Direct simulations of flexible cylindrical fiber suspensions in finite Reynolds number flows

Abstract

Direct simulations of flexible cylindrical fiber suspensions in a finite Reynolds number flow are reported. The simulation method is based on a lattice Boltzmann equation and a flexible fiber model. A slender solid body is discretized into a chain of cylindrical segments contacting each other at the their ends through ball and socket joints that allow adjacent segments to rotate around the joints in three dimensional space. A constraint force is imposed at each joint. In general, motion and rotational matrices of each segment are functions of constraint forces. It is necessary to linearize the rotational matrices in forces and torques so that constraint forces could be solved using joint contacting conditions. Therefore, quaternion parameters as well as rotational matrix could be expanded in a power series of the length of time step up to a second order. A half leapfrog algorithm D. Fincham, [CCP5 Quarterly, 2, 6 (1981)] is modified to ensure the ball and socket joint conditions to be satisfied at each time step. The validation of the present flexible fiber method is tested by using a rigid particle method. It is shown that the computational results are consistent with the existing experimental and theoretical results at finite Reynolds number flows. With the present method, nonlinear inertial interactions between fluid and flexible filaments can be naturally studied. A few applications are included.

A novel Quaternion integration approach for describing the behaviour of non-spherical particles

“…In many other research papers, such as [1,4,15,24,30,33,35], the integration of a unit Quaternion is solved based on Taylor series expansion, and Eq. (30), or an equivalent form, is adopted.…”

Papermaking fibre-suspension flow simulations at multiple scales

“…The only property of the system that distinguishes it from a general large displacement fluid-structure interaction (FSI) problem is that fibres are slender. Although general methods for solving FSI problems are available [4][5][6], and it is worth mentioning that lattice-Boltzmann simulations have been used to simulate the motion of isolated fibres [7], general methods are costly from the point of computations. Most fibre-suspension models thus aim to reduce computational requirements by exploiting the slenderness of fibres.…”

Simulation of swimming of a flexible filament using the generalized lattice-spring lattice-Boltzmann method

“…To further validate the GLLM, the sedimentation of a flexible fiber in fluid by the gravity is simulated by using two different methods: one is the present method and the other is the lattice Boltzmann flexible particle method (LBFPM), which was developed, validated and applied to simulate the flexible fiber suspensions and flexible wings (Qi, 2006;Qi et al, 2010;Liu et al, 2011) The simulation is performed in a box of ðN x ; N y ; N z Þ ¼ ð2L; 4L; 1:1LÞ¼(100, 400, 100) where L ¼90 is the length of the fiber. The walls are set at both the ends of the z-direction and a periodic condition is imposed in the x-and y-directions.…”

“…Qi (2006) used the lattice Boltzmann method to attack the Navier-Stokes equation while a solid body was discretized as a chain of rigid segments contacting each other at the their ends through ball and socket joints that allow adjacent segments to be bent. Buxton et al (2005) used the lattice Boltzmann method to solve the Navier-Stokes equations and a lattice spring method to model the deformation of a flexible body.…”