . . . . . . . . . 213.14 u component for low contour at Vt = 15 m/s and Vs = 1 m/s. . . . . 253.15 u component for high contour at Vt = 20 m/s and Vs = 1 m/s. . . . . 253.16 u component for high contour at Vt = 20 m/s and Vs = 2 m/s. . . . . 253.17 Rotor position in terms of chord length. . . . . . . . . . . . . . . . . 263.18 The spatio-temporal description of the u-component in the flow fieldfor the high contour (Vt = 20 m/s, Vs = 1 m/s) is shown above (a)along with the measuring volume (in yellow) used for averaging. Thelower plot (b) is the associated averaged flow for the u-component. . . 273.19 Spatio-temporal behaviour of u component for high contour surface atVt = 10 m/s, Vs = 1 m/s. . . . . . . . . . . . . . . . . . . . . . . . . 283.20 Spatio-temporal behaviour of u component for high contour surface atVt = 10 m/s, Vs = 3 m/s. . . . . . . . . . . . . . . . . . . . . . . . . 283.21 Spatio-temporal behaviour of u component for high contour surface atVt = 20 m/s, Vs = 1 m/s. . . . . . . . . . . . . . . . . . . . . . . . . 293.22 Spatio-temporal behaviour of u component for high contour surface atVt = 20 m/s, Vs = 3 m/s. . . . . . . . . . . . . . . . . . . . . . . . . 293.23 v component for high contour at Vt = 20 m/s. . . . . . . . . . . . . . 303.24 v component for low contour at Vt = 10 m/s. . . . . . . . . . . . . . . 30xList of Figures3.25 Reversal flow boundary. . . . . . . . . . . . . . . . . . . . . . . . . . 313.26 Spatio-temporal behaviour of Vd for low contour surface at Vt = 10m/s,Vs = 1 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.27 Spatio-temporal behaviour of Vd for high contour surface at Vt =20 m/s, Vs = 1 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.28 Light intensity as a function of fibre concentration . . . . . . . . . . . 343.29 High contour concentration ROI?s . . . . . . . . . . . . . . . . . . . . 343.30 Concentration for high contour: (a) Vt = 10 m/s, Vs = 1 m/s, (b) Vt =10 m/s, Vs = 2 m/s, (c) Vt = 10 m/s, Vs = 3 m/s, (d) Vt = 20 m/s,Vs = 1 m/s, (e) Vt = 20 m/s, Vs = 2 m/s, (f) Vt = 20 m/s, Vs =3 m/s. 364.1 The UBC MR8 pilot pressure screen. . . . . . . . . . . . . . . . . . . 424.2 Screen open area blinding procedure: (a) wrapping the spool withrubber strip and (b) securing the strip with a stainless steel clamp toprevent leakage from the spool edges. . . . . . . . . . . . . . . . . . . 434.3 Plugging envelope for Type B cylinder at different consistencies, (50/50hardwood/softwood mixture). . . . . . . . . . . . . . . . . . . . . . . 464.4 The extrapolated Vs-Vt relationship of Figure 4.3. . . . . . . . . . . . 464.5 The x-intercepts of the extrapolated Vs-Vt relationship of Figure 4.4is plotted against consistency suggesting that there would be no offsetwhen there are no fibres in the suspension (CF = 0%). . . . . . . . . 474.6 Pressure difference across Type B screen cylinder prior to plugging ata range of slot velocities (50/50 hardwood/softwood mixture). . . . . 474.7 Power consumption by the rotor as a function of rotor speed at differentslot velocities (CF = 0%). . . . . . . . . . . . . . . . . . . . . . . . . 48xiList of Figures4.8 Effect of reject rate on plugging envelope for the Type B screen (100%softwood suspension with 1.0% consistency). . . . . . . . . . . . . . . 494.9 Plugging envelope for the Type B screen using different softwood/hardwoodratios, CF =1.0%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.10 Pressure difference across the Type B cylinder for different softwood/hardwoodratios, CF = 1.0%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.11 Minimum rotor tip speed for the Type B screen at different contam-inant ratios (50/50 hardwood/softwood mixture, CF = 1.5%) Vt = 2m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.12 Pressure difference across the Type B screen at different contaminantratios, (50/50 hardwood/softwood mixture, CF = 1.5%. . . . . . . . . 524.13 Plastic speck diameter distribution. . . . . . . . . . . . . . . . . . . . 534.14 Effect of contour height on the plugging envelope. The contour heightsof the Type A, B and C screen cylinders is 1.2 mm, 0.9 mm and 0.6mm, respectively. (50/50 hardwood/softwood mixture, CF = 1.5%). . 544.15 Pressure difference across cylinders, (50/50 hardwood/softwood mix-ture, CF = 1.5%). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.16 Effect of wire width and slot width on plugging boundary, (50/50 hard-wood/softwood, CF = 1.0%). Type B: 0.9 mm contour height/3.2 mmwire width/0.15 mm slot width. Type D: 0.6 mm /2.3 mm/0.15 mm.Type E: 0.6 mm /3.2 mm/0.10 mm. . . . . . . . . . . . . . . . . . . 554.17 Thickening of pulp with rotor and slot velocity changes (Type A screen,CF = 1.0%, 50:50 SW:HW). . . . . . . . . . . . . . . . . . . . . . . . 57xiiList of Figures5.1 Fibre trapping and clearing by rotor, Vt = 5 m/s and Vs = 3 m/s. (a)xr/chord = -1.0, (b) xr/chord = 0.35, (c) xr/chord = 0.6, (d) xr/chord= 1, (e) xr/chord = 1.35, (f) xr/chord = 4.0. . . . . . . . . . . . . . 615.2 Tension on a fibre trapped on wire edge. . . . . . . . . . . . . . . . . 635.3 Tension on the fibre portion above slot at Vt = 5 m/s. . . . . . . . . 645.4 Tension on fibre portion above slot at Vt = 20 m/s. . . . . . . . . . . 655.5 Tension on fibre segments above the slot as a function of smooth rotortip speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.6 Universal curve-fitted u component above the cylinder surface as afunction of rotor position for 0 ? Vs ? 4 m/s. . . . . . . . . . . . . . 665.7 Corrected slot velocity along a 3 mm fibre within the slot. . . . . . . 675.8 Tension changes with different trapped fibre positions are shown schemat-ically in images (a) and (b) and analytically in a comparison of the fibreforces. In this example, a fibre with l/Lf in the range of 0.50 to 0.66is trapped (i.e. differences in drag force are less than the friction force). 685.9 Changes in trapping position due to changes in the flow field (Vt = 5m/s and Vs = 1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.10 Estimates of the accumulation of 3 mm fibres on the low contour wireduring one foil cycle at Vt = 10 m/s. . . . . . . . . . . . . . . . . . . 725.11 Accumulation of fibres within screen slots during rotor cycles, (a) ac-cumulation is less than the cleansing effect, i.e. no fibres left fromthe previous cycle (b) accumulation effect equals the cleansing effect(plugging point), (c) accumulation effect is greater than the cleansingeffect (plugging takes place). . . . . . . . . . . . . . . . . . . . . . . . 73xiiiList of Figures5.12 Accumulation number, Nac, for a 3 mm fibre as a function of slotvelocity at different rotor speeds. . . . . . . . . . . . . . . . . . . . . 74A.1 Effect of slot velocity on fibre length distribution with a low contourwire and smooth rotor at Vt = 20 m/s. . . . . . . . . . . . . . . . . . 89A.2 Effect of slot velocity on fibre length distribution with a low contourwire and smooth rotor at Vt = 25 m/s. . . . . . . . . . . . . . . . . . 89A.3 Effect of slot velocity on fibre length distribution with a high contourwire and smooth rotor at Vt = 20 m/s. . . . . . . . . . . . . . . . . . 90A.4 Effect of slot velocity on fibre length distribution with a high contourwire and smooth rotor at Vt = 25 m/s. . . . . . . . . . . . . . . . . . 90A.5 Effect of smooth rotor speed and contour height on fibre fractionationat various slot velocities. . . . . . . . . . . . . . . . . . . . . . . . . . 91A.6 Effect of contour height and vortex strength on short and long fibrefractionation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91A.7 Effect of rotor on fibre fractionation at the same flow field. . . . . . . 92C.1 Fibre length distributions of 0:100 SW:HW sample. . . . . . . . . . . 96C.2 Fibre length distributions of 25:75 SW:HW sample. . . . . . . . . . . 97C.3 Fibre length distributions of 50:50 SW:HW sample. . . . . . . . . . . 97C.4 Fibre length distributions of 75:25 SW:HW sample. . . . . . . . . . . 98C.5 Fibre length distributions of 100:0 SW:HW sample. . . . . . . . . . . 98C.6 Frequency of 3 mm fibres in different SW:HW samples. . . . . . . . . 99xivList of SymbolsAlphanumeric SymbolsSymbol Meaning UnitA Screen open area m2A0, A2 Parameters used in CD curve fitsAv Vortex area m2C Consistency (concentration) of fibresC1, C2 Capacity characteristic constantsCF Feed consistencyCS Consistency through slotCU Consistency of the stream above slotChord Air foil chord length mCD Drag coefficientCD? Drag coefficient of a cylinder normal to flowCL Lift coefficientci Sensitivity coefficientd Stagnation point length mD Fibre and particle diameter mfc Coefficient of frictionh Wire contour height mH Exit layer height mHr Rotor-wire tip gap mk1, k2, k3 Accumulation constantsl Fibre length above slot mL Wire inclined surface length mLf Fibre length mLr Distance on the image plane mlr Distance of the reference point mNac Accumulation numberP Pressure kg/(m.s2)xvList of SymbolsSymbol Meaning UnitRe Reynolds numberRv Reject rates Slot width mT Thickening factorTs Tension on fibre portion within slot kg.m/s2Tu Tension on fibre portion above slot kg.m/s2u x-direction velocity component m/sus Standard uncertaintyv y-direction velocity component m/sVd Velocity parallel to wire inclined surface m/sVs Slot velocity m/sV ?s Maximum slot velocity m/sVt Rotor tip speed m/sV ?t Threshold rotor tip speed m/sVu Upstream flow velocity m/sw Wire width mX Horizontal coordiante of particle in image plane mXe End location of particle pixelXs Start location of particle pixelxr Foil leading edge-origin tangential distance mxac Accumulation distance per foil cycle mz Stream line elevation mGreek SymbolsSymbol Meaning Unit? Angle between the flow and fibre degrees?1 Magnification factor m/pixel? Dynamic viscosity kg/(m.s)? Contact angle degrees?1, ?2 Parameters used in CD,? curve fits? Density kg/m3? Circulation m2/sxviList of AbbreviationsAbbreviationsAbbreviation MeaningCSS Cross Sectional ScreenCFD Computational Fluid DynamicsNACA National Advisory Committee for AeronauticsHSV High speed videographyHW HardwoodLDV Laser Doppler VelocimetryOCC Old corrugated containerPIV Particle Image VelocimetryROI Region of interestSW SoftwoodVFD Variable frequency drivexviiAcknowledgementsDuring the last few years that I spent working on this research, I have receivedhelp and support from many people to whom I would like to express my sincereappreciation.First of all, I would like to thank my supervisors Prof. James Olson and Prof.Mark Martinez who patiently introduced me to the challenging field of pulp screening.I would like to acknowledge their continuous support, advice and patience. Withouttheir help, this work would have not been accomplished.I would also like to acknowledge the financial support of NSERC and Aikawa FibreTechnologies (AFT).Special thanks to Dr. Robert Gooding for his support, feedback and proofreadingof this thesis and published work.I would like to thank all my colleagues and friends at the University of BritishColumbia for their valuable help especially George Soong, Nici Darychuck, Dr. Shel-don Green, Ario Madani, Sean Delfel, my brother Zaid and Mahdi Salehi.Finally, I would like to thank my lovely wife Jennifer for her support and under-standing.xviiiChapter 1IntroductionThe purpose of the present investigation arises from an interest in the screening ofpapermaking fibre suspensions. Periodic roughness elements, formed into a screensurface, are used as a means of separating pulp fibres from contaminants. Figure 1.1shows the principal features of a typical industrial screen used for pulp screening. Ascreen receives a feed stream of pulp and separates it into an accept stream of cleanedpulp and a reject stream where oversized contaminants are concentrated. Screens arealso used to enhance pulp quality by fractionating one type of fibre length from oth-ers. A screen cylinder within the pulp screen has apertures that allow pulp fibres topass while blocking fibre bundles, plastic specks and other contaminants. The rotoris thought to work by creating three important effects: (1) generating pressure pulsa-tions which backflush and clean the screen plate apertures of any incipient blockages,(2) accelerating the pulp suspension on the feed side of the screen to a high tangen-tial velocity and (3) inducing turbulence at the surface of the screen to help keep theapertures clear.The capacity of the screen is commonly defined as the maximum throughput (i.e.the mass flow rate) before the apertures become plugged with pulp. For the purposeof this study, ?capacity? will be expressed as slot velocity, with the screen openarea, slot width and accept consistency taken as constants. Capacity is a functionof fibre length, feed consistency, aperture size and geometry, rotor speed and rotor11.1. ObjectivesFigure 1.1: Schematic of the principal flows through a pulp screen.type. Over the decades, there have been various experimental and computationalstudies conducted to understand the performance of pressure screening in terms offibre passage and debris removal efficiency. However, there are relatively few studieson the fundamental aspects of capacity.1.1 ObjectivesThe goal of this study is to develop a theoretical and experimental understandingof the factors that limit the capacity of pulp pressure screens. This requires theassessment of the flow patterns above and within the apertures of a pressure screenand the investigation of the maximum capacity in terms of main variables such as fibrelength, feed consistency, aperture size and geometry, rotor type and debris content.The specific objectives of this thesis are to:? Use High Speed Videography (HSV) to investigate the flow of pulp fibres in the21.2. Outlineregion between the pulp screen rotor and the slotted screen wall.? Use Particle Image Velocimetry (PIV) to measure the stream-wise and aperturevelocities and understand the complex hydrodynamics in the critical regionbetween the rotor and the screen wall.? Experimentally determine the effect of rotor speed on screen capacity.? Experimentally determine the effect of pulp type on screen capacity.? Experimentally determine the effect of screen aperture geometry on screen ca-pacity.? Analytically determine the factors that affect screen capacity and develop acapacity model.1.2 OutlineA review of published work is presented in Chapter 2. Chapter 2 mainly focuseson the flow of fibres near screen surface and the effect of wall geometry, rotor andflocculation on fibre screening. Chapter 3 presents experimental assessments of theflow behaviour, using PIV technique, and observations of the flow of individual fibresnear the screen surface. Chapter 4 assesses the factors that limit capacity using a pilotpressure screen. By utilising the data presented in the previous chapters, Chapter 5discusses a new model for screen capacity. Finally, Chapter 6 provides conclusionsand discusses opportunities for future work.3Chapter 2Literature Review2.1 Flow of Fibres Near a Screen WallGooding and Kerekes [18] used high-speed photography to capture the trajectories offibres near a single slot in a cross flow. They showed a low fibre concentration layernear the wall which was one of the factors limiting fibre passage, and was called the"wall effect". They also observed that under certain flow conditions, fibres wouldbecome "trapped" on the downstream edge of the slot. Kumar [31] experimentallydetermined the effect of fibre length, slot width and flow velocities on the probabilityof fibre passage. He found that fibre passage varied with the ratio of fibre lengthto slot width. This work was later investigated by Olson and Wherrett [41]. Theyshowed that fibre passage can be characterized by the single function first proposedby Kumar.Yu and DeFoe [52] studied the flow patterns at the feed-side surface of smooth andcontoured screen cylinders under steady flow conditions. They speculated that fibremats containing fibres and contaminants can form on the surface of the cylinder andthat these mats remixed and were diluted during screen operation. In a further study,Yu and DeFoe [53] showed that for contoured cylinders, vortex flow is an effectivemeans of preventing fibres from residing on slot openings or stapling between twoopenings. Stapling is a mechanism in which the two ends of a fibre are drawn into42.2. Effect of Wall Geometry, Local Flows and Flocculation on Fibre Screeningadjacent apertures with the fibre immobilized on the land area between them [17].Gooding [16] examined the flow patterns and turbulence levels of various smoothand contoured screen slots in a steady cross-flow to obtain a mechanistic understand-ing of what determines slot resistance and the conditions that lead to minimum valuesof slot resistance. He also observed how fibres build up within the slot and consideredthe contribution of the incipient fibre blockages to flow resistance. The concentrationand orientation of fibres in a turbulent flow near a smooth wall was assessed by Olson[39] and found to be a function of fibre length.Yong et al. [51] used high-speed video photography to determine the trajectoryof nylon fibres approaching narrow screen apertures in a laboratory pulp screen.However, the very stiff model fibres and the relatively low rotor speeds differed fromindustrial screening conditions, which limited the relevance of the study.2.2 Effect of Wall Geometry, Local Flows andFlocculation on Fibre ScreeningScreen cylinder contours have an important effect on screening efficiency and capacity.Heise [23] recommends the use of screen cylinders which minimize turbulence betweenthe rotor and the screen surface in order to maximize screening efficiency. Niinimaki etal. [38] found that the efficiency of probability screening is more dependent on contourroughness than on slot width. Increasing the contour height led to an improvementin screen capacity and reduction in debris removal efficiency.Halonen et al. [21] defined fluidization as a process of loosening fibre contactsinside flocs. Depending on the conditions and properties of the pulp on the contouredscreen surface, the fluidized state may extend the cleansing effect induced by the rotor52.2. Effect of Wall Geometry, Local Flows and Flocculation on Fibre Screeningaccording to Frejborg [13]. Bliss [4] agreed with the idea of extended fluidization andstated that turbulence allows the openings to pass more fibres after the cleaning pulseof the rotor in the case of a contoured screen than for that of a smooth screen.Mokamati et al. [35] developed a CFD simulation of the flow through a screenslot and considered the effect of various screen contours. As contour height increased,turbulence intensity near the wall increased. Moreover, turbulence intensity near thewall increased with decreasing wire width. It was thus shown that the ratio of contourheight to wire width controls the boundary layer thickness and turbulence intensitynear the wall.Yu and DeFoe [54] showed that the size of the apertures in a screen cylinderwas the dominant factor affecting a screen?s contaminant removal efficiency. As onewould expect, the larger the aperture size, the lower was the contaminant removalefficiency and the higher was the volumetric and mass throughput. They also showedthat aperture velocity cannot be used as a general guideline for predicting screenperformance.Kerekes [30] investigated the behaviour of pulp flocs at the entry to constrictionsusing high speed cine photography. The elongational strain imposed by the accel-erating flow in the entry stretched the floc but did not rupture it. When flocs didrupture, they did so by tensile stretching rather than by shear. On entering the con-striction, fibres did not maintain their relative lateral position perpendicular to theflow direction; rather, they tended to concentrate along the wall of the constriction,making subsequent floc dispersion more difficult. Blaser [3] observed the behaviour ofpreflocculated ferric hydroxide flocs subjected to either a two-dimensional strainingflow or simple shear flow. He found that the simple shear flow led to the rotationof the flocs. In the extensional flow, no rotation occurred and the flocs were broken62.3. Effect of Rotor on Flowapart along the straining axis.Paul et al. [44] showed that the use of higher viscous liquid as the suspendingmedium produces increased screen capacity. The maximum mass flow rate, i.e. max-imum aperture velocity, increases as the suspending medium viscosity increases. Thereduction in floc size in more viscous liquids produces a decrease in the pressure lossacross the screen plate. The exit layer height increases with increasing viscosity atconstant accept and rotor velocities. The exit layer was defined by Gooding [18] andmathematically analyzed by Olson and Kerekes [40]. Fibres within this layer arecandidates to pass through screen apertures.2.3 Effect of Rotor on FlowRotor design is critical in determining pulp screen performance. The effects of pres-sure pulse magnitude, pulse width and frequency on capacity are not, however, wellunderstood.Karvinen and Halonen [29] assessed pressure pulsations using experimental andcomputational techniques for a foil-type rotor. They speculated that the backflushingaction of the pressure pulse arose from a Venturi effect created by the acceleration ofthe flow through the gap between the moving rotor tip and stationary screen plate.This acceleration causes the local pressure on the feed side of the screen plate todecrease to the point that there is a reversal in the flow through the aperture.Pinon et al. [45] measured the pressure pulse in a laboratory pulp screen. Their re-sults showed that increased rotor speed increased pulse strength. Although increasedrotor speed shortened the duration of the pulse, the shape of the pulse was relativelyunchanged.72.3. Effect of Rotor on FlowLevis [32] found that a wider gap between the foil and screen surface leads toincreased debris removal efficiency, albeit with lower capacity. Niinimaki et al. [37]found that screen capacity is sensitive to changes in foil "angle of attack" and thusthe foil angle could be varied to optimize screen performance.Feng et al. [12] simulated the pressure pulse using CFD and compared the resultsto experimental measurements over a wide range of foil tip speeds, angles-of-attack,clearances, and foil cambers. The pressure pulse peak was found to increase linearlywith the square of tip speed for all angles-of-attack studied. The positive pressurepeak near the leading edge of the foil was eliminated for foils operating at a positiveangle-of-attack. The results also showed that the magnitude of the negative pressurepeak increased as clearance decreased.The effect of varying pulse frequency on rotor performance was studied by Delfelet al. [9] numerically and experimentally. They used a novel multi-element foil (MEF)rotor. The results show that a two-foil rotor had greater capacity and reduced powerconsumption in comparison to a three-foil rotor with identical foil geometry. TheCFD model they introduced hypothesised a back-flush flow caused by the accelera-tion of the flow under the foil (Bernoulli?s effect). However, they used a solid wallboundary condition rather than modelling the slots in the cylinder wall, which mayhave influenced the results.In general, most published work has focused on the effect of flow on screen per-formance without taking into full account such industrial factors such as the effect ofthe fibre network or contour geometry on overall performance. More importantly, thepublished work has not led to a detailed and rigorous understanding of the hydraulicaperture clearing mechanism which is critical to reliable screen operation.8Chapter 3Experimental Study of Flow FieldsNear Screen Cylinder Surface3.1 IntroductionThis work considers the turbulent cross-flow of a Newtonian fluid within a movingupper boundary, i.e. the screen rotor, and a contoured, slotted lower boundary un-dergoing suction as shown in Figure 3.1. The two-dimensional roughness of the lowerboundary is formed by placing the roughness elements in a test coupon transverseto the approaching flow. The test coupon is made from contoured wires banded to-gether to form a regularly-spaced array of two-dimensional roughness elements whichdefine narrow slots in between. Turbulent flow over a rough wall has been studiedextensively because of its importance in a range of industrial applications ([24], [43],[5], [19]).3.2 Experimental DetailsThe present study measures the flow field and concentration of pulp fibres near apulp screen wall. The experiments were conducted with a Phantom R? high-speedvideo camera using a cross-sectional screen (CSS). The CSS is a laboratory-scale93.2. Experimental DetailsFigure 3.1: Flow geometry studied experimentally.screen modelled on the cross-section of a Hooper PSV 2100 pulp screen [[14], [12],[45], [51]]. The CSS has a depth of 50 mm and the partially-slotted cylinder has aninside diameter of 290 mm. Figure 3.2 provides a schematic drawing of the associatedflow loop. Feed flow is supplied from a 150 litre reservoir through the feed port to theCSS. Accept and reject flows are controlled using magnetic flow meters, flow controlvalves and a LabViewTM-based control system. Two rotors were used in this study:The one used for most tests had NACA 0015 foils with a 6 degree angle-of-attack.This angle minimizes the positive component of the pressure pulse according to Fenget al. [12], which is desirable since the positive pressure pulse component is notthought to help clear the aperture, but may instead jam the slot with trapped fibresand force deformable contaminants through the aperture. Pulp screens can typicallybe found with cylinders ranging from 0.3 to 1.2 m in diameter. The chord length ofthe foil has an important effect on the shape and magnitude of the pressure pulseand, in turn, on the performance of a pulp screen [14]. The chord length for thisfirst rotor was 4 cm which is comparable to the length of some foils used in industrialscreens and gives 11 chord lengths per revolution. The gap between the rotor and103.2. Experimental Detailsthe wall was set to 2 mm. The second rotor was a non-industrial, solid-core rotorwith no elements on its surface and was used to provide a steady circumferential flowwithin the screen (i.e. without pulsations). The gap between this rotor and the wallwas 14.5 mm.The primary component of the experimental system is the test coupon whichrepresents the slotted rough wall. All test coupons used in these tests were 50 mmwide. Two coupons with different contour heights were tested (see Figure 3.3 andTable 3.1). The geometry of the rough wall used in this study was modelled onindustrial pulp screen cylinders. The coupons were made from commercial, stainlesssteel, screen cylinder wires. The design of the flow channel is modular so that thetest coupons can be flush-mounted inside the apparatus and replaced easily.The high-speed video camera was placed in front of the screen coupon. Exposuretime was set at 10?20 ?s. Depth of field was less than 1 mm. This allows theexamination of velocity in the flow away from walls of the CSS. The framing rate wasset at 20000?54000 frames-per-second (fps). Thus a fibre moving at 10 m/s in thefield of view would move approximately 0.25 mm between frames and have a blur ofapproximately 12 ?m, which is less than a fibre diameter. A 1000 W halogen lampwas set up at the back of the apparatus. The front cover and a small window onthe back side of the CSS were constructed of 25 mm Plexiglas R? plate. The backwindow was covered by a diffuser for better lighting uniformity. All recorded movieswere converted into grey scale images for further analysis by MATLAB R?. A particleimage velocimetry software (PIVLab) was used to investigate the flow field abovethe rough wall. PIVlab is a MATLAB R? time-resolved particle image velocimetry(PIV) tool. The high-speed camera allows the use of the PIV technique without theneed for specialized lighting. The present approach does, however, require a very113.2. Experimental Detailshigh framing rate (> 50000 fps) resulting in a low image resolution (512?380 pixels).There is a compromise between the camera frame rate and the image resolution. Dueto noise limitations, pulp fines, which are up to 250 ?m in length, were used as seedingparticles. Laser Doppler Velocimetry (LDV) was used to compare the traceability ofpulp fines to Dantec PSP 20 seeding particles by measuring the u component 2 mmabove the coupon with the solid-core rotor. The disagreement between the pulp finesand the seeding particles was less than 1% for rotor speeds up to 20 m/s.Concentration tests were conducted with a very low concentration of 0.03% (30g/100 litres of water) of bleached softwood kraft pulp having an average fibre lengthof 2.5 mm. At such low consistencies, pulp suspensions have the same flow propertiesas water when in a fully turbulent state [20]. The flow velocities in pulp screens aregenerally in the order of 5 m/s and consistency is in the range of 1?3% . Under theseconditions the flow of pulp would be in the turbulent flow regime [17]. Slot velocitiesin the range of 0 to 4 m/s were used in the experiments. Table 3.2 summarizes thetest conditions.Figure 3.2: Schematic diagram of the Cross-Sectional Screen apparatus (CSS).123.2. Experimental DetailsFigure 3.3: Close-up of the wire cross-section at the entry to the slot showing char-acteristic wire dimensionsTable 3.1: Coupon geometryContour type Height, h Wire Width, w Slot Width, s(mm) (mm) (mm)Low 0.6 3.2 0.15High 1.2 3.2 0.15Table 3.2: Experimental test conditionsTest Suspension Rotor Speed, Vt Slot Velocity Vs(concentration) (m/s) (m/s)Flow field fibre fines (0.02%) 5 - 20 0 - 4Concentration bleached kraft pulp (0.03%) 10 - 20 0 - 3133.3. Results and Discussion3.3 Results and Discussion3.3.1 Steady State Flow AnalysisThe flow patterns at the slot entry, including the location of the stagnation pointand height of the exit layer are studied in this section as a function of the contourgeometry, rotor velocity and slot velocity. Figure 3.4 shows the wall geometry forthese tests where a smooth rotor was used to provide a steady circumferential flow.The effect of flow conditions and contour height on vortex size are shown in Figures3.5 and 3.6. The figures show a reduction in vortex size as slot velocity increases,consistent with Gooding [16]. Vortex size also increases with increasing roughness(i.e. increased contour height). This agrees with Mokamati et al. [35]; however, thepresent study suggests a stagnation point closer to the slot entry than they found,which may be a consequence of differences in the channel geometry and the type ofparticles used in the studies. The average velocity between the smooth rotor and thescreen surface, i.e. the upstream velocity, Vu, was found to be proportional to rotorspeed (i.e. Vu ? 40% Vt) but independent of the wall roughness and slot velocity. Thepresence of the side walls at the front and back of the CSS slows the fluid rotationalvelocity with respect to the foil [12].Figure 3.7 shows the effect of velocity ratio (i.e. Vs/Vu) on vortex size. Vortexsize is assessed here by the reattachment distance, d, measured from the edge of theslot entry to the stagnation point on the wall, as shown in Figure 3.4 and normalizedby the wire slope length, L. As expected, the reattachment distance decreases whenslot velocity increases or rotor speed decreases with the two effects being of roughlyequal significance. Figure 3.8 shows the effect of the velocity ratio (Vs/Vu) on exitlayer height, H, normalized by the slot width. Exit layer height is defined as the143.3. Results and Discussionvertical distance from the wall to the exit layer streamline above the wire, i.e. theupper limit of the flow passing from the adjacent wall through the slot. Accordingly,higher slot velocities will increase the exit layer height proportionally for a constantupstream velocity. These results agree with Olson?s [39] and Gooding?s [15] work.While Figure 3.8 shows a fairly linear effect, this relationship is strongly influencedby the data points at high Vs/Vu, (i.e. 2) while a typical range of industrial values isapproximately between 0.1 and 0.3.Circulation, ?, can be calculated by integrating the vorticity within the vortexabove the slot. For a finite area, circulation divided by area gives the average normalcomponent of vorticity in the region. Circulation increases with higher slot andupstream velocities as shown in Figures 3.9 and 3.10. The circulation levels for thehigh and low contours were roughly the same, with the lower contour having highercirculation values in some instances. The significance of circulation in pulp screeningapplications has not been conclusively determined, but it may be that higher levelsof circulation tend to encourage the passage of both fibres and contaminants as wellas discouraging the accumulation of fibres at the slot entry.Appendix A shows the effect of stream-wise and slot velocities on fibre fractiona-tion.Figure 3.4: Smooth rotor-wall flow geometry.153.3. Results and DiscussionFigure 3.5: Slot-entry vortex for a high contour at (a) Vt = 10 m/s, Vs = 1 m/s, (b)Vt = 10 m/s, Vs = 4 m/s, (c) Vt = 20 m/s, Vs = 1 m/s, (d) Vt = 20 m/s, Vs = 4 m/s.Figure 3.6: Slot-entry vortex for a low contour at (a) Vt = 10 m/s, Vs = 1 m/s, (b)Vt = 10 m/s, Vs = 4 m/s, (c) Vt = 20 m/s, Vs = 1 m/s, (d) Vt = 20 m/s, Vs = 4 m/s.163.3. Results and DiscussionFigure 3.7: Vortex stagnation point length.Figure 3.8: Exit layer height (normalized by slot width) versus the ratio of slot velocityand upstream velocity.173.3. Results and DiscussionEfftfFlCiltiEffect?of?Flow?on?Circulation?600040005000Vt = 5 m/sVt = 10 m/sVt = 15 m/sVt=20m/s30004000??A v(1/s)Vt = 20 m/s10002000 000.20.40.60.81V s/VtMG?1232st u511 522.5Figure 3.9: High contour circulation within the vortex as a function of flow ratio.EfftfFlCiltiEffect?of?Flow?on?Circulation?600040005000Vt = 5 m/sVt = 10 m/sVt = 15 m/sVt=20m/s3000??A v(1/s)Vt  20 m/s10002000 000.20.40.60.81V s/VtMG0632st5511.52.52uFigure 3.10: Low contour circulation within the vortex as a function of flow ratio.183.3. Results and Discussion3.3.2 Time-Varying Flow AnalysisThe rotor foil creates a complex flow field near the wall and is thought to impart botha time-varying circumferential flow and a pressure pulsation that, in turn, creates aflow reversal in the slot. Figure 3.11 shows the rotor-wall geometry used for this study.The foil location is used as a reference for all time-varying data. Figure 3.12 shows theregions of interests (ROI) where the dynamic behaviour of the velocity components inthe x direction, u, and y direction, v, are averaged, as well as the reference plane wherespatio-temporal values are assessed. The ROI for the v component is chosen above theslot since velocity components within the slot could not be evaluated experimentallyin this study due to noise and shading effects. While the ROI for the v componentmay lie over part of the recirculating zone, it is assumed that the integrated flowacross the entry to the contour corresponds to the flow through the slot.Figure 3.11: Foil rotor-wall geometry.Figures 3.14?3.16 show that the u component of velocity drops to approximately0.3 of the rotor tip speed under the foil (i.e. at xr/chord = 0.2) before it acceleratesunder the trailing half of the foil. The highest value is seen at the trailing tip of193.3. Results and DiscussionFigure 3.12: ROI?s for u and v components.the foil (i.e. one chord length) and the u-component continues at higher than theaverage stream-wise velocity for up to three chord lengths. The finding that theflow decelerates during the passage of the foil, as shown in Figures 3.14?3.16, meritssome discussion since the passage of the foil is also associated with a decrease inpressure (i.e. a suction pulse). The notion of a decrease in pressure accompanying adecrease in velocity is counter to an intuitive application of the Bernoulli Equation.An explanation for this paradox comes through an understanding of the steady andunsteady forms of the Bernoulli Equation.From a frame of reference set on the foil with the foil moving at a velocity of u1and with a circumferential flow velocity u2 as shown in Figure 3.13a, the apparentvelocity approaching the foil is ?u3. This apparent velocity accelerates to a velocityof ?u4 as the flow passes through the restriction between the foil and screen cylinder.Conservation of mass leads to an increase in velocity of ?u. Following on the steadyform of the Bernoulli Equation [46], and neglecting elevation affects a pressure dropis predicted according to the following equation,(P3 ? P4) = ?u24 ? u232(3.1)203.3. Results and DiscussionFigure 3.13: The flow between the foil and cylinders surface are examined for twoalternate frames of reference: (a) a steady flow problem follows from fixing the frameof reference on the foil, which is moving at u1. The flow between the foil and cylindersurface increases by an amount ?u. (b) An unsteady flow situation results from fixingthe frame of reference to the screen cylinder. The apparent velocity under the rotoris decreased by an amount ?u relative to the general flow velocity.With the same flow conditions, but with the frame of reference set at a locationon the screen cylinder, the apparent velocity under the rotor can be seen to decreasefrom u2 to u5 as shown in Figure 3.13b. While the pressures remain the same (i.e.P3 = P2, P5 = P4), the differences between the under-foil velocities result from thepresence of the integral term in the unsteady form of the Bernoulli EquationP2?+u222+ gZ2 =P5?+u252+ gZ5 +? 52?u?tds (3.2)As discussed previously, values of the u component in Figures 3.14?3.16 are basedon the averages made over the ROI shown in Figure 3.12, where the u componentROI is located at a distance of 0.5 mm from the cylinder surface (i.e. y/Hr = 0.25).A different perspective on the same dataset is given in Figure 3.17, which shows thechanges in the velocity vector field as a function of rotor position. These vector images213.3. Results and Discussionreinforce what was shown in Figures 3.14?3.16, with the velocity being relatively lowas the rotor passes (xr/chord = 0.1) but then rising in the foil wake (xr/chord =1.25). It is useful to understand variations of the u component as a function notonly of xr, but also for a range of distances from the cylinder surface. The powerof the PIV technique used in this study is that it can be used to create databasesthat can generate not only vector plots (such as those shown in Figure 3.17) or plotsdescribing the variation in an averaged flow value (e.g. Figures 3.14?3.16), but thePIV data can also yield the full spatio-temporal description of the flow field, as shownin Figure 3.18(a). In these spatio-temporal plots, the magnitude of the u componentis expressed chromatically not only as a function of xr, but for the full range of y =0 to Hr. In particular, the value of the u component is assessed in Figure 3.18(a) ata series of y values along the reference plane shown in Figure 3.12. To reduce themeasurement noise, averages are taken in the xr-direction over a relatively narrow (0.2mm wide) band for each value of y. To illustrate the connection between the spatial-temporal and line graphs, Figure 3.18(a) and 3.18(b) present two perspectives on thesame dataset. Figure 3.18(a) also includes an illustration of the averaging volume usedfor the purpose of generating Figure 3.18(b) consistent with the methodology shownin Figure 3.12. Figure 3.18(b) is the result of the averaging process, comparable toFigure 3.15, albeit over a smaller range of xr/chord. The finding remains the same:illustrating a fairly constant value of the u component of velocity ahead of the foil(i.e. for negative values of xr/chord), then a drop in velocity with the passage offoil and acceleration in the wake. Figures 3.19-3.22 show similar spatio-temporalplots of the u component (normalized by Vt) for a range of rotor tip and average slotvelocities. In general, the value of u/Vt is seen to drop to below 0.3 in the gap underthe rotor, consistent with Figures 3.14?3.16. These figures also show the acceleration223.3. Results and Discussion(i.e. increasing u) that takes place under the trailing half of the rotor foil (xr/chordbetween 0.5 and 1). The degree of acceleration near the wires (i.e. y/Hr < 0.1) issmaller in comparison to the flow behind the rotor in the mainstream where suctionhas less effect on the stream-wise flow.Changes in the v component of velocity for different rotor and slot velocitiesand high and low contours are shown in Figures 3.23?3.24. These figures show thatreversal flows (i.e. periods of positive v component values) are supported with highrotor speeds and low average slot velocities. For the high contour and Vt = 20 m/s(Figure 3.23), the reversal flow starts at xr/chord ? 0.5 for Vs = 1 m/s and lastsfor ? 1.5 chord lengths. When the slot velocity is increased to 4 m/s, the reversalflow is relatively unchanged in absolute terms, but is naturally much smaller wheninstantaneous v component is normalized by the average slot velocity, Vs. When rotorspeed is reduced (Figure 3.24), the flow reversal is seen to disappear when slot velocityis increased from 1 to 4 m/s. The implication for an industrial screen application isthat plugging of the slots may become more problematic when rotor speeds are lowand slot velocities are high, as is commonly reported. Note that the v component isapplied through a ROI that is 2.75 mm wide versus the 0.15 mm slot width where Vsis calculated. Thus a Vs of 4 m/s corresponds to an average value of v = - 0.22 m/s,which is consistent with the values seen in Figures 3.23 and 3.24.The existence of a pressure (suction) pulse associated with the passage of a rotorfoil has been shown in many studies ([45], [14], [27], [7], [37]). Theoretical studies,using computational fluid dynamics ([11], [12], [50], [10]) have also shown that theacceleration of flow under the foil gives rise to a suction pulse, but these studieswere done either with a solid or highly-simplified model of the porous cylinder wall.In general, most of these studies have associated pressure pulse signature with an233.3. Results and Discussionimmediate flow reversal without taking into consideration the conservation of a con-fined mass passing through the slot between the rotor and the screen surface, whichcould explain the discrepancy with the results shown in Figures 3.23?3.24, where thebackflush flow is delayed slightly.Based on the above results, Figure 3.25 shows the cases where reversal flow occurs.It was experimentally shown by Gonzalez [14] that the magnitude of pressure pulsesdecreases as the consistency increases. Moreover, the presence of the side walls at thefront and back of the CSS slows the rotational velocity of the fluid relative to the foil.The increased relative velocity would account for higher pressure pulses [12]. Giventhe low consistency used in these tests and the lower fluid velocity relative to the foil,this figure represents the largest possible backflushing region for this particular rotor.An investigation of the velocity changes along the contour surface is also of interest.A velocity, Vd, along the contour surface was defined in Figure 3.11 and measured asa function of rotor position for both contours at different flow conditions as shown inFigures 3.26 and 3.27. Of particular interest is the location of the stagnation point(Vd = 0) which is relatively close to the slot entry (xd/L ? 0.2) for both contourheights and does not move significantly with the passage of the rotor ? even whenthere is flow reversal.The uncertainty of the PIV measurements is mainly caused by the techniquerandom error and the setup systematic error. The highest relative uncertainties ofthe velocity above the wires and within the vortex with 95% confidence intervalswere ?6.6% and ?16.4%, respectively. The higher uncertainty within the vortexwas expected as rotation and shear can be a large source of uncertainty in PIVmeasurements [47]. Details of PIV uncertainty analysis is shown in Appendix B.243.3. Results and DiscussiontrFigure 3.14: u component for low contour at Vt = 15 m/s and Vs = 1 m/s.Figure 3.15: u component for high contour at Vt = 20 m/s and Vs = 1 m/s.Figure 3.16: u component for high contour at Vt = 20 m/s and Vs = 2 m/s.253.3. Results and DiscussionFigure 3.17: Rotor position in terms of chord length.263.3. Results and DiscussionFigure 3.18: The spatio-temporal description of the u-component in the flow fieldfor the high contour (Vt = 20 m/s, Vs = 1 m/s) is shown above (a) along with themeasuring volume (in yellow) used for averaging. The lower plot (b) is the associatedaveraged flow for the u-component.273.3. Results and Discussionxr / chordy / Hr  ?1 0 1 2 3 4 500.20.40.60.81u/V t00.20.40.60.81Figure 3.19: Spatio-temporal behaviour of u component for high contour surface atVt = 10 m/s, Vs = 1 m/s.xr / chordy / Hr  ?1 0 1 2 3 4 500.20.40.60.81u/V t00.20.40.60.81Figure 3.20: Spatio-temporal behaviour of u component for high contour surface atVt = 10 m/s, Vs = 3 m/s.283.3. Results and Discussionxr / chordy / Hr  ?1 0 1 2 3 4 500.20.40.60.81u/V t00.20.40.60.81Figure 3.21: Spatio-temporal behaviour of u component for high contour surface atVt = 20 m/s, Vs = 1 m/s.xr / chordy / Hr  ?1 0 1 2 3 4 500.20.40.60.81u/V t00.20.40.60.81Figure 3.22: Spatio-temporal behaviour of u component for high contour surface atVt = 20 m/s, Vs = 3 m/s.293.3. Results and Discussion0 6-0.4-0.200.20.40.60.8v (m/s)Vt= 20 m/s, Vs = 1 m/sVt= 20 m/s, Vs = 4 m/s-0.8- .-1 0 1 2 3 4 5 6 7 8 9 10xr/chordFigure 3.23: v component for high contour at Vt = 20 m/s.0 8.0 6 V 10 / V 1 /t= m s s = m s.   ,    0 4 V 10 / V 4 /t= m s s = m s.   ,    0 2.00 2- .0 4- .0 6- .0 8- . 1 0 1 2 3 4 5 6 7 8 9 10- / h dx c orrFigure 3.24: v component for low contour at Vt = 10 m/s.303.3. Results and DiscussionFigure 3.25: Reversal flow boundary.313.3. Results and Discussionxr / chordx d / L  ?1 0 1 2 3 4 500.20.40.60.81V d / V u?0.200.20.40.6Figure 3.26: Spatio-temporal behaviour of Vd for low contour surface at Vt = 10 m/s,Vs = 1 m/s.xr / chordx d / L  ?1 0 1 2 3 4 500.20.40.60.81V d / V u?0.200.20.40.6Figure 3.27: Spatio-temporal behaviour of Vd for high contour surface at Vt = 20 m/s,Vs = 1 m/s.323.3. Results and Discussion3.3.3 Fibre Concentration AnalysisThe dynamic change of pulp concentration near the screen surface was also studiedfor dilute (0.03%) pulp suspensions. In contrast to the PIV studies, kraft pulp fibresrather than pulp fines were used for the fibre concentration tests. As a first step,the relationship between fibre concentration and light intensity was determined bymeasuring the average light intensity over 1000 frames for an area away from the slotentrance. At this remote location, the local fibre concentration could be assumed tobe equal to the feed concentration. For calibration purposes, a smooth rotor was usedand the tip speed was set at 10 m/s with no flow through the slot. Figure 3.28 showsthe associated calibration curve, with a linear relationship between light intensityand concentration. A foil rotor was then introduced to study the variations in fibreconcentration. Two regions of interest were chosen for concentration analysis: Thefirst region was between the rotor and the screen surface (?above screen? region), andthe second region is in the discharge flow from the slot (?slot discharge? region) asshown in Figure 3.29.Concentration as a function of flow for the high contour screen coupon is shown inFigure 3.30. Local concentration values were normalized by the average concentrationof the region, Co, above the screen surface at Vt = 10 m/s and Vs = 0 m/s. A numberof interesting observations can be made: First, one can see that the ?above screen?concentration is slightly (10%) above the mainstream concentration and this effect isseen fairly consistently for various Vt and Vs. This may be because of the withdrawalof fluid through the slotted surface with a lower concentration of fibres. The fibresthat do not pass through the slots enrich the flow adjacent the screen surface slightly.The concentration in the slot exhaust region shows more complex influences. Atthe lower tip speed (10 m/s), the slot exhaust flow is slightly depleted of fibres at333.3. Results and DiscussionR ? = 0.9940.40.60.81alized Light Intensity 00.20.05 0.1 0.15 0.2 0.25NormaFib er concentration (g/litre)Figure 3.28: Light intensity as a function of fibre concentrationFigure 3.29: High contour concentration ROI?s343.3. Results and Discussionthe lowest slot velocity (1 m/s), as one would expect from the aforementioned ?walleffect?. Likewise, it follows from various fundamental screening studies [[18], [31],[41]] that concentration should increase with slot velocity, which is seen here. At thehighest slot velocity (3 m/s; Figure 3.30(c) the concentration was found to be higherthan the ?above screen? concentration, which suggests that the higher slot velocityhas eliminated the influence of the wall effect and fibre trapping may have boostedthe consistency within the slot entrance.At the higher, and more typical, rotor speed (20 m/s) the effects are similar,as shown in Figure 3.30(d)?3.30(f), but a low-consistency zone of that is relativelydeplete of fibres is now apparent one to two chord lengths behind the rotor foil, whichmay be an important and beneficial factor in ensuring reliable screen capacity. Thisdepletion may occur because of larger flow structures in the wake of the foil combinedwith some degree of backflushing through the slot.353.3. Results and Discussion?1 0 1 2 3 4 5 6 7 8 90.7511.25xr/chordC/C o?1 0 1 2 3 4 5 6 7 8 90.7511.25?1 0 1 2 3 4 5 6 7 8 90.7511.25?1 0 1 2 3 4 5 6 7 8 90.7511.25?1 0 1 2 3 4 5 6 7 8 90.7511.25?1 0 1 2 3 4 5 6 7 8 90.7511.25(e)(f)(a)(b)(c)(d)--- Above screen ROI --- Slot exhaust ROI Figure 3.30: Concentration for high contour: (a) Vt = 10 m/s, Vs = 1 m/s, (b) Vt =10 m/s, Vs = 2 m/s, (c) Vt = 10 m/s, Vs = 3 m/s, (d) Vt = 20 m/s, Vs = 1 m/s, (e)Vt = 20 m/s, Vs = 2 m/s, (f) Vt = 20 m/s, Vs =3 m/s.363.4. Summary and Conclusions3.4 Summary and ConclusionsThe flow field near a rough slotted surface in steady and time-varying cross-flow wasstudied experimentally for different degrees of roughness and different upstream andaperture velocities. While this problem is of general interest, the present study wasmade in the context of the flow of a fibrous suspension in a pulp screen. Particle-image velocimetry was used in this study to measure the flow patterns near theslotted surface. The size of the vortices within the roughness contours was foundto be dependent on the geometry of the contours and the flow velocities. Vorticesincrease in size with lower aperture velocities and higher contour heights. This studyalso considered the flow through slots in the slotted surface. The height of the exitlayer that passes from the main flow through the slotted apertures was found toincrease with slot velocity.For the dynamic studies, the stream-wise flow decelerates under the leading edgeof the rotor before it increases under the trailing half of the rotor then gradually dropsto an average value that is independent of slot velocity. A flow reversal was observedin some, but not all, of the flow configurations.Studies of fibre concentration showed that the concentration within the contourswas generally (but not always) lower than in the flow above the screen surface. Thisis consistent with published mechanisms of fibre motion near a bifurcating flow. Azone with reduced fibre concentration was observed in the wake of the rotor foil. Thismay be industrially significant in avoiding the blockage of the apertures with fibres,though the reversal flow through the slot and turbulent flows in the wake of the foilare also believed to be important in avoiding aperture blockages.This study provides a number of insights into this complex and important flowproblem of unsteady flow adjacent to a rough slotted wall. It builds on previous373.4. Summary and Conclusionsstudies to elucidate mechanisms related to the flow resistance of the flow throughthe slotted wall and the potential for the apertures in the wall to be obstructed withfibres carried in the flow.38Chapter 4Maximum Capacity of a PilotPressure Screen4.1 IntroductionThe objective of the work presented in this chapter is to investigate the factors af-fecting the capacity of fibre suspension pressure screens. The capacity of the screenis defined in this work as the maximum throughput before the apertures permanentlyplug with pulp. Throughput, in turn, is represented by slot velocity, Vs, which isthe key process variable driving throughput. Maximum slot velocity is a functionof feed fibre length, feed consistency, screen plate aperture size and geometry, rotorspeed and rotor type. Although many studies have been conducted to understand thefactors affecting the performance of pulp screens, only a few were focused on factorsaffecting the capacity of screening,([34], [17], [33], [25], [22]).Niinimaki [36] categorized the matting of fibres on the inner surface of the screenand pulsations by the foils as macro phenomena, and the hydrodynamic forces ex-erted on the fibres and fluidization due to turbulence on the screen surface as microphenomena. Halonen et al. [21] defined fluidization as a process of loosening fibrecontacts inside flocs. Fibre suspension can display fluid-like behavior that may justifi-ably be called fluidized under certain circumstances. This occurs in turbulent regime394.1. Introductionand, in this state, the suspension can be assigned a viscosity and otherwise followsthe laws of fluid mechanics [2]. By using contoured screen cylinders, the turbulenceconditions on the screen surface are improved and fluidization can extend the effectinduced by the rotor, [13]. It is widely believed that rotor pulses disrupt the fibremat and lift trapped particles away from the screen apertures, [36].Martinez et al. [33] introduced a screen capacity model by assuming that screenblinding limits volumetric capacity and that blinding occurs when a fibre floc becomesimmobilized in a screen slot. The essential analysis was a force balance on a singlefloc in a slot with the forces arising from the flow through the slot, friction of the flocagainst the slot wall, and the rotor pulsation. However, this model does not embracemany of the complexities of screen operation such as fibre trapping and rotor wakeeffects.Hamelin et al. [22] conducted a series of pilot screening trials for a range of foilconfigurations. For each rotor configuration tested, the maximum slot velocity-powercurve was determined by setting the rotor speed to a constant value and increasingthe slot velocity until the onset of plugging. The point of maximum slot velocityversus rotor power, creates a failure envelope (or maximum slot velocity envelope) foreach rotor and is used to compare the performance of various configurations.The mechanism of plugging is still not clear. This study examines the factorsaffecting maximum capacity from a macroscopic level and theorises a simple pluggingmodel that can be used in future work to understand screen capacity.404.2. Experimental Details4.2 Experimental DetailsThis work studies the effect of screen cylinder geometry and pulp properties on ca-pacity. The experiments were conducted at the Pulp and Paper Centre, UBC witha Beloit MR8 laboratory pressure screen, shown in Figure 4.1. The MR8 is 212 mmin diameter and is equipped with a variable frequency drive (VFD) to control therotor speed up to 20 m/s. An AFT EP foil rotor was used for all trials and the rotor-cylinder gap was kept at 4 mm. The pulp is supplied from a 1500 L tank through afeed port. The reject and accept streams are returned to the feed tank. Pulp tem-perature was maintained constant at a nominal value of 40 oC by the virtue of a 5kW electric heater attached to the feed tank. The pulp feed consistency, CF , was alsomonitored and kept constant throughout every test. To prevent the reject line fromplugging, the reject volumetric rate, Rv, for most tests was fixed at 20% .Five screen cylinder designs which differed in slot width and wire type were tested.Table 4.1 shows the cylinders and their geometric configurations. The cylinder openarea varies greatly with the slot and wire widths, which then calls for large changes inpumping rates to maintain the specific slot velocity. Due to limited pumping capacityof the loop, the cylinders? open area was modified by blinding part of the cylinder?sopen area. Also, it was found in preliminary tests that the first segment of the cylinderwas plugged even when all other segments were clear. This is thought to be becauseof insufficient acceleration of the tangential velocity of the pulp adjacent to the screencylinder and that the pulp is not fluidized, [1]. Blinding of the initial segment of thecylinder is also thought to reduce the influence of this artefact. Figure 4.2 showsthe blinding procedure. To minimize the effect of feed flow on screen performance,the difference in open area for different cylinders was minimized by blinding the firstand last spools for most cylinders (Type A-D) and the first spool only for the Type414.2. Experimental DetailsFigure 4.1: The UBC MR8 pilot pressure screen.E cylinder. The number of blinded spools was limited to two in order not to affectthe thickening behaviour over the cylinder?s axial length. The effects of consistency,reject rate and contaminant content were also studied in these tests. The pulp usedfor most tests was a mix of 50/50 hardwood/softwood kraft pulp to simulate a de-ink, kraft pulp [26]. The ratio of hardwood/softwood was also changed to study theimpact of fibre length on maximum capacity.Trials were conducted by reducing the rotor speed, Vt, at constant slot velocity,Vs, until the screen plugged. The slot velocity was then increased and the procedurewas repeated. A plugging envelope for the minimum rotor speed was generated fordifferent cylinders, pulp types and consistencies. It was found that the minimumrotor speed needed to prevent plugging was repeatable within ? 0.2 m/s and theerror associated with the measured values was small enough to be neglected.424.2. Experimental DetailsTable 4.1: Screen wire geometriesCylinder Designation Contour Height Wire Width Slot Width Open Area(mm) (mm) (mm) (m2)A 1.2 3.2 0.15 0.00453B 0.9 3.2 0.15 0.00453C 0.6 3.2 0.15 0.00453D 0.6 2.3 0.15 0.00619E 0.6 3.2 0.10 0.00482Figure 4.2: Screen open area blinding procedure: (a) wrapping the spool with rubberstrip and (b) securing the strip with a stainless steel clamp to prevent leakage fromthe spool edges.434.3. Results and Discussion4.3 Results and Discussion4.3.1 Effect of Consistency on CapacityThe effect of pulp consistency is discussed in this section. Figure 4.3 shows the plug-ging envelope for the Type B cylinder. This figure merits special attention inasmuchas it illustrates the essential topic of this thesis study. The zone to the right of theline represents the normal operating zone of a pulp screen, while plugging occurs tothe left. The dividing line shown in the figure thus represents screen capacity for aparticular furnish and screen configuration. As pulp consistency increases, the rotorspeed needed to prevent plugging at the same slot velocity also increases. At 2.0%consistency, tests were conducted only at slot velocities greater than 1.5 m/s due toreject line thickening issues. This graph also reinforces some valuable findings:? Linearity: The relationship between Vs and Vt is remarkably linear, which leadsto the proposal of a simple capacity equation ofV ?s = C1 + C2 Vt (4.1)This Equation suggests that plugging occurs when Vs > V ?s . C1 and C2 arecharacteristic capacity constants.? Parallelism: Another significant feature of Figure 4.3 is that the slopes of thelines, C2, are relatively similar and difference occurs mainly on the offset ofthese lines, C1, as shown in Figure 4.4. Indeed if one plots the x-intercepts ofthe lines, (?C1/C2, which is equal to V ?t ), as a function of consistency (Figure4.5), one is reassured by the suggestion that at 0% consistency, there is no offset.444.3. Results and Discussion? Threshold Rotor Speed: It follows from Figure 4.5 that a minimum rotor speed,V ?t , must be attained to obtain any significant capacity. Moreover, a morechallenging application, (i.e. a high consistency, increased presence of longfibre, narrow slots) would require a stronger / more frequent rotor action andhigher threshold rotor tip speed.By comparing the reversal flow envelope, Figure 3.25 with the plugging envelopefor the Type B screen cylinder, one can see that the screen is running at a regionwhere no reversal flow is present, suggesting other mechanisms that maintain thescreen operation. For example, at CF = 1% and V ?s = 2 m/s, Vt ? 8.5 m/s in Figure4.3 while Figure 3.25 suggests reversal occurs for Vt between 10 and 15 m/s. Whilethe screens are not the same, the reversal flow pressure pulses generated by the CSSrotor are in fact greater than those generated by the MR8 rotor running at the samespeed for the following reasons:? Smaller foil-screen surface gap for the CSS tests.? Higher angle of attack for the CSS foil (0o for the MR8 rotor).? Water was used for the reversal flow test but the plugging envelope zone wasproduced with 1.0% pulp.? The presence of front and back walls in the CSS tests reduced the relativevelocity of the fluid with respect to rotor speed, creating higher pressure pulsesfor its rotor.It is also found that the pressure difference across the screen, i.e. the pressuremeasured in the feed line to the screen minus the pressure in the accept line, increaseswith slot velocity and pulp consistency, as shown in Figure 4.6.454.3. Results and Discussion00.511.522.533.544.54 6 8 10 12 14 16V s(m/s)Vt (m/s)C = 0.5% C = 1.0%C = 1.5% C = 2.0%Operational ZonePlugging ZoneFFFFFigure 4.3: Plugging envelope for Type B cylinder at different consistencies, (50/50hardwood/softwood mixture).00.511.522.533.544.50 2 4 6 8 10 12 14 16V s(m/s)Vt (m/s)C = 0.5%C = 1.0%C = 1.5%C = 2.0%FFFFFigure 4.4: The extrapolated Vs-Vt relationship of Figure 4.3.464.3. Results and Discussiony = 4.37x - 0.075R? = 0.998701234567890 0.5 1 1.5 2V t*(m/s)CF  (%)Figure 4.5: The x-intercepts of the extrapolated Vs-Vt relationship of Figure 4.4 isplotted against consistency suggesting that there would be no offset when there areno fibres in the suspension (CF = 0%).0204060801000 1 2 3 4 5DP (kPa)Vs (m/s)waterC  = 0.5%C = 1.0%C = 1.5%C = 2.0%FFFFFigure 4.6: Pressure difference across Type B screen cylinder prior to plugging at arange of slot velocities (50/50 hardwood/softwood mixture).474.3. Results and Discussion22.533.544.55Power (kW)Vs = 1 m/sVs = 4 m/s00.511.50 5 10 15 20 25PVt (m/s)Figure 4.7: Power consumption by the rotor as a function of rotor speed at differentslot velocities (CF = 0%).4.3.2 Effect of Feed Flow Rate on CapacityThe first trial to evaluate the effect of flow rate on power consumption was conductedwith water. Figure 4.7 shows the power consumed by the rotor for different slotvelocities. Higher slot velocities are naturally associated with higher feed rates atthe same reject rate. Higher feed rates increase the tangential velocity within thescreen and reduces the power consumed by the rotor. However, a higher tangentialflow, which is created here with higher Rv, also reduces the relative flow velocity withrespect to rotor speed causing reduced pulse strength and plugging of the cylinder ata higher Vt, as shown in Figure 4.8. This behaviour was previously observed by Delfelet al. [9]. They showed that a three-foil rotor reduces the capacity of a cylinder withrespect to two-foil rotor as it increases the circumferential (swirl) flow velocity withrespect to rotor speed.484.3. Results and Discussion1.522.533.54V s(m/s)Rv = 0.15Rv = 0.25Rv = 0.35Rv = 0.4500.514 6 8 10 12 14Vt (m/s)Figure 4.8: Effect of reject rate on plugging envelope for the Type B screen (100%softwood suspension with 1.0% consistency).4.3.3 Effect of Pulp Properties and Contaminants onCapacityThe influence of pulp properties was assessed by mixing softwood and hardwoodkraft pulp in different ratios (see Appendix C for more details). Figure 4.9 shows theplugging envelope for the Type B cylinder. The figure shows the linearity betweenrotor speed and slot velocity. Average fibre length is seen to have a large impact onthe plugging envelope. As the average fibre length increases, (i.e. as the softwoodratio increases) the rotor speed needed to prevent plugging becomes higher. Figure4.10 shows the pressure difference across the cylinder immediately prior to plugging.It is significant that for the same slot velocity, the pressure difference across thescreen does not change with pulp type; nevertheless, the rotor speed needed to preventplugging does increase with increasing softwood ratio. This indicates that an increased494.3. Results and Discussionnegative pressure pulse is required for increasing softwood concentrations which maybe because the softwood creates stronger incipient blockages (softwood has a higheryield stress [6]). For example, at 3 m/s slot velocity and 100% softwood pulp, thenegative pressure pulse associated with the rotor minimum speed is 45% greaterthan the negative pulse needed at the same slot velocity but with 100% hardwoodsuspension.The effect of contaminants on capacity was also studied given that contaminantslevels can be high, for example, in recycled pulp. Mill debris, i.e. heavily contam-inated material gathered from the rejects of third stage of OCC screen, was addedto a 1.5% 50/50 hardwood/softwood pulp blend and the minimum rotor tip speed tomaintain reliable screen operation was assessed. The mass of the debris with respectto the mass of the pulp was gradually increased, but no significant effect was foundon capacity. The minimum rotor tip speed was, however, sensitive to the additionof cubical polyethylene specks but even a very high (2%) loading level led only to amodest increase in rotor speed (Figure 4.11). One explanation for the increased Vtis the reduction in cylinder open area which, in turn, increases the slot velocity andcauses early plugging. Figure 4.12 shows an increase in pressure difference with anincreased specks concentration, which results from the higher slot velocity and smalleropen area. The other explanation is a faster accumulation of fibres on the pluggedspecks that leads to faster plugging. The specks ranged in size, but were mostly inthe range of 0.05 to 0.3 mm in nominal diameter, as shown in Figure 4.13.4.3.4 Effect of Cylinder Geometry on CapacityThis section focuses on the effect of screen cylinder geometry on maximum capacity.Figure 4.14 shows the effect of contour height on the plugging envelope for three504.3. Results and Discussion00.511.522.533.544.554 6 8 10 12 14 16V s(m/s)Vt (m/s)(0:100) SW:HW(25:75)(50:50)(75:25)(100:0) Generated by Foxit PDF Creator ? Foxit Softwarehttp://www.foxitsoftware.com   For evaluation only.Figure 4.9: Plugging envelope for the Type B screen using different soft-wood/hardwood ratios, CF =1.0%.406080100?P (kPa)(0:100) SW:HW(25:75)(50:50)(75:25)(100:0) 0200 1 2 3 4 5Vs (m/s)Figure 4.10: Pressure difference across the Type B cylinder for different soft-wood/hardwood ratios, CF = 1.0%.514.3. Results and Discussion6810121416V t(m/s)0240 2 4 6 8 10 12 14mass of debris/total solid mass (%)Mill DebrisPlastic specksFigure 4.11: Minimum rotor tip speed for the Type B screen at different contaminantratios (50/50 hardwood/softwood mixture, CF = 1.5%) Vt = 2 m/s.152025303540?P (kPa)05100 2 4 6 8 10 12 14mass of debris/total solid mass (%)Mill debrisPlastic specksFigure 4.12: Pressure difference across the Type B screen at different contaminantratios, (50/50 hardwood/softwood mixture, CF = 1.5%.524.3. Results and DiscussionFigure 4.13: Plastic speck diameter distribution.different cylinder types. As reported in industry, increased contour height increasescapacity at lower slot velocities, but the benefit of increased contour height appearsto disappear, or at least to be substantially diminished, in the range of industrialinterest (i.e. above 12 m/s). This lack of benefit is somewhat surprising, but it maybe that the contour height is of significant benefit at low rotor speeds (as shownin Figure 4.14) and higher consistencies due to increased turbulence that results inthe flow field above the cylinder surface that the relative importance of this effectdiminishes with higher slot velocities. The overall pressure difference was not foundto change with contour height as shown in Figure 4.15.Tests also were conducted with different cylinder slot and wire widths. The plug-ging envelopes for Types D and E cylinders are compared with Type B are shownin Figure 4.16. The open area for Type D cylinder is larger than other cylinderswhich requires higher feed flow rate for the same slot velocities. This figure shows534.3. Results and Discussion22.533.544.5V s (m/s)Typ e ATyp e BTyp e C00.511.54 6 8 10 12 14 16Vt (m/s)Figure 4.14: Effect of contour height on the plugging envelope. The contour heightsof the Type A, B and C screen cylinders is 1.2 mm, 0.9 mm and 0.6 mm, respectively.(50/50 hardwood/softwood mixture, CF = 1.5%).5060708090?P  (kPa)Ty p e ATyp e BTyp e C2030400 1 2 3 4 5Vs (m/s)Figure 4.15: Pressure difference across cylinders, (50/50 hardwood/softwood mixture,CF = 1.5%).544.3. Results and Discussion22.533.544.5V s(m/s)00.511.54 6 8 10 12 14 16Vt (m/s)Type ETyp e DTyp e BFigure 4.16: Effect of wire width and slot width on plugging boundary, (50/50hardwood/softwood, CF = 1.0%). Type B: 0.9 mm contour height/3.2 mm wirewidth/0.15 mm slot width. Type D: 0.6 mm /2.3 mm/0.15 mm. Type E: 0.6 mm/3.2 mm/0.10 mm.that relative to the Type B cylinder, the shallower contour and narrower wire of theType D cylinder leads to reduced capacity. Looking back at Figure 4.14 one sees thatthe contour height has limited influence on capacity. The impact of wire width maycome from a narrower slot ?pitch? (i.e. the distance between slots). This is likely dueto the presence of the softwood pulp and potential for slot-to-slot stapling given thatover 60% of the fibre mass are candidates for stapling, which is far above the levelsat which stapling is expected to occur [17].The effect of the narrow slot is seen for the Type E cylinder. Capacity is substan-tially reduced, which is likely a consequence of fewer fibres being required to fill theslot to create a blockage.554.4. Summary and Conclusions4.3.5 Effect of Rotor and Slot Velocity on RejectThickeningRotor and slot velocities have a significant impact on accept and reject consistencies.To study this effect, reject and feed samples were collected for the Type A screencylinder at different slot velocities to evaluate thickening behaviour. Thickening fac-tor, T , is defined as the reject consistency divided by the feed consistency. Samplecollection started at a higher rotor speed and stopped just before screen plugging.Figure 4.17 shows the thickening behaviour of 1.0% feed consistency pulp as rotorspeed was reduced for two slot velocities. Thickening factor is fairly constant at higherrotor speeds but below ? 12 m/s, T starts to increase linearly with reduced rotorspeed. It may be that at higher rotor speeds, the reversal flow dilutes the pulp abovethe screen cylinder. When the rotor speed decreases, water reversal decreases andhigher consistency results. It may also be that at lower rotor speeds, the incipientblockages are not completely cleared by the rotor, resulting in an effectively narrowerslot and reduced fibre passage. Higher slot velocity also means more fibre passagethrough the screen slots as reported in the fundamental studies of Gooding [15] andKumar [31]. Due to reject line thickening, this test could not be easily conductedwith higher consistencies or lower slot velocities.4.4 Summary and ConclusionsPilot screen experiments with different screen cylinders and pulp combinations wereconducted to show the effect of common industrial variables on the maximum capacityof a pressure screen.Feed consistency and fibre length were found to have very significant influences564.4. Summary and Conclusions1.61.822.22.4TVs = 1 m/sVs = 2 m/s11.21.46 8 10 12 14 16Vt (m/s)Figure 4.17: Thickening of pulp with rotor and slot velocity changes (Type A screen,CF = 1.0%, 50:50 SW:HW).on capacity. Contaminants had a very limited effect. A higher contour was found todelay plugging but this effect was limited to low slot velocities. Slot width and wirewidth had significantly more influence on capacity.The results leads to an appreciation of two regimes of screen operation: (1) aplugging zone, below the threshold rotor speed, V ?t and (2) an operational regime,where there are appreciable slot flows with appreciable fibre concentrations. Theboundary between these two regimes is relatively linear and is described by thresholdvalues of V ?s and V?t (Equation 4.1).A particular cylinder and pulp combination led to some estimates of the constantsleading to the equation:V ?s = 0.5Vt ? 2.2CF (4.2)Valid for 0.5 ? C ? 2%, 0 ? Vs ? 4 m/s and 0 ? Vt ? 16 m/s.574.4. Summary and ConclusionsFuture studies may be directed to a more comprehensive examination of the con-stants of Equation 4.1 as well as the influence of different rotor types. The linear formof Equation 4.1 suggests a relatively simple fundamental model may drive capacity.58Chapter 5New Model for Pressure ScreenCapacity5.1 IntroductionThe capacity of a pulp screen is defined as the maximum throughput before the aper-tures become plugged with pulp. Capacity is a function of fibre length, consistency,aperture size and geometry, rotor speed and rotor type ([34], [17], [33], [25], [8]).Various experimental and computational studies have been conducted to understandthe performance of pressure screening in terms of fibre passage and debris removalefficiency. Relatively little is known, however, about the fundamental aspects of ca-pacity.A new approach is introduced here to understand the maximum capacity of a pulppressure screen. The model is based on the concept of trapped fibres accumulatingon the cylinder slot edge which in turn leads to plugging. The lodged fibres onthe slot edge continue to build up when there are no changes in the tangential flowfield above the cylinder surface. These changes delay the accumulation for a certainperiod of time of the rotor cycle. If the accumulation continues beyond a certainthreshold value, cylinders plug immediately. The model introduced complements theeffect of the reversal flow on fibre accumulation. Indeed while this work defines and595.2. Mathematical Model Detailsanalyses some fundamental mechanisms that govern capacity, a comprehensive modeland rigorous validation remain beyond the scope of this study.5.1.1 Visual Observation of Fibre Motion Near the ScreenSurfaceThe motion of individual fibres near the low contour coupon using CSS was examined.Figure 5.1 shows the accumulation of a dilute suspension fibres on the down streamedge of a slot. When the rotor approaches the slot (Figure 5.1(b)), trapped fibresremain on the edge and only start dislodging when the flow at the trailing edge of therotor accelerates, not because of the rotor negative pulse (Figure 5.1(c/d)). The slotedge remains clear of any accumulation of fibres (Figure 5.1(e)) until the tangentialflow velocity drops to a certain value when accumulation starts again (Figure 5.1(f)).It is believed that the same behaviour takes place in real applications, even thoughthe consistency is much higher. The linearity and similarity in plugging envelopes(shown in Chapter 4) supports the application of this concept to include a wide rangeof fibre concentrations.5.2 Mathematical Model DetailsThe effect of the flow field on the forces applied on pulp fibres and consequently theireffect on capacity is studied herein. The experimental data used for this model arepresented in detail in Chapters 3 and 4. The model considers a force balance on alodged fibre on the downstream edge of the slot that prevents this fibre from moving.The fibre continues to be lodged as long as this force difference is lower than thefrictional force generated between the fibre and the wire surface. In order to assess605.2. Mathematical Model DetailsFigure 5.1: Fibre trapping and clearing by rotor, Vt = 5 m/s and Vs = 3 m/s. (a)xr/chord = -1.0, (b) xr/chord = 0.35, (c) xr/chord = 0.6, (d) xr/chord = 1, (e)xr/chord = 1.35, (f) xr/chord = 4.0.these forces, an accurate drag coefficient estimate at moderate Reynolds number isneeded. Vakil and Green [49] studied the flow around two-dimensional cylinders atmoderate Reynolds numbers, 1 ? Re ? 40. They presented the drag, CD and lift, CL,coefficients as best curve fits to computational data. They also showed that the aspectratio Lf/D of the fibre-like cylinders has no significant effect on the drag coefficientfor Lf/D > 10. Their fitted data were used in this study to measure the total forceson fibre portions above and within the slot. The drag coefficient is calculated based615.2. Mathematical Model Detailson the following equationCD = CD,?(A2 cos(2?) + A0) (5.1)in whichCD,?(Re, Lf/D) = ?1R?2e (5.2)andRe =?VdD?(5.3)where ? is the angle between the flow and the fibre (and assumed to be 0o in thisstudy). Details of the parameters A0, A2, ?1, and ?2 can be found in Vakil and Green[49]. Analysis of the screen slot flow field confirms that the Re values are generallywithin the range specified by Vakil and Green, with Re equal to 15 at a slot velocityof 1 m/s and 45 for a slot velocity of 3 m/s.In this study, the possibilities of a 3mm fibre remaining immobilized (or ?trapped?)on the wire surface were studied. Assuming a fibre diameter, D, of 0.015 mm, thefibre was divided into 20 segments to keep the Lf/D ratio = 10. These forces theninterpolated to examine the possibility of 300 landing positions of a fibre on the wireedge.To evaluate fibre friction on a curved surface, Vakil and Green [48] comparedthe fibre model with the Capstan Equation either in the classical or modified form(see Jung et al. [28]). The simple form of the Capstan Equation provides the ratioof tension on the tauter side to the slacker side of a rope wrapping a cylinder asa function of the coefficient of friction and the wrap angle. Though the equationis derived for a continuous rope, they model such a system with a finite number ofsegments in their discrete approach. Generally speaking, they were able to match the625.2. Mathematical Model DetailsFigure 5.2: Tension on a fibre trapped on wire edge.fibre model simulations with the Capstan Equation for low values of the coefficient offriction and wrap angle. The same approach was adopted here; the average flow fielddata were measured previously over different contour heights in Chapter 3. Figure5.2 shows the tension forces and the contact angle between the fibre and the wireedge.A Matlab code was developed to estimate the tension on a fibre portion above andwithin the slot by using the steady-state flow field data generated by a smooth rotor,(Section 3.3) with the low contour. Velocity vectors parallel to the trapped fibre wereused to calculate drag forces on each segment. It was found that the tension on thefibre portion above the slot, Tu, is not strongly affected by the slot velocity, Vs, asshown in Figures 5.3 and 5.4. It was possible, therefore, to formulate the tensionabove the slot solely as a function of the stream main velocity component, u, abovethe screen surface. Figure 5.5 shows the tension forces on fibre portions above theslot as a function of the smooth rotor speed. By normalizing the u component withrespect to rotor tip speed, Vt, the same profile was observed at different slot velocities,635.2. Mathematical Model Details-10010203040506070800 0.2 0.4 0.6 0.8 1T u(10-6 N)l/LfVs = 1 m/sVs = 2 m/sVs = 3 m/sAverageFigure 5.3: Tension on the fibre portion above slot at Vt = 5 m/s.as shown in Figure 5.6.Since the tension on fibre portion above the slot depends on the stream mainvelocity, a curve fitted formula (Equation 5.4), was developed to estimates Tu(i) atany rotor position for any fibre segment above the slot. The tension data presentedin Figure 5.5 were used in this formula.Tu(i) = [0.71 (u/Vt)Vt + 0.3 l(i)2 + 0.92 (u/Vt)Vt ? 0.02 l(i)? 0.75] ? 10?6 (5.4)The total tension on the fibre portion above the slot can then be estimated as:Tu =n?i=1Tu(i) (5.5)The tension within the slot was calculated using a corrected slot velocity that is645.2. Mathematical Model Details-10010203040506070800 0.2 0.4 0.6 0.8 1T u(10-6 N)l/LfVs = 1 m/sVs = 2 m/sVs = 3 m/sAverageFigure 5.4: Tension on fibre portion above slot at Vt = 20 m/s.30 40 50 60 70 80 T u(10-6  N)Vt = 05 (m/s)Vt = 10 (m/s)Vt = 15 (m/s)Vt = 20 (m/s)-10 0 10 20 0 0.2 0.4 0.6 0.8 1l/LfFigure 5.5: Tension on fibre segments above the slot as a function of smooth rotortip speed.655.2. Mathematical Model Details0.20.40.60.81u / Vt0 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11xr / chordFigure 5.6: Universal curve-fitted u component above the cylinder surface as a func-tion of rotor position for 0 ? Vs ? 4 m/s.a function of the local slot width. Figure 5.7 shows the changes in the v componentas a function of the slot distance along the slot axis and associated change in slotwidth. This correction does not take into consideration the circulation that takesplace within the slot itself (shown by Mokamati et al. [35]) and was only a functionof the slot widthTs =n?j=1Ts(j) (5.6)whereTs(j) =12? v(j)2CD(i)D l(j) (5.7)By examining the tension difference, |Tu?Ts|, as a function of the rotor position,the portion of a fibre on the slot leading edge that can support a trapped state can beestimated. This state is illustrated in Figures 5.8(a) and (b) for a 3 mm fibre trappedon a low contour wire edge. For example, when the tension on the fibre portion abovethe slot is greater than the tension on the fibre within the slot, the fibre remainstrapped as long as the tension difference is lower than or equal to the friction forceexcreted on the fibre (Figure 5.8(b)). Trapped fibres will only be released when the665.2. Mathematical Model Details00.511.52y (mm)2.53 0.2 0.4 0.6 0.8 1v/VsFigure 5.7: Corrected slot velocity along a 3 mm fibre within the slot.tension difference is higher than the friction force on the trapped fibre. Note thatfibre repositioning on the slot edge is not possible in the present model.By examining the probability of fibre trapping on a slot edge, the accumulationof fibres can then be used as an indication of screen plugging as suggested in Section5.1.1. Figure 5.9 shows trapping possibilities at three different rotor positions. Asthe flow velocity above the cylinder surface changes with the rotor position, theaccumulation of fibres will be disrupted due to changes in the force balance appliedto hold fibres with a certain trapped lengths in position. Following on this model,when the flow above a wire stabilizes at the characteristic quasi-steady u/Vt value,as shown in Figure 5.6 for ? xr/chord > 3, accumulation for a certain fibre positionstarts and continues until it gets disturbed by the next foil passage.Figure 5.10 shows the proportion of a 3 mm fibre trapped on slot edge accordingto the aforementioned model. The l/Lf values shown for a particular Vs represent675.2. Mathematical Model Details0.40.60.811.21.4ce / Tuat (l=L)-0.200.20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Forcl / LTu Ts |Tu - Ts| Friction force(b) Tu > Ts region (a) Tu < Ts region                                       (a)                                                              (b)fFigure 5.8: Tension changes with different trapped fibre positions are shown schemat-ically in images (a) and (b) and analytically in a comparison of the fibre forces. Inthis example, a fibre with l/Lf in the range of 0.50 to 0.66 is trapped (i.e. differencesin drag force are less than the friction force).685.2. Mathematical Model Details051015202530350 0.2 0.4 0.6 0.8 1|Tu-T s|. 10-6(N)l/LfTension  difference (Xr/chord = +0.85; maximum u)(Xr/chord = -2.0; steady state)(Xr/chord = +0.4; minimum u)Friction force (Xr/chord = +0.85)Figure 5.9: Changes in trapping position due to changes in the flow field (Vt = 5 m/sand Vs = 1).the 3 mm fibres landing with a portion length = l above the slot to be trappedon the slot edge. These fibres remain trapped and other fibres that land with thesame l/Lf value will build up over time. When the flow field changes, as it doeswith rotor position, and to an extent that the l/Lf value is no longer within therange where trapping is supported for the instantaneous value of u, the fibres willbe cleared. Figure 5.10 also shows that accumulation cannot happen when there isa reversal flow. For example at Vs = 1 m/s, no accumulation takes place duringreversal flow phase. This reversal time is still shorter than the disturbance timecreated by the rotor which is defined here as when u/Vt is substantially differentfrom its average value, i.e. roughly 0 < xr/chord < 2 in Figure 5.10. Once the flowstabilizes, accumulation starts again. The figure also suggests that accumulation isroughly affected by the xr/chord ratio. It is important to note that rotor cycles havethe same overall form but they naturally take shorter times for higher rotor speeds.695.2. Mathematical Model DetailsThis means accumulation is directly proportional to slot velocity and inversely torotor speed.Figure 5.11 describes this model of fibre mass build-up on screen slots. This modelrepresents a process of accumulation equalling deposition followed by removal. Fibredeposition occurs over time between rotor passings and removal is caused by rotorpassage over the apertures. The removal allows fibres to pass through the slots butcontinued accumulation of fibres would lead to complete plugging of the cylinder,Figure 5.11(c).The accumulation of 3 mm fibres within a slot is shown in Figure 5.10 for threedifferent slot velocities. For Vs = 1 m/s, there is a narrow band of l/Lf possibilities(? 2% of total) that will become trapped. As the rotor foil passes, the band movessignificantly and there is then a reverse flow that is assumed to release all trappedfibres. At xr/chord ? 3, the mainstream flow has stabilized so that fibres can accu-mulate until the return of the foil passage, i.e. the l/Lf band does not shift more thanthe width of the band. This period of accumulation is designated as xac/chord. Notethat the same data for [10 < xr/chord < 11] and [-1 < xr/chord < 0] are repeatedin Figure 5.6. A similar sequence of events is seen for Vs = 2 m/s and Vs = 4 m/sexcept that there is no reverse flow in these other two cases. The width of the l/Lfband and the initial point of the xac/chord interval are approximately the same forall three cases. This suggests that the initiation of plugging will increase linearly withlower rotor speeds. This occurs because the tangential flow spends a longer time overthe aperture, giving Vs a longer time to draw fibres into the aperture and therebyincrease deposition.Screen capacity can, in turn, be modelled as the critical case where fibres accu-mulate and fill the slot before the release phase occurs. As discussed previously, in705.2. Mathematical Model Detailsreference to Figure 3.25, the backflushing action which has traditionally be consid-ered essential to the release phase, may be supplemented by the action of a turbulentwake flow or, as discussed in reference to Figure 5.10, flow instabilities which movethe instantaneous value of l/Lf so that previously trapped fibres are shed. What ismost critical to this trapping-capacity model is the accumulation of fibres. It followsfrom the above force balance that given l/Lf band that leads to trapping is relativelyconstant in width and that the xac/chord interval is relatively constant in length,one can develop a fibre Accumulation Number, Nac, as described in Equation 5.8. Inparticular, and as a first-order approximation, the equation assumes that the deliveryof fibres to the trapping location is proportional to the slot velocity, Vs, and upstreamconsistency, CU . The percentage of delivered fibres that impact the downstream slotedge with a value of l/Lf within the band that produces trapping was found aboveto be relatively constant and is embraced within the constant, k1. The time for thebuild-up of fibres is proportional to the length accumulation zone, xac/chord as seenin Figure 5.10 (with the simple conversion of chord length to distance also being em-bedded within k1) and inversely proportional to upstream velocity, which is relatedby a constant to rotor tip speed, Vt. Figure 5.12 is an illustration of Equation 5.8.Nac = [CU Vs]xacchord1Vtk1 (5.8)If plugging is assumed to occur at the same critical value, N ?ac, then Equation 5.8can be rearranged as follows, with k2 = [N ?ac/chord k1] and V?s is the minimum slotvelocity for screen operationV ?s = k21CUVt1xac(5.9)715.2. Mathematical Model DetailsFigure 5.10: Estimates of the accumulation of 3 mm fibres on the low contour wireduring one foil cycle at Vt = 10 m/s.Equation 5.9 captures the linear nature of the the relationship between Vt and Vsobserved in Figure 4.3, reproduced below as Figure 5.12, and the first term of thescreen capacity, Equation 4.1, reproduced below as Equation 5.10V ?t = k1Vs + k2 (5.10)Equation 5.9 does not account for the intercepts with the axis. It only accountsfor fibre deposition, not fibre accumulation which depends on removal as well asdeposition. This suggests that the physical significance of second term in Equation5.10 is linked to fibre removal. This is supported by the observation that extrapolationto Vs = 0 gives a threshold velocity V ?t = k2 required to attain a non-zero Vs. Values ofk2 from the axis intercepts in Figure 4.4 are nearly linearly proportional to consistency,i.e. V ?t = k3CF This link between consistency and Vt suggests that removal is governedby fibre network strength hydrodynamic force.725.2. Mathematical Model Detailsdeposition??timecleaning?timeby?rotor?wake(a)es?Rotor?foil?1Rotor?foil?2ped?fibr(b)s?of?trapRotor?foil?1Rotor?foil?2Mas(c)(c)Mass??at?which?plugging?occurs? TimeRotor?foil?1Rotor?foil?2Figure 5.11: Accumulation of fibres within screen slots during rotor cycles, (a) accu-mulation is less than the cleansing effect, i.e. no fibres left from the previous cycle(b) accumulation effect equals the cleansing effect (plugging point), (c) accumulationeffect is greater than the cleansing effect (plugging takes place).735.3. Summary and Conclusions345678N acVt = 5 m/sVt = 10 m/sVt = 20 m/s0120 1 2 3 4Vs (m/s)Figure 5.12: Accumulation number, Nac, for a 3 mm fibre as a function of slot velocityat different rotor speeds.The above observations offer a basis for linking the empirical findings of Chapter 4to a mechanistic model of screen plugging based on mass balances and force balances.Doing so is beyond the scope of this thesis but remains a promising topic for futurework.5.3 Summary and ConclusionsIt is proposed that the accumulation of fibres within screen cylinder slots is a keymechanism leading to cylinder plugging. Fibres need to staple between two screenapertures to be trapped. Fibres start to accumulate on the downstream edge of theslot when the drag force difference applied on fibre portions above and within theslot is smaller than the fibre-wall friction force. Fibres continue to accumulate on theslot edge until a disturbance in the flow field is introduced. This mechanism likely745.3. Summary and Conclusionsacts in concert with other effects: The negative pulse generated by the rotor can alsoprevent accumulation, as does the rotor wake afterwards.The model suggests that the plugging of screen cylinder is strongly dependenton fibre length distribution, thickening along the screen cylinder and the fluctuationof the flow generated by the rotor foils. More variables, such as slot width, fibrestiffness, fibre-wall friction coefficient, turbulence effects and debris content shouldalso be included in the development of a comprehensive screen capacity model.75Chapter 6Summary and Conclusions6.1 ConclusionsIn this chapter, the conclusions of the main three chapters of this thesis are firstexplained and the final conclusion is then stated.6.1.1 Flow Field Study (Chapter 3)The flow field near a slotted porous surface in steady and time-varying crossflowwas studied experimentally in this chapter for different degrees of roughness anddifferent upstream and aperture velocities. While this problem is of general interest,the present study was made in the context of the flow of a fibrous suspension in apulp screen. Particle-image velocimetry was used in this study to measure the flowpatterns near the slotted surface. The size of the vortex within the roughness contourswas found to be dependent on the geometry of the contour and the flow velocities.Vortices increase in size with lower aperture velocities and higher contour heights.This study also considered the flow through slots in the slotted surface. The heightof the exit layer that passes from the main flow through the slotted apertures wasfound to increase with slot velocity.The dynamic studies revealed that the stream-wise flow decelerates under theleading edge of the screen rotor, for approximately the first half of the rotor element.766.1. ConclusionsThe flow increases under the trailing half of the rotor and then gradually drops to anaverage value that is independent of slot velocity.A flow reversal was observed in some, but not all, of the flow configurations. Lowerslot velocities and higher rotor speeds supported the occurrence of a flow reversal.Indeed a particular rates of these speeds defined the boundary between reversal andnon-reversal flow regimes.Studies of particle concentration showed that the concentration within the contourand leading into the slot, was generally, but not always, lower than in the flow abovethe screen surface. This is consistent from published mechanisms of fibre motion ata bifurcating flow. A depleted zone with reduced fibre concentration was observedin the wake of the rotor foil, which may be industrially significant in avoiding theblockage of the apertures with fibres.In conclusion, reversal flow through the slot and turbulent flows (i.e. the rotorpulse) in the wake of the foil, however, remain the principal mechanisms in avoidingaperture blockages. This study provides a number of insights into the complex andindustrially important flow problem of unsteady flow adjacent a rough slotted walland the potential for the apertures in the wall to be obstructed with fibrous particlesbeing carried in the flow.6.1.2 Pilot Pulp Screen Capacity (Chapter 4)Pilot screen experiments with different screen cylinder aperture geometries and pulpcombinations were conducted in this chapter to determine the factors that affect themaximum capacity of a pilot pressure screen. The screen plugging envelopes wereshown to be linear, suggesting a simple relationship between rotor and slot velocities.A characteristic equation was proposed to describe screen capacity.776.1. ConclusionsA higher contour height was found to delay plugging but this effect was limitedto low slot velocities. Slot width and wire width were found to be significantly moreimportant than contour height. Pulp consistency and character (i.e. fibre lengthdistribution) both had significant effects on screen capacity.A comparison of the flow conditions where backflushing occurred (from Chapter3) with the operating envelope of the pilot screen suggests that the screen can stilloperate at lower rotor speeds where a negative pulse is not expected to be present.In conclusion, this suggests that an alternate fibre removal mechanism exists inaddition to backflushing and wake turbulence.6.1.3 Model of Pulp Screen Capacity (Chapter 5)It is theorised in this chapter that the progressive accumulation of fibres on screencylinder slots is a precursor of plugging. Fibres need not to staple across adjacentscreen apertures to be trapped. Fibres accumulate on the slot?s downstream leadingedge when the drag force difference applied on fibre portions above and within theslot is smaller than the friction force between the fibre and slot edge. Fibres thusaccumulate on the slot edge, and continue to build up with time until a disturbancein the flow field is introduced.In conclusion, a flow filed disturbance need to be a reversal flow to prevent accu-mulation is a screen slot. The negative pulse generated by the rotor can clear the slot(unplug) immediately while the rotor wake continues to prevent fibre deposition afterpassage of the foil. A computational model was created based on the aforementionedforce balance mechanism. It suggests that the plugging of pressure screen accordingto this mechanism is strongly dependent on fibre average length and the fluctuationof the flow generated by the rotor foils.786.2. Future Work6.2 Future WorkFurther work on this subject is clearly desirable. Following are specific suggestions.There is interest in investigating fibre-wall interaction and the effect of fibre stiff-ness on the total forces applied on trapped fibres, as this is key to the force balancemechanism of trapping. Additionally, the effect of different rotor designs on stream-wise flow fields and turbulence levels near screen surface should also be investigated.Dynamic behaviour of the flow near screen apertures and within slots should bestudied in more details to associate the instantaneous effect on flow direction withinthe slots. A detailed understanding of the small-scale geometry of the slot entranceis required to understand and design high performance screen cylinders. this couldbe based on high speed videos to characterize the accumulation of fibres, along withCFD simulation of the time-varying flow validated by PIV experiments.Finally, improved screen wire and rotor designs capable of delaying fibre accumu-lations are also suggested to improve pressure screen capacity. These improvementsshould also take in consideration the overall performance of the screen on contaminantremoval efficiency, fractionation, and thickening as well as capacity.79References[1] A. Ammala, O. Dahl, H. Kuopanportti, and J. Niinimaki. The effect of backflow in an axially fed pressure screen. Papier Ja Puu, 81(4):210?215, 1999.[2] C. P. J. Bennington and R. J. Kerekes. Power requirments for pulp suspensionfluidization. Tappi J., 29(2):253?258, 1996.[3] S. Blaser. Flocs in shear and strain flows. J. Colloid and Interface Sci.,225(2):273?284, 2000.[4] L. Bliss. Screening in the stock preparation system. In Proc. Tappi Stock Prepa-ration Short Course, pages 59?75, Atlanta, GA, 1990.[5] P. Bradshaw and F. Y. H. Wong. The reattachment and relaxation of a turbulentshear layer. J. Fluid Mechanics, 52:113?135, 1972.[6] B. Dalpke and R. J. Kerekes. The influence of fibre properties on the apparentyield stress of flocculated pulp suspensions. J. Pulp and Paper Science, 31(1):39? 43, 2005.[7] S. Delfel. A numerical and experimental investigation into pressure screen foilrotor dynamics. PhD thesis, The University of British Columbia, Canada, 2009.[8] S. Delfel, C. Ollivier-Gooch, J. Olson, and P. Wallace. Experimental measure-80Referencesment of pressure pulses from a pulp screen rotor. volume 1, pages 763 ? 772,Montreal, Canada, 2010.[9] S. Delfel, J. Olson, C. Ollivier-Gooch, and R. Gooding. Effect of pulse frequencyand cylinder diameter on pressure screen rotor performance. In 65th AppitaAnnual Conf., pages 89?96, Rotorua, New Zealand, 2011.[10] S. Delfel, J. A. Olson, D. M. Martinez, A. Regairaz, C. F. Ollivier-Gooch, andA. Huovinen. Influence of cylinder design and other factors on capacity andpower consumption in a pressure screen. Appita J., 64(1):55?61, 2011.[11] S. Dong, M. Salcudean, and I. Gartshore. The effect of slot shape on the perfor-mance of a pressure screen. Tappi J., 3(5):3?7, 2004.[12] M. Feng, J. Gonzalez, J. A. Olson, C. Ollivier-Gooch, and R. W. Gooding.Numerical simulation and experimental measurement of pressure pulses producedby a pulp screen foil rotor. J. Fluids Eng., 127(2):347?357, 2005.[13] F. Frejborg. Improved operation of TMP plant trough optimization of screening.Pulp Paper Canada, 89(1):107?112, 1989.[14] J. Gonzalez. Characterization of design parameters for a free foil rotor in apressure screen. MASc thesis, The University of British Columbia, Canada,2002.[15] R. W. Gooding. The passage of fibres through slots in pulp screening. MAScthesis, The University of British Columbia, Canada, 1986.[16] R. W. Gooding. Flow resistance of screen plate apertures. PhD thesis, TheUniversity of British Columbia, Canada, 1996.81References[17] R. W. Gooding and D. F. Craig. The effect of slot spacing on pulp screencapacity. Tappi J., 75(2):71?75, 1992.[18] R. W. Gooding and R. J. Kerekes. Motion of fibres near a screen slot. J. PulpPaper Sci., 15(2):59?62, 1989.[19] G. Gregoire, M. Faver-Marinet, and F. Julien Saint Amand. Modeling of tur-bulent fluid flow over a rough wall with or without suction. Trans. ASME,125:636?642, 2003.[20] J. Gullichsen and E. Harkonen. Medium consistency technology i: Fundamentaldata. Tappi J., 64(6):69?71, 1981.[21] L. Halonen, R. Ljokkoi, and K. Peltonen. Improved screening concepts. In Proc.Tappi Pulping Conf., pages 61?66, Seattle, WA, 1989.[22] M. Hamelin, S. Delfel, J. Olson, and C. Ollivier-Gooch. High performance multi-element foil (MEF) pulp screen rotor - pilot plant and mill trials. J. of Pulp andPaper Science, 36:3?4, 2011.[23] O. Heise. Screening foreign material and stickies. Tappi J., 75(2):78?81, 1992.[24] J. Jimenez. Turbulent flows over rough wall. Ann. Rev. Fluid Mech., 36:173?196,2004.[25] H. Jokinen, A. Ammala, J. A. Virtanen, K. Lindroos, and J. Niinimaki. Pressurescreen capacity-current findings on the role of wire width and height. Tappi J.,6(1):3?10, 2007.82References[26] F. Julien Saint Amand and B. Perrin. Fundamentals of screening: Experimen-tal approach and modelling. In Proc. Tappi Pulping Conf., pages 1019?1031,Montreal, 1998.[27] F. Julien Saint Amand and B. Perrin. Fundamentals of screening: Effect of rotordesign and fibre properties. In Proc. of Tappi Pulping Conf., pages 941?955,Orlando, FL, 1999.[28] J. H. Jung, N. Pan, and T. J. Kang. Capstan equation including bending rigidityand non-linear frictional behavior. Mechanism and Machine Theory, 43(6):661?675, 2008.[29] R. Karvien and L. Halonen. The effect of various factors on pressure pulsationof a screen. Paperi ja Puu, 66(7):80?83, 1984.[30] R. Kerekes. Pulp floc behavior in entry flow to constriction. Tappi J., 66(1):88?91, 1983.[31] A. Kumar. The passage of fibres though screen apertures. PhD thesis, TheUniveristy of British Columbia, Canada, 1991.[32] S. Levis. Screening of secondary fibers. Progress in Paper Recycling, 1(1):31?45,1991.[33] D. M. Martinez, R. W. Gooding, and N. Roberts. A force balance model of pulpscreen capacity. Tappi J., 82(4):181?187, 1999.[34] C. McCarthy. Various factors affect pressure screen operation and capacity. Pulpand Paper, 62(9):233?237, 1988.83References[35] S. Mokamati, J. A. Olson, and R. W. Gooding. Numerical study of separatedcross-flow near a two-dimensional rough wall with narrow apertures and suction.Canadian J. Chem. Eng., 88(1):33?47, 2010.[36] J. Niinimaki. Phenomena affecting the efficiency of a pressure screen. In Proc.Tappi Pulping Conf., pages 957?966, 1999.[37] J. Niinimaki, A. Ammala, H. Kuopanportti, and S. Nissila. The settings ofhydrofoils in a pressure screen. In Proc. Int. Symposium on Filtration, pages71?78, Las Palmas, Canary Islands, 1998.[38] J. Niinimaki, O. Dahl, H. Kuopanportti, and A. Ammala. Compa.son of pressurescreen baskets with different slot widths and profile heights - selection of the rightsurface for a groundwood application. Paperi ja Puu, 80(8):601?605, 1998a.[39] J. A. Olson. The effect of fibre length on passage througth a single screen aperture.PhD thesis, The University of British Columbia, Canada, 1996.[40] J. A. Olson and R. Kerekes. Motion of fibres in turbulent flow. J. Fluid Mechan-ics, 377:47?64, 1998.[41] J. A. Olson and G. Wherrett. A model of fibre fractionation by slotted screenapertures. J. Pulp Paper Sci., 24(12):398?402, 1998.[42] Specialist Committee on Uncertainty Analysis. Uncertainty analysis particleimage velocimetry. In Proc. of the 25th ITTC, volume 2, pages 453?455, Fukuoka,Japan, 2008.[43] V. C. Patel. Flow at high Reynolds number and over rough surfaces-achilles heelof cfd. ASME J. Fluid Eng., 120:434?444, 1998.84References[44] T. Paul, G. Duffy, and D. Chen. Viscosity control as a new way to improvepressure screen performance. Tappi J., 83(9):61?100, 2000.[45] V. Pinon, R. W. Gooding, and J. A. Olson. Measurements of pressure pulsesfrom a solid core screen rotor. Tappi J., 2(10):9?12, 2003.[46] P. J. Pritchard, editor. Fox and McDonald?s Introduction to Fluid Mechanics.Wiley, 2011.[47] B. Timmins. Automatic Particle Image Velocimetry Uncertainty Quantification.MASc thesis, Utah State University, USA, 2011.[48] A. Vakil and S. Green. Drag and lift coefficients of inclined finite circular cylin-ders at moderate Reynolds numbers. Computers and Fluids, 38(9):1771?1781,2009.[49] A. Vakil and S. Green. Flexible fiber motion in the flow field of a cylinder. Int.J. Multiphase Flow, 37(2):173?186, 2011.[50] T. Wikstrom and T. Rasmuson. Transition modelling of pulp suspensions ap-pliled to a pressure screen. J. Pulp Paper Sci., 28:374?378, 2002.[51] A. Yong, S. Mokamati, Daniel Ouellet, R. W. Gooding, and J. A. Olson. Exper-imental measurement of fibre motion at the feed surface of a pulp screen. AppitaJ., 61(6):485?489, 2008.[52] C. J. Yu and R. J. DeFoe. Fundamental study of screening hydraulics, Part 1:Flow patterns at the feed-side surface of screen baskets; mechanism of fiber-matformation and remixing. Tappi J., 77(8):219?226, 1994a.85References[53] C. J. Yu and R. J. DeFoe. Fundamental study of screening hydraulics, Part 2:Fiber orientation in the feed side of a screen basket. Tappi J., 77(9):119?124,1994b.[54] C. J. Yu, R. J. DeFoe, and B. R. Crossley. Fundamental study of screeninghydraulics, Part 3: Model for calculating effective open area. Tappi J., 77(9):125?131, 1994c.86AppendicesA Flow and Wire Geometry Effects on FibreFractionationThe effect of stream-wise flow and slot velocity is discussed briefly in this appendix.By inspecting Figures A.1-A.4, one can see that the fractionation of longer fibres canbe easily achieved with low contour wires. It is shown in Figures 3.9 and 3.10 thathigher level of circulations, i.e. higher level of energy, can be achieved with higherslot velocities. Higher circulation levels tend to curl fibres (CSS high speed videosphysically prove it) forcing them to follow the vortex flow and increasing their chancesto enter the slot.Shorter fibres tend to follow the flow within the vortex and it is easier for them toenter the slot. Longer and stiffer fibres cannot bend easily to follow the vortex flowand the chances of them being rejected with lower contour screen wires are higher.When slot velocity increases, the tendency for fractionation drops as fibres are forcedto enter the slot (Figure A.5). Figure A.6 explains this concept where higher contourscreate larger vortices allowing longer fibre to be more easily accepted in comparisonto low contour screen wires.The foil rotor has a stronger effect on stream-wise flow, creating higher levels ofcirculation when it passes the slots than in comparison to a smooth rotor at the same87A. Flow and Wire Geometry Effects on Fibre Fractionationaverage stream-wise flow velocities, allowing longer fibres to be accepted as well, asshown in Figure A.7.88A. Flow and Wire Geometry Effects on Fibre Fractionation456789requency (%)Fe ed SampleVt = 20, Vs = 1Vt = 20, Vs = 2Vt = 20, Vs = 3 01230 1 2 3 4 5FrFibre LengthFigure A.1: Effect of slot velocity on fibre length distribution with a low contour wireand smooth rotor at Vt = 20 m/s.456789requency (%)Fe ed SampleVt = 25, Vs = 1Vt = 25, Vs = 2Vt = 25, Vs = 301230 1 2 3 4 5FrFibre LengthFigure A.2: Effect of slot velocity on fibre length distribution with a low contour wireand smooth rotor at Vt = 25 m/s.89A. Flow and Wire Geometry Effects on Fibre Fractionation11.522.53Frequency(%)F e ed SampleVt = 20 m/s, Vs = 1 m/sVt = 20 m/s, Vs = 2 m/s00.50 1 2 3 4 5FFibre Length (mm)Figure A.3: Effect of slot velocity on fibre length distribution with a high contourwire and smooth rotor at Vt = 20 m/s.11.522.53Frequency (%)Fe ed SampleVt = 25 m/s, Vs = 1m/sVt = 25 m/s, Vs = 2 m/s00.50 1 2 3 4 5FFibre Length (mm)Figure A.4: Effect of slot velocity on fibre length distribution with a high contourwire and smooth rotor at Vt = 25 m/s.90A. Flow and Wire Geometry Effects on Fibre FractionationSmoothrotorfibrefractionationSmooth?rotor?fibre?fractionation1 0.9fra cti on  f e e d0.70.8on  a cce p t / si z e  fType1,Ut=20m/sLowcontourVt=20m/s0.6si z e  f ra ctiType 1, Ut  20 m/sType 1, Ut = 25 m/sType 3, Ut = 20 m/sType 3, Ut = 25 m/sLow contour, Vt 20 m/sLow contour, Vt= 25 m/sHigh contour, Vt= 20 m/sHigh contour, Vt= 25 m/s0.5012345V s(m/s)Figure A.5: Effect of smooth rotor speed and contour height on fibre fractionation atvarious slot velocities.Figure A.6: Effect of contour height and vortex strength on short and long fibrefractionation.91A. Flow and Wire Geometry Effects on Fibre Fractionation2345requency (%)Fe edVt = 20, Vs = 1, EP RotorVt = 25, Vs = 1, Smooth Rotor010 1 2 3 4 5FrFibre Length (mm)Figure A.7: Effect of rotor on fibre fractionation at the same flow field.92B. PIV Uncertainty AnalysisB PIV Uncertainty AnalysisParticle Image Velocimetry (PIV) measurement error depends on the PIV algorithmused, a wide range of user inputs, flow characteristics, and the experimental setup.Since these factors vary in time and space, they lead to non-uniform error throughoutthe flow field [47].The uncertainty analysis presented in this study followed the procedure recom-mended by [42]. The principle of the PIV measurement on flow speed u can bedescribed by the following equationu = ?14X4t+ ?u (B.1)The flow speed is detected by means of the displacement of particle images 4X, andthe time interval of successive images 4t. The magnification factor, ?1, must be beidentified through the calibration. Table B.1 shows the PIV measurement dimensions.Since no laser was used, the virtual test plane was assumed to be perpendicular to theview field with a maximum deviation of 5o. Calibration was conducted by measuringthe screen wire width. The magnification factor was determined by the distance ofthe reference point, lr and the distance on the image plane, Lr?1 =lrLr(B.2)The PIV measurement based on the visualized flow image, and the informationof the image differs from the flow field due to the velocity lag of the tracer particlefrom acceleration and the projection procedure from the 3-D physical space to the2-D image plane. These uncertainty factors of flow visualization are consolidated in93B. PIV Uncertainty AnalysisTable B.1: Principal dimensions for PIV measurmentFlow maximum speed 8 m/sDistance of reference points lr 3.2 mmDistance of reference image Lr 195 pixelMagnification factor ?1 0.016 mm/pixelTime interval 4t 1.852? 10?5 sSpatial resolution 320? 240 pixelsDistance from the target lt 60 mmCorrelation area size 64? 64 pixelsSearch area size 32? 32 pixelsa parameter ?u. In general, the ?u is hard to detect systematically, and it is usuallycategorized as an uncertainty factor rather than a measurement parameter [42]. Theerror from the particle velocity lag was experimentally found to be less than 0.5%and for this case, ?u = 8? 1000? 0.005 = 40 mm/s. The 3-D out-of-plane velocitycomponent was assumed to be 1.0% of the maxium flow velocity and the error wasestimated as 8? 1000? .01? tan(1/2? 5.25/60) = 3.5 mm/s.TablesB.2 and B.3 show all the uncertainties, propogation and accumulation ofuncertainties of measurment parameters for velocity and position, respectively. Theuncertainty of 4t is small enough to be neglected. Full details of all standard uncer-tainties, us(xi), and sensitivity factors, ci, evaluation procedure can be found in [42].The total combined uncertainties were calculated based on the following summationuc =?u2u + (ux?u/?x)2 (B.3)The expanded uncertainty in velocity was found to be ?3.5% for the 8 m/s flow.The uncertainties of model test were not included in this analysis.94B. PIV Uncertainty AnalysisTable B.2: Uncertainties for velocityPrmt. Category Error sources us(xi) ci cius(xi) uc?1 Calibration Reference image 0.5 pixel 8.42? 10?5 mm/pixel2 4.21? 10?5Physical distance 0.005 mm 5.13? 10?3 1/pixel 2.56? 10?5Image distortion 0.95 pixel 8.42? 10?5 mm/pixel2 8.00? 10?5by lensView field position 0.5 mm 2.74? 10?4 1/pixel 1.37? 10?4Normal view angle 0.087 rad 1.43? 10?3 mm/pixel 1.24? 10?4 2.07? 10?44X Acquisition Normal view angle 0.087 rad 1.43? 10?3 mm/pixel 1.24? 10?4Reduction Mismatching error 0.1 pixel 1.0 0.1Sub pixel analysis 0.03 pixel 1.0 0.03 0.104?u Experiment Particle trajectory 40 mm/s 1.0 40 mm/s3-D effects 3.5 mm/s 1.0 3.5 mm/s 40.15?1 Magnification factor 2.07? 10?4 mm/pixel 4.88? 105 pixel/s 101 mm/s4X Image displacement 0.104 pixel 888.6 mm/pixel/s 92.41?u Experiment 40.15 mm/s 1.0 40.15 mm/sCombined uncertainty uu 142.66 mm/sTable B.3: Uncertainties for positionParameter Category Error sources us(xi) ci cius(xi)Xs, Xe Acquisition Digital error 0.5 pixel 0.0164 mm/pixel 8.2? 10?3Non-uniformity of 16 pixel 0.0164 mm/pixel 0.263distributionXo Calibration Origion correlation 2.0 pixel 0.0164 mm/pixel 0.033?1 Magnification factor 2.07? 10?4 mm/pixel 160 pixel 0.033Combined uncertainty ux 0.267 mm95C. Characterization of Fibres Used for Capacity TrialsC Characterization of Fibres Used for CapacityTrialsDifferent pulp combinations were used to evaluate the effect of average fibre lengthon maximum screen capacity as seen in Section 4.3. The softwood to hardwood ratiowas varied from 0 to 100 during the course of experiments. Figures C.1-C.5 show thefibre length distributions for these combinations.The model introduced in Chapter 5 was based on a fibre length of 3 mm. Althoughthe impact of the average fibre length on the model was not explicitly taken intoconsideration, it was found that the frequency of 3 mm fibre, Figure C.6, increasedlinearly with the increase of softwood ratio. This might be used in future work toinclude the effect of fibre length or the average fibre length in the developed model.345678quency (%)0:100 HW:SW0120 1 2 3 4 5FreqFi bre Length (mm)Figure C.1: Fibre length distributions of 0:100 SW:HW sample.96C. Characterization of Fibres Used for Capacity Trials345678quency (%)25:75 HW:SW0120 1 2 3 4 5FreqFi bre Length (mm)Figure C.2: Fibre length distributions of 25:75 SW:HW sample.345678quency (%)50:50 HW:SW0120 1 2 3 4 5FreqFibre Len gth (mm)Figure C.3: Fibre length distributions of 50:50 SW:HW sample.97C. Characterization of Fibres Used for Capacity Trials345678quency (%)75:25 HW:SW0120 1 2 3 4 5FreqFibre Le ngth (mm)Figure C.4: Fibre length distributions of 75:25 SW:HW sample.345678quency (%)100:0 HW:SW0120 1 2 3 4 5FreqFibre Le ngth (mm)Figure C.5: Fibre length distributions of 100:0 SW:HW sample.98C. Characterization of Fibres Used for Capacity TrialsR ? = 0.99640.81.21.62requency (%)00.40 25 50 75 100FrSW:HW (%)Figure C.6: Frequency of 3 mm fibres in different SW:HW samples.99

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