github/CoolProp
1
1
Fork 0
mirror of https://github.com/CoolProp/CoolProp.git synced 2026-01-22 20:38:01 -05:00
Code Issues Packages Projects Releases Wiki Activity

First cut at Twu alpha function implementation

Browse Source
This commit is contained in:
Ian Bell
2016-06-28 20:01:53 -06:00
parent 61146d02bc
commit d6443aa66f
2 changed files with 90 additions and 37 deletions
Download Patch File Download Diff File Expand all files Collapse all files

113
src/Backends/Cubics/GeneralizedCubic.cpp
View File

@@ -1,4 +1,5 @@
#include "GeneralizedCubic.h"
#include "CPnumerics.h"
#include <cmath>
const double AbstractCubic::T_r = 1.0;
@@ -109,41 +110,83 @@ double AbstractCubic::aii_term(double tau, std::size_t i, std::size_t itau)
}
}
else{
// Here we are using the full Mathias-Copeman formulation, introducing
// some additional computational effort, so we only evaluate the parameters that
// we actually need to evaluate, otherwise we just set their value to zero
// See info on the conditional (ternary) operator : http://www.cplusplus.com/articles/1AUq5Di1/
// Furthermore, this should help with branch prediction
double Di = 1-sqrt_Tr_Tci/sqrt(tau);
double dDi_dtau = (itau >= 1) ? (1.0/2.0)*sqrt_Tr_Tci/(pow(tau,1.5)) : 0;
double d2Di_dtau2 = (itau >= 2) ? -(3.0/4.0)*sqrt_Tr_Tci/(pow(tau,2.5)) : 0;
double d3Di_dtau3 = (itau >= 3) ? (15.0/8.0)*sqrt_Tr_Tci/(pow(tau,3.5)) : 0;
double d4Di_dtau4 = (itau >= 4) ? -(105.0/16.0)*sqrt_Tr_Tci/(pow(tau,4.5)) : 0;
double Bi = 1, dBi_dtau = 0, d2Bi_dtau2 = 0, d3Bi_dtau3 = 0, d4Bi_dtau4 = 0;
for (int n = 1; n <= 3; ++n){
const std::vector<double> &C = get_C_ref(static_cast<int>(n));
Bi += C[i]*pow(Di, n);
dBi_dtau += (itau < 1) ? 0 : (n*C[i]*pow(Di,n-1)*dDi_dtau) ;
d2Bi_dtau2 += (itau < 2) ? 0 : n*C[i]*((n-1)*pow(dDi_dtau,2) + Di*d2Di_dtau2)*pow(Di, n-2);
d3Bi_dtau3 += (itau < 3) ? 0 : n*C[i]*(3*(n-1)*Di*dDi_dtau*d2Di_dtau2 + (n*n-3*n+2)*pow(dDi_dtau,3)+pow(Di,2)*d3Di_dtau3)*pow(Di, n-3);
d4Bi_dtau4 += (itau < 4) ? 0 : n*C[i]*(6*(n*n-3*n+2)*Di*pow(dDi_dtau,2)*d2Di_dtau2 + (n*n*n-6*n*n+11*n-6)*pow(dDi_dtau,4)
+(4*n*dDi_dtau*d3Di_dtau3+3*n*pow(d2Di_dtau2,2)-4*dDi_dtau*d3Di_dtau3-3*pow(d2Di_dtau2,2) )*pow(Di,2)
+ pow(Di,3)*d4Di_dtau4 )*pow(Di, n-4);
}
switch (itau){
case 0:
return a0_ii(i)*Bi*Bi;
case 1:
return 2*a0_ii(i)*Bi*dBi_dtau;
case 2:
return 2*a0_ii(i)*(Bi*d2Bi_dtau2 + dBi_dtau*dBi_dtau);
case 3:
return 2*a0_ii(i)*(Bi*d3Bi_dtau3 + 3*dBi_dtau*d2Bi_dtau2);
case 4:
return 2*a0_ii(i)*(Bi*d4Bi_dtau4 + 4*dBi_dtau*d3Bi_dtau3 + 3*pow(d2Bi_dtau2, 2));
default:
throw -1;
switch (aii_model){
case AII_MATHIAS_COPEMAN:
{
// Here we are using the full Mathias-Copeman formulation, introducing
// some additional computational effort, so we only evaluate the parameters that
// we actually need to evaluate, otherwise we just set their value to zero
// See info on the conditional (ternary) operator : http://www.cplusplus.com/articles/1AUq5Di1/
// Furthermore, this should help with branch prediction
double Di = 1-sqrt_Tr_Tci/sqrt(tau);
double dDi_dtau = (itau >= 1) ? (1.0/2.0)*sqrt_Tr_Tci/(pow(tau,1.5)) : 0;
double d2Di_dtau2 = (itau >= 2) ? -(3.0/4.0)*sqrt_Tr_Tci/(pow(tau,2.5)) : 0;
double d3Di_dtau3 = (itau >= 3) ? (15.0/8.0)*sqrt_Tr_Tci/(pow(tau,3.5)) : 0;
double d4Di_dtau4 = (itau >= 4) ? -(105.0/16.0)*sqrt_Tr_Tci/(pow(tau,4.5)) : 0;
double Bi = 1, dBi_dtau = 0, d2Bi_dtau2 = 0, d3Bi_dtau3 = 0, d4Bi_dtau4 = 0;
for (int n = 1; n <= 3; ++n){
const std::vector<double> &C = get_C_ref(static_cast<int>(n));
Bi += C[i]*pow(Di, n);
dBi_dtau += (itau < 1) ? 0 : (n*C[i]*pow(Di,n-1)*dDi_dtau) ;
d2Bi_dtau2 += (itau < 2) ? 0 : n*C[i]*((n-1)*pow(dDi_dtau,2) + Di*d2Di_dtau2)*pow(Di, n-2);
d3Bi_dtau3 += (itau < 3) ? 0 : n*C[i]*(3*(n-1)*Di*dDi_dtau*d2Di_dtau2 + (n*n-3*n+2)*pow(dDi_dtau,3)+pow(Di,2)*d3Di_dtau3)*pow(Di, n-3);
d4Bi_dtau4 += (itau < 4) ? 0 : n*C[i]*(6*(n*n-3*n+2)*Di*pow(dDi_dtau,2)*d2Di_dtau2 + (n*n*n-6*n*n+11*n-6)*pow(dDi_dtau,4)
+(4*n*dDi_dtau*d3Di_dtau3+3*n*pow(d2Di_dtau2,2)-4*dDi_dtau*d3Di_dtau3-3*pow(d2Di_dtau2,2) )*pow(Di,2)
+ pow(Di,3)*d4Di_dtau4 )*pow(Di, n-4);
}
switch (itau){
case 0:
return a0_ii(i)*Bi*Bi;
case 1:
return 2*a0_ii(i)*Bi*dBi_dtau;
case 2:
return 2*a0_ii(i)*(Bi*d2Bi_dtau2 + dBi_dtau*dBi_dtau);
case 3:
return 2*a0_ii(i)*(Bi*d3Bi_dtau3 + 3*dBi_dtau*d2Bi_dtau2);
case 4:
return 2*a0_ii(i)*(Bi*d4Bi_dtau4 + 4*dBi_dtau*d3Bi_dtau3 + 3*pow(d2Bi_dtau2, 2));
default:
throw -1;
}
}
case AII_TWU:
{
// Here we are using the Twu formulation, introducing
// some additional computational effort, so we only evaluate the parameters that
// we actually need to evaluate, otherwise we just set their value to zero
// See info on the conditional (ternary) operator : http://www.cplusplus.com/articles/1AUq5Di1/
// Furthermore, this should help with branch prediction
double A = pow(Tr_over_Tci/tau, M_Twu[i]*N_Twu[i]);
const double L = L_Twu[i], M = M_Twu[i], N = N_Twu[i];
double B1 = (itau < 1) ? 0 : N/tau*(L*M*A - M + 1);
double dB1_dtau = (itau < 2) ? 0 : N/powInt(tau,2)*(-L*M*M*N*A - L*M*A + M - 1);
double d2B1_dtau2 = (itau < 3) ? 0 : N/powInt(tau,3)*(L*M*M*M*N*N*A + 3*L*M*M*N*A + 2*L*M*A - 2*M + 2);
double d3B1_dtau3 = (itau < 4) ? 0 : -N/powInt(tau,4)*(L*powInt(M,4)*powInt(N,3)*A + 6*L*M*M*M*N*N*A + 11*L*M*M*N*A + 6*L*M*A -6*M + 6);
double dam_dtau, d2am_dtau2, d3am_dtau3, d4am_dtau4;
double am = a0_ii(i)*pow(Tr_over_Tci/tau,N*(M-1))*exp(L*(1-pow(Tr_over_Tci/tau,M*N)));
if (itau == 0){
return am;
}
else{
// Calculate terms as needed
dam_dtau = a0_ii(i)*B1;
d2am_dtau2 = (itau < 2) ? 0 : B1*dam_dtau + am*dB1_dtau;
d3am_dtau3 = (itau < 3) ? 0 : B1*d2am_dtau2 + am*d2B1_dtau2 + 2*dB1_dtau*dam_dtau;
d4am_dtau4 = (itau < 4) ? 0 : B1*d3am_dtau3 + am*d3B1_dtau3 + 3*dB1_dtau*d2am_dtau2 + 3*d2B1_dtau2*dam_dtau;
}
switch (itau){
case 1: return dam_dtau;
case 2: return d2am_dtau2;
case 3: return d3am_dtau3;
case 4: return d4am_dtau4;
default: throw -1;
}
}
default: throw -1;
}
}
}

14
src/Backends/Cubics/GeneralizedCubic.h
View File

@@ -14,6 +14,7 @@
#include <vector>
#include <cmath>
enum AII_Model {AII_MODEL_NOT_SPECIFIED = 0, AII_MATHIAS_COPEMAN, AII_TWU};
class AbstractCubic
{
protected:
@@ -27,6 +28,8 @@ protected:
std::vector< std::vector<double> > k; ///< The interaction parameters (k_ii = 0)
bool simple_aii; ///< True if the Mathias-Copeman equation for a_ii is not being used
std::vector<double> C1, C2, C3; ///< The Mathias-Copeman coefficients for a_ii
std::vector<double> L_Twu, M_Twu, N_Twu; ///< The Twu coefficients for a_ii
AII_Model aii_model; ///< Enumeration for the aii model in use
public:
static const double rho_r, T_r;
/**
@@ -53,7 +56,7 @@ public:
N = static_cast<int>(Tc.size());
k.resize(N, std::vector<double>(N, 0));
/// If no Mathias-Copeman coefficients are passed in (all empty vectors), use the predictive scheme for m_ii
simple_aii = (C1.empty() && C2.empty() && C3.empty());
simple_aii = (C1.empty() && C2.empty() && C3.empty() && L_Twu.empty() && M_Twu.empty() && N_Twu.empty());
};
/// Set the kij factor for the ij pair
void set_kij(std::size_t i, std::size_t j, double val){ k[i][j] = val; }
@@ -95,7 +98,14 @@ public:
void set_C_MC(double c1, double c2, double c3){
C1.resize(1); C2.resize(1); C3.resize(1);
C1[0] = c1, C2[0] = c2; C3[0] = c3;
simple_aii = false;
simple_aii = false; aii_model = AII_MATHIAS_COPEMAN;
}
/// Set the three Twu constants in one shot for a pure fluid
void set_C_Twu(double L, double M, double N){
L_Twu.resize(1); L_Twu[0] = L;
M_Twu.resize(1); M_Twu[0] = M;
N_Twu.resize(1); N_Twu[0] = N;
simple_aii = false; aii_model = AII_TWU;
}
/// Get the leading constant in the expression for the pure fluid attractive energy term