Numerical study of flows of complex fluids between eccentric cylinders using transformation functions

Abstract

SUMMARYIn this paper, we investigate uid ows between eccentric cylinders by means of two stream-tube analyses. The ÿrst method considers a one-to-one global transformation function that allows the physical domain to be transformed into a mapped domain, used as computational domain, that involves concentric streamlines. The second approach uses local transformations and domain decomposition techniques to deal with mixed ow regimes. Both formulations are particularly adapted for handling time-dependent constitutive equations, since particle-tracking problems are avoided. Mass conservation is veriÿed in both formulations and the relevant numerical procedure can be carried out using simple meshes built on the mapped streamlines. Fluids obeying anelastic and viscoelastic constitutive equations are considered in the calculations. The numerical results are consistent with those in the literature for the ow rates tested. Application of the method to the K-BKZ memory-integral constitutive equation highlights signiÿcant di erences between the model predictions and those provided by more simple rheological models.

A fully deterministic micro–macro simulation of complex flows involving reversible network fluid models

“…We can notice that by adding Eqs. (7) and (10) and integrating over the conformation space Ω p we obtain the fiber conservation balance (12).…”

“…In order to facilitate the coupling between the microscopic solver and the macroscopic one, we propose the use of the stream tube method (deeply described in [6,[10][11][12][13][14]23,24]) for solving the resulting macroscopic anisotropic Stokes problem. This technique is based on a domain transformation that maps the physical domain into a simple reference domain in which the streamlines are parallel to one of the coordinate axis.…”