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namespace teqp {
/**
* The EOS of Monika Thol and colleagues. DOI:10.1063/1.4945000
*/
inline auto build_LJ126_TholJPCRD2016() {
std::string contents = R"(
{
"EOS": [
{
"BibTeX_CP0": "",
"BibTeX_EOS": "Thol-THESIS-2015",
"STATES": {
"reducing": {
"T": 1.32,
"T_units": "LJ units",
"rhomolar": 0.31,
"rhomolar_units": "LJ units"
}
},
"T_max": 1200,
"T_max_units": "LJ units",
"Ttriple": 0.661,
"Ttriple_units": "LJ units",
"alphar": [
{
"d": [4, 1, 1, 2, 2, 3, 1, 1, 3, 2, 2, 5],
"l": [0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2, 1],
"n": [0.52080730e-2, 0.21862520e+1, -0.21610160e+1, 0.14527000e+1, -0.20417920e+1, 0.18695286e+0, -0.62086250e+0, -0.56883900e+0, -0.80055922e+0, 0.10901431e+0, -0.49745610e+0, -0.90988445e-1],
"t": [1.000, 0.320, 0.505, 0.672, 0.843, 0.898, 1.205, 1.786, 2.770, 1.786, 2.590, 1.294],
"type": "ResidualHelmholtzPower"
},
{
"beta": [0.625, 0.638, 3.91, 0.156, 0.157, 0.153, 1.16, 1.73, 383, 0.112, 0.119],
"d": [1, 1, 2, 3, 3, 2, 1, 2, 3, 1, 1],
"epsilon": [ 0.2053, 0.409, 0.6, 1.203, 1.829, 1.397, 1.39, 0.539, 0.934, 2.369, 2.43],
"eta": [2.067, 1.522, 8.82, 1.722, 0.679, 1.883, 3.925, 2.461, 28.2, 0.753, 0.82],
"gamma": [0.71, 0.86, 1.94, 1.48, 1.49, 1.945, 3.02, 1.11, 1.17, 1.33, 0.24],
"n": [-0.14667177e+1, 0.18914690e+1, -0.13837010e+0, -0.38696450e+0, 0.12657020e+0, 0.60578100e+0, 0.11791890e+1, -0.47732679e+0, -0.99218575e+1, -0.57479320e+0, 0.37729230e-2],
"t": [2.830, 2.548, 4.650, 1.385, 1.460, 1.351, 0.660, 1.496, 1.830, 1.616, 4.970],
"type": "ResidualHelmholtzGaussian"
}
],
"gas_constant": 1.0,
"gas_constant_units": "LJ units",
"molar_mass": 1.0,
"molar_mass_units": "LJ units",
"p_max": 100000,
"p_max_units": "LJ units",
"pseudo_pure": false
}
],
"INFO":{
"NAME": "LennardJones",
"REFPROP_NAME": "LJF",
"CAS": "N/A"
}
}
)";
return teqp::build_multifluid_JSONstr({ contents }, "{}", "{}");
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};
/**
Jiri Kolafa and Ivo Nezbeda
Fluid Phase Equilibria, 100 (1994) 1-34
The Lennard-Jones fluid: An accurate analytic and theoretically-based equation of state
doi: 10.1016/0378-3812(94)80001-4
*/
class LJ126KolafaNezbeda1994{
private:
template<typename T>
auto POW2(const T& x) const {
return x*x;
}
template<typename T>
auto POW3(const T& x) const{
return POW2(x)*x;
}
const double MY_PI = EIGEN_PI;
const std::vector<std::tuple<int, double>> c_dhBH {
{-2, 0.011117524},
{-1, -0.076383859},
{ 0, 1.080142248},
{ 1, 0.000693129}
};
const double c_ln_dhBH = -0.063920968;
const std::vector<std::tuple<int, double>> c_Delta_B2_hBH {
{-7, -0.58544978},
{-6, 0.43102052},
{-5, 0.87361369},
{-4, -4.13749995},
{-3, 2.90616279},
{-2, -7.02181962},
{ 0, 0.02459877}
};
const std::vector<std::tuple<int, int, double>> c_Cij = {
{ 0, 2, 2.01546797},
{ 0, 3, -28.17881636},
{ 0, 4, 28.28313847},
{ 0, 5, -10.42402873},
{-1, 2, -19.58371655},
{-1, 3, 75.62340289},
{-1, 4, -120.70586598},
{-1, 5, 93.92740328},
{-1, 6, -27.37737354},
{-2, 2, 29.34470520},
{-2, 3, -112.3535693},
{-2, 4, 170.64908980 },
{-2, 5, -123.06669187},
{-2, 6, 34.42288969 },
{-4, 2, -13.37031968},
{-4, 3, 65.38059570},
{-4, 4, -115.09233113},
{-4, 5, 88.91973082},
{-4, 6, -25.62099890}
};
const double gamma = 1.92907278;
// Form of Eq. 29
template<typename TTYPE>
auto get_dhBH(const TTYPE& Tstar) const {
TTYPE summer = c_ln_dhBH*log(Tstar);
for (auto [i, C_i] : c_dhBH){
summer += C_i*pow(Tstar, i/2.0);
}
return forceeval(summer);
}
template<typename TTYPE>
auto get_d_dhBH_d1T(const TTYPE& Tstar) const {
TTYPE summer = c_ln_dhBH;
for (auto [i, C_i] : c_dhBH){
summer += (i/2.0)*C_i*pow(Tstar, i/2.0);
}
return forceeval(-Tstar*summer);
}
// Form of Eq. 29
template<typename TTYPE>
auto get_DeltaB2hBH(const TTYPE& Tstar) const {
TTYPE summer = 0.0;
for (auto [i, C_i] : c_Delta_B2_hBH){
summer += C_i*pow(Tstar, i/2.0);
}
return forceeval(summer);
}
template<typename TTYPE>
auto get_d_DeltaB2hBH_d1T(const TTYPE& Tstar) const {
auto summer = 0.0;
for (auto [i, C_i] : c_Delta_B2_hBH){
summer += (i/2.0)*C_i*pow(Tstar, i/2.0);
}
return forceeval(-Tstar*summer);
}
// Eq. 5 from K-N
template<typename TTYPE, typename RHOTYPE>
auto get_ahs(const TTYPE& Tstar, const RHOTYPE& rhostar) const {
auto zeta = MY_PI/6.0*rhostar*pow(get_dhBH(Tstar), 3);
return forceeval(Tstar*(5.0/3.0*log(1.0-zeta) + zeta*(34.0-33.0*zeta+4.0*POW2(zeta))/(6.0*POW2(1.0-zeta))));
}
// Eq. 4 from K-N
template<typename TTYPE, typename RHOTYPE>
auto get_zhs(const TTYPE& Tstar, const RHOTYPE& rhostar) const {
std::common_type_t<TTYPE, RHOTYPE> zeta = MY_PI/6.0*rhostar*POW3(get_dhBH(Tstar));
return forceeval((1.0+zeta+zeta**zeta-2.0/3.0*POW3(zeta)*(1+zeta))/POW3(1.0-zeta));
}
// Eq. 30 from K-N
template<typename TTYPE, typename RHOTYPE>
auto get_a(const TTYPE& Tstar, const RHOTYPE& rhostar) const{
std::common_type_t<TTYPE, RHOTYPE> summer = 0.0;
for (auto [i, j, Cij] : c_Cij){
summer += Cij*pow(Tstar, i/2.0)*pow(rhostar, j);
}
return forceeval(get_ahs(Tstar, rhostar) + exp(-gamma*POW2(rhostar))*rhostar*Tstar*get_DeltaB2hBH(Tstar)+summer);
}
public:
// We are in "simulation units", so R is 1.0, and T and rho that go into alphar are actually T^* and rho^*
template<typename MoleFracType>
double R(const MoleFracType &) const { return 1.0; }
template<typename TTYPE, typename RHOTYPE, typename MoleFracType>
auto alphar(const TTYPE& Tstar, const RHOTYPE& rhostar, const MoleFracType& /*molefrac*/) const {
return forceeval(get_a(Tstar, rhostar)/Tstar);
}
};
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/**
J. KARL JOHNSON, JOHN A. ZOLLWEG and KEITH E. GUBBINS
The Lennard-Jones equation of state revisited
MOLECULAR PHYSICS,1993, VOL. 78, No. 3, 591-618
doi: 10.1080/00268979300100411
*/
class LJ126Johnson1993 {
private:
template<typename T>
auto POW2(const T& x) const -> T{
return x*x;
}
template<typename T>
auto POW3(const T& x) const -> T{
return POW2(x)*x;
}
template<typename T>
auto POW4(const T& x) const -> T{
return POW2(x)*POW2(x);
}
const double gamma = 3.0;
const std::vector<double> x {
0.0, // placeholder for i=0 term since C++ uses 0-based indexing
0.8623085097507421,
2.976218765822098,
-8.402230115796038,
0.1054136629203555,
-0.8564583828174598,
1.582759470107601,
0.7639421948305453,
1.753173414312048,
2.798291772190376e03,
-4.8394220260857657e-2,
0.9963265197721935,
-3.698000291272493e01,
2.084012299434647e01,
8.305402124717285e01,
-9.574799715203068e02,
-1.477746229234994e02,
6.398607852471505e01,
1.603993673294834e01,
6.805916615864377e01,
-2.791293578795945e03,
-6.245128304568454,
-8.116836104958410e03,
1.488735559561229e01,
-1.059346754655084e04,
-1.131607632802822e02,
-8.867771540418822e03,
-3.986982844450543e01,
-4.689270299917261e03,
2.593535277438717e02,
-2.694523589434903e03,
-7.218487631550215e02,
1.721802063863269e02
};
// Table 5
template<typename TTYPE>
auto get_ai(const int i, const TTYPE& Tstar) const -> TTYPE{
switch(i){
case 1:
return x[1]*Tstar + x[2]*sqrt(Tstar) + x[3] + x[4]/Tstar + x[5]/POW2(Tstar);
case 2:
return x[6]*Tstar + x[7] + x[8]/Tstar + x[9]/POW2(Tstar);
case 3:
return x[10]*Tstar + x[11] + x[12]/Tstar;
case 4:
return x[13];
case 5:
return x[14]/Tstar + x[15]/POW2(Tstar);
case 6:
return x[16]/Tstar;
case 7:
return x[17]/Tstar + x[18]/POW2(Tstar);
case 8:
return x[19]/POW2(Tstar);
default:
throw teqp::InvalidArgument("i is not possible in get_ai");
}
}
// Table 6
template<typename TTYPE>
auto get_bi(const int i, const TTYPE& Tstar) const -> TTYPE{
switch(i){
case 1:
return x[20]/POW2(Tstar) + x[21]/POW3(Tstar);
case 2:
return x[22]/POW2(Tstar) + x[23]/POW4(Tstar);
case 3:
return x[24]/POW2(Tstar) + x[25]/POW3(Tstar);
case 4:
return x[26]/POW2(Tstar) + x[27]/POW4(Tstar);
case 5:
return x[28]/POW2(Tstar) + x[29]/POW3(Tstar);
case 6:
return x[30]/POW2(Tstar) + x[31]/POW3(Tstar) + x[32]/POW4(Tstar);
default:
throw teqp::InvalidArgument("i is not possible in get_bi");
}
}
// Table 7
template<typename FTYPE, typename RHOTYPE>
auto get_Gi(const int i, const FTYPE& F, const RHOTYPE& rhostar) const -> RHOTYPE{
if (i == 1){
return forceeval((1.0-F)/(2.0*gamma));
}
else{
// Recursive definition of the other terms;
return forceeval(-(F*powi(rhostar, 2*(i-1)) - 2.0*(i-1)*get_Gi(i-1, F, rhostar))/(2.0*gamma));
}
}
template<typename TTYPE, typename RHOTYPE>
auto get_alphar(const TTYPE& Tstar, const RHOTYPE& rhostar) const{
std::common_type_t<TTYPE, RHOTYPE> summer = 0.0;
auto F = exp(-gamma*POW2(rhostar));
for (int i = 1; i <= 8; ++i){
summer += get_ai(i, Tstar)*powi(rhostar, i)/static_cast<double>(i);
}
for (int i = 1; i <= 6; ++i){
summer += get_bi(i, Tstar)*get_Gi(i, F, rhostar);
}
return forceeval(summer);
}
public:
// We are in "simulation units", so R is 1.0, and T and rho that
// go into alphar are actually T^* and rho^*
template<typename MoleFracType>
double R(const MoleFracType &) const { return 1.0; }
template<typename TTYPE, typename RHOTYPE, typename MoleFracType>
auto alphar(const TTYPE& Tstar, const RHOTYPE& rhostar, const MoleFracType& /*molefrac*/) const {
return forceeval(get_alphar(Tstar, rhostar)/Tstar);
}
};