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UBC Theses and Dissertations

Experimental investigation of a model forming fabric Gilchrist, Seth 2006

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Experimental Investigation of aModel Forming FabricbySeth GilchristB.Sc., The University of Wyoming, 2003A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinThe Faculty of Graduate Studies(Mechanical Engineering)The University Of British ColumbiaSeptember, 2006c© Seth Gilchrist 2006AbstractPaper making involves three fabrics: forming, pressing, and drying. The formingfabric is responsible for sheet forming, the initial dewatering of a low concentrationpulp suspension into a wet sheet of paper. In the process of forming, topographicaland hydrodynamic marks can be transferred from the drainage media (the formingfabric) to the sheet produced.An experimental investigation of a model forming fabric was performed to identifythe geometric parameters having the largest influence on hydrodynamic wire mark.The data were also compared with the numerical simulations of Huang.To simplify the problem, justifiable engineering simplifications were made. Thesecond phase (the fibres) was removed and the machine-direction filaments were ne-glected. This reduced the problem to investigation of flow through a bank of dissimilarcylinders. It was desired to find the most important geometrical parameter to reduceflow non-uniformity in the paper side flow field.Particle image velocimetry, pressure drop and flow visualization tests were con-ducted to investigate the flow through the array of cylinders. It was found that witha cylinder surface separation of 0.75× the paper side cylinder diameter the pressuredrop tended toward the sum of the rows, and the paper side flow field was nearlyidentical to the paper side row only flow field, regardless of the backing side cylinderdimensions and configuration. It was seen that when the pressure drop through thebank of cylinders was equal to the sum of the rows’ pressure drops the paper sideflow field was the same as the paper side row only flow field. As such, pressure dropcan act as an indication of when the machine side row will not affect the paper sideflow field.iiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiStatement of Co-Authorship . . . . . . . . . . . . . . . . . . . . . . . . . ixNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Fabric Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Development of the Modern Forming Fabric . . . . . . . . . . . . . . 72.3 The Problem of Wire Mark . . . . . . . . . . . . . . . . . . . . . . . 9Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Project Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2 Previous Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2.1 Investigating the Fabrics . . . . . . . . . . . . . . . . . . . . . 134.2.2 Investigating the Sheet . . . . . . . . . . . . . . . . . . . . . . 16Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Manuscript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.3 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 245.4 PIV Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . 275.5 ∆P Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 32iii5.6 H2 Bubble Visualization Results and Discussion . . . . . . . . . . . . 355.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.8 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.2 Forming Fabric Application . . . . . . . . . . . . . . . . . . . . . . . 416.3 Validation of Huang’s Results . . . . . . . . . . . . . . . . . . . . . . 42Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 Recommendations for Further Research . . . . . . . . . . . . . . . . 49A Appendix Experimental Design . . . . . . . . . . . . . . . . . . . . . . 51A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51A.2 Phase Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . . 51A.3 Geometry Simplification . . . . . . . . . . . . . . . . . . . . . . . . . 52A.4 Flow Velocity and Reynolds number . . . . . . . . . . . . . . . . . . . 55Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56B Appendix Experimental Setup and Methods . . . . . . . . . . . . . 57B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57B.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57B.3 Test Section Flow Characteristics . . . . . . . . . . . . . . . . . . . . 59B.3.1 Test Section Sensor Details . . . . . . . . . . . . . . . . . . . . 65B.4 PIV Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66B.4.1 PIV Equipment Details . . . . . . . . . . . . . . . . . . . . . . 67B.5 Pressure Drop Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 67B.5.1 Pressure Drop Equipment Details . . . . . . . . . . . . . . . . 68B.6 Hydrogen Bubble Generation System Setup . . . . . . . . . . . . . . 68Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70C Appendix Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . 71C.1 Single Valued, Multi-Variable Functions . . . . . . . . . . . . . . . . 71C.2 PIV uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76ppendix AAppendix BAppendix C60ivList of Figures1.1 The forming section of a fourdrinier machine. . . . . . . . . . . . . . 21.2 Forming section of a twin wire former. . . . . . . . . . . . . . . . . . 21.3 Parts of a fine paper machine. . . . . . . . . . . . . . . . . . . . . . . 32.1 Left to right: Single-layer, double-layer, and triple-layer fabrics. . . . 52.2 Cross sections of six popular fabric geometries . . . . . . . . . . . . . 62.3 Forming fabric coordinate system. . . . . . . . . . . . . . . . . . . . . 72.4 Shed definition for single-layer, double-layer and triple-layer fabrics. . 82.5 Topographical wire mark. . . . . . . . . . . . . . . . . . . . . . . . . 94.1 Helle’s results of formation with flow orientation parallel and perpen-dicular to the long knuckles. . . . . . . . . . . . . . . . . . . . . . . . 144.2 A comparison of drainage times for the two long knuckle orientations. 144.3 Forming wire with formed sheet, ground at an incline to show web-penetration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.4 Linear FFT of a sheet of paper. . . . . . . . . . . . . . . . . . . . . . 174.5 Results of Danby’s multiple sheet split tests for twin-wire SC paper. . 195.1 Flow loop test section. . . . . . . . . . . . . . . . . . . . . . . . . . . 255.2 Schematic of test section flow loop. . . . . . . . . . . . . . . . . . . . 265.3 Schematic of the simplified forming fabric geometry . . . . . . . . . . 265.4 Stream wise velocity variation for changingXS/d forD/d = 1.5, G2/G1= 1 and Y/G1 = 0.5 at Re = 65. . . . . . . . . . . . . . . . . . . . . 275.5 Cross stream velocity variation for changing XS/d for D/d = 1.5,G2/G1 = 1 and Y/G1 = 0.5 at Re = 65. . . . . . . . . . . . . . . . 285.6 Stream wise velocity variation for changing Y/G1 for D/d = 1.5,G2/G1 = 1, XS/d = 0.75 at Re = 65. . . . . . . . . . . . . . . . . . 295.7 Cross stream velocity variation for changing Y/G1 for D/d = 1.5,G2/G1 = 1, XS/d = 0.75 at Re = 65. . . . . . . . . . . . . . . . . . 305.8 Stream wise velocity component for changing staggering with D/d =3, G2/G1 = 2, and XS/d = 0 at Re = 25. . . . . . . . . . . . . . . . 315.9 Pressure drop through a bank of cylinders with D/d = 1.5, G2/G1 =1 and Y/G1 = 0.5 at Re = 65 with changing XS/d. . . . . . . . . . . 325.10 Pressure drop through a bank of cylinders with D/d = 1.5, G2/G1 =1 and Y/G1 = 0 at Re = 65 with changing XS/d. . . . . . . . . . . . 335.11 Pressure drop through a bank of cylinders with D/d = 1.5, G2/G1 =1, and XS/d = 0.75 at Re = 65 with changing Y/G1. . . . . . . . . . 34v5.12 Pressure drop through a bank of cylinders with D/d = 1.5, G2/G1 =2, Y/G1 = 0.5 at Re = 65 and changing XS/d. . . . . . . . . . . . . 345.13 Comparison of pressure drop as a function of Re through cylinderswith D/d = 1.5, G2/G1 = 1, XS/d = 0.75 and two staggerings. . . . 355.14 Hydrogen bubble visualizations for variations of XS/d with D/d = 1.5,G2/G1 = 2, Y/G1 = 0.5 at Re = 65. . . . . . . . . . . . . . . . . . . 365.15 Relative velocities for variations of XS/d with D/d = 1.5, G2/G1 =2, Y/G1 = 0.5 at Re = 65. . . . . . . . . . . . . . . . . . . . . . . . 366.1 Huang’s computational stream wise velocity results plotted with thePIV results for D/d = 1.5, G2/G1 = 1, XS/d = 0.75, g1 = 2 andY/G1 = 0.5 at Re = 65. . . . . . . . . . . . . . . . . . . . . . . . . . 426.2 Huang’s computational cross stream velocity results plotted with thePIV results for D/d = 1.5, G2/G1 = 1, XS/d = 0.75, and Y/G1 =0.5 at Re = 65. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.3 Comparison of PIV and computational stream wise velocities for a caseof D/d = 3, G2/G1 = 2, XS/d = 0, Y/G1 = 0.5 at Re = 25 . . . . . 456.4 Comparison of PIV and computational cross stream velocities for acase of D/d = 3, G2/G1 = 2, XS/d = 0, Y/G1 = 0.5 at Re = 25 . . 467.1 Method for determining the internal 3D geometry of a forming fabric. 49A.1 The support of CD filaments . . . . . . . . . . . . . . . . . . . . . . . 53A.2 Cross section of a forming fabric showing the CD filaments contactingthe CD face. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54A.3 The resulting 2D bank of cylinders obtained from the above simplifi-cations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54B.1 Cylinder frame equipt with 9.53mm and 19mm diameter cylinders. . . 58B.2 Locations of the pressure and hydrogen bubble ports . . . . . . . . . 59B.3 The test section fully installed. Flow is from left to right . . . . . . . 59B.4 Schematic of the Test Section Flow Loop . . . . . . . . . . . . . . . . 60B.5 Image of test section flow at 2cm/s. Flow is from bottom to top ofimage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61B.6 Image of test section flow at 4cm/s. Flow is from bottom to top ofimage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62B.7 Data extracted from Figs. B.5 and B.6 . . . . . . . . . . . . . . . . . 63B.8 Normalized test section velocity with a 135.3mm field of view. . . . . 63B.9 Empty test section velocity vectors at location of PIV data collection. 64B.10 Stopwatch measured test section velocity for comparison with PIV. . 65B.11 The interrogation areas from the two masked PIV images with a knowntime separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66B.12 The two interrogation areas are then compared by cross-correlation tofind the average particle displacement and hence velocity. . . . . . . . 67B.13 PIV arrangement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68viC.1 Screen shot of the spread sheet used to calculate uncertainty. . . . . . 74C.2 Screen shot of the spread sheet used to find the venturi constant anduncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76viiAcknowledgementsI would like to thank Sheldon Green, Ali Vakil, Dan Dressler, and Barb Murry fromthe University of British Columbia’s department of Mechanical Engineering for theirprofessions and personal help throughout the course of this project.I would also like to thank Dale Johnson, Roger Danby, Graham Jackson and the restof the team at Asten Johnson for continued financial and material support.viiiStatement of Co-AuthorshipSeth Gilchrist conducted all the experiments and analysis described in this thesis.My role in the thesis was primarily supervisory; most of the intellectual content ofthe thesis is Seth’s.Dr. Sheldon I. Green, P.Eng.ixNomenclatureCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross machine directiond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paper side cylinder diameterD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Machine side cylinder diameterD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inlet pipe diameter (§C.1)D1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Venturi inlet diameterD2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Venturi throat diameter∆P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure dropG1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paper side row centre spacingG2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Machine side row centre spacingH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test section heightk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Venturi constantk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Viscosimeter constantm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .MassMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Machine directionµ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ViscosityRe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reynolds numberρ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Densityu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x-direction velocityU0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Upstream flow velocityUTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test section velocityUpipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inlet pipe velocityv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y-direction velocityV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VolumeW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test section widthXC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Cylinder row centre separationXS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylinder row surface separationy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Horizontal PositionY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Row staggeringz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Fabric normalxChapter 1IntroductionOf the common commodities in the modern world, there are few thathave as great an impact on our daily lives as paper. Paper, in its variousforms, has been used for thousands of years to record and disseminateinformation. In modern times the uses of paper have expanded greatlyinto medicine, packaging, manufacturing, and industrial production. Thecontinual development of paper and papermaking techniques has advancedto the point that it requires advanced scientific and engineering methods.To be classified as paper a product must be produced using particularmeans. In its purest form paper is made from a fibrous material that hasbeen separated into individual fibres. These fibres are then suspended inwater and a screen, or other drainage medium, is used to dewater thesuspension, leaving a thin sheet of material. Paper has been made thisway for nearly two thousand years, since the initial development by Ts’aiLun in A.D. 105[2].Today the process is essentially the same. The first, and still most com-mon, paper machines are called fourdriniers. They are named after HenryFourdriner who filed the first patent for them in England in 1806[2]. Onthese machines the pulp/water mixture is distributed into a long, thin jetin the headbox and is then sprayed onto a moving fabric. The formingsection of a fourdrinier machine is shown in Fig. 1.1. In this image thewater/pulp solution is coming out of the headbox in the background of theimage and is being filtered through the forming fabric, the white, wovenstructure visible in the fore- and mid-ground. As the water is drained off,a mat of pulp and additives is formed on the forming fabric.In an effort to reduce the one-sided nature of paper produced on four-drinier machines the twin-wire former was developed. On these machinesthe pulp suspension is injected into a gap between two forming fabrics.The forming section of a twin wire former is shown in Fig. 1.2.Regardless of the type of forming section used, the end result is a mat ofpulp fibres and additives. This mat is then transfered into a mechanicalpressing section for additional dewatering and finally to a heated dryersection where water is removed by heat and air. Once the page has been1Chapter 1. IntroductionFigure 1.1: The forming section of a fourdrinier machine.[1].Figure 1.2: Forming section of a twin wire former[3].2Chapter 1. IntroductionFigure 1.3: Parts of a fine paper machine[4].dried it can be further processed by calendering, coating or other specialtreatments. A schematic of a full twin wire paper machine is shown ifFig. 1.3.3Bibliography[1] Papermachine service industries〈http://www.papermachine.com/photos/deckles/d8.jpg〉, March 2006.[2] Dard Hunter. Papermaking: The History and Technique of an Ancient Craft.Dover Publications, Inc., New York, New York, 1974.[3] James Olson. University of British Columbia, Vancouver, BC CHBE-401 ClassNotes: Papermaking Papermachine - Forming, Mar 11, 2005.[4] Hannu Paulapuro. Papermaking Part 1, Stock Preparation and Wet End. FapetOy, Helsinki, Finland, 2000.4Chapter 2Motivation2.1 Fabric BasicsIt can be argued that of the three fabrics used in papermaking – forming,pressing and drying – the forming fabric is the most important. Once thesheet has been formed there is little that can be done in later sections of thepapermaking machine to correct errors in properties like fibre alignment,sheet strength, formation, wire mark, surface feel and optical quality. Inaddition to having a significant influence on these physical sheet properties,the forming fabric heavily influences the efficiency of the papermakingprocess. Efficiency in papermaking is a very broad term, it applies notonly to the energetic performance but also to the retention of fibres, finesand chemical additives.The process of depositing pulp fibres onto a forming fabric in an indus-trial setting happens at very high speed, often in the rage of 100km/hr ornearly 5500ft/min, so even small changes in the energy required to movethe fabric can have a large affect on operating cost. In regards to reten-tion, the fabric’s capability of retaining fibres, fines and additives in thepaper mat while allowing for high drainage rates helps to reduce machinesize, and allows smaller machines to run faster. When the pulp suspen-sion is deposited onto the forming wire, fines and additives, which areoften smaller than the openings in the fabric structure, must be retained,while water quickly and evenly drains from the paper surface through theforming fabric.Figure 2.1: Left to right: Single-layer, double-layer, and triple-layer fabrics[5].5Chapter 2. MotivationFigure 2.2: Cross sections of six popular fabric geometries[9].With all of these factors in mind, engineers and technologists have beenworking for many years to develop forming fabrics that have a low runningresistance and and good pulp and fines retention. Many designs have beenconceived over the years and a few of the more common types are show inFig. 2.1. The cross sections for these types of fabrics are shown in Fig. 2.2.Before entering a discussion of development of fabric geometries, one mustbecome familiar with the common coordinate system and other definingterms. The coordinates of a forming fabric are generally defined by itsalignment on the papermachine. There are two principal directions, themachine direction (MD) and the cross-machine direction (CMD or CD).As the names imply, MD is oriented with the unit vector that pointsin the direction of fabric movement. CD lies in the plane of the fabric,perpendicular to MD. This is shown graphically in Fig. 2.3.The definition of a forming fabric as woven structure that retains solidswhile allowing liquids to pass through is very broad. As can be seen inFig. 2.2 there are many cross-sectional variations of this definition. Thereare also a number of different weaves that are possible in the perpendicularplane, that is, the fabric plane. The geometry in this plane is commonly6Chapter 2. Motivation$        Figure 2.3: Forming fabric coordinate system[5].referred to as the fabric shed. The shed defines the number of cross ma-chine direction filaments before the weave pattern is repeated. In thesimplest case of a forming fabric that has only one layer, the shed is givenas a single number. As the complexity of the fabric increases the shed de-finition must account for the two sided nature of the forming fabric. Forthis reason, multi-layered fabrics are defined using two numbers, the firstfor the paper side and the second for the machine side. Shed patterns forsingle, double and triple-layer fabrics are shown in Fig. 2.4.Another commonly used term in forming fabric design is frame length.This term refers to the physical length of a particular opening in a fabricstructure. For example, it could be said that the CD frame length on thewear side of the triple-layer fabric shown in Fig. 2.4 is longer than the CDframe length on the paper side.2.2 Development of the Modern Forming FabricThe technological complexity of forming fabrics has gone through a sig-nificant maturation in the last 50 years. Initially, paper was formed on abronze wire mesh similar to a heavy duty screen. For this reason, manystill refer to the woven structure as the “forming wire”, even though theyhave not been made of wire for many years. In 1951 a papermachine inEast Germany used the first synthetic forming fabric[8]. This fabric, made7Chapter 2. MotivationFigure 2.4: Shed definition for single layer, double layer and triple layer fabrics[9].8Chapter 2. Motivationof the new material polyamide, provided unsatisfactory results. However,this initiative started a period of development that led to the design of themyriad of filaments and geometries that are shown in the previous figures.Even with the development of so many complex and effective fabrics, thedouble-layer remains the most common type due to familiarity, wear is-sues, and cost. For these reasons, the double-layer fabric has gone througha number of improvements, one of the major improvements was the intro-duction of the extra weft added design. All of these designs are shown inFig. 2.2.2.3 The Problem of Wire MarkWire mark is the imprint or image of the forming fabric that is left on thefinished paper. Wire mark is not desirable due to a number of problems itcan cause in production and application. During production, wire markingcan cause release problems of the pulp mat from the forming fabric; in ap-plication, wire mark is associated with printing problems and undesirableoptical properties.Figure 2.5: Topographical wire mark[6].Wire mark can be broken down into two categories, topographical andhydrodynamic. Topographical wire mark is the physical imprint of theforming fabric on the paper. This is common on papers that are made onfabrics with a high plane difference, such as tissue papers. A closeup oftopographical wire marking on a sheet of paper is shown in Fig. 2.5.The second general category, hydrodynamic wire mark (also called shadowmark), is created by the fluid mechanics of the flow through the forming9Chapter 2. Motivationfabric. Under the right conditions, flow non-uniformities can be transmit-ted significant distances upstream and can have an affect on the papermaking surface of the fabric. These affects manifest themselves as changesin paper density and can change the printing characteristics of the paper.Hydrodynamic wire mark is generally less visible than topographical wiremark. It tends to show up only on printed surfaces and is therefore only aconcern for finer paper grades. In the manufacturing of finer paper grades,a tighter weave is used on the forming surface of the fabric, therefore thelength scale of the density changes is small and consequently less obviousto the casual observer. However, the results can be seen after printingwith undesirable characteristics such as ink strike-through (ability to seethe ink on the opposite side of the paper) and patterns in fully inkedregions with characteristics that make them highly visible to the humaneye[7].The research in this paper is primarily focused on the mechanism of hy-drodynamic wire marking. Specifically, the hydrodynamic wire marking ofdouble and triple-layer fabrics. If a section of a multi-layer fabric is takenin the z-MD plane there are essentially two layers of CD filaments thatwill be seen, the small diameter paper side filaments and the large diam-eter machine side filaments. Based on the relative diameter, spacing andseparation of these filaments the upstream flow will be modified, possiblyredistributing the pulp fibres, causing hydrodynamic wire mark. The goalof this research is to gain an insight into the geometrical configurationswith the highest probability of significant wire mark.10Bibliography[5] Sabit Adanur. Paper Machine Clothing. Asten, Inc, Basel, Switzerland, 1997.[6] R. Danby. The impact of multilayer fabrics on sheet formation and wire mark.Pulp & Paper Canada, 87(8):69–74, Aug 1986.[7] T. Helle. Analysis of wire mark in printing paper. Journal of Pulp and PaperScience, 14(4):J91–J94, Jul 1988.[8] T. Helle. Paper forming wires over 75 years. Pulp & Paper Canada, 91(6):107–114,Jun 1990.[9] Hannu Paulapuro. Papermaking Part 1, Stock Preparation and Wet End. FapetOy, Helsinki, Finland, 2000.11Chapter 3Project GoalsAs has been discussed in the previous sections, the characteristics of thefinal sheet of paper are very susceptible to manufacturing conditions. Theconditions at the initial stage of paper formation are determined largelyby the pulp stock, headbox flow, and forming fabric geometry and speed.Characterization of the affects of the forming fabric geometry are verydifficult and in the past have largely relied on experience.During sheet formation, water is drained through the matrix of the formingfabric. The geometry of the filaments in the fabric influence the path andlocal drainage velocity. Water will flow more readily in locations with largegaps or less obstruction. This increased flow volume directs the flow ofpulp and fines, increasing the mass of material in the flow path, possiblycreating a hydrodynamic wire mark.In double and triple-layered fabrics there are essentially two layers of CDfilaments. The paper side filaments are small diameter in order to providesupport for the pulp fibres, and the machine side filaments are large di-ameter to reduce the running load and increase the wear life of the fabric.Depending on the relative diameters, horizontal filament spacings, verticallayer separations and layer off-sets, the fabric may have a larger propensityto hydrodynamically mark the sheet of paper.The purpose of the current research is to use experimental means to char-acterize and identify how the geometry of two rows of dissimilar cylindersinfluence the paper side pattern. This will then be applied to formingfabric filament geometries in order to find configurations that could influ-ence the paper making surface of the forming fabric. The end goal is toproduce a body of information that can be applied during the design offuture forming fabrics to produce a finer, more predictable sheet of paper.Additionally, the results of the experiments will be used to validate thework of Zhaolin Huang who performed the computational version of thisstudy for his masters work at the University of British Columbia in 2003.12Chapter 4Literature Review4.1 IntroductionAlthough forming fabrics are possibly the most important cloth on thepapermachine, the design of a suitable geometry for a given paper gradeand machine has been left largely to experience and intuition. There hasbeen much research into a suitable method to design and chose a fabricusing a quantitative scale like the Beran FSI or Johnson DI (discussed inmore detail in §4.2.1). However, these methods are based only on the paperside of the fabric and rely on gross properties like fabric air permeabilityand weave density. It is only recently that the tools have advanced toa degree that engineers can make quantitative measurements of the flowfield through a model forming fabric.The previous research in this field can be roughly broken down into twosections, the investigation of the fabric itself, and the investigation of thesheet produced. They happened roughly in that order. While investi-gations of fibre orientation in the final sheet[16] were conducted beforedetailed investigations of the fabric-paper relationship, it wasn’t until thedevelopment of optical FFT methods in the mid 1980’s that engineerscould evaluate the post production sheet for density variations on the or-der of a typical forming fabric frame length.4.2 Previous Research4.2.1 Investigating the FabricsThe earliest work done on the effects of the micro-scale geometry of theforming fabric was published by Torbjorn Helle in 1978[17]. In this paper,Helle investigated the affect of the orientation of the long knuckles on thepaper side of the fabric. There are two possible orientations, MD and CD.Helle modified a hand-sheet former to induce a flow similar to that whichis found in the formation region. He then formed extremely light weightpaper with the long knuckles both MD and CD. He timed the drainageand then used a scanning electron microscope to view the final sheet ofpaper. His results are shown in Figs. 4.1 and 4.2.13Chapter 4. Literature ReviewFlow Direction Flow DirectionFigure 4.1: Helle’s results of formation with flow orientation parallel and perpendicu-lar to the long knuckles. Low weight paper is shown on the left with a higher weightpaper on the right[17].Figure 4.2: A comparison of drainage times for the two long knuckle orientations[17].14Chapter 4. Literature ReviewAs is visible in both figures, the orientation of the paper making surfacefilaments in a forming fabric were found to be extremely important to thedrainage speed and paper quality.This paper was followed a year later by Robert Beran’s milestone paper,The evaluation and selection of forming fabrics[11]. In this paper, Berancoins one of the most influential terms in the world of forming fabric designand selection, the fibre support index (FSI). FSI is a quantitative way ofevaluating the performance of a particular forming fabric on a particularpapermachine. It is a function of the forming fabric filament geometry,and the statistical distribution of fibre orientations and lengths.The first mention of the possibility of hydrodynamic wire marking was putforward by Helle in his 1980 paper on the influence of the forming fabricstructure on the final sheet[18]. In this paper Helle states,It is frequently claimed that there also is a ‘drainage wire mark’; thatis a fines and fillers distribution pattern in the surface layer of the wire-side of the paper, reflecting the strand knuckle pattern...There seems,however, not as yet to be real experimental evidence for this, in spite ofseveral attempts to prove it.The paper goes on to corroborate the conclusions of Beran’s 1979 paper onFSI. He justifies the importance of the CD filaments using a simple beam-bending model and discusses the results in the context of the preferredMD alignment of the pulp fibres. Using a simple beam bending analysisof individual pulp fibres, and data on the consistency of the paper webat the wet line, Helle predicts a possible basis weight increase of 25% inlocations above drainage passeges. The extent of the penetration of thepaper web into the forming fabric structure is qualitatively displayed usinga techneque where a sheet of paper and forming fabric were potted andground at an angle to visualize different depths into the structure. Thisis shown in Fig. 4.3.The next paper of consequence attempting to define a quantitative mea-sure of the forming fabric structure’s affect on the final sheet was publishedby Dale Johnson in 1984[22]. This paper conveys the methods and resultsof experiments to determine the relationships between fibre length, MDframe length, paper mat weight and fabric drainage rate. This investiga-tion showed that, despite their higher flow resistance when clean, doublelayered forming fabrics had lower flow resistance and higher drainage rateswhen compared to the single layer fabrics once a mat developed. It washypothesized that this was due to the superior support and consequentlyless clogging due to the low MD frame length.15Chapter 4. Literature ReviewFigure 4.3: Forming wire with formed sheet, ground at an incline to show web-penetration. The lowest penetration is at the top-left of the figure, and highestpenetration is at the bottom-right.[18].Perhaps the most critical development from Johnson’s 1984 paper was thedrainage index (DI). This quantitative number related the coefficients ofthe Beran FSI, the structure of the forming fabric and the air permeabilityto predict the drainage characteristics of a given design.The validity of the DI in predicting the drainage characteristics of multi-layered fabrics was displayed in Johnson’s next paper in 1986[23]. Inthis document, Johnson showed that the decreasing MD frame lengths innewer double and triple-layer fabrics increased both first pass and overallretention. He also presented results that showed a correlation between DIand cumulative drainage, in which drainage increased as a function of DI,regardless of the fabric’s air permeability.4.2.2 Investigating the SheetThe next stage in the research involved taking a closer look at the finalsheet that was formed. The earliest work published that discussed wiremark from a final product reference frame was published by Roger Danbyin 1986[12]. In this paper, Danby compared the wire mark on sheets ofpaper that were produced on the same machine running single, double and16Chapter 4. Literature Reviewtriple-layer fabrics. In doing so he was able to postulate that wire markwas not only a function of optical severity, but also relied on the “frequencyand continuity”, more of which made the marking more obvious.Figure 4.4: Linear FFT of a sheet of paper is shown in A with the correspondingforming fabric shown in B[19].Building on this paper, Helle released a work in 1988 that used a linearFFT of the light transmission through the final sheet to investigate the fre-quency of the wire mark and compared that to the forming fabric used[19].He found that there is a direct correlation between the density changes inthe sheet and the forming fabric imprint. Figure 4.4 shows the results ofone of his FFTs of a sheet formed on a double-layer fabric.In this figure, Helle identifies the origins of each of the peaks that showup in the FFT. One thing that is of particular importance to the workdone in this thesis is the MD direction peak at λ = 2.22mm. Helle has noexplanation for this peak based on the paper side of the forming fabric. Ithas been hypothesized that this peak is, in fact, due to the geometry of themachine side of the forming fabric. Since there was no feature on the paperside of the forming fabric that could create this density variation, and allother density variations were related to the forming fabric geometry, itis not unreasonable to believe that this peak may originate from anotherstructure within the fabric.17Chapter 4. Literature ReviewHelle also touches on one of the more difficult hurdles for double layerfabrics – the type and direction of the wire mark. He briefly discusses theimpact of the direction and continuity of the marking and its overall effecton printability and, more importantly, readability. He recognizes that thehuman eye has particular sensitivities that make certain wire marks moreobvious and intrusive than others.The next paper to discuss the origins and impact of wire mark was pub-lished in 1994 by Danby[13]. This paper was pragmatic and discussed theimpact on the previously recognized density variations on the printing ofthe sheet. Danby showed that the density variations produced by wiremarking affect the printing of half-tone dots by absorbing the ink differ-ently. The areas with higher density have lower ink absorption and andmore dot spreading; areas with lower density have higher absorption anda greater tendency for strike through.Later that same year Sabit Adanur published a milestone paper correlatingBeran’s FSI and Johnson’s DI to many sheet properties including breakinglength, burst strength, tear strength, and sheet thickness[10]. Adanur alsocorrelated the same properties to the much more general warp × weftcount and related the plane difference to the sheet thickness and sheetdensity. The plane difference is defined as the z -direction (see Fig. 2.3on page 7) height difference between the most prominent weft and warpknuckles.Adanur found that breaking load increased linearly with both FSI andDI in both the MD and CD directions. Tear strength was found to be afunction of DI and FSI. Burst strength was linear with DI. Sheet thicknesswas found to be a function of FSI. There was also a correlation betweenbreaking load, burst strength and tear strength with warp × weft counthowever, the correlations were much more complicated than when theseproperties were compared to DI and FSI. Sheet thickness was found todecrease with a tighter weave (higher warp × weft count) and increasewith higher plane difference.Adanur hypothesized that the increase in strength with the increasing DIand FSI was related to the amount of interaction between fibres. FSIand DI both increased with greater fibre support and when the fibres hadmore support they interacted with each other more since there was lessroom for fibre deflection and movement. This increased interaction hada corresponding increase in the strength and number of bonds formedbetween fibres, leading to a stronger piece of paper.18Chapter 4. Literature ReviewIn 2000 Roger Danby published a paper that used 2D FFT analysis toinvestigate transmitted light wire mark (density variations) and comparedthe results to the top-side structure of the forming fabric[15]. He used thisanalysis to encourage an informed, engineering style selection of formingfabrics based on the individual needs of the end user. Danby proceeded todiscuss the evolution of fabrics for various uses from tissue to liner board.One thing that was noticeable in his discussion was that there had been atendency to higher FSI and the use of double and triple-layer fabrics even,though they have a reduced drainage area. Often, especially with triplelayer fabrics, the drainage area decrease significantly, but a correspondingincrease in FSI and DI lead to a better forming fabric.Figure 4.5: Results of Danby’s multiple sheet split tests for twin-wire SC paper[14].Danby’s next publication, in 2002, investigated the uses of Asten John-son’s computer simulated printing software and also explored the internalstructure of a sheet of super calendared (SC) paper[14]. In his investiga-tion of the internal structure, Danby split a sheet of SC paper three times.He then observed the light transmission properties of the sheet sectionsand determined that the wire mark existed only in the 12.5% of the sheetthat was closest to the forming wire. These results are shown in Fig. 4.5.19Chapter 4. Literature ReviewThe final author that has published work that investigated the interactionof the forming fabric and its affect on the final sheet was Zhaolin Huang.In 2006, Huang published his paper on the numerical simulation of flowaround two rows of cylinders of different diameters[21]. While at firstglance this may seem to have little to do with forming fabrics, his mastersthesis, defended in 2003, relates the work in his 2006 paper to an investi-gation of the affects of different CD filament geometries in a double andtriple-layer forming fabric[20]. The work that is presented in this thesisis the experimental version of the work conducted by Huang in his 2003document.Huang investigated a variety of geometries and two Reynolds numbersin his work. He limited his Re to 6.5 for steady simulations, and 65 forunsteady simulations. For the majority of his work Huang performed hiscalculations at Re = 6.5. He determined that the comparative results(that is, the trends observed between different configurations) upstreamof the bank of cylinders were unaffected by the lower Re, and since thesteady calculations were faster and less computationally intensive, he usedthem as his primary data source.Huang modelled his geometries off of a commercial triple-layer formingfabric. He used a 73 x 75 mesh fabric that, when sectioned in the MD-zplane, showed two distinct layers of CD filaments. After performing aninvestigation of the commercial fabric, Huang computed flow fields for anumber of different geometries to investigate the affects of the differentparameters. He presented them as normalized velocities, 1/4 of a paperside filament diameter upstream of the front row of cylinders.The results of Huang’s investigation can be summed up as:• Variations in Re from steady to unsteady values changed the magnitude of thevelocity variations in the upstream (US) flow field, but did not change the shapeor trends of the variations.• When cylinder surface separation between the two rows was ≥ 0.7 times thepaper side filament diameter, the US flow field was identical to the single rowflow field, regardless of second row configuration.• When paper side and machine side filament spacings were equal the US flowfield was nearly identical to the single row flow field, regardless of second rowconfiguration.20Bibliography[10] S. Adanur. Effects of forming fabric structural parameters on sheet properties.Tappi Journal, 77(10):187–195, Oct 1994.[11] R.L. Beran. The evaluation and selection of forming fabrics. Tappi, 62(4):39–44,Apr 1979.[12] R. Danby. The impact of multilayer fabrics on sheet formation and wire mark.Pulp & Paper Canada, 87(8):69–74, Aug 1986.[13] R. Danby. The impact of forming fabric structures on print quality. Pulp &Paper Canada, 95(1):48–51, Jan 1994.[14] R. Danby. Sc print quality influenced by fibre length, fabric structures, andmachine drainage characteristics. Tappi Journal, 1(9):3–9, Nov 2002.[15] R. Danby and P. Plouffe. Print quality improvements through forming fabricdesign changes. Pulp & Paper Canada, 101(9):66–69, Sep 2000.[16] P. Glynn, H.W.H. Jones, and W. Gallay. The fundamentals of curl in paper.Pulp and Paper Magazine of Canada, 60:T316–T323, November 1959.[17] T. Helle. How forming fabric design affects drainage and release. Pulp & PaperCanada, 79(11):91–98, November 1978.[18] T. Helle. The influence of wire structure on sheet forming. Paper Technologyand Industry, 21(4):123–131, May 1980.[19] T. Helle. Analysis of wire mark in printing paper. Journal of Pulp and PaperScience, 14(4):J91–J94, Jul 1988.[20] Z. Huang. Numerical simulations of flow through model paper machine formingfabrics. Master’s thesis, The University of British Columbia, Vancouver, BritishColumbia, Canada, 2003.[21] Z. Huang, J.A. Olson, R.J. Kerekes, and S.I. Green. Numerical simulation of theflow around rows of cylinders. Computers & Fluids, 35(5):485–491, June 2006.[22] D.B. Johnson. Retention and drainage of forming fabrics. Pulp & Paper Canada,85(6):T167–T172, June 1984.[23] D.B. Johnson. Retention and drainage of multi-layer fabrics. Pulp & PaperCanada, 87(5):56–59, May 1986.21Chapter 5ManuscriptBy: Seth Gilchrist and Dr. Sheldon Green5.1 IntroductionWhen paper is made, a dilute suspension of pulp and water (generallyabout 0.7% pulp by mass) is passed through a forming fabric. This processremoves the water and leaves a mat of pulp. This pulp mat is drained usinginertia and suction and is then passed to a mechanical press, thermal dryer,and, in some cases, special processing before being wound onto a role fortransportation.In order to create a high quality, even density sheet of paper the initialdrainage of the pulp suspension through the forming fabric must occuruniformly. For this reason much effort has gone into the development offorming fabrics that allow for even and fast drainage, low running resis-tance, and good fibre retention. However, specific engineering researchinto flow patterns and governing dynamics of flows through the formingfabrics has only recently been initiated.Another unique aspect of forming fabrics is their two-sidedness. This isgenerated by the need to have a very fine structure to support the paper onthe top side of the fabric (filaments of ∼0.15mm diameter) and a coursermesh on the bottom of the fabric (filaments of ∼0.3mm diameter). Thesedifferent sides of the fabric serve to provide substantial support for thepulp fibres while increasing wear life and lowering the running resistanceof the forming fabric.Due to their relevance, flows through banks of cylinders have been wellstudied. Flows that concern single cylinders and groupings of similar cylin-ders are the most well understood[25, 35, 36, 38, 39, 40, 41]. There are alsoa number of studies that focus on flows through arrangements of cylindersat higher Reynolds numbers[27, 29, 33, 37]. Even with all the work thathas been done on flows through banks of cylinders there are aspects ofthese flows that are not well characterized. These include flows throughbanks of cylinders at low Re, banks of cylinders of nonuniform sizes and0A version of this chapter will be submitted for publication.22Chapter 5. Manuscriptspacings, and examination of the flows upstream of the bank of cylinders.In order to investigate paper formation some simplifications were requiredto reduce the complexity of the problem. In the real case, flows are multi-phase and highly 3-dimensional. However, a review of the literature allowsfor reasonable engineering simplifications to make the problem manage-able, yet still applicable.Due to the low concentration of pulp fibres in the flow it is possible tomodel the fluid as pure water. Additionally, due to the flow dynamicsencountered just before the forming fabric (in the headbox region) it be-comes possible to neglect one direction of the filaments in the formingfabric and model the fabric as a 2D bank of nonuniform cylinders. Previ-ous authors have used both theory and experiments to provide evidencethat the machine-direction (MD) orientation of the fibres as they exit theheadbox make it possible to reasonably neglect the MD filaments of theforming fabric[24, 26, 30, 34]. However, it is worth mentioning that thecurrent study is concerned with purely incident flows, that is there is onlya x -component in the approach flow, but in many of the studies, partic-ularly those performed by Helle, the flows impinge the forming fabric atan angle, so there is a x and y-component of velocity.In order to effectively model the forming fabric, a notion of the flow’s Remust be obtained. The drainage velocity in the region of jet impingementcan be quite high, however studies have shown that the bulk velocity in thisregion is on the order of 0.05m/s to 0.50m/s[28]. Based on this velocity,the top-side filament diameter, and modelling the fluid as pure water, itis found that Red ∈ [6.5, 65].While flows at low Re are encountered in a number of applications, such asthose utilizing drainage screens and flow conditioners, it is not as commonto experience flows through banks of nonuniform cylinders. Additionally,most research into cylinder flow is concerned with the nature of vortexshedding due to its impact on the vibrational characteristics of a bank ofcylinders. For this reason, flows upstream of a bank of cylinders have notbeen well investigated.5.2 Literature ReviewA number of previous studies have examined the flow structures associ-ated with flows through banks of cylinders. Some of these papers canbe found in the references, but includes many more authors and works.23Chapter 5. ManuscriptHowever, with all of the work that has been published regarding the inter-actions of two or more cylinders in cross flow, only one author was foundto investigate low Re flow through two rows of non-uniform cylinders.Zhaolin Huang’s paper and thesis[31, 32] are the numerical equivalent tothe experimental work presented in this paper.In these documents, Huang examined the flow through a single row ofcylinders, as well as symmetric and asymmetric banks of cylinders at dif-ferent separations and staggerings. In his paper, Huang found that forcylinder flows in a confined channel at Re = 100, the vortex shedding isdependent on the cylinder centre separation. He also showed that the sec-ond row of cylinders had little affect upstream for a row surface separationof 0.7 times the upstream cylinder diameter (0.7d).In his thesis, Huang did a more in depth investigation of the affect up-stream of the cylinder bank due to changing the configuration of the tworows of cylinders. He gave extensive results comparing the upstream flowfield of one row of cylinders to that of multiple rows of cylinders. Healso investigated the effect of adding small diameter filler cylinder in theupstream row as well as that of an asymmetric alignment in the secondrow. These last two were to find the impact of a misplaced filament in theweaving of a forming fabric.The distillation of his thesis was that if the cylinder surface spacing be-tween the two rows was greater than 0.7d, the upstream flow field waslargely undisturbed from that of a single row of cylinders.5.3 Experimental MethodsThe experiments were carried out in a flow loop circulating a glycerol so-lution for Reynolds number matching. The target Re for the experimentswas 10 ≤ Re ≤ 65. For the velocities that the flow loop was capable of, andthe diameter of the upstream cylinders, a viscosity of 12 ≤ µ ≤ 18 cP wasrequired, or an ∼65(m/m)% glycerin/water mixture. The test section ofthe flow loop is shown in Fig. 5.1.The test section measured 30x30 cm, and contained a frame for holding thebank of cylinders. It was of a closed loop configuration driven by a 20hpelectric pump. Velocity measurement was via a venturi flow meter locateddownstream of the pump and upstream of the test section. The flow thenpassed through a diffuser, conditioning screens and honeycomb. The testsection was located immediately downstream of the flow conditioner andwas constructed of acrylic to facilitate flow field observation. Flow was24Chapter 5. Manuscript$       Figure 5.1: Flow loop test section.then returned to the tank through a 4” return line. A schematic of theflow loop is shown in Fig. 5.2.The primary means of data collection were through particle image ve-locimetry (PIV), pressure drop measurement, and hydrogen bubble gen-eration. The PIV provided instantaneous flow field observations and wasarranged to give the best resolution of the flow field just upstream ofthe bank of cylinders. The pressure drop measurements were made witha Validyne Engineering DP103 calibrated for a differential pressure of 0–0.1” of water (0–25Pa). The pressure data were collected through pressureports located on the bottom of the test section upstream and downstreamof the bank of cylinders. The test section was also fitted with an hydrogenbubble generation wire for qualitative flow visualization. The pressureports and hydrogen bubble wire can be seen in Fig. 5.1.Flow within the test section was observed with the bubble generation wireto be even to within 5% over 83% of the test section, with the boundarylayers being somewhat less than 2cm thick at the location of the cylinderbank. These measurements were made using the H2 bubble wire and ahigh-definition video camera at multiple velocities.The simplification of the forming fabric structure made it possible to modelthe fabric as a 2-dimensional bank of cylinders of various sizes and stagger-ings. Even in this simplified format there were a large number of possibleconfigurations. Huang developed a nomenclature that has been used todefine the cylinder arrangement and coordinate system. This system isshown in Fig. 5.3.25Chapter 5. ManuscriptFigure 5.2: Schematic of test section flow loop.XSXCMD-z face$      Figure 5.3: Schematic of the simplified forming fabric geometry.26Chapter 5. Manuscript5.4 PIV Results and DiscussionA number of different configuration were evaluated using PIV. In order tokeep the plots uncluttered only one uncertainty bar has been included oneach plot. The given uncertainty bars represents the maximum uncertaintyfor 80% confidence. The values of these bars are fairly typical across allplots. The PIV data was also smoothed using a moving average and insome cases a polynomial fit with a 10% span.XS/dXS/dXS/d$      Figure 5.4: Stream wise velocity variation for changing XS/d for D/d = 1.5, G2/G1= 1, Y/G1 = 0.5 at Re = 65. The results of each curve are statistically the same.Fig. 5.4 shows the effects on the stream wise component of the velocityd/4 upstream of the bank of cylinders when changing the cylinder surfaceseparation for an arrangement of D/d = 1.5, G2/G1 = 1, and Y/G1 =0.5 (fully staggered), at Re = 65. The cross stream component for thesame arrangement is shown in Fig. 5.5.Figs. 5.6 and 5.7 show the effects d/4 upstream of the cylinders on thestream wise and cross stream velocity components of staggering for anarrangement of D/d = 1.5, G2/G1 = 1, XS/d = 0.75 at Re = 65.27Chapter 5. ManuscriptXS/dXS/dXS/d$     Figure 5.5: Cross stream velocity variation for changing XS/d for D/d = 1.5, G2/G1= 1, Y/G1 = 0.5 at Re = 65. The results of each curve are statistically the same.28Chapter 5. ManuscriptFigure 5.6: Stream wise velocity variation for changing Y/G1 for D/d = 1.5, G2/G1= 1, XS/d = 0.75 at Re = 65. The results of each curve are statistically the same.29Chapter 5. ManuscriptFigure 5.7: Cross stream velocity variation for changing Y/G1 for D/d = 1.5, G2/G1= 1, XS/d = 0.75 at Re = 65. The results of each curve are statistically the same.30Chapter 5. ManuscriptFigure 5.8: Stream wise velocity component for changing staggering with D/d = 3,G2/G1 = 2, and XS/d = 0 at Re = 25.Fig. 5.8 shows the stream wise velocity component d/4 upstream of thecylinders for variations in staggering with D/d = 3, G2/G1 = 2, XS/d =0 at Re = 25.Examination of the PIV data shows a number of interesting characteristics.Figs. 5.4 and 5.5 show that for and equal cylinder spacing in each row,changing the row separation had negligible effect. This was not true foruneven cylinder spacings, as can be seen in Fig. 5.8. Fig. 5.8 shows thatfor a surface separation of XS/d = 0 the second row alignment with thefirst row was more critical than diameter ratio or relative spacing.Figs. 5.6 and 5.7 show that for a cylinder surface separation of XS/d = 0.75there were no effects seen in the upstream flow field for any staggerings.This is a similar result obtained by Huang. He found that for a separationof XS/d = 0.7 at an Re = 65 changing the row staggering had little affecton the upstream flow field.31Chapter 5. Manuscript5.5 ∆P Results and DiscussionPressure drop data was collected for all of the presented PIV cases. Inaddition to that data there were many cases for which only ∆P data was.The PIV data was more laborious to take, so only extremes had beenevaluated. The ∆P data was much more straight forward and was used totake measurements on intermediate configurations.The uncertainty bars on the ∆P plots were determined using:δf(x1, x2, . . . , xn) =⎡⎣( ∂f∂x1δx1)2+(∂f∂x2δx2)2+ . . . +(∂f∂xnδxn)2⎤⎦1/2(5.1)In this equation, the value of δn was given by manufacturer specifications,or by two standard deviations in the case of sampled data., XS/dXS/d$      Figure 5.9: Pressure drop through a bank of cylinders with D/d = 1.5, G2/G1 = 1and Y/G1 = 0.5 at Re = 65 with changing XS/d.Fig. 5.9 shows the pressure drop as a function of changing XS/d for aconfiguration of D/d = 1.5, G2/G1 = 1, and Y/G1 = 0.5 (fully staggered)at Re = 65. The negative value of XS/d indicates that the leading edge ofthe downstream cylinder was upstream of the trailing edge of the upstreamcylinder. This was only possible for staggered configurations. Fig. 5.10shows the pressure drop through the same bank of cylinders as presentedin Fig. 5.9, but with Y/G1 = 0 (tandem).32Chapter 5. Manuscript, XS/dXS/d$      Figure 5.10: Pressure drop through a bank of cylinders with D/d = 1.5, G2/G1 = 1and Y/G1 = 0 at Re = 65 with changing XS/d.It can be seen in Fig. 5.9 that the pressure drop through the bank ofcylinders converged to the sum of the rows’ pressure drops with a surfaceseparation of XS/d = 0.75. Fig. 5.10 shows the same result. This indicatesthat for XS/d ≥ 0.75 the flows through each row of cylinders was essentiallyindependent.Fig. 5.9 corresponds to the PIV data in Figs. 5.4 and 5.5.Fig. 5.11 shows the pressure drop for changing staggerings for a configu-ration of D/d = 1.5, G2/G1 = 1, and XS/d = 0.75 at Re = 65.The results shown in Fig. 5.11 show that for XS/d = 0.75 and G2 = G1the pressure drop coefficient is independent of the row staggering. Whenthis data is considered in conjunction with the PIV data shown in Figs. 5.6and 5.7 it is seen that for this configuration the upstream flow fields werealso the same, regardless of staggering.Fig. 5.12 shows the pressure drop through a bank of cylinders with un-equal G1 and G2, and changing XS/d. The plot shows that for unequalcylinder spacings there is no affect on pressure drop coefficient once therow separation is ≥ 0.75d.33Chapter 5. ManuscriptFigure 5.11: Pressure drop through a bank of cylinders with D/d = 1.5, G2/G1 = 1,and XS/d = 0.75 at Re = 65 with changing Y/G1., XS/dXS/d$      Figure 5.12: Pressure drop through a bank of cylinders with D/d = 1.5, G2/G1 = 2,Y/G1 = 0.5 at Re = 65 and changing XS/d.34Chapter 5. ManuscriptFigure 5.13: Comparison of pressure drop as a function of Re through cylinders withD/d = 1.5, G2/G1 = 1, XS/d = 0.75 and two staggerings.Fig. 5.13 shows the pressure drop coefficient as a function of Reynoldsnumber for staggered and tandem configurations of D/d = 1.5, G1/G2 =1, XS/d = 0.75.The Reynolds number data shows that k increases at low Re, and asymp-totically approaches a lower value as Re increases. These figures also showthe pressure drop is the same for the staggered and tandem configurationswhen XS/d = 0.75, regardless of Reynolds number.Comparison of th PIV data with the corresponding ∆P data suggests alink between the pressure drop and the upstream flow field. Examina-tion of Figs. 5.9 throuhg 5.12 shows that for XS/d ≥ 0.75 there is nochange in pressure drop, regardless of the second row configuration. Thecorresponding PIV data show that the flow field upstream of these con-figurations looks like that of just 1 row of cylinders. This indicates that,when ∆P → ∑∆Prows, the upstream flow field will be like that of flowthrough only the first row of cylinders.5.6 H2 Bubble Visualization Results andDiscussion35Chapter 5. Manuscript$ XS/d = -0.25 XS/d = 0.75XS/d = 2.75 Empty     Figure 5.14: Hydrogen bubble visualizations for variations of XS/d with D/d = 1.5,G2/G1 = 2, Y/G1 = 0.5 at Re = 65.$ XS/dXS/dXS/d     Figure 5.15: Relative velocities for variations of XS/d with D/d = 1.5, G2/G1 = 2,Y/G1 = 0.5 at Re = 65.36Chapter 5. ManuscriptThe images in Fig. 5.14 show the flow visualizations obtained via hydrogenbubble visualization for variations in XS/d for a configuration of D/d =1.5, G2/G1 = 2, and Y/G1 = 0.5 at Re = 65. The qualitative compari-son of the velocities obtained from the the visualizations are contained inFig. 5.15.These flow fields correspond to the pressure drop data shown in Fig. 5.12.These data show that, for a cylinder surface separation of XS/d ≥ 0.75,the flow field remains the same and the pressure drop coefficient convergesto the sum of the rows’ pressure drops.this result corroborates the earlier result that when the pressure drop isequal to the sum of the row’s pressure drops the upstream flow field willbe the same as the upstream flow field for just the first row of cylinders.5.7 ConclusionsFrom the data presented it has been shown that:• There is little or no effect on the upstream flow for row surface separations of0.75d or more, regardless of downstream row configuration.• The pressure drop through the bank of cylinders converges to the sum of therows’ pressure drops for surface separations of 0.75d and greater, regardless ofdownstream row configuration.• When the pressure drop through a bank of cylinders is equal to the sum ofthe rows’ pressure drops, the upstream flow field will be the same as that for asingle row.• For equal values of G1 and G2 the flow upstream will be identical to the one rowflow field, regardless of staggering and separation. In these cases the pressuredrop may be higher than the sum of the rows’ pressure drops if cylinder surfaceseparation is less than 0.75d.• The value of the pressure drop coefficient asymptotically approaches a valuewith increasing Reynolds number. Further, for a cylinder surface separationof XS/d = 0.75 and G1 = G2 the pressure drop coefficient is the same forstaggered and tandem configurations, regardless of Reynolds number.In the context of a multi-layer papermaking forming fabric, this indicatesthat the paper side flow field contributed by the cross-machine directionfilaments will be the same as a single-layer fabric provided the backingside filaments are at least 0.75d away from the paper side filaments. Ad-ditionally, it can be expected that the upstream flow will be unaffected by37Chapter 5. Manuscriptthe backing side filaments if the pressure drop of the complete fabric isapproximately equal to the sum of the fabric layers.5.8 AcknowledgementsThe authors would like to thank Asten Johnson and NSERC for financialand material support.38Bibliography[24] S. Adanur. Effects of forming fabric structural parameters on sheet properties.Tappi Journal, 77(10):187–195, Oct 1994.[25] P.W. Bearman and A.J. Wadcock. The interaction between a pair of circularcylinders normal to a stream. Journal of Fluid Mechanics, 61(3):499–511, 1973.[26] R.L. Beran. The evaluation and selection of forming fabrics. Tappi, 62(4):39–44,Apr 1979.[27] M.J. Braun. Fluid flow structures in staggered banks of cylinders located in achannel. Transactions of the ASME, 117:36–44, March 1995.[28] B. Dalpke, R.J. Kerekes, and S.I. Green. Modelling jet impingement and theinitial drainage zone in roll forming. Journal of Pulp and Paper Science, 30(3):65–70, March 2004.[29] P. Le Gal, M.P. Chauvre, and Y. Takeda. Collective behaviour of wakes down-stream a row of cylinders. Physics of Fluids, 8(8):2097–2106, 1996.[30] T. Helle. How forming fabric design affects drainage and release. Pulp & PaperCanada, 79(11):91–98, November 1978.[31] Z. Huang. Numerical simulations of flow through model paper machine formingfabrics. Master’s thesis, The University of British Columbia, Vancouver, BritishColumbia, Canada, 2003.[32] Z. Huang, J.A. Olson, R.J. Kerekes, and S.I. Green. Numerical simulation of theflow around rows of cylinders. Computers & Fluids, 35(5):485–491, June 2006.[33] C. Iwaki, K.H. Cheong, H. Monji, and G. Matsui. Piv measurement of the verticalcross-flow structure over tube bundles. Experiments in Fluids, 37:350–363, 2004.[34] D.B. Johnson. Retention and drainage of multi-layer fabrics. Pulp & PaperCanada, 87(5):56–59, May 1986.[35] H.J. Kin and P.A. Durbin. Investigation of the flow between a pair of circularcylinders in the flopping regime. Journal of Fluid Mechanics, 196:431–448, 1988.[36] D.R. Polak and D.S. Weaver. Vortex shedding in normal triangular tube arrays.Journal of Fluids and Structures, 9:1–17, 1995.39Bibliography[37] D. Ghosh Roychowdhury, Sarit Kumar Das, and T. Sundararajan2. Numericalsimulation of laminar flow and heat transfer over banks of staggered cylinders.International Journal for Numerical Methods in Fluids, 39:23–40, 2002.[38] D. Sumner, S.J. Price, and M.P. Pa¨ıdoussis. Flow-pattern identification for twostaggered circular cylinders in cross-flow. Journal of Fluid Mechanics, 411:263–303, 2000.[39] D. Sumner, S.S.T. Wong, S.J. Price, and M.P. Pad¨oussis. Fluid behaviour of side-by-side circular cylinders in steady cross-flow. Journal of Fluids and Structures,13:309–338, 1999.[40] C.H.K. Williamson. Evolution of a single wake behind a pair of bluff bodies.Journal of Fluid Mechanics, 159:1–18, 1985.[41] S. Ziada. Flow periodicity and acoustic resonance in parallel triangle tube bun-dles. Journal of Fluids and Structures, 14:197–219, 2000.40Chapter 6Discussion6.1 IntroductionThe results presented in §5 provide new knowledge regarding the flow char-acteristics through a bank of cylinders consisting of two rows of differentgeometries at low Reynolds number. This information has interpretationsthat impact the design of papermaking forming fabrics. This section dis-cusses the applications of the new knowledge and places it into the contextof multi-layer forming fabric design.In addition to being applicable to the design of forming fabrics, the resultscan be used to validate the work of Zhaolin Huang, who performed thecomputational version of this study during his masters degree at the Uni-versity of British Columbia in 2003[42]. While the exact configurationsthat he simulated could not be tested, similar configurations show resultsthat agree with his findings. Where there were large discrepancies, anothergraduate student, Ali Vakil, performed simulations using Huang’s meth-ods on geometries that were identical to the corresponding experiments.6.2 Forming Fabric ApplicationThe data found in the experiments presented in §5 have direct applicationsto papermaking and forming fabric design.1. The data presented in Figs. 5.4 and 5.5 show that for an identical cylindercentre separation on both the paper and machine sides of the forming fabric,the paper side flow field is undisturbed from the single row solution. This istrue even with a larger cylinder in the second row, full staggering and small tonegative row separations.In terms of forming fabric design, this indicates that if the paper side andmachine side have the same weave density (weft × warp count), the separation,staggering, and filament diameter ratio would not affect the paper side flowfield.2. If the paper side of the fabric and the machine side have different weave density,the separation between the filaments must be ≥ 0.75d, otherwise there is apossibility that the machine side weave will alter the paper side flow field. The41Chapter 6. Discussionresults in Figs. 5.8,5.12, 5.14 and 5.15 show that if G1 	= G2 then for rowseparations of less than 0.75d there will be an effect on the paper side flow field.3. Figs. 5.9 – 5.12 can be compared with the corresponding flow fields shown inFigs. 5.4 – 5.7 and 5.14 – 5.15. These figures show that when the pressure dropthrough the two rows of filaments is equal to the sum of the rows’ individualpressure drops that the paper side flow field will be undisturbed from the singlerow case.This can be used in the design of triple-layer fabrics. Traditional triple-layerfabrics are essentially made by binding two single layer fabrics together. If, oncebound, the pressure drop of the final fabric is approximately equal to the sumof the pressure drop of the two individual fabrics, then in can be assumed thatthe paper side flow field will be largely undisturbed from the single, paper sidefabric flow field.6.3 Validation of Huang’s ResultsFigure 6.1: Huang’s computational stream wise velocity results plotted with the PIVresults for D/d = 1.5, G2/G1 = 1, XS/d = 0.75, g1 = 2 and Y/G1 = 0.5 at Re =65.42Chapter 6. DiscussionFigure 6.2: Huang’s computational cross stream velocity results plotted with the PIVresults for D/d = 1.5, G2/G1 = 1, XS/d = 0.75, and Y/G1 = 0.5 at Re = 65.43Chapter 6. DiscussionMost of the results found by Huang in his computational investigation ofa model forming fabric show similar trends and numbers to the data foundby the current study. Huang did not present any pressure drop results inhis thesis or paper, so that data is unavailable for aiding validation.Figs. 6.1 and 6.2 show the PIV data for D/d = 1.5, G2/G1 = 1, g1 = 2,XS/d = 0.75 and Y/G1 = 0.5 and Huang’s data for D/d = 1.615, G2/G1= 1, g1 = 2.692, XS/d = 1.923 and Y/G1 = 0.5 plotted on the sameaxes. It is seen that for these similar configurations the plots are nearlycoincident. The uncertainty bars shown on the plots are for the PIV andrepresent the uncertainty for 80% confidence. Huang did not report anyuncertainties.Examination of these figures shows that Huang’s data corresponds to thePIV data. In the stream wise velocity field, Fig. 6.1 shows that the max-imum velocity seen by Huang was approximately 1.26U0, the PIV datashows similar values of between 1.23U0 and 1.27U0. The minimum velocityseen by Huang for these test was in the vicinity of just over 0.5U0, whilethe minimum velocity seen in the PIV was between 0.5U0 and 0.6U0.In the cross stream direction, the plots show good agreement in terms ofmagnitude and shape. Huang shows the velocity ranging from -0.37U0 to0.37U0, with a linear change between. The PIV data ranges from approx-imately -0.40U0 to 0.35U0. This is shown in Fig. 6.2.For the G1 	= G2 comparisons, a new set of simulations were performed.The computations discussed here were exicuted by Ali Vakil of the Uni-versity of British Columbia’s department of Mechanical Engineering usingHuang’s methods. Vakil simulated the exact configuration that was testedby PIV and reported velocity fields for the viscous and inviscid flows andpressure drop for the viscous flow.Figs. 6.3 and 6.4 show the d/4 upstream velocity fields for a configurationof D/d = 3, G2/G1 = 2, XS/d = 0, Y/G1 = 0.5 at Re = 25. Theuncertainty bars represent a typical 80% confidence uncertainty.It is seen from these images that the PIV results don’t show as good ofan agreement for these simulations as the results for the G1 = G2 cases.The results are closer to the inviscid solution, but in general fall betweenthe viscous and inviscid solutions. Vakil also solved for the pressure dropof the viscous solution and obtained a value of k = 22.9. The measuredvalue for the experiments was k = 21.24 ± 2.04.44Chapter 6. DiscussionFigure 6.3: Comparison of PIV and computational stream wise velocities for a caseof D/d = 3, G2/G1 = 2, XS/d = 0, Y/G1 = 0.5 at Re = 2545Chapter 6. DiscussionFigure 6.4: Comparison of PIV and computational cross stream velocities for a caseof D/d = 3, G2/G1 = 2, XS/d = 0, Y/G1 = 0.5 at Re = 2546Chapter 6. DiscussionThe source of the discrepancies between the PIV and computations is un-known. It has been suggested that the problem lies is the computation’sability to model the onset of separation. However, even with these dif-ferences, the computations remain a powerful tool in examination of theaffect of the second row filament geometries.In order to determine the effect of the velocity discrepancy, it must bedetermined how the fibres and fines are influenced by the flow conditions.If the u-component of the velocity dominates the behaviour of a fibre, thehigher sheer rates in the viscous solution would tend to align the fibreswith the x -direction and they would pass though the forming fabric. Inthis case the computations would under estimate the fibre retention. If, onthe other hand, the v-component of the velocity dominates the flow, thehigher shear rates seen in the viscous simulation in the machine direction(the computational y-direction) would help the fibre retain its initial MDorientation, bridging more fabric filaments, increasing retention. In thiscase the computations would over estimate the fibre retention.The PIV served to validate Huang’s results for the G1 = G2 cases. Itwas not possible to reproduce the G1 	= G2 computational flow fields inthe experiments, however, the pressure drop data from the computationsmatched the experimental value, giving credence to the results. In thecase of the G1 	= G2 simulations, the viscous solution consistently showedhigher shear in the x and y-directions than the experiments. To determineif this would lead to an under estimate, or an over estimate of the retentionmore must be known about the influence of the flow on the behaviour ofthe pulp fibres.47Bibliography[42] Z. Huang. Numerical simulations of flow through model paper machine formingfabrics. Master’s thesis, The University of British Columbia, Vancouver, BritishColumbia, Canada, 2003.48Chapter 7Recommendations for FurtherResearchThere are two avenues that are of interest and should be investigated,either coincidently or consecutively. The next step in the modelling ofthe flow is to move from 2D to 3D and include the effects of the machinedirection filaments on the upstream flow field. The other direction ofinterest is determining how the flow field influences the deposition of thepulp fibres and fines.Figure 7.1: Method for determining the internal 3D geometry of a forming fabric.In the modelling of the 3D forming fabric one of the more significantchallenges is likely to be the determination of an appropriate geometry.Because little is known about the internal structure of forming fabrics, theexact geometries of the filament knuckles and path of the woven strandswill have to be obtained. One method of doing this is shown in Fig. 7.1.In this figure, the forming fabric in question is potted in a hard material.An end mill is then used to make consecutive, thin cuts. Each cut willbe on the order of 0.001” inch and by imaging the filament geometries49Chapter 7. Recommendations for Further Researchafter each cut it will be possible to construct a fully 3D, accurate CADmodel of the complete forming fabric. This model can then be used asa computational domain, or could be physically replicated using rapidprototyping for experimental analysis.The other direction of interest is the modelling of the effects of the flowfield on the pulp fibres that will constitute the final sheet of paper. Asan initial investigation, this is best done computationally. The flexibilityof the computational domain and flow conditions make it relatively easyto investigate affects of the different components of the flow field. It alsoallows for the modelling of a standardized pulp fibre, something that wouldbe very difficult to obtain experimentally.Initially, the fibres could be considered on a 2D basis, with the 3D eval-uation performed once a satisfactory 3D computational domain has beendetermined using the methods discussed previously.50Appendix AExperimental DesignA.1 IntroductionInvestigation of flow through a forming fabric poses a number of exper-imental and engineering challenges. In application, the flow through aforming fabric is multi-phase, highly 3-dimensional, and happens at a verysmall scale and hence low, but not Stokes flow, Reynolds numbers. In or-der to totally evaluate the flow structures these complications have to beovercome, however, before doing a fully 3D, multi-phase, unsteady simula-tion of the sheet forming process there are some reasonable simplificationsin the geometry and flow conditions that can made to make the problemmanageable, yet still applicable.This appendix details the simplifications, and their justifications, that wereused in the design of the experiments.A.2 Phase SimplificationThe first simplification was the elimination of the second phase. In prac-tise, flows through forming fabrics are primarily liquid. The consistency(c) in the forming section is low, generally less than 1% (c = mfibre/mtotal),but an examination of fibre-fibre interactions is also necessary.The first consideration in the phase simplification was to determine wherewire mark exists in the paper. Roger Danby published a paper in 2002 inwhich he split a sheet of super calendar paper three times and examinedeach part of the sheet in succession[48]. He found that wire mark is onlypresent in the 12.5% of the sheet that is closest to the forming fabric.Concequently, an investigation into wiremark should be limited to theinital stages of sheet formation. The results of Danby’s light transmissiontest are shown in Fig. 4.5 on page 19.Since Danby showed that wire mark exists only in the 12.5% of the sheetclosest to the fabric, it can be said that wire mark is developed primar-ally in early stages of sheet formation. During formation the suspensionof fibres is subjected to three basic processes: drainage, oriented shear,and turbulence[52, Ch. 1]. While, in reality, all of these processes are51Appendix A. Experimental Designtaking place at the same time, they can be said to dominate in the or-der listed. Furthermore, as formation progresses the there comes a pointwhere the deposited fibre mat dominates the flow field and the geometryof the forming fabric becomes less important[51].Since the fibre mat will dominate the forming process in the later stagesof formation, the drainage process is of primary concern. Drainage can befurther broken down into two mechanisms depending on c and crowdingnumber (CN). CN is defined as the number of fibres intersecting a sphere,centred on the middle of a particular fibre, with a diameter equal to thelength of the fibre. Hence for higher consistencies, the CN is also generallyhigher. For low c and/or CN the predominant mechanism is filtration. Infiltration fibres are highly mobile and fibre-fibre interactions are low. Forhigher c and/or CN thickening dominates. In this mechanism fibre-fibreinteractions are high and the developing mat acts more like a tangle thana free suspension.As mentioned previously, formation is generally done at low consistencyand low crowding number. Because the primary concern is in the initialstages of formation, before the fibre mat has formed, the dominating flowwill be drainage undergoing the filtration mechanism. This indicates thatthe fibre-fibre interactions are low and can be neglected, justifying theelimination of the solid phase.A.3 Geometry SimplificationAnother complicating factor in the investigation of a forming fabric is thecomplicated geometry. These geometries, shown in Figs. 2.1 and 2.2 onpage 5, have associated complex three dimensional flow fields. For thepurpose of a preliminary investigation, modelling of the full 3D flow isdifficult to verify and impractical to apply. For this reason a justifiablesimplification is required.The affects of the geometry of a forming fabric on the formation processhave been investigated in the past. In 1978 Torbjorn Helle published a pa-per investigating the influence of the forming fabric geometry on drainagerate[49]. In this paper he showed that if the prominent knuckles of theforming fabric are aligned in the CD then drainage rates are higher. Thisindicates that the cross direction filaments play an important part in thesupport of the fibre web, resisting fabric clogging.Then, in 1979, Robert Beran published the first paper addressing thesubject of forming fabric classification that extended beyond the typical52Appendix A. Experimental DesignFigure A.1: The support of CD filaments[44].percent open area, strand diameter, and air permeability[45]. In his paperhe sought an off-machine characterization of forming fabrics based not onlyon the typical parameters, but also dependent on the surface structure ofthe fabric under investigation. To this end Beran developed the FabricSupport Index (FSI)FSI is a function of a number of different geometric and operational pa-rameters. It accounts for the weave density in MD and CD, fibre lengthdistribution, and fibre orientation. One of the results of his analysis is thatthe CD filaments in a forming fabric play a larger role in support of thefibre mat than the MD filaments[45]. This suggests that one possible geo-metrical simplification would be to isolate the effect of the CD filamentsthrough use of a 2D geometry consisting of only cross-machine directionfilaments.Hella and Beran’s work was expanded upon by D.B. Johnson in 1986 withthe development of the Drainage Index (DI)[50]. The DI aims to predictthe drainage rate of a fabric based upon the support of individual fibresand the associated blocking of flow passages. His work showed that theCD filaments played a larger role in the support of the fibre web, resistingblockage of the forming fabric and consequently allowing higher drainagerates.Another important paper influencing the simplification of a model form-ing fabric was published by Sabit Adanur in 1994. In his paper Adanurinvestigated the affect of the Beran FSI and the Johnson DI on a numberof physical sheet properties, including tear strength, breaking load, burststrength, sheet thickness and sheet density[44]. Adanur also demonstrates53Appendix A. Experimental DesignCD z faceFigure A.2: Cross section of a forming fabric showing the CD filaments contactingthe CD face[Adapted from 43].XSXCMD-z face$      Figure A.3: The resulting 2D bank of cylinders obtained from the above simplifica-tions.the previously seen effects of the CD filaments, justifying their additionalimportance in web support using qualitative means. Fig. A.1 shows howthe CD filaments support fibres that are preferentially aligned in the MDdue to the headbox hydrodynamics.These papers show that an effective simplification of a forming fabric wouldbe the elimination of the machine direction filaments and consideration ofonly the cross-machine direction filaments.In the work presented in this thesis, the CD filaments are represented bya series of linear cylinders. Figure A.2 shows a cross-section of a formingfabric in the MD-z and CD-z planes. If the CD filaments that contactthe MD-z face are considered, the 2D bank of cylinders shown in Fig. A.3are obtained. This flow field is more easily investigated as flow througha bank of cylinders of different dimensions and is easily applied to thedevelopment of future forming fabrics.54Appendix A. Experimental DesignA.4 Flow Velocity and Reynolds numberThe final flow condition that must be considered is the Reynolds numberof the flow through a forming fabric. There is a relatively small amount ofresearch in this area when compared to the impact of the geometry of thefabric, but a paper published by Barbara Dalpke in 2004 addressed theheadbox jet impingement in twin wire formers using numerical methods[47].Dalpke investigated the drainage flow for single wires[46] and twin wiregap formers[47]. Her numerical results showed drainage velocities canspike as high as 4.5m/s on single wire machines with high impingementangle[46], but showed that velocities are more commonly in the range of0.05 to 0.5m/s on twin wire machines[47].Using a forming fabric with paper-side filaments of ∼0.15 mm diameterand modelling the stock solution as pure water, the Reynolds numberrange is approximately 6.5 to 65. The value of Re = 6.5 is seen only inthe later stages of formation, when the paper web will have a significantimpact on the drainage flow. Consequently, a Re ≈ 65 will be seen in theinitial drainage and initial layup of the paper.The literature above makes it possible to apply the following simplificationsand flow conditions:1. Elimination of the fibres due to the low consistency and CN.2. Elimination of the MD filaments due to their smaller role in sheet support.3. Test conditions using 6.5 ≤ Re ≤ 65 based on typical fabric geometries andformation flow velocities.55Bibliography[43] Astenjohnson forming fabrics page. 〈http://www.astenjohnson.com/〉, October2005.[44] S. Adanur. Effects of forming fabric structural parameters on sheet properties.Tappi Journal, 77(10):187–195, Oct 1994.[45] R.L. Beran. The evaluation and selection of forming fabrics. Tappi, 62(4):39–44,Apr 1979.[46] B. Dalpke, S.I. Green, and R.J. Kerekes. Modelling of jet impingement in twin-wire paper-machines: impingement on one fabric. TAPPI Engineering Confer-ence, pages 513–527, Sep 2000.[47] B. Dalpke, R.J. Kerekes, and S.I. Green. Modelling jet impingement and theinitial drainage zone in roll forming. Journal of Pulp and Paper Science, 30(3):65–70, March 2004.[48] R. Danby. Sc print quality influenced by fibre length, fabric structures, andmachine drainage characteristics. Tappi Journal, 1(9):3–9, Nov 2002.[49] T. Helle. How forming fabric design affects drainage and release. Pulp & PaperCanada, 79(11):91–98, November 1978.[50] D.B. Johnson. Retention and drainage of multi-layer fabrics. Pulp & PaperCanada, 87(5):56–59, May 1986.[51] J.H. Jong, W.D. Baines, and I.G. Currie. Experimental characteristics of formingfabrics and fibre mats. Journal of Pulp and Paper Science, 25(3):95–99, Mar1999.[52] J.D. Parker. The Sheet-Forming Process. Tappi Press, Atlanta, GA, 1972.56Appendix BExperimental Setup and MethodsB.1 IntroductionThree methods of data collection were used to collect the principal data forthe evaluation of the forming fabric. Particle image velocimetry (PIV) andhydrogen bubble generation were used to evaluate the flow approachingthe model forming fabric and pressure drop measurements were used toevaluate the flow through the model forming fabric.The velocity profile of the forming fabric approach flow is of primary im-portance to the evaluation of the possible wire marking. If the flow velocityis higher in one region than another more pulp and fines will be directedto that location, increasing the density of the paper over that flow path,creating a hydrodynamic wire mark. The pressure drop results providean indication of the drainage rate of the forming fabric. The lower thepressure drop at a given Re the faster the drainage.Each of these three methods will be discussed in more detail following adescription of the actual test facility.B.2 Experimental SetupThere were three major stipulations for the test apparatus that was de-signed for these experiments. It had to accommodate the experimentalmethods discussed in §B.1, it was desirable to have it capable of continu-ous operation, and it had to include a configurable model forming fabric.In order for it to be capable of continuous operation it was decided thata flow loop configuration would be used. The loop would be driven bya 20 HP variable speed pump and would be located at the University ofBritish Columbia’s, Pulp and Paper Centre. Flow would exit the pumpinto a 1.5” diameter line where velocity measurement would be made viaa venturi with a 0-15pisd differential pressure sensor for high Re measure-ments and a 0-0.5psid differential pressure sensor for the low Re velocitymeasurements.57Appendix B. Experimental Setup and MethodsThe actual test section had a frontal projection of 30x30cm and was con-structed of acrylic so as to be clear for PIV, and hydrogen bubble obser-vation. The test section contained a recess to accommodated a frame thatheld cylinders that acted as the model forming fabric.$ $&      Figure B.1: Cylinder frame equipt with 9.53mm and 19mm diameter cylinders.The frame was fitted with mounting holes that were spaced out by 9.53mm(0.375”) perpendicular to the test section flow and 19mm (0.75”) parallelto the test section flow. It was fitted with cylinders of three diameters,9.53mm (.375”), 19mm (.75”) and 28.58mm (1.125”). The maximum cylin-der diameter was chosen such that the centre of the test section would beas close as possible to 7 diameters from end of the cylinders while keepingwith standard cylinder diameters[55]. Since PIV was to be taken upstreamof the cylinder bank, and not interstitially, they did not need to be fabri-cated from acrylic. An image of the frame is shown in Fig. B.1.The test section pressure ports were located upstream and downstreamof the cylinder frame so that differential pressure measurements could bemade across the bank of cylinders.Ports for the H2 generation wire were installed in the middle of the testsection upstream of the cylinder bank so that a 0.002” diameter platinumwire could be suspended across the test section for hydrogen bubble gen-eration. Both of these can be seen in Fig. B.2.58Appendix B. Experimental Setup and Methods$       Figure B.2: Locations of the pressure and hydrogen bubble portsFigure B.3: The test section fully installed. Flow is from left to right59Appendix B. Experimental Setup and MethodsFigure B.4: Schematic of the Test Section Flow LoopThe full test section is shown in Fig. B.3. Figure B.4 shows a schematicof the flow loop’s final configuration.B.3 Test Section Flow CharacteristicsIn order to have confidence in the data produced, the test section flow uni-formity had to be evaluated at different velocities. This was done usingboth PIV and hydrogen bubble generation. To evaluate the flow unifor-mity using hydrogen bubbles a high definition digital video camera (SonyHDV Handycam Camcorder, Model HDR-FX1) was placed under the testsection and lines of hydrogen bubbles were generated in the flow. Indi-vidual images were then captured from the video and hydrogen bubbleline was digitized into coordinate data with respect to an origin definedcoincident with the hydrogen bubble wire. The distance travelled wasnormalized by the average distance travelled. This method was not usedto find the test section velocity. The images from the test section flowuniformity tests are shown in Figs. B.5 and B.6 and the correspondingdigitized data is shown in Fig. B.760Appendix B. Experimental Setup and MethodsFigure B.5: Image of test section flow at 2cm/s. Flow is from bottom to top of image.61Appendix B. Experimental Setup and MethodsFigure B.6: Image of test section flow at 4cm/s. Flow is from bottom to top of image.62Appendix B. Experimental Setup and MethodsFigure B.7: Data extracted from Figs. B.5 and B.6The hydrogen bubble generation system showed that the velocity in thetest section was even to within 5% over 83% of the test section for both2cm/s and 4cm/s at a viscosty of 15.17cP.The test section velocity and flow uniformity were also investigated usingthe PIV system. The setup of the PIV will be detailed in §B.4, howeverthe empty test section results will be discussed here.$        Figure B.8: Normalized test section velocity with a 135.3mm field of view.63Appendix B. Experimental Setup and Methods$      Figure B.9: Empty test section velocity vectors at location of PIV data collection.The camera was setup below the test section with a field of view of135.3mm, the largest field of view used in the PIV tests. The velocitywas set by the venturi to 3.89cm/s, at a viscosity 13.26cP, correspondingto Red = 65 for the 19mm diameter cylinders. The results were normalizedby the set velocity and plotted as a function of position in pixels. FigureB.8 shows the resultant velocity plot and Fig. B.9 shows the vectors plottedon a PIV image.As can be seen in Fig. B.8 the PIV shows the average test section velocityto be 4.05cm/s, 4.1% higher than the 3.89cm/s that was set using theventuri.The velocity was also verified using observations of the flow in the test sec-tion. A mark was placed on the side of the test section 10cm downstreamfrom the hydrogen bubble generation wire. Hydrogen bubbles were timedtravelling down the test section and the velocity computed. The averagetime for 10cm was 2.534 seconds with a standard deviation of 0.085. Thisgives an average velocity of 3.95cm/s. Assuming a position uncertainty of±2mm, and a time uncertain of ±1σ, the velocity range is Vmax = 4.16cm/sand Vmin = 3.74cm/s. The velocity data is shown in Fig. B.10.The range of velocities from the time/displacement method include boththe PIV measurements with an average velocity of 4.05cm/s ± 0.06cm/s64Appendix B. Experimental Setup and Methods5 10 15 20 253.63.73.83.944.14.24.34.44.54.6RunMeasured Velocity, cm/sAccepted DataRejected DataAverage of Good DataFigure B.10: Stopwatch measured test section velocity for comparison with PIV.and the venturi pressure drop measurements with an average of 3.89cm/s± 0.07cm/s.B.3.1 Test Section Sensor DetailsThe specific equipment used to determine flow loop conditions were:• High Velocity Pressure Sensor:Sensotec Model FDWRange: 0 – 15 psidPart #: 060-G763-03Order Code: FDW2BJ,2D5B6QS/N: 1009322• Low Velocity Pressure Sensor:Sensotec Model FDWRange: 0 – 0.5 psidPart #: 060-G250-09Order Code: FDW1AN,2G5A6AS/N: 1094994Date: 5/12/2006• Viscosity Measurement:Gilmont Instruments Viscosimeter Size # 2Model GV-2200S/N: 2457465Appendix B. Experimental Setup and MethodsB.4 PIV Setup$        Figure B.11: The interrogation areas from the two masked PIV images with a knowntime separationParticle image velocimetry (PIV) is a method for finding the velocity ofa flow field with minimal interference. To calculate PIV velocity profilesthe flow was seeded with small (10 micron in this case), neutrally buoyantparticles. The the particles were then illuminated by two light sheets thatwere spatially coincident and temporally separated by a known time. Thepositions of the seeding particles illuminated by the two flashes were cap-tured as two separate images by a digital camera. These two images werethen masked to maximize calculation efficiency and divided into small in-terrogation areas which were then compared on a one-to-one basis betweenthe two images. The result was an average velocity for each interrogationarea. This process is shown in Figs. B.11 and B.12.The PIV system was setup with the laser sheet directed from the side ofthe test section, aimed to illuminate the area upstream of the cylinderbank. Imaging was done from below using a 1 mega-pixel, 8-bit digitalcamera. A drawing of the setup is shown if Figure B.13.To determine if there was a consistent offset error in the PIV system,the velocity in the empty test section was evaluated by PIV and then66Appendix B. Experimental Setup and Methods$        Figure B.12: The two interrogation areas are then compared by cross-correlation tofind the average particle displacement and hence velocity.compared to velocities measured by a manual time/displacement method.The results of this analysis were discussed in §B.3.B.4.1 PIV Equipment DetailsThe specific equipment used in the PIV analysis was:• Signal Generator:Berkeley Nucleonics Corporation Model 500DS/N: 22659• Lasers:New Wave Research Gemini PIV 15HzLaser-1 S/N: 10288, Aug 2000Laser-2 S/N: 10289, Aug 2000• Camera:Roper Scientific MEGAPLUS Model ES 1.0S/N: 93036000CS3NAB.5 Pressure Drop SetupThe pressure drop measurements were made directly. The wet/wet differ-ential pressure sensor had a range of 0-0.1” water with a 10V DC output,67Appendix B. Experimental Setup and MethodsFigure B.13: PIV arrangement.and was manufacturer calibrated to an accuracy of ±0.25%FS. The pres-sure was measured across the bank of cylinders and the output was readoff an occiliscope after a consistent reading for a minimum of 60 seconds.The locations of the pressure ports are visible in Fig. B.2 on page 59.B.5.1 Pressure Drop Equipment DetailsThe specific equipment used for the pressure drop measurements were:• Pressure Drop Sensor:Validyne Engineering Model DP103-06-10306N1S4DS/N: 127315• Carrier Demodulator:Validyne Engineering Model CD15-A-1-A-1S/N: 118923B.6 Hydrogen Bubble Generation System SetupThe hydrogen bubble generation system was implemented to provide thecapability to visualize time dependent variations in the flow field and pro-vide quick, qualitative flow field visualization. It also provided a means toevaluate the flow conditions of the test section, making sure that flow waseven and steady at multiple velocities.The bubbles were generated off of a 0.002” diameter platinum wire. Hy-drogen bubbles released off of the wire can be expected to have a diameterof about half that of the generating wire, so the bubbles produced were68Appendix B. Experimental Setup and Methodsnominally 0.001” in diameter[53]. It was necessary to find the rise veloc-ity of the bubbles in order to show that they would follow the test sectionflow. For Stokes flow the drag coefficient is known to be[54],CD =24Refor Re ≤ 1 (B.1)CD =FD1/2 · ρ · U2 · l2 (B.2)To find the terminal velocity of the hydrogen bubbles in water the buoy-ancy equation reduces to,FD = (ρfluid − ρbubble) · V · g (B.3)FD = 7.20693E − 11NCombing equations B.1 and B.2 and rearranging for velocity we get,U =FD12 · µ · d (B.4)U =7.21E − 1112 · 15E − 5 · 2.54E − 5U = 1.31E − 5m/sThe running velocity of the test section is variable, but is of the orderof 10−2 m/s, or three orders of magnitude greater than the rise velocityof the hydrogen bubbles. It is therefore possible to neglect the bubble’sperpendicular velocity.69Bibliography[53] Richard J. Goldstein, editor. Fluid Mechanics Measurements. Taylor and Francis,Washington, DC, second edition, 1996.[54] B.R. Munson, D.F. Young, and T.H. Okiishi. Fundamentals of Fluid Mechanics.John Wiley and Sons, Inc., New York, New York, 1998.[55] D. Sumner, S.S.T. Wong, S.J. Price, and M.P. Pad¨oussis. Fluid behaviour of side-by-side circular cylinders in steady cross-flow. Journal of Fluids and Structures,13:309–338, 1999.70Appendix CUncertainty AnalysisC.1 Single Valued, Multi-Variable FunctionsThe uncertainty analysis used in this project followed the general engineer-ing method. A single valued, multi-variable function, such as the Reynoldsnumber, is differentiated by each of its variables. The total uncertaintyassociated with a given function is then the vector sum of the changescreated by each variable independently.The equations for the uncertainty of the various functions are given alongwith screen shots of the spread sheets used to calculate them.Density uncertainty was found from:ρ =mV(C.1)δρ =⎡⎣(∂ρ∂mδm)2+(∂ρ∂VδV)2⎤⎦1/2(C.2)Where,∂ρ∂m=1m∂ρ∂V= − mV 2Inlet pipe velocity uncertainty was found from:Upipe = k⎧⎪⎪⎨⎪⎪⎩2 ∆Pρ[(D1D2)4 − 1]⎫⎪⎪⎬⎪⎪⎭1/2(C.3)δUpipe =⎡⎣(∂Upipe∂kδk)2+(∂U∂∆PδP)2+(∂U∂ρδρ)2+(∂U∂D1δD1)2+(∂U∂D2δD2)2⎤⎦1/2(C.4)Where,∂Upipe∂k=⎧⎪⎪⎨⎪⎪⎩2 ∆Pρ[(D1D2)4 − 1]⎫⎪⎪⎬⎪⎪⎭1/271Appendix C. Uncertainty Analysis∂Upipe∂∆P= k⎧⎪⎪⎨⎪⎪⎩24 ∆P ρ[(D1D2)4 − 1]⎫⎪⎪⎬⎪⎪⎭1/2∂Upipe∂ρ= −k⎧⎪⎪⎨⎪⎪⎩2 ∆P4ρ3[(D1D2)4 − 1]⎫⎪⎪⎬⎪⎪⎭1/2∂Upipe∂D1= k−2D31D22∆P√2(D41 −D42)2√∆P ρ(D41−D42)ρ∂Upipe∂D2= k⎧⎪⎪⎨⎪⎪⎩2D52∆P√2(D42 −D41)2√−∆P ρ(D42−D41)ρ+ 2D2√ −2∆P(D42 −D41) ρ⎫⎪⎪⎬⎪⎪⎭Test section velocity uncertainty was found from:UTS =πUpipeD24HW(C.5)δUTS =⎡⎣( ∂UTS∂UpipeδUpipe)2+(∂UTS∂DδD)2+(∂UTS∂HδH)2+(∂UTS∂WδW)2⎤⎦1/2(C.6)Where,∂UTS∂Upipe=πD24HW∂UTS∂D=UpipeπD2HW∂UTS∂H= −UpipeπD24H2W∂UTS∂W= −UpipeπD24HW 2Viscosity uncertainty was found from:µ = k (ρfluid − ρball) t (C.7)δµ =⎡⎣(∂µ∂kδk)2+(∂µ∂tδt)2+(∂µ∂ρfluidδρfluid)2+(∂µ∂ρballδρball)2⎤⎦1/2(C.8)Where,∂µ∂k= (ρfluid − ρball) t∂µ∂t= k (ρfluid − ρball)∂µ∂ρfluid= kt72Appendix C. Uncertainty Analysis∂µ∂ρball= −ktReynolds Number uncertainty was found from:Re =ρUdµ(C.9)δRe =⎡⎣(∂Re∂ρδρ)2+(∂Re∂UδU)2+(∂Re∂dδd)2+(∂Re∂µδµ)2⎤⎦1/2(C.10)Where,∂Re∂ρ=Udµ∂Re∂U=ρdµ∂Re∂d=ρUµ∂Re∂µ= −ρUdµ2Pressure drop coefficient uncertainty was found from:k =∆P12ρU2TS(C.11)δk =⎡⎣( ∂k∂∆Pδ (∆P ))2+(∂k∂ρδρ)2+(∂k∂UTSδUTS)2⎤⎦1/2(C.12)Where,∂k∂∆P=112ρU2TS∂k∂ρ= − ∆P12ρU2TS∂k∂UTS= − 2∆P12ρU3TSThese equations were entered into a Microsoft Excel spread sheet and theuncertainty was calculated. A screen shot of the spread sheet is shown inFig. C.1.The venturi constant uncertainty was found using time displacement datafrom the test section H2 bubble generation system. Since it only needed tobe evaluated once, MatLab was used to find the derivatives of the functionfor k and Microsoft Excel was used to evaluate the functions. The MatLabcommand window is give below.73Appendix C. Uncertainty AnalysisFigure C.1: Screen shot of the spread sheet used to calculate uncertainty.74Appendix C. Uncertainty Analysis>> syms k s h w pi t d1 p r d2>> k = (s*h*w)/(pi/4*t*d1^2*((2*p)/(r*((d1/d2)^4-1)))^0.5)k =2*s*h*w/pi/t/d1^2*2^(1/2)/(p/r/(d1^4/d2^4-1))^(1/2)>> diff(k,s)ans =2*h*w/pi/t/d1^2*2^(1/2)/(p/r/(d1^4/d2^4-1))^(1/2)>> diff(k,h)ans =2*s*w/pi/t/d1^2*2^(1/2)/(p/r/(d1^4/d2^4-1))^(1/2)>> diff(k,w)ans =2*s*h/pi/t/d1^2*2^(1/2)/(p/r/(d1^4/d2^4-1))^(1/2)>> diff(k,t)ans =-2*s*h*w/pi/t^2/d1^2*2^(1/2)/(p/r/(d1^4/d2^4-1))^(1/2)>> diff(k,d1)ans =-4*s*h*w/pi/t/d1^3*2^(1/2)/(p/r/(d1^4/d2^4-1))^(1/2)+4*s*h*w/pi/t*>d1*2^(1/2)/(p/r/(d1^4/d2^4-1))^(3/2)*p/r/(d1^4/d2^4-1)^2/d2^4>> diff(k,d2)ans =-4*s*h*w/pi/t*d1^2*2^(1/2)/(p/r/(d1^4/d2^4-1))^(3/2)*p/r/(d1^4/d2^>4-1)^2/d2^5>> diff(k,p)ans =-s*h*w/pi/t/d1^2*2^(1/2)/(p/r/(d1^4/d2^4-1))^(3/2)/r/(d1^4/d2^4-1)>> diff(k,r)ans =s*h*w/pi/t/d1^2*2^(1/2)/(p/r/(d1^4/d2^4-1))^(3/2)*p/r^2/(d1^4/d2^4-1)Where,k = Venturi constants = H2 bubble line displacementh = Test section heightw = Test section widtht = H2 bubble line timed1 = Venturi inlet diameterd2 = Venturi throat diameterp = Pressure dropr = Fluid densityThe spread sheet for calculation of the venturi constant and its uncertaintyis shown in Fig. C.2.75Appendix C. Uncertainty AnalysisFigure C.2: Screen shot of the spread sheet used to find the venturi constant anduncertainty.C.2 PIV uncertaintyThe PIV uncertainty is a two part process. First it must be determined ifthere is a consistent offset in the PIV data. This analysis was discussed in§B.3. It must also be determined whether a sufficient number of imagespairs were taken to have confidence in the PIV values.Using the data from the empty test section test shown in Fig. B.9 thestandard deviation for each velocity vector was examined. It was foundthat the maximum standard deviation after averaging over 70 image pairswas 14% of the average value. While this is quite high, it was only the casefor 3 out of 1476 vectors. The averaga standard deviation was 2.42% of theaverage value over all cross-correlated vectors. This provides confidencein the avaerage values of the vectors found via PIV.The uncertainty in each average vector was found using a Student’s t-distribution. The PIV software returned the average, the standard devia-tion, and the number of valid vectors used to find these quantities. Thesequantities were then placed into equation C.13 to find the 80% confidenceuncertainty.V elocity = Vmean ± t0.1 · σV√N(C.13)76Appendix C. Uncertainty AnalysisThe one-sided value of t0.1 = 3.078 gives a ± confidence of (1− 2 · 0.1) = 0.8.The representations of the typical uncertainty, such as the bars shownon the plots in §5.4, were found using a two part process. First, theuncertainties for the regions of high velocity gradient, such as the vicinityof y/G1 = 2 in Fig. 5.4 were neglected. These uncertainties tended tobe quite high due to the different velocities that existed within a giveninterrogation area and were not considered representative of the plot’sgeneral uncertainty. Second, the maximum uncertainty in regions of lowvelocity gradient, such as in the vicinity of y/G1 = 1.75 in the same figure,was taken as typical of the plot uncertainty.77

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