lk.cpp

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//! @file lk.cpp Lee-Kesler equation of state

// This file is part of Cantera. See License.txt in the top-level directory or
// at http://www.cantera.org/license.txt for license and copyright information.

#include "lk.h"
#include <math.h>

namespace tpx
{

static double b[2][4] = {{0.1181193, 0.265728, 0.154790, 0.030323},
    {0.2026579, 0.331511, 0.027655, 0.203488}
};
static double c[2][4] = {{0.0236744, 0.0186984, 0.0, 0.042724},
    {0.0313385, 0.0503618, 0.016901, 0.041577}
};
static double d[2][2] = {{1.55488e-5, 6.23689e-5},{4.8736e-5, 0.740336e-5}};
static double beta[2] = {0.65392, 1.226};
static double gamma[2] = {0.060167, 0.03754};

//--------------------------- member functions ------------------

double leekesler::W(int n, double egrho, double Gamma)
{
    return (n == 0 ? (1.0 - egrho)/(2.0*Gamma) :
            (n*W(n-1, egrho, Gamma) - 0.5*pow(Rho,2*n)*egrho)/Gamma);
}

double leekesler::up()
{
    return -(8314.3/Mw)*T*(1.0 + T*I()/Tcr); // + h_0(T)
}

double leekesler::hdep()
{
    double tr = T/Tcr;
    return tr*tr*I() + (1.0 - z())*tr;
}

double leekesler::sdep()
{
    double tr = T/Tcr;
    return tr*I() + J() - log(z());
}

double leekesler::sp()
{
    const double Pref = 101325.0;
    double rgas = 8314.3/Mw;
    return rgas*(log(Pref/(Rho*rgas*T)) - (T/Tcr)*I() - J());
}

double leekesler::I() // \int_0^\rho_r (1/\rho_r)(dZ/dT_r) d\rho_r
{
    double Bp, Cp, Dp;
    double rtr = Tcr/T;
    double rtr2 = rtr*rtr;
    double rvr = 8314.3*Tcr*Rho/(Pcr*Mw); // 1/v_r^\prime
    double rvr2 = rvr*rvr;
    double egrho;

    egrho = exp(-gamma[Isr]*rvr2);
    Bp = rtr2*b[Isr][1] + 2.0*rtr*rtr2*b[Isr][2] + 3.0*rtr2*rtr2*b[Isr][3];
    Cp = rtr2*c[Isr][1] - 3.0*c[Isr][2]*rtr2*rtr2;
    Dp = -d[Isr][1]*rtr2;
    double r = Bp*rvr + 0.5*rvr2*Cp + 0.2*pow(rvr,5)*Dp
               - 3.0*c[Isr][3]*rtr2*rtr2*(beta[Isr]*W(0,egrho,gamma[Isr])
                                          + gamma[Isr]*W(1,egrho,gamma[Isr]));
    return r;
}

double leekesler::J() // \int_0^\rho_r (1/\rho_r)(Z - 1) d\rho_r
{
    double BB, CC, DD;
    double rtr = Tcr/T;
    double rtr2 = rtr*rtr;
    double rvr = 8314.3*Tcr*Rho/(Pcr*Mw); // 1/v_r^\prime
    double rvr2 = rvr*rvr;
    double egrho;

    egrho = exp(-gamma[Isr]*rvr2);
    BB = b[Isr][0] - rtr*(b[Isr][1]
                          + rtr*(b[Isr][2] + rtr*b[Isr][3]));
    CC = c[Isr][0] - rtr*(c[Isr][1] - c[Isr][2]*rtr*rtr);
    DD = d[Isr][0] + d[Isr][1]*rtr;
    double r = BB*rvr + 0.5*rvr2*CC + 0.2*pow(rvr,5)*DD
               + c[Isr][3]*rtr2*rtr*(beta[Isr]*W(0,egrho,gamma[Isr])
                                     + gamma[Isr]*W(1,egrho,gamma[Isr]));
    return r;
}

double leekesler::z()
{
    double zz, rvr2, BB, CC, DD, EE;
    double rtr = Tcr/T; // 1/T_r
    double rvr = Rho*8314.3*Tcr/(Pcr*Mw);
    rvr2 = rvr*rvr;
    BB = b[Isr][0] - rtr*(b[Isr][1]
                          + rtr*(b[Isr][2] + rtr*b[Isr][3]));
    CC = c[Isr][0] - rtr*(c[Isr][1] - c[Isr][2]*rtr*rtr);
    DD = d[Isr][0] + d[Isr][1]*rtr;
    EE = exp(-gamma[Isr]*rvr2);

    zz = 1.0 + BB*rvr + CC*rvr2 + DD*pow(rvr,5)
         + c[Isr][3]*pow(rtr,3)*rvr2*
         (beta[Isr] + gamma[Isr]*rvr2)*EE;
    return zz;
}

double leekesler::Pp()
{
    return 8314.3*z()*Rho*T/Mw;
}

double leekesler::Psat()
{
    double tr = 1.0 - Tcr/T;
    double lpr;

    if (Isr == 0) {
        lpr = 5.395743797*tr + 0.05524287*tr*tr + 0.06853005*tr*tr*tr;
    } else {
        lpr = 7.259961465*tr - 0.549206092*tr*tr + 0.177581752*tr*tr*tr;
    }
    return Pcr*exp(lpr);
}

double leekesler::ldens()
{
    double x = 1.0 - T/Tcr;

    // for simple fluid
    double rho_r;
    if (Isr == 0) {
        rho_r = 5.2307 + 15.16*x - 21.9778*x*x + 18.767*x*x*x;
    } else {
        rho_r = 6.166930606 + 17.42866964*x - 18.62589833*x*x
                + 11.73957224*x*x*x;
        rho_r *= 1.0;
    }
    return Pcr*rho_r*Mw/(8314.3*Tcr);
}

double leekesler::Tcrit()
{
    return Tcr;
}
double leekesler::Pcrit()
{
    return Pcr;
}
double leekesler::Vcrit()
{
    return 0.2901*8314.3*Tcr/(Pcr*Mw);
}
double leekesler::Tmin()
{
    return -100.0;
}
double leekesler::Tmax()
{
    return 10000.0;
}
double leekesler::MolWt()
{
    return Mw;
}
}