Modelling the Dynamics of Flexible and Rigid Fibres

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A particle-level simulation technique has been developed for modelling fibre suspension flow in a converging channel of a papermachine headbox. The fibre model is represented by a chain of elements connected together. The model was verified by the simulation of rigid fibre dynamics in a simple shear flow. The period of rotation was found to be in a very good agreement with theory and reference data. The model was then employed to simulate fibre motion in a converging channel of a papermachine headbox. Fibre suspension motion was resolved using two-step procedure. Velocity field was calculated by means of a commercial CFD code ANSYS Fluent with RSM turbulence model applied and used as an input to the in-house code allowing to simulate fibre dynamics. Results of the calculations were used to construct the fibre orientation probability distribution (FOPD) which was found to be consistent with available experimental data.

Batchelor G. K., 1962. Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech., 44, 419-440. DOI: 1017/S002211207000191X.

Brenner H., 1964. The Stokes resistance of an arbitrary particle-IV Arbitrary fields of flow. J. Fluid Mech., 19, 702-727. DOI: 10.1016/0009-2509(64)85084-3.

Bretherton F.P., 1962. The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech., 14, 284-304. DOI: 10.1017/S002211206200124X.

Goldsmith H.L. and Mason S.G., 1967. The microrheology of dispersions. In: Eirich F.R. (Ed.). Rheology: Theoryand applications. New York, Vol. 4, 85-250.

Jeffery G.B., 1922. The motion of ellipsoidal particles immersed in a viscous flow. Proc. R. Soc. A, 102, 161-179.

Jetsu P., Kellomaäki M., Karema H., Salmela J., Lappalainen T., Piirto M., 2001. Coherent structures of suspension flow and their inheritance in paper. In: 12th Fundamental Research Symposium, Oxford, UK, September 2001.

Leppanen T., 2007. Effect of fiber orientation on cockling of paper. PhD Thesis. University of Kuopio, Finland.

Lindström S.B., Uesaka T., 2008. Particle-level simulation of forming of the fibre net- work in papermaking. Int. J. Eng. Sci., 46, 858-876. DOI: 10.1016/j.ijengsci.2008.03.008.

Morsi S.A., Alexander A.J., 1972. An investigation of particle trajectories in two phase flow systems. J. FluidMech., 55, 193-208. DOI: 10.1017/S0022112072001806.

Niskanen H., Eloranta H., Hämälainen J.P., 2011. On the orientation of flexible fibres in a contracting channel flow. Int. J. Multiphase Flow, 37, 336-345. DOI: 10.1016/j.ijmultiphaseflow.2010.11.006.

Olson J.A., Frigaard I., Chan C., Hämälainen J.P., 2004. Fiber orientation modelling applied to contracting flows related to papermaking: The one-dimensional headbox. Int. J. Multiphase Flow, 30, 51-66. DOI: 10.1016/j.ijmultiphaseflow.2003.10.006.

Putkiranta M., Eloranta H., Pärssinen T., Saarenrinne P., 2009. Evolution of the fibre orientation distribution in streamwise elongational flow. In: Madetoja E., Niskanen H., Hämälainen J.P. (Eds.), Papermaking ResearchSymposium. Kuopio, Finland, 1-4 June, 2009.

Ross R.F., Klingenberg D.J., 1997. Dynamic simulation of flexible fibers composed of linked rigid bodies. J. Chem. Phys., 106, 2949-2960. DOI: 10.1063/1.473067.

Sasic S., Almstedt A.E., 2010. Dynamics of fibres in a turbulent flow field - A Novel particle-level simulation technique. Int. J. Heat Fluid Flow, 31, 1058-1064. DOI: 10.1016/j.ijheatfluidflow.2010.05.009.

Schmid C.F., Klingenberg D.J., Scott C.T., 2000. Simulation of fibre flocculation: Effect of fibre properties and inter-fibre friction. J. Rheol., 44, 781-809. DOI: 10.1122/1.551116.

Ullmar M., 1998. On fibre orientation mechanisms in a headbox nozzle. PhD Thesis. Royal Institute of Technology, Stockholm, Sweden.

Yamamoto S., Matsuoka T., 1993. A method for dynamic simulation of rigid and flexible fibers in a flow field. J. Chem. Phys., 98, 644-650. DOI: 10.1063/1.464607.

Yamamoto S., Matsuoka T., 1994. Viscosity of dilute suspension of rodlike particles: A numerical simulation method. J. Chem. Phys., 100, 3317-3324. DOI: 10.1063/1.466423.

Yamamoto S., Matsuoka T., 1995. Dynamics simulation of fiber suspension in shear flow. J. Chem. Phys., 102, 2254-2260. DOI: 10.1063/1.468746.

Yamamoto S., Matsuoka T., 1999. Dynamics simulation of rod-like and plat-like particle dispersed system. Comp. Mat. Sci., 102, 169-176. DOI: 10.1016/S0927-0256(98)00103-7.

Chemical and Process Engineering

The Journal of Committee of Chemical and Process of Polish Academy of Sciences

Journal Information

IMPACT FACTOR 2016: 0.971

CiteScore 2016: 1.03

SCImago Journal Rank (SJR) 2016: 0.395
Source Normalized Impact per Paper (SNIP) 2016: 0.873

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