### 1.2.13. Non-Newtonian Flow

Some fluids are non-Newtonian; that is, they do not obey the simple linear relationship between shear stress and shear strain rate. Many practical fluids fall into this class, and their behavior is generally well understood and described using various mathematical models.

ANSYS CFX has several models for calculating viscosity based on shear strain rate. These models are listed in Table 1.2: Non-Newtonian Models where is the dynamic viscosity, and is the shear strain rate.

Table 1.2: Non-Newtonian Models

Model | Description | Settings
--- | --- | ---

Bingham

This is a model for viscoplastic fluids.

Examples of viscoplastic fluids include tomato paste and tooth paste. A few electro-rheological fluids can be modeled as Bingham fluids with the yield stress as a function of the intensity of the electric field, or the electric current.

Note that ANSYS CFX supports only a single-valued yield stress. The yield stress may be evaluated as a CEL expression with, for instance, values that vary over time or iteration. Yield stress values that vary spatially are not supported.

Yield Stress:

Viscosity Consistency:
Minimum Shear Strain Rate
Maximum Shear Strain Rate
Bird Carreau | This is a model intended for shear-thinning fluids. The model reverts to a Newtonian behavior of for , or . Examples of shear-thinning fluids include applesauce, banana puree, and orange juice concentrate. | Low Shear Viscosity:
High Shear Viscosity:
Time Constant:
Power Law Index:
Carreau Yasuda | This is a generalization of Carreau's original model. | Low Shear Viscosity:
High Shear Viscosity:
Time Constant:
Power Law Index:
Yasuda Exponent:
Casson | This model is a variation of the Bingham model for viscoplastic fluids with a square root/quadratic dependency. | Yield Stress:
Viscosity Consistency:
Minimum Shear Strain Rate
Maximum Shear Strain Rate
Cross | This is a model intended for shear-thinning fluids. | Low Shear Viscosity:
Time Constant:
Power Law Index:
Herschel Bulkley | This is a model for viscoplastic fluids that, after yield, exhibits a power law behavior in shear stress versus shear strain rate. | Yield Stress:
Viscosity Consistency:
Minimum Shear Strain Rate
Maximum Shear Strain Rate
Time Constant:
Power Law Index:
Ostwald de Waele | This is perhaps the most popular viscosity model because of its simplicity. However, it does not have bounded behavior either on the low or high shear limits, unlike Carreau’s models. | Viscosity Consistency:
Minimum Shear Strain Rate
Maximum Shear Strain Rate
Time Constant:
Power Law Index:

At the start of a steady-state calculation of non-Newtonian flow, the CFX-Solver may take several time steps to ‘get going.’ This is probably due to excessively high fluid viscosities resulting from small or zero initial velocities. In such cases, you can promote faster convergence by specifying a sensible initial velocity field.

Note: If you want to model a non-Newtonian fluid without using any of the available models, you can specify a viscosity by value and use an expression. Note that shear strain rate is available as a CFX system variable. When developing your expression, you should consider non-physical shear strain rates and the possibility of divide-by-zero errors. One way of doing this is to use the available built-in functions `min` and `max` to bound the values of shear strain rate.

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