cubic equation of state More...

#include <cl_GM_EoS_Cubic.hpp>

Inheritance diagram for belfem::gasmodels::EoS_Cubic:

Collaboration diagram for belfem::gasmodels::EoS_Cubic:

Public Member Functions
	EoS_Cubic (Gas &aParent, const GasModel aGasModel)
	~EoS_Cubic ()
void	remix ()
	call the remix function of the equation of state
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	dpdT (const real T, const real v) const
	\( \frac{\partial p}{\partial T } = \frac{R}{ v - b} - \frac{a \,\frac{\partial \alpha}{\partial T }}{ \left( v-b \, r_1\right) \, \left( v-b \, r_2\right)} \)
real	d2pdT2 (const real T, const real v) const
	\( \frac{\partial^2 p}{\partial T^2} = - \frac{a \, \frac{\partial^2 \alpha}{\partial T^2}}{ \left( v-b \, r_1\right) \, \left( v-b \, r_2\right)} \)
real	dpdv (const real T, const real v) const
	\( \frac{\partial p}{\partial v} = -\frac{R \, T }{\left( v - b\right)^2} - \frac{a \, \alpha \left[ b \, \left( r_1 + r_2 \right) - 2 \, v \right] }{ \left[\left( v-b \, r_1\right) \, \left( v-b \,r_2\right) \right]^2} \)
real	d2pdv2 (const real T, const real v) const
	\( \frac{\partial^2 p}{\partial v^2} = 2 \, \left\{ \frac{R \, T }{\left( v - b\right)^3} - \frac{a \, \alpha \left[ b^2 \, \left( r_1^2 + r_1\,r_2 + r_2^2 \right) - 3 \, b \, \left(r_1 + r_2 \right) \, v + 3 \, v^2 \right] }{ \left[\left( v-b \, r_1\right) \, \left( v-b \,r_2\right) \right]^3} \right\} \)
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
real	hdep (const real T, const real p) const
	enthalpy departure \( h - h^{\circ} = p\, v - R\,T + \frac{T \, \frac{\partial a}{\partial T} - a}{b \, \left( r_2 - r_1\right)} \, \ln \left[ \frac{v - b \, r_1}{v - b \, r_2}\right] \)
real	cpdep (const real T, const real p) const
real	sdep (const real T, const real p) const
real	dhdepdp (const real T, const real p) const
real	dsdepdT (const real T, const real p) const
real	dsdepdp (const real T, const real p) const
real	hdep0 (const real T) const
real	cpdep0 (const real T) const
real	sdep0 (const real T) const
real	dsdepdT0 (const real T) const
void	eval_critical_point (real &T, real &p, real &v) const
real	v (const uint aIndex, const real T, const real p) const
real	hdep (const uint aIndex, const real T, const real p) const
real	cpdep (const uint aIndex, const real T, const real p) const
Public Member Functions inherited from belfem::gasmodels::EoS
	EoS (Gas &aParent)
virtual	~EoS ()=default
virtual real	dvdT (const real T, const real v) const
virtual real	h (const real T, const real p) const
virtual real	hvap (const real T, const real p) const
virtual real	cv (const real T, const real p) const
virtual real	cp (const real T, const real p) const
virtual real	s (const real T, const real p) const
virtual real	dsdT (const real T, const real p) const
virtual real	dsdp (const real T, const real p) const
virtual real	w (const real T, const real p) const
	speed of sound in m/s ( helmholtz only )
virtual real	pi (const real T, const real p) const
virtual real	dpidp (const real T, const real p) const
virtual real	p_vap (const real T) const
virtual real	T_vap (const real p) const
Gas *	parent ()
	expose the parent of this EoS

Additional Inherited Members
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

cubic equation of state

\( p = \frac{R \, T }{ v - b} - \frac{a \, \alpha}{ \left( v-b \, r_1\right) \, \left( v-b \, r_2\right)} \)

See also: Gas Models Usage Guide

Constructor & Destructor Documentation

◆ EoS_Cubic()

belfem::gasmodels::EoS_Cubic::EoS_Cubic	(	Gas &	aParent,
		const GasModel	aGasModel )

◆ ~EoS_Cubic()

belfem::gasmodels::EoS_Cubic::~EoS_Cubic ( )

Member Function Documentation

◆ alpha()

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

virtual

thermal expansion coefficient

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

Parameters

T	temperature in K
p	pressure in Pa

Reimplemented from belfem::gasmodels::EoS.

◆ beta()

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

virtual

isochoric stress coefficient

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

Parameters

T	temperature in K
p	pressure in Pa

Reimplemented from belfem::gasmodels::EoS.

◆ cpdep() [1/2]

real belfem::gasmodels::EoS_Cubic::cpdep	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ cpdep() [2/2]

real belfem::gasmodels::EoS_Cubic::cpdep	(	const uint	aIndex,
		const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ cpdep0()

real belfem::gasmodels::EoS_Cubic::cpdep0 ( const real T ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ d2pdT2()

real belfem::gasmodels::EoS_Cubic::d2pdT2	(	const real	T,
		const real	v ) const

virtual

\( \frac{\partial^2 p}{\partial T^2} = - \frac{a \, \frac{\partial^2 \alpha}{\partial T^2}}{ \left( v-b \, r_1\right) \, \left( v-b \, r_2\right)} \)

Reimplemented from belfem::gasmodels::EoS.

◆ d2pdv2()

real belfem::gasmodels::EoS_Cubic::d2pdv2	(	const real	T,
		const real	v ) const

virtual

\( \frac{\partial^2 p}{\partial v^2} = 2 \, \left\{ \frac{R \, T }{\left( v - b\right)^3} - \frac{a \, \alpha \left[ b^2 \, \left( r_1^2 + r_1\,r_2 + r_2^2 \right) - 3 \, b \, \left(r_1 + r_2 \right) \, v + 3 \, v^2 \right] }{ \left[\left( v-b \, r_1\right) \, \left( v-b \,r_2\right) \right]^3} \right\} \)

Reimplemented from belfem::gasmodels::EoS.

◆ dhdepdp()

real belfem::gasmodels::EoS_Cubic::dhdepdp	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ dpdT()

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

virtual

\( \frac{\partial p}{\partial T } = \frac{R}{ v - b} - \frac{a \,\frac{\partial \alpha}{\partial T }}{ \left( v-b \, r_1\right) \, \left( v-b \, r_2\right)} \)

Implements belfem::gasmodels::EoS.

◆ dpdv()

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

virtual

\( \frac{\partial p}{\partial v} = -\frac{R \, T }{\left( v - b\right)^2} - \frac{a \, \alpha \left[ b \, \left( r_1 + r_2 \right) - 2 \, v \right] }{ \left[\left( v-b \, r_1\right) \, \left( v-b \,r_2\right) \right]^2} \)

Implements belfem::gasmodels::EoS.

◆ dsdepdp()

real belfem::gasmodels::EoS_Cubic::dsdepdp	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ dsdepdT()

real belfem::gasmodels::EoS_Cubic::dsdepdT	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ dsdepdT0()

real belfem::gasmodels::EoS_Cubic::dsdepdT0 ( const real T ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ eval_critical_point()

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

virtual

Implements belfem::gasmodels::EoS.

◆ hdep() [1/2]

real belfem::gasmodels::EoS_Cubic::hdep	(	const real	T,
		const real	p ) const

virtual

enthalpy departure \( h - h^{\circ} = p\, v - R\,T + \frac{T \, \frac{\partial a}{\partial T} - a}{b \, \left( r_2 - r_1\right)} \, \ln \left[ \frac{v - b \, r_1}{v - b \, r_2}\right] \)

Reimplemented from belfem::gasmodels::EoS.

◆ hdep() [2/2]

real belfem::gasmodels::EoS_Cubic::hdep	(	const uint	aIndex,
		const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ hdep0()

real belfem::gasmodels::EoS_Cubic::hdep0 ( const real T ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ kappa()

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

virtual

isothermal compressibility coefficient

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

Parameters

T	temperature in K
p	pressure in Pa

Reimplemented from belfem::gasmodels::EoS.

◆ p()

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

virtual

pressure in Pa

Implements belfem::gasmodels::EoS.

◆ remix()

void belfem::gasmodels::EoS_Cubic::remix ( )

virtual

call the remix function of the equation of state

Reimplemented from belfem::gasmodels::EoS.

◆ sdep()

real belfem::gasmodels::EoS_Cubic::sdep	(	const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ sdep0()

real belfem::gasmodels::EoS_Cubic::sdep0 ( const real T ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

◆ T()

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

virtual

temperature in K

Implements belfem::gasmodels::EoS.

◆ v() [1/2]

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

virtual

specific volume in m^3/kg

Implements belfem::gasmodels::EoS.

◆ v() [2/2]

real belfem::gasmodels::EoS_Cubic::v	(	const uint	aIndex,
		const real	T,
		const real	p ) const

virtual

Reimplemented from belfem::gasmodels::EoS.

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

src/physics/gasmodels/cl_GM_EoS_Cubic.hpp
src/physics/gasmodels/cl_GM_EoS_Cubic.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ EoS_Cubic()

◆ ~EoS_Cubic()

Member Function Documentation

◆ alpha()

◆ beta()

◆ cpdep() [1/2]

◆ cpdep() [2/2]

◆ cpdep0()

◆ d2pdT2()

◆ d2pdv2()

◆ dhdepdp()

◆ dpdT()

◆ dpdv()

◆ dsdepdp()

◆ dsdepdT()

◆ dsdepdT0()

◆ eval_critical_point()

◆ hdep() [1/2]

◆ hdep() [2/2]

◆ hdep0()

◆ kappa()

◆ p()

◆ remix()

◆ sdep()

◆ sdep0()

◆ T()

◆ v() [1/2]

◆ v() [2/2]