Class for calculating the equation of state of water. More...

#include <WaterPropsIAPWS.h>

Collaboration diagram for WaterPropsIAPWS:

Public Member Functions
	WaterPropsIAPWS ()
	Base constructor. More...

	WaterPropsIAPWS (const WaterPropsIAPWS &right)
	Copy constructor. More...

WaterPropsIAPWS &	operator= (const WaterPropsIAPWS &right)
	assignment constructor More...

	~WaterPropsIAPWS ()
	destructor More...

void	setState_TR (doublereal temperature, doublereal rho)
	Set the internal state of the object wrt temperature and density. More...

doublereal	helmholtzFE () const
	Calculate the Helmholtz free energy in mks units of J kmol-1 K-1, using the last temperature and density. More...

doublereal	Gibbs () const
	Calculate the Gibbs free energy in mks units of J kmol-1 K-1. More...

doublereal	enthalpy () const
	Calculate the enthalpy in mks units of J kmol-1 using the last temperature and density. More...

doublereal	intEnergy () const
	Calculate the internal energy in mks units of J kmol-1. More...

doublereal	entropy () const
	Calculate the entropy in mks units of J kmol-1 K-1. More...

doublereal	cv () const
	Calculate the constant volume heat capacity in mks units of J kmol-1 K-1 at the last temperature and density. More...

doublereal	cp () const
	Calculate the constant pressure heat capacity in mks units of J kmol-1 K-1 at the last temperature and density. More...

doublereal	molarVolume () const
	Calculate the molar volume (kmol m-3) at the last temperature and density. More...

doublereal	pressure () const
	Calculates the pressure (Pascals), given the current value of the temperature and density. More...

doublereal	density (doublereal temperature, doublereal pressure, int phase=-1, doublereal rhoguess=-1.0)
	Calculates the density given the temperature and the pressure, and a guess at the density. More...

doublereal	density_const (doublereal pressure, int phase=-1, doublereal rhoguess=-1.0) const
	Calculates the density given the temperature and the pressure, and a guess at the density, while not changing the internal state. More...

doublereal	density () const
	Returns the density (kg m-3) More...

doublereal	temperature () const
	Returns the temperature (Kelvin) More...

doublereal	coeffThermExp () const
	Returns the coefficient of thermal expansion. More...

doublereal	coeffPresExp () const
	Returns the isochoric pressure derivative wrt temperature. More...

doublereal	isothermalCompressibility () const
	Returns the coefficient of isothermal compressibility for the state of the object. More...

doublereal	dpdrho () const
	Returns the value of dp / drho at constant T for the state of the object. More...

doublereal	psat_est (doublereal temperature) const
	This function returns an estimated value for the saturation pressure. More...

doublereal	psat (doublereal temperature, int waterState=WATER_LIQUID)
	This function returns the saturation pressure given the temperature as an input parameter, and sets the internal state to the saturated conditions. More...

doublereal	densSpinodalWater () const
	Return the value of the density at the water spinodal point (on the liquid side) for the current temperature. More...

doublereal	densSpinodalSteam () const
	Return the value of the density at the water spinodal point (on the gas side) for the current temperature. More...

int	phaseState (bool checkState=false) const
	Returns the Phase State flag for the current state of the object. More...

doublereal	Tcrit () const
	Returns the critical temperature of water (Kelvin) More...

doublereal	Pcrit () const
	Returns the critical pressure of water (22.064E6 Pa) More...

doublereal	Rhocrit () const
	Return the critical density of water (kg m-3) More...

Private Member Functions
void	calcDim (doublereal temperature, doublereal rho)
	Calculate the dimensionless temp and rho and store internally. More...

void	corr (doublereal temperature, doublereal pressure, doublereal &densLiq, doublereal &densGas, doublereal &delGRT)
	Utility routine in the calculation of the saturation pressure. More...

void	corr1 (doublereal temperature, doublereal pressure, doublereal &densLiq, doublereal &densGas, doublereal &pcorr)
	Utility routine in the calculation of the saturation pressure. More...

Private Attributes
WaterPropsIAPWSphi *	m_phi
	pointer to the underlying object that does the calculations. More...

doublereal	tau
	Dimensionless temperature. More...

doublereal	delta
	Dimensionless density. More...

int	iState
	Current state of the system. More...

Detailed Description

Class for calculating the equation of state of water.

The reference is W. Wagner, A. Prub, "The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use," J. Phys. Chem. Ref. Dat, 31, 387, 2002.

This class provides a very complicated polynomial for the specific Helmholtz free energy of water, as a function of temperature and density.

\[ \frac{M\hat{f}(\rho,T)}{R T} = \phi(\delta, \tau) = \phi^o(\delta, \tau) + \phi^r(\delta, \tau) \]

where

\[ \delta = \rho / \rho_c \quad \mathrm{and} \quad \tau = T_c / T \]

The following constants are assumed

\[ T_c = 647.096\mathrm{\;K} \]

\[ \rho_c = 322 \mathrm{\;kg\,m^{-3}} \]

\[ R/M = 0.46151805 \mathrm{\;kJ\,kg^{-1}\,K^{-1}} \]

The free energy is a unique single-valued function of the temperature and density over its entire range.

Note, the base thermodynamic state for this class is the one used in the steam tables, i.e., the liquid at the triple point for water has the following properties:

u(273.16, rho) = 0.0
s(273.16, rho) = 0.0
psat(273.16) = 611.655 Pascal
rho(273.16, psat) = 999.793 kg m-3

Therefore, to use this class within Cantera, offsets to u() and s() must be used to put the water class onto the same basis as other thermodynamic quantities. For example, in the WaterSSTP class, these offsets are calculated in the following way. The thermodynamic base state for water is set to the NIST basis here by specifying constants EW_Offset and SW_Offset. These offsets are calculated on the fly so that the following properties hold:

Delta_Hfo_idealGas(298.15, 1bar) = -241.826 kJ/gmol
So_idealGas(298.15, 1bar) = 188.835 J/gmolK

The offsets are calculated by actually computing the above quantities and then calculating the correction factor.

This class provides an interface to the WaterPropsIAPWSphi class, which actually calculates the \( \phi^o(\delta, \tau) \) and the \( \phi^r(\delta, \tau) \) polynomials in dimensionless form.

All thermodynamic results from this class are returned in dimensional form. This is because the gas constant (and molecular weight) used within this class is allowed to be potentially different than that used elsewhere in Cantera. Therefore, everything has to be in dimensional units. Note, however, the thermodynamic basis is set to that used in the steam tables. (u = s = 0 for liquid water at the triple point).

This class is not a ThermoPhase. However, it does maintain an internal state of the object that is dependent on temperature and density. The internal state is characterized by an internally stored \( \tau\) and a \( \delta \) value, and an iState value, which indicates whether the point is a liquid, a gas, or a supercritical fluid. Along with that the \( \tau\) and a \( \delta \) values are polynomials of \( \tau\) and a \( \delta \) that are kept by the WaterPropsIAPWSphi class. Therefore, whenever \( \tau\) or \( \delta \) is changed, the function setState() must be called in order for the internal state to be kept up to date.

The class is pretty straightforward. However, one function deserves mention. The density() function calculates the density that is consistent with a particular value of the temperature and pressure. It may therefore be multivalued or potentially there may be no answer from this function. It therefore takes a phase guess and a density guess as optional parameters. If no guesses are supplied to density(), a gas phase guess is assumed. This may or may not be what is wanted. Therefore, density() should usually at least be supplied with a phase guess so that it may manufacture an appropriate density guess. density() manufactures the initial density guess, nondimensionalizes everything, and then calls WaterPropsIAPWSphi::dfind(), which does the iterative calculation to find the density condition that matches the desired input pressure.

The phase guess defines are located in the .h file. they are

WATER_GAS
WATER_LIQUID
WATER_SUPERCRIT

There are only three functions which actually change the value of the internal state of this object after it's been instantiated

setState_TR(temperature, rho)
density(temperature, pressure, phase, rhoguess)
psat(temperature, waterState);

The setState_TR() is the main function that sets the temperature and rho value. The density() function serves as a setState_TP() function, in that it sets internal state to a temperature and pressure. However, note that this is potentially multivalued. Therefore, we need to supply in addition a phase guess and a rho guess to the input temperature and pressure. The psat() function sets the internal state to the saturated liquid or saturated gas state, depending on the waterState parameter.

Because the underlying object WaterPropsIAPWSphi is privately held, you can be sure that the underlying state of this object doesn't change except due to the three function calls listed above.

Definition at line 158 of file WaterPropsIAPWS.h.

Constructor & Destructor Documentation

WaterPropsIAPWS ( )

Base constructor.

Definition at line 40 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::m_phi.

WaterPropsIAPWS ( const WaterPropsIAPWS & right )

Copy constructor.

Definition at line 49 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, WaterPropsIAPWS::m_phi, WaterPropsIAPWS::tau, and WaterPropsIAPWSphi::tdpolycalc().

~WaterPropsIAPWS ( )

destructor

Definition at line 71 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::m_phi.

Member Function Documentation

WaterPropsIAPWS & operator= ( const WaterPropsIAPWS & right )

assignment constructor

Definition at line 59 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, WaterPropsIAPWS::iState, WaterPropsIAPWS::m_phi, WaterPropsIAPWS::tau, and WaterPropsIAPWSphi::tdpolycalc().

void setState_TR	(	doublereal	temperature,
		doublereal	rho
	)

Set the internal state of the object wrt temperature and density.

Parameters

temperature	temperature (kelvin)
rho	density (kg m-3)

Definition at line 630 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::calcDim(), WaterPropsIAPWS::delta, WaterPropsIAPWS::m_phi, WaterPropsIAPWS::tau, and WaterPropsIAPWSphi::tdpolycalc().

Referenced by WaterPropsIAPWS::corr(), WaterPropsIAPWS::corr1(), PDSS_Water::cp_R_ref(), WaterPropsIAPWS::density(), PDSS_Water::dthermalExpansionCoeffdT(), WaterSSTP::dthermalExpansionCoeffdT(), PDSS_Water::enthalpy_RT_ref(), PDSS_Water::entropy_R_ref(), WaterSSTP::getCp_R_ref(), WaterSSTP::getEntropy_R_ref(), WaterSSTP::getGibbs_RT_ref(), PDSS_Water::gibbs_RT_ref(), PDSS_Water::molarVolume_ref(), WaterPropsIAPWS::psat(), WaterSSTP::satPressure(), PDSS_Water::setDensity(), WaterSSTP::setDensity(), PDSS_Water::setState_TR(), PDSS_Water::setTemperature(), and WaterSSTP::setTemperature().

doublereal helmholtzFE ( ) const

Calculate the Helmholtz free energy in mks units of J kmol-1 K-1, using the last temperature and density.

Definition at line 95 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, WaterPropsIAPWS::m_phi, WaterPropsIAPWSphi::phi(), Cantera::Rgas, Cantera::T_c, WaterPropsIAPWS::tau, and WaterPropsIAPWS::temperature().

doublereal Gibbs ( ) const

Calculate the Gibbs free energy in mks units of J kmol-1 K-1.

using the last temperature and density

Definition at line 304 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWSphi::gibbs_RT(), WaterPropsIAPWS::m_phi, Cantera::Rgas, Cantera::T_c, WaterPropsIAPWS::tau, and WaterPropsIAPWS::temperature().

Referenced by WaterSSTP::getGibbs_RT(), WaterSSTP::getGibbs_RT_ref(), WaterSSTP::getStandardChemPotentials(), and PDSS_Water::gibbs_mole().

doublereal enthalpy ( ) const

Calculate the enthalpy in mks units of J kmol-1 using the last temperature and density.

Definition at line 636 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWSphi::enthalpy_RT(), WaterPropsIAPWS::m_phi, Cantera::Rgas, Cantera::T_c, WaterPropsIAPWS::tau, and WaterPropsIAPWS::temperature().

Referenced by PDSS_Water::enthalpy_mole(), PDSS_Water::enthalpy_RT_ref(), WaterSSTP::getEnthalpy_RT(), WaterSSTP::getEnthalpy_RT_ref(), and PDSS_Water::gibbs_RT_ref().

doublereal intEnergy ( ) const

Calculate the internal energy in mks units of J kmol-1.

Definition at line 643 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWSphi::intEnergy_RT(), WaterPropsIAPWS::m_phi, Cantera::Rgas, Cantera::T_c, WaterPropsIAPWS::tau, and WaterPropsIAPWS::temperature().

Referenced by WaterSSTP::getIntEnergy_RT(), and PDSS_Water::intEnergy_mole().

doublereal entropy ( ) const

Calculate the entropy in mks units of J kmol-1 K-1.

Definition at line 650 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWSphi::entropy_R(), WaterPropsIAPWS::m_phi, and Cantera::Rgas.

Referenced by PDSS_Water::entropy_mole(), PDSS_Water::entropy_R_ref(), WaterSSTP::getEntropy_R(), and WaterSSTP::getEntropy_R_ref().

doublereal cv ( ) const

Calculate the constant volume heat capacity in mks units of J kmol-1 K-1 at the last temperature and density.

Definition at line 656 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWSphi::cv_R(), WaterPropsIAPWS::m_phi, and Cantera::Rgas.

Referenced by PDSS_Water::cv_mole(), and WaterSSTP::cv_mole().

doublereal cp ( ) const

Calculate the constant pressure heat capacity in mks units of J kmol-1 K-1 at the last temperature and density.

Definition at line 662 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWSphi::cp_R(), WaterPropsIAPWS::m_phi, and Cantera::Rgas.

Referenced by PDSS_Water::cp_mole(), PDSS_Water::cp_R_ref(), WaterSSTP::getCp_R(), and WaterSSTP::getCp_R_ref().

doublereal molarVolume ( ) const

Calculate the molar volume (kmol m-3) at the last temperature and density.

Definition at line 668 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, Cantera::M_water, and Cantera::Rho_c.

Referenced by PDSS_Water::molarVolume(), and PDSS_Water::molarVolume_ref().

doublereal pressure ( ) const

Calculates the pressure (Pascals), given the current value of the temperature and density.

The density is an independent variable in the underlying equation of state

Returns: returns the pressure (Pascal)

Definition at line 103 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, WaterPropsIAPWS::m_phi, Cantera::M_water, WaterPropsIAPWSphi::pressureM_rhoRT(), Cantera::Rgas, Cantera::Rho_c, Cantera::T_c, WaterPropsIAPWS::tau, and WaterPropsIAPWS::temperature().

Referenced by PDSS_Water::pressure(), and WaterSSTP::pressure().

doublereal density	(	doublereal	temperature,
		doublereal	pressure,
		int	phase = `-1`,
		doublereal	rhoguess = `-1.0`
	)

Calculates the density given the temperature and the pressure, and a guess at the density.

Sets the internal state.

Note, below T_c, this is a multivalued function.

The density() function calculates the density that is consistent with a particular value of the temperature and pressure. It may therefore be multivalued or potentially there may be no answer from this function. It therefore takes a phase guess and a density guess as optional parameters. If no guesses are supplied to density(), a gas phase guess is assumed. This may or may not be what is wanted. Therefore, density() should usually at least be supplied with a phase guess so that it may manufacture an appropriate density guess. density() manufactures the initial density guess, nondimensionalizes everything, and then calls WaterPropsIAPWSphi::dfind(), which does the iterative calculation to find the density condition that matches the desired input pressure.

Parameters

temperature	Kelvin
pressure	: Pressure in Pascals (Newton/m**2)
phase	: guessed phase of water : -1: no guessed phase
rhoguess	: guessed density of the water : -1.0 no guessed density

Returns: Returns the density. If an error is encountered in the calculation the value of -1.0 is returned.

Definition at line 111 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, WaterPropsIAPWSphi::dfind(), Cantera::int2str(), WaterPropsIAPWS::m_phi, Cantera::M_water, Cantera::Rgas, Cantera::Rho_c, WaterPropsIAPWS::setState_TR(), Cantera::T_c, WaterPropsIAPWS::tau, and WaterPropsIAPWS::temperature().

Referenced by WaterProps::coeffThermalExp_IAPWS(), PDSS_Water::constructSet(), PDSS_Water::cp_R_ref(), WaterProps::density_IAPWS(), PDSS_Water::dthermalExpansionCoeffdT(), WaterSSTP::dthermalExpansionCoeffdT(), PDSS_Water::enthalpy_RT_ref(), PDSS_Water::entropy_R_ref(), WaterSSTP::getCp_R_ref(), WaterSSTP::getEnthalpy_RT_ref(), WaterSSTP::getEntropy_R_ref(), WaterSSTP::getGibbs_RT_ref(), WaterSSTP::getStandardVolumes_ref(), PDSS_Water::gibbs_RT_ref(), WaterSSTP::initThermoXML(), WaterProps::isothermalCompressibility_IAPWS(), PDSS_Water::molarVolume_ref(), PDSS_Water::satPressure(), PDSS_Water::setPressure(), WaterSSTP::setPressure(), WaterProps::thermalConductivityWater(), and WaterProps::viscosityWater().

doublereal density_const	(	doublereal	pressure,
		int	phase = `-1`,
		doublereal	rhoguess = `-1.0`
	)		const

Calculates the density given the temperature and the pressure, and a guess at the density, while not changing the internal state.

Note, below T_c, this is a multivalued function.

The density() function calculates the density that is consistent with a particular value of the temperature and pressure. It may therefore be multivalued or potentially there may be no answer from this function. It therefore takes a phase guess and a density guess as optional parameters. If no guesses are supplied to density(), a gas phase guess is assumed. This may or may not be what is wanted. Therefore, density() should usually at least be supplied with a phase guess so that it may manufacture an appropriate density guess. density() manufactures the initial density guess, nondimensionalizes everything, and then calls WaterPropsIAPWSphi::dfind(), which does the iterative calculation to find the density condition that matches the desired input pressure.

Parameters

pressure	: Pressure in Pascals (Newton/m**2)
phase	: guessed phase of water : -1: no guessed phase
rhoguess	: guessed density of the water : -1.0 no guessed density

Returns: Returns the density. If an error is encountered in the calculation the value of -1.0 is returned.

Definition at line 170 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, WaterPropsIAPWSphi::dfind(), Cantera::int2str(), WaterPropsIAPWS::m_phi, Cantera::M_water, Cantera::Rgas, Cantera::Rho_c, Cantera::T_c, WaterPropsIAPWS::tau, WaterPropsIAPWSphi::tdpolycalc(), and WaterPropsIAPWS::temperature().

Referenced by WaterPropsIAPWS::densSpinodalSteam(), and WaterPropsIAPWS::densSpinodalWater().

doublereal density ( ) const

Returns the density (kg m-3)

The density is an independent variable in the underlying equation of state

Returns: Returns the density (kg m-3)

Definition at line 232 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, and Cantera::Rho_c.

Referenced by WaterPropsIAPWS::corr(), WaterPropsIAPWS::corr1(), and WaterPropsIAPWS::psat().

doublereal temperature ( ) const

Returns the temperature (Kelvin)

Returns: Returns the internally stored temperature

Definition at line 237 of file WaterPropsIAPWS.cpp.

References Cantera::T_c, and WaterPropsIAPWS::tau.

Referenced by WaterPropsIAPWS::calcDim(), WaterPropsIAPWS::density(), WaterPropsIAPWS::density_const(), WaterPropsIAPWS::densSpinodalSteam(), WaterPropsIAPWS::densSpinodalWater(), WaterPropsIAPWS::dpdrho(), WaterPropsIAPWS::enthalpy(), WaterPropsIAPWS::Gibbs(), WaterPropsIAPWS::helmholtzFE(), WaterPropsIAPWS::intEnergy(), WaterPropsIAPWS::pressure(), WaterProps::thermalConductivityWater(), and WaterProps::viscosityWater().

doublereal coeffThermExp ( ) const

Returns the coefficient of thermal expansion.

alpha = d (ln V) / dT at constant P.

Returns: Returns the coefficient of thermal expansion

Definition at line 296 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::coeffPresExp(), WaterPropsIAPWS::delta, WaterPropsIAPWS::isothermalCompressibility(), Cantera::M_water, Cantera::Rgas, and Cantera::Rho_c.

Referenced by WaterProps::coeffThermalExp_IAPWS(), PDSS_Water::dthermalExpansionCoeffdT(), WaterSSTP::dthermalExpansionCoeffdT(), PDSS_Water::thermalExpansionCoeff(), and WaterSSTP::thermalExpansionCoeff().

doublereal coeffPresExp ( ) const

Returns the isochoric pressure derivative wrt temperature.

beta = M / (rho * Rgas) (d (pressure) / dT) at constant rho

Note for ideal gases this is equal to one.

beta = delta (phi0_d() + phiR_d())
        - tau delta (phi0_dt() + phiR_dt())

Definition at line 291 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, WaterPropsIAPWSphi::dimdpdT(), WaterPropsIAPWS::m_phi, and WaterPropsIAPWS::tau.

Referenced by WaterPropsIAPWS::coeffThermExp(), and WaterProps::thermalConductivityWater().

doublereal isothermalCompressibility ( ) const

Returns the coefficient of isothermal compressibility for the state of the object.

kappa = - d (ln V) / dP at constant T.

units - 1/Pascal

Returns: returns the isothermal compressibility

Definition at line 277 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, WaterPropsIAPWS::dpdrho(), and Cantera::Rho_c.

Referenced by WaterPropsIAPWS::coeffThermExp(), WaterSSTP::isothermalCompressibility(), PDSS_Water::isothermalCompressibility(), WaterProps::isothermalCompressibility_IAPWS(), and WaterPropsIAPWS::phaseState().

doublereal dpdrho ( ) const

Returns the value of dp / drho at constant T for the state of the object.

units - Joules / kg

Returns: returns dpdrho

Definition at line 284 of file WaterPropsIAPWS.cpp.

References WaterPropsIAPWS::delta, WaterPropsIAPWSphi::dimdpdrho(), WaterPropsIAPWS::m_phi, Cantera::M_water, Cantera::Rgas, Cantera::T_c, WaterPropsIAPWS::tau, and WaterPropsIAPWS::temperature().

Referenced by WaterPropsIAPWS::densSpinodalSteam(), WaterPropsIAPWS::densSpinodalWater(), WaterPropsIAPWS::isothermalCompressibility(), WaterProps::thermalConductivityWater(), and WaterProps::viscosityWater().

doublereal psat_est ( doublereal temperature ) const

This function returns an estimated value for the saturation pressure.

It does this via a polynomial fit of the vapor pressure curve. units = (Pascals)

Parameters

temperature Input temperature (Kelvin)

Returns: Returns the estimated saturation pressure

Definition at line 242 of file WaterPropsIAPWS.cpp.

Referenced by WaterPropsIAPWS::densSpinodalSteam(), WaterPropsIAPWS::densSpinodalWater(), PDSS_Water::pref_safe(), and WaterPropsIAPWS::psat().

doublereal psat	(	doublereal	temperature,
		int	waterState = `WATER_LIQUID`
	)

This function returns the saturation pressure given the temperature as an input parameter, and sets the internal state to the saturated conditions.

Note this function will return the saturation pressure, given the temperature. It will then set the state of the system to the saturation condition. The input parameter waterState is used to either specify the liquid state or the gas state at the desired temperature and saturated pressure.

If the input temperature, T, is above T_c, this routine will set the internal state to T and the pressure to P_c. Then, return P_c.

Parameters