Numerical investigation on flapping of a flexible filament in a viscoelastic fluid flow

The flapping of a flexible filament in a uniform incoming flow of viscoelastic fluid of polymeric solution was numerically investigated. This paper aims at examining the effects of fluid elasticity on the filament flapping behavior by a comparison with its counterpart in the Newtonian flow. Specifically, the FENE-MCR model was used as the constitutive equation for the viscoelastic fluid. The simulations of fluid flow were based on the lattice Boltzmann method to solve the Navier-Stokes (N-S) equations, the finite difference method to solve the constitutive equation of the polymer stress, the finite element method to solve the motion equation of the filament, and a penalty immersed boundary method to deal with the fluid-structure interaction. From the numerical results obtained, it was found that for a relatively weak fluid elasticity of We<20, the critical mass ratio of the filament to the fluid increases dramatically for the transition from a steady state to a periodically flapping state. However, for a stronger elasticity of We>20, increasing We number leads to a tendency of the critical mass ratio to be an approximate value of ～0.43. Moreover, it was demonstrated that increasing We number is also commensurate with the decrease of the time-averaged drag coefficient, the flapping amplitude, and the flapping frequency of the flexible filament. The above-mentioned facts indicate that enhancing the fluid elasticity has the increasing suppressing effects on the filament flapping behaviors.