Fundamental Helmholtz equation of state for hydrogen, after Leachman, Jacobsen, Penoncello and Lemmon 2009, doi 10.1063/1.3160306. More...

#include <cl_GM_EoS_Hydrogen.hpp>

Inheritance diagram for belfem::gasmodels::EoS_Hydrogen:

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Collaboration diagram for belfem::gasmodels::EoS_Hydrogen:

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Public Member Functions
	EoS_Hydrogen (Gas &aParent, const HelmholtzModel aModel)
	~EoS_Hydrogen ()
Public Member Functions inherited from belfem::gasmodels::Helmholtz
	Helmholtz (Gas &aParent, const string &aLabel)
virtual	~Helmholtz ()=default
const real &	T_min () const
	minumum temperature for gas model ( triple point )
const real &	T_max () const
	maximum temperature for gas model
const real &	T_crit () const
	critical temperature
const real &	v_crit () const
	critical volume
virtual real	p_vap (const real T) const
virtual real	T_vap (const real p) const
real	hvap (const real T, const real p) const
	vaporization enthalpy in J/kg
real	phi (const real T, const real v) const
	the main energy function, where phi = f / ( R * T )
real	p (const real T, const real v) const
	pressure in Pa
real	v (const real T, const real p) const
	specific volume in m^3/kg
real	T (const real p, const real v) const
	temperature in K
real	dpdv (const real T, const real v) const
real	dpdT (const real T, const real v) const
real	dvdT (const real T, const real v) const
real	u (const real T, const real p) const
real	h (const real T, const real p) const
real	s (const real T, const real p) const
real	cv (const real T, const real p) const
real	cp (const real T, const real p) const
real	w (const real T, const real p) const
	speed of sound in m/s ( helmholtz only )
real	dsdT (const real T, const real p) const
real	dsdp (const real T, const real p) const
real	alpha (const real T, const real p) const
	thermal expansion coefficient
real	beta (const real T, const real p) const
	isochoric stress coefficient
real	kappa (const real T, const real p) const
	isothermal compressibility coefficient
void	remix ()
	this function remixes the cubic help gas
void	eval_critical_point (real &T, real &p, real &v) const
	return the critical point data
void	update_Tv (const real T, const real v) const
	reset all state variales
void	update_Tp (const real T, const real p) const
const real &	phir () const
	the main energy function, real gas contribution
const real &	phir_d () const
const real &	phir_dd () const
const real &	phir_t () const
const real &	phir_tt () const
const real &	phir_dt () const
const real &	phi0 () const
const real &	phi0_t () const
const real &	phi0_tt () const
Public Member Functions inherited from belfem::gasmodels::EoS
	EoS (Gas &aParent)
virtual	~EoS ()=default
virtual real	d2pdT2 (const real T, const real v) const
virtual real	d2pdv2 (const real T, const real v) const
virtual real	hdep (const real T, const real p) const
virtual real	cpdep (const real T, const real p) const
virtual real	sdep (const real T, const real p) const
virtual real	dhdepdp (const real T, const real p) const
virtual real	dsdepdT (const real T, const real p) const
virtual real	dsdepdp (const real T, const real p) const
virtual real	hdep0 (const real T) const
virtual real	cpdep0 (const real T) const
virtual real	sdep0 (const real T) const
virtual real	dsdepdT0 (const real T) const
virtual real	v (const uint aIndex, const real T, const real p) const
virtual real	hdep (const uint aIndex, const real T, const real p) const
virtual real	cpdep (const uint aIndex, const real T, const real p) const
virtual real	pi (const real T, const real p) const
virtual real	dpidp (const real T, const real p) const
Gas *	parent ()
	expose the parent of this EoS

Protected Member Functions
real	compute_phi0 () const
real	compute_phir () const
real	compute_phi0_t () const
real	compute_phi0_tt () const
real	compute_phir_d () const
real	compute_phir_dd () const
real	compute_phir_t () const
real	compute_phir_tt () const
real	compute_phir_dt () const
Protected Member Functions inherited from belfem::gasmodels::Helmholtz
void	delete_cubic_eos ()
void	set_critical_point_in_data_object ()
void	set_reference_point ()
void	set_reference_point (const real aTref, const real aPref)
void	init_Tvap_poly ()
virtual real	pi_vap (const real T) const
virtual real	psi_vap (const real T) const
virtual real	dpvap_dT (const real T, const real aPvap, const real aPiVap) const
bool	is_liquid (const real T, const real p) const

Additional Inherited Members
Static Protected Member Functions inherited from belfem::gasmodels::Helmholtz
static real	ipow (real x, uint n)
	integer power by binary exponentiation, for the coefficient tables of the residual functions.
static real	hpow (const real x, const real sqrt_x, const int n)
	x^( n / 2 ) for a signed half integer exponent given as n = 2j.
Protected Attributes inherited from belfem::gasmodels::Helmholtz
const string	mLabel
EoS_Cubic *	mCubicEoS = nullptr
Vector< real >	mNvap
Vector< real >	mKvap
Vector< real >	mTvap
Vector< real >	mVliq
	initial solution for inversion of pvap
real	mH0 = 0.0
real	mS0 = 0.0
real	mU0 = 0.0
const real &	mTau = mHelmholtzVals[ BELFEM_HELMHOLTZ_TAU ]
const real &	mDelta = mHelmholtzVals[ BELFEM_HELMHOLTZ_DELTA ]
real	mTcrit = BELFEM_QUIET_NAN
	critical temperature in K
real	mPcrit = BELFEM_QUIET_NAN
	critical pressure in Pa
real	mRhocrit = BELFEM_QUIET_NAN
	critical density in kg/m^3
real	mVcrit = BELFEM_QUIET_NAN
	critical specific volume in m^3/kg
real	mTtriple = BELFEM_QUIET_NAN
	triple point in K
real	mTmax = BELFEM_QUIET_NAN
	maximum temperature of gas model in K
real	mPmax = BELFEM_REAL_MAX
Protected Attributes inherited from belfem::gasmodels::EoS
Gas &	mParent
	gas object that owns this class
Statevals &	mStatevals
	statevals object
const real &	mR
	specific gas constant
const real &	mM
	molar mass in kg/Mol

Detailed Description

Fundamental Helmholtz equation of state for hydrogen, after Leachman, Jacobsen, Penoncello and Lemmon 2009, doi 10.1063/1.3160306.

Covers all three spin variants - parahydrogen, normal hydrogen and orthohydrogen - selected by the HelmholtzModel passed to the constructor, which swaps the whole coefficient set including the critical point and the vapor pressure ancillary. Normal hydrogen is the one that carries CAS 1333-74-0 and is what the gas tables resolve by default.

Valid from the triple point to 1000 K and to 2000 MPa.

Unlike its methane and oxygen siblings the tau exponents of this formulation do not sit on a half integer grid, so the powers are evaluated with std::pow rather than the hpow helper of the base.