Abstract
Papermaking flows are extremely challenging for modelling and simulation, if one accepts their full complexity. A wide range of particles, including fibres, fibre fragments (fines) and fillers (non-organic particles), flow and interact with each other in a non-dilute suspension, a complex geometry and at a high flow rate. Different simulation approaches are reviewed from particle-level simulations, through meso-scale simulations to the full flow geometry of the papermaking line. Their application to papermaking and potential to provide fundamental understanding as well as direct process-optimization support are discussed.
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Leppänen T (2007) Effect of fibre orientation on cockling of paper. PhD thesis, University of Kuopio, Finland
Karlsson M, Hämäläinen J (2004) A model-based decision-aid system to add value to papermaking. Neittaanmäki P, Rossi T, Majava K, Pironneau O (eds) CD Proceedings of 4th ECCOMAS 2004, vol I. Jyväskylä, Finland
Madetoja E (2007) Novel process line approach for model-based optimization in papermaking—sensitivity and uncertainty analysis. PhD thesis, University of Kuopio, Finland
Wu J, Aidun CK (2010) A method for direct simulation of flexible fiber suspensions using lattice-Boltzmann equation with external boundary force field. Int J Multip Flow 36(3): 202–209
Wu J, Aidun CK (2010) Simulating 3D deformable particle suspensions using lattice Boltzmann method with discrete external boundary force. Int J Numer Methods Fluids 62(7): 765–783
Aidun CK, Clausen JR (2010) Lattice-Boltzmann method for complex flows. Annu Rev Fluid Mech 42: 439–472
Qi D (2006) Direct simulations of flexible cylindrical fiber suspensions in finite Reynolds number flows. J Chem Phys 125: 114901
Tornberg A-K, Shelley MJ (2004) Simulating the dynamics and interactions of flexible fibres in Stokes flows. J Comput Phys 196: 8–40
Batchelor GK (1970) Slender-body theory for particles of arbitrary cross-section in Stokes flow. J Fluid Mech 44(3): 419–440
Yamane Y, Kaneda Y, Doi M (1994) Numerical simulation of semi-dilute suspensions of rodlike particles in shear flow. J Non-Newton Fluid Mech 54: 405–421
Fan X, Phan-Thien N, Zheng R (1998) A direct simulation of fibre suspensions. J Non-Newton Fluid Mech 74: 113–135
Tornberg A-K, Gustavsson K (2006) A numerical method for simulations of rigid fiber suspensions. J Comput Phys 215(1): 172–196
Yamamoto S, Matsuoka T (1995) Dynamic simulation of fiber suspensions in shear flow. J Chem Phys 102: 2254–2260
Yamamoto S, Matsuoka T (1996) Dynamic simulation of microstructure and rheology of fiber suspensions. Polym Eng Sci 36(19): 2396–2403
Skjetne P, Ross RF, Klingenberg DJ (1997) Simulation of single fiber dynamics. J Chem Phys 107(6): 2108–2121
Joung CG, Phan-Thien N, Fan XJ (2001) Direct simulation of flexible fibers. J Non-Newton Fluid Mech 99: 1–36
Joung CG, Phan-Thien N, Fan XJ (2002) Viscosity of curved fibers in suspensions. J Non-Newton Fluid Mech 102: 1–17
Joung CG (2003) Direct simulation studies of suspended particles and fibre-filled suspensions. PhD thesis, University of Sydney, Australia
Jayageeth C, Sharma VI, Singh A (2009) Dynamics of short fiber suspensions in bounded shear flow. Int J Multip Flow 35: 261–269
Brady JF, Bossis G (1988) Stokesian dynamics. Annu Rev Fluid Mech 20: 111–157
Claeys IL, Brady JF (1993) Suspensions of prolate spheroids in Stokes-flow. 1. Dynamics of a finite number of particles in an unbounded fluid. J Fluid Mech 251: 411–442
Claeys IL, Brady JF (1993) Suspensions of prolate spheroids in Stokes-flow. 2. Statistically homogeneous dispersions. J Fluid Mech 251: 443–477
Ross RF, Klingenberg DJ (1997) Dynamic simulation of flexible fibers composed of linked rigid bodies. J Chem Phys 106(7): 2949–2960
Schmid CF, Klingenberg DJ (2000) Mechanical flocculation in flowing fiber suspensions. Phys Rev Lett 84: 290–293
Schmid CF, Switzer LH, Klingenberg DJ (2000) Simulations of fiber flocculation: Effects of fiber properties and interfiber friction. J Rheol 44: 781–809
Switzer LH, Klingenberg DJ (2003) Rheology of sheared flexible fiber suspensions via fiber-level simulations. J Rheol 47(3): 759–778
Switzer LH, Klingenberg DJ (2003) Simulations of fiber floc dispersion in linear flow fields. Nord Pulp Pap Res J 18(2): 141–144
Switzer LH, Klingenberg DJ (2004) Flocculation in simulations of sheared fiber suspensions. Int J Multip Flow 30: 67–87
Kim S, Karrila SJ (1991) Microhydrodynamics: principles and selected applications. Butterworth-Heinemann, Stoneham, MA
Wang G, Yu W, Zhou C (2006) Optimization of the rod chain model to simulate the motions of a long flexible fiber in simple shear flows. Eur J Mech B Fluids 25: 337–347
Soszynski RM, Kerekes RJ (1988) Elastic interlocking of nylon fibers suspended in liquid. Nord Pulp Pap Res J 3: 172–184
Sundararajakumar RR, Koch DL (1997) Structures and properties of sheared fiber suspensions with mechanical contacts. J Non-Newton Fluid Mech 73: 205–239
Joseph G, Zenit R, Hunt M, Rosenwinkel A (2001) Particle-wall collisions in a viscous fluid. J Fluid Mech 433: 329–346
Lindström SB, Uesaka T (2007) Simulation of the motion of flexible fibres in viscous fluid flow. Phys Fluids 19: 113307
Lindström SB, Uesaka T (2008) Simulation of semidilute suspensions of non-Brownian fibres in shear flow. J Chem Phys 128: 024901
Lindström SB (2008) Modelling and simulation of paper structure development. PhD thesis, Mid Sweden University, Sundsvall, Sweden
Lindström SB, Uesaka T (2009) A numerical investigation of the rheology of sheared fibre suspensions. Phys Fluids 21: 083301
Weinane E, Liu J-G (1996) Essentially compact schemes for unsteady viscous incompressible flows. J Comput Phys 126: 122–138
Weinane E, Liu J-G (1997) Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on nonstaggered grids. J Comput Phys 138: 57–82
Switzer LH, Klingenberg DJ, Scott CT (2004) Handsheet formation and mechanical testing via fiber-level simulations. Nord Pulp Pap Res J 19: 434–439
Miettinen PPJ, Ketoja JA, Klingenberg DJ (2007) Simulated strength of wet fibre networks. Int J Pulp Pap Sci 33(4): 198–205
Miettinen PPJ, Ketoja JA (2008) Simulation of triaxial deformation of wet fiber networks. Nord Pulp Pap Res J 23(3): 264–271
Lindström SB, Uesaka T (2008) Particle-level simulation of forming of the fibre network in papermaking. Int J Eng Sci 46: 858–876
Lindström SB, Uesaka T, Hirn U (2009) Evolution of the paper structure along the length of a twin-wire former. In: 14th Fund research symposium, vol 1. Oxford, UK, pp 207–245
Kulachenko A, Uesaka T, Lindström SB (2008) Reinventing mechanics of fibre networks. In: Progress in paper physics seminar. Espoo, Finland, pp 185–187, 193
Kulachenko A, Lindström SB, Uesaka T (2009) Strength of wet fibre networks—size scaling. In: Proceedings of papermaking research symposium, Finland
Folgar F, Tucker C III (1984) Orientation behaviour of fibers in concentrated suspensions. J Reinf Plast Compos 3(2): 98–119
Advani S, Tucker C III (1987) The use of tensors to describe and predict fiber orientation in short fibre composites. J Rheol 31(8): 751–784
Olson JA, Kerekes RJ (1998) The motion of fibres in turbulent flow. J Fluid Mech 377: 47–64
Petrie C (1999) The rheology of fibre suspensions. J Non-Newton Fluid Mech 87: 369–402
Krochak P, Olson J, Martinez D (2008) The orientation of semidilute rigid fiber suspensions in a linearly contracting channel. Phys Fluids 20: 073303
Bernstein O, Shapiro M (1994) Direct determination of the orientation distribution function of cylindrical particles immersed in laminar and turbulent shear flows. J Aerosol Sci 25(1): 113–136
Krushkal E, Gallily I (1988) On the orientation distribution of non-spherical aerosol particles in general shear flow. Part 2. The turbulent case. J Aerosol Sci 19(2): 197–211
Olson J, Frigaard I, Chan C, Hämäläinen J (2004) Modelling turbulent fibre suspension flowing in a planar contraction: the one-dimensional headbox. Int J Multip Flow 30: 51–66
Parsheh M, Brown M, Aidun C (2006) Variation of fiber orientation in turbulent flow inside a planar contraction with different shapes. Int J Multip Flow 32: 1354–1369
Krochak P, Olson J, Martinez M (2009) Fiber suspension flow in a tapered channel: the effect of flow/fiber coupling. Int J Multiph Flow 35: 676–688
Shin M, Koch D (2005) Rotational and translational dispersion of fibres in isotropic turbulent flows. J Fluid Mech 540: 143–173
Jeffery GB (1923) The motion of ellipsoidal particles immersed in a viscous fluid. Proc Roy Soc A 102: 161–179
Mortensen P, Andersson H, Gillissen J, Boersma BJ (2008) Dynamics of prolate ellipsoidal particles in turbulent channel flow. Phys Fluids 20: 093302
Olson J (2001) The motion of fibres in turbulent flow, stochastic simulation of isotropic homogenous turbulence. Int J Multip Flow 27: 2083–2103
Schiek R, Shaqfeh E (1995) A nonlocal theory for stress in bound, Brownian suspensions of slender, rigid fibres. J Fluid Mech 296: 271–324
Parsheh M, Brown M, Aidun C (2005) On the orientation of stiff fibres suspended in turbulent flow in planar contraction. J Fluid Mech 545: 245–269
Hyensjö M (2008) Fibre orientation modelling applied to contracting flows related to papermaking. PhD thesis, Royal Institute of Technology, Stockholm
Eloranta H (2005) Fluid mechanics of the papermaking machine headbox—instabilities and disturbances in the slice chamber. PhD thesis, Tampere University of Technology
Olson J (2002) Analytic estimate of the fibre orientation distribution in a headbox flow. Nord Pulp Pap Res J 17(3): 302–306
Putkiranta M, Eloranta H, Pärssinen T, Saarenrinne P (2009) Evolution of the fiber orientation distribution in streamwise elongational flow. In: CD proceedings of papermaking research symposium, 2009. Kuopio, Finland
Mason SG (1954) Fibre motion and floccation. Pulp Pap Mag Canada 55(13): 96–102
Karema H, Salmela J, Tukiainen M, Lepomäki H (2001) Prediction of paper formation by fluidisation and reflocculation experiments’. In: 12th Fund research symposium, pp 559–589
Kerekes RJ (1983) Pulp floc behavior in entry flow to constrictions. Tappi J 66(1): 88–91
Steen M (1990) Turbulence and flocculation in fibre suspensions. PhD thesis, University of Trondheim
Ramkrishna D (2000) Population balances—theory and applications to particulate systems in engineering. Academic Press, San Diego
ANSYS CFX-11.0 Electronical manual
Hämäläinen T, Hämäläinen J, Salmela J (2007) Evolution of fibre flocs in a turbulent pipe expansion flow. In: 6th international conference on Multiphase flow (CD Proceedings)
Hämäläinen J (1993) Mathematical modeling and simulation of fluid flows in the headbox of paper machines. PhD thesis, University of Jyväskylä
Hämäläinen J, Tarvainen P, Aspholm P (2005) HOCS FIBRE—new tool for optimized fibre orientation angles. In: 91st annual meeting PAPTAC, CD proceedings
Jäsberg A (2007) Flow behaviour of fibre suspension in straight pipes: new experimental techniques and multiphase modeling. PhD thesis, University of Jyväskylä, Finland
Hammarström D (2004) A model for simulation of fiber suspension flows. Licentiate thesis, Royal Institute of Technology, Stockholm, Sweden
Niklas M, Asendrych D (2006) Modelling of fluid flow with complex rheology. Syst J Transdiscipl Syst Sci 11: 63–73
Kondora G, Asendrych D (2009) Flow simulation in a disc refiner. In: Proceedings of 14th conference on Model fluid flows, Budapest
Ventura C, Blanco A, Negro C, Ferreira P, Garcia F, Rasteiro M (2007) Modeling pulp fiber suspension rheology. Tappi J 6(7): 17–23
Ventura C, Garcia F, Ferreira P, Rasteiro M (2008) Flow dynamics of pulp fiber suspensions. Tappi J 7(8): 20–26
Wikström T (2002) Flow and rheology of pulp suspensions at medium consistency. PhD thesis, Chalmers University of Technology, Sweden
Huhtanen JP (2004) Modeling of fiber suspension flows in refiner and other papermaking processes by combining non-Newtonian fluid dynamics and turbulence. PhD thesis, Tampere University of Technology, Finland
Hämäläinen J, Hämäläinen T, Madetoja E, Ruotsalainen H (2008) CFD-based optimization for complete industrial process: Papermaking. In: Thévenin D, Janiga G (eds) Optimization and computational fluid dynamics. Springer, Berlin
Hämäläinen J, Mäkinen R, Tarvainen P (2000) Optimal design of paper machine headboxes. Int J Numer Methods Fluids 34: 685–700
Hämäläinen J, Miettinen K, Tarvainen P, Toivanen J (2003) Interactive solution approach to a multiobjective optimization problem in a paper machine headbox design. J Opt Theory Appl 116(2): 265–281
Toivanen J, Hämäläinen J, Miettinen K, Tarvainen P (2003) Designing paper machine headbox using GA. Mater Manuf Process 18(3): 533–541
Hämäläinen J, Tarvainen P (2000) CFD-based shape and control optimization applied to a paper machine headbox. In: 86th annual meeting PAPTAC, pp A99–A102
Hämäläinen J, Tarvainen P (2002) CFD-optimized headbox flows. Pulp Pap Can 103: 39–41
Avikainen M, Hämäläinen J, Tarvainen P (2010) HOCS Fibre: CFD-based software for fibre orientation profile optimization for conventional and dilution headboxes. Nord Pulp Pap Res J (in press)
Hämäläinen J, Miettinen K, Madetoja E, Mäkelä MM, Tarvainen P (2004) Multiobjective decision making for papermaking. In: Wedley WC (eds) CD proceedings of 17th MCDM 2004. Whistler, British Columbia
Hämäläinen J., Madetoja E, Ruotsalainen H (2008) Simulation-based optimization and decision support for papermaking. In: Jin Y, Zhai H, Li Z (eds) Proceedings of ICPPB’08, vol I. Nanjing, China
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Hämäläinen, J., Lindström, S.B., Hämäläinen, T. et al. Papermaking fibre-suspension flow simulations at multiple scales. J Eng Math 71, 55–79 (2011). https://doi.org/10.1007/s10665-010-9433-5
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DOI: https://doi.org/10.1007/s10665-010-9433-5