Detailed Description

A latent heat model of vaporisation of water considering the critical temperature.

The model uses an equation for a general expression of the latent heat of vaporisation of water in the vicinity of and far away from the critical temperature, which was presented by Torquato and Stell in [38].

Denoting the critical temperature as \(T_c\), and introducing a dimensionless variable \(\tau=(T_c-T)/T_c\) associated with temperature \(T\), the equation is given by

\[ L(\tau) = a_1 \tau^{\beta}+a_2 \tau^{\beta+\Delta} +a_4 \tau^{1-\alpha+\beta} +\sum_{n=1}^{M}(b_n \tau^n),\,\text{[kJ/kg]}, \]

where the parameters of \(b_n\) are obtained by the least square method by fitting the equation with the experiment data.

In this model, the parameter set of \(M=5\) is taken for a high accuracy. All parameters are given below:

\(\alpha=1/8,\,\beta=1/3,\, \Delta=0.79-\beta\),
\(a_1=1989.41582,\, a_2=11178.45586, a_4=26923.68994\),
\(b_n:=\{-28989.28947, -19797.03646, 28403.32283, -30382.306422, 15210.380\}\).

The critical temperature is 373.92 \(^{\circ}\)C.

A comparison of this model with the model of MaterialPropertyLib::LinearWaterVapourLatentHeat is given in the following figure.

Definition at line 60 of file WaterVapourLatentHeatWithCriticalTemperature.h.

#include <WaterVapourLatentHeatWithCriticalTemperature.h>

Inheritance diagram for MaterialPropertyLib::WaterVapourLatentHeatWithCriticalTemperature:

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Collaboration diagram for MaterialPropertyLib::WaterVapourLatentHeatWithCriticalTemperature:

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Public Member Functions
	WaterVapourLatentHeatWithCriticalTemperature (std::string name)

void	checkScale () const override

PropertyDataType	value (VariableArray const &variable_array, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const override

PropertyDataType	dValue (VariableArray const &variable_array, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const override

Public Member Functions inherited from MaterialPropertyLib::Property
virtual	~Property ()

virtual PropertyDataType	initialValue (ParameterLib::SpatialPosition const &pos, double const t) const

virtual PropertyDataType	value () const

virtual PropertyDataType	value (VariableArray const &variable_array, VariableArray const &variable_array_prev, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

virtual PropertyDataType	dValue (VariableArray const &variable_array, VariableArray const &variable_array_prev, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

virtual PropertyDataType	d2Value (VariableArray const &variable_array, Variable const variable1, Variable const variable2, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const
	Default implementation: 2nd derivative of any constant property is zero.

virtual void	setProperties (std::vector< std::unique_ptr< Phase > > const &phases)
	Default implementation:

void	setScale (std::variant< Medium , Phase , Component * > scale)

template<typename T >
T	initialValue (ParameterLib::SpatialPosition const &pos, double const t) const

template<typename T >
T	value () const

template<typename T >
T	value (VariableArray const &variable_array, VariableArray const &variable_array_prev, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	value (VariableArray const &variable_array, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	dValue (VariableArray const &variable_array, VariableArray const &variable_array_prev, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	dValue (VariableArray const &variable_array, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	d2Value (VariableArray const &variable_array, Variable const &variable1, Variable const &variable2, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

Additional Inherited Members
Protected Attributes inherited from MaterialPropertyLib::Property
std::string	name_

PropertyDataType	value_
	The single value of a property.

PropertyDataType	dvalue_

std::variant< Medium , Phase , Component * >	scale_

Constructor & Destructor Documentation

◆ WaterVapourLatentHeatWithCriticalTemperature()

MaterialPropertyLib::WaterVapourLatentHeatWithCriticalTemperature::WaterVapourLatentHeatWithCriticalTemperature ( std::string name )

inlineexplicit

Definition at line 63 of file WaterVapourLatentHeatWithCriticalTemperature.h.

    {
        name_ = std::move(name);
    }

References MaterialPropertyLib::name, and MaterialPropertyLib::Property::name_.

Member Function Documentation

◆ checkScale()

void MaterialPropertyLib::WaterVapourLatentHeatWithCriticalTemperature::checkScale ( ) const

inlineoverridevirtual

Reimplemented from MaterialPropertyLib::Property.

Definition at line 68 of file WaterVapourLatentHeatWithCriticalTemperature.h.

    {
        if (!std::holds_alternative<Phase*>(scale_))
        {
            OGS_FATAL(
                "The property 'WaterVapourLatentHeatWithCriticalTemperature' "
                "is "
                "implemented on the 'phase' scale only.");
        }
    }

References OGS_FATAL, and MaterialPropertyLib::Property::scale_.

◆ dValue()

PropertyDataType MaterialPropertyLib::WaterVapourLatentHeatWithCriticalTemperature::dValue	(	VariableArray const &	variable_array,
		Variable const	variable,
		ParameterLib::SpatialPosition const &	pos,
		double const	t,
		double const	dt ) const

overridevirtual

This virtual method will compute the property derivative value based on the variables that are passed as arguments with the default implementation using empty variables array for the previous time step.

The default implementation of this method only returns the property value derivative without altering it.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 73 of file WaterVapourLatentHeatWithCriticalTemperature.cpp.

{
    if (variable != Variable::temperature)
    {
        OGS_FATAL(
            "WaterVapourLatentHeatWithCriticalTemperature::dValue is "
            "implemented "
            "for "
            "the derivative with respect to temperature only.");
    }
    const double T = variable_array.temperature;
 
    if (T >= T_c)
    {
        return 0.0;
    }
 
    constexpr std::array dc = {c[0] * beta,
                               c[1] * (beta + Delta),
                               c[2] * (1 - alpha + beta),
                               c[3],
                               c[4] * 2,
                               c[5] * 3,
                               c[6] * 4,
                               c[7] * 5};
 
    double const tau = (T_c - T) / T_c;
    double const tau_p2 = tau * tau;
    double const tau_p3 = tau_p2 * tau;
    double const tau_p4 = tau_p3 * tau;
    std::array v = {std::pow(tau, beta - 1),
                    std::pow(tau, beta + Delta - 1),
                    std::pow(tau, -alpha + beta),
                    1.,
                    tau,
                    tau_p2,
                    tau_p3,
                    tau_p4};
 
    // The formula gives the value in kJ/kg/K, and the value is return in
    // the unit of J/kg/K.
    return -1000.0 *
#if __GNUC__ < 9 || (__GNUC__ == 9 && (__GNUC_MINOR__ < 3))
           std::inner_product
#else
           std::transform_reduce
#endif
           (begin(dc), end(dc), begin(v), 0.) /
           T_c;
}

References MaterialPropertyLib::alpha, MaterialPropertyLib::beta, MaterialPropertyLib::c, MaterialPropertyLib::Delta, OGS_FATAL, MaterialPropertyLib::T_c, MaterialPropertyLib::temperature, and MaterialPropertyLib::VariableArray::temperature.

◆ value()

PropertyDataType MaterialPropertyLib::WaterVapourLatentHeatWithCriticalTemperature::value	(	VariableArray const &	variable_array,
		ParameterLib::SpatialPosition const &	pos,
		double const	t,
		double const	dt ) const

overridevirtual

This virtual method will compute the property value based on the variables that are passed as arguments with the default implementation using empty variables array for the previous time step.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 34 of file WaterVapourLatentHeatWithCriticalTemperature.cpp.

{
    const double T = variable_array.temperature;
 
    if (T >= T_c)
    {
        return 0.0;
    }
 
    double const tau = (T_c - T) / T_c;
    double const tau_p2 = tau * tau;
    double const tau_p3 = tau_p2 * tau;
    double const tau_p4 = tau_p3 * tau;
    double const tau_p5 = tau_p4 * tau;
 
    std::array v = {std::pow(tau, beta),
                    std::pow(tau, beta + Delta),
                    std::pow(tau, 1 - alpha + beta),
                    tau,
                    tau_p2,
                    tau_p3,
                    tau_p4,
                    tau_p5};
 
    // The formula gives the value in kJ/kg, and the return value is in the
    // units of J/kg.
 
    return 1000.0 *
#if __GNUC__ < 9 || (__GNUC__ == 9 && (__GNUC_MINOR__ < 3))
           std::inner_product
#else
           std::transform_reduce
#endif
           (begin(c), end(c), begin(v), 0.);
}

References MaterialPropertyLib::alpha, MaterialPropertyLib::beta, MaterialPropertyLib::c, MaterialPropertyLib::Delta, MaterialPropertyLib::T_c, and MaterialPropertyLib::VariableArray::temperature.

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

MaterialLib/MPL/Properties/Enthalpy/WaterVapourLatentHeatWithCriticalTemperature.h
MaterialLib/MPL/Properties/Enthalpy/WaterVapourLatentHeatWithCriticalTemperature.cpp

Detailed Description

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ WaterVapourLatentHeatWithCriticalTemperature()

Member Function Documentation

◆ checkScale()

◆ dValue()

◆ value()