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

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.