oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM > Class Template Reference

#include <generalised_newtonian_constitutive_models.h>

Inheritance diagram for oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >:

Public Member Functions
	SiskoTanMilRegWithBlendingConstitutiveEquation (double *alpha_pt, double *flow_index_pt, double *critical_second_invariant_pt)
	"Cutoff regularised" Sisko constitutive equation More...
double	calculate_cutoff_viscosity ()
double	calculate_viscosity_offset_at_zero_shear (double &cut_off_viscosity)
double	calculate_zero_shear_viscosity ()
	Function that calculates the viscosity at zero I2. More...
void	report_cut_off_values (double &cut_off_invariant, double &cut_off_viscosity, double &zero_shear_viscosity)
	Report cutoff values. More...
void	calculate_fitting_parameters_of_cubic (double &a, double &b)
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 *	Alpha_pt
	pre-factor alpha More...
double *	Flow_index_pt
	power law index n More...
double *	Critical_second_invariant_pt

Detailed Description

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

A GeneralisedNewtonianConstitutiveEquation class defining a Sisko fluid using Tanner and Milthorpe's (1983) regularisation with a smooth transition using a cubic (for n < 1)

Constructor & Destructor Documentation

SiskoTanMilRegWithBlendingConstitutiveEquation()

template<unsigned DIM>

oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::SiskoTanMilRegWithBlendingConstitutiveEquation ( double *  alpha_pt, double *  flow_index_pt, double *  critical_second_invariant_pt  )

inline

"Cutoff regularised" Sisko constitutive equation

get the cutoff viscosity

get the zero shear viscosity

      : GeneralisedNewtonianConstitutiveEquation<DIM>(),
        Alpha_pt(alpha_pt),
        Flow_index_pt(flow_index_pt),
        Critical_second_invariant_pt(critical_second_invariant_pt)
    {
      double cut_off_viscosity = calculate_cutoff_viscosity();
 
      double zero_shear_viscosity = calculate_zero_shear_viscosity();
 
      oomph_info << "SiskoTanMilRegWithBlendingConstitutiveEquation: "
                 << " zero shear viscosity = " << zero_shear_viscosity
                 << std::endl;
 
      oomph_info << "SiskoTanMilRegWithBlendingConstitutiveEquation: "
                 << " cut off viscosity = " << cut_off_viscosity << std::endl;
 
      oomph_info << "                                              "
                 << " cutoff invariant = " << *Critical_second_invariant_pt
                 << std::endl;
    }

References oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_zero_shear_viscosity(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, and oomph::oomph_info.

Member Function Documentation

calculate_cutoff_viscosity()

template<unsigned DIM>

double oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity ( )

inline

Function that calculates the viscosity at the cutoff invariant Note: this is NOT the viscosity at zero I2

    {
      // Calculate the Newtonian cutoff viscosity from the constitutive
      // equation and the cutoff value of the second invariant
      return 1.0 +
             (*Alpha_pt) * pow((2.0 * sqrt((*Critical_second_invariant_pt))),
                               *Flow_index_pt - 1.0);
    }

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

Referenced by oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_zero_shear_viscosity(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::report_cut_off_values(), and oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::SiskoTanMilRegWithBlendingConstitutiveEquation().

calculate_fitting_parameters_of_cubic()

template<unsigned DIM>

void oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic ( double &  a, double &  b  )

inline

    {
      // get the viscosity at the cutoff invariant
      double Cut_off_viscosity = calculate_cutoff_viscosity();
 
      // calculate the offset at zero shear
      double epsilon =
        calculate_viscosity_offset_at_zero_shear(Cut_off_viscosity);
 
      a =
        1.0 /
        (4.0 * pow((*Critical_second_invariant_pt), 3.0) *
         pow((*Critical_second_invariant_pt), 5.0 / 2.0)) *
        (8.0 * (Cut_off_viscosity + epsilon - 1.0) *
           pow((*Critical_second_invariant_pt), 5.0 / 2.0) +
         pow(2.0, (*Flow_index_pt)) * ((*Flow_index_pt) - 1.0) * (*Alpha_pt) *
           pow((*Critical_second_invariant_pt), 2.0) *
           pow((*Critical_second_invariant_pt), (*Flow_index_pt) / 2.0) -
         pow(2.0, (*Flow_index_pt) + 2.0) * (*Alpha_pt) *
           pow((*Critical_second_invariant_pt), (*Flow_index_pt) / 2.0 + 2.0));
 
      b =
        1.0 /
        (4.0 * pow((*Critical_second_invariant_pt), 2.0) *
         pow((*Critical_second_invariant_pt), 5.0 / 2.0)) *
        (-12.0 * (Cut_off_viscosity + epsilon - 1.0) *
           pow((*Critical_second_invariant_pt), 5.0 / 2.0) -
         pow(2.0, (*Flow_index_pt)) * ((*Flow_index_pt) - 1.0) * (*Alpha_pt) *
           pow((*Critical_second_invariant_pt), 2.0) *
           pow((*Critical_second_invariant_pt), (*Flow_index_pt) / 2.0) +
         3.0 * pow(2.0, (*Flow_index_pt) + 1.0) * (*Alpha_pt) *
           pow((*Critical_second_invariant_pt), (*Flow_index_pt) / 2.0 + 2.0));
    }

References a, oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Alpha_pt, b, oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_viscosity_offset_at_zero_shear(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, oomph::SarahBL::epsilon, oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Flow_index_pt, and Eigen::bfloat16_impl::pow().

Referenced by oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::dviscosity_dinvariant(), and oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::viscosity().

calculate_viscosity_offset_at_zero_shear()

template<unsigned DIM>

double oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_viscosity_offset_at_zero_shear ( double &  cut_off_viscosity )

inline

Offset by how much the zero shear rate viscosity lies above the viscosity at I2_cutoff Hard-coded to a value that ensures a smooth transition

    {
      return cut_off_viscosity / 5.0;
    }

Referenced by oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), and oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_zero_shear_viscosity().

calculate_zero_shear_viscosity()

template<unsigned DIM>

double oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_zero_shear_viscosity ( )

inline

Function that calculates the viscosity at zero I2.

Offset by how much the zero shear rate viscosity lies above the viscosity at I2_cutoff

    {
      // get the viscosity at the cutoff point
      double cut_off_viscosity = calculate_cutoff_viscosity();
 
      double epsilon =
        calculate_viscosity_offset_at_zero_shear(cut_off_viscosity);
 
      return cut_off_viscosity + epsilon;
    }

References oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_viscosity_offset_at_zero_shear(), and oomph::SarahBL::epsilon.

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

dviscosity_dinvariant()

template<unsigned DIM>

double oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< 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 >.

    {
      // Get the parameters of the cubic
      double a;
      double b;
 
      calculate_fitting_parameters_of_cubic(a, b);
 
      // 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 sign * 3.0 * a *
                 pow(sign * second_invariant_of_rate_of_strain_tensor, 2.0) +
               2.0 * b * second_invariant_of_rate_of_strain_tensor;
      }
      else
      {
        return (*Alpha_pt) * pow(2.0, (*Flow_index_pt) - 2.0) *
               ((*Flow_index_pt) - 1.0) *
               second_invariant_of_rate_of_strain_tensor *
               pow(sign * second_invariant_of_rate_of_strain_tensor,
                   ((*Flow_index_pt) - 1.0) / 2.0 - 2.0);
      }
    }

References a, oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Alpha_pt, b, oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Flow_index_pt, Eigen::bfloat16_impl::pow(), and SYCL::sign().

report_cut_off_values()

template<unsigned DIM>

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

inline

Report cutoff values.

    {
      cut_off_invariant = *Critical_second_invariant_pt;
      cut_off_viscosity = calculate_cutoff_viscosity();
      zero_shear_viscosity = calculate_zero_shear_viscosity();
    }

References oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_zero_shear_viscosity(), and oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt.

viscosity()

template<unsigned DIM>

double oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< 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 >.

    {
      // Get the parameters of the cubic
      double a;
      double b;
 
      calculate_fitting_parameters_of_cubic(a, b);
 
      double zero_shear_viscosity = calculate_zero_shear_viscosity();
 
      // 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 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 a * pow(sign * second_invariant_of_rate_of_strain_tensor, 3.0) +
               b * pow(sign * second_invariant_of_rate_of_strain_tensor, 2.0) +
               zero_shear_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 1.0 + (*Alpha_pt) * pow((2.0 * measure_of_rate_of_strain),
                                       *Flow_index_pt - 1.0);
      }
    }

References a, b, oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_zero_shear_viscosity(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Flow_index_pt, Eigen::bfloat16_impl::pow(), SYCL::sign(), and sqrt().

Member Data Documentation

Alpha_pt

template<unsigned DIM>

double* oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Alpha_pt

private

pre-factor alpha

Referenced by oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), and oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::dviscosity_dinvariant().

Critical_second_invariant_pt

template<unsigned DIM>

double* oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt

private

value of the second invariant below which we have constant (Newtonian) viscosity – assumed to be always positive

Referenced by oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::dviscosity_dinvariant(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::report_cut_off_values(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::SiskoTanMilRegWithBlendingConstitutiveEquation(), and oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::viscosity().

Flow_index_pt

template<unsigned DIM>

double* oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::Flow_index_pt

private

power law index n

Referenced by oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::dviscosity_dinvariant(), and oomph::SiskoTanMilRegWithBlendingConstitutiveEquation< DIM >::viscosity().

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The documentation for this class was generated from the following file:

• generalised_newtonian_constitutive_models.h