Redlich-Kwong equation of state: p = RT/(1/rho - b) - a/( sqrt(T / Tc) * (1/rho^2 + b/rho) with a = 0.42748 * (R*Tc)^2 / Pc b = 0.08664 * (R*Tc) / Pc. More...

#include <RedlichKwongEoS.h>

Inheritance diagram for Nektar::RedlichKwongEoS:

[legend]

Static Public Member Functions
static EquationOfStateSharedPtr	create (const LibUtilities::SessionReaderSharedPtr &pSession)
	Creates an instance of this class. More...

Static Public Attributes
static std::string	className
	Name of the class. More...

Protected Member Functions
virtual NekDouble	v_GetTemperature (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetPressure (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetEntropy (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetDPDrho_e (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetDPDe_rho (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetEFromRhoP (const NekDouble &rho, const NekDouble &p)

virtual NekDouble	v_GetRhoFromPT (const NekDouble &rho, const NekDouble &p)

Protected Member Functions inherited from Nektar::EquationOfState
	EquationOfState (const LibUtilities::SessionReaderSharedPtr &pSession)
	Constructor. More...

virtual NekDouble	v_GetSoundSpeed (const NekDouble &rho, const NekDouble &e)

Protected Attributes
NekDouble	m_a

NekDouble	m_b

NekDouble	m_Tc

NekDouble	m_Pc

Protected Attributes inherited from Nektar::EquationOfState
NekDouble	m_gamma

NekDouble	m_gasConstant

Private Member Functions
	RedlichKwongEoS (const LibUtilities::SessionReaderSharedPtr &pSession)

virtual	~RedlichKwongEoS (void)

NekDouble	Alpha (const NekDouble &T)

NekDouble	LogTerm (const NekDouble &rho)

Friends
class	MemoryManager< RedlichKwongEoS >

Additional Inherited Members
Public Member Functions inherited from Nektar::EquationOfState
virtual	~EquationOfState ()

NekDouble	GetTemperature (const NekDouble &rho, const NekDouble &e)
	Calculate the temperature. More...

NekDouble	GetPressure (const NekDouble &rho, const NekDouble &e)
	Calculate the pressure. More...

NekDouble	GetSoundSpeed (const NekDouble &rho, const NekDouble &e)
	Calculate the sound speed. More...

NekDouble	GetEntropy (const NekDouble &rho, const NekDouble &e)
	Calculate the entropy. More...

NekDouble	GetDPDrho_e (const NekDouble &rho, const NekDouble &e)
	Calculate the partial derivative of P(rho,e) with respect to rho. More...

NekDouble	GetDPDe_rho (const NekDouble &rho, const NekDouble &e)
	Calculate the partial derivative of P(rho,e) with respect to e. More...

NekDouble	GetEFromRhoP (const NekDouble &rho, const NekDouble &p)
	Obtain the internal energy from rho and P. More...

NekDouble	GetRhoFromPT (const NekDouble &p, const NekDouble &T)
	Obtain the density from P and T. More...

Detailed Description

Redlich-Kwong equation of state: p = RT/(1/rho - b) - a/( sqrt(T / Tc) * (1/rho^2 + b/rho) with a = 0.42748 * (R*Tc)^2 / Pc b = 0.08664 * (R*Tc) / Pc.

Definition at line 49 of file RedlichKwongEoS.h.

Constructor & Destructor Documentation

◆ RedlichKwongEoS()

Nektar::RedlichKwongEoS::RedlichKwongEoS ( const LibUtilities::SessionReaderSharedPtr & pSession )

private

Definition at line 47 of file RedlichKwongEoS.cpp.

References m_a, m_b, Nektar::EquationOfState::m_gasConstant, m_Pc, and m_Tc.

     : EquationOfState(pSession)
 {
     pSession->LoadParameter("Tcrit", m_Tc);
     pSession->LoadParameter("Pcrit", m_Pc);
 
     m_a = 0.42748 * m_gasConstant * m_gasConstant * m_Tc * m_Tc / m_Pc;
     m_b = 0.08664 * m_gasConstant * m_Tc / m_Pc;
 }

◆ ~RedlichKwongEoS()

virtual Nektar::RedlichKwongEoS::~RedlichKwongEoS ( void )

inlineprivatevirtual

Definition at line 90 of file RedlichKwongEoS.h.

References Alpha(), and LogTerm().

90 {};

Member Function Documentation

◆ Alpha()

NekDouble Nektar::RedlichKwongEoS::Alpha ( const NekDouble & T )

private

Definition at line 257 of file RedlichKwongEoS.cpp.

References m_Tc.

Referenced by v_GetDPDe_rho(), v_GetDPDrho_e(), v_GetEFromRhoP(), v_GetEntropy(), v_GetPressure(), v_GetRhoFromPT(), and ~RedlichKwongEoS().

 {
     return 1.0 / sqrt(T / m_Tc);
 }

◆ create()

static EquationOfStateSharedPtr Nektar::RedlichKwongEoS::create ( const LibUtilities::SessionReaderSharedPtr & pSession )

inlinestatic

Creates an instance of this class.

Definition at line 55 of file RedlichKwongEoS.h.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and CellMLToNektar.cellml_metadata::p.

     {
         EquationOfStateSharedPtr p =
             MemoryManager<RedlichKwongEoS>::AllocateSharedPtr(pSession);
         return p;
     }

◆ LogTerm()

NekDouble Nektar::RedlichKwongEoS::LogTerm ( const NekDouble & rho )

private

Definition at line 262 of file RedlichKwongEoS.cpp.

References m_b.

Referenced by v_GetDPDe_rho(), v_GetEFromRhoP(), v_GetEntropy(), v_GetTemperature(), and ~RedlichKwongEoS().

 {
     return log(1 + m_b * rho);
 }

◆ v_GetDPDe_rho()

NekDouble Nektar::RedlichKwongEoS::v_GetDPDe_rho	(	const NekDouble &	rho,
		const NekDouble &	e
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 147 of file RedlichKwongEoS.cpp.

References Alpha(), Nektar::EquationOfState::GetTemperature(), LogTerm(), m_a, m_b, Nektar::EquationOfState::m_gamma, and Nektar::EquationOfState::m_gasConstant.

 {
     NekDouble T       = GetTemperature(rho, e);
     NekDouble alpha   = Alpha(T);
     NekDouble logTerm = LogTerm(rho);
 
     // First calculate the denominator 1/rho^2 + 2*b/rho - b^2
     //    and sqrt(Alpha) = 1+f_w*(1-sqrt(Tr))
     NekDouble denom = 1.0 / (rho * rho) + m_b / rho;
 
     // Compute cv = dedT_rho
     NekDouble cv = m_gasConstant / (m_gamma - 1) +
                    3 * m_a * alpha * logTerm / (4 * m_b * T);
 
     // Now we obtain dPdT_rho
     NekDouble dPdT =
         m_gasConstant / (1.0 / rho - m_b) + m_a * alpha / (denom * 2 * T);
 
     // The result is dPde_rho = dPdT_rho / cv
     return dPdT / cv;
 }

◆ v_GetDPDrho_e()

NekDouble Nektar::RedlichKwongEoS::v_GetDPDrho_e	(	const NekDouble &	rho,
		const NekDouble &	e
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 127 of file RedlichKwongEoS.cpp.

References Alpha(), Nektar::EquationOfState::GetDPDe_rho(), Nektar::EquationOfState::GetTemperature(), m_a, m_b, and Nektar::EquationOfState::m_gasConstant.

 {
     NekDouble T     = GetTemperature(rho, e);
     NekDouble alpha = Alpha(T);
     NekDouble dPde  = GetDPDe_rho(rho, e);
 
     // Calculate dPdrho_T
     NekDouble dPdrho_T =
         m_gasConstant * T / ((1.0 - m_b * rho) * (1.0 - m_b * rho)) -
         m_a * alpha * rho * (m_b * rho + 2) /
             ((1 + m_b * rho) * (1 + m_b * rho));
 
     // Calculate dedrho_T
     NekDouble dedrho_T = -3 * m_a * alpha / (2 * (1 + m_b * rho));
 
     // The result is dPdrho_e = dPdrho_T - dPde_rho * dedrho_T
     return dPdrho_T - dPde * dedrho_T;
 }

◆ v_GetEFromRhoP()

NekDouble Nektar::RedlichKwongEoS::v_GetEFromRhoP	(	const NekDouble &	rho,
		const NekDouble &	p
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 170 of file RedlichKwongEoS.cpp.

References Alpha(), LogTerm(), m_a, m_b, Nektar::EquationOfState::m_gamma, Nektar::EquationOfState::m_gasConstant, and m_Tc.

 {
     NekDouble logTerm = LogTerm(rho);
     // First calculate the temperature, which can be expressed as
     //      (T^1/2)^3 + A* T^1/2 + B = 0
     NekDouble A, B;
 
     A = -p * (1.0 / rho - m_b) / m_gasConstant;
     B = -m_a * sqrt(m_Tc) * (1.0 / rho - m_b) /
         (1.0 / (rho * rho) + m_b / rho) / m_gasConstant;
 
     // Use ideal gas solution as starting guess for iteration
     NekDouble sqrtT = sqrt(p / (rho * (m_gamma - 1)));
     // Newton-Raphson iteration to find T^(1/2)
     NekDouble tol      = 1e-6;
     NekDouble maxIter  = 100;
     NekDouble residual = 1;
     NekDouble f, df;
     unsigned int cnt = 0;
     while (abs(residual) > tol && cnt < maxIter)
     {
         f        = sqrtT * sqrtT * sqrtT + A * sqrtT + B;
         df       = 3 * sqrtT * sqrtT + A;
         residual = f / df;
         sqrtT -= residual;
         ++cnt;
     }
     if (cnt == maxIter)
     {
         cout << "Newton-Raphson in RedlichKwongEoS::v_GetEFromRhoP did not "
                 "converge in "
              << maxIter << " iterations (residual = " << residual << ")"
              << endl;
     }
 
     // Calculate T
     NekDouble T = sqrtT * sqrtT;
 
     // Calculate internal energy
     return m_gasConstant * T / (m_gamma - 1) -
            3 * m_a * Alpha(T) / (2 * m_b) * logTerm;
 }

◆ v_GetEntropy()

NekDouble Nektar::RedlichKwongEoS::v_GetEntropy	(	const NekDouble &	rho,
		const NekDouble &	e
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 112 of file RedlichKwongEoS.cpp.

References Alpha(), Nektar::EquationOfState::GetTemperature(), LogTerm(), m_a, m_b, Nektar::EquationOfState::m_gamma, and Nektar::EquationOfState::m_gasConstant.

 {
     NekDouble T       = GetTemperature(rho, e);
     NekDouble logTerm = LogTerm(rho);
     // Entropy for an ideal gas
     NekDouble sIg =
         m_gasConstant / (m_gamma - 1) * log(T) - m_gasConstant * log(rho);
 
     NekDouble deltaS = m_gasConstant * log(1 - m_b * rho);
     deltaS -= m_a * Alpha(T) * logTerm / (2 * m_b * T);
 
     return sIg + deltaS;
 }

◆ v_GetPressure()

NekDouble Nektar::RedlichKwongEoS::v_GetPressure	(	const NekDouble &	rho,
		const NekDouble &	e
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 101 of file RedlichKwongEoS.cpp.

References Alpha(), Nektar::EquationOfState::GetTemperature(), m_a, m_b, Nektar::EquationOfState::m_gasConstant, and CellMLToNektar.cellml_metadata::p.

 {
     NekDouble T = GetTemperature(rho, e);
 
     NekDouble p = m_gasConstant * T / (1.0 / rho - m_b) -
                   m_a * Alpha(T) / (1.0 / (rho * rho) + m_b / rho);
 
     return p;
 }

◆ v_GetRhoFromPT()

NekDouble Nektar::RedlichKwongEoS::v_GetRhoFromPT	(	const NekDouble &	rho,
		const NekDouble &	p
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 214 of file RedlichKwongEoS.cpp.

References Alpha(), m_a, m_b, and Nektar::EquationOfState::m_gasConstant.

 {
     // First solve for the compressibility factor Z using the cubic equation
     //    Z^3 + k1 * Z^2 + k2 * Z + k3 = 0
     //    for RedlichKwong:
     //        k1 = -1.0, k2 = A - B - B^2,  k3 = -AB
     //    where A = a*alpha(T)*P/(RT)^2, B = bP/(RT)
     NekDouble A = m_a * Alpha(T) * p / (m_gasConstant * m_gasConstant * T * T);
     NekDouble B = m_b * p / (m_gasConstant * T);
 
     NekDouble k1 = -1.0;
     NekDouble k2 = A - B - B * B;
     NekDouble k3 = -A * B;
 
     // Use ideal gas (Z=1) as starting guess for iteration
     NekDouble Z = 1.0;
     // Newton-Raphson iteration to find Z
     NekDouble tol      = 1e-6;
     NekDouble maxIter  = 100;
     NekDouble residual = 1;
     NekDouble f, df;
     unsigned int cnt = 0;
     while (abs(residual) > tol && cnt < maxIter)
     {
         f        = Z * Z * Z + k1 * Z * Z + k2 * Z + k3;
         df       = 3 * Z * Z + 2 * k1 * Z + k2;
         residual = f / df;
         Z -= residual;
         ++cnt;
     }
     if (cnt == maxIter)
     {
         cout << "Newton-Raphson in RedlichKwongEoS::v_GetRhoFromPT did not "
                 "converge in "
              << maxIter << " iterations (residual = " << residual << ")"
              << endl;
     }
 
     // Now calculate rho = p/(ZRT)
     return p / (Z * m_gasConstant * T);
 }

◆ v_GetTemperature()

NekDouble Nektar::RedlichKwongEoS::v_GetTemperature	(	const NekDouble &	rho,
		const NekDouble &	e
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 58 of file RedlichKwongEoS.cpp.

References LogTerm(), m_a, m_b, Nektar::EquationOfState::m_gamma, Nektar::EquationOfState::m_gasConstant, and m_Tc.

 {
     // First we need to evaluate the log term
     //    ln[1 + b*rho]
     NekDouble logTerm = LogTerm(rho);
 
     // The temperature can be expressed as an equation in the form
     //      (T^1/2)^3 + A* T^1/2 + B = 0, which we solve iteratively
     NekDouble A, B;
 
     A = -e * (m_gamma - 1) / m_gasConstant;
     B = -3.0 * m_a / (2.0 * m_b * m_gasConstant) * (m_gamma - 1) * sqrt(m_Tc) *
         logTerm;
 
     // Use ideal gas solution as starting guess for iteration
     NekDouble sqrtT = sqrt(e * (m_gamma - 1) / m_gasConstant);
     // Newton-Raphson iteration to find T^(1/2)
     NekDouble tol      = 1e-6;
     NekDouble maxIter  = 100;
     NekDouble residual = 1;
     NekDouble f, df;
     unsigned int cnt = 0;
     while (abs(residual) > tol && cnt < maxIter)
     {
         f        = sqrtT * sqrtT * sqrtT + A * sqrtT + B;
         df       = 3 * sqrtT * sqrtT + A;
         residual = f / df;
         sqrtT -= residual;
         ++cnt;
     }
     if (cnt == maxIter)
     {
         cout << "Newton-Raphson in RedlichKwongEoS::v_GetTemperature did not "
                 "converge in "
              << maxIter << " iterations (residual = " << residual << ")"
              << endl;
     }
 
     // Calculate the temperature
     return sqrtT * sqrtT;
 }

Friends And Related Function Documentation

◆ MemoryManager< RedlichKwongEoS >

friend class MemoryManager< RedlichKwongEoS >

friend

Definition at line 52 of file RedlichKwongEoS.h.

Member Data Documentation

◆ className

std::string Nektar::RedlichKwongEoS::className

static

Initial value:

=
    GetEquationOfStateFactory().RegisterCreatorFunction(
        "RedlichKwong", RedlichKwongEoS::create,
        "Redlich-Kwong equation of state.")

Name of the class.

Definition at line 64 of file RedlichKwongEoS.h.

◆ m_a

NekDouble Nektar::RedlichKwongEoS::m_a

protected

Definition at line 67 of file RedlichKwongEoS.h.

Referenced by RedlichKwongEoS(), v_GetDPDe_rho(), v_GetDPDrho_e(), v_GetEFromRhoP(), v_GetEntropy(), v_GetPressure(), v_GetRhoFromPT(), and v_GetTemperature().

◆ m_b

NekDouble Nektar::RedlichKwongEoS::m_b

protected

Definition at line 68 of file RedlichKwongEoS.h.

Referenced by LogTerm(), RedlichKwongEoS(), v_GetDPDe_rho(), v_GetDPDrho_e(), v_GetEFromRhoP(), v_GetEntropy(), v_GetPressure(), v_GetRhoFromPT(), and v_GetTemperature().

◆ m_Pc

NekDouble Nektar::RedlichKwongEoS::m_Pc

protected

Definition at line 70 of file RedlichKwongEoS.h.

Referenced by RedlichKwongEoS().

◆ m_Tc

NekDouble Nektar::RedlichKwongEoS::m_Tc

protected

Definition at line 69 of file RedlichKwongEoS.h.

Referenced by Alpha(), RedlichKwongEoS(), v_GetEFromRhoP(), and v_GetTemperature().

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RedlichKwongEoS()

◆ ~RedlichKwongEoS()

Member Function Documentation

◆ Alpha()

◆ create()

◆ LogTerm()

◆ v_GetDPDe_rho()

◆ v_GetDPDrho_e()

◆ v_GetEFromRhoP()

◆ v_GetEntropy()

◆ v_GetPressure()

◆ v_GetRhoFromPT()

◆ v_GetTemperature()

Friends And Related Function Documentation

◆ MemoryManager< RedlichKwongEoS >

Member Data Documentation

◆ className

◆ m_a

◆ m_b

◆ m_Pc

◆ m_Tc