#include <generalised_newtonian_constitutive_models.h>

Inheritance diagram for oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >:

Public Member Functions
	HerschelBulkleyTanMilRegConstitutiveEquation (double yield_stress_pt, double flow_index_pt, double *critical_second_invariant_pt)
	"Cutoff regularised" Herschel Bulkley constitutive equation More...

double	calculate_cut_off_viscosity ()
	Function that calculates the cut off viscosity. More...

void	report_cut_off_values (double &cut_off_invariant, double &cut_off_viscosity)
	Report cutoff values. 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 *	Critical_second_invariant_pt

Detailed Description

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

A GeneralisedNewtonianConstitutiveEquation class defining a Herschel-Bulkley fluid using Tanner and Milthorpe's (1983) regularisation

Constructor & Destructor Documentation

◆ HerschelBulkleyTanMilRegConstitutiveEquation()

template<unsigned DIM>

oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::HerschelBulkleyTanMilRegConstitutiveEquation	(	double *	yield_stress_pt,
		double *	flow_index_pt,
		double *	critical_second_invariant_pt
	)

inline

"Cutoff regularised" Herschel Bulkley constitutive equation

       : GeneralisedNewtonianConstitutiveEquation<DIM>(),
         Yield_stress_pt(yield_stress_pt),
         Flow_index_pt(flow_index_pt),
         Critical_second_invariant_pt(critical_second_invariant_pt)
     {
       // Calculate the Newtonian cutoff viscosity from the constitutive
       // equation and the cutoff value of the second invariant
       double cut_off_viscosity = calculate_cut_off_viscosity();
  
       oomph_info << "HerschelBulkleyTanMilRegConstitutiveEquation: "
                  << " cutoff viscosity = " << cut_off_viscosity << std::endl;
  
       oomph_info << "                                              "
                  << " cutoff invariant = " << *Critical_second_invariant_pt
                  << std::endl;
     }

References oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::calculate_cut_off_viscosity(), oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::Critical_second_invariant_pt, and oomph::oomph_info.

Member Function Documentation

◆ calculate_cut_off_viscosity()

template<unsigned DIM>

double oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::calculate_cut_off_viscosity ( )

inline

Function that calculates the cut off viscosity.

     {
       return (*Yield_stress_pt) /
                (2.0 * sqrt((*Critical_second_invariant_pt))) +
              pow((2.0 * sqrt((*Critical_second_invariant_pt))),
                  *Flow_index_pt - 1.0);
     }

References oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::Critical_second_invariant_pt, oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::Flow_index_pt, Eigen::bfloat16_impl::pow(), sqrt(), and oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::Yield_stress_pt.

Referenced by oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::HerschelBulkleyTanMilRegConstitutiveEquation(), oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::report_cut_off_values(), and oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::viscosity().

◆ dviscosity_dinvariant()

template<unsigned DIM>

double oomph::HerschelBulkleyTanMilRegConstitutiveEquation< 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
       double sign = -1.0;
       if (second_invariant_of_rate_of_strain_tensor >= 0.0)
       {
         sign = 1.0;
       }
  
       if (sign * second_invariant_of_rate_of_strain_tensor <
           (*Critical_second_invariant_pt))
       {
         return 0.0;
       }
       else
       {
         return sign * pow(2.0, (*Flow_index_pt) - 2.0) *
                  ((*Flow_index_pt) - 1.0) *
                  pow(sign * second_invariant_of_rate_of_strain_tensor,
                      ((*Flow_index_pt) - 1.0) / 2.0 - 1.0) -
                sign * (*Yield_stress_pt) /
                  (4.0 * pow(sign * second_invariant_of_rate_of_strain_tensor,
                             3.0 / 2.0));
       }
     }

References oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::Critical_second_invariant_pt, oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::Flow_index_pt, Eigen::bfloat16_impl::pow(), SYCL::sign(), and oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::Yield_stress_pt.

◆ report_cut_off_values()

template<unsigned DIM>

void oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::report_cut_off_values	(	double &	cut_off_invariant,
		double &	cut_off_viscosity
	)

inline

Report cutoff values.

     {
       cut_off_invariant = *Critical_second_invariant_pt;
       cut_off_viscosity = calculate_cut_off_viscosity();
     }

References oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::calculate_cut_off_viscosity(), and oomph::HerschelBulkleyTanMilRegConstitutiveEquation< DIM >::Critical_second_invariant_pt.

◆ viscosity()

template<unsigned DIM>

double oomph::HerschelBulkleyTanMilRegConstitutiveEquation< 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
       double sign = -1.0;
       if (second_invariant_of_rate_of_strain_tensor >= 0.0)
       {
         sign = 1.0;
       }
  
       // std::cout<<"I2 "<<second_invariant_of_rate_of_strain_tensor<<std::endl;
  
       // if the second invariant is below the cutoff we have a constant,
       // Newtonian viscosity
       if (sign * second_invariant_of_rate_of_strain_tensor <
           (*Critical_second_invariant_pt))
       {
         return calculate_cut_off_viscosity();
       }
       else
       {
         // 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);
  
         return (*Yield_stress_pt) / (2.0 * measure_of_rate_of_strain) +
                pow((2.0 * measure_of_rate_of_strain), *Flow_index_pt - 1.0);
       }
     }