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cantera/ext/tpx/CarbonDioxide.cpp
Dave Goodwin a2a33f1cac *** empty log message ***
2005-09-30 16:38:09 +00:00

361 lines
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/* FILE: CarbonDioxide.cpp
* DESCRIPTION:
* representation of substance Carbon Dioxide
* values and functions are from
* "Thermodynamic Properties in SI" bu W.C. Reynolds
* AUTHOR: me@rebeccahhunt.com: GCEP, Stanford University
*
*/
#include "CarbonDioxide.h"
#include <math.h>
#include <string.h>
namespace tpx {
/*
* Carbon Dioxide constants
*/
static const double Tmn = 216.54; // [K] minimum temperature for which calculations are valid
static const double Tmx = 1500.0; // [K] maximum temperature for which calculations are valid
static const double Tc=304.21; // [K] critical temperature
static const double Roc=464.00; // [kg/m^3] critical density
static const double To=216.54; // [K] reference Temperature
static const double R=188.918; // [] gas constant for CO2 J/kg/K
static const double Gamma=5.0E-6; // [??]
static const double u0=3.217405E5; // [] internal energy at To
static const double s0=2.1396056E3; // [] entropy at To
static const double Tp=250; // [K] ??
static const double Pc=7.38350E6; // [Pa] critical pressure
static const double M=44.01; // [kg/kmol] molar density
/*
* array Acarbdi is used by the function named Pp
*/
static const double Acarbdi[]={
2.2488558E-1,
-1.3717965E2,
-1.4430214E4,
-2.9630491E6,
-2.0606039E8,
4.5554393E-5,
7.7042840E-2,
4.0602371E1,
4.0029509E-7,
-3.9436077E-4,
1.2115286E-10,
1.0783386E-7,
4.3962336E-11,
-3.6505545E4,
1.9490511E7,
-2.9186718E9,
2.4358627E-2,
-3.7546530E1,
1.1898141E4
};
/*
* array F is used by the function named Psat
*/
static const double F[]={
-6.5412610,
-2.7914636E-1,
-3.4716202,
-3.4989637,
-1.9770948E1,
1.3922839E2,
-2.7670389E2,
-7.0510251E3
};
/*
* array D is used by the function ldens
*/
static const double D[]={
4.6400009E2,
6.7938129E2,
1.4776836E3,
-3.1267676E3,
3.6397656E3,
-1.3437098E3
};
/*
* array G is used by the function sp
*/
static const double G[]={
8.726361E3,
1.840040E2,
1.914025,
-1.667825E-3,
7.305950E-7,
-1.255290E-10,
3.2174105E5,
2.1396056E3
};
/*
* C returns a multiplier in each term of the sum
* in P-3, used in conjunction with C in the function Pp
* j is used to represent which of the values in the summation to calculate
* j=0 is the second additive in the formula in reynolds
* j=1 is the third...
* (this part does not include the multiplier rho^n)
*/
double CarbonDioxide::C(int j,double Tinverse, double T2inverse, double T3inverse, double T4inverse) {
switch(j) {
case 0 :
return Acarbdi[0]*T +
Acarbdi[1] +
Acarbdi[2] * Tinverse +
Acarbdi[3] * T2inverse +
Acarbdi[4] * T3inverse ;
case 1 :
return Acarbdi[5] *T +
Acarbdi[6] +
Acarbdi[7] * Tinverse ;
case 2 :
return Acarbdi[8]*T + Acarbdi[9];
case 3 :
return Acarbdi[10]*T + Acarbdi[11];
case 4 :
return Acarbdi[12];
case 5 :
return Acarbdi[13] *T2inverse +
Acarbdi[14] *T3inverse +
Acarbdi[15] *T4inverse;
case 6 :
return Acarbdi[16] *T2inverse +
Acarbdi[17] *T3inverse +
Acarbdi[18] *T4inverse;
default :
return 0.0;
}
}
/* cprime
* derivative of C(i)
*/
inline double CarbonDioxide::Cprime(int j, double T2inverse, double T3inverse, double T4inverse) {
switch(j) {
case 0 :
return Acarbdi[0] +
- Acarbdi[2] * T2inverse +
-2 * Acarbdi[3] * T3inverse +
-3 * Acarbdi[4] * T4inverse ;
case 1 :
return Acarbdi[5] -
Acarbdi[7] * T2inverse;
case 2 :
return Acarbdi[8] ;
case 3 :
return Acarbdi[10] ;
case 4 :
return 0;
case 5 :
return
-2 *Acarbdi[13] *T3inverse +
-3 *Acarbdi[14] *T4inverse +
-4 *Acarbdi[15]* pow(T,-5);
case 6 :
return
-2 *Acarbdi[16] *T3inverse +
-3 *Acarbdi[17] *T4inverse +
-4 *Acarbdi[18] *pow(T,-5);
default :
return 0.0;
}
}
/*
* I = integral from o-rho { 1/(rho^2) * H(i, rho) d rho }
* ( see section 2 of Reynolds TPSI )
*/
inline double CarbonDioxide::I(int j, double ergho, double Gamma) {
switch (j) {
case 0:
return Rho;
case 1:
return pow(Rho, 2)/2;
case 2:
return pow(Rho, 3)/ 3;
case 3:
return pow(Rho, 4)/ 4;
case 4:
return pow(Rho, 5)/ 5;
case 5:
return (1 - ergho ) / double(2 * Gamma);
case 6:
return ( 1 - ergho * double( Gamma * pow(Rho,2) + double(1) ) )/ double(2 * Gamma * Gamma);
default:
return 0.0;
}
}
/* H returns a multiplier in each term of the sum
* in P-3
* this is used in conjunction with C in the function Pp
* this represents the product rho^n
* i=0 is the second additive in the formula in reynolds
* i=1 is the third ...
*/
double CarbonDioxide::H(int i, double egrho) {
if (i < 5)
return pow(Rho,i+2);
else if (i == 5)
return pow(Rho,3)*egrho;
else if (i == 6)
return pow(Rho,5)*egrho;
else
return 0;
}
/*
* internal energy
* see Reynolds eqn (15) section 2
* u = (the integral from T to To of co(T)dT) +
* sum from i to N ([C(i) - T*Cprime(i)] + uo
*/
double CarbonDioxide::up() {
double Tinverse = 1.0/T;
double T2inverse = pow(T, -2);
double T3inverse = pow(T, -3);
double T4inverse = pow(T, -4);
double egrho = exp(-Gamma*Rho*Rho);
double sum = 0.0;
// Equation C-6 integrated
sum += G[0]*log(T/To);
int i;
for (i=1; i<=5; i++)
sum += G[i]*(pow(T,i) - pow(To,i))/double(i);
for (i=0; i<=6; i++) {
sum += I(i,egrho, Gamma) *
( C(i, Tinverse, T2inverse, T3inverse, T4inverse) - T*Cprime(i,T2inverse, T3inverse, T4inverse) );
}
sum += u0;
return sum + m_energy_offset;
}
/*
* entropy
* see Reynolds eqn (16) section 2
*/
double CarbonDioxide::sp() {
double Tinverse = 1.0/T;
double T2inverse = pow(T, -2);
double T3inverse = pow(T, -3);
double T4inverse = pow(T, -4);
double egrho = exp(-Gamma*Rho*Rho);
double sum = 0.0;
for (int i=2; i<=5; i++)
sum += G[i]*(pow(T,i-1) - pow(To,i-1))/double(i-1);
sum += G[1]*log(T/To);
sum -= G[0]*(1.0/To - 1.0/T);
for (int i=0; i<=6; i++) {
sum -= Cprime(i,T2inverse, T3inverse, T4inverse)*I(i,egrho,Gamma);
}
sum += s0 - R*log(Rho);
return sum + m_entropy_offset;
}
/*
* Equation P-3 in Reynolds
* P - rho - T
* returns P (pressure)
*/
double CarbonDioxide::Pp(){
double Tinverse = pow(T,-1);
double T2inverse = pow(T, -2);
double T3inverse = pow(T, -3);
double T4inverse = pow(T, -4);
double egrho = exp(-Gamma*Rho*Rho);
double P = Rho*R*T;
// when i=0 we are on second sum of equation (where rho^2)
for(int i=0; i<=6; i++) {
P += C(i,Tinverse, T2inverse, T3inverse, T4inverse)*H(i,egrho);
}
return P;
}
/*
* Equation S-2 in Reynolds
* Pressure at Saturation
*/
double CarbonDioxide::Psat(){
double log, sum=0,P;
if ((T < Tmn) || (T > Tc)) {
cout << " error in Psat " << TempError << endl;
set_Err(TempError); // Error("CarbonDioxide::Psat",TempError,T);
}
for (int i=1;i<=8;i++)
sum += F[i-1] * pow((T/Tp -1),double(i-1));
log = ((Tc/T)-1)*sum;
P=exp(log)*Pc;
//cout << "Psat is returning " << P << " at T " << T << " and Pc " << Pc << " and Tp " << Tp << endl;
return P;
}
/*
* Equation D2 in Reynolds
* liquid density, of rho_f
*/
double CarbonDioxide::ldens() {
double xx=1-(T/Tc), sum=0;
if ((T < Tmn) || (T > Tc)) {
cout << " error in ldens " << TempError << endl;
set_Err(TempError);
}
for(int i=1;i<=6;i++)
sum+=D[i-1]*pow(xx,double(i-1)/3.0);
return sum;
}
/*
* the following functions allow users
* to get the properties of CarbonDioxide
* that are not dependent on the state
*/
double CarbonDioxide::Tcrit() {return Tc;}
double CarbonDioxide::Pcrit() {return Pc;}
double CarbonDioxide::Vcrit() {return 1.0/Roc;}
double CarbonDioxide::Tmin() {return Tmn;}
double CarbonDioxide::Tmax() {return Tmx;}
char * CarbonDioxide::name() {return "CarbonDioxide";}
char * CarbonDioxide::formula() {return "CO2";}
double CarbonDioxide::MolWt() {return M;}
}
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