Using the Non-Newtonian Generalized Models

Using the Non-Newtonian Generalized Models in Turbulent Flows

The Non-Newtonian Generalized models are now available for turbulent flows; previously they were available for laminar flows only.

Note that this approach is not strictly valid, as the turbulence models have been designed for Newtonian fluids; the production at the wall is known to be different for non-Newtonian fluids. Also the turbulence models do not account for any viscoelasticity of the flow. However, in many cases, the results that you obtain from using the (incorrect) turbulence model can be better than the results that you would obtain by assuming a laminar flow.

If you use the Non-Newtonian Generalized models in a turbulent flow, you do so at your own risk.

Using the Non-Newtonian Models in Multiphase Flows

The Non-Newtonian Generalized models are available for multiphase flows. However, the following restrictions apply:

• The Non-Newtonian Generalized Cross Fluid model is not compatible with the Multiphase model.
• The dispersed phase cannot be specified as a Non-Newtonian fluid. Consequently, you cannot define any interphase interactions between Non-Newtonian phases (which have to be continuous).

Selecting a Non-Newtonian Model

The graph below shows a comparison of the models from [23]. The three-parameter Cross model and the four-parameter Carreau-Yasuda model both display good agreement with the experimental data for this shear-thinning material.

However, these models require you to provide the values of zero-shear and infinite shear at the Newtonian plateaus. In contrast, the two-parameter Power Law requires fewer inputs and has good agreement in the main-shear thinning (or shear thickening) zone but loses accuracy as the fluid approaches a Newtonian plateau.

These methods are available for the material property Dynamic Viscosity for both laminar and turbulent liquid flow. They can be used with single phase and multiphase flows. The coefficient properties for this function are set in the Properties window.

Non-Newtonian Generalized Power Law Properties

Non-Newtonian Generalized Power Law

This method comprises two rheology models into one:

• Hershel-Bulkley
• Power Law/Ostwald de Waele

Exposes the following terms from Eqn. (705):

• 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 ${\tau }_0=0$.

Non-Newtonian Generalized Cross Fluid Properties

Non-Newtonian Generalized Cross Fluid

Exposes the following terms from Eqn. (702):

• Cross Rate Constant $m$
• Zero Shear Viscosity ${\mu }_0$
• Infinite Shear Viscosity ${\mu }_{\infty }$
• Critical Shear Rate ${\dot{\gamma }}_c$

Non-Newtonian Generalized Carreau-Yasuda Fluid Properties

Non-Newtonian Generalized Carreau-Yasuda Fluid

Exposes the following terms from Eqn. (703):

• 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 enhance convergence.