Description and validation of a flexible fiber model, implemented in a general-purpose CFD code

A flexible fiber model  has been implemented in a general purpose open-source computational fluid dynamics code. The fibers are modeled as chains of cylindrical segments. Each segment is tracked individually and  their equations of motion account for the hydrodynamic forces and torques from the interaction with the fluid, the elastic bending and twisting torques, and the connectivity forces and moments that ensure the fiber integrity. The segment inertia is taken into account and a one-way coupling with the fluid phase is considered. The model is applied to the rotational motion of an isolated fiber in a low segment Reynolds number  shear flow. In the case of a stiff fiber, the computed period of rotation is in good agreement with the one computed using Jeffery's equation for an equivalent spheroid aspect ratio. A qualitative comparison is made with experimental data for flexible fibers. These results show that the implemented model can reproduce the known dynamical behavior of rigid and flexible fibers successfully.

[1]  H. Brenner,et al.  Particle motions in sheared suspensions , 1959 .

[2]  Jelena Andric Implementation of a flexible fiber model in a general purpose CFD code , 2012 .

[3]  J. Hämäläinen,et al.  Papermaking fibre-suspension flow simulations at multiple scales , 2011 .

[4]  F. Bretherton The motion of rigid particles in a shear flow at low Reynolds number , 1962, Journal of Fluid Mechanics.

[5]  R. G. Cox The motion of long slender bodies in a viscous fluid Part 1. General theory , 1970, Journal of Fluid Mechanics.

[6]  Andreas Wiegmann,et al.  Multiphase simulation of fiber suspension flows using immersed boundary methods , 2012 .

[7]  Dewei Qi Direct simulations of flexible cylindrical fiber suspensions in finite Reynolds number flows. , 2006, The Journal of chemical physics.

[8]  C. Aidun,et al.  Numerical study of rotational diffusion in sheared semidilute fibre suspension , 2011, Journal of Fluid Mechanics.

[9]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[10]  D. Klingenberg,et al.  Simulations of fiber flocculation: Effects of fiber properties and interfiber friction , 2000 .

[11]  D. Klingenberg,et al.  DYNAMIC SIMULATION OF FLEXIBLE FIBERS COMPOSED OF LINKED RIGID BODIES , 1997 .

[12]  S. G. Mason,et al.  Particle motions in sheared suspensions: IX. Spin and deformation of threadlike particles , 1959 .

[13]  R. G. Cox The motion of long slender bodies in a viscous fluid. Part 2. Shear flow , 1971, Journal of Fluid Mechanics.

[14]  D. Tritton,et al.  Physical Fluid Dynamics , 1977 .

[15]  G. B. Jeffery The motion of ellipsoidal particles immersed in a viscous fluid , 1922 .

[16]  M. Sommerfeld,et al.  Multiphase Flows with Droplets and Particles , 2011 .

[17]  Stefan B. Lindström,et al.  MODELLING AND SIMULATION OF PAPER STRUCTURE DEVELOPMENT , 2008 .

[18]  S. G. Mason,et al.  Particle motions in sheared suspensions: X. Orbits of flexible threadlike particles , 1959 .

[19]  Sangtae Kim,et al.  Microhydrodynamics: Principles and Selected Applications , 1991 .

[20]  Satoru Yamamoto,et al.  Dynamic simulation of fiber suspensions in shear flow , 1995 .