The GERG04 class implements the GERG 2004 equation of state. More...

#include <gerg04.hpp>

Inheritance diagram for GERG04:

Public Member Functions
	GERG04 (const arma::vec &composition=Composition::defaultComposition)
	GERG04 constructor. More...

virtual arma::vec	evaluate (const double pressure, const double temperature) const override
	Evaluate the GERG 2004 equation of state at the given pressure and temperature. More...

arma::vec	evaluateAllProperties (const double pressure, const double temperature) const
	Evaluate all available gas properties at a given pressure and temperature. More...

virtual double	calculateCompressibility (const double pressure, const double temperature) const override
	Calculate compressibility Z at given pressure and temperature. More...

virtual bool	setComposition (const arma::vec &composition, const bool force=true) override
	Set the composition. More...

double	findDensity (const double pressure, const double temperature) const
	Find the density of the gas at a given pressure and temperature. More...

double	findSpeedOfSound (const double temperature, const double density) const
	Find the soundspeed in the gas at a given temperature and density. More...

const arma::uvec &	indicesOfNonZeroComponents () const
	Get the indices of the non-zero components in the composition. More...

Public Member Functions inherited from EquationOfStateBase
virtual	~EquationOfStateBase ()

	EquationOfStateBase (const arma::vec &composition=Composition::defaultComposition)
	EquationOfStateBase constructor. More...

virtual arma::vec	evaluate (const double pressure, const double temperature, const arma::vec &composition)
	Virtual function for evaluating the EOS at a new composition. More...

virtual double	calculateStandardDensity () const

double	getMolarMassOfMixture () const
	Get the molar mass of the gas.

const arma::vec &	getComposition () const
	Get the current composition stored in the EOS instance.

Private Member Functions
double	findDensity (const double pressure, const double temperature, double &density, double &aroidelta, double &arijdelta, double &aroideltadelta, double &arijdeltadelta) const
	Internal (private) function used in the process of evaluating the GERG 2004 equations. More...

void	evaluateAlpha_roi_deltas (const double tred_temperature, const double start_rhored, const double start_rhored_pow_minusOne, const double start_rhored_pow_minusTwo, double &aroidelta, double &arijdelta, double &aroideltadelta, double &arijdeltadelta) const
	Internal (private) function used in the process of evaluating the GERG 2004 equations. More...

void	setNonZeroComponents ()
	Internal (private) function that updates the non-zero components. More...

void	calculateCoefficients ()
	Set the pressure and temperature independent coefficients. More...

Private Attributes
const arma::uword	N = 10
	Number of components.

arma::vec	X
	Composition in order CH4, N2, CO2, C2H6, C3H8, nC4H10, iC4H10, nC5H12, iC5H12, nC6H14.

arma::vec	Tc = {190.56, 126.19, 304.13, 305.32, 369.83, 425.13, 407.82, 469.7, 460.35, 507.82}
	Critical temperature [K] for components CH4, N2, CO2, C2H6, C3H8, nC4H10, iC4H10, nC5H12, iC5H12, nC6H14.

arma::vec	rhoc = {10.1416.04, 11.1828.01, 10.6244.01, 6.8730.07, 544.1, 3.9258.12, 3.8658.12, 3.2172.15, 3.2772.15, 2.7186.18}
	Critical density [kg/m3] for components CH4, N2, CO2, C2H6, C3H8, nC4H10, iC4H10, nC5H12, iC5H12, nC6H14.

arma::uvec	m_indices
	The indices of the non-zero gas fractions (components). More...

arma::uvec	m_firstIndices
	The indices of the two first non-zero gas fractions (components). More...

arma::uvec	m_lastIndices
	The indices of the two last non-zero gas fractions (components). More...

double	rhored
	Inverse reducing function for mixture density \(1/\rho_r(\bar x)\).

double	tred
	Reducing function for mixture temperature \(T_r(\bar x)\).

double	Ra
	Gas constant of mixture [J/mol K].

Static Private Attributes
static arma::mat	betav
	\(\beta_{v, ij}\) density interaction coefficient, from table A3.8

static arma::mat	betat
	\(\beta_{T, ij}\) temperature coefficient, from table A3.8

static arma::mat	gammav
	\(\gamma_{v, ij}\) density interaction coefficient, from table A3.8

static arma::mat	gammat
	\(\gamma_{T, ij}\) temperature interaction coefficient, from table A3.8

static arma::mat	noipol
	\(n_{oi, k}\), from Table A3.2 in TM15, used in the first sum of alpha^r_{oi}

static arma::mat	doipol
	\(d_{oi, k}\), from Table A3.2 in TM15, used in the first sum of alpha^r_{oi}

static arma::mat	toipol
	\(t_{oi, k}\), from Table A3.2 in TM15, used in the first sum of alpha^r_{oi}

static arma::mat	noiexp
	\(n_{oi, k}\), from Table A3.3 in TM15, used in the second sum of alpha^r_{oi}

static arma::mat	doiexp
	\(d_{oi, k}\), from Table A3.3 in TM15, used in the second sum of alpha^r_{oi}

static arma::mat	coiexp
	\(c_{oi, k}\), from Table A3.3 in TM15, used in the second sum of alpha^r_{oi}

static arma::mat	toiexp
	\(t_{oi, k}\), from Table A3.3 in TM15, used in the second sum of alpha^r_{oi}

static arma::mat	Fij
	\(F_{ij}\) interaction coefficient

static arma::cube	nijpol
	\(n_{ij, k}\), from Table A3.7 in TM15, used in the first sum of alpha^r_{ij}

static arma::cube	dijpol
	\(d_{ij, k}\), from Table A3.7 in TM15, used in the first sum of alpha^r_{ij}

static arma::cube	tijpol
	\(t_{ij, k}\), from Table A3.7 in TM15, used in the first sum of alpha^r_{ij}

static arma::cube	nijexp
	\(n_{ij, k}\), from Table A3.7 in TM15, used in the second sum of alpha^r_{ij}

static arma::cube	dijexp
	\(d_{ij, k}\), from Table A3.7 in TM15, used in the second sum of alpha^r_{ij}

static arma::cube	tijexp
	\(t_{ij, k}\), from Table A3.7 in TM15, used in the second sum of alpha^r_{ij}

static arma::cube	nuijexp
	\(\nu_{ij, k}\), from Table A3.7 in TM15, used in the second sum of alpha^r_{ij}

static arma::cube	epijexp
	\(\epsilon_{ij, k}\), from Table A3.7 in TM15, used in the second sum of alpha^r_{ij}

static arma::cube	beijexp
	\(\beta_{ij, k}\), from Table A3.7 in TM15, used in the second sum of alpha^r_{ij}

static arma::cube	gaijexp
	\(\gamma_{ij, k}\), from Table A3.7 in TM15, used in the second sum of alpha^r_{ij}

static arma::mat	noik
	\(n^o_{oi, k}\), from Table A3.1 in TM15, used in alpha^o_{oi}

static arma::mat	voik
	\(n^o_{oi, k}\), from Table A3.1 in TM15, used in alpha^o_{oi}

static arma::cube	nijpol_times_tijpol
	\(n_{ij, k} \times t_{ij, k}\) (GERG04::nijpol x GERG04::tijpol)

static arma::cube	nijpol_times_tijpol_times_tijpol_minus_one
	\((n_{ij, k} \times t_{ij, k}) \times (t_{ij, k} - 1)\) ((GERG04::nijpol x GERG04::tijpol) x (GERG04::tijpol - 1.0))

static arma::cube	nijexp_times_tijexp
	\(n_{ij, k} \times t_{ij, k}\) (GERG04::nijexp x GERG04::tijexp)

static arma::cube	nijexp_times_tijexp_times_tijexp_minus_one
	\((n_{ij, k} \times t_{ij, k}) \times (t_{ij, k} - 1)\) ((GERG04::nijpol x GERG04::tijpol) x (GERG04::tijpol - 1.0))

static arma::cube	nijpol_times_dijpol
	\(n_{ij, k} \times d_{ij, k}\) (GERG04::nijpol x GERG04::dijpol)

static arma::cube	nijpol_times_dijpol_times_tijpol
	\(n_{ij, k} \times d_{ij, k} \times t_{ij, k}\) (GERG04::nijpol x GERG04::dijpol x GERG04::tijpol)

static arma::cube	nijpol_times_dijpol_times_dijpol_minus_one
	\(n_{ij, k} \times d_{ij, k} \times(d_{ij, k} - 1) \) (GERG04::nijpol x GERG04::dijpol x (GERG04::dijpol - 1.0))

Additional Inherited Members
Protected Attributes inherited from EquationOfStateBase
arma::vec	m_molarMass = { 16.04, 30.07, 44.1, 58.12, 58.12, 72.15, 72.15, 86.18, 28.13, 44.01}
	The molar mass [g/mol] of the different gas components, in order C1, C2, C3, iC4, nC4, iC5, nC5, C6, N2, CO2.

arma::vec::fixed< 10 >	m_composition = arma::vec(10)
	The composition of the gas as fractions, in order C1, C2, C3, iC4, nC4, iC5, nC5, C6, N2, CO2.

double	m_molarMassOfMixture
	The molar mass of the gas mixture [g/mol].

double	m_density = 0
	Cache density for optimization [kg/m3].

Detailed Description

The GERG04 class implements the GERG 2004 equation of state.

This is a higly accurate, but extremely complex equation of state. It has explicit forms for a lot of properties like heat capacity etc., which are utilized where possible.

Warning: Note that the composition stored internally in GERG04::X is not in the typical order, but in order C1, C2, C3, iC4, nC4, iC5, nC5, C6, N2, CO2.

More info:

Constructor & Destructor Documentation

◆ GERG04()

GERG04::GERG04 ( const arma::vec & composition = Composition::defaultComposition )

explicit

GERG04 constructor.

Initializes the coefficients that only depend on composition.

Parameters

composition Gas composition in arma::vec, in the order C1, C2, C3, iC4, nC4, iC5, nC5, C6, N2, CO2.

Member Function Documentation

◆ calculateCoefficients()

void GERG04::calculateCoefficients ( )

private

Set the pressure and temperature independent coefficients.

This calculates and sets the pressure and temperature independent factors GERG04::rhored and GERG04::tred, which are stored for efficient' computation.

◆ calculateCompressibility()

virtual double GERG04::calculateCompressibility	(	const double	pressure,
		const double	temperature
	)		const

overridevirtual

Calculate compressibility Z at given pressure and temperature.

Parameters

pressure	Gas pressure [Pa].
temperature	Gas temperature [K].

Returns: Compressibility factor Z [-].

Implements EquationOfStateBase.

◆ evaluate()

virtual arma::vec GERG04::evaluate	(	const double	pressure,
		const double	temperature
	)		const

overridevirtual

Evaluate the GERG 2004 equation of state at the given pressure and temperature.

This is a wrapper around evaluateAllProperties(), which selects the wanted properties from that function. This could perhaps be optimized a bit, since some of the calculations are not required. But the brunt of the cpu time is spent in findDensity() anyway, so there probably isn't that much to save.

Parameters

pressure	Gas pressure [Pa]
temperature	Gas temperature [K]

Returns: See EquationOfStateBase::evaluate().

Implements EquationOfStateBase.

◆ evaluateAllProperties()

arma::vec GERG04::evaluateAllProperties	(	const double	pressure,
		const double	temperature
	)		const

Evaluate all available gas properties at a given pressure and temperature.

We have implemented 15 of the explicit equations for different properties given in the GERG 2004 documentation.

The method returns an arma::vec containing:

compressibility factor Z
partial derivative of Z wrt. temperature at constant pressure \(\frac{\partial Z}{\partial T}|_p\)
partial derivative of Z wrt. pressure at constant temperature \(\frac{\partial Z}{\partial p}|_T\)
partial derivative of Z wrt. temperature at constant density \(\frac{\partial Z}{\partial T}|_\rho\)
entropy S
internal energy U
heat capacity at constant volume \(c_v\)
enthalpy H
heat capacity at constant pressure \(c_p\)
gibbs free energy G
Joule-Thomson coefficient
speed of sound
isothermal throttling coefficient
density ρ
isentropic exponent \(\gamma = \frac{c_p}{c_v}\)

Warning: Other than the compressibility factor, the partial derivatives, and the heat capacity, the output of this function has not been tested properly. Feel free to implement tests for the other results.

Parameters

pressure	Gas pressure [Pa].
temperature	Gas temperature [K].

Returns: An arma::vec containing all the properties. See the detailed description for more details.

◆ evaluateAlpha_roi_deltas()

void GERG04::evaluateAlpha_roi_deltas	(	const double	tred_temperature,
		const double	start_rhored,
		const double	start_rhored_pow_minusOne,
		const double	start_rhored_pow_minusTwo,
		double &	aroidelta,
		double &	arijdelta,
		double &	aroideltadelta,
		double &	arijdeltadelta
	)		const

private

Internal (private) function used in the process of evaluating the GERG 2004 equations.

Parameters

tred_temperature	Inverse reduced mixture temperature.
start_rhored	Reduced mixture density.
start_rhored_pow_minusOne	pow(reduced mixture density, -1)
start_rhored_pow_minusTwo	pow(reduced mixture density, -2)
aroidelta	Output argument – left sum in eq. (7.21b) in TM15 (also appears in other equations).
arijdelta	Output argument – the right (double) sum in eq. (7.21b) in TM15 (also appears in other equations).
aroideltadelta	Output argument – the left sum in eq. (7.21c) in TM15 (also appears in other equations).
arijdeltadelta	Output argument – the right (double) sum in eq. (7.21c) in TM15 (also appears in other equations).

◆ findDensity() [1/2]

double GERG04::findDensity	(	const double	pressure,
		const double	temperature
	)		const

Find the density of the gas at a given pressure and temperature.

Parameters

pressure	Gas pressure [Pa].
temperature	Gas temperature [K].

Returns: Gas density [kg/m3]

◆ findDensity() [2/2]

double GERG04::findDensity	(	const double	pressure,
		const double	temperature,
		double &	density,
		double &	aroidelta,
		double &	arijdelta,
		double &	aroideltadelta,
		double &	arijdeltadelta
	)		const

private

Internal (private) function used in the process of evaluating the GERG 2004 equations.

Uses Newton-Raphson to find the density, so will be pretty cpu heavy (depending on the starting point).

Parameters

pressure	Gas pressure [P].
temperature	Gas Temperature [K].
density	Gas density [kg/m3].
aroidelta	Output argument - left sum in eq. (7.21b) in TM15 (also appears in other equations).
arijdelta	Output argument - the right (double) sum in eq. (7.21b) in TM15 (also appears in other equations).
aroideltadelta	Output argument - the left sum in eq. (7.21c) in TM15 (also appears in other equations).
arijdeltadelta	Output argument - the right (double) sum in eq. (7.21c) in TM15 (also appears in other equations).

Returns: The gas density [kg/m3] as well as many other factors via the output arguments.

◆ findSpeedOfSound()

double GERG04::findSpeedOfSound	(	const double	temperature,
		const double	density
	)		const

Find the soundspeed in the gas at a given temperature and density.

Parameters

temperature	Gas temperature [K].
density	Gas density [kg/m3]

Returns: Speed of sound in gas [m/s].

◆ indicesOfNonZeroComponents()

const arma::uvec& GERG04::indicesOfNonZeroComponents ( ) const

inline

Get the indices of the non-zero components in the composition.

Warning: Note that the components are stored internally in GERG04 in a different order than the input order and the usual order, so it's not straight-forward to relate this to usual composition.

Returns: The indices of the non-zero components.

◆ setComposition()

virtual bool GERG04::setComposition	(	const arma::vec &	composition,
		const bool	force = `true`
	)

overridevirtual

Set the composition.

This calls EquationOfStateBase::setComposition(), updates the non-zero component indices GERG04::m_indices, and calculates the inverse reducing function for mixture density GERG04::rhored and the reducing function for mixture temperature GERG04::tred.

Parameters

composition	New gas composition.
force	If the composition should be changed even if it's within machine precision of the previous composition.

Returns: True if composition was changed, else false.

Reimplemented from EquationOfStateBase.

◆ setNonZeroComponents()

void GERG04::setNonZeroComponents ( )

private

Internal (private) function that updates the non-zero components.

This function updates GERG04::m_indices, GERG04::m_firstIndices, and GERG04::m_lastIndices according to the current composition stored in GERG04::X.

Member Data Documentation

◆ m_firstIndices

arma::uvec GERG04::m_firstIndices

private

The indices of the two first non-zero gas fractions (components).

Warning: Note that the components are stored internally in GERG04 in a different order than the input order and the usual order, so it's not straight-forward to relate this to usual composition.

◆ m_indices

arma::uvec GERG04::m_indices

private

The indices of the non-zero gas fractions (components).

Warning: Note that the components are stored internally in GERG04 in a different order than the input order and the usual order, so it's not straight-forward to relate this to usual composition.

◆ m_lastIndices

arma::uvec GERG04::m_lastIndices

private

The indices of the two last non-zero gas fractions (components).

Warning: Note that the components are stored internally in GERG04 in a different order than the input order and the usual order, so it's not straight-forward to relate this to usual composition.

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

D:/Code/transient-pipeline-flow-gh-pages/src/equationofstate/gerg04.hpp

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ GERG04()

Member Function Documentation

◆ calculateCoefficients()

◆ calculateCompressibility()

◆ evaluate()

◆ evaluateAllProperties()

◆ evaluateAlpha_roi_deltas()

◆ findDensity() [1/2]

◆ findDensity() [2/2]

◆ findSpeedOfSound()

◆ indicesOfNonZeroComponents()

◆ setComposition()

◆ setNonZeroComponents()

Member Data Documentation

◆ m_firstIndices

◆ m_indices

◆ m_lastIndices