Rheology Models Reference

Generalized Newtonian Model

The Generalized Newtonian model simulates the behavior of viscous non-Newtonian liquids. The type of Generalized Newtonian fluid can be selected through the Dynamic Viscosity property.

Viscoelastic Model

The Viscoelastic model expresses the behavior of the fluid as the sum of the behaviors of 1–8 modes. Each mode acts according to a rheology law specified for it under the Material Properties node of the model. In this way, you can model behaviors that are intermediate between those behaviors produced by individual models.

Viscoelastic Properties

Number of Modes

The number of nodes Viscoelastic mode n that appear under Liquid > [liquid] > Material Properties. See Viscoelastic Mode N.

Square-root conformal

When On, the viscous solver uses a square-root conformal formulation that is stable at high Weissenberg numbers. Not applicable to the vertical temperature shift factor in non-isothermal simulations. When Off, the solver uses the formulation based on the stress tensor. The default is Off. Applicable to both single- and multiphase flows. See Viscoelastic Fluids.

SUPG

The value for the Streamline-Upwind-Petrov-Galerkin advection stabilization term ${\tau }_{\text{SUPG}}$ in Eqn. (1040). The default value is 0.3.

DEVSS

The Discrete Elastic Viscous Split Stress stabilization factor for velocity-stress coupling, $\alpha$ in Eqn. (1024). The default value is 1.0.

Damping

The non-dimensional parameter for use with the PhanThien-Tanner/JS.-exp method. Set the parameter to a non-zero value to make convergence easier, at a cost of additional iterations. The default value is 0.0.

When the Square-root conformal property is On, a diffusion term is introduced to enhance numerical stabilization. The default of 0.0 works for most cases and meaning no numerical diffusion is added to the conformal formulation. Higher values assist convergence, but very high values, above 1.0, can result in lower accuracy.

Steady-State terms only

When On, this property removes the transient term $d\mathbf{T}/dt$ in the viscoelastic constitutive equation and introduces pseudo-equilibrium stresses. See Viscoelastic Fluids. This property is Off by default.

Thixotropic Model

The Thixotropic model simulates the behavior of fluids that reduce viscosity over time as shear increases and return to a more viscous state when the strain is removed. This model is supported for both single and multiphase flows.

Thixotropic Properties

Diffusion

Numerical diffusivity, a constant used as a coefficient for a Hermitian (self-adjoint) term that is added to a kinetic equation, Eqn. (728) or Eqn. (729), for stabilization. The default value is 0.0, in which there is no contribution to these equations.

SUPG

The value for the Streamline-Upwind-Petrov-Galerkin advection stabilization term, ${\beta }_{\text{SUPG}}$ in Eqn. (1039). The default value is 1.0.

Material Property Methods for Rheology

Dynamic Viscosity

You can obtain suitable parameter values for the following viscosity models by curve-fitting an experimentally determined flow curve, giving the viscosity as a function of shear-rate, to the viscosity functions given by Eqn. (738), Eqn. (739), and Eqn. (740).

Method	Corresponding Method Node
Constant	Constant Exposes Viscosity $\mu$ in Eqn. (696). The value is independent of shear rate and temperature. See Newtonian Fluids.
Field Function	Field Function Allows you to set a scalar field function to specify viscosity.
Newtonian Allows you to specify a viscosity that depends on temperature but is independent of shear rate. Temperature dependency is achieved by time-temperature superposition. For viscoelastic models, you specify here the viscosity that is shifted according to the selected temperature-shift law replacing the solvent viscosity ${\mu }_s$ in Eqn. (707). The shifted polymer viscosity and the relaxation time that you specify for the chosen viscoelastic model under Viscoelastic Mode N replace the polymer viscosity ${\mu }_0$ and the relaxation time $\lambda$ respectively in any constitutive equation. See Eqn. (742), Eqn. (743), and Eqn. (744). For generalized Newtonian fluids, the specified viscosity is shifted according to the selected temperature-shift law.	Newtonian Exposes Viscosity ${\mu }_{ref}$ in Eqn. (737). This option is available only when the Viscous Energy model is activated and the Horizontal and Vertical Temperature Shift Factors are set to any method available for Time-Temperature Superposition.
Non-Newtonian Generalized Carreau-Yasuda Fluid	Non-Newtonian Generalized Carreau-Yasuda Fluid Exposes the following terms from Eqn. (740): Power Constant $n$ a Parameter $a$ Zero Shear Viscosity ${\mu }_0$ Infinite Shear Viscosity ${\mu }_{\infty }$ Relaxation Time $\lambda$ Also provides the Viscosity Under-Relaxation Factor, which you can reduce to improve convergence.
Non-Newtonian Generalized Cross Fluid	Non-Newtonian Generalized Cross Fluid Exposes the following terms from Eqn. (739): Cross Rate Constant $m$ Zero Shear Viscosity ${\mu }_0$ Infinite Shear Viscosity ${\mu }_{\infty }$ Critical Shear Rate ${\dot{\gamma }}_c$
Non-Newtonian Generalized Power Law This method combines two rheology models: Herschel-Bulkley Power Law/Ostwald-de Waele	Generalized Power Law Exposes the following terms from Eqn. (738): Consistency Factor $k$ Power Law Exponent $n$ Yield Stress Threshold ${\tau }_0$ Yielding Viscosity ${\mu }_0$ Minimum Viscosity Limit and Maximum Viscosity Limit: minimum and maximum values allowed for ${\mu }_{}$ To obtain the Power Law/Ostwald de Waele viscosity function, set the yield stress ${\tau }_0=0$. See Eqn. (701).

Viscoelastic Mode N

You set the number of Viscoelastic Modes in the Viscoelastic model. Simcenter STAR-CCM+ adds this number of material property nodes. For each Viscoelastic Mode, choose the Method then set the properties within the corresponding method node.

Method	Corresponding Method Node
Oldroyd-B	Oldroyd-B Exposes Viscosity ${\mu }_0$ and Lambda $\lambda$ from Eqn. (711).
GiesekusLeonov	GiesekusLeonov Exposes Viscosity ${\mu }_0$, Lambda $\lambda$, and Alpha $\alpha$ from Eqn. (718).
PhanThien-Tanner/JS.-lin	PhanThien-Tanner/JS.-lin Exposes Viscosity ${\mu }_0$, Lambda $\lambda$, Epsilon $ϵ$, and Xi $\xi$ from Eqn. (714).
PhanThien-Tanner/JS.-exp	PhanThien-Tanner/JS.-exp Exposes Viscosity ${\mu }_0$, Lambda $\lambda$, Epsilon $ϵ$, and Xi $\xi$ from Eqn. (716).
Extended PomPom	Extended PomPom Exposes Viscosity ${\mu }_0$, Lambda $\lambda$, and Alpha $\alpha$ from Eqn. (720). Also Q and 1/eps $1/ϵ$ from Eqn. (721).
Rolie-Poly	Rolie-Poly Exposes Viscosity ${\mu }_0$, Lambda $\lambda$, and Rouse Relaxation Time ${\lambda }_R$ from Eqn. (723). Also exposes Beta $\beta$ and delta $\delta$ from Eqn. (724).

Structure Variable

Selects the model describing the time evolution of structure parameter $\lambda$, measuring the level of microstructure in the thixotropic phase.

Method	Corresponding Method Node
Generic Kinetic	Generic Kinetic Exposes kinetic rate constants $k_1$ and $k_2$ and model parameters $a$, $b$, $c$ and $d$ from Eqn. (728). This is the default.
Irreversible Structural Breakdown	Irreversible Structural Breakdown Exposes kinetic constant $k$, model parameters $e$ and $f$, and the steady state value of the structure parameter ${\lambda }_{ss}$ from Eqn. (729).

Thixotropic Factor

Selects the viscosity $\eta$ of the thixotropic phase.

Method	Corresponding Method Node
Power-Law	Power-Law Exposes exponent $n$ from Eqn. (730). This is the default.
Field Function	Field Function Used to specify a scalar field function.

Thixotropic Boundary Settings

Mass Flow Inlet, Velocity Inlet

Structure Variable Condition Specification

At inlets, flow can be specified as either initially fully developed or already thixotropic.

Method	Corresponding Physics Value Nodes
Structured condition At the inlet, the thixotropic fluid has a fully structured network, the Structure Variable $\lambda =1$.	None.
Fully-developed condition Used when conditions upstream and entrace effects are irrelevant, and only the region of fully-developed flow matters.	None.

Thixotropic Field Functions

Apparent Viscosity

The apparent viscosity as given by Eqn. (730). This value is defined at the cell center and can depend on time, shear rate, temperature, and structure variable $\lambda$.

Structure Variable

Structure parameter $\lambda$ in Eqn. (728) and Eqn. (729).