Journal of Engineering Mathematics

, Volume 71, Issue 1, pp 55–79 | Cite as

Papermaking fibre-suspension flow simulations at multiple scales

  • J. Hämäläinen
  • S. B. Lindström
  • T. Hämäläinen
  • H. Niskanen
Article

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.

Keywords

Computational fluid dynamics Convection–diffusion Microhydrodynamics Population balance 

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References

  1. 1.
    Leppänen T (2007) Effect of fibre orientation on cockling of paper. PhD thesis, University of Kuopio, FinlandGoogle Scholar
  2. 2.
    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, FinlandGoogle Scholar
  3. 3.
    Madetoja E (2007) Novel process line approach for model-based optimization in papermaking—sensitivity and uncertainty analysis. PhD thesis, University of Kuopio, FinlandGoogle Scholar
  4. 4.
    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): 202–209CrossRefGoogle Scholar
  5. 5.
    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): 765–783MATHGoogle Scholar
  6. 6.
    Aidun CK, Clausen JR (2010) Lattice-Boltzmann method for complex flows. Annu Rev Fluid Mech 42: 439–472ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Qi D (2006) Direct simulations of flexible cylindrical fiber suspensions in finite Reynolds number flows. J Chem Phys 125: 114901ADSCrossRefGoogle Scholar
  8. 8.
    Tornberg A-K, Shelley MJ (2004) Simulating the dynamics and interactions of flexible fibres in Stokes flows. J Comput Phys 196: 8–40MATHADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Batchelor GK (1970) Slender-body theory for particles of arbitrary cross-section in Stokes flow. J Fluid Mech 44(3): 419–440MATHADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    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: 405–421CrossRefGoogle Scholar
  11. 11.
    Fan X, Phan-Thien N, Zheng R (1998) A direct simulation of fibre suspensions. J Non-Newton Fluid Mech 74: 113–135MATHCrossRefGoogle Scholar
  12. 12.
    Tornberg A-K, Gustavsson K (2006) A numerical method for simulations of rigid fiber suspensions. J Comput Phys 215(1): 172–196MATHADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Yamamoto S, Matsuoka T (1995) Dynamic simulation of fiber suspensions in shear flow. J Chem Phys 102: 2254–2260ADSCrossRefGoogle Scholar
  14. 14.
    Yamamoto S, Matsuoka T (1996) Dynamic simulation of microstructure and rheology of fiber suspensions. Polym Eng Sci 36(19): 2396–2403CrossRefGoogle Scholar
  15. 15.
    Skjetne P, Ross RF, Klingenberg DJ (1997) Simulation of single fiber dynamics. J Chem Phys 107(6): 2108–2121ADSCrossRefGoogle Scholar
  16. 16.
    Joung CG, Phan-Thien N, Fan XJ (2001) Direct simulation of flexible fibers. J Non-Newton Fluid Mech 99: 1–36MATHCrossRefGoogle Scholar
  17. 17.
    Joung CG, Phan-Thien N, Fan XJ (2002) Viscosity of curved fibers in suspensions. J Non-Newton Fluid Mech 102: 1–17MATHCrossRefGoogle Scholar
  18. 18.
    Joung CG (2003) Direct simulation studies of suspended particles and fibre-filled suspensions. PhD thesis, University of Sydney, AustraliaGoogle Scholar
  19. 19.
    Jayageeth C, Sharma VI, Singh A (2009) Dynamics of short fiber suspensions in bounded shear flow. Int J Multip Flow 35: 261–269CrossRefGoogle Scholar
  20. 20.
    Brady JF, Bossis G (1988) Stokesian dynamics. Annu Rev Fluid Mech 20: 111–157ADSCrossRefGoogle Scholar
  21. 21.
    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: 411–442MATHADSCrossRefGoogle Scholar
  22. 22.
    Claeys IL, Brady JF (1993) Suspensions of prolate spheroids in Stokes-flow. 2. Statistically homogeneous dispersions. J Fluid Mech 251: 443–477ADSCrossRefGoogle Scholar
  23. 23.
    Ross RF, Klingenberg DJ (1997) Dynamic simulation of flexible fibers composed of linked rigid bodies. J Chem Phys 106(7): 2949–2960ADSCrossRefGoogle Scholar
  24. 24.
    Schmid CF, Klingenberg DJ (2000) Mechanical flocculation in flowing fiber suspensions. Phys Rev Lett 84: 290–293ADSCrossRefGoogle Scholar
  25. 25.
    Schmid CF, Switzer LH, Klingenberg DJ (2000) Simulations of fiber flocculation: Effects of fiber properties and interfiber friction. J Rheol 44: 781–809ADSCrossRefGoogle Scholar
  26. 26.
    Switzer LH, Klingenberg DJ (2003) Rheology of sheared flexible fiber suspensions via fiber-level simulations. J Rheol 47(3): 759–778ADSCrossRefGoogle Scholar
  27. 27.
    Switzer LH, Klingenberg DJ (2003) Simulations of fiber floc dispersion in linear flow fields. Nord Pulp Pap Res J 18(2): 141–144CrossRefGoogle Scholar
  28. 28.
    Switzer LH, Klingenberg DJ (2004) Flocculation in simulations of sheared fiber suspensions. Int J Multip Flow 30: 67–87MATHCrossRefGoogle Scholar
  29. 29.
    Kim S, Karrila SJ (1991) Microhydrodynamics: principles and selected applications. Butterworth-Heinemann, Stoneham, MAGoogle Scholar
  30. 30.
    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: 337–347MATHCrossRefGoogle Scholar
  31. 31.
    Soszynski RM, Kerekes RJ (1988) Elastic interlocking of nylon fibers suspended in liquid. Nord Pulp Pap Res J 3: 172–184CrossRefGoogle Scholar
  32. 32.
    Sundararajakumar RR, Koch DL (1997) Structures and properties of sheared fiber suspensions with mechanical contacts. J Non-Newton Fluid Mech 73: 205–239CrossRefGoogle Scholar
  33. 33.
    Joseph G, Zenit R, Hunt M, Rosenwinkel A (2001) Particle-wall collisions in a viscous fluid. J Fluid Mech 433: 329–346MATHADSGoogle Scholar
  34. 34.
    Lindström SB, Uesaka T (2007) Simulation of the motion of flexible fibres in viscous fluid flow. Phys Fluids 19: 113307ADSCrossRefGoogle Scholar
  35. 35.
    Lindström SB, Uesaka T (2008) Simulation of semidilute suspensions of non-Brownian fibres in shear flow. J Chem Phys 128: 024901ADSCrossRefGoogle Scholar
  36. 36.
    Lindström SB (2008) Modelling and simulation of paper structure development. PhD thesis, Mid Sweden University, Sundsvall, SwedenGoogle Scholar
  37. 37.
    Lindström SB, Uesaka T (2009) A numerical investigation of the rheology of sheared fibre suspensions. Phys Fluids 21: 083301ADSCrossRefGoogle Scholar
  38. 38.
    Weinane E, Liu J-G (1996) Essentially compact schemes for unsteady viscous incompressible flows. J Comput Phys 126: 122–138MathSciNetCrossRefGoogle Scholar
  39. 39.
    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: 57–82MathSciNetCrossRefGoogle Scholar
  40. 40.
    Switzer LH, Klingenberg DJ, Scott CT (2004) Handsheet formation and mechanical testing via fiber-level simulations. Nord Pulp Pap Res J 19: 434–439CrossRefGoogle Scholar
  41. 41.
    Miettinen PPJ, Ketoja JA, Klingenberg DJ (2007) Simulated strength of wet fibre networks. Int J Pulp Pap Sci 33(4): 198–205Google Scholar
  42. 42.
    Miettinen PPJ, Ketoja JA (2008) Simulation of triaxial deformation of wet fiber networks. Nord Pulp Pap Res J 23(3): 264–271CrossRefGoogle Scholar
  43. 43.
    Lindström SB, Uesaka T (2008) Particle-level simulation of forming of the fibre network in papermaking. Int J Eng Sci 46: 858–876CrossRefGoogle Scholar
  44. 44.
    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 207–245Google Scholar
  45. 45.
    Kulachenko A, Uesaka T, Lindström SB (2008) Reinventing mechanics of fibre networks. In: Progress in paper physics seminar. Espoo, Finland, pp 185–187, 193Google Scholar
  46. 46.
    Kulachenko A, Lindström SB, Uesaka T (2009) Strength of wet fibre networks—size scaling. In: Proceedings of papermaking research symposium, FinlandGoogle Scholar
  47. 47.
    Folgar F, Tucker C III (1984) Orientation behaviour of fibers in concentrated suspensions. J Reinf Plast Compos 3(2): 98–119CrossRefGoogle Scholar
  48. 48.
    Advani S, Tucker C III (1987) The use of tensors to describe and predict fiber orientation in short fibre composites. J Rheol 31(8): 751–784ADSCrossRefGoogle Scholar
  49. 49.
    Olson JA, Kerekes RJ (1998) The motion of fibres in turbulent flow. J Fluid Mech 377: 47–64MATHADSCrossRefGoogle Scholar
  50. 50.
    Petrie C (1999) The rheology of fibre suspensions. J Non-Newton Fluid Mech 87: 369–402MATHCrossRefGoogle Scholar
  51. 51.
    Krochak P, Olson J, Martinez D (2008) The orientation of semidilute rigid fiber suspensions in a linearly contracting channel. Phys Fluids 20: 073303ADSCrossRefGoogle Scholar
  52. 52.
    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): 113–136CrossRefGoogle Scholar
  53. 53.
    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): 197–211CrossRefGoogle Scholar
  54. 54.
    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: 51–66MATHCrossRefGoogle Scholar
  55. 55.
    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: 1354–1369MATHCrossRefGoogle Scholar
  56. 56.
    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: 676–688CrossRefGoogle Scholar
  57. 57.
    Shin M, Koch D (2005) Rotational and translational dispersion of fibres in isotropic turbulent flows. J Fluid Mech 540: 143–173MATHADSCrossRefGoogle Scholar
  58. 58.
    Jeffery GB (1923) The motion of ellipsoidal particles immersed in a viscous fluid. Proc Roy Soc A 102: 161–179MATHADSGoogle Scholar
  59. 59.
    Mortensen P, Andersson H, Gillissen J, Boersma BJ (2008) Dynamics of prolate ellipsoidal particles in turbulent channel flow. Phys Fluids 20: 093302ADSCrossRefGoogle Scholar
  60. 60.
    Olson J (2001) The motion of fibres in turbulent flow, stochastic simulation of isotropic homogenous turbulence. Int J Multip Flow 27: 2083–2103MATHCrossRefGoogle Scholar
  61. 61.
    Schiek R, Shaqfeh E (1995) A nonlocal theory for stress in bound, Brownian suspensions of slender, rigid fibres. J Fluid Mech 296: 271–324MATHADSMathSciNetCrossRefGoogle Scholar
  62. 62.
    Parsheh M, Brown M, Aidun C (2005) On the orientation of stiff fibres suspended in turbulent flow in planar contraction. J Fluid Mech 545: 245–269MATHADSCrossRefGoogle Scholar
  63. 63.
    Hyensjö M (2008) Fibre orientation modelling applied to contracting flows related to papermaking. PhD thesis, Royal Institute of Technology, StockholmGoogle Scholar
  64. 64.
    Eloranta H (2005) Fluid mechanics of the papermaking machine headbox—instabilities and disturbances in the slice chamber. PhD thesis, Tampere University of TechnologyGoogle Scholar
  65. 65.
    Olson J (2002) Analytic estimate of the fibre orientation distribution in a headbox flow. Nord Pulp Pap Res J 17(3): 302–306CrossRefGoogle Scholar
  66. 66.
    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, FinlandGoogle Scholar
  67. 67.
    Mason SG (1954) Fibre motion and floccation. Pulp Pap Mag Canada 55(13): 96–102Google Scholar
  68. 68.
    Karema H, Salmela J, Tukiainen M, Lepomäki H (2001) Prediction of paper formation by fluidisation and reflocculation experiments’. In: 12th Fund research symposium, pp 559–589Google Scholar
  69. 69.
    Kerekes RJ (1983) Pulp floc behavior in entry flow to constrictions. Tappi J 66(1): 88–91Google Scholar
  70. 70.
    Steen M (1990) Turbulence and flocculation in fibre suspensions. PhD thesis, University of TrondheimGoogle Scholar
  71. 71.
    Ramkrishna D (2000) Population balances—theory and applications to particulate systems in engineering. Academic Press, San DiegoGoogle Scholar
  72. 72.
    ANSYS CFX-11.0 Electronical manualGoogle Scholar
  73. 73.
    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)Google Scholar
  74. 74.
    Hämäläinen J (1993) Mathematical modeling and simulation of fluid flows in the headbox of paper machines. PhD thesis, University of JyväskyläGoogle Scholar
  75. 75.
    Hämäläinen J, Tarvainen P, Aspholm P (2005) HOCS FIBRE—new tool for optimized fibre orientation angles. In: 91st annual meeting PAPTAC, CD proceedingsGoogle Scholar
  76. 76.
    Jäsberg A (2007) Flow behaviour of fibre suspension in straight pipes: new experimental techniques and multiphase modeling. PhD thesis, University of Jyväskylä, FinlandGoogle Scholar
  77. 77.
    Hammarström D (2004) A model for simulation of fiber suspension flows. Licentiate thesis, Royal Institute of Technology, Stockholm, SwedenGoogle Scholar
  78. 78.
    Niklas M, Asendrych D (2006) Modelling of fluid flow with complex rheology. Syst J Transdiscipl Syst Sci 11: 63–73Google Scholar
  79. 79.
    Kondora G, Asendrych D (2009) Flow simulation in a disc refiner. In: Proceedings of 14th conference on Model fluid flows, BudapestGoogle Scholar
  80. 80.
    Ventura C, Blanco A, Negro C, Ferreira P, Garcia F, Rasteiro M (2007) Modeling pulp fiber suspension rheology. Tappi J 6(7): 17–23Google Scholar
  81. 81.
    Ventura C, Garcia F, Ferreira P, Rasteiro M (2008) Flow dynamics of pulp fiber suspensions. Tappi J 7(8): 20–26Google Scholar
  82. 82.
    Wikström T (2002) Flow and rheology of pulp suspensions at medium consistency. PhD thesis, Chalmers University of Technology, SwedenGoogle Scholar
  83. 83.
    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, FinlandGoogle Scholar
  84. 84.
    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, BerlinGoogle Scholar
  85. 85.
    Hämäläinen J, Mäkinen R, Tarvainen P (2000) Optimal design of paper machine headboxes. Int J Numer Methods Fluids 34: 685–700MATHCrossRefGoogle Scholar
  86. 86.
    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): 265–281MATHCrossRefGoogle Scholar
  87. 87.
    Toivanen J, Hämäläinen J, Miettinen K, Tarvainen P (2003) Designing paper machine headbox using GA. Mater Manuf Process 18(3): 533–541CrossRefGoogle Scholar
  88. 88.
    Hämäläinen J, Tarvainen P (2000) CFD-based shape and control optimization applied to a paper machine headbox. In: 86th annual meeting PAPTAC, pp A99–A102Google Scholar
  89. 89.
    Hämäläinen J, Tarvainen P (2002) CFD-optimized headbox flows. Pulp Pap Can 103: 39–41Google Scholar
  90. 90.
    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)Google Scholar
  91. 91.
    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 ColumbiaGoogle Scholar
  92. 92.
    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, ChinaGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • J. Hämäläinen
    • 1
  • S. B. Lindström
    • 2
  • T. Hämäläinen
    • 3
  • H. Niskanen
    • 3
  1. 1.Centre of Computational Engineering and Integrated Design (CEID), Department of Mathematics and PhysicsLappeenranta University of TechnologyLappeenrantaFinland
  2. 2.Fibre and Polymer TechnologyRoyal Institute of TechnologyStockholmSweden
  3. 3.Department of Physics and MathematicsUniversity of Eastern FinlandKuopioFinland

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