Non-Newtonian Fluids

For many industrial fluids, it is not sufficient to assume a linearly viscous fluid behavior due to their complex microstructure. These fluids exhibit non-Newtonian behavior.

Although any fluid with a viscosity that is not constant is considered non-Newtonian, not all non-Newtonian fluids behave in the same way—there are different types. The types that Simcenter STAR-CCM+ can model are described as follows:

Generalized Newtonian: A Generalized Newtonian fluid is the simplest mathematical description of a non-Newtonian fluid. The constant viscosity in Eqn. (696) is replaced by an apparent viscosity $μ = μ (\dot{γ}, T)$ that is a function of shear-rate and/or temperature.
Viscoplastic: Viscoplastic fluids fall within the same category as Generalized Newtonian fluids, but with the addition of a yield stress. Viscoplastic fluids only start to flow if the deformation exceeds a critical shear stress value.
The following diagram shows the shear stress as a function of shear rate for different types of fluids. A Newtonian fluid gives a straight line through the origin where the slope is given by the constant viscosity. For the shear-thinning (pseudoplastic) fluid, the shear stress gives a concave downward curve with increasing shear rate, which corresponds to a decrease in viscosity as the shear rate increases. The shear-thickening (dilatant) fluid shows the opposite behavior. The shear stress gives a concave upward curve with increasing shear rate, which corresponds to an increase in viscosity as the shear rate increases. The viscoplastic fluid, commonly termed Bingham plastic, must exceed the yield stress before it can move.
Viscoelastic: Viscoelastic fluids exhibit both viscous and elastic behavior when undergoing deformation. Their stresses not only depend on the current motion of the fluid, but also on the history of the motion. The deformation that the fluid experienced in the past influences the current stresses. In contrast to a purely elastic material, the influence of the past deformation decreases over time. This effect can be quantified by use of the so-called relaxation time.; Each viscoelastic model provides a constitutive equation which solves the full stress tensor $T (D)$ . Most complex fluids are slightly viscoelastic. However, if the shear viscosity is the most important attribute and elastic effects are small, they can often be treated as Generalized Newtonian fluids. Typical viscoelastic fluids are: polymer melts, rubbers, and bread dough. Weakly viscoelastic fluids include shampoos, paints, and polymer solutions.
Multiphase: Some multiphase fluids are non-Newtonian when the mixture viscosity depends on the volume fraction of the dispersed phase $μ = μ (ϕ)$ . Multiphase non-Newtonian fluids can be modeled with separate phases or as a single phase mixture (assuming that the volume fraction remains constant). These multiphase non-Newtonian fluids are often viscoplastic and include emulsions, suspensions, and biological fluids (blood, joint fluid).

The following table provides an overview of the available non-Newtonian fluids in Simcenter STAR-CCM+ along with their discretization methods and characteristics:


Approach	Discretization	Shear normal stresses	Turbulence
Generalized Newtonian	FV	No	Yes
Generalized Newtonian	FE	No	No
Viscoelastic	FE	Yes	No
Multiphase	FV	Yes	No

The finite element (FE) solver is tailored to solve viscoelastic models. Simulations that involve Generalized Newtonian fluids using the finite volume (FV) solver can make use of most of the turbulence models available to Newtonian fluids.