Numerical simulation of buckling and asymmetric behavior of flexible filament using temporal second-order immersed boundary method
Authors: Kanchan Mithun , Maniyeri Ranjith 
Published: September 2019

Purpose
The purpose of this paper is to perform two-dimensional numerical simulation involving fluid-structure interaction of flexible filament. The filament is tethered to the bottom of a rectangular channel with oscillating fluid flow inlet conditions at low Reynolds number. The simulations are performed using a temporal second-order finite volume-based immersed boundary method (IBM). Further, to understand the relation between different aspect ratios i.e. ratio of filament length to channel height (Len/H) and fixed channel geometry ratio, i.e. ratio of channel height to channel length (H/Lc) on mixing and pumping capabilities.

Design/methodology/approach
The discretization of governing continuity and Navier–Stokes equation is done by finite-volume method on a staggered Cartesian grid. SIMPLE algorithm is used to solve fluid velocity and pressure terms. Two cases of oscillatory flow conditions are used with the flexible filament tethered at the center of bottom channel wall. The first case is sinusoidal oscillatory flow with phase shift (SOFPS) and second case is sinusoidal oscillatory flow without phase shift (SOF). The simulation results are validated with filament dynamics studies of previous researchers. Further, parametric analysis is carried to study the effect of filament length (aspect ratio), filament bending rigidity and Reynolds number on the complex deformation and behavior of flexible filament interacting with nearby oscillating fluid motion.

Findings
It is found that selection of right filament length and bending rigidity is crucial for fluid mixing scenarios. The phase shift in fluid motion is also found to critically effect filament displacement dynamics, especially for rigid filaments. Aspect ratio, suitable for mixing applications is dependent on channel geometry ratio. Symmetric deformation is observed for filaments subjected to SOFPS condition irrespective of bending rigidity, whereas medium and low rigidity filaments placed in SOF condition show severe asymmetric behavior. Two key findings of this study are: symmetric filament conformity without appreciable bending produces sweeping motion in fluid flow, which is highly suited for mixing application; and asymmetric behavior shown by the filament depicts antiplectic metachronism commonly found in beating cilia. As a result, it is possible to pin point the type of fluid motion governing fluid mixing and fluid pumping. The developed computational model can, thus, successfully demonstrate filament-fluid interaction for a wide variety of similar problems.

Originality/value
The present study uses a temporal second-order finite volume-based IBM to examine flexible filament dynamics for various applications such as fluid mixing. Also, it highlights the relationship between channel geometry ratio and filament aspect ratio and its effect on filament sweep patterns. The study further reports the effect of filament displacement dynamics with or without phase shift for inlet oscillating fluid flow condition.