Direct numerical simulation of an individual fiber in an arbitrary flow field - an immersed boundary method
Journal article, 2009
An immersed boundary method for three-dimensional, time-dependent flows is presented in this work and applied to simulating the behaviour of an individual fibre in various flow regimes. The fibre is placed in a periodic box and has either a fixed position or is allowed to move freely (including translation and rotation) through the domain. The immersed boundary method is used to match the fluid velocity with the velocity of the interface of the fibre, by mirroring the velocity field along the normal of the local triangulated immersed boundary segment to guarantee that the fluid accurately takes into account the presence of an immersed body. As a result of the procedure, there is a fictitious velocity field inside the immersed boundary, mirroring the boundary layer. The method applied is second-order accurate for the drag on the fibre and is intended to be used for fully resolving the flow field around arbitrary moving bodies immersed in a fluid.
The immersed boundary method is employed on a selection of different fibre shapes, aiming at predicting the behaviour of real fibres in realistic flow situations. A grid refinement study and the study of the influence of the size of the periodic box used for the simulations are carried out. It is shown by grid refinement that the simulations performed here are truly DNS.
The force exerted by the fluid on a fibre is directly calculated by integrating the pressure and viscous forces over the objects immersed. The resulting coarse-grained drag and lift force functions can be employed calculations of fluid-fibre flows on a larger scale (e.g. Eulerian-Eulerian simulations of air-fibre flows).