Modeling Rheology

Materials having no memory can be described by an instantaneous relationship between the shear rate in a general flow and the stress. The shear rate is evaluated through the second invariant of the rate of deformation tensor, or strain rate tensor, which describes the rate of change of deformation. These are the Generalized Newtonian materials. Simcenter STAR-CCM+ models these materials under the Material Properties node for the fluid, using the options Dynamic Viscosity > Carreau-Yasuda, Cross Fluid, or Power Law.

Materials with memory retain deformation even after the deforming force stops, and only gradually resume their initial shape. Materials such as polymers and rubber often exhibit memory effects. In those cases, the shear stress tensor is the sum of a solvent component and a viscoelastic component. Simcenter STAR-CCM+ models the solvent component as a Generalized Newtonian material, using the Dynamic Viscosity property mentioned above. It models the viscoelastic component as the sum of 1 to 8 modes. Each mode provides a simplified or partial model of the viscoelastic behavior and obeys one of the following differential constitutive equations:

Each viscoelastic mode is coupled to the others, to improve convergence, but this improvement comes at a considerable computational and memory cost that increases rapidly with the number of modes. This is especially true in 3D simulations.

The only variables required by Generalized Newtonian flows are velocity and pressure. Additional variables, such as temperature, are optional.

Viscoelastic flows require additional variables to model the viscoelastic component:

The components of the Rate of Deformation tensor (the same for all modes), $D$ in Eqn. (707)
Components of the Extra-Stress tensor for each viscoelastic mode, $T^{p}$ in Eqn. (706), determined by the "well-established DEVSS" numerical technique [206]

Two important effects can be modelled by viscoelastic fluids that cannot be modeled with a Generalized Newtonian approach alone:

Normal stresses, which drive effects such as extrudate swelling
Elongational flow resistance (sometimes called “extensional viscosity”), which has a major impact in the vortex growth mechanism

Thixotropic fluids decrease in viscosity over time when flow is applied to a sample that has been previously at rest. Viscosity returns when the flow is discontinued. Flows of paper and pulp, polymer, food, pharmaceuticals, molten metals, unfired ceramics, paints, gels, inks, drilling muds, and unset concrete all exhibit thixotropic flow. Thixotropic fluids have an underlying structure, measured by

λ

, which breaks down reversibly (Eqn. (728)) or irreversibly (Eqn. (729)) under flow.

Flows of fiber-reinforced polymeric composites are used extensively in various polymer melt processes such as extrusion, injection, and compression molding. Generally, in a suspension of fiber, the flow field alters the orientation of the fibers; at the same time, the presence of fibers (and their mean orientation) changes the stress response of the suspension. Simcenter STAR-CCM+ can simulate fiber suspensions as either one-way and two-way coupled. In the one-way coupled simulation, the fiber orientation can be predicted based on the local flow field; however in this case, it is presumed that the presence of the fibers and their mean orientation do not alter the stress response of the suspension. By contrast, in a two-way coupled simulation, the fibers interact with the flow field variables and the flow field alters fiber orientation simultaneously. The two-way coupled simulation (with both fiber orientation prediction and fiber suspension rheology) is only available for generalized Newtonian fluids. For viscoelastic fluids, only one-way coupling (with only fiber orientation prediction) is available.

Simcenter STAR-CCM+ provides the Chemorheology model to simulate the behavior of fluids that change their rheological properties due to an underlying curing process. Curing is widely used in different industries for manufacturing of various products including rubber, composites, electronics and packaging. For example, raw rubber is a soft material with very weak mechanical properties. It is therefore cured in a mold—the process is called vulcanization. During the vulcanization process, a compound consisting of uncured rubber and curing agents fills the mold cavity within the injection cycle. The compound is then heated to a temperature at which the curing starts. At the curing stage, an irreversible reaction takes place producing a three-dimensional molecular network, and the weak material has been transformed into a strong elastic product.