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Understanding of no-load power in low consistency refining Rajabi Nasab, Nina 2013

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UNDERSTANDING OF NO-LOAD POWER IN LOW CONSISTENCYREFININGbyNina Rajabi NasabB.Sc., Sharif University of Technology, Tehran, Iran, 2005M.Sc., Chalmers University of Technology, Goteborg, Sweden, 2007A 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)August 2013c? Nina Rajabi Nasab, 2013AbstractLow Consistency (LC) refining is the primary means of improving the strength andsmoothness of paper by imparting energy to fibres through repeated fibre-bar inter-actions. The useful part of the energy modifies the morphology of the fibres and theremaining, no-load power, mainly overcomes the hydraulic, pumping and mechanicallosses in the refiner. This thesis is aimed to explore the no-load power in LC refiningboth experimentally and computationally. The contribution of this thesis comes inthree parts.Firstly, the effect of consistency, operational and plate design parameters on no-load power was experimentally determined on two pilot scale LC refiners with differentplate diameters. The obtained data were used to provide a statistical model forprediction of no-load power. To study the effect of diameter and groove depth, theno-load power consumption of some mills corresponding to their operating conditions,and the specifications of the relevant refiner discs were collected. Based on this model,no-load power is described in terms of two main components, hydraulic and pumpingpowers, and an empirical equation is proposed.Secondly, we numerically examined the two-dimensional flow of a Newtonian fluidin the gap formed between two opposing cavities which represent the cross-sectionalflow in LC refiner. A large number of unsteady simulations were conducted to char-acterize the effect of gap size on the flow field over the range of velocities. Then, weexamined material transport between the cavities by introducing a passive scalar toiiAbstractrepresent the motion of tracer particles. Over the range of parameters studied, weidentify two characteristic flow fields, defined as either steady or unsteady. We alsofind that particles are transported to the region near the leading edges of the barsonly under the conditions of unsteady flow.Thirdly, we extended the numerical study by characterizing the effect of cavitydepth on the flow field over the range of velocities. We find that the aspect ratioof the cavity dictates three characteristic flow fields based on the number of vorticesformed within cavity and we propose criteria for cavity aspect ratio in terms of therefiner application.iiiPrefaceIn this section, we briefly explain the contents of the papers that have been ac-cepted, submitted or will be submitted for publication from this thesis and clarifythe contributions of co-authors in the papers. We also include the list of conferencecontributions.Journal Papers? Rajabi Nasab, N., Olson, J.A., Heymer, J. & Martinez, D.M. (2013) Under-standing of No-load Power in Low Consistency Refiners. Canadian Journal ofChemical Engineering.This publication has focused on understanding the no-load power in Low Con-sistency refiners using experiments. Chapter 3 includes the contents of thispublication. The author of the thesis was the principal contributor to this pub-lication. Dr. Jens Heymer has designed the experimental flow loop and assistedwith writing the paper. Professors James Olson and Mark Martinez supervisedthe research and assisted with writing the paper.? Rajabi Nasab, N., Mithrush, T., Olson, J.A. & Martinez, D.M. (2013), Tur-bulent flow between two parallel corrugated walls: The case with motion of onewall perpendicular to the corrugation cavities, Submitted.In this publication, we present results of a computational study of the flowfield in the cross section of refiner. Chapter 4 includes the contents of thisivPrefacepublication. The author of this thesis was the principal contributor to thispublication. T. Mithrush assisted with the simulations and Professors JamesOlson and Mark Martinez supervised the research. All the co-authors assistedwith writing the paper.Contributions to refereed conference proceedings? Rajabi Nasab, N., J.A. Olson, J. Heymer & D.M. Martinez, ?ExperimentalStudy of Low Consistency Refiner No-load Power?, PAPERCON ConferenceProceedings, New Orleans, LA, April 21-25, pp. 1539-1551 (2012).Conference posters? Rajabi Nasab, N., Mithrush, T., Olson, J.A. & Martinez, D.M., ?Insightinto the Flow Field of LC Refiners: The Relationship to the Beating Effect?,January 29-31, Are, Sweden (2013).? Rajabi Nasab, N., Olson, J.A. & Martinez, D.M., ?Understanding no-loadpower in LC refining?, PacWest Conference, June 10-13, Sun Peaks, BC, Canada(2009)? Rajabi Nasab, N., Olson, J.A. & Martinez, D.M., ?Understanding no-loadpower in LC refining?, Pulp and Paper Technical Association of Canada (PAP-TAC) Conference, February 4-5, Montreal, Canada (2009)? Rajabi Nasab, N., Olson, J.A.& Martinez, D.M., ?Understanding no-loadpower in LC refining?, Pulp and Paper Technical Association of Canada (PAP-TAC) Conference, February 5-7, Montreal, Canada (2008)vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Low consistency refiner . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Flow field between two rotating discs . . . . . . . . . . . . . . . . . . 92.3 Turbulent flow between two parallel corrugated walls . . . . . . . . . 122.4 Effect of groove depth in refining . . . . . . . . . . . . . . . . . . . 172.5 Summary of literature . . . . . . . . . . . . . . . . . . . . . . . . . . 18viTable of Contents2.6 Objectives of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 182.7 Approaches of the thesis . . . . . . . . . . . . . . . . . . . . . . . . 193 Experimental Measurement of the No-load Power in LC Refining 203.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 Time-Dependent Cross-Sectional Flow Field of LC Refiners . . . 464.1 Computational framework . . . . . . . . . . . . . . . . . . . . . . . . 484.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 534.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Effect of Cavity Aspect Ratio on the Cross-Sectional Flow Field 665.1 Computational framework . . . . . . . . . . . . . . . . . . . . . . . . 675.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 685.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726 Summary of Thesis and Future Research Direction . . . . . . . . . 736.1 Summary of contributions . . . . . . . . . . . . . . . . . . . . . . . . 736.2 Limitations of the study . . . . . . . . . . . . . . . . . . . . . . . . . 746.3 Future research directions . . . . . . . . . . . . . . . . . . . . . . . . 76Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78viiTable of ContentsAppendicesA Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85B Comparison of Water and Pulp . . . . . . . . . . . . . . . . . . . . . 104C Pulp Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105viiiList of Tables2.1 Different flow regimes inside an enclosed smooth rotor-stator . . . . . 103.1 Specifications of all nine lab refiner plates . . . . . . . . . . . . . . . 223.2 Range of operating variables for the experimental setup . . . . . . . . 233.3 Comparison of Pn? for three plates with B = 1mm and different groovewidths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.4 Coefficients of the proposed correlation for all plates with 16?? diameters 383.5 Plate design and operating conditions of both lab and mill refiners . . 404.1 A summary of the numerical conditions tested. In Series 1, we exam-ined the effect of Re and the spacing between the plates G/L on theflow field. The numerical simulations were conducted with B/L = 0.4.In total, 30 simulations were conducted. In series 2, we employed parti-cle tracking, as a passive scalar, for 2 different gap sizes; G/L = 0.0625and G/L = 1.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.2 Range of Y ? for three different regions of moving cavity, stationarycavity and the spacing between these two cavities . . . . . . . . . . . 605.1 A summary of the numerical conditions tested. In Series 3, we exam-ined the effect of Re and aspect ratio T/W on the flow field. In total72 simulations were conducted. . . . . . . . . . . . . . . . . . . . . . 67ixList of TablesA.1 Values of mechanical power measured for Plate 1 and Plate 3 as shownin Figure 3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85A.2 Values of hydraulic power measured for Plate 1 . . . . . . . . . . . . 86A.3 Values of hydraulic power measured for Plate 2 . . . . . . . . . . . . 87A.4 Values of hydraulic power measured for Plate 3 . . . . . . . . . . . . 88A.5 Values of hydraulic power measured for Plate 4 . . . . . . . . . . . . 89A.6 Values of hydraulic power measured for Plate 5 . . . . . . . . . . . . 90A.7 Values of hydraulic power measured for Plate 6 . . . . . . . . . . . . 91A.8 Values of PowerNL and Powern measured for Plate 1 . . . . . . . . . 92A.9 Values of PowerNL and Powern measured for Plate 2 . . . . . . . . . 94A.10 Values of PowerNL and Powern measured for Plate 3 . . . . . . . . . 96A.11 Values of PowerNL and Powern measured for Plate 4 . . . . . . . . . 97A.12 Values of PowerNL and Powern measured for Plate 5 . . . . . . . . . 99A.13 Values of PowerNL and Powern measured for Plate 6 . . . . . . . . . 102B.1 Values of Power?n and Powern measured for water and pulp with con-sistencies of 1.5% and 3.5% for Plate 2 when Q = 600lpm . . . . . . . 104C.1 Freeness of fibres at various gap sizes for Plate 2 when Q = 500lpm asshown in Figure 3.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105C.2 Length-weighted (LW ) average length of fibres at various gap sizes forpulp suspension of C = 3.5% for Plate 2 when Q = 500lpm as shownin Figure 3.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106C.3 Tensile index at various gap sizes for pulp suspension of C = 3.5% forPlate 2 when Q = 500lpm as shown in Figure 3.8 . . . . . . . . . . . 106xList of Figures2.1 (a) Illustration of the configuration of a LC disc refiner and schematicof the grinding surface of an LC disc refiner. One disc is stationary inwhich a dilute papermaking fibre suspension is fed into the machine.Patterns are machined on to the surface of the plate. (b) cross sectionof the topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Schematic graph of power vs. gap size . . . . . . . . . . . . . . . . . 62.3 Schematic of the different geometries found in the literature which ap-proximate the case considered. (a) Pressure-driven laminar flow overcorrugated walls. (b) Pressure-driven turbulent flow over one corru-gated wall. (c) Lid driven cavity flow. This case can be either laminaror turbulent. (d) Lid-driven flow over opposing corrugated walls. Thisgeometry represents the case considered in this work. . . . . . . . . . 132.4 Schematic of the phenomenological flow fields found over ribbed rough-ness elements: (a) d-type flow; (b) k-type flow. . . . . . . . . . . . . . 152.5 Schematic of the flow in the cavities of a refiner plate. ?+? and ??represent opposing flow fields in z-direction. . . . . . . . . . . . . . . 173.1 Illustration of the LC refiner loop used for all trials . . . . . . . . . . 213.2 Comparison of mechanical loss respect to the total no-load power fortwo 16?? plates (Q = 1000 lpm and G = 9mm) . . . . . . . . . . . . . 24xiList of Figures3.3 Comparison between power of water and pulp with two different con-sistencies for Plate 2: (a) Hydraulic power, (b) Total no-load powerwhen Q = 600 lpm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.4 Total power vs. gap for Plate 7: (a) Q = 600 lpm, ? = 600 rpm, (b)Q = 600 lpm, ? = 800 rpm . . . . . . . . . . . . . . . . . . . . . . . . 283.5 Total power vs. gap for Plate 2: Q = 500 lpm and ? = 1200 rpm . . . 293.6 Freeness of fibers at various gap sizes between rotor and stator forPlate 2 and Q = 500 lpm . . . . . . . . . . . . . . . . . . . . . . . . . 303.7 Length-weighted (LW ) average length of fibers at various gap sizesbetween rotor and stator for Plate 2 and Q = 500 lpm . . . . . . . . . 303.8 Tensile of fibers at various gap sizes between rotor and stator for Plate2 and Q = 500 lpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.9 Graphs of total no-load power collected for water vs. gap for twodifferent rotational speeds and various flow rates for two 16?? plates (a)Plate 2 and (b) Plate 5. At no flow case (hydraulic power), the no-loadpower is independent of gap. (2 : Q = 0 lpm;? : Q = 600 lpm; ? :Q = 800 lpm;4 : Q = 1000 lpm) . . . . . . . . . . . . . . . . . . . . . 323.10 Correlation between hydraulic power number and dimensionless gapfor all 16?? plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.11 Cubic dependency of hydraulic power on rotational speed shown forall 16?? plates at G = 9mm . . . . . . . . . . . . . . . . . . . . . . . . 343.12 Increase in total no-load power as a function of flow rate for Plate 4at G = 9mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.13 Correlation between hydraulic power number and ? for all 16?? lab plates 36xiiList of Figures3.14 Correlation between predicted and measured no-load powers for allplates with 16?? diameters . . . . . . . . . . . . . . . . . . . . . . . . . 393.15 Correlation between hydraulic power and diameter for the range of laband mill plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.16 Correlation between predicted and measured hydraulic no-load powersfor all plates including both lab and mill dimensions . . . . . . . . . . 433.17 Comparison of predicted and measured hydraulic no-load power re-spect to ? for all 12?? plates . . . . . . . . . . . . . . . . . . . . . . . . 444.1 Schematic of the corrugated geometry considered. Here the upperwall translates at a constant velocity of U and is separated from thelower plate by a gap G. The corrugations are considered as repeatedpatterns of rectangular cavities of width W = 4.8mm and depth T .The cavities are separated by a spacing of B = 3.2mm . . . . . . . . 474.2 Schematic of the physical domain as well as the computational domain.The computational domain is limited to one repeating cavity pattern oflength L. Periodic boundary conditions, highlighted by the red dashedlines, on the left and right sides of the domain are shown. A slidingmesh is used dividing the computational domain at y = 0 . . . . . . . 494.3 Characterizing the sensitivity of the solution to the mesh size and timesteps. In (a), the mesh density dependency N is shown as a functionof Cd using a time step of ?t = 2 ? 10?7s. In (b), the effect of timestep is shown for the case with N = 154800. Here ?tc = 2 ? 10?7 s.In both simulations: Rel = 1.6 ? 105, B/L = 0.4, T/L = 0.4 andG/L = 0.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50xiiiList of Figures4.4 A comparison of the numerical solution of two opposing corrugatedcavities passing over each other to that of flow in a 3D channel drivenby a moving lid measured by Friesing in 1936. The numerical simula-tions were conducted with Rel = 4? 104, G/L = 0.25 and B/L = 0.4. 524.5 Estimates of flow field when Rel = 1.6?105, G/L = 0.0625, T/L = 0.4and B/L = 0.4. The streamlines are shown superimposed on the normof the velocity field. This is traditionally called the ?speed? and thecolor map of the speed is dimensional with units of m/s. The upperwall is translating from left to right at a velocity of 20m/s. The timesteps have been scaled by the periodic time L/U and are presented att? = [0, 0.2, 0.4, 0.6, 0.8]. . . . . . . . . . . . . . . . . . . . . . . . . . . 544.6 Estimates of the stream function when Rel = 1.6?105, G/L = 0.0625,T/L = 0.4 and B/L = 0.4. The upper wall is translating from leftto right at a velocity of 20m/s. The color map represents the streamfunction at t? = 0.2 and is given in units of kg/s. . . . . . . . . . . . 554.7 Estimates of the pressure field when Rel = 1.6 ? 105, G/L = 0.0625,T/L = 0.4 and B/L = 0.4. The upper wall is translating fromleft to right at a velocity of 20m/s. The color map represents thepressure field and is given in units of kPa (gage). The time stepshave been scaled by the periodic time L/U and are presented at t? =[0, 0.2, 0.4, 0.6, 0.8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56xivList of Figures4.8 Estimates of flow and pressure fields when Rel = 1.6?105, G/L = 1.25,T/L = 0.4 and B/L = 0.4. The upper wall is translating from left toright at a velocity of 20m/s. The color map of the velocity field andpressure distribution are respectively given in units of m/s and kPa(gage). The time steps have been scaled by the periodic time L/U andare presented at t2? = 0.2 and t5? = 0.8. . . . . . . . . . . . . . . . . 574.9 Estimates of drag coefficient as a function of time for various G/L.Here Rel = 1.6? 105, T/L = 0.4 and B/L = 0.4. . . . . . . . . . . . . 584.10 Estimate of the bound between steady and unsteady behavior. Alisting of the range of the simulations is given as Series 1 in Table 4.1.The boundary between steady and unsteady is drawn as the whiteline in the figure and represents a threshold when the coefficient ofvariations diminishes below 0.05. The contour in this plot is coefficientof variation as defined by ?CdCd . . . . . . . . . . . . . . . . . . . . . . . 594.11 A schematic of the positions where the particles are released for thesimulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.12 Histogram of the particle positions released from Position 1 in (a)unsteady and (b) steady flow fields. . . . . . . . . . . . . . . . . . . . 624.13 Histogram of the particle positions released from Position 2 in (a)unsteady and (b) steady flow fields. . . . . . . . . . . . . . . . . . . . 634.14 Histogram of the particle positions released from Position 3 in (a)unsteady and (b) steady flow fields. . . . . . . . . . . . . . . . . . . . 64xvList of Figures5.1 Flow pattern in three different cavity aspect ratios when Re = 1.6 ?105. (a) k-type cavity with no vortex (T/W = 0.146). (b) d-typecavity with one main vortex (T/W = 1). (c) d-type cavity with morethan one vortices (T/W = 5). . . . . . . . . . . . . . . . . . . . . . . 695.2 Contours of Cd respect to the variations of cavity depth and Reynoldsnumber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70xviNomenclatureSymbolsA,K Constant values depend on inner and outer diameters, and also barsand grooves geometryA? Normalized bar crossing areaB Bar width, mmBEL Bar edge length, km/revC Consistency of pulp, %Cq Dimensionless flow rate, Q?Ro3Di Inner diameter of discDo Outer diameter of discG Gap between rotor and stator, mmG? Dimensionless gap, G/Rok the height of roughnessk1, k2 Empirical constantsL Cavity pitch, B +WM Constant value which covers sector and bar anglesN Number of grid pointsPn No-load power number, Powern??3Ro5Pn? Hydraulic power number, Powern???3Ro5xviiNomenclaturePowerM Mechanical loss, kWPowern Total no-load power excluding mechanical loss, kWPowern? Hydraulic no-load power, kWPowerNL Total no-load power, kWPowerP Pumping no-load Power, kWPowerr Refining power, kWPowert Total power, kWQ Flow rate, lpmRi Inner radius of discRo Outer radius of discRe Reynolds number, ?Ro2?Rel Reynolds number based on the cavity pitch, UL?T Groove depth, mmU Velocity of moving wall, m/sW Groove width, mmGreek? Correlation constant?? Ratio of the rotational speed of core flow between rotor and stator to therotational speed of rotor?turb Empirical turbulent flow parameter, CqRe15? Bar angle, [?]? Sector angle, [?]? Rotational speed, rpmxviiiAcknowledgmentsIn the first place, I would like to express my sincere gratitude to my supervisors,Professor James A. Olson and Professor D. Mark Martinez for their leadership andcontinual support during my research. Above all and the most needed, they providedme support and friendly help in various ways. I am deeply grateful to ProfessorRichard J. Kerekes for his guidance, suggestions and valuable discussions throughoutthe course of this research.In addition, I am deeply thankful to Dr. Ali Vakil for his helpful discussions andcritical comments. His passion for scientific problems has taught me a lot.I would like to thank my colleagues and the staff at the Pulp and Paper Center fortheir valuable insights on the various works we did together, specially Ali Elahimehr,Dr. Pirooz Darabi and Dr. Jens Heymer. This work would not be done without thehelp of George Soong.I gratefully acknowledge financial support of the Natural Sciences and EngineeringResearch Council of Canada through the Collaborative Research and Developmentprogram and through the support of our partners BC Hydro, FP Innovations, Cata-lyst Papers, Howe Sound Pulp and Paper, West Fraser Quesnel River Pulp, Canfor,Andritz, Arkema, Honeywell, WestCan Engineering, Advanced Fiber Technologies,Ontario Power Authority and CEATI international.I am grateful to my committee members Professor Richard J. Kerekes, Dr. DanaGrecov and Dr. Rodger Beatson for their great comments and input about my re-xixAcknowledgmentssearch.And finally, I would like to specially thank:? My brother, Mazdak: Thanks for your unconditional love. You are the bestgift of my life. No matter how far we are apart, I never stop loving, missingand caring about you.? My husband, Farzad: Thanks for your love, patience and kindness. Thank youfor always being by my side and for giving me the sweetest moments of my life.You are a constant comfort to me.xxDedicationTo my parents,Mahnaz & Mansourfor their endless love and support;xxiChapter 1IntroductionDuring the mechanical pulping process, multiple stages of high consistency (HC)refiners are used to convert wood chips into fibres. Pre-washed wood chips are fed intothe HC refiners at a consistency of 20?40%, and are broken into individual fibres bythe forces imposed by the bars of the opposing rotor and stator surfaces. Consistencyis defined as the ratio of the mass of fibres to the total mass of pulp suspension. Therefining action is continued further by a low consistency (LC) refiner after dilutingthe pulp suspension to a consistency of about 3 ? 4%. A mechanical process wherefibres are treated at consistencies under 6% is defined as low consistency (LC) refining[1, 2].HC refining is an energy intensive process. About 60% of the total electricalenergy in mechanical pulping process is consumed by the HC refiners [3]. To reduceenergy consumption, mechanical pulp producers are increasingly using energy efficientLC refining to offset the total energy consumed in the process. However, LC refiners,unlike HC refiners, have substantial no-load power, that is, the power to mostlyovercome the hydraulic, pumping and mechanical losses in the refiner. At best,the no-load power is 20% of the total applied power and depending on the refinertechnology, can be as high as 50% for larger refiners [4, 5, 6]. Understanding theno-load power and how it is consumed during refining is the first step in enhancingthe refining efficiency. Finding ways to decrease the no-load power would allow moreenergy to be transferred to the fibres thus increasing net LC refining power.1Chapter 1. IntroductionIn this work, a new correlation to estimate the no-load power in the LC refining ispresented. The proposed correlation provides guidelines to evaluate the effect of bothoperational and geometrical parameters on the no-load power. In addition, a series ofnumerical simulations are presented which obtain detailed insight into the LC refinerflow field. This methodology helps to better understand the no-load power.This thesis is presented in 5 chapters. The motivation for this work is givenin chapter 1. Chapter 2 introduces LC refiners, no-load power and flow fields in LCrefiners and more relevant literature in details. Following this, Chapter 3 presents theexperimental methodology that leads to better understand the no-load power in LCrefiner and the affecting parameters. In chapters 4 and 5, the numerical methodologyis explained that results to explore the flow field in the cross section of refiner. Thehighlights of this work are summarized in Chapter 6 as well as recommendations forfuture research.2Chapter 2BackgroundIn this thesis, we study the no-load power consumed in low consistency (LC) refinersin an attempt to minimize it. It is evident that the subject area, although quitespecialized, touches on many related areas and as such, are reviewed in this chapter.First, we introduce LC refiner in ?2.1 and survey the literature on no-load power.Then, we provide an overview of studies related to the power consumption due tothe flow field between roughened rotor-stator discs in ?2.2. The flow field in refineris similar to the flow field between two roughened rotating discs, which have beenstudied in detail, both experimentally and numerically.Moreover, there are numerous works that considered the turbulent flow in thechannel formed between two periodic corrugated walls which resembles the cross-sectional flow field of refiner. To better understand the flow field inside the refiner,in ?2.3, we try to summarise only those that appear to be most relevant.2.1 Low consistency refinerLC refiners are mechanical devices employed to modify papermaking fibre morphol-ogy. They are rotary devices having bar patterns on both the rotor and stator (Figure2.1). The rotor and stator are either disc or conical in shape and, during refining,are separated by a gap of about three-ten fibre diameters. Papermaking fibres arepumped axially through the hub of the stator, flow radially through the grooves of3Chapter 2. Background(a)? ?     Rotor  Stator ? Inlet Outlet           (b)  Rotor Stator U W T G B Figure 2.1: (a) Illustration of the configuration of a LC disc refiner and schematic ofthe grinding surface of an LC disc refiner. One disc is stationary in which a dilutepapermaking fibre suspension is fed into the machine. Patterns are machined on tothe surface of the plate. (b) cross section of the topography4Chapter 2. Backgroundthe discs, and are trapped between bars in the narrow gap between the rotor andstator. The fibres are ?beaten? or ?refined? by repeated impacts with the bars. Theythen leave the refiner radially and are subjected to further processing. Comprehen-sive details regarding the action of refiners on the changes in morphology of thepapermaking fibre can be found in the review by Page [7].This investigation focuses solely on disc refiners. Each disc is specified by a typicalarrangement of bars and grooves with constant sectional and grinding angles. Themain design parameters for disc refiners are inner and outer diameters (Di, Do), barwidth (B), groove width (W ), groove depth (T ), sector angle (?), and bar angle (?).Plate designs are typically characterized by Bar Edge Length (BEL) which is thetotal length of bar during a single rotation of the refiner disc and is estimated usingTAPPI standard TIP 0508-05 (1994). Later in 2009, Roux et al. [8] modified thedefinition proposed by TAPPI as follows:BEL = (2pi)2(Ro3 ?Ri33(W +B)2)(2.1)where Ro and Ri are the outer and inner radii of refiner disc, respectively.LC refiners have substantial ?no-load? power, that is, power to overcome thehydraulic, pumping and mechanical losses in the refiner. Generally, no-load powerrefers to the power used by the refiner for purposes other than changes in fibremorphology. Some researchers state that no-load power is the energy threshold atwhich the papermaking fibre undergoes changes in its morphology. Others define no-load power as the minimum energy required to rotate the rotor in a pulp suspension[9, 10]. Both definitions are correct, but clarity is needed to understand where eachone plays a role.To help distinguish these concepts, the schematic power curve of refining is shown5Chapter 2. Background  Refining Region No-load Region  Gap Total Applied Power   A Figure 2.2: Schematic graph of power vs. gap sizein Figure 2.2. This figure can be interpreted according to the two different defini-tions of no-load power. The refining region is defined to be the region where energyincreases rapidly with decreasing gap size. In this area the rapid increase in slope iscaused by changes in fibre morphology. At the lower limit of this region, the pointmarked ?A? is considered to be the no-load definition as determined by changes infibre morphology, and is the starting point of refiner loading. The point of refinerloading, where the variations in pulp properties are evident, occurs at different gapsizes depending on pulp type [11]. As gap increases, the curve asymptotically ap-proaches a constant value. This limit is defined to be the second definition of no-loadpower, i.e. the minimum energy required for free disc rotation in pulp suspension.Based on these different definitions, no-load power can be measured either at thefully open position or at the smaller gaps with pulp [12, 13] or with water [14]. Inindustry, either the total applied power measured for a pulp suspension at a gap of2.5mm, which is close to point ?A? on the right or the backed-off power is considered6Chapter 2. Backgroundto be the no-load power. As it is reported, the difference in no-load power obtainedfrom each of these definitions can be as much as 35% [15].Many authors have advanced scaling laws to correlate the power consumed tooperating conditions in order to understand the mechanism of refining [16, 17, 18,19, 5, 20, 21]. In essence, the following form has been proposed:Powert = Powerr + PowerNL (2.2)where Powert is the total power consumed, Powerr is the net power consumed tomodify the morphology of the fibre, and PowerNL is the no-load power. Most ofthese researchers have separated no-load power into three different contributions:? Hydraulic losses (Powern?): required energy to rotate the refiner disc in pulpsuspension close to the stationary disc.? Pumping losses (PowerP ): required energy consumed by refiner when pumpingpulp suspension from inlet to outlet of refiner.? Mechanical losses (PowerM): loss due to shaft and bearings friction.Based on this classification, a number of these research groups indicate thatPowerNL is related primarily to flow rate Q, rotational velocity ? , and the inner andouter diameters of the refiner plates, i.e. Di and Do, respectively. In 1967, Banks[22] proposed the following relationship to express the no-load power consumed by adisc refiner:PowerNL = k1?3Do5 + k2?2Do2 + PowerM (2.3)where k1 and k2 are empirical constants and PowerM represents the mechanicallosses. The first term in Equation 2.3 represents the power losses due to the turbulent7Chapter 2. Backgroundrotating motion of the disc in the stock and the second term represents the powerlosses due to pumping effect. Subsequently, Herbert et al. [5] suggested a similarformula for no-load power; however, the pumping term has included volumetric flowrate, Q:PowerNL = k1?3(Do5 ?23Di5)+ k2Q?2Do2 + PowerM (2.4)The most recently used formula to calculate the no-load power in industry [23] isas follows, however this empirical formula does not dimensionally sound correct:PowerNL = 102( ?100)3(Do100)4.3( 2WW +B)(T4)(2.5)Other relationships can be found in review given by Ebeling [18]. What is clearfrom these proposed formulas and others found in the literature is that there is noevidence of gap dependency in no-load power, and not all of the important operatingand design parameters are considered.In a recent work, Batchelor et al. [24] showed the relationship between power andgap size. According to their study, shown schematically in Figure 2.2, by increasingthe gap size, the applied power decreases and then approaches an asymptotic value atwide gaps. In their study, they proposed a negative exponential function to predictthe net power and a linear function to estimate the no-load power respect to the gapsize variations. For the smaller gaps, Luukkenen and Mohlin [25, 26, 27] demonstratethat the power is proportional to 1/G.These scaling laws however are rather incomplete as factors known to be importantare not considered in these descriptions. Several studies have been undertaken in anattempt to understand how various parameters affect the operation of refiners and theamount of energy consumed in the refining process. Dietemann et al. [4] and Rihs [9]8Chapter 2. Backgroundfound that increasing flow rate increases the no-load power slightly. Their work alsointroduced rotational speed as the main parameter and showed that no-load poweris proportional to the rotational speed cubed.Lundin [11] compared both mechanical and chemical pulp with water. Compar-ison of measured no-load power under similar operating conditions using water andmechanical pulp, in which the fibers are shorter than in chemical pulp, showed lessthan 10% change in the no-load power. Contrary to this, a significant difference wasfound between the no-load power of water and chemical pulp with long fibres. Thesame result has been reported by Dietemann et al. [4], Rihs [9] and Luukkenen [27].In mechanical pulping the average length of fibres is shorter compared to chemicalpulps and it is assumed to not influence the fluids turbulent viscosity. For long fibrespulps there can be an increase in power consumption due to the higher viscosity [28].The refiner plate outer diameter has a significant effect on no-load power [5, 22].Studies investigating the effect of groove depth showed that no-load power increasedwith deeper bars [29, 30]. In the most recent work, Dietemann et al. [4] postulatethat the no-load power increases with increasing the number of bars and grooves onthe plates.2.2 Flow field between two rotating discsIn order to understand no-load power in refining, it is instructive to understand theflow field inside the rotor-stator system. A wide range of studies has been conductedon turbulent flow confined between both stationary and rotating discs enclosed by ashroud [31, 32, 33, 34] and Launder et al. [35] published an extensive review on thiscomplex flow field.In addition, a comprehensive theoretical and experimental study of the flow inside9Chapter 2. BackgroundRegime Gap Description Best equationRegime 1 Small Laminar Flow, merged boundary layer Pn? = piG?ReRegime 2 Large Laminar Flow, separate boundary layer Pn? = 1.85G?110Re? 12Regime 3 Small Turbulent flow, merged boundary layer Pn? = 0.04G??16Re? 14Regime 4 Large Turbulent flow, separate boundary layer Pn? = 0.051G?110Re? 15Table 2.1: Different flow regimes inside an enclosed smooth rotor-statoran enclosed rotor-stator system has been carried out by Daily and Nece [36, 37] forboth smooth and rough surfaces. They have classified flow in four different regimesbased on Reynolds number and gap size between two plates. In their study, torquedata have been collected over a range of disc Reynolds numbers (Re = ?Ro2/?)from 103 to 107 for different gap sizes. It is worth mentioning that Reynolds numberranges from 106 to 5? 107 for most refiners used in industry. Table 2.1 gives a briefdescription of all four flow regimes where Pn? is the dimensionless power number inthe absence of pumping effects, and G? represents the non-dimensional gap size. Fora given G?, all four regimes may or may not be experienced for the practical rangeof Reynolds number, Re.They also reported a similar experiment for rough discs with relative roughnessesof Rok ? 1000, 2000 and 3200 for three different gap sizes and for 4?103 < Re < 6?106.k is the height of the roughness and Ro is the outer radius. The similar four flowregimes were that were originally obtained for smooth discs when roughness wasadded. It was reported that roughness had no significant effect on the Pn? in thelaminar regimes (1) and (2); while in the turbulent regimes (3) and (4), Pn? increasedas roughness increased. The point that the effects of roughness are apparent first hasbeen approximated by the below expression:10Chapter 2. BackgroundRe?Pn? = 0.55? 103(Rok)2/5(2.6)Beyond this critical Reynolds number, Pn? becomes greater than for correspondingsmooth discs. The zone of fully rough flow starts from:Re?Pn? = 0.575? 104(Rok)1/10(2.7)and the suggested formula to predict Pn? at a fully rough flow zone is given by:1?Pn?= 7.6log(Rok)? 4.8G?14 (2.8)Daily et al. [38] looked into the effect of superposed radial outflow on the to-tal power number (Pn) of a rotating disc and proposed the following expression forturbulent flow 2? 106 < Re < 107 when outflow is small:Pn = Pn?(1 + 13.9???turbG??18 ) (2.9)In this formula, ?? is the ratio of the rotational speed of core flow between ro-tor and stator to the rotational speed of rotor. ?turb is the empirical turbulent flowparameter which relates the superposed flow rate to the rotational speed. This pa-rameter is defined by Owen and Rogers based on a 1/7-power-law assumption forthe turbulent case: ?turb = CqRe15 where Cq = Q?Ro3 is the non-dimensional flow rate[39, 33].11Chapter 2. Background2.3 Turbulent flow between two parallelcorrugated wallsUnderstanding the flow field in the cross section of LC refiners is difficult. The dif-ficulty stems from the complexity of the moving boundary. There are a number ofgeometries in the literature which mimic aspects of the flow considered in LC refinersand insight into the industrial case can be gained by considering these first. We cate-gorize these geometries into four groups which will be summarized below (see Figure2.3). The major works for category I (see Figure 2.3a) are for pressure-driven Stokesflow between two stationary corrugated walls [40, 41, 42, 43, 44]. This is a slightgeneralization of the unidirectional problem of pressure driven 2D Poiseuille laminarflow between two flat parallel plane boundaries. This case has received consider-able attention in the literature because of the potential that corrugated walls havefor increasing the heat and mass transfer efficiencies in various transport processes.In general, most authors consider the limiting case in which the amplitude of thecorrugations are small in comparison to the spacing of the channel walls, i.e. whenT/G ? 0 and estimate the flow field using asymptotic methods. As expected, atlowest order, the solution approximates that of Poiseuille flow. At higher order, thesolution displays quite complicated behavior in which the flow decelerates where thechannel expands and accelerates where it contracts. An adverse pressure gradientis evident during deceleration. This may subsequently lead to flow separation andtransition.In the second category II are pressure-driven turbulent flows over rough walls(Figure 2.3b). Like category I, we find a substantial amount of literature in this arearelated to boundary layer control. This literature begins with an understanding of12Chapter 2. Background? ? (a) (b) (c) (d) Figure 2.3: Schematic of the different geometries found in the literature which approx-imate the case considered. (a) Pressure-driven laminar flow over corrugated walls.(b) Pressure-driven turbulent flow over one corrugated wall. (c) Lid driven cavityflow. This case can be either laminar or turbulent. (d) Lid-driven flow over opposingcorrugated walls. This geometry represents the case considered in this work.the turbulent boundary layer formed over a smooth plate. Nikuradse [45] gives thefollowing correlation for the velocity near the wallu+ = 1?ln y+ + Bo (2.10)where u+ is the dimensionless velocity defined by u??/?w ; y+ is the dimensionlessdistance normal to the wall defined by y??w/??2; ? is the Von Karman constant;Bo is a empirically-determined constant; and ? and ? are the density and kinematic13Chapter 2. Backgroundviscosity of the fluid. Zanoun et al. [46] and Jimenez [47] have summarized theliterature and shown that ? and Bo vary in the range of [?,Bo] ? [0.38, 0.45]?[3.5, 6.1].With roughness elements Nikuradse [45] has shown that the velocity field near thewall is given by an equation of the formu+ = 1?ln y+ + Bo ??Bo(k+s ) (2.11)where k+s is a roughness Reynolds number defined by ks??w/??2. The roughnessfunction, ?Bo, depends on type of roughness such as sand, sand mixture, threads,spheres etc. Examples of the form of ?Bo are given by Mokamati et al. [48].A number of authors have examined the local flow field within the roughnesselements either by direct flow visualization or through computation [49, 50, 51, 52,53, 54]. With flow over square-ribbed roughness elements, [55] phenomenologicallycharacterized two distinct flow fields, i.e. d? or k? type. This is illustrated in Figure2.4. Simpson [56] advances that the the transition from d?type to k?type occurswhen the aspect ratio of the cavity is T/W ? 0.25 and later, this value reported byother researchers [47, 57, 58]. With d?type roughness, T/W > 0.25, the cavity isoccupied primarily by a single vortex, with two minor vortices found in the lowercorners. This flow is usually considered to be steady. With k?type roughness, i.e.T/W < 0.25, the central vortex is absent and there is penetration of the streamlinesfrom the outer flow into the cavity. In contrast to d?type, this flow displays sometime dependent behavior as Keshmiri et al. [59] indicate the potential for vortexshedding.In the third category III are driven cavity flows (Figure 2.3c). Driven cavity flows,by definition, are bounded internal flows resulting from the motion of a boundary.Most studies have been performed on rectangular cavities with the upper boundary14Chapter 2. BackgroundFigure 2.4: Schematic of the phenomenological flow fields found over ribbed roughnesselements: (a) d-type flow; (b) k-type flow.translating at a constant velocity [60, 61, 62]. The case where G = 0 represents animportant flow that has been a benchmark for fundamental fluid mechanics studies inall aspects of experimental, theoretical and numerical work. The flow contained in thisgeometry is similar to that described for the d-type classification in category II flows:an internal bounded vortex exists with corner vortices in the lower corners. It hasbeen shown by Pan and Acrivos [62] and Hellou and Coutanceau [63] that for Stokesflow as the ratio T/W increases above unity a transition occurs where the cornervortices grow progressively larger and coalesce into a second primary vortex. Furtherincreasing T/W , this process continues and it has been proven mathematically byMoffat [64] that an infinitely deep cavity would have an infinite number of equallyspaced vortices. Exploring higher Reynolds numbers lid-driven cavity flow has beenobserved to become quasi-periodic above Reynolds number of 7400 and chaotic aboveReynolds number of approximately 11000 [65, 66]. A comprehensive review of fluid15Chapter 2. Backgroundmechanics in the driven cavity is provided by Shankar and Deshpande [67].The case where G > 0 is of interest, because it represents a geometry similarto that found in a LC refiner. Wittberg et al. [68] and Khohkar [69] simulated athree-dimensional cavity with an imposed pressure gradient along the cavity axis.The formation of multiple primary vortices under T/W ratio of 1.5 was observed,as in the case of G = 0 above. Note that these works lack any description of time-dependency in cases where Reynolds exceeds the onset of periodic/chaotic behavior.In recent years, the flow field in periodically temporal lid-driven cavity has beenextensively examined for both laminar and turbulent flows [70, 71, 72] where the flowin the cavity is driven by a flat lid with oscillatory motion, e.g. sinusoidal motion.Although this oscillatory motion causes the periodic time-dependent behaviours inthe flow field, it can not describe the time-dependent flow field in the refiner crosssection. In the refiner, motion of a spatially periodic boundary leads to the temporalvariation in the flow.There are only a limited number of studies in category IV (see Figure 2.3d)and these have been found within the Pulp & Paper literature. These studies havefocussed on high-speed photography and describe the flow field qualitatively [68, 73,74, 75]. For very dilute suspensions, Fox et al. [76, 77] reported that the suspensionflows inward in the stationary and outward in the moving cavities (see Figure 2.5).Minor recirculation currents, called secondary and tertiary flows, have also beenobserved. Note that all descriptions of the refiner flow field mentioned above lack anydescription of time dependency. Clearly this flow geometry resembles driven cavityflow where the shear imposed on the top of each cavity acts impulsively, i.e. it is nota uniform driving force. Nissan [74] is one of a few researchers who has mentionedthat chaotic behavior inside the refiner arises in a time-dependent driven cavity flow.16Chapter 2. BackgroundUTertiary Flow Secondary Flow Primary FlowFigure 2.5: Schematic of the flow in the cavities of a refiner plate. ?+? and ??represent opposing flow fields in z-direction.In the most recent work, Kondora and Asendrych [78] numerically simulated andinvestigated the effect of pulp consistency for the three-dimensional unsteady flowin LC refiner. Their results demonstrated the general flow pattern reported by Fox[76, 77] and most importantly, identified the inward flow in the stator grooves.2.4 Effect of groove depth in refiningBased on the literature [79, 30, 22], Groove depth is expected to be high enoughto let the proper amount of pulp suspension pumped in the refiner and low enoughto refine the large amount of fibres. Excessive groove depth results in more fibrespassing through the refiner untreated; while decreased groove depth brings the fibersto the bar edges and promoting refining action, but restricting flow rate and reducinghydraulic capacity.On the other hand, it was found that hydrodynamic losses in refiner increases17Chapter 2. Backgroundwith the deeper bars [29, 30]. In 1976, Siewert and Selder [80] reported a linearrelationship between groove depth and no-load power. Antku and Ludwig [79] foundthat reducing a groove depth from 6mm to 3mm alters no-load power about 40%.2.5 Summary of literatureAlthough pervious researchers have made huge number of advances, as listed above,there are some limitations and unanswered questions that we are willing to focus onthem in this thesis:? The present descriptions of refiners by scaling laws are by no means a compre-hensive measure of the no-load power consumed during operating. They reflectthe fact that energy is consumed and is related to factors such as diameter androtational speed, but other factors known to be important are not consideredin these descriptions.? The flow patterns within the refiner are complex and have yet to be understood.In general, flow is observed to occur radially outward in the grooves of the rotorand inward in the grooves of the stator. Secondary and tertiary flows havebeen reported. Neither the effect of gap size nor groove dimension have beenconsidered in this analysis.2.6 Objectives of the thesisThe overall goal of this study is to minimize the no-load power consumption duringthe pulping process in low consistency refining. As a result, the specific objectives ofthis study include the following:18Chapter 2. Background? To develop a correlation to estimate the no-load power by determining theeffect of pulp suspension rheology, plate design and refiner operating conditionsindividually.? To extend our understanding of time-dependent flow field in LC refining, specif-ically, for various gap sizes and groove aspect ratios.2.7 Approaches of the thesisGiven these objectives, our research approaches are focused on targeting each one ofthese objectives separately:? Chapter 3: A series of experimental studies is conducted to measure the no-loadpower for a number of laboratory and industrial LC refiners. We measure thepower consumed as a function of gap size, flow rate, and rotational speed forboth water and mechanical pulp with different consistencies. A dimensionalanalysis is performed on this data set to develop a scaling law.? Chapter 4: A deeper understanding of the no-load power is studied computa-tionally in this chapter. Simulation of this problem is particulary difficult as itinvolves the time-dependent, three-dimensional flow of a multiphase suspensionin a swirling turbulent flow. Due to this complexity, the geometry is reduced toa simpler geometry, i.e. two-dimensional flow field in the cross section of a LCrefiner. A large number of unsteady simulations are conducted over the rangeof velocities and gap sizes considering water as the fluid inside the refiner.? Chapter 5: The two-dimensional numerical study is extended to investigate theeffect of groove aspect ratio for a wide range of velocities. All results in thisstudy are obtained from the steady-state simulations.19Chapter 3Experimental Measurement of theNo-load Power in LC RefiningIn this chapter, we experimentally measure the effect of most of the affecting param-eters on no-load power in LC refiners and ultimately, we aim to develop a correlationfor no-load power. Despite the literature contains a large number of experimentaland theoretical studies of the no-load power in LC refining and also different correla-tions have been proposed, but there is no comprehensive experimental investigationof the effect of all significant parameters and the suggested formulas just cover a fewof these parameters.The chapter proceeds as follows. Below in ?3.1 we introduce the experimentalsetup for the laboratory refiners. Then, in ?3.2 we qualitatively introduces the mainresults for the effect of gap size, rotational speed, flow rate, rotational speed, pulpsuspension consistency and bar and groove widths on the pilot scale refiners. In ?3.3,we propose a new correlation for our laboratory refiners based upon our findings ofthe previous section and then, by collecting data of inner and outer diameters andgroove depth for various mill refiners, we will be able to extend our correlation toindustrial scales. Finally, the chapter ends with conclusion in ?3.4.20Chapter 3. Experimental Measurement of the No-load Power in LC Refining            Refiner Pump Tank 2 Tank 1     Figure 3.1: Illustration of the LC refiner loop used for all trials3.1 Experimental setupIn this work, we used a series of refiner plates with constant inner and outer diameters(Di, Do) and constant groove depth (T ) to experimentally understand the effect ofsome parameters on no-load power. Experiments were performed in two flow loopswith two different refiners varying in size; a 12??(0.305m) Sprout-Waldron single discas well as a 16??(0.406m) Aikawa single disc refiner. Both flow loops consist of twolarge tanks, a centrifugal pump, and a single disc LC refiner (Figure 3.1). Fluid ispumped from the first tank to the refiner; then passes through the center of sta-21Chapter 3. Experimental Measurement of the No-load Power in LC RefiningDo Di B W T Angle BEL(in) (in) (mm) (mm) (mm) [?] (km/rev)Plate 1 16 8.75 1.0 2.4 4.8 15 5.59Plate 2 16 8.75 1.6 3.2 4.8 15 2.74Plate 3 16 8.75 3.2 4.8 4.8 15 0.99Plate 4 16 8.75 2.0 3.6 4.8 15 2.01Plate 5 16 8.75 1.0 1.6 4.8 15 10.1Plate 6 16 8.75 1.0 1.3 4.8 15 12.9Plate 7 12 6.5 3.2 4.8 3.2 15 0.417Plate 8 12 6.5 1.6 3.2 3.2 15 1.159Plate 9 12 6.5 1.0 2.8 3.2 15 1.85Table 3.1: Specifications of all nine lab refiner platestor, is forced outward from refiner and then returns back to the second tank. Theouter diameter of refiner disc in one loop is 12??(0.305m) and in the other loop is16??(0.406m). The experiments were carried out in six pairs of rotor and stator discswith different bar and groove widths and constant groove depth of 4.8mm for the16?? diameter refiner and three different pairs of rotor and stator discs with differentbar and groove widths and identical groove depth of 3.2mm for 12?? diameter refiner.Table 3.1 includes the geometrical characteristics of each pair of the discs.Each refiner loop is instrumented such that for a given gap size, rotational speed,flow rate, and the total power can be recorded using LABVIEW software. A largenumber of trials were conducted to measure no-load power as a function of thesevariables for both water and low consistency pulp suspension as the circulating flu-ids. The pulp used was a Chemi-Thermo-Mechanical-Pulp (CTMP) which is beingproduced by a combination of the mechanical and chemical processes [81, 82].For experiments conducted with plates 7?9, the rotational speed was varied from400 to 1200 rpm while the gap size was changed from 0.2 to 5mm. Measurementswere obtained with both water and pulp for 300, 600 and 900 lpm flow rates for all22Chapter 3. Experimental Measurement of the No-load Power in LC Refining12?? plates 16?? plates-Water 16?? plates-Pulp9.4? 105 < Re < 2.8? 106 1.6? 106 < Re < 6.3? 106 1.6? 106 < Re < 6.3? 1060.0013 < G? < 0.035 0.005 < G? < 0.045 0.0001 < G? < 0.0450.011 < Cq < 0.1 0.007 < Cq < 0.075 0.007 < Cq < 0.075Table 3.2: Range of operating variables for the experimental setup12?? plates. Likewise, for the plates 1? 6, the rotational speed was varied from 400 to1500 rpm while the gap size changes from 0.5mm to maximum possible size of 9mmfor water and from very small gap, i.e. 0.02mm to 9mm for pulp experiments. Therange of flow rate changes from 600 to 1500 lpm for all 16?? plates. A summary of therange of the non-dimensional variables for two series of plates is shown in Table 3.2.Some experiments were repeated 3? 4 times which yields error for all these casesof less than 6%. One source of error in these measurements was the variation oftemperature for each case since the water/suspension re-circulated a closed loop nu-merous times. It was difficult to keep a constant fluid temperature for each trial.Temperature in the 12?? refiner loop had been varying between 25?C to 40?C for wa-ter and 55?C to 65?C for pulp suspension. Likewise, fluid temperature in the 16??refiner loop had been changing between 30?C to 45?C for water and 55?C to 65?Cfor pulp suspension.Figure 3.2 compares both the mechanical loss and the total no-load power forthe 16?? disc refiner. Total no-load power has measured for water at Q = 1000 lpmand G = 9mm. Shaft and bearing losses (i.e. mechanical power) are measured byrotating refiner disc in the absence of water at various rotational speeds. This poweris mainly the function of rotor speed and increases slowly as the motor speed growsup. Furthermore, as shown in this figure, plate design and gap size between rotorand stator have no effect on the measured mechanical losses. In comparison withthe total no-load power, the ratio of the mechanical loss to the total no-load power23Chapter 3. Experimental Measurement of the No-load Power in LC Refining048121620100 300 500 700 900 1100 1300Power (kW) Rotational speed (rpm) Plate3, Gap=2 mmPlate1, Gap=2 mmPlate3, Gap=9 mmPlate1, Gap=9 mmPlate3, Total no-load powerMechanical loss Figure 3.2: Comparison of mechanical loss respect to the total no-load power for two16?? plates (Q = 1000 lpm and G = 9mm)decreases as the motor speed goes up.Since the aim of the study is to gain knowledge about the hydraulic/pumpinglosses, the mechanical power consumption has been deducted from all reported powersfrom here on. The experimental results obtained for the 16?? plates were collectedin two steps; for the first step, the hydraulic power (Powern?) due to the rotationof the rotor in fluid was measured and then at the next step, the total no-loadpower (Powern) which covers both hydraulic and pumping powers, was measured.To measure the hydraulic power, the valve was closed, no flow was allowed to pumpthrough the refiner and water was confined between rotor and stator. It should bewarned that closing the valve while under power may result in steam generationand dangerous pressurization of the refiner casing. The power data was collected byvarying gap size and rotational speed. The total no-load power was measured whenthere was flow through the refiner. By collecting data for six 16?? plates, the obtaineddata is used to provide a statistical model for prediction of no-load power based onall operational variables, say rotational speed (?), flow rate (Q) and gap size (G) and24Chapter 3. Experimental Measurement of the No-load Power in LC Refiningalso geometrical parameters, bar width (B), and groove width (W ). To do this, themodel will be presented in terms of these non-dimensional variables:Pn =Powern??3Ro5, Cq =Q?Ro3, Re = ?Ro2?,G? = GRo(3.1)This form of formula can be applied to plates with constant Ri, Ro and T . Finally,collected data for both 16?? and 12?? lab refiners and also a series of mill data reportedin the literature [27] has been used to generalize the correlation to a wide range ofrefiner sizes.3.2 ResultsThe pulp used in all experiments is a Chemi-Thermo-Mechanical-Pulp (CTMP) con-sisting of spruce, pine and fir (SPF) tree species. Initial length-weighted average fibrelength of these fibres is about 1.9mm. To study the effect of consistency of pulp onno-load power, one plate with 16?? diameter (Plate 2) and another plate with 12??diameter (Plate 7) have been chosen and experiments were run for both pulp andwater. For Plate 2, pulps with consistencies of 1.5% and 3.5% have been used andfor Plate 7, the consistency of pulp was chosen to be around 3%. The density of lowconsistency pulp suspension is approximated as the density of water.By comparison of power for both water and mechanical pulp for the 16?? plate,it was initially observed that at wide gaps there is almost no significant differencebetween the measured power for water and for pulp suspensions with 1.5% and 3.5%consistencies. Figure 3.3a and Figure 3.3b show the hydraulic and total no-loadpowers, respectively, as a function of rotational speed for these three different fluidsat wide gaps. The total no-load power was collected for constant flow rate of 600 lpm.25Chapter 3. Experimental Measurement of the No-load Power in LC RefiningA strong correlation for rotational speed can be seen; while under similar conditions,almost the same hydraulic and total no-load powers were measured for both pulpand water. As mentioned in ?2.1, the difference of less than 10% in the no-loadpower of water and mechanical pulp has been reported previously [4, 9, 11, 27]. Theidentical behaviours of these two fluids in the no-load region may also be explained bythe range of temperatures that each of them have been measured at. As mentionedearlier, experiments of 16?? refiner loop with pulp suspension have been performed inthe higher temperature of 55?C to 65?C; while the temperature of experiments withwater was ranged between 30?C to 45?C.Figure 3.4a and Figure 3.4b shows the comparison of water with 3% pulp for the12?? plate and two different rotational speeds. Based on these figures, the behavioursof both pulp and water are almost the same at wide gaps and by closing the gapbetween rotor and stator, from a specific gap (Gl) around 2mm, their trends startseparating.Likewise, Figure 3.5 reveals trends of power as a function of gap size of Plate 2with 16?? diameter for water, 1.5% and 3.5% pulps. Gap varies from closed distanceto the wide gap of 9mm. By decreasing the gap from 9mm down to the gap around2mm, the behaviors of all fluids are similar to each other and there is only about6 ? 7% variation which is in the range of experimental errors. For the gaps smallerthan 2mm, a sudden separation happens in trends of pulp and water.Lets introduce the starting point of separation as point of refiner loading, Gl. Toinvestigate the reason behind the sudden change in the slope of pulp curve, pulpproperties were examined for G < Gl. Figure 3.6 to Figure 3.8 display freeness, fibrelength and tensile variations of fibres by gap size, respectively. Results represent datafor the 16?? refiner at a constant flow rate of Q = 500 lpm and three different rotational26Chapter 3. Experimental Measurement of the No-load Power in LC Refining(a)051015202530500 600 700 800 900 1000 1100 1200 1300Hydraulic Power (kW)Rotational Speed (rpm)3.5% Pulp1.5% PulpWater(b)051015202530500 600 700 800 900 1000 1100 1200 1300Total No-Load Power (kW) Rotational Speed (rpm) 3.5% Pulp1.5% PulpWaterFigure 3.3: Comparison between power of water and pulp with two different consis-tencies for Plate 2: (a) Hydraulic power, (b) Total no-load power when Q = 600 lpm.27Chapter 3. Experimental Measurement of the No-load Power in LC Refining(a)12340 1 2 3 4 5 6Total  Power (kW) Gap (mm) Water-600rpm 3% Pulp-600rpm(b)135790 1 2 3 4 5 6Total  Power (kW) Gap (mm) Water-800rpm 3% Pulp-800rpmFigure 3.4: Total power vs. gap for Plate 7: (a) Q = 600 lpm, ? = 600 rpm, (b)Q = 600 lpm, ? = 800 rpm28Chapter 3. Experimental Measurement of the No-load Power in LC Refining0 1 2 3 4 5 6 7 8 9 102030405060708090Gap (mm)Total Power (kW)   GlWater1.5% Pulp3% PulpFigure 3.5: Total power vs. gap for Plate 2: Q = 500 lpm and ? = 1200 rpmspeeds. Figure 3.6 shows the effect of gap size on freeness (standard measure for theability for water to drain through the pulp). By decreasing the gap between rotorand stator, freeness starts dropping for G < 2mm. As it is shown in Figure 3.7, thelength of fibres starts shortening for G < 2mm as well. Figure 3.8 shows that theincrease in tensile strength of the paper has a similar behavior as the other propertieswith decreasing gap.From all three figures above, it appears that at higher rotational speeds the refinerstarts to change properties of fibre at larger gaps, but the point of refiner loading (Gl)does not go further than 2mm for all three rotational speeds. It may be concludedthat the value of Gl ? 2mm relates to the initial length-weighted average fibre length29Chapter 3. Experimental Measurement of the No-load Power in LC Refining1502002503003504004500 2 4 6 8 10Freeness (mlCSF) Gap (mm) 1200RPM1000RPM800RPMFigure 3.6: Freeness of fibers at various gap sizes between rotor and stator for Plate2 and Q = 500 lpm00.511.522.50 1 2 3 4 5 6 7 8 9 10Fibre Length (mm) Gap (mm) 1200RPM1000RPM800RPMFigure 3.7: Length-weighted (LW ) average length of fibers at various gap sizes be-tween rotor and stator for Plate 2 and Q = 500 lpmof these fibres which is about 1.9mm. Beyond this point, the behavior of both waterand pulp are identical for Gl < G. Figure 3.9a and Figure 3.9b include the graphs ofpower respect to the gap for two 16?? plates. Each figure shows power for two differentrotational speeds and different flow rates. The trends in each figure are categorizedto two groups; one for 600 rpm and the other for 800 rpm. The trends at each grouprepresent hydraulic power and also total no-load power obtained for different flowrates of 600 lpm, 800 lpm and 1000 lpm.Since the total no-load power shown for different flow rates consists of both hy-30Chapter 3. Experimental Measurement of the No-load Power in LC Refining3537394143450 2 4 6 8 10Tensile Index (N.m/g) Gap (mm) 1200RPM1000RPM800RPMFigure 3.8: Tensile of fibers at various gap sizes between rotor and stator for Plate 2and Q = 500 lpmdraulic and pumping powers, it can be seen that for a constant flow rate of 800 lpmat wide gaps, say 9mm, about 10% of total no-load power consumption goes to thepumping power; while for the same flow rate and smaller gaps, say 2mm, the pump-ing power covers about 25% of the total no-load power and this value is higher forsmaller gap sizes. From these figures, we see that hydraulic power is dependent onrotational speed. Pumping power, which is the difference between the total no-loadpower and hydraulic power, depends on gap size, rotational speed and flow rate. Hy-draulic power can be interpreted as the total no-load power when Q = 0 lpm and isindependent of gap size; while by increasing the flow rate, the amount of total no-load power increases slowly. Further, the data suggests that the total no-load powerdecreases by increasing the gap.The hydraulic power and gap for all trials is plotted in Figure 3.10 as non-dimensional hydraulic power (Pn? = Powern???3Ro5) and non-dimensional gap size. It shouldbe noted that error bar on each data point shows the standard deviation of hydraulicpower numbers collected for a wide range of rotational speeds at a specific gap. Asindicated in this figure, Pn? does not vary by changing the gap size for all six platesand trends show straight lines for all gap sizes from small gaps to wide gaps. Pn?s31Chapter 3. Experimental Measurement of the No-load Power in LC Refining(a)0246810120 2 4 6 8 10 12Power (kW) Gap (mm) 800 rpm 600 rpm (b)0246810120 2 4 6 8 10 12Power (kW) Gap (mm) 800 rpm 600 rpm Figure 3.9: Graphs of total no-load power collected for water vs. gap for two differentrotational speeds and various flow rates for two 16?? plates (a) Plate 2 and (b) Plate5. At no flow case (hydraulic power), the no-load power is independent of gap.(2 : Q = 0 lpm;? : Q = 600 lpm; ? : Q = 800 lpm;4 : Q = 1000 lpm)32Chapter 3. Experimental Measurement of the No-load Power in LC Refiningfor all plates are close to each other and the difference between the upper Pn? whichallocated to Plate 1 and the lower one for Plate 6 is about 10% and can be explainedby the difference in bar and groove widths. Later, it will be explained how Pn? canbe related to the geometry of plates.0.0350.0370.0390.0410.0430.0450.0470 0.01 0.02 0.03 0.04 0.05 0.06Hydraulic power number  G* Plate1Plate2Plate3Plate4Plate5Plate6Figure 3.10: Correlation between hydraulic power number and dimensionless gap forall 16?? platesFigure 3.9 shows that the total no-load power decreases with increasing gap. Inthe other word, since experimental data indicates that hydraulic power is independentof gap size, the only term that can vary by gap is pumping power. Following Nece andDaily [37], we propose that PowerP ? G?18 which stands in good agreement with ourobservations. Figure 3.11 shows the relation between hydraulic power and rotationalspeed for all plates at wide gaps, e.g. 8 or 9 mm. It indicates that hydraulic powerdepends on ?3, which means that Pn? is independent of Reynolds Number, Re.The collected data show a slight dependency of total no-load power number onReynolds number which means that pumping power number is dependent on Reynoldsnumber. Results indicate that pumping power is proportional to ?2.2 or pumpingpower number is proportional to Re0.2. This finding is in good agreement with whatDaily et al. found [38].33Chapter 3. Experimental Measurement of the No-load Power in LC Refining01020304050600 500 1000 1500Hydraulic Power (kW) Rotational Speed (rpm) Plate1Plate2Plate3Plate4Plate5Plate6Figure 3.11: Cubic dependency of hydraulic power on rotational speed shown for all16?? plates at G = 9mmFigure 3.12 shows how no-load power increases by flow rate. This figure representspower as a function of flow rate for Plate 4 for three rotational speeds at wide gap of9mm. Power at Q = 0 lpm represents hydraulic power where there is no evidence ofpumping effect. Graphs show a slight and linear relation between total no-load powerand flow rate. Based on the obtained data, 20% increase in the flow rate makes a 5%change in no-load power.As mentioned earlier, there is a difference in the measured Pn? of all six platesthat is a function of bar and groove width variations. First, we examine the threeplates with bar width of B = 1mm. As it is shown in Table 3.3, Plate 1 with thewidest groove width consumes more hydraulic power. Therefore, for the plates withthe identical bar width, the wider the groove width is, the higher energy consumes.A study to relate the values of Pn? to plates geometry is indicated that the dif-ference between the hydraulic powers of the plates cannot be explained by BEL of34Chapter 3. Experimental Measurement of the No-load Power in LC Refining0481216200 500 1000 1500 2000Power (kW) Flowrate (lpm) 600 RPM800 RPM1000 RPMFigure 3.12: Increase in total no-load power as a function of flow rate for Plate 4 atG = 9mmW (mm) Pn?Plate 1 2.4 0.0439Plate 5 1.6 0.0417Plate 6 1.3 0.0396Table 3.3: Comparison of Pn? for three plates with B = 1mm and different groovewidthsplates but by a new parameter:? = WW +B(3.2)where ? is called ?Roughness density?. Figure 3.13 shows how Pn? relates to ?.Roux et al. [83] define n = 2piRoW+B as the total number of bars and grooves that canpotentially exist on refiner disc in radial direction without any angle. Based on thisdefinition, ? generally represents ratio of area of grooves to the total area of refinerdisc. In other words, for the refiner plates with a constant groove depth, ? is theratio of the total grooves area to the total area of both grooves and bars. Increasing35Chapter 3. Experimental Measurement of the No-load Power in LC Refining0.5 0.55 0.6 0.65 0.7 0.75 0.80.0390.040.0410.0420.0430.0440.045?P*n  Figure 3.13: Correlation between hydraulic power number and ? for all 16?? lab plates? leads to smaller surface between bars and greater groove volume and consequentlyto the more energy dissipation.In a most recent work, Elahimehr et al. [84] are shown that:A? = 1.14(BW +B)2( ?2pi)0.4( 1sin?)0.5(3.3)where A? presents the normalized bar crossing area and ? and ? are sector andbar angles, respectively. Combining this relation with our new roughness densityparameter, ?, gives:A? = M(1? ?)2 (3.4)36Chapter 3. Experimental Measurement of the No-load Power in LC Refiningwhere M is a constant value and covers both sector and bar angles which are constantfor all 16?? plates.3.3 DiscussionIn the previous sections, the effect of consistency (C), operating parameters (?,G,Q)and some geometrical parameters (W,B) on no-load power was qualitatively andindividually studied. By combining the formats of the previous formulas proposed topredict the no-load power (see Equations 2.3 and 2.4) and the equation proposed byDaily et al. [38] (see Equation 2.9), we propose a new correlation to quantitativelyrelate all six parameters to no-load power:Powern = A0?3(WW +B)?+K0?2.2QG?18 (3.5)Applying non-dimensional parameters changes the formula to:Pn = A?? +KCqRe0.2G??18 (3.6)where A and K are constant values and depend on inner and outer diameters, andalso bars and grooves geometry. This form of formula is applicable to all plates withconstant Ri, Ro and T .The first term represents the hydraulic power number where there is no effect ofpumping power. Hydraulic power is the major part of no-load power consumption.Pn? is independent of Re and G?. Since the only differences between the plates arebar and groove widths, what makes variation in hydraulic power is roughness density,?. From Least-Square curve fitting method, ? was calculated as ? = 0.478? 0.005.The second term is the pumping power and shows the required power to pump37Chapter 3. Experimental Measurement of the No-load Power in LC Refiningfluid from inlet to outlet. Based on the findings, it varies linearly by flow rate. On theother hand, experiments are shown that pumping power number is not independentof Re and as it is indicated in Figure 3.9, this power is dependent on gap size. Theform of non-dimensional parameters in this correlation is in good agreement withwhat suggested by Daily et al. [38].Figure 3.14 shows the measured power numbers versus the predicted power num-bers calculated by the proposed correlation of Equation 3.6 for all trials of 16?? platesand as it can be seen, the predicted values are in good agreement with the experi-mental data. The values of all coefficients corresponding to the correlation for the16?? plates are summarized in Table 3.4.Plate A ? K R2All 16?? plates 0.0515? 0.0002 0.478? 0.005 0.0115? 0.001 0.91Table 3.4: Coefficients of the proposed correlation for all plates with 16?? diametersBased on the literatures, a few studies has been done on the effect of groove depthon no-load power. The common conclusion of all these literatures is that no-loadpower is dependent on the groove depth and decreasing the groove depth restrictingflow rate and reducing hydraulic and pumping capacity [29, 30] and therefore reducesno-load power consumption. In the more general case of rotor-stator confined bya stationary housing, some empirical equations have been proposed for the powerconsumption as a function of roughness for the turbulent flow between rotor andstator [37, 85]. Based on these studies, power increases by increasing the roughness forthe fully rough surfaces and this dependency can be described either by logarithmicor power laws.On the other hand, analyses of losses due to the rotation of a smooth disc in afluid indicate that disc friction is a function of diameter to the 5th power [86, 87]. For38Chapter 3. Experimental Measurement of the No-load Power in LC Refining0.04 0.045 0.05 0.055 0.06 0.065 0.070.040.0450.050.0550.060.0650.07Predicted Power NumberMeasured Power Number  Figure 3.14: Correlation between predicted and measured no-load powers for allplates with 16?? diametersthe discs with roughness, it is shown that the power does not consume exactly withthe diameter to the 5th power and this value is a little smaller than 5 [85, 37].Table 3.5 is summarized all data for different sizes of disc refiners collected fromlab and mill refiner machines. Mill data are collected from mechanical pulp andpaper mills. The refiner operational variables were controlled and recorded by themills Distributed Control system (DCS).Figure 3.15 indicates P ???3 respect to outer diameter of various disc refiners col-39Chapter 3. Experimental Measurement of the No-load Power in LC RefiningRefiners Do BEL W B T ? Powern?(in) (km/rev) (mm) (mm) (mm) (rpm) (kW )Mill 1 58 486.00 3 1.45 5.2 425 473Mill 2 55 377 2.6 1.15 4 425 307Mill 3 42 96.72 3.1 2.05 6.1 509 308Mill 4 58 368 3.77 2.375 6.5 400 350Mill 5 26 15 3.4 3.4 7.45 900 203Mill 6 52 410 2.4 1 5 425 420Mill 7 58 320 2.29 1.52 6.1 425 660Mill 8 72 414 3.21 1.6 7.35 320 800Mill 9 24 16 3.2 2 6.4 900 100Mill 10 34 30 3.175 3.175 6.35 600 159Plate 1 16 5.59 2.4 1 4.8 1200 30.2Plate 2 16 2.74 3.2 1.6 4.8 1200 29.3Plate 3 16 0.99 4.8 3.2 4.8 1200 27.7Plate 4 16 2.01 3.6 2 4.8 1200 29.2Plate 5 16 10.1 1.6 1 4.8 1200 28.6Plate 6 16 12.9 1.3 1 4.8 1200 27.2Plate 7 12 0.417 4.8 3.2 3.2 1200 11.2Plate 8 12 1.159 3.2 1.6 3.2 1200 11.7Plate 9 12 1.85 2.8 1 3.2 1200 12.1Table 3.5: Plate design and operating conditions of both lab and mill refinerslected from mill and lab refiner machines. The results presented here stand in goodagreement with what Daily et al. [38] and Poullikkas [85] have found and P ???3 is notexactly but closely proportional to the outer diameter to the 5th power. Moreover,as Herbert and Marsh [5] proposed DiDo ? 0.6 to have the optimum value of refiningpower, recently this ratio is considered in almost all the disc refiner designs.From the observed relationships between different variables affecting on hydraulicpower, correlation is sought for an exponential multiple regression form. A leastsquare fit curve is applied on all data listed in Table 3.5 and the following values areobtained:40Chapter 3. Experimental Measurement of the No-load Power in LC Refining0 0.4 0.8 1.2 1.6 20510152025Do (m)P???3 (m5)Figure 3.15: Correlation between hydraulic power and diameter for the range of laband mill platesPn? = (1.14? 0.2)(TRo)0.716?0.050( WW +B)0.478?0.005(3.7)orPowern? = (1.14? 0.2)??3 (Ro)4.284?0.050 (T )0.716?0.050(WW +B)0.478?0.005(3.8)Based on these equations, hydraulic power is proportional to Ro4.284?0.050 which41Chapter 3. Experimental Measurement of the No-load Power in LC Refiningis in good agreement with the formula proposed by AFT/FinebarTM [23]. BothEquation 2.5 and the proposed correlation in Equation 3.8 show that the no-loadpower depends on T and WW+B , however, in the former equation, the no-load poweris linearly proportional to these two variables, but in the latter equation, the no-loadpower is proportional to T 0.716?0.050 and( WW+B)0.478?0.005.To determine the quality of the proposed correlation, measured hydraulic powervalues are plotted with values calculated from the Equation 3.7 in Figure 3.16. Thedash lines in the figure indicate a good correlation between both experimental andcorrelated values, R2 ? 0.91.Although there is a good agreement between the measured and predicted val-ues, this figure may occlude the dependence of the data on for all three 12?? plates.Hence, in Figure 3.17, we present the hydraulic no-load power, for both predictedand measured, as a function of ? to magnify the disagreement, for instance, for aclose-up window in the range of 0 < Powern? < 20. As expected, Powern? increasesby increasing ? and both graphs follows the same trend. Deviation of measured datafrom the predicted values can be explained by the experimental errors.3.4 ConclusionIn this chapter, no-load power was experimentally measured for two pilot refinerswith 12?? and 16?? diameters for a wide range of gap sizes, groove widths, bar widths,rotational speeds and flow rates with the constant bar angles. The no-load poweris considered to have two main components: hydraulic power and pumping power.Hydraulic power goes to overcome the hydraulic and viscous losses in the fluid andthe pumping power goes to pumping fluid from the inlet to outlet. Hydraulic poweris the dominant power with respect to the pumping power. The effect of the design42Chapter 3. Experimental Measurement of the No-load Power in LC Refining 020040060080010000 100 200 300 400 500 600 700 800Measured hydraulic no-load power (kW) Predicted hydraulic no-load power (kW) Hydraulic no-load power99% Confidence IntervalsFigure 3.16: Correlation between predicted and measured hydraulic no-load powersfor all plates including both lab and mill dimensionsand operating variables was experimentally investigated and the following correlationwas proposed:Pn = A?? +KCqRe0.2G??18 (3.9)where A and K are constant. The first term on the right presents the hydraulicpower and the second term presents the pumping power. The effect of refiner diameterand groove depth on hydraulic power was determined from a series of mill trials and43Chapter 3. Experimental Measurement of the No-load Power in LC Refining0481216200.6 0.65 0.7 0.75Hydraulic no-load power (kW) ? Predicted ValuesMeasured ValuesFigure 3.17: Comparison of predicted and measured hydraulic no-load power respectto ? for all 12?? platesa predictive equation was proposed:Powern? = (1.14? 0.2)??3 (Ro)4.284?0.05 (T )0.716?0.05(WW +B)0.478?0.005(3.10)It should be noted that these correlations should be applied to estimate the no-loadpower in LC refiners running with mechanical pulp in the range of our experimentaldata and they are not recommended to predict the no-load power in LC refiners44Chapter 3. Experimental Measurement of the No-load Power in LC Refiningrunning with chemical pulp. The ranges of gap sizes and discs diameters for our dateare limited to 1mm to 9mm and 12?? to 72??, respectively.Based on the above empirical expressions and the obtained data, it can be con-cluded that:? Hydraulic power is the dominant component and accounts for more than 90%of total no-load power at wide gaps, depending on the flow rate.? The power consumption of a smooth disc is exactly proportion to Ro5; whilefor the refiner discs with mounted bars and grooves, the effect of Ro decreasesjust a little bit (Hydraulic power is not exactly proportion to Ro5) and instead,the effect of groove height (T ) will be appear.? The effect of plate pattern can be described by the non-dimensional parameter,? = WW+B , which indicates the plates roughness density.? The no-load power depends on the gap between two discs. This implies thatthe net power at a specific gap requires that the no-load power is known at thatgap.? Almost no difference between the no-load power of water and low consistencymechanical pulp has been measured.? The no-load power correlation shows that increase of 20% in T,Q, ?, ? and Romakes about 13%, 5%, 10%, 50% and 62% change in no-load power. Thisresult further suggests that rotational speed and outer diameter have the mostsignificant effects on the no-load power.45Chapter 4Time-Dependent Cross-SectionalFlow Field of LC RefinersIn this work, we consider the turbulent, time-dependent flow in the channel formedbetween two periodic corrugated walls (see Figure 4.1). The flow is driven by thesteady translation of the upper wall at a rate U , in the direction perpendicularto the corrugations, while the lower wall is stationary. The corrugations in thiswork are rectangular cavities of depth T and width W with a spacing of B betweenadjacent cavities. Although this flow occurs in a number of natural and industrialsettings, the motivation of this work stems from a Pulp & Paper application, namely,an understanding of the flow field in a low consistency (LC) refiner. One of theopen remaining questions in this area is the effect of the time-dependent flow on theefficiency of operation of these devices when the amplitude of the corrugations arelarge in comparison to the channel spacing G.Therefore, we propose the following simulations to individually evaluate the ef-fect of gap size on the flow field between the opposing corrugated walls. In ?4.1, wepresent formally the geometry, the equations of motion and the corresponding dimen-sionless groups which govern the considered flow field. In this section, we describethe computational methodology as well as some validation cases to ensure that ourpredictions are reasonable. The results from our simulations are presented in ?4.2.Here, we begin the discussion by characterizing the time dependent behavior as a46Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners? ? ? ? ? ? ? ? Figure 4.1: Schematic of the corrugated geometry considered. Here the upper walltranslates at a constant velocity of U and is separated from the lower plate by agap G. The corrugations are considered as repeated patterns of rectangular cavitiesof width W = 4.8mm and depth T . The cavities are separated by a spacing ofB = 3.2mmfunction of gap size. The time dependent behavior is characterized through fluctu-ations in the drag coefficient in most simulations. In a number of cases, we furtherhighlight this result through particle tracking using a one-way coupling. The chaptercloses with the conclusion section in ?4.3.47Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners4.1 Computational frameworkIn this section, we present the numerical method used to solve the equations ofmotion for geometry shown in Figure 4.1. When the channel coordinates are scaledwith L = B +W , the fluid velocity by U and time by L/U , the governing equationsin dimensionless form reduce to:? ? u? = 0 (4.1)?u??t?+ (u? ? ?)u? = ??P ? + 1Rel?2u? (4.2)where u? and P ? represent the normalized fluid velocity and pressure; and Rel is theReynolds number based on L (Rel = UL/?). The channel is bounded in the regionymax = G(12+ TGft(x, t;W/L))Top Wall (4.3)ymin = ?G(12+ TGfb(x;W/L))Bottom Wall (4.4)where fi are the functions describing the shape of the top and bottom walls. Theno-slip conditions are applied on the upper and lower walls. Periodic conditions areapplied on the left and right faces of the domain (see Figure 4.2).The equations of motion were solved numerically using a commercially availableCFD package, FLUENT, using a 2nd order accurate finite volume method with arealizable k??model as the closure equations for turbulence. There is some indicationin the literature that this turbulence model should be adequate for our purposes asboth Mesalhy et al. [88] and Shafiqul et al. [53] have used this for driven cavity flow.For all cases, the flow domain was discretized using a non-uniform structured mesh48Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC RefinersRotorStatorGComputational DomainUpper FluidLowerFluidSliding Mesh InterfacePeriodic BoundaryxyUWTBUFigure 4.2: Schematic of the physical domain as well as the computational domain.The computational domain is limited to one repeating cavity pattern of length L. Pe-riodic boundary conditions, highlighted by the red dashed lines, on the left and rightsides of the domain are shown. A sliding mesh is used dividing the computationaldomain at y = 0(see Figure 4.2). A sliding mesh was employed to help capture the time dependentcomponents of the solution [89]. The sliding mesh model is the most accurate methodto model unsteady cases in FLUENT. Here, the domain is divided in two regions thatare treated separately: the moving cavity region and the stationary cavity region.The sliding interface applies to the edge between two zones and at each time step,the upper mesh moves and the fluxes at the sliding interfaces are recomputed. Byrunning the sliding mesh model more computational time is required. The near-wall mesh spacing was set so that the distance away from the wall of the first nodesatisfied the criteria y+ < 1. By doing so we were able to resolve the flow field inthe laminar sublayer through an enhanced wall treatment method. To reduce thecomputational time, the steady-state solution was used to initialize the computation.49Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners0 1 2 3x 1052.933.13.23.33.43.5 x 10?3NCd0 2 4 62.933.13.23.33.43.5 x 10?3?t?tcCd(a) (b)Figure 4.3: Characterizing the sensitivity of the solution to the mesh size and timesteps. In (a), the mesh density dependency N is shown as a function of Cd using atime step of ?t = 2 ? 10?7s. In (b), the effect of time step is shown for the casewith N = 154800. Here ?tc = 2 ? 10?7 s. In both simulations: Rel = 1.6 ? 105,B/L = 0.4, T/L = 0.4 and G/L = 0.25.Here, the SIMPLE [90] methodology was used for the pressure-velocity coupling.Once initialized, a pressure-implicit operator splitting (PISO) method [89, 90] wasused for the unsteady calculations. Convergence was achieved when the residuals ofall variables were less than 1? 10?7 and periodic behavior was observed in the dragcoefficient.In chapter 3, we experimentally showed that the measured no-load power for LCrefiner when running with mechanical pulp is almost the same as when it runs withwater. Thus, in this study, we consider water as the fluid between two corrugatedwalls with the density of 998.3kg/m3 and viscosity of 0.001003kg/m.s.At this point, we turn our attention to the precision of the numerical estimatesand characterize the dependency of the solution on mesh size and size of the timestep. To do so a series of cases were considered in which we estimate drag coefficientCd as a function of the number of grid points (N). Here, drag coefficient covers both50Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refinerspressure drag and shear stress drag. As the drag coefficient varies both temporallyand spatially, we reportCd =UL2?LU0? L0Cd(x, t;N)dxdt (4.5)In Figure 4.3, we consider the sensitivity of the solution to mesh size and showthat Cd diminishes with an increasing number of grid points. With N ? 1.5?104, weconsider the solution to be grid independent. In addition to this, it was importantto choose the appropriate time step ?t = ?x/U where ?x is the smallest grid sizeat the interface of moving and stationary regions in the direction of U . Here we setthe characteristic time of the problem to ?tc = 2? 10?7 s for Rel = 1.6? 105.Using the method outlined by Celik [91], the numerical uncertainty in the fine gridsolution was determined to be ?0.18%. We attempt to further evaluate our numericalsetup by comparing the results to experimental data of lid-driven cavity flow collectedby Friesing [92](see Figure 4.4). The cavity in this case is three-dimensional and theends are sealed. We compare the effect of varying the aspect ratio of the channelT/W in terms of the relative increase in the drag coefficient, in comparison to thatover a flat plate, i.e. Cd/Cf ? 1, where Cf is the drag coefficient for a flat plate. Asshown, the numerical simulations approximate the experimental data reasonably well,especially when T/W is large. Larger discrepancies are evident with T/W ? 0.146.We attribute the differences due the differences in the geometries simulated: we areconducting a 2D simulation with a corrugated wall passing over a system of cavitieswhile Friesing [92] considers lid-driven flow in a long thin cavity.Finally, with this numerical setup two separate studies were performed. In thefirst study we examine the effect of G and investigate the flow field at fixed L andT . In the second study, we examine the interaction between opposing cavities by51Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC RefinersG/L T/L W/L RelSeries 1 0.0625? 1.25 0.4 0.6 0.4? 6.4? 105Series 2 0.0625 & 1.25 0.4 0.6 3.2? 105Table 4.1: A summary of the numerical conditions tested. In Series 1, we examinedthe effect of Re and the spacing between the plates G/L on the flow field. Thenumerical simulations were conducted with B/L = 0.4. In total, 30 simulationswere conducted. In series 2, we employed particle tracking, as a passive scalar, for 2different gap sizes; G/L = 0.0625 and G/L = 1.25.0 0.5 1 1.5 202468TWCdCf ? 1  ExperimentalNumericalFigure 4.4: A comparison of the numerical solution of two opposing corrugated cav-ities passing over each other to that of flow in a 3D channel driven by a movinglid measured by Friesing in 1936. The numerical simulations were conducted withRel = 4? 104, G/L = 0.25 and B/L = 0.4.52Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refinersintroducing a passive scalar into the simulation, at a certain location, and examiningit spread through the domain. A listing of the numerical studies conducted are givenin Table 4.1.4.2 Results and discussionWe begin the examination of the results and consider the effect of the gap size G onthe flow field. The data that we will consider is given as Series 1 in Table 4.1 and asshown the aspect ratio of the cavity is held constant. Before we proceed to the mainfindings in this series of simulations, it is instructive to examine phenomenologicallythe time dependency created by opposing cavities. This is shown in Figure 4.5. Thefirst observation that can be made from this figure is that the flow field in the cavitiesof the lower stationary wall is characterized by one dominant vortex. Seemingly,there appears to be no vortex on the top wall, but this observation is incorrect as thepresence of the vortex is masked by the translation of the wall. If we examine thestream function (see Figure 4.6), we do indeed, find that a vortex is present on the topwall, with the same features of that on the bottom wall. If we continue to examinethe velocity field as a function of non-dimensional time (t? = Ut/L), we see that att? = 0.2, the vortex in the central horizontal plane deflects upwards and extends intothe gap between the opposing cavities. The vortex in the cavity appears to be skewedto the right. Following this, and in particular at t? = 0.8, a similar feature is apparentbut in this case, the vortex extends into the central portion and is skewed somewhatto the left. The pressure field (see Figure 4.7) displays this unique behavior whenthe vortex is skewed left or right; it can be seen that a continuous connected lowpressure region exists across the opposing cavities. Clearly, time-dependent behavioris apparent in this case.53Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners?	?	?	?	?	0510152025Figure 4.5: Estimates of flow field when Rel = 1.6 ? 105, G/L = 0.0625, T/L = 0.4and B/L = 0.4. The streamlines are shown superimposed on the norm of the velocityfield. This is traditionally called the ?speed? and the color map of the speed isdimensional with units of m/s. The upper wall is translating from left to right at avelocity of 20m/s. The time steps have been scaled by the periodic time L/U andare presented at t? = [0, 0.2, 0.4, 0.6, 0.8].54Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners86420Figure 4.6: Estimates of the stream function when Rel = 1.6 ? 105, G/L = 0.0625,T/L = 0.4 and B/L = 0.4. The upper wall is translating from left to right at avelocity of 20m/s. The color map represents the stream function at t? = 0.2 and isgiven in units of kg/s.In contrast to this, we present another representative case in which we displayanother characteristic flow field (see Figure 4.8). This simulation was conductedat larger G and what is evident is that the flow field is steady. This is not unex-pected upon examination of the governing equation. As shown in Equation 4.3, theterm that causes the time-dependency in flow diminishes by increasing the gap andconsequently, flow behaves as Couette flow between two parallel plates at wide gaps.In order to characterize this effect in a more succinct manner, we examine thedrag coefficient. We do so by examining the drag coefficient as a function of time,Cd(t), defined asCd(t) =1L? L0Cd(x, t;N)dx (4.6)This is shown in Figure 4.9 where we see that the temporal variations increase withdiminishing gap size and what is evident in this figure is that the variations arenegligible with G/L ? 0.75 .We define the flow field to be at steady-state when the coefficient of variation,55Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners-30-1501530?	?	?	?	?	Figure 4.7: Estimates of the pressure field when Rel = 1.6 ? 105, G/L = 0.0625,T/L = 0.4 and B/L = 0.4. The upper wall is translating from left to right at avelocity of 20m/s. The color map represents the pressure field and is given in unitsof kPa (gage). The time steps have been scaled by the periodic time L/U and arepresented at t? = [0, 0.2, 0.4, 0.6, 0.8].56Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners0 5 10 15 20 23 -15 -10 0 5 10 -5 ???  ???  ???  ???  ???  ???  Figure 4.8: Estimates of flow and pressure fields when Rel = 1.6? 105, G/L = 1.25,T/L = 0.4 and B/L = 0.4. The upper wall is translating from left to right at avelocity of 20m/s. The color map of the velocity field and pressure distribution arerespectively given in units of m/s and kPa (gage). The time steps have been scaledby the periodic time L/U and are presented at t2? = 0.2 and t5? = 0.8.57Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners0 0.2 0.4 0.6 0.8 1?0.0100.010.02t*  Cd(t)G/L= 1.25G/L= 0.25 G/L= 0.75G/L= 0.0625 Figure 4.9: Estimates of drag coefficient as a function of time for various G/L. HereRel = 1.6? 105, T/L = 0.4 and B/L = 0.4.i.e. the standard deviation (?Cd) divided by the mean (Cd), is less than 0.05. Alarge number of simulations were conducted in which we attempted to define theboundary between steady and unsteady flow. Figure 4.10 displays the contours of?CdCdas a function of both G/L and Re. The white line that divides the graph in tworegions shows the conditions of gap size and the moving cavity velocity where flow iseither steady or unsteady.Depending on Reynolds number, transition from unsteady flow at small gaps tosteady flow at wide gaps takes place at different values of G/L; i.e. transition forflow fields with Re of 0.4 ? 105 and 6.4 ? 105 appears at G/L of 0.67 and 0.75, re-spectively. In other words, in terms of time-dependent parameter shown in Equation4.3, (TGft(x, t;W/L)), the flow is defined as steady when the gap between the platesis greater than twice the depth of the cavity. Pulsating flow is established when thegap size diminishes below this limit.At this point, we would like to examine the behavior of the flow field further58Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC RefinersReGL  SteadyUnsteady1 2 3 4 5 6x 1050.20.40.60.811.20.511.522.5?CdCd = 0 .05Figure 4.10: Estimate of the bound between steady and unsteady behavior. A listingof the range of the simulations is given as Series 1 in Table 4.1. The boundarybetween steady and unsteady is drawn as the white line in the figure and representsa threshold when the coefficient of variations diminishes below 0.05. The contour inthis plot is coefficient of variation as defined by ?CdCd .59Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refinersand address the question ?is fluid exchanged between the rotating and stationarycavities??. To do so, we examine the evolution of a passive particle, introduced atdifferent locations in either steady (large gaps) or unsteady (small gap) cases. In thisone-way coupled simulation, we released particles at three different locations:? Position 1 - in the channel formed between the two walls? Position 2 - in the moving cavity on the upper wall? Position 3 - in the stationary cavity on the lower wallThese positions are highlighted in Figure 4.11. Six simulations are reported andconditions under which they were performed are given in Table 4.1. We begin thediscussion of these results by defining the order in which we will present the results.We discuss the results in the order of the position and present percentage of timethe particles remained at a particular elevation ?1 ? Y ? ? 1 in the domain whereY ? = yT+G/2 (see Figures 4.12-4.14). For each figure, Y? represents the normalizedvertical positions of particles in one of these zones: moving cavity, stationary cavityor the area between two cavities. Table 4.2 summarizes the range of Y ? for each zonedepends on the gap size. The total calculated time for tracking the location of eachparticle is 120L/U .Location of particles G/L = 0.0625 G/L = 1.25Moving cavity 0.0725 ? Y ? ? 1 0.61 ? Y ? ? 1Spacing between two cavities ?0.0725 ? Y ? ? 0.0725 ?0.61 ? Y ? ? 0.61Stationary cavity ?1 ? Y ? ? ?0.0725 ?1 ? Y ? ? ?0.61Table 4.2: Range of Y ? for three different regions of moving cavity, stationary cavityand the spacing between these two cavitiesAs an example, in Figure 4.12, the particle was released at Position 1 and we seethat under unsteady condition, the tracer particle diffuses over the entire domain. In60Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC RefinersGU123Figure 4.11: A schematic of the positions where the particles are released for thesimulations.contrast with this, under steady condition, we find that the tracer particles remainon a steady trajectory and at nearly the same elevation it was released. For the othertwo cases simulated we find somewhat similar results. As shown in Figures 4.13a and4.14a, the particles spread over the entire domain under the unsteady conditions. Atsteady state (see Figures 4.13b and 4.14b), the particles remain in the cavity in whichthey were released. Here the particles follow the motion of the vortex in the cavity.4.3 ConclusionIn this chapter, two-dimensional numerical simulations have been performed for afully developed turbulent flow in the space between two opposing cavities; one cavityis moving and the other is stationary. This case resembles the flow field in thecross section of refiner. Due to complexity of three-dimensional flow in the refiner,this geometry can give insight into some features of tangential flow field inside the61Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners(a)?1 ?0.5 0 0.5 102468Particle position (Y*)Time (%)(b)?1 ?0.5 0 0.5 1020406080100Particle position (Y*)Time (%)Figure 4.12: Histogram of the particle positions released from Position 1 in (a) un-steady and (b) steady flow fields.62Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners(a)?1 ?0.5 0 0.5 10246Particle position (Y*)Time (%)(b)?1 ?0.5 0 0.5 102468101214Particle position (Y*)Time (%)Figure 4.13: Histogram of the particle positions released from Position 2 in (a) un-steady and (b) steady flow fields.63Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refiners(a)?1 ?0.5 0 0.5 1012345Particle position (Y*)Time (%)(b)?1 ?0.5 0 0.5 1051015Particle position (Y*)Time (%)Figure 4.14: Histogram of the particle positions released from Position 3 in (a) un-steady and (b) steady flow fields.64Chapter 4. Time-Dependent Cross-Sectional Flow Field of LC Refinerscavities of a LC refiner. Unsteady simulations have been conducted to obtain detailsof flow field for different gap sizes and velocities. For the range of parameters studied,two characteristic flow fields were identified: unsteady and steady flows. Resultsdemonstrated that the temporal variations which arise from the presence of repeatedcorrugations on the opposing walls, diminish with increasing gap size. We defined theflow field as steady-state when the coefficient of variation, i.e. the standard deviation(?Cd) divided by the mean drag coefficient (Cd), is less than 0.05. Also, we showedthat the flow field is periodically unsteady when the gap size is small.The most significant part of this work is found when we consider particle trans-port between the cavities. We find that particles are transported to the region nearthe leading edges of the bars only under the conditions of unsteady flow. Particletransport is enhanced by the presence of the large pressure gradients formed underthe conditions of unsteady flow which arises by decreasing the gap size.65Chapter 5Effect of Cavity Aspect Ratio onthe Cross-Sectional Flow FieldFlow in a refiner is three-dimensional, and as such, is influenced by both radial andtangential flows. The radial flow accounts for flow in the longitudinal direction ofbars and grooves whereas tangential flow is induced by the rotation of the rotor. Thepresent chapter serves to extend our understanding of flow field in the tangentialdirection of refiners. Hence, we explore the effect of cavity depth and wall velocity onthe flow field. The rest of geometrical parameters are kept constant in this study. Inthis chapter, as in chapter 4, two-dimensional simulations are performed of the flowin the channel formed between two periodic corrugated walls.In the context of the existing refining literature (see chapter 2) our study is some-what unique in that we examine the effect of groove depth on the hydrodynamicdrag. These results lead us to extend our understanding of no-load power as manyauthors indicate that drag increases with depth. An outline of this chapter is asfollows. Below, in ?5.1 we give a brief outline of the the computational domain,boundary conditions and numerical schemes. We open up ?5.2 by introducing therelevant governing equations, then present the results regarding the effect of cavitydepth on both flow pattern and the drag coefficient and finally the chapter finisheswith concluding remarks in ?5.3.66Chapter 5. Effect of Cavity Aspect Ratio on the Cross-Sectional Flow FieldG/L T/L W/L ReSeries 3 0.25 0-5 0.6 0.4? 6.4? 105Table 5.1: A summary of the numerical conditions tested. In Series 3, we examinedthe effect of Re and aspect ratio T/W on the flow field. In total 72 simulations wereconducted.5.1 Computational frameworkHaving fixed the gap size between two corrugated walls, a series of two-dimensionalsimulations are performed using FLUENT. The flow of interest passes through twoopposing corrugated walls (see Figure 4.1). As explained in Chapter 4, a non-uniformstructured grid with sliding mesh method and realizable k ? ? turbulent model areused. Numerous simulations are carried out for various depth size with upper wallvelocity of U . Table 5.1 summarizes the specifications of computational domain inwhich the variables T/L and Re are varied. In total 72 simulations were conducted.As shown in Figure 4.2, there are two walls confined flow and impose the no-slipconditions to the flow. The lower wall is stationary and the upper wall moves at avelocity, U . As a consequence, the grid in the stator remains stationary and the gridin the rotor moves by the same velocity as the moving wall. Periodic conditions areapplied on the left and right faces of the domain.With the above-mentioned numerical setup (more details in Chapter 4), a series ofstudies were performed to examine the effect of aspect ratio of the cavities (T/W ) forthe steady flow field and categorize the flow using a similar scheme to that outlinedby Perry et al. [55].67Chapter 5. Effect of Cavity Aspect Ratio on the Cross-Sectional Flow Field5.2 Results and discussionIn this section, we present the numerical results to show the effect of cavity aspectratio by keeping the bar and cavity widths constant; thus the only variable is thecavity depth. To study the effect of cavity depth on the flow field, it is convenientto show the dependent variables of the problem by normalizing the Navier-Stokesequation using the moving cavity velocity (U) and the domain dimensions (L, T ).The Navier-Stokes equation in the x-dimension is given as:u??u??x?+ v??u??y?= ??P??x?+ 1Rel(?2u??x?2+(LT)2 ?2u??y?2)(5.1)This normalized form of Navier-Stokes shows that the two affecting parameterson the flow field are Reynolds number, Rel, and cavity ratio, TL . Since bar widthis constant, in this section all the results are presented with respect to the moreconventional term of T/W where 0 ? TW ? 5. As described in ?2.4, cavities withTW < 0.25 are categorized as k-type cavities. Also, cavities with 0.25 <TW arecategorized as d-type cavities where all the laboratory and industrial scale refinerscavities have the aspect ratios that insert them in this type.In term of energy consumption, Figure 4.4 depicts drag coefficient as a functionof TW for Re = 0.4 ? 105. In the range of d-type cavities, drag coefficient decreasesby increasing the cavity depth, up to T/W ? 0.5 ? 1 and then, after this range ofcavity aspect ratio, Cd slightly goes up for higher cavity depths.On the other hand, in term of flow field, Figure 5.1 depicts the flow pattern insidethree different cavity geometries. Based on the number of vortices inside each cavity,lets introduce a new classification for cavities:68Chapter 5. Effect of Cavity Aspect Ratio on the Cross-Sectional Flow Field? Type I: This type covers all the k-type cavities that have no main vortex.? Type II: This type includes all d-type cavity ratios that have just one primaryvortex.? Type III: All d-type cavity ratios that have more than one vortex.(a) (b) (c) ? ? ? Figure 5.1: Flow pattern in three different cavity aspect ratios when Re = 1.6? 105.(a) k-type cavity with no vortex (T/W = 0.146). (b) d-type cavity with one mainvortex (T/W = 1). (c) d-type cavity with more than one vortices (T/W = 5).Based on the refining point of view, cavities are expected to be high enough tolet the proper amount of flow pumped in the refiner and low enough to refine thelarge amount of fibres, while having the minimum drag coefficient. Therefore, if thecavity depth is too high, there may be multiple primary vortices inside the cavity. In69Chapter 5. Effect of Cavity Aspect Ratio on the Cross-Sectional Flow Fieldthis case, in spite of increasing the hydraulic capacity, some fibres could be trappedin the lower vortices. It results in less fibres treated. If the groove depth is too low,then hydraulic capacity would be low and also it may result in high drag coefficient.In order to better explain the characteristic of various types of refiner cavities interms of drag coefficient, hydraulic capacity and fibers treatment, we would like tocombine our knowledge regarding the energy consumption and flow pattern insidedifferent cavities. In this regards, the domain of each type is distinguished by thedashed lines on the drag coefficient contours for different cavity ratios and Reynoldsnumbers (Figure 5.2):R eTW  1 2 3 4 5 6x 10523.55246810121416x 10?3R e  1 2 3 4 5 6x 10500.250.5Type IIType IIIType IFigure 5.2: Contours of Cd respect to the variations of cavity depth and Reynoldsnumber.? Type I covers all the k-type cavities where there is no primary vortex insidethe cavity. By increasing the T/W from 0 up to 0.146 drag coefficient goes up70Chapter 5. Effect of Cavity Aspect Ratio on the Cross-Sectional Flow Fieldand reaches its maximum at T/W = 0.146. After this point, Cd goes down byincreasing the cavity ratio. Therefore, Type I is the area that the maximumdrag coefficient coincides with the lowest hydraulic capacity. Industrial refinerscan hardly be categorized in this group. Transition between Type I and Type IItakes place at different cavity ratios which directly proportional to the Reynoldsnumber.? Type II: This type includes all cavity ratios that have just one primary vor-tex and relatively has the lowest drag coefficient. Depending on the Reynoldsnumber, the specific ratio that the number of primary vortices changes fromone to two can be varying between 2.5 to 4. At higher Reynolds numbers themainstream flow induces higher shear at the top of the cavity increasing mo-mentum transfer to the cavity fluid. The primary vortex formed in the cavitythen has elevated angular momentum and is able to sustain its form for largeraspect ratios at higher Reynolds numbers as depicted in Figure 5.2.? Type III: All cavity ratios that have more than one vortex are categorized inthis group. In this area, increasing the cavity ratio makes slight changes in thedrag coefficient while provides higher hydraulic capacity. On the other hand,fibres may trap in the lower main vortices which makes some fibres leavingrefiner untreated.As a result, among all types of refiner cavities, Type I cavities lead to highenergy consumption and low hydraulic capacity and Type III cavities could resultin unsuccessful refining action. So the only desirable category to fulfill the refiningmission with the minimum drag coefficient is suggested as Type II.71Chapter 5. Effect of Cavity Aspect Ratio on the Cross-Sectional Flow Field5.3 ConclusionWe ran two-dimensional simulations of the flow between two moving and stationarycavities to evaluate the effect of cavity depth on flow field at the cross-section of LCrefiner. All the simulation in this chapter were performed for the steady flow field.We identified three characteristic flow fields for cavity depth variation based on thenumber of vortices formed within the cavity and the drag coefficient.Type I covers all the k-type cavities where there is no primary vortex insidethe cavity. In this flow field, the maximum drag coefficient coincide with the lowesthydraulic capacity which make these range of cavity ratios unqualified for the refiningpurpose. Type II includes all cavity ratios that have just one primary vortex andrelatively has the lowest drag coefficient in the d-type cavities. Type II cavitieswere suggested for the refining purpose. In this range of cavities, drag coefficientis minimum while we have more fibers successfully treated. All cavity ratios thathave more than one vortex are categorized in Type III. Despite Type III providesmaximum hydraulic capacity, fibres may trap in the lower main vortices which makessome fibres leaving refiner untreated.72Chapter 6Summary of Thesis and FutureResearch Direction6.1 Summary of contributionsThe main contributions of this thesis can be summarized in three categories: Newempirical correlation to estimate no-load power in low consistency refining, the effectof gap size on the time-dependent flow field in refiner, and the effect of groove depthon refiner flow field.1. New empirical correlation to estimate no-load powerThe experimental data were collected over a wide range of affecting parameterson the no-load power consumption in low consistency refiners.? A new statistical model was provided for prediction of no-load power, de-scribed in terms of two main components: hydraulic and pumping powers.? The hydraulic and pumping powers were measured separately and theircontributions on the total no-load power were examined for a wide rangeof gap sizes. Hydraulic power was shown to be the dominant component.? In contrast to general belief, no-load power was shown to depend on theplate gap. This implies that knowing the net power at a specific gaprequires knowledge of the no-load power at that gap.73Chapter 6. Summary of Thesis and Future Research Direction2. Effect of gap size on the time-dependent flow field in refinerA series of unsteady simulations were carried out to investigate the effect ofgap size on the cross section of refiner flow field and particle trajectories over awide range of Reynolds number.? We identified two characteristic flow fields, defined by either as steady orunsteady.? We found that particles are transported to the region near the leadingedges of the bars only under the conditions of unsteady flow.3. Effect of groove depth on refiner flow fieldA series of steady numerical simulations were performed to investigate the effectof groove depth on the cross section of refiner flow field over a wide range ofReynolds number.? We found that the aspect ratio of the cavity dictates the number of vorticesformed within cavity. With W/T ? 0, we find a flow field characterizedby multiple vortices with centers aligned on top of each other. As theaspect ratio increases, the number of vortices diminishes.6.2 Limitations of the studyAlthough we have made a number of advances, we must also acknowledge somelimitations of our experimental and computational studies.Chapter 3. In terms of experimental work, some major limitations should belisted as:74Chapter 6. Summary of Thesis and Future Research Direction? Low consistency pulp suspension behaves much like water [93]. In this regard,we applied the same rheological properties for low consistency pulp suspensionas water.? We did not measure the no-load power for very small gaps; i.e. in the orderof pulp diameters. At these gaps, the refiner plates clashed when using water.When the fluid accelerated, the internal pressure decreases and the plates aredrawn towards another. Usually this is avoided when the gear mechanism forthe gap adjustment is accurate enough to hold the rotor in place.? To develop the total no-load power correlation, we could not find any relation-ship between the effect of plates design and the pumping power of each plate.It is important to mention that the difference between the pumping powers ofthe various plates was mostly in the range of experimental error. To calcu-late the pumping coefficient (K) for all 16?? plates, we used all the pumpingpowers for different operating conditions and plate designs and then proposedthe correlation only with respect to operating conditions, not the geometricalparameters.? Each mill no-load power value presents one power value at a random wide gapfor the fixed rotational speed and flow rate. This means that we did not haveenough data to distinguish the pumping and hydraulic powers. So based on theexperimental observations, we considered 90% of the total mill no-load powersas the hydraulic power.Chapters 4 & 5. In terms of computational study, the main restrictions are asfollows:? It is important to recognize that running the two-dimensional models neglects75Chapter 6. Summary of Thesis and Future Research Directionsome aspects of the flow field in the radial direction as well as the effect of thestationary case around both refiner discs.? In these chapters, the effect of fibres was neglected and therefore, a pure waterflow in the tangential direction was simulated.6.3 Future research directionsThe results in this thesis also provide a strong foundation for future work. This sectiondiscusses several lines of research arising from this work which can be pursued.? To explore the effect of plate design parameters on the no-load power, we haveperformed two series of experiments with identical plates but different bar andgroove widths. A systematic experimental study of other geometrical parame-ters such as grinding and sectional angles and also groove depth is of practicalinterest.? There is a significant disconnect between the experimental study of no-loadpower and the numerical analysis. It would be great to extend this work to thethree-dimensional numerical study to obtain more details of the flow field in theradial direction and its effect on the tangential flow. To accomplish this study,it is better to include the housing around two refiner discs. Numerical approachprovides a faster and cost efficient tool to optimize the LC refiner plate design.? Water has been considered as the fluid between two cavities in our 2D simula-tions. The next step would be to extend the simulations to investigate the flowfield in the case of running water with fibres with various lengths.? In this thesis, we have focused on the investigation of the no-load power concept76Chapter 6. Summary of Thesis and Future Research Directionand how the main affecting parameters can change the consumption of this idlepower in low consistency refiners. This opens up interesting area to explore howcontrolling these parameters to minimize the no-load power, affects the refiningzone and consequently, the papermaking fibres quality.77Bibliography[1] R. J. Kerekes, R. M. Soszynski, and T. Doo, ?The flocculation of pulp fibres,?in Papermaking Raw Materials: Their Interaction with the Production Processand Their Effect on Paper Properties-Transactions of the Eighth FundamentalResearch Symposium, (Oxford, UK), pp. 265?310, Mechanical Engineering Pub-lications Limited, September 1985.[2] P. E. Sharpe and J. L. Rodarmel, ?Low consistency refiner plate design andselection,? Pulp & paper Canada, vol. 89, no. 2, pp. 51?57, 1988.[3] M. Jackson and N. Wild, ?Mechanical pulp mills,? Energy Cost Reduction in thePulp and Paper Industry, Browne, TC tech. ed., Paprican, p. 15, 1999.[4] P. Dietemann and J.-C. Roux, ?A study of disc refiner running in no-load con-ditions,? Cellulose chemistry and technology, vol. 39, no. 5-6, pp. 459?471, 2005.[5] W. Herbert and P. G. Marsh, ?Mechanics and fluid dynamics of a disk refiner,?Tappi J., vol. 51, no. 5, pp. 235?239, 1968.[6] J. Lumiainen, ?Is the lowest refining intensity the best in low consistency refin-ing of hardwood pulps?,? in Tappi Press: Papermakers Conference, (Atlanta),pp. 115?126, 1994.[7] D. H. Page, ?The beating of chemical pulps?the action and the effects,? inFundamentals of Papermaking, 9th Fundamental Research Symposium, (Oxford),1989.[8] J.-C. Roux, J. F. Bloch, R. Bordin, and P. Nortier, ?The net normal forceper crossing point: a unified concept for the low consistency refining of pulpsuspensions,? in 14th Fundamental Research Symposium: Advances in Pulp andPaper Research, (Oxford), pp. 51?83, 2009.[9] J. Rihas, ?Low consistency refining, theory vs practice,? in 3rd InternationalRefining Seminar, (Atlanta, GA, US), March 1995.[10] Tappi Stock Preparation Committee, ?An introduction to refining variables,?Tappi Journal, vol. 54, no. 10, pp. 1738?1741, 1971.[11] T. Lundin, Tailoring pulp fibre properties in low consistency refining. A?boAkademi, 2008.78Bibliography[12] W. Brecht and W. H. Siewert, ?Zur theoretisch-technischen beurteilung desmahlprozesses moderner mahlmaschinen,? Das Papier, vol. 20, no. 1, pp. 4?14,1966.[13] L. Westman, ?Idling losses in the low-consistency refining of chemical pulp,?Svensk Papperstidning, vol. 87, no. 3, pp. R8?R13, 1984.[14] H. Selder and W. H. Siewert, ?Escher wyss fibersorter for the high density screen-ing of recycled fibres,? in Papermakers Conference, Proceedings of the TechnicalAssociation of the Pulp and Paper industry, 1980.[15] N. Rajabi Nasab, J. A. Olson, J. Heymer, and D. M. Martinez, ?Experimentalstudy of low consistency refiner no-load power,? in PAPERCON ConferenceProceedings, (New Orleans, LA), pp. 1539?1551, April 2012.[16] A. Arjas, J. Huuskonen, and N. Ryti, ?Principles of the evaluation of the perfor-mance of a beating machine and of the beating result,? Paperi Ja Puu, vol. 52,no. 4, pp. 269?276, 1970.[17] D. R. Dalzell, ?A comparison of paper mill refining equipment,? Tappi Journal,vol. 44, no. 4, pp. 241?244, 1961.[18] K. Ebeling, ?A critical review of current theories for the refining of chemicalpulps,? in Int. Symposium on Fundamental Concepts of Refining, (Appleton,WI), pp. 1?34, 1980.[19] E. Glasl, ?Power saving in refining,? Paper Technology and Industry, vol. 17,no. 5, pp. 200?203, 1976.[20] P. J. Leider and A. H. Nissan, ?Understanding the disk refiner; the mechanicaltreatment of the fibers,? Tappi J., vol. 60, no. 10, pp. 85?89, 1977.[21] P. J. Leider and J. Rihs, ?Understanding the disk refiner; the hydraulic behav-ior,? Tappi J., vol. 60, no. 9, pp. 98?102, 1977.[22] W. A. Banks, ?Design considerations and engineering characteristics of disc re-finers,? Paper Technology and Industry, vol. 8, no. 4, pp. 363?369, 1967.[23] Finebar refining technology, ?Introduction to stock prep refining.? http://www.aikawagroup.com/downloads/Training_Manual.pdf, 2001.[24] W. Batchelor, T. Lundin, and P. Fardim, ?A method to estimate fiber trappingin low-consistency refining,? Tappi J., vol. 5, no. 8, p. 31, 2006.[25] U.-B. Mohlin, ?Refining intensity and gap clearance,? in 9th International Re-fining Conference, Pira, (Leatherhead, UK), 2006.79Bibliography[26] U.-B. Mohlin and B. Roos, ?Experiences from using a gap sensor in lc-refining,?in International Pulp Refining Seminar, (Helsinki, Finland), pp. 37?40, June2007.[27] A. Luukkonen, Development of a methodology to optimize low consistency refin-ing of mechanical pulp. PhD thesis, University of British Columbia, Vancouver,Canada, 2011.[28] B. Dalpke and R. J. Kerekes, ?The influence of fibre properties on the apparentyield stress of flocculated pulp suspensions,? Journal of pulp and paper science,vol. 31, no. 1, pp. 39?43, 2005.[29] C. Baker, ?Refining and improved paper machine runnability,? in proceedings of7th PIRA international refining conference & exhibition, (Stockholm, Sweden),pp. 25?26, 2003.[30] A. Mrozin?ski, ?Modelling of waste-paper stock treatment process in disc refin-ers,? Journal of POLISH CIMAC, no. 3, pp. 113?119, 2010.[31] P. Cooper and E. Reshotko, ?Turbulent flow between a rotating disk and aparallel wall,? AIAA Journal, vol. 13, pp. 573?578, 1975.[32] A. P. Morse, ?Assessment of laminar-turbulent transition in closed disc geome-tries,? Journal of Turbomachinary, vol. 113, pp. 131?138, 1991.[33] J. M. Owen and R. H. Rogers, Flow and heat transfer in rotating-disc systems.New York, NY (USA); John Wiley and Sons Inc., 1989.[34] C. M. Vaughan, A numerical investigation into the effect of an external flow fieldon the sealing of a rotor-stator cavity. PhD thesis, University of Sussex, 1987.[35] B. Launder, S. Poncet, and E. Serre, ?Laminar, transitional, and turbulentflows in rotor-stator cavities,? Annual Review of Fluid Mechanics, vol. 42, no. 1,pp. 229?248, 2010.[36] J. W. Daily and R. E. Nece, ?Chamber dimension effects on induced flow andfrictional resistance of enclosed rotating disks,? Journal of Basic Engineering,vol. 82, pp. 217?232, 1960.[37] R. E. Nece and J. W. Daily, ?Roughness effects on frictional resistance of enclosedrotating disks,? Journal of Basic Engineering, vol. 82, pp. 553?562, 1960.[38] J. W. Daily, W. D. Ernest, and V. V. Asbedian, Enclosed Rotating Disks withSuperposed Throughflow: Mean Steady and Periodic Unsteady Characteristics ofthe Induced Flow. Department of Civil Engineering, Massachusetts Institute ofTechnology, 1964.80Bibliography[39] J. M. Owen, ?An approximate solution for the flow between a rotating and astationary disk,? in ASME, paper No. 88-GT-293, 33rd Int. Gas Turbine Con-ference, (Amsterdam), 1988.[40] J. L. Goldstein and E. M. Sparrow, ?Heat/mass transfer characteristics for flowin a corrugated wall channel,? ASME Transactions Journal of Heat Transfer,vol. 99, pp. 187?195, 1977.[41] J. E. O?Brien and E. M. Sparrow, ?Corrugated duct heat transfer, pressure dropand flow visualization,? Transactions of the ASME, J. of Heat Transfer, vol. 104,pp. 410?416, 1982.[42] G. V. Wang and S. P. Vanka, ?Convective heat transfer in periodic wavypassages,? International Journal of Heat and Mass Transfer, vol. 38, no. 17,pp. 3219?3230, 1995.[43] S. Selvarajan, E. G. Tulapurkara, and V. V. Ram, ?A numerical study of flowthrough wavy-walled channels,? International journal for numerical methods influids, vol. 26, pp. 519?531, 1998.[44] I. J. Sobey, ?On flow through furrowed channels; part i. calculated flow patterns,?J. Fluid Mech, vol. 96, pp. 1?26, 1980.[45] J. Nikuradse, Laws of flow in rough pipes. National Advisory Committee forAeronautics Washington, 1950.[46] E.-S. Zanoun, F. Durst, and H. Nagib, ?Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows,? Physics of Fluids, vol. 15,pp. 3079?3089, 2003.[47] J. Jime?nez, ?Turbulent flows over rough walls,? Annual Review of Fluid Me-chanics, vol. 36, pp. 173?196, 2004.[48] S. Mokamati, J. A. Olson, D. M. Martinez, and R. W. Gooding, ?Experimentalstudy of a turbulent cross-flow near a two-dimensional rough wall with narrowapertures,? AIChE Journal, vol. 54, no. 10, pp. 2516?2526, 2008.[49] S. E. Coleman, V. I. Nikora, S. R. McLean, and E. Schlicke, ?Spatially averagedturbulent flow over square ribs,? Journal of engineering mechanics, vol. 133,no. 2, pp. 194?204, 2007.[50] J. Cui, V. C. Patel, and C.-L. Lin, ?Large-eddy simulation of turbulent flow in achannel with rib roughness,? International journal of heat and fluid flow, vol. 24,no. 3, pp. 372?388, 2003.81Bibliography[51] S. Leonardi, P. Orlandi, and R. A. Antonia, ?Properties of d-and k-type rough-ness in a turbulent channel flow,? Physics of Fluids, vol. 19, p. 125101, 2007.[52] S. Leonardi, P. Orlandi, R. J. Smalley, L. Djenidi, and R. A. Antonia, ?Directnumerical simulations of turbulent channel flow with transverse square bars onone wall,? Journal of Fluid Mechanics, vol. 491, pp. 229?238, 2003.[53] M. Shafiqul Islam, M. Kaminaga, R. Hino, and M. Monde, ?Prediction of turbu-lent flow structure in a fully developed rib-roughened narrow rectangular chan-nel,? Journal of Thermal Science, vol. 18, no. 2, pp. 126?136, 2009.[54] P. Orlandi, S. Leonardi, and R. A. Antonia, ?Turbulent channel flow with eithertransverse or longitudinal roughness elements on one wall,? Journal of FluidMechanics, vol. 561, no. 1, pp. 279?305, 2006.[55] A. E. Perry, W. H. Schofield, and P. N. Joubert, ?Rough wall turbulent boundarylayers,? Journal of Fluid Mechanics, vol. 37, pp. 383?413, 1968.[56] R. L. Simpson, ?A generalized correlation of roughness density effects on theturbulent boundary layer,? AIAA Journal, vol. 11, pp. 242?244, 1973.[57] I. Tani, ?Turbulent boundary layer development over rough surfaces,? in Per-spectives in turbulence studies, pp. 223?249, Springer, 1987.[58] P. R. Bandyopadhyay, ?Rough-wall turbulent boundary layers in the transitionregime,? Journal of Fluid Mechanics, vol. 180, no. 1, pp. 231?266, 1987.[59] A. Keshmiri, M. A. Cotton, and Y. Addad, ?Numerical simulations of flow andheat transfer over rib-roughened surfaces,? in 17th Annual conference of CFDsociety of Canada, (Ottawa, Canada), 3rd-5th May 2009.[60] A. K. Prasad and J. R. Koseff, ?Reynolds number and end-wall effects on alid-driven cavity flow,? Physics of Fluids A: Fluid Dynamics, vol. 1, p. 208,1989.[61] M. D. Deshpande and P. N. Shankar, ?Direct numerical simulation of a complexturbulent flow,? Current Science, vol. 66, no. 10, pp. 767?770, 1994.[62] F. Pan and A. Acrivos, ?Steady flows in rectangular cavities,? Journal of FluidMechanics, vol. 28, no. 4, pp. 643?655, 1967.[63] M. Hellou and M. Coutanceau, ?Cellular stokes flow induced by rotation of acylinder in a closed channel,? Journal of Fluid Mechanics, vol. 236, pp. 557?577,1992.[64] H. K. Moffatt, ?Viscous and resistive eddies near a sharp corner,? Journal ofFluid Mechanics, vol. 18, no. 1, pp. 1?18, 1964.82Bibliography[65] Y.-F. Peng, Y.-H. Shiau, and R. R. Hwang, ?Transition in a 2-d lid-driven cavityflow,? Computers & Fluids, vol. 32, no. 3, pp. 337?352, 2003.[66] C. W. Leong and J. M. Ottino, ?Experiments on mixing due to chaotic advectionin a cavity,? Journal of Fluid Mechanics, vol. 209, no. 1, pp. 463?499, 1989.[67] P. N. Shankar and M. D. Deshpande, ?Fluid mechanics in the driven cavity,?Annual Review of Fluid Mechanics, vol. 32, no. 1, pp. 93?136, 2000.[68] L. P. Wittberg, M. Bjo?rkman, G. Khokhar, U.-B. Mohlin, and A. Dahlkild,?Flow conditions in the grooves of a low-consistency refiner,? Nordic Pulp andPaper Research Journal, vol. 28, no. 2, pp. 173?183, 2012.[69] G. Kohkar, Numerical simulation of the flow in a disc refiner. PhD thesis, KTH,2011.[70] S. Sriram, A. P. Deshpande, and S. Pushpavanam, ?Analysis of spatiotemporalvariations and flow structures in a periodically driven cavity,? ASME-Journal ofFluid Engineering, vol. 128, no. 3, p. 413, 2006.[71] M. J. Vogel, A. H. Hirsa, and J. M. Lopez, ?Spatio-temporal dynamics of aperiodically driven cavity flow,? Journal of Fluid Mechanics, vol. 478, pp. 197?226, 2003.[72] W.-L. Chien, H. Rising, and J. M. Ottino, ?Laminar mixing and chaotic mixingin several cavity flows,? Journal of Fluid Mechanics, vol. 170, no. 1, pp. 355?377,1986.[73] D. H. Page, J. Kosky, and D. Booth, ?Some initial observations on the action ofthe beater,? BP & BIRA Bulletin October, pp. 15?22, 1962.[74] A. H. Nissan, ?Possible mechanism for stapling on bars of disc refiners,? Tappijournal, vol. 72, no. 1, pp. 132?133, 1989.[75] V. N. Goncharov, ?Force factors in a disk refiner and their effect on the beatingprocess,? Bumazh. Prom, vol. 5, pp. 12?14, 1971.[76] T. S. Fox, R. S. Brodkey, and A. H. Nissan, ?High-speed photography of stocktransport in a disk refiner,? Tappi, vol. 62, no. 3, pp. 55?58, 1979.[77] T. S. Fox, ?Inside a disk refiner,? in International Symposium on the Fundamen-tals Concepts of Refining, Appleton, pp. 281?313, 1980.[78] G. Kondora and D. Asendrych, ?Flow modelling in a low consistency disc re-finer,? Nordic Pulp and Paper, vol. 28, pp. 119?130, March 2013.83Bibliography[79] J. Antku and C. J. Ludwig, ?Optimizing refiner plate bar height will reduceenergy consumption,? 1986.[80] H. Siewert and H. Selder, ?Energiewirtschaftliche aspekte derganzstoffmahlung,? Vortragen auf der Informationstagung Energieverbrauch derVereinigun Pack-und Wellpapappenpapiere, 1976.[81] C. J. Biermann, Handbook of pulping and papermaking. Academic press, 1996.[82] D. Gorski, ATMP Process: Improved Energy Efficiency in TMP Refining Utiliz-ing Selective Wood Disintegration and Targeted Application of Chemicals. PhDthesis, Mid Sweden University, 2011.[83] J.-C. Roux and G. Joris, ?Angular parameters beyond specific edge load,?TAPPSA Journal, July 2005.[84] A. Elahimehr, J. A. Olson, D. M. Martinez, and J. Heymer, ?Estimating the areaand number of bar crossings in refiner plates,? Nordic Pulp and Paper Journal,2013.[85] A. Poullikkas, ?Surface roughness effects on induced flow and frictional resistanceof enclosed rotating disks,? Journal of fluids engineering, vol. 117, no. 3, pp. 526?528, 1995.[86] G. T. Csanady, Theory of turbomachines. McGraw-Hill, 1964.[87] A. J. Stepanoff, Centrifugal and Axial Flow Pumps. 1962.[88] O. M. Mesalhy, S. S. A. Aziz, and M. M. El-Sayed, ?Flow and heat transferover shallow cavities,? International Journal of Thermal Sciences, vol. 49, no. 3,pp. 514?521, 2010.[89] Fluent, ?Fluent 6.2 Tutorial guide,? 2005.[90] Fluent, ?Chapter 22. Using the solver,? 2001.[91] I. B. Celik, U. Ghia, and P. J. Roache, ?Procedure for estimation and report-ing of uncertainty due to discretization in cfd applications,? Journal of fluidsEngineering-Transactions of the ASME, vol. 130, no. 7, 2008.[92] H. Friesing, ?Measurement of the drag associated with recessed surfaces: cut-outs of rectangular and elliptical planform,? Z.W.B.F.B., No. 628, 1936.[93] T. Timonen and J. Halttunen, ?Effect of variations in a pulp flow on samplingand process measurements,? in In: Ilic, D., Borsic, M., & Butorac, J.(eds). XVIIIMEKO World Congress. Metrology in the 3rd Millennium. Book of Summaries.Proceedings. June 22-27, 2003, Dubrovnik, Croatia. HMD-Croatian MetrologySociety, Zagreb, Croatia.84Appendix AExperimental DetailsIn chapter 3, we measured the total no-load power in a 16?? low consistency refinerwhen running with water. As explained, first, we measured the mechanical power,PowerM , to know the losses due to the shaft and bearings friction. Thus, we ran re-finer in the absence of water for different gap sizes and rotational speeds and recordedthe values of PowerM(G,?).Plate 1: BEL = 5.59km/revGap(mm) ?(rpm) PowerM(kW )2.02 205.74 0.372.04 496.82 0.411.99 597.3 0.581.99 798.78 0.931.98 1000.54 1.351.98 1202.11 1.851.98 1403.85 2.471.99 1504.86 2.819.09 498.85 0.499.08 599.4 0.669.08 800.87 1.059.09 1001.25 1.489.09 1194.44 1.979.09 1404.92 2.549.09 1505.57 2.85Plate 3: BEL = 0.99km/revGap(mm) ?(rpm) PowerM(kW )2.06 403.66 0.262.06 504.89 0.432.06 605.38 0.582.05 796.06 0.972.05 997.78 1.452.05 1098.91 1.672.04 1199.53 1.919.03 404.86 0.309.00 505.62 0.469.01 595.39 0.659.02 998.81 1.539.00 1099.4 1.799.00 1200.44 2.029.03 203.69 0.279.01 304.31 0.28Table A.1: Values of mechanical power measured for Plate 1 and Plate 3 as shownin Figure 3.285Appendix A. Experimental DetailsIn the next step, the hydraulic power, Power?n, was calculated. So, refiner was runwith water, while no flow was allowed to pump through the refiner and the values ofPowerNL were measured for various gap sizes and rotational speeds. By subtractingthe mechanical power from the total no-load power measured in this step, the valuesof Power?n were estimated.Power?n(G,?) = PowerNL(G,?,Q = 0)? PowerM(G,?) (A.1)Plate 1: BEL = 5.59km/rev?(rpm) Gap(mm) PowerNL(kW ) Power?n(kW )400.55 1.01 1.43 1.04497.03 1.05 2.54 2.02597.75 1.04 4.10 3.42799.38 0.99 9.33 8.27398.08 1.98 1.41 1.03497.08 1.94 2.54 2.02600.00 1.92 4.11 3.42799.37 1.87 9.32 8.261000.91 1.98 17.77 16.271101.89 1.94 23.07 21.32400.23 5.05 1.43 1.05496.59 5.03 2.53 2.01600.00 5.02 4.12 3.44800.00 5.02 9.30 8.241000.80 4.98 17.48 15.981101.35 4.94 22.88 21.12398.13 8.08 1.41 1.03497.04 8.08 2.53 2.01600.00 8.07 4.11 3.43799.06 8.06 9.21 8.161000.60 8.03 17.59 16.091101.57 7.99 22.90 21.15398.06 8.98 1.41 1.03496.85 8.95 2.53 2.01600.00 8.95 4.11 3.42799.20 8.96 9.21 8.151000.73 8.93 17.52 16.021101.52 8.90 22.75 20.99Table A.2: Values of hydraulic power measured for Plate 186Appendix A. Experimental DetailsPlate 2: BEL = 2.74km/rev?(rpm) Gap(mm) PowerNL(kW ) Power?n(kW )1396.63 8.96 38.72 43.711203.73 8.89 24.29 26.94999.48 8.88 14.10 15.25806.57 8.95 7.72 8.05602.62 8.99 3.55 3.461394.00 8.00 38.50 43.461201.00 8.00 24.40 27.08999.00 7.88 14.20 15.37798.00 7.95 7.73 8.08603.40 7.80 3.47 3.361396.00 5.00 38.40 43.331202.00 5.00 24.60 27.321001.00 5.00 14.14 15.29799.00 5.02 7.76 8.11602.00 4.80 3.47 3.371394.67 0.57 38.00 42.851202.19 0.51 24.89 27.67999.08 0.48 14.09 15.23797.42 0.49 7.80 8.17601.83 0.45 3.50 3.40Table A.3: Values of hydraulic power measured for Plate 287Appendix A. Experimental DetailsPlate 3: BEL = 0.99km/rev?(rpm) Gap(mm) PowerNL(kW ) Power?n(kW )502.88 0.96 2.42 1.90604.82 0.93 4.00 3.32799.40 0.86 8.62 7.77503.77 1.92 2.41 1.88607.46 1.94 4.07 3.42802.00 1.89 8.71 8.04997.14 1.84 16.01 15.211097.81 1.77 21.30 19.551198.74 1.74 27.41 25.40502.98 5.02 2.41 1.88605.89 5.01 4.03 3.41805.64 4.97 8.60 8.08996.35 4.92 16.14 15.241097.08 4.88 21.12 19.381198.08 4.90 27.20 25.19502.59 8.04 2.42 1.90607.53 8.04 4.04 3.35805.25 8.02 8.60 8.17995.99 7.97 16.03 15.041096.96 7.94 21.50 19.76502.34 9.04 2.40 1.87605.78 9.06 4.00 3.31794.10 9.03 8.26 7.78995.77 9.00 16.16 14.771096.69 8.97 21.06 19.32Table A.4: Values of hydraulic power measured for Plate 388Appendix A. Experimental DetailsPlate 4: BEL = 2.01km/rev?(rpm) Gap(mm) PowerNL(kW ) Power?n(kW )596.38 1.02 3.42 3.21799.87 1.28 7.98 8.101003.82 1.15 14.98 15.761196.15 1.08 24.61 26.451400.04 0.97 37.89 41.291502.26 0.97 46.51 50.99597.24 2.98 3.49 3.29800.57 2.93 7.93 8.041004.62 3.11 15.08 15.881197.24 2.63 24.84 26.711401.00 2.57 38.47 41.961502.86 2.51 46.58 51.06598.05 4.42 3.50 3.30801.54 4.34 8.07 8.211005.12 4.26 15.24 16.061197.66 4.19 25.21 27.151401.33 4.13 38.79 42.331503.41 4.08 48.10 52.84600.00 4.86 3.54 3.34802.05 4.81 8.04 8.161005.73 4.76 15.21 16.031197.96 4.67 25.20 27.131402.11 4.64 38.70 42.231503.63 4.59 48.11 52.85599.17 7.86 3.56 3.36802.63 7.83 8.04 8.171004.00 7.80 15.25 16.071198.58 7.75 25.26 27.201403.11 7.68 38.84 42.391504.30 7.65 48.09 52.82600.05 8.93 3.58 3.38803.35 8.88 8.04 8.171005.00 8.83 15.21 16.021199.56 8.78 25.14 27.051403.30 8.72 38.80 42.341505.62 8.72 48.09 52.83Table A.5: Values of hydraulic power measured for Plate 489Appendix A. Experimental DetailsPlate 5: BEL = 10.1km/rev?(rpm) Gap(mm) PowerNL(kW ) Power?n(kW )591.67 8.98 3.77 3.10680.73 9.07 5.65 4.82793.05 9.06 8.45 7.41880.59 9.03 11.57 10.35984.01 8.99 15.77 14.30492.96 7.99 2.41 1.89591.63 8.03 3.79 3.12680.66 7.95 5.70 4.87792.88 7.95 8.52 7.48880.58 8.01 11.70 10.47983.82 7.93 15.92 14.46680.04 7.12 5.74 4.91792.87 6.95 8.71 7.67880.37 7.04 11.78 10.56983.66 7.00 15.77 14.31492.75 5.93 2.39 1.88592.08 6.06 3.89 3.22679.60 5.97 5.74 4.92792.78 6.01 8.75 7.71983.24 6.10 15.88 14.42492.49 5.00 2.38 1.87591.78 4.99 3.90 3.23680.25 5.11 5.60 4.78792.46 5.00 8.62 7.58881.68 5.00 11.50 10.27983.42 5.16 15.75 14.29492.28 2.05 2.38 1.86592.48 2.07 3.83 3.16681.37 2.04 5.66 4.84792.09 1.98 8.70 7.66983.59 2.01 15.32 13.86491.80 0.92 2.37 1.85592.75 1.09 3.81 3.14682.05 1.01 5.75 4.92791.92 1.00 8.80 7.76882.18 1.10 11.55 10.32983.40 1.04 15.62 14.16Table A.6: Values of hydraulic power measured for Plate 590Appendix A. Experimental DetailsPlate 6: BEL = 12.9km/rev?(rpm) Gap(mm) PowerNL(kW ) Power?n(kW )495.21 9.00 2.23 1.72593.56 9.00 3.81 3.14680.84 9.05 5.63 4.81793.23 9.03 8.15 7.11882.94 9.07 11.08 9.85983.88 9.07 14.80 13.34495.21 8.00 2.24 1.72593.27 8.02 3.80 3.13680.92 8.02 5.64 4.81793.12 8.09 8.15 7.11883.20 7.97 11.08 9.84983.73 8.02 14.79 13.33495.21 6.00 2.25 1.74593.19 6.03 3.84 3.16793.30 6.02 8.27 7.22983.49 6.06 14.90 13.44495.21 4.96 2.26 1.74593.04 4.99 3.87 3.19793.39 5.02 8.24 7.20983.50 5.09 15.06 13.60495.21 2.98 2.25 1.73592.91 2.53 3.78 3.10983.65 2.99 15.06 13.60495.21 2.03 2.26 1.74592.95 1.92 3.83 3.16793.46 2.09 8.27 7.22983.02 2.05 15.02 13.56495.21 1.09 2.25 1.73592.65 1.03 3.84 3.17793.48 1.01 8.17 7.13Table A.7: Values of hydraulic power measured for Plate 691Appendix A. Experimental DetailsFinally, we measured PowerNL for different gap sizes, rotational speeds and flowrates when there was flow pumped through the refiner and by subtracting the mechan-ical power, Powern which covers both hydraulic and pumping powers, was measured.Powern(G,?,Q) = PowerNL(G,?,Q)? PowerM(G,?) (A.2)where Powern = Power?n + PowerPTable A.8: Values of PowerNL and Powern measured forPlate 1Plate 1: BEL = 5.59km/rev?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )596.07 503.79 8.06 4.44 3.76596.46 509.97 9.05 4.43 3.76798.21 518.23 5.00 10.13 9.08593.93 600.21 0.98 4.99 4.32594.52 604.84 2.03 4.93 4.26605.85 625.03 3.98 4.99 4.30596.06 600.09 5.04 4.81 4.13595.67 596.97 8.05 4.52 3.84597.20 589.20 9.05 4.57 3.89797.85 619.80 1.98 10.83 9.78796.35 605.78 3.91 10.44 9.39798.31 592.43 5.01 10.27 9.21796.95 595.00 8.05 9.92 8.87798.81 591.94 9.04 9.97 8.91492.89 817.31 1.17 3.23 2.72504.75 807.60 2.13 3.29 2.75504.83 796.51 4.01 3.29 2.76495.39 807.53 5.07 3.10 2.58494.83 818.79 8.09 3.00 2.48497.71 803.59 9.07 3.08 2.56593.80 791.33 1.11 5.24 4.56594.55 804.77 2.10 5.14 4.47594.64 795.68 4.00 5.07 4.39596.09 802.48 5.07 5.00 4.32607.13 805.29 8.10 5.13 4.43598.49 805.33 9.10 4.89 4.21796.24 796.44 1.05 11.32 10.27797.72 809.70 2.02 11.17 10.12Continued on next page92Appendix A. Experimental DetailsTable A.8 ? continued from previous page?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )800.14 790.81 3.97 11.11 10.06797.71 795.45 5.06 10.53 9.48797.55 790.19 8.10 10.32 9.27800.27 790.96 9.10 10.36 9.30504.26 1015.02 1.23 3.59 3.06504.96 1008.62 2.17 3.55 3.02504.97 1005.56 4.06 3.34 2.80506.06 1004.52 5.11 3.41 2.88505.84 998.41 8.14 3.35 2.82498.02 994.45 9.12 3.23 2.71605.07 1007.73 1.20 5.61 4.92605.54 996.40 2.14 5.58 4.88594.73 999.93 4.05 5.28 4.61595.87 1009.94 5.09 5.20 4.52595.47 1007.21 8.13 5.13 4.45598.63 1006.06 9.12 5.11 4.43795.80 1013.27 1.12 11.84 10.79797.17 991.96 2.05 11.70 10.65801.25 989.61 4.04 11.34 10.28797.75 992.86 5.10 11.09 10.03804.45 1008.19 8.13 11.09 10.03800.07 1005.48 9.13 11.09 10.04998.86 994.51 8.12 19.93 18.441001.97 993.93 9.12 19.99 18.49504.75 1209.49 2.20 3.59 3.05505.18 1201.02 4.08 3.56 3.03506.00 1201.33 5.13 3.57 3.03505.80 1203.27 8.13 3.54 3.00498.55 1210.66 9.13 3.36 2.84605.41 1183.18 1.23 5.95 5.25605.56 1199.61 2.20 5.79 5.09595.00 1192.13 4.07 5.45 4.78595.85 1208.15 5.12 5.41 4.74595.60 1211.38 8.13 5.25 4.57599.25 1194.59 9.14 5.24 4.56795.84 1194.55 1.14 12.07 11.03798.41 1210.19 2.17 12.20 11.15802.20 1204.71 4.06 11.72 10.66797.65 1209.22 5.14 11.23 10.18Continued on next page93Appendix A. Experimental DetailsTable A.8 ? continued from previous page?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )797.25 1217.52 8.14 11.19 10.14800.38 1212.14 9.15 11.19 10.14999.03 1194.25 5.14 20.96 19.46999.16 1191.04 8.15 20.59 19.091002.14 1189.98 9.17 20.59 19.08Table A.9: Values of PowerNL and Powern measured forPlate 2Plate 2: BEL = 2.74km/rev?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )1198.82 1404.16 5.15 33.42 31.411001.93 1402.42 9.05 19.94 18.43994.61 1402.26 5.02 20.62 19.14997.94 1401.92 4.08 21.05 19.56797.50 1408.25 9.06 10.83 9.78802.19 1416.15 5.02 11.36 10.30801.89 1398.76 4.07 11.50 10.441160.72 1196.86 6.12 29.50 27.601197.83 1201.25 5.03 32.63 30.621001.29 1210.33 9.04 19.28 17.781002.35 1196.66 8.15 19.19 17.68999.69 1198.65 6.01 19.58 18.081005.41 1197.34 5.03 20.34 18.821000.26 1196.05 4.05 20.43 18.93797.39 1198.27 9.03 10.52 9.47798.26 1199.15 8.03 10.62 9.56806.74 1196.24 6.01 10.88 9.81801.88 1198.70 5.03 11.09 10.03796.48 1199.07 4.07 11.01 9.96604.55 1205.14 9.02 5.01 4.32602.59 1194.14 8.03 5.01 4.32602.70 1196.70 6.01 5.09 4.40602.02 1198.51 5.00 5.12 4.431195.32 1006.82 8.10 31.15 29.141204.06 1008.42 6.10 31.48 29.461198.72 1007.93 5.01 32.28 30.26Continued on next page94Appendix A. Experimental DetailsTable A.9 ? continued from previous page?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )1205.22 1011.40 4.03 32.53 30.501198.31 996.94 1.98 33.80 31.791000.88 999.26 9.02 18.93 17.431002.57 1000.69 8.11 18.94 17.44999.96 1013.31 6.12 19.60 18.10994.42 1008.26 5.04 19.68 18.191005.46 1003.02 4.14 20.62 19.11796.98 1002.16 9.01 10.03 8.98798.53 1006.62 8.11 9.99 8.93796.92 999.51 6.11 10.36 9.31802.13 999.50 5.05 10.76 9.70799.02 998.80 4.20 10.80 9.75604.17 996.94 9.01 4.80 4.11600.57 1000.85 8.10 4.74 4.05603.01 1004.75 6.11 4.75 4.06598.38 999.19 5.05 4.89 4.21600.17 1004.59 4.21 4.99 4.301204.21 789.36 6.05 31.31 29.281197.55 807.15 4.98 31.42 29.411206.73 805.56 3.89 33.04 31.001000.62 804.42 8.98 18.40 16.891002.90 799.37 8.10 18.41 16.90999.87 804.59 6.09 18.53 17.031005.13 796.65 5.02 19.45 17.941002.88 801.84 3.98 19.71 18.20796.54 797.67 8.98 10.05 9.00798.91 806.34 8.09 10.07 9.02807.09 810.92 6.10 10.06 8.99801.04 804.84 5.04 10.47 9.41798.87 795.20 4.08 10.50 9.45595.31 798.95 8.10 4.48 3.80603.01 799.42 6.10 4.57 3.88596.83 800.80 5.06 4.50 3.83595.42 797.76 4.13 4.73 4.051000.60 606.42 6.02 18.50 16.991004.12 601.22 4.86 18.92 17.411003.74 604.02 4.10 19.24 17.73800.11 606.97 4.99 10.03 8.98596.55 609.06 5.03 4.42 3.74Continued on next page95Appendix A. Experimental DetailsTable A.9 ? continued from previous page?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )595.86 605.26 4.10 4.56 3.88Table A.10: Values of PowerNL and Powern measuredfor Plate 3Plate 3: BEL = 0.99km/rev?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )504.39 610.34 5.01 2.84 2.31502.04 611.42 8.09 2.79 2.26599.02 616.85 2.02 4.57 3.89605.90 611.91 5.01 4.64 3.95602.94 608.25 8.06 4.39 3.70602.91 598.18 9.12 4.29 3.60800.77 621.36 1.96 9.50 8.45805.28 612.67 8.05 9.57 8.50793.98 595.72 9.11 9.04 7.99503.66 796.40 2.06 3.05 2.52501.88 806.46 8.08 2.84 2.31495.69 798.25 9.13 2.75 2.23599.25 796.51 2.02 4.80 4.12597.17 806.82 5.02 4.67 3.99602.79 807.12 8.09 4.59 3.90603.40 806.98 9.15 4.53 3.84800.89 811.76 1.98 9.93 8.88798.90 796.38 4.99 10.02 8.97804.88 808.37 8.09 9.84 8.77793.62 799.86 9.14 9.41 8.37995.67 815.94 8.09 17.62 16.13502.37 1007.35 8.09 3.07 2.54495.71 1005.54 9.16 2.89 2.37601.63 1016.19 2.11 5.08 4.39592.02 996.31 8.11 4.71 4.04603.27 999.74 9.17 4.72 4.03801.82 990.45 2.03 10.29 9.23799.22 1002.95 5.04 10.24 9.19794.21 1008.38 8.12 10.20 9.16793.81 991.95 9.17 9.73 8.69Continued on next page96Appendix A. Experimental DetailsTable A.10 ? continued from previous page?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )500.24 1188.00 2.12 3.30 2.78508.58 1191.95 5.07 3.32 2.78600.75 1198.22 2.12 5.22 4.53801.82 1217.66 2.10 10.73 9.67799.49 1216.07 5.07 10.80 9.75Table A.11: Values of PowerNL and Powern measuredfor Plate 4Plate 4: BEL = 2.01km/rev?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )596.08 610.42 2.22 4.50 3.82795.77 603.80 4.39 9.84 8.80797.32 596.91 5.24 9.71 8.66796.74 605.55 8.21 9.26 8.21796.36 604.48 9.06 9.28 8.231000.33 601.21 4.31 18.58 17.081001.87 600.55 5.18 18.10 16.601197.96 591.12 2.18 31.63 29.621205.17 601.51 4.23 30.50 28.471195.32 597.47 5.12 29.46 27.451402.95 590.55 2.10 48.37 45.761398.76 607.05 4.12 46.68 44.08604.04 811.95 2.01 4.69 4.00602.97 790.87 4.07 4.55 3.86595.43 799.82 4.96 4.44 3.76803.77 798.51 4.02 10.50 9.44799.35 795.59 4.93 10.10 9.05798.03 795.08 8.04 9.62 8.56796.74 798.78 9.09 9.58 8.531004.11 798.35 4.88 19.12 17.611001.68 798.52 9.07 17.66 16.161195.24 809.67 2.11 31.92 29.921206.00 798.77 3.93 31.80 29.771201.09 807.44 4.83 30.80 28.78604.95 1010.60 2.15 4.94 4.25604.04 1007.12 4.03 4.68 3.99Continued on next page97Appendix A. Experimental DetailsTable A.11 ? continued from previous page?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )595.21 1001.48 4.97 4.47 3.791001.51 999.55 4.20 19.92 18.411004.34 1009.51 4.94 19.69 18.181002.49 1005.34 8.07 18.51 17.001001.45 1002.51 9.11 18.46 16.961194.50 1009.50 4.12 32.36 30.361197.50 998.06 4.90 31.46 29.451195.10 1003.98 9.10 29.72 27.72605.38 1190.08 2.18 5.16 4.47604.05 1203.31 4.03 4.94 4.25596.32 1198.09 5.02 4.74 4.07604.33 1196.02 9.11 4.72 4.03798.35 1196.36 7.95 10.45 9.40797.30 1204.15 9.11 10.39 9.33994.12 1209.60 5.02 19.70 18.211003.19 1214.40 7.96 19.49 17.981001.82 1193.72 9.12 19.22 17.711195.43 1195.39 3.96 33.40 31.401198.38 1205.51 4.98 32.67 30.651199.39 1195.37 7.96 31.63 29.621195.95 1200.45 9.13 31.13 29.131401.61 1200.61 1.95 53.17 50.561400.38 1203.49 4.09 51.04 48.431402.50 1211.61 4.94 49.58 46.971399.91 1196.17 9.13 47.87 45.271606.55 1191.57 1.91 75.13 71.841605.45 1191.50 4.07 72.93 69.641595.73 1197.47 4.94 69.80 66.55596.16 1400.04 2.01 5.09 4.41593.83 1400.15 4.25 4.99 4.32596.22 1402.36 5.04 4.97 4.29604.82 1409.85 7.96 4.89 4.19604.25 1411.11 9.11 4.97 4.28797.38 1396.98 9.13 10.72 9.671002.84 1401.74 7.98 19.99 18.481001.93 1408.91 9.17 19.91 18.411195.77 1395.91 4.24 33.94 31.941198.44 1414.89 5.04 33.66 31.641195.85 1401.46 7.99 31.97 29.97Continued on next page98Appendix A. Experimental DetailsTable A.11 ? continued from previous page?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )1195.71 1407.16 9.17 32.11 30.101400.34 1395.50 4.17 51.94 49.341402.76 1407.59 5.03 51.51 48.901400.56 1395.14 8.22 48.37 45.771399.99 1398.12 9.18 48.19 45.581607.11 1399.46 1.92 78.93 75.641605.44 1399.50 4.15 74.47 71.191607.63 1396.41 5.16 73.87 70.581604.80 1400.05 8.24 71.00 67.72Table A.12: Values of PowerNL and Powern measuredfor Plate 5Plate 5: BEL = 10.1km/rev?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )592.26 507.09 0.98 4.43 3.76592.20 486.65 2.04 4.36 3.69592.12 474.91 2.59 4.33 3.66591.89 468.51 3.04 4.30 3.63592.03 499.54 4.09 4.28 3.61591.67 493.75 5.03 4.29 3.62591.58 494.13 5.99 4.26 3.59591.60 498.02 8.00 4.25 3.58591.68 500.61 9.00 4.23 3.56690.57 586.10 0.98 6.82 5.98690.96 562.98 1.86 6.83 5.99691.37 550.47 2.46 6.61 5.77690.03 539.32 2.93 6.61 5.77691.96 522.20 4.08 6.54 5.70691.58 512.84 5.01 6.46 5.61691.50 510.35 6.04 6.37 5.53692.64 517.41 8.01 6.36 5.51691.74 520.43 8.98 6.36 5.51595.56 587.31 1.15 4.61 3.93595.90 594.90 2.04 4.60 3.92596.41 594.30 2.53 4.58 3.90596.03 591.34 3.10 4.47 3.80Continued on next page99Appendix A. Experimental DetailsTable A.12 ? continued from previous page?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )596.76 583.42 4.11 4.51 3.83596.27 595.76 5.20 4.32 3.64596.30 598.03 6.59 4.33 3.65596.06 599.60 7.88 4.32 3.64596.27 601.16 9.17 4.32 3.64694.90 608.01 8.12 6.56 5.70694.50 609.52 8.96 6.53 5.68797.32 615.48 1.10 9.81 8.75796.99 620.89 2.07 10.14 9.09796.57 608.82 2.49 10.03 8.98796.50 608.71 3.09 10.03 8.98796.64 611.52 4.05 9.81 8.76796.52 600.76 5.11 9.62 8.57796.55 597.47 5.97 9.59 8.54796.44 605.41 7.96 9.48 8.43796.19 611.11 9.04 9.45 8.40882.73 656.59 1.00 13.29 12.05982.93 662.31 3.07 18.25 16.79983.00 638.49 3.96 18.18 16.72982.65 633.90 4.77 18.09 16.63982.70 622.00 5.86 17.66 16.20982.63 625.01 8.10 17.40 15.94983.06 631.99 8.89 17.40 15.94892.95 682.14 1.02 13.95 12.70892.51 692.25 2.55 13.82 12.57892.27 704.63 2.95 13.88 12.62892.48 687.68 4.07 13.72 12.47892.34 685.28 5.04 13.47 12.21892.51 683.76 6.03 13.50 12.25892.56 692.82 8.12 13.39 12.14892.64 698.81 8.97 13.40 12.15984.23 713.55 1.01 17.70 16.24592.12 801.64 1.07 4.75 4.08592.08 786.80 2.07 4.70 4.03592.56 800.62 2.67 4.70 4.03592.56 801.17 2.99 4.67 4.00592.49 799.41 5.05 4.47 3.80592.76 802.54 6.09 4.47 3.80593.13 807.24 7.97 4.48 3.81Continued on next page100Appendix A. Experimental DetailsTable A.12 ? continued from previous page?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )593.21 807.71 8.98 4.47 3.80684.37 832.55 1.04 7.01 6.18682.14 815.21 2.08 6.86 6.03682.44 805.38 2.57 6.81 5.98681.76 796.71 3.15 6.70 5.88682.10 792.97 3.99 6.70 5.87682.21 792.20 5.10 6.51 5.68682.13 796.04 6.05 6.41 5.58681.61 800.52 8.07 6.38 5.55681.04 802.96 9.00 6.33 5.50791.58 791.45 2.55 10.28 9.25788.39 781.41 3.16 10.13 9.10790.67 794.83 4.00 10.05 9.01790.40 791.90 4.93 9.57 8.53785.29 792.26 5.98 9.43 8.40786.81 796.21 8.00 9.36 8.33787.38 798.39 8.99 9.32 8.29892.77 796.10 2.54 14.21 12.96893.17 823.05 3.17 14.20 12.95893.01 808.85 3.95 14.12 12.86892.83 801.54 5.01 13.27 12.02892.95 781.24 6.10 13.21 11.96892.86 786.32 8.15 13.21 11.96892.74 784.22 8.99 13.21 11.96983.25 787.73 2.05 18.70 17.24983.20 790.30 2.49 18.61 17.15983.19 791.16 3.00 18.50 17.04982.80 763.99 4.19 18.16 16.70982.39 789.95 5.08 17.67 16.21982.48 788.47 6.02 17.46 16.00982.80 796.84 8.15 17.38 15.92982.41 802.00 9.00 17.28 15.82101Appendix A. Experimental DetailsTable A.13: Values of PowerNL and Powern measuredfor Plate 6Plate 6: BEL = 12.9km/rev?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )588.78 317.45 8.03 3.77 3.11588.96 320.71 9.08 3.78 3.12588.63 360.05 9.07 3.81 3.15785.02 426.57 7.97 8.30 7.28785.86 428.00 9.01 8.31 7.28489.02 495.79 5.00 2.43 1.92578.85 504.17 8.07 3.73 3.08578.58 509.12 9.11 3.73 3.08682.32 514.50 7.91 5.88 5.06681.47 517.46 9.05 5.79 4.96787.16 546.10 1.00 9.05 8.02789.86 499.40 5.05 8.56 7.53785.79 501.44 6.07 8.43 7.40785.98 509.16 7.97 8.45 7.42787.32 512.89 8.99 8.47 7.44892.07 582.00 1.23 12.55 11.30892.08 534.77 2.44 12.71 11.46891.78 517.81 2.98 12.64 11.39891.75 500.18 4.92 12.05 10.80589.29 594.57 3.11 4.12 3.46589.46 597.13 4.96 4.05 3.39589.20 597.45 6.08 4.01 3.34589.21 599.31 7.97 4.01 3.34589.07 601.10 9.01 4.08 3.41681.65 618.23 7.92 5.93 5.11682.39 615.43 9.01 5.92 5.10791.71 609.63 1.14 9.27 8.23791.38 596.92 5.02 8.70 7.66790.23 600.88 6.00 8.68 7.64791.15 606.57 7.93 8.70 7.66790.95 608.06 9.02 8.71 7.67881.12 657.12 1.10 12.58 11.36881.16 620.11 2.51 12.44 11.21881.34 609.80 2.92 12.37 11.15880.95 600.13 4.03 11.86 10.64880.85 597.82 4.94 11.67 10.44Continued on next page102Appendix A. Experimental DetailsTable A.13 ? continued from previous page?(rpm) FlowRate(lpm) Gap(mm) PowerNL(kW ) Powern(kW )880.85 601.11 5.95 11.76 10.53880.74 610.55 7.92 11.72 10.50881.42 617.08 9.04 11.72 10.50982.19 610.61 2.15 16.61 15.15982.26 580.18 2.97 16.75 15.30982.40 579.79 4.03 16.18 14.73982.46 587.92 5.09 16.08 14.62982.02 593.13 6.01 15.91 14.45589.03 820.26 5.97 4.20 3.53589.01 815.42 8.03 4.18 3.51588.77 816.31 9.07 4.18 3.51689.65 799.36 8.01 6.21 5.36689.40 799.17 9.02 6.21 5.37785.76 829.87 1.06 9.50 8.48786.75 804.84 2.44 9.49 8.46786.19 803.92 2.97 9.24 8.21789.61 805.84 4.02 8.94 7.91786.78 809.50 4.98 8.88 7.85788.80 811.52 6.07 8.86 7.83789.22 813.76 7.98 8.81 7.78787.28 813.31 9.05 8.81 7.78881.06 812.04 1.05 12.99 11.76880.65 783.64 1.97 12.92 11.70880.95 790.12 2.50 12.93 11.70880.45 788.08 2.98 12.56 11.33881.23 789.03 6.02 11.94 10.71880.68 791.23 8.05 11.84 10.61881.09 793.58 9.01 11.84 10.61981.40 814.55 2.11 17.32 15.87981.59 787.19 3.10 16.71 15.25981.48 778.92 3.92 16.30 14.84981.66 777.03 4.94 16.25 14.79981.79 775.78 6.08 16.29 14.83981.72 786.13 7.94 16.28 14.82103Appendix BComparison of Water and PulpIn addition to water, we measured the values of no-load power for our 16?? LC refinerwhen running by pulp with two different consistencies of C = 1.5% and 3.5% to beable to compare the no-load powers measured by water and mechanical pulp:(a) Values of hydraulic powerPlate 2: BEL = 2.74km/revWater Pulp, C = 1.5% Pulp, C = 3.5%?(rpm) Power?n(kW ) ?(rpm) Power?n(kW ) ?(rpm) Power?n(kW )1203.73 26.71 583.37 3.21 608.08 3.42999.48 16.32 784.90 7.82 700.93 5.00806.57 7.98 985.94 14.69 796.98 8.03602.62 3.43 1187.27 25.63 997.76 15.11500.52 2.15 1197.56 25.62(b) Values of PowernPlate 2: BEL = 2.74km/revWater Pulp, C = 1.5% Pulp, C = 3.5%?(rpm) Powern(kW ) ?(rpm) Powern(kW ) ?(rpm) Powern(kW )1000.78 15.48 794.23 7.73 603.47 3.10796.48 7.92 985.18 14.55 701.20 5.20603.79 3.26 1199.53 24.57 809.20 7.64501.81 1.57 1003.75 14.26Table B.1: Values of Power?n and Powern measured for water and pulp with consis-tencies of 1.5% and 3.5% for Plate 2 when Q = 600lpm104Appendix CPulp PropertiesIn chapter 3, we also measured some pulp properties for the pulp suspension of C =3.5% to determine the starting point of refiner loading (Gl). The chosen propertieswere freeness, fibre length and tensile:Plate 2: BEL = 2.74km/rev, C = 3.5% and Q = 500lpm? = 800rpm ? = 1000rpm ? = 1200rpmGap Freeness Gap Freeness Gap Freeness(mm) (mlCSF ) (mm) (mlCSF ) (mm) (mlCSF )8.93 385.9 9.02 385.9 8.96 385.96.07 385.9 6.07 385.9 6.02 385.92.48 375.2 2.55 372.5 2.50 370.71.49 368.4 1.48 366 1.29 364.20.76 363 0.73 348.2 0.69 350.350.28 357.3 0.30 307.2 0.30 288.650.09 335.6 0.09 271.85 0.12 246.60.02 293.7 0.04 255.6 0.01 208.45Table C.1: Freeness of fibres at various gap sizes for Plate 2 when Q = 500lpm asshown in Figure 3.6105Appendix C. Pulp PropertiesPlate 2: BEL = 2.74km/rev, C = 3.5% and Q = 500lpm? = 800rpm ? = 1000rpm ? = 1200rpmGap FibreLength Gap FibreLength Gap FibreLength(mm) (mm) (mm) (mm) (mm) (mm)8.93 1.93 9.02 1.93 8.97 1.936.07 1.93 6.07 1.93 6.02 1.9282.48 1.90 2.55 1.93 2.50 1.951.49 1.81 1.48 1.92 1.29 1.870.76 1.76 0.73 1.89 0.70 1.820.28 1.73 0.30 1.83 0.30 1.580.09 1.64 0.09 1.46 0.12 1.300.02 1.55 0.04 1.37 0.01 1.24Table C.2: Length-weighted (LW ) average length of fibres at various gap sizes forpulp suspension of C = 3.5% for Plate 2 when Q = 500lpm as shown in Figure 3.7Plate 2: BEL = 2.74km/rev, C = 3.5% and Q = 500lpm? = 800rpm ? = 1000rpm ? = 1200rpmGap TensileIndex Gap TensileIndex Gap TensileIndex(mm) (N.m/g) (mm) (N.m/g) (mm) (N.m/g)8.93 38.28 9.02 38.28 8.97 38.286.07 38.28 6.07 38.28 6.02 38.282.48 38.29 2.55 37.78 2.50 38.651.49 38.20 1.48 39.34 1.29 41.030.76 42.20 0.73 39.42 0.70 40.170.28 41.46 0.30 39.66 0.30 42.870.09 40.26 0.09 41.56 0.12 41.440.02 41.63 0.04 42.64 0.01 43.71Table C.3: Tensile index at various gap sizes for pulp suspension of C = 3.5% forPlate 2 when Q = 500lpm as shown in Figure 3.8106

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