Non-Newtonian fluids in ANSYS Fluent
Non-Newtonian fluids are a class of fluids whose viscosity is not constant and changes with the applied shear stress or strain rate, making them distinct from Newtonian fluids like water or air. In ANSYS Fluent, a leading computational fluid dynamics (CFD) software, these fluids can be accurately modeled using advanced rheological models such as Power Law, Herschel-Bulkley, and Carreau. These models allow engineers to simulate complex fluid behaviors found in industries like food processing, pharmaceuticals, and oil and gas, where materials like ketchup, blood, or drilling muds exhibit non-linear viscosity characteristics. In this article, we will help you gain a better understanding of non-Newtonian fluids, the various models available in ANSYS Fluent, and how to simulate them effectively using this software.
What are non-Newtonian Fluids?
Non-Newtonian fluids are a fascinating class of materials whose viscosity is not constant and depends on the applied shear stress or strain rate (Fig.1). Unlike Newtonian fluids, such as water or air, where viscosity remains uniform under different flow conditions, non-Newtonian fluids exhibit behaviors that vary based on external forces.
Figure 1- Viscosity changes versus shear rate (stress) variations
General classification of non-Newtonian fluids
Overall, non-Newtonian fluids can be categorized into three primary groups: Viscoelastic Fluids, Time-Dependent and Time-Independent (Fig.2).
Figure 2- General classification of non-Newtonian fluids
Viscoelastic Fluids:
Exhibit both viscous and elastic properties (Fig.3), partially storing energy and partially releasing it as heat. They behave like liquids under slow deformation but show elasticity (solid-like behavior) under rapid deformation.
Example: Polymer solutions, biological fluids, and molten plastics.
Figure 3- Schematic of a viscoelastic fluid
Time-Independent Fluids:
Their viscosity depends only on the applied shear rate but not on the duration of shearing. They can be classified into (Fig.4):
- Shear-Thinning (Pseudoplastic): Viscosity decreases with increasing shear rate (e.g., paint, blood).
- Shear-Thickening (Dilatant): Viscosity increases with increasing shear rate (e.g., cornstarch in water).
- Bingham Plastic: Requires a yield stress before it starts flowing (e.g., toothpaste, ketchup)
Figure 4- Time-independent non-Newtonian fluids
Time-Dependent Fluids:
Their viscosity changes over time when subjected to shear stress. They can be divided into (Fig.5):
- Thixotropic Fluids: Viscosity decreases over time under constant shear (e.g., yogurt, some paints).
- Rheopectic Fluids: Viscosity increases over time under constant shear (e.g., gypsum suspensions).
Figure 5- Time-Dependent non-Newtonian fluids
What non-Newtonian models are supported in ANSYS Fluent?
Generally, Ansys Fluent supports several non-Newtonian fluid models, including the Power Law model, Carreau model (for pseudo-plastics), Cross model, Casson model and Herschel-Bulkley model (for Bingham plastics) which allows for simulating fluids with shear-dependent viscosity behaviors.
Table 1- Types of Non-Newtonian Models Supported in ANSYS Fluent
Carreau-Yasuda Model
This model describes a smooth transition between Newtonian and shear-thinning behavior. At low shear rates, the fluid behaves as a Newtonian fluid with viscosity , and at high shear rates, it asymptotically approaches the viscosity .
![\mu = \mu_{\infty} + \frac{\mu_{0} - \mu_{\infty}}{[1 + (\lambda\dot{\gamma})^{a}]^{\frac{1-n}{a}}}](https://cfdland.com/wp-content/ql-cache/quicklatex.com-0f1b291a01ebfa5c2e3dc5c357f4bf21_l3.png "Rendered by QuickLaTeX.com")
Applications: Commonly used for polymer solutions, blood flow modeling, and biological fluids. As an example, check this learning product from our CFDSHOP about Non-newtonian Blood In Artery CFD Simulation, ANSYS Fluent Training.
Non-newtonian Blood In Artery CFD Simulation, ANSYS Fluent Training
Casson Model
The Casson model is used for fluids with yield stress, meaning that the fluid does not begin to flow until a critical shear stress is exceeded.
Applications: Used for blood, chocolate, and printing inks.
Power Law Model
This is one of the simplest non-Newtonian models, often called the Ostwald-de Waele model. It defines fluids where viscosity depends on the shear rate.
n<1 → Shear-thinning (pseudoplastic fluids) (e.g., paint, ketchup, polymer solutions)
n>1 → Shear-thickening (dilatant fluids) (e.g., cornstarch-water mixture)
Applications: Found in food fluids, cosmetics, and polymer solutions.
Cross Model
Similar to the Carreau model, this model describes shear-thinning behavior, but with a different functional form for the viscosity reduction.
Applications: Used in polymer melts, coatings, and suspensions.
Herschel-Bulkley Model
A generalization of the Bingham and Power Law models, this equation describes fluids that require a yield stress before they start to flow, followed by shear-thinning or shear-thickening behavior.
Applications: Common in drilling muds, mayonnaise, and toothpaste. For instance, we could validated a numerical paper:
Heat Transfer In Non-newtonian Nanofluid CFD Simulation, Numerical Paper Validation
Bingham Model
The simplest yield-stress model, this equation states that the fluid behaves like a solid until the applied shear stress exceeds , after which it flows with a constant viscosity.
Applications: Used for mud, suspensions, and some slurries.
How to model non-Newtonian fluid flows by ANSYS Fluent?
Here, as an example, we will define the Power Law model from the previously mentioned models for our case. Other models follow the same process for their definition in ANSYS Fluent.
Exact navigation in ANSYS Fluent (Fig.7):
- Go to: Materials → Create/Edit
- In the Fluid Materials window, click New to define a custom fluid.
- Under the Viscosity section, select Power Law from the dropdown menu.
- Enter the values for Consistency Index (k) and Flow Index (n).
- Click OK to save the changes.
Figure 7- How to Set the Non-Newtonian viscosity Power
Temperature dependent viscosity
In non-isothermal flows, the temperature varies across the fluid, affecting physical properties like viscosity (Fig.8).
Figure 8- Non-isothermal fluid flow: impact of temperature variation
In non-isothermal non-Newtonian flows, viscosity depends on both shear rate and temperature. The total viscosity is given by:
where H(T) represents temperature dependence following the Arrhenius law:
![H(T) = \exp\left[\alpha\left(\frac{1}{T-T_0} - \frac{1}{T_a-T_0}\right)\right]](https://cfdland.com/wp-content/ql-cache/quicklatex.com-c019c56c7865bf3878646bddd85f6537_l3.png "Rendered by QuickLaTeX.com")
where α is a parameter that represents the ratio of the activation energy to the thermodynamic constant. is a reference temperature for which the enthalpy or heat function H (T) equals 1. is a temperature shift, which is set to 0 by default, representing the lowest thermodynamically acceptable temperature (Fig.9).
Temperature dependence is factored in only when the energy equation is enabled, and if α=0, temperature dependence is ignored even if the energy equation is being solved. This setup is typically used in thermodynamic or kinetic models where temperature influences reaction rates or other temperature-dependent properties.
Figure 9- Set the Non-Newtonian viscosity Power in a non-isothermal non-Newtonian flows
Conclusion
Simulating non-Newtonian fluids in ANSYS Fluent is essential for accurately modeling fluid behaviors that deviate from the constant viscosity of Newtonian fluids. By utilizing advanced rheological models such as Power Law, Herschel-Bulkley, and Carreau, engineers can effectively simulate complex fluid dynamics in various industries, including food processing, pharmaceuticals, and oil and gas. These models provide a robust approach to understanding shear-dependent viscosity behaviors and allow for precise predictions in real-world applications. Additionally, temperature-dependent viscosity further enhances the accuracy of simulations by factoring in the effects of temperature on fluid properties. Overall, ANSYS Fluent offers a comprehensive platform for simulating non-Newtonian fluids, enabling engineers to address a wide range of fluid flow challenges.
FAQs
1- What are non-Newtonian fluids?
Non-Newtonian fluids are fluids whose viscosity changes with shear stress or strain rate, unlike Newtonian fluids where viscosity remains constant.
2- How can I model non-Newtonian fluids in ANSYS Fluent?
ANSYS Fluent offers models like Power Law, Herschel-Bulkley, and Carreau. Select a model in the Materials window and input relevant parameters.
3- How do I handle temperature dependence in non-Newtonian fluids?
Temperature dependence only needed when the energy equation is enabled and temperature effects are significant. It is modeled using the Arrhenius law, activated when the energy equation is enabled, with the parameter α controlling the temperature effect.
4- Can I simulate non-Newtonian fluids in steady-state simulations?
Yes, both steady-state and transient simulations are possible in ANSYS Fluent for non-Newtonian fluids.
5- How do I choose the appropriate non-Newtonian model in ANSYS Fluent?
Choose based on fluid behavior:
- Power Law: Shear-thinning/thickening.
- Herschel-Bulkley: Fluids with yield stress.
- Carreau/Cross: Shear-thinning with Newtonian transition.
- Casson: Yield stress fluids (e.g., blood, chocolate).
6- Can I simulate non-Newtonian models like Phan–Thien and Tanner (PTT), Giesekus, Finite Extensible Nonlinear Elastic (FENE) in ANSYS Fluent?
No, to simulate these advanced models, you would need to write UDFs (User Defined Functions). These models are more complex and require custom coding to implement them in ANSYS Fluent, as they are not directly available in the standard model library.