Regularization Model

Regularization Model = <MODEL>

Description / Usage

This card is used to specify the model for the regularization used in the generalized Newtonian viscosity.

Currently used for HERSCHEL_BULKLEY models

Choices for <MODEL> in HERSCHEL_BULKLEY fluids:

EPSILON

Epsilon regularization applied to both the power law term and the yield term (default for HERSCHEL_BULKLEY)

$$\mu ={\mu }_0(\dot{\gamma }+ϵ{)}^{n-1}+\frac{{\tau }_y}{(\dot{\gamma }+ϵ)}$$

PAPANASTASIOU

Papanastasiou regularization applied to the yield parameter (default for HERSCHEL_BULKLEY_PAPANASTASIOU)

$$\mu ={\mu }_0{\dot{\gamma }}^{n-1}+(1-exp(-f\dot{\gamma }))\frac{{\tau }_y}{\dot{\gamma }}$$

EPSILON_YIELD_ONLY

Epsilon regularization applied only to the yield term

$$\mu ={\mu }_0(\dot{\gamma }{)}^{n-1}+\frac{{\tau }_y}{(\dot{\gamma }+ϵ)}$$

PAPANASTASIOU_EPSILON

Papanastasiou regularization applied to the yield term and an epsilon on the power law term

$$\mu ={\mu }_0(\dot{\gamma }+ϵ{)}^{n-1}+(1-exp(-f\dot{\gamma }))\frac{{\tau }_y}{\dot{\gamma }}$$

Examples

The following is a sample card that sets Papanastasiou regularization to a HERSCHEL_BULKLEY fluid with an epsilon on the power law term

Liquid Constitutive Equation = HERSCHEL_BULKLEY
...
Regularization Model         = PAPANASTASIOU_EPSILON
Yield Exponent               = CONSTANT 200
Epsilon Regularization       = CONSTANT 1e-12

Without the epsilon term

Liquid Constitutive Equation = HERSCHEL_BULKLEY
...
Regularization Model         = PAPANASTASIOU
Yield Exponent               = CONSTANT 200

Similarly applying only to the Yield term for epsilon regularization

Liquid Constitutive Equation = HERSCHEL_BULKLEY
...
Regularization Model         = EPSILON_YIELD_ONLY
Epsilon Regularization       = CONSTANT 1e-5

Or to both terms

Liquid Constitutive Equation = HERSCHEL_BULKLEY
...
# optional this is the default
Regularization Model         = EPSILON
Epsilon Regularization       = CONSTANT 1e-5

Technical Discussion

See Description/Usage for Liquid Constitutive Equation