#include <generalised_newtonian_constitutive_models.h>

Inheritance diagram for oomph::HerschelBulkleyMenDutRegConstitutiveEquation< DIM >:

Public Member Functions
	HerschelBulkleyMenDutRegConstitutiveEquation (double yield_stress_pt, double flow_index_pt, double *zero_shear_viscosity_pt)
	"Exponentially regularised" Herschel Bulkley constitutive equation More...

double	viscosity (const double &second_invariant_of_rate_of_strain_tensor)
	Viscosity ratio as a fct of strain rate invariant. More...

double	dviscosity_dinvariant (const double &second_invariant_of_rate_of_strain_tensor)
	Deriv of viscosity w.r.t. strain rate invariant. More...

Public Member Functions inherited from oomph::GeneralisedNewtonianConstitutiveEquation< DIM >
	GeneralisedNewtonianConstitutiveEquation ()
	Empty constructor. More...

virtual	~GeneralisedNewtonianConstitutiveEquation ()
	Empty virtual destructor. More...

Private Attributes
double *	Yield_stress_pt
	yield stress tau_y More...

double *	Flow_index_pt
	power law index n More...

double *	Zero_shear_viscosity_pt
	the viscosity at zero shear rate More...

Detailed Description

template<unsigned DIM>
class oomph::HerschelBulkleyMenDutRegConstitutiveEquation< DIM >

A GeneralisedNewtonianConstitutiveEquation class defining a Herschel-Bulkley fluid using Mendes and Dutra's (2004) regularisation

Constructor & Destructor Documentation

◆ HerschelBulkleyMenDutRegConstitutiveEquation()

template<unsigned DIM>

oomph::HerschelBulkleyMenDutRegConstitutiveEquation< DIM >::HerschelBulkleyMenDutRegConstitutiveEquation	(	double *	yield_stress_pt,
		double *	flow_index_pt,
		double *	zero_shear_viscosity_pt
	)

inline

"Exponentially regularised" Herschel Bulkley constitutive equation

       : GeneralisedNewtonianConstitutiveEquation<DIM>(),
         Yield_stress_pt(yield_stress_pt),
         Flow_index_pt(flow_index_pt),
         Zero_shear_viscosity_pt(zero_shear_viscosity_pt)
     {
     }

Member Function Documentation

◆ dviscosity_dinvariant()

template<unsigned DIM>

double oomph::HerschelBulkleyMenDutRegConstitutiveEquation< DIM >::dviscosity_dinvariant ( const double & second_invariant_of_rate_of_strain_tensor )

inlinevirtual

Deriv of viscosity w.r.t. strain rate invariant.

Implements oomph::GeneralisedNewtonianConstitutiveEquation< DIM >.

     {
       // Pre-multiply the second invariant with +/-1 depending on whether it's
       // positive or not
       // Also, because the viscosity is exactly zero at zero invariant,
       // we have to add a small value to it
       double sign = -1.0;
       double eps = 0.0;
       if (second_invariant_of_rate_of_strain_tensor == 0.0)
       {
         eps = 1.0e-30;
         sign = 1.0;
       }
       else if (second_invariant_of_rate_of_strain_tensor > 0.0)
       {
         sign = 1.0;
       }
  
       // Calculate the square root of the absolute value of the
       // second invariant of the rate of strain tensor
       double measure_of_rate_of_strain =
         sqrt(sign * (second_invariant_of_rate_of_strain_tensor + eps));
  
       return (1.0 - exp(-(*Zero_shear_viscosity_pt) * 2.0 *
                         measure_of_rate_of_strain / (*Yield_stress_pt))) *
                (sign * pow(2.0, (*Flow_index_pt) - 2.0) *
                   ((*Flow_index_pt) - 1.0) *
                   pow(sign * (second_invariant_of_rate_of_strain_tensor + eps),
                       ((*Flow_index_pt) - 1.0) / 2.0 - 1.0) -
                 sign * (*Yield_stress_pt) /
                   (4.0 *
                    pow(sign * (second_invariant_of_rate_of_strain_tensor + eps),
                        3.0 / 2.0))) +
              sign *
                (((*Zero_shear_viscosity_pt) *
                  exp(-(*Zero_shear_viscosity_pt) * 2.0 *
                      measure_of_rate_of_strain / (*Yield_stress_pt))) /
                 ((*Yield_stress_pt) * measure_of_rate_of_strain)) *
                (pow(2.0, (*Flow_index_pt) - 1.0) *
                   pow(sign * (second_invariant_of_rate_of_strain_tensor + eps),
                       ((*Flow_index_pt) - 1.0) / 2.0) +
                 (*Yield_stress_pt) / (2.0 * measure_of_rate_of_strain));
     }

References CRBond_Bessel::eps, Eigen::bfloat16_impl::exp(), oomph::HerschelBulkleyMenDutRegConstitutiveEquation< DIM >::Flow_index_pt, Eigen::bfloat16_impl::pow(), SYCL::sign(), sqrt(), oomph::HerschelBulkleyMenDutRegConstitutiveEquation< DIM >::Yield_stress_pt, and oomph::HerschelBulkleyMenDutRegConstitutiveEquation< DIM >::Zero_shear_viscosity_pt.

◆ viscosity()

template<unsigned DIM>

double oomph::HerschelBulkleyMenDutRegConstitutiveEquation< DIM >::viscosity ( const double & second_invariant_of_rate_of_strain_tensor )

inlinevirtual

Viscosity ratio as a fct of strain rate invariant.

Implements oomph::GeneralisedNewtonianConstitutiveEquation< DIM >.

     {
       // Pre-multiply the second invariant with +/-1 depending on whether it's
       // positive or not
       // Also, because the viscosity is exactly zero at zero invariant,
       // we have to add a small value to it
       double sign = -1.0;
       double eps = 0.0;
       if (second_invariant_of_rate_of_strain_tensor == 0.0)
       {
         eps = 1.0e-30;
         sign = 1.0;
       }
       else if (second_invariant_of_rate_of_strain_tensor > 0.0)
       {
         sign = 1.0;
       }
  
       // Calculate the square root of the absolute value of the
       // second invariant of the rate of strain tensor
       double measure_of_rate_of_strain =
         sqrt(sign * (second_invariant_of_rate_of_strain_tensor + eps));
  
       return (1.0 - exp(-(*Zero_shear_viscosity_pt) * 2.0 *
                         measure_of_rate_of_strain / (*Yield_stress_pt))) *
              ((*Yield_stress_pt) / (2.0 * measure_of_rate_of_strain) +
               pow((2.0 * measure_of_rate_of_strain), *Flow_index_pt - 1.0));
     }