Direct numerical simulations of suspensions of spherical particles in a viscoelastic fluid in sliding tri-periodic domains
Wook Ryol Hwang, Martien A. Hulsen, Heh Han Meijer, TH Kwon · TU/e Research Portal · 2004
We present a new finite element scheme for direct numerical simulations of suspensions of spherical particles formulated with a viscoelastic (Oldroyd-B) fluid in simple shear flow in a well-defined tri-periodic computational domain, which is an extension of the authors previous 2-D work [J. Comput. Phys. 194 (2004) 742; J. Non-Newt. Fluid Mech. (in press)]. The sliding tri-periodic domain concept, through which suspensions in the unbounded domain can be treated by a representative particulate problem in a unit cell, has been combined with the DEVSS/DG finite element scheme, by introducing the sliding tri-periodic cell constraint. The force-free torque-free rigid body motion of the spherical particle is described by the rigid-shell description and implemented by Lagrangian multipliers only on the particle boundary, which allows general treatments for boundary-crossing particles. In our formulation, the bulk stress is obtained by simple boundary integrals. Through the several example problems, we discuss the rheological properties (e.g., the bulk shear viscosity, the first/second normal stress coefficients) and the flow-induced microstructural development in suspensions of spherical particles formulated with a viscoelastic fluid