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)

\[\mu = \mu_0 (\dot{\gamma} + \epsilon)^{n-1} + \frac{\tau_y}{(\dot{\gamma} + \epsilon)}\]

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

\[\mu = \mu_0 (\dot{\gamma})^{n-1} + \frac{\tau_y}{(\dot{\gamma} + \epsilon)}\]

PAPANASTASIOU_EPSILON

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

\[\mu = \mu_0 (\dot{\gamma}+ \epsilon)^{n-1} + (1-exp(-f \dot{\gamma})) \frac{\tau_y}{\dot{\gamma}}\]

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