a model for the helmholtz energy, specifically user for cryogenic fluids More...

#include <cl_GM_Helmholtz.hpp>

Inheritance diagram for belfem::gasmodels::Helmholtz:

Collaboration diagram for belfem::gasmodels::Helmholtz:

Public Member Functions
	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
Ideal gas contribution to the reduced Helmholtz energy
phi0 and its first and second derivatives with respect to tau. They take no arguments: the state is whatever update_Tp or update_Tv last set, and tau = T_crit / T and delta = v_crit / v are read from the cache. Each is evaluated once per state and then served from that cache.
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
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
virtual real	compute_phi0 () const
virtual real	compute_phir () const
virtual real	compute_phi0_t () const
virtual real	compute_phi0_tt () const
virtual real	compute_phir_d () const
virtual real	compute_phir_dd () const
virtual real	compute_phir_t () const
virtual real	compute_phir_tt () const
virtual real	compute_phir_dt () const

Static Protected Member Functions
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
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

a model for the helmholtz energy, specifically user for cryogenic fluids

See also: Gas Models Usage Guide

Constructor & Destructor Documentation

◆ Helmholtz()

belfem::gasmodels::Helmholtz::Helmholtz	(	Gas &	aParent,
		const string &	aLabel )

◆ ~Helmholtz()

virtual belfem::gasmodels::Helmholtz::~Helmholtz ( )

virtualdefault

Member Function Documentation

◆ alpha()

real belfem::gasmodels::Helmholtz::alpha	(	const real	T,
		const real	p ) const

virtual

thermal expansion coefficient

\( \alpha = \frac{1}{v} \left( \frac{\partial v}{\partial T}\right)_p \)

Reimplemented from belfem::gasmodels::EoS.

◆ beta()

real belfem::gasmodels::Helmholtz::beta	(	const real	T,
		const real	p ) const

virtual

isochoric stress coefficient

\( \beta = \frac{1}{p} \left( \frac{\partial p}{\partial T}\right)_v \)

Reimplemented from belfem::gasmodels::EoS.

◆ compute_phi0()

real belfem::gasmodels::Helmholtz::compute_phi0 ( ) const

protectedvirtual

Reimplemented in belfem::gasmodels::EoS_Hydrogen, belfem::gasmodels::EoS_Methane, belfem::gasmodels::EoS_Nitrogen, and belfem::gasmodels::EoS_Oxygen.

◆ compute_phi0_t()

real belfem::gasmodels::Helmholtz::compute_phi0_t ( ) const

protectedvirtual

Reimplemented in belfem::gasmodels::EoS_Hydrogen, belfem::gasmodels::EoS_Methane, belfem::gasmodels::EoS_Nitrogen, and belfem::gasmodels::EoS_Oxygen.

◆ compute_phi0_tt()

real belfem::gasmodels::Helmholtz::compute_phi0_tt ( ) const

protectedvirtual

Reimplemented in belfem::gasmodels::EoS_Hydrogen, belfem::gasmodels::EoS_Methane, belfem::gasmodels::EoS_Nitrogen, and belfem::gasmodels::EoS_Oxygen.

◆ compute_phir()

real belfem::gasmodels::Helmholtz::compute_phir ( ) const

protectedvirtual

Reimplemented in belfem::gasmodels::EoS_Hydrogen, belfem::gasmodels::EoS_Methane, belfem::gasmodels::EoS_Nitrogen, and belfem::gasmodels::EoS_Oxygen.

◆ compute_phir_d()

real belfem::gasmodels::Helmholtz::compute_phir_d ( ) const

protectedvirtual

Reimplemented in belfem::gasmodels::EoS_Hydrogen, belfem::gasmodels::EoS_Methane, belfem::gasmodels::EoS_Nitrogen, and belfem::gasmodels::EoS_Oxygen.

◆ compute_phir_dd()

real belfem::gasmodels::Helmholtz::compute_phir_dd ( ) const

protectedvirtual

Reimplemented in belfem::gasmodels::EoS_Hydrogen, belfem::gasmodels::EoS_Methane, belfem::gasmodels::EoS_Nitrogen, and belfem::gasmodels::EoS_Oxygen.

◆ compute_phir_dt()

real belfem::gasmodels::Helmholtz::compute_phir_dt ( ) const

protectedvirtual

Reimplemented in belfem::gasmodels::EoS_Hydrogen, belfem::gasmodels::EoS_Methane, belfem::gasmodels::EoS_Nitrogen, and belfem::gasmodels::EoS_Oxygen.

◆ compute_phir_t()

real belfem::gasmodels::Helmholtz::compute_phir_t ( ) const

protectedvirtual

Reimplemented in belfem::gasmodels::EoS_Hydrogen, belfem::gasmodels::EoS_Methane, belfem::gasmodels::EoS_Nitrogen, and belfem::gasmodels::EoS_Oxygen.

◆ compute_phir_tt()

real belfem::gasmodels::Helmholtz::compute_phir_tt ( ) const

protectedvirtual

Reimplemented in belfem::gasmodels::EoS_Hydrogen, belfem::gasmodels::EoS_Methane, belfem::gasmodels::EoS_Nitrogen, and belfem::gasmodels::EoS_Oxygen.

◆ cp()

real belfem::gasmodels::Helmholtz::cp	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ cv()

real belfem::gasmodels::Helmholtz::cv	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ delete_cubic_eos()

void belfem::gasmodels::Helmholtz::delete_cubic_eos ( )

protected

◆ dpdT()

real belfem::gasmodels::Helmholtz::dpdT	(	const real	T,
		const real	v ) const

virtual

Implements belfem::gasmodels::EoS.

◆ dpdv()

real belfem::gasmodels::Helmholtz::dpdv	(	const real	T,
		const real	v ) const

virtual

Implements belfem::gasmodels::EoS.

◆ dpvap_dT()

real belfem::gasmodels::Helmholtz::dpvap_dT	(	const real	T,
		const real	aPvap,
		const real	aPiVap ) const

protectedvirtual

◆ dsdp()

real belfem::gasmodels::Helmholtz::dsdp	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ dsdT()

real belfem::gasmodels::Helmholtz::dsdT	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ dvdT()

real belfem::gasmodels::Helmholtz::dvdT	(	const real	T,
		const real	v ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ eval_critical_point()

void belfem::gasmodels::Helmholtz::eval_critical_point	(	real &	T,
		real &	p,
		real &	v ) const

virtual

return the critical point data

Parameters

T
p
v

Implements belfem::gasmodels::EoS.

◆ h()

real belfem::gasmodels::Helmholtz::h	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ hpow()

real belfem::gasmodels::Helmholtz::hpow	(	const real	x,
		const real	sqrt_x,
		const int	n )

inlinestaticprotected

x^( n / 2 ) for a signed half integer exponent given as n = 2j.

The square root is passed in so that the caller hoists it out of the loop over the coefficient table.

◆ hvap()

real belfem::gasmodels::Helmholtz::hvap	(	const real	T,
		const real	p ) const

virtual

vaporization enthalpy in J/kg

Parameters

T
p

Returns

Reimplemented from belfem::gasmodels::EoS.

◆ init_Tvap_poly()

void belfem::gasmodels::Helmholtz::init_Tvap_poly ( )

protected

◆ ipow()

real belfem::gasmodels::Helmholtz::ipow	(	real	x,
		uint	n )

inlinestaticprotected

integer power by binary exponentiation, for the coefficient tables of the residual functions.

Measured on the 40 term methane table, building tau^t with hpow() instead of std::pow costs 109 ns against 605 ns. Note that std::pow is still used elsewhere in this class, in particular for the vapor pressure ancillary.

◆ is_liquid()

bool belfem::gasmodels::Helmholtz::is_liquid	(	const real	T,
		const real	p ) const

protected

◆ kappa()

real belfem::gasmodels::Helmholtz::kappa	(	const real	T,
		const real	p ) const

virtual

isothermal compressibility coefficient

\( \kappa = -\frac{1}{v} \left( \frac{\partial v}{\partial p}\right)_T \)

Reimplemented from belfem::gasmodels::EoS.

◆ p()

real belfem::gasmodels::Helmholtz::p	(	const real	T,
		const real	v ) const

virtual

pressure in Pa

Parameters

T
v

Returns

Implements belfem::gasmodels::EoS.

◆ p_vap()

real belfem::gasmodels::Helmholtz::p_vap ( const real T ) const

virtual

Parameters

T	vapor temperature in K

Returns: vapor pressure in Pa

Reimplemented from belfem::gasmodels::EoS.

◆ phi()

real belfem::gasmodels::Helmholtz::phi	(	const real	T,
		const real	v ) const

the main energy function, where phi = f / ( R * T )

Parameters

T	temperature in K
v	mass specific volume in m^3/kg

Returns

◆ phi0()

const real & belfem::gasmodels::Helmholtz::phi0 ( ) const

◆ phi0_t()

const real & belfem::gasmodels::Helmholtz::phi0_t ( ) const

◆ phi0_tt()

const real & belfem::gasmodels::Helmholtz::phi0_tt ( ) const

◆ phir()

const real & belfem::gasmodels::Helmholtz::phir ( ) const

the main energy function, real gas contribution

◆ phir_d()

const real & belfem::gasmodels::Helmholtz::phir_d ( ) const

◆ phir_dd()

const real & belfem::gasmodels::Helmholtz::phir_dd ( ) const

◆ phir_dt()

const real & belfem::gasmodels::Helmholtz::phir_dt ( ) const

◆ phir_t()

const real & belfem::gasmodels::Helmholtz::phir_t ( ) const

◆ phir_tt()

const real & belfem::gasmodels::Helmholtz::phir_tt ( ) const

◆ pi_vap()

real belfem::gasmodels::Helmholtz::pi_vap ( const real T ) const

inlineprotectedvirtual

Reimplemented in belfem::gasmodels::EoS_Oxygen.

◆ psi_vap()

real belfem::gasmodels::Helmholtz::psi_vap ( const real T ) const

inlineprotectedvirtual

Reimplemented in belfem::gasmodels::EoS_Oxygen.

◆ remix()

void belfem::gasmodels::Helmholtz::remix ( )

virtual

this function remixes the cubic help gas

Reimplemented from belfem::gasmodels::EoS.

◆ s()

real belfem::gasmodels::Helmholtz::s	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ set_critical_point_in_data_object()

void belfem::gasmodels::Helmholtz::set_critical_point_in_data_object ( )

protected

◆ set_reference_point() [1/2]

void belfem::gasmodels::Helmholtz::set_reference_point ( )

protected

◆ set_reference_point() [2/2]

void belfem::gasmodels::Helmholtz::set_reference_point	(	const real	aTref,
		const real	aPref )

protected

◆ T()

real belfem::gasmodels::Helmholtz::T	(	const real	p,
		const real	v ) const

virtual

temperature in K

Implements belfem::gasmodels::EoS.

◆ T_crit()

const real & belfem::gasmodels::Helmholtz::T_crit ( ) const

inline

critical temperature

◆ T_max()

const real & belfem::gasmodels::Helmholtz::T_max ( ) const

inline

maximum temperature for gas model

◆ T_min()

const real & belfem::gasmodels::Helmholtz::T_min ( ) const

inline

minumum temperature for gas model ( triple point )

◆ T_vap()

real belfem::gasmodels::Helmholtz::T_vap ( const real p ) const

virtual

Parameters

p	vapor pressure in Pa

Returns: vapor temperature in K

Reimplemented from belfem::gasmodels::EoS.

◆ u()

real belfem::gasmodels::Helmholtz::u	(	const real	T,
		const real	p ) const

◆ update_Tp()

void belfem::gasmodels::Helmholtz::update_Tp	(	const real	T,
		const real	p ) const

inline

◆ update_Tv()

void belfem::gasmodels::Helmholtz::update_Tv	(	const real	T,
		const real	v ) const

inline

reset all state variales

◆ v()

real belfem::gasmodels::Helmholtz::v	(	const real	T,
		const real	p ) const

virtual

specific volume in m^3/kg

Implements belfem::gasmodels::EoS.

◆ v_crit()

const real & belfem::gasmodels::Helmholtz::v_crit ( ) const

inline

critical volume

◆ w()

real belfem::gasmodels::Helmholtz::w	(	const real	T,
		const real	p ) const

virtual

speed of sound in m/s ( helmholtz only )

Parameters

T
p

Returns

Reimplemented from belfem::gasmodels::EoS.

Member Data Documentation

◆ mCubicEoS

EoS_Cubic* belfem::gasmodels::Helmholtz::mCubicEoS = nullptr

protected

◆ mDelta

const real& belfem::gasmodels::Helmholtz::mDelta = mHelmholtzVals[ BELFEM_HELMHOLTZ_DELTA ]

protected

◆ mH0

real belfem::gasmodels::Helmholtz::mH0 = 0.0

protected

◆ mKvap

Vector< real > belfem::gasmodels::Helmholtz::mKvap

protected

◆ mLabel

const string belfem::gasmodels::Helmholtz::mLabel

protected

◆ mNvap

Vector< real > belfem::gasmodels::Helmholtz::mNvap

protected

◆ mPcrit

real belfem::gasmodels::Helmholtz::mPcrit = BELFEM_QUIET_NAN

protected

critical pressure in Pa

◆ mPmax

real belfem::gasmodels::Helmholtz::mPmax = BELFEM_REAL_MAX

protected

◆ mRhocrit

real belfem::gasmodels::Helmholtz::mRhocrit = BELFEM_QUIET_NAN

protected

critical density in kg/m^3

◆ mS0

real belfem::gasmodels::Helmholtz::mS0 = 0.0

protected

◆ mTau

const real& belfem::gasmodels::Helmholtz::mTau = mHelmholtzVals[ BELFEM_HELMHOLTZ_TAU ]

protected

◆ mTcrit

real belfem::gasmodels::Helmholtz::mTcrit = BELFEM_QUIET_NAN

protected

critical temperature in K

◆ mTmax

real belfem::gasmodels::Helmholtz::mTmax = BELFEM_QUIET_NAN

protected

maximum temperature of gas model in K

◆ mTtriple

real belfem::gasmodels::Helmholtz::mTtriple = BELFEM_QUIET_NAN

protected

triple point in K

◆ mTvap

Vector< real > belfem::gasmodels::Helmholtz::mTvap

protected

◆ mU0

real belfem::gasmodels::Helmholtz::mU0 = 0.0

protected

◆ mVcrit

real belfem::gasmodels::Helmholtz::mVcrit = BELFEM_QUIET_NAN

protected

critical specific volume in m^3/kg

◆ mVliq

Vector< real > belfem::gasmodels::Helmholtz::mVliq

protected

initial solution for inversion of pvap

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

src/physics/gasmodels/cl_GM_Helmholtz.hpp
src/physics/gasmodels/cl_GM_Helmholtz.cpp

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Helmholtz()

◆ ~Helmholtz()

Member Function Documentation

◆ alpha()

◆ beta()

◆ compute_phi0()

◆ compute_phi0_t()

◆ compute_phi0_tt()

◆ compute_phir()

◆ compute_phir_d()

◆ compute_phir_dd()

◆ compute_phir_dt()

◆ compute_phir_t()

◆ compute_phir_tt()

◆ cp()

◆ cv()

◆ delete_cubic_eos()

◆ dpdT()

◆ dpdv()

◆ dpvap_dT()

◆ dsdp()

◆ dsdT()

◆ dvdT()

◆ eval_critical_point()

◆ h()

◆ hpow()

◆ hvap()

◆ init_Tvap_poly()

◆ ipow()

◆ is_liquid()

◆ kappa()

◆ p()

◆ p_vap()

◆ phi()

◆ phi0()

◆ phi0_t()

◆ phi0_tt()

◆ phir()

◆ phir_d()

◆ phir_dd()

◆ phir_dt()

◆ phir_t()

◆ phir_tt()

◆ pi_vap()

◆ psi_vap()

◆ remix()

◆ s()

◆ set_critical_point_in_data_object()

◆ set_reference_point() [1/2]

◆ set_reference_point() [2/2]

◆ T()

◆ T_crit()

◆ T_max()

◆ T_min()

◆ T_vap()

◆ u()

◆ update_Tp()

◆ update_Tv()

◆ v()

◆ v_crit()

◆ w()

Member Data Documentation

◆ mCubicEoS

◆ mDelta

◆ mH0

◆ mKvap

◆ mLabel

◆ mNvap

◆ mPcrit

◆ mPmax

◆ mRhocrit

◆ mS0

◆ mTau

◆ mTcrit