Term in the ideal-gas specific heat equation that is polynomial term. More...

#include <Helmholtz.h>

Inheritance diagram for phi0_cp0_poly:

Public Member Functions
	phi0_cp0_poly (double a, double t, double Tc, double T0)
	Constructor with just a single double value. More...

	phi0_cp0_poly (std::vector< double > a, std::vector< double > t, double Tc, double T0, int iStart, int iEnd)
	Constructor with std::vectors. More...

	~phi0_cp0_poly ()
	Destructor. More...

void	to_json (rapidjson::Value &el, rapidjson::Document &doc)

double	base (double tau, double delta)

double	dTau (double tau, double delta)

double	dTau2 (double tau, double delta)

double	dDelta (double tau, double delta)

double	dDelta2 (double tau, double delta)

double	dDelta2_dTau (double tau, double delta)

double	dDelta_dTau (double tau, double delta)

double	dDelta_dTau2 (double tau, double delta)

double	dTau3 (double tau, double delta)

double	dDelta3 (double tau, double delta)

Public Member Functions inherited from phi_BC
	phi_BC ()

virtual	~phi_BC ()

Detailed Description

Term in the ideal-gas specific heat equation that is polynomial term.

for a term of the form

\[ \frac{c_p^0}{R}=cT^t, t \neq 0,-1 \]

the contribution is found from

\[ \frac{1}{T}\int_{T_0}^T c T^t dT-\int_{T_0}^T \frac{c T^t}{T}dT \]

\[ \frac{c}{T}\left(\frac{T^{t+1}}{t+1}-\frac{T_0^{t+1}}{t+1}\right)-c\left(\frac{T^{t}}{t}-\frac{T_0^{t}}{t}\right) \]

\[ cT^{t}\left(\frac{1}{t+1}-\frac{1}{t}\right)-c\frac{T_0^{t+1}}{T(t+1)}+c\frac{T_0^t}{t} \]

or in terms of $$$$

\[ cT_c^{t}\tau^{-t}\left(\frac{1}{t+1}-\frac{1}{t}\right)-c\frac{T_0^{t+1}\tau}{T_c(t+1)}+c\frac{T_0^t}{t} \]

if t = 0

\[ \frac{1}{T}\int_{{T_0}}^T c dT - \int_{{T_0}}^T {\frac{c}{T}} dT = \frac{{c(T - {T_0})}}{T} - c\ln \left( {\frac{T}{{{T_0}}}} \right) = c\left( {1 - \frac{\tau }{{{\tau _0}}}} \right) - c\ln \left( {\frac{{{\tau _0}}}{\tau }} \right) \]

if t = -1

\[ \frac{1}{T}\int_{{T_0}}^T {\frac{c}{T}} dT - \int_{{T_0}}^T {\frac{c}{{{T^2}}}} dT = \frac{c}{T}\ln \left( {\frac{T}{{{T_0}}}} \right) + c\left( {\frac{1}{T} - \frac{1}{{{T_0}}}} \right) = \frac{{c\tau }}{{{T_c}}}\ln \left( {\frac{{{\tau _0}}}{\tau }} \right) + \frac{c}{{{T_c}}}\left( {\tau - {\tau _0}} \right) \]

Definition at line 881 of file Helmholtz.h.

Constructor & Destructor Documentation

phi0_cp0_poly::phi0_cp0_poly	(	double	a,
		double	t,
		double	Tc,
		double	T0
	)

inline

Constructor with just a single double value.

Definition at line 888 of file Helmholtz.h.

phi0_cp0_poly::phi0_cp0_poly	(	std::vector< double >	a,
		std::vector< double >	t,
		double	Tc,
		double	T0,
		int	iStart,
		int	iEnd
	)

inline

Constructor with std::vectors.

Definition at line 895 of file Helmholtz.h.

phi0_cp0_poly::~phi0_cp0_poly ( )

inline

Destructor.

Definition at line 900 of file Helmholtz.h.

Member Function Documentation

double phi0_cp0_poly::base	(	double	tau,
		double	delta
	)

inlinevirtual

Returns the base, non-dimensional, Helmholtz energy term (no derivatives) [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc/T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 905 of file Helmholtz.h.

double phi0_cp0_poly::dDelta	(	double	tau,
		double	delta
	)

inlinevirtual

Returns the first partial derivative of Helmholtz energy term with respect to delta [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 926 of file Helmholtz.h.

double phi0_cp0_poly::dDelta2	(	double	tau,
		double	delta
	)

inlinevirtual

Returns the second partial derivative of Helmholtz energy term with respect to delta [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 927 of file Helmholtz.h.

double phi0_cp0_poly::dDelta2_dTau	(	double	tau,
		double	delta
	)

inlinevirtual

Returns the third mixed partial derivative (delta2,dtau1) of Helmholtz energy term with respect to delta and tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 928 of file Helmholtz.h.

double phi0_cp0_poly::dDelta3	(	double	tau,
		double	delta
	)

inlinevirtual

Returns the third partial derivative of Helmholtz energy term with respect to delta [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 932 of file Helmholtz.h.

double phi0_cp0_poly::dDelta_dTau	(	double	tau,
		double	delta
	)

inlinevirtual

Returns the second mixed partial derivative (delta1,dtau1) of Helmholtz energy term with respect to delta and tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 929 of file Helmholtz.h.

double phi0_cp0_poly::dDelta_dTau2	(	double	tau,
		double	delta
	)

inlinevirtual

Returns the third mixed partial derivative (delta1,dtau2) of Helmholtz energy term with respect to delta and tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 930 of file Helmholtz.h.

double phi0_cp0_poly::dTau	(	double	tau,
		double	delta
	)

virtual

Returns the first partial derivative of Helmholtz energy term with respect to tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc/T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 2071 of file Helmholtz.cpp.

double phi0_cp0_poly::dTau2	(	double	tau,
		double	delta
	)

virtual

Returns the second partial derivative of Helmholtz energy term with respect to tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc/T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 2092 of file Helmholtz.cpp.

double phi0_cp0_poly::dTau3	(	double	tau,
		double	delta
	)

virtual

Returns the third partial derivative of Helmholtz energy term with respect to tau [-]

Parameters

tau	Reciprocal reduced temperature where tau=Tc / T
delta	Reduced pressure where delta = rho / rhoc

Implements phi_BC.

Definition at line 2113 of file Helmholtz.cpp.

void phi0_cp0_poly::to_json	(	rapidjson::Value &	el,
		rapidjson::Document &	doc
	)

virtual

Implements phi_BC.

Definition at line 2055 of file Helmholtz.cpp.

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

CoolProp/Helmholtz.h
CoolProp/Helmholtz.cpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation