|
[Sponsors] |
November 18, 2021, 05:48 |
Peng Robinson Equation of state
|
#1 |
Senior Member
Join Date: Dec 2019
Posts: 215
Rep Power: 7 |
Hi everyone,
is anyone familiar with the implementation of the Peng Robinson EQS? It is implemented differently than the basic equation. What confuses me first is that in PengRobinsonGas.C a compressibility factor is calculated: Code:
template<class Specie> Foam::PengRobinsonGas<Specie>::PengRobinsonGas ( const dictionary& dict ) : Specie(dict), Tc_(readScalar(dict.subDict("equationOfState").lookup("Tc"))), Vc_(readScalar(dict.subDict("equationOfState").lookup("Vc"))), Zc_(1.0), Pc_(readScalar(dict.subDict("equationOfState").lookup("Pc"))), omega_(readScalar(dict.subDict("equationOfState").lookup("omega"))) { Zc_ = Pc_*Vc_/(RR*Tc_); } But in PengRobinsonGasl.H there is something similar to the original equation implemented: Code:
// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * // template<class Specie> inline Foam::scalar Foam::PengRobinsonGas<Specie>::rho ( scalar p, scalar T ) const { scalar Z = this->Z(p, T); return p/(Z*this->R()*T); } template<class Specie> inline Foam::scalar Foam::PengRobinsonGas<Specie>::h(scalar p, scalar T) const { scalar Pr = p/Pc_; scalar Tr = T/Tc_; scalar B = 0.07780*Pr/Tr; scalar kappa = 0.37464 + 1.54226*omega_ - 0.26992*sqr(omega_); scalar alpha = sqr(1 + kappa*(1 - sqrt(Tr))); scalar Z = this->Z(p, T); return RR*Tc_ *( Tr*(Z - 1) - 2.078*(1 + kappa)*sqrt(alpha) *log((Z + 2.414*B)/(Z - 0.414*B)) ); } template<class Specie> inline Foam::scalar Foam::PengRobinsonGas<Specie>::cp(scalar p, scalar T) const { scalar Tr = T/Tc_; scalar a = 0.45724*sqr(RR*Tc_)/Pc_; scalar b = 0.07780*RR*Tc_/Pc_; scalar kappa = 0.37464 + 1.54226*omega_ - 0.26992*sqr(omega_); scalar alpha = sqr(1 + kappa*(1 - sqrt(Tr))); scalar A = a*alpha*p/sqr(RR*T); scalar B = b*p/(RR*T); scalar Z = this->Z(p, T); scalar ap = kappa*a*(kappa/Tc_ - (1 + kappa)/sqrt(T*Tc_)); scalar app = kappa*a*(1 + kappa)/(2*sqrt(pow3(T)*Tc_)); scalar M = (sqr(Z) + 2*B*Z - sqr(B))/(Z - B); scalar N = ap*B/(b*RR); const scalar root2 = sqrt(2.0); return app*(T/(2*root2*b))*log((Z + (root2 + 1)*B)/(Z - (root2 - 1)*B)) + RR*sqr(M - N)/(sqr(M) - 2*A*(Z + B)) - RR; } template<class Specie> inline Foam::scalar Foam::PengRobinsonGas<Specie>::s ( scalar p, scalar T ) const { scalar Pr = p/Pc_; scalar Tr = T/Tc_; scalar B = 0.07780*Pr/Tr; scalar kappa = 0.37464 + 1.54226*omega_ - 0.26992*sqr(omega_); scalar Z = this->Z(p, T); return - RR*log(p/Pstd) + RR *( log(Z - B) - 2.078*kappa*((1 + kappa)/sqrt(Tr) - kappa) *log((Z + 2.414*B)/(Z - 0.414*B)) ); } template<class Specie> inline Foam::scalar Foam::PengRobinsonGas<Specie>::psi ( scalar p, scalar T ) const { scalar Z = this->Z(p, T); return 1.0/(Z*this->R()*T); } template<class Specie> inline Foam::scalar Foam::PengRobinsonGas<Specie>::Z ( scalar p, scalar T ) const { scalar Tr = T/Tc_; scalar a = 0.45724*sqr(RR*Tc_)/Pc_; scalar b = 0.07780*RR*Tc_/Pc_; scalar kappa = 0.37464 + 1.54226*omega_ - 0.26992*sqr(omega_); scalar alpha = sqr(1 + kappa*(1 - sqrt(Tr))); scalar A = a*alpha*p/sqr(RR*T); scalar B = b*p/(RR*T); scalar a2 = B - 1; scalar a1 = A - 2*B - 3*sqr(B); scalar a0 = -A*B + sqr(B) + pow3(B); scalar Q = (3*a1 - a2*a2)/9.0; scalar Rl = (9*a2*a1 - 27*a0 - 2*a2*a2*a2)/54.0; scalar Q3 = Q*Q*Q; scalar D = Q3 + Rl*Rl; scalar root = -1; if (D <= 0) { scalar th = ::acos(Rl/sqrt(-Q3)); scalar qm = 2*sqrt(-Q); scalar r1 = qm*cos(th/3.0) - a2/3.0; scalar r2 = qm*cos((th + 2*constant::mathematical::pi)/3.0) - a2/3.0; scalar r3 = qm*cos((th + 4*constant::mathematical::pi)/3.0) - a2/3.0; root = max(r1, max(r2, r3)); } else { // One root is real scalar D05 = sqrt(D); scalar S = pow(Rl + D05, 1.0/3.0); scalar Tl = 0; if (D05 > Rl) { Tl = -pow(mag(Rl - D05), 1.0/3.0); } else { Tl = pow(Rl - D05, 1.0/3.0); } root = S + Tl - a2/3.0; } return root; } template<class Specie> inline Foam::scalar Foam::PengRobinsonGas<Specie>::cpMcv ( scalar p, scalar T ) const { scalar Tr = T/Tc_; scalar a = 0.45724*sqr(RR*Tc_)/Pc_; scalar b = 0.07780*RR*Tc_/Pc_; scalar kappa = 0.37464 + 1.54226*omega_ - 0.26992*sqr(omega_); scalar alpha = sqr(1 + kappa*(1 - sqrt(Tr))); scalar A = alpha*a*p/sqr(RR*T); scalar B = b*p/(RR*T); scalar Z = this->Z(p, T); scalar ap = kappa*a*(kappa/Tc_ - (1 + kappa)/sqrt(T*Tc_)); scalar M = (sqr(Z) + 2*B*Z - sqr(B))/(Z - B); scalar N = ap*B/(b*RR); return RR*sqr(M - N)/(sqr(M) - 2*A*(Z + B)); } I hope some can clearify this to me |
|
|
|
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
Writing an equation of state | FAKHREDDINE | CFX | 2 | April 3, 2017 13:08 |
Simple piston movement in cylinder- fluid models | arun1994 | CFX | 4 | July 8, 2016 03:54 |
continuity equation was diverging in transient state | stenber | FLUENT | 0 | March 19, 2016 23:37 |
How can I add an equation of state for rho and cp ?? | Canesin | OpenFOAM Programming & Development | 0 | May 14, 2010 18:52 |
Real gas equation of state for gas mixture | ahourri | FLUENT | 0 | April 30, 2008 12:23 |