A Direct Numerical Simulation Method for Flow of Brownian Fiber Suspensions in Complex Geometries

Abstract

A two-way coupled, direct simulation technique is proposed for the numerical solution of Brownian fiber suspension flows in complex geometries. The isothermal, incompressible, non-Newtonian Navier-Stokes equations are solved in an Eulerian framework using the finite volume method for the spatial discretization and a third-order Runge-Kutta scheme for the time integration. A conservative immersed boundary method is employed for the treatment of complex geometries. The fibers are treated in a Lagrangian manner. Therefore, complex geometries are retrieved naturally. The conformation of fibers is obtained by solving Jeffery's equation for an ensemble of rigid fibers. Brownian motion is simulated by a three-dimensional Wiener process. The proposed method does not require a moment closure model. The simulator is validated in a plane channel flow and a cylinder flow at the limit of extremely strong Brownian motion. Then, we use it to solve four problems, that is, a circular cylinder in a cross flow, the flow in a channel with periodic constrictions, the flow in a 4:1 contraction channel and the flow in a rectangular pipe with cylindrical constrictions.

Keywords:

• Complex geometry
• direct numerical simulation
• fiber suspension
• Monte-Carlo method
• stochastic simulation

Acknowledgments

This project is funded by the International Graduate School of Science and Engineering (IGSSE) at Technische Universität München. We thank Eric Shaqfeh for his interest in this investigation.

Notes

Current affiliation for A. Moosaie: Department of Mechanical Engineering, Yasouj University, Yasouj, Iran.