Numerical modeling of air-fiber flows
The dynamics of fiber suspensions are of great importance in applications such as the dry-forming process of pulp mats for use in hygiene products. In this forming process, fibers are transported in flowing air. The fibers interact with the fluid, and may interact with each other and interlock in flocs. The characteristics of the suspension structure are essential for the design and optimization of the forming process, and for improving the quality of the final products. Particularly, it is desired to achieve a uniform fiber distribution in the pulp mats. Thus, it is of high interest to develop tools, which can be used to perform comprehensive studies of the complex phenomenon of fiber suspension flows.
This work is concerned with numerical analysis of fiber suspensions, related to the mat-forming process. For that purpose, a particle-level fiber model has been implemented into an open source computational fluid dynamics (CFD) code. A fiber is modeled as a chain of rigid cylindrical segments. The segments interact with the flow through hydrodynamic drag forces, and may interact with each other through short-range attractive forces. The segments are tracked individually using Lagrangian particle tracking (LPT). The implemented model comprises two alternatives, the flexible and the rigid fiber model, respectively.
The equations of motion of a flexible fiber represent the application of Euler's second laws for rigid body motion for the fiber segments. The flexible fiber model takes into account all the degrees of freedom necessary to realistically reproduce the fiber dynamics. Connectivity forces act between the adjacent fiber segments to ensure the fiber integrity. The rigid fiber model keeps the relative orientation between the segments fixed. The equations of motion are formulated for the fiber as a whole, while the hydrodynamic contributions are taken into account from the individual segments. The fiber inertia is taken into account in both alternatives of the model. The fiber model has been coupled with imposed flow fields, or with flow fields computed by the CFD solvers.
The behavior of the implemented model is compared with analytical and experimental results available in the literature. The simulation results show that the model correctly predicts the dynamics of isolated rigid and flexible fibers in creeping shear flow.
The model is used to study the dynamics of flexible and rigid fibers in high Reynolds number flows and in geometries that are representative for the mat-forming process. The effects of fiber properties, such as fiber inertia and fiber length are analyzed.
Simulations are carried out to investigate the rheology of suspensions of flexible and curved fibers in creeping shear flow of a Newtonian fluid. The effects of fiber flexibility and fiber curvature on the specific viscosity and the normal stress differences are examined.
Finally, aggregation of rod-like fibers is investigated in a turbulent flow of an asymmetric planar diffuser. The influences of the average flow gradient, the fiber inertia and the turbulence dispersion on the aggregation rate are analyzed. The study identifies a darting fiber motion as a mechanism that significantly enhances fiber collisions and aggregation.