RVector PolynomialModelling::startModel( ){
if ( startModel_.size() == powInt( f_.size(), 3 ) ) return startModel_;
RVector p( powInt( f_.size(), 3 ), 0.0 );
f_.clear();
p.setVal( 1.0, 0, (SIndex)( powInt( f_.size(), dim_ ) ) );
if ( pascalTriangle_ ){
for ( Index k = 0; k < f_.size(); k ++ ){
for ( Index j = 0; j < f_.size(); j ++ ){
for ( Index i = 0; i < f_.size(); i ++ ){
//** remove elements outside of the Pascal's triangle
if ( powCombination_ > 0 ) {
if ( ( i + j + k ) > powCombination_ ) p[ k*( f_.size() * f_.size() ) + j * f_.size() + i ] = 0.0;
} else {
if ( ( i + j + k ) >= ( f_.size() + serendipityStyle_ * ( dim_ -1) ) ) p[ k*( f_.size() * f_.size() ) + j * f_.size() + i ] = 0.0;
}
}
}
}
}
return p;
}
double R717Class::viscosity_Trho(double T, double rho)
{
/*
From "The Viscosity of Ammonia"
by A. Fenghour and W.A. Wakeham and V. Vesovic and J.T.R. Watson and J. Millat and E. Vogel
J. Phys. Chem. Ref. Data, Vol. 24, No. 5, 1995
*/
double sum=0, e_k=386.0,sigma=0.2957,M=17.03026,sum2=0.0;
int i,j;
double T_star,G_eta_star,eta0,B_eta_star,B_eta,b_1,deltaeta_h;
double a[]={4.99318220,-0.61122364,0.0,0.18535124,-0.11160946};
double c[]={-0.17999496e1,0.46692621e2,-0.53460794e3,0.33604074e4,-0.13019164e5,
0.33414230e5,-0.58711743e5,0.71426686e5,-0.59834012e5,0.33652741e5,
-0.12027350e5,0.24348205e4,-0.20807957e3};
// indices are backwards from paper
double d[5][3]={{0,0.17366936e-2,0.0},
{0.0,-0.64250359e-2,0.0},
{2.19664285e-1,0.0,1.67668649e-4},
{0.0,0.0,-1.49710093e-4},
{-0.83651107e-1,0.0,0.77012274e-4}};
// rho is units of mol/L, so convert the density from kg/m^3 to mol/L (poorly documented in paper)
rho=rho/M;
sum=0;
T_star=T/e_k;
for (i=0;i<=4;i++)
{
sum+=a[i]*powInt(log(T_star),i);
}
G_eta_star=exp(sum);
// From REFPROP fluid file: !=0.021357*SQRT(MW)*(unknown factor of 100) [Chapman-Enskog term]
// Seems like there is a typo in Fenghour - or am I missing something?
eta0=0.021357*sqrt(T*M)*100/(sigma*sigma*G_eta_star);
sum=0;
for (i=0;i<=12;i++)
{
sum+=c[i]*powInt(sqrt(T_star),-i);
}
B_eta_star=sum;
B_eta=B_eta_star*(0.6022137*sigma*sigma*sigma);
b_1=B_eta*eta0;
sum=0;
for (i=2;i<=4;i++)
{
sum2=0.0;
for (j=0;j<=4;j++)
{
// indices of d are backwards from paper
sum2+=d[j][i-2]/powInt(T_star,j);
}
sum+=sum2*powInt(rho,i);
}
deltaeta_h=sum;
return (eta0+b_1*rho+deltaeta_h)/1e6;
}
double R744Class::viscosity_Trho(double T, double rho)
{
int i;
double e_k=251.196,Tstar,sumGstar=0.0,Gstar,eta0;
double a[]={0.235156,-0.491266,5.211155e-2,5.347906e-2,-1.537102e-2};
double e[]={0,3.635074e-3,7.209997e-5, 0,0,0,0,3.00306e-20};
//double d11=0.4071119e-2,d21=0.7198037e-4,d64=0.2411697e-16,d81=0.2971072e-22,d82=-0.1627888e-22;
double summer=0;
Tstar=T/e_k;
for (i=0;i<=4;i++)
{
sumGstar += a[i]*powInt(log(Tstar),i);
}
Gstar=exp(sumGstar);
eta0=1.00697*sqrt(T)/Gstar;
for (i=1;i<=7;i++)
summer += e[i]*pow(rho,i);
double delta_eta_g = summer;
// No critical enhancement in viscosity
//double delta_eta_c = 0.0;
//double B = 18.56 + 0.014*T;
//double V0 = 7.41e-4 - 3.3e-7*T;
//double eta_l = delta_eta_c+1/(B*(1/rho-V0));
return (eta0+delta_eta_g)/1e6;
}
PolynomialModelling::PolynomialModelling( uint dim, uint nCoeffizient,
const std::vector < RVector3 > & referencePoints, const RVector & startModel )
: dim_( dim ), referencePoints_( referencePoints ), f_( PolynomialFunction < double >( nCoeffizient ) ) {
pascalTriangle_ = false;
serendipityStyle_ = false;
startModel_ = startModel;
powCombination_ = 0;
this->regionManager().setParameterCount( powInt( nCoeffizient, 3 ) );
}
double AirClass::viscosity_Trho(double T, double rho)
{
/*
E.W. Lemmon and R.T Jacobsen, Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon and Air
International Journal of Thermophysics, Vol. 25, No. 1, January 2004, p.28
*/
double e_k=103.3, //[K]
sigma=0.360; //[nm]
double eta0,etar,OMEGA,delta,tau,Tstar;
double b[]={0.431,-0.4623,0.08406,0.005341,-0.00331};
// Ideal-gas part
Tstar = T/(e_k);
OMEGA=exp(b[0]*powInt(log(Tstar),0)
+b[1]*powInt(log(Tstar),1)
+b[2]*powInt(log(Tstar),2)
+b[3]*powInt(log(Tstar),3)
+b[4]*powInt(log(Tstar),4));
eta0=0.0266958*sqrt(28.9586*T)/(sigma*sigma*OMEGA);
// Residual part
double N[]={0,10.72,1.122,0.002019,-8.876,-0.02916};
double t[]={0,0.2,0.05,2.4,0.6,3.6};
double d[]={0,1,4,9,1,8};
double l[]={0,0,0,0,1,1};
double g[]={0,0,0,0,1,1};
delta = rho/(10.4477*28.9586);
tau = 132.6312/T;
etar=N[1]*pow(tau,t[1])*pow(delta,d[1])*exp(-g[1]*pow(delta,l[1]))
+N[2]*pow(tau,t[2])*pow(delta,d[2])*exp(-g[2]*pow(delta,l[2]))
+N[3]*pow(tau,t[3])*pow(delta,d[3])*exp(-g[3]*pow(delta,l[3]))
+N[4]*pow(tau,t[4])*pow(delta,d[4])*exp(-g[4]*pow(delta,l[4]))
+N[5]*pow(tau,t[5])*pow(delta,d[5])*exp(-g[5]*pow(delta,l[5]));
return (eta0+etar)/1e6; // uPa-s to Pa-s
}
double AirClass::conductivity_Trho(double T, double rho)
{
/*
E.W. Lemmon and R.T Jacobsen, Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon and Air
International Journal of Thermophysics, Vol. 25, No. 1, January 2004, p.28
*/
double e_k=103.3, //[K]
sigma=0.360, //[nm]
Tref=265.262, //[K]
zeta0=0.11, //[nm]
LAMBDA=0.055,
q_D=0.31; //[nm]
double eta0,OMEGA,delta,tau,Tstar,lambda0,lambdar,num,
cp,cv,OMEGA_tilde,OMEGA_tilde0,zeta,nu,gamma,R0,lambdac,k,
pi=3.141592654,mu;
double b[]={0.431,-0.4623,0.08406,0.005341,-0.00331};
double N[]={0,1.308,1.405,-1.036,8.743,14.76,-16.62,3.793,-6.142,-0.3778};
double t[]={0,0,-1.1,-0.3,0.1,0.0,0.5,2.7,0.3,1.3};
double d[]={0,0,0,0,1,2,3,7,7,11};
double l[]={0,0,0,0,0,0,2,2,2,2};
double g[]={0,0,0,0,0,0,1,1,1,1};
delta=rho/(10.4477*28.9586);
tau=132.6312/T;
Tstar=T/(e_k);
OMEGA=exp(b[0]*powInt(log(Tstar),0)
+b[1]*powInt(log(Tstar),1)
+b[2]*powInt(log(Tstar),2)
+b[3]*powInt(log(Tstar),3)
+b[4]*powInt(log(Tstar),4));
eta0=0.0266958*sqrt(28.9586*T)/(sigma*sigma*OMEGA);
lambda0=N[1]*eta0+N[2]*pow(tau,t[2])+N[3]*pow(tau,t[3]);
lambdar=N[4]*pow(tau,t[4])*pow(delta,d[4])*exp(-g[4]*pow(delta,l[4]))
+N[5]*pow(tau,t[5])*pow(delta,d[5])*exp(-g[5]*pow(delta,l[5]))
+N[6]*pow(tau,t[6])*pow(delta,d[6])*exp(-g[6]*pow(delta,l[6]))
+N[7]*pow(tau,t[7])*pow(delta,d[7])*exp(-g[7]*pow(delta,l[7]))
+N[8]*pow(tau,t[8])*pow(delta,d[8])*exp(-g[8]*pow(delta,l[8]))
+N[9]*pow(tau,t[9])*pow(delta,d[9])*exp(-g[9]*pow(delta,l[9]));
R0=1.01;
nu=0.63;
gamma=1.2415;
k=1.380658e-23; //[J/K]
num=X_tilde(T,crit.T/T,delta)-X_tilde(Tref,crit.T/Tref,delta)*Tref/T;
// no critical enhancement if numerator of Eq. 10 is negative
if (num<0)
return (lambda0+lambdar)/1e6;
cp=Props('C','T',T,'D',rho,(char *)"Air");
cv=Props('O','T',T,'D',rho,(char *)"Air");
mu=Props('V','T',T,'D',rho,(char *)"Air")*1e6; //[uPa-s]
zeta=zeta0*pow(num/LAMBDA,nu/gamma); //[nm]
OMEGA_tilde=2.0/pi*((cp-cv)/cp*atan(zeta/q_D)+cv/cp*(zeta/q_D));
OMEGA_tilde0=2.0/pi*(1.-exp(-1./(q_D/zeta+1.0/3.0*(zeta/q_D)*(zeta/q_D)/delta/delta)));
lambdac=rho*(cp*1000.0)*k*R0*T/(6*pi*zeta*mu)*(OMEGA_tilde-OMEGA_tilde0)*1e18; // 1e18 is conversion to mW/m-K (not described in paper)
return (lambda0+lambdar+lambdac)/1e6;
}
double R507AClass::rhosatL(double T)
{
double theta;
theta=1-T/343.765;
return exp(6.059998874+1.305406634077e+00*pow(theta,0.21588)+0.585710808997*theta-2.09578513606*theta*theta+4.667514451*powInt(theta,3)-3.93369379654*powInt(theta,4));
}
double R507AClass::rhosatV(double T)
{
double theta;
theta=1-T/343.765;
return exp(+2.685721675+2.703462155742e+00*pow(theta,-0.031591)-12.9219949523*theta+48.3326995201*theta*theta-301.352305753*powInt(theta,3)+953.161091912*powInt(theta,4)-1667.82041758*powInt(theta,5)+1132.7963359*powInt(theta,6));
}
double R717Class::conductivity_Trho(double T, double rho)
{
/*
From "Thermal Conductivity of Ammonia in a Large
Temperature and Pressure Range Including the Critical Region"
by R. Tufeu, D.Y. Ivanov, Y. Garrabos, B. Le Neindre,
Bereicht der Bunsengesellschaft Phys. Chem. 88 (1984) 422-427
*/
/*
Does not include the critical enhancement. Comparison of EES (without enhancement) and Refprop (with enhancement) give
errors in saturated liquid and saturated vapor conductivities of
T < 325K, error < 0.1%
325K < T < 355 K, error <1%
Nearly all practical conditions will be in the <325K range
*/
double lambda_0,lambda_tilde;
double a= 0.3589e-1;
double b=-0.1750e-3;
double c= 0.4551e-6;
double d= 0.1685e-9;
double e=-0.4828e-12;
double lambda_1= 0.16207e-3;
double lambda_2= 0.12038e-5;
double lambda_3=-0.23139e-8;
double lambda_4= 0.32749e-11;
// This variable appears to be unused in the code:
//double a_zeta_plus=0.7;
double LAMBDA=1.2, nu=0.63, gamma =1.24, DELTA=0.50, rhoc_visc=235,t,zeta_0_plus=1.34e-10,a_zeta=1,GAMMA_0_plus=0.423e-8;
double pi=3.141592654,a_chi,k_B=1.3806504e-23,X_T,DELTA_lambda,dPdT,eta_B,DELTA_lambda_id,DELTA_lambda_i;
lambda_0=a+b*T+c*T*T+d*T*T*T+e*T*T*T*T;
lambda_tilde=lambda_1*rho+lambda_2*rho*rho+lambda_3*rho*rho*rho+lambda_4*rho*rho*rho*rho;
if (0)//(T>Tc)
{
t=fabs((T-reduce.T)/reduce.T);
a_chi=a_zeta/0.7;
eta_B=(2.60*1.6*t)*1e-5;
dPdT=(2.18-0.12/exp(17.8*t))*1e5; //[Pa-K]
X_T=0.61*rhoc_visc+16.5*log(t);
// Along the critical isochore (only a function of temperature) (Eq. 9)
DELTA_lambda_i=LAMBDA*(k_B*T*T)/(6*pi*eta_B*(zeta_0_plus*pow(t,-nu)*(1+a_zeta*pow(t,DELTA))))*dPdT*dPdT*GAMMA_0_plus*pow(t,-gamma)*(1+a_chi*pow(t,DELTA));
DELTA_lambda_id=DELTA_lambda_i*exp(-36*t*t);
if (rho<0.6*reduce.rho)
{
DELTA_lambda=DELTA_lambda_id*(X_T*X_T)/(X_T*X_T+powInt(0.6*rhoc_visc-0.96*rhoc_visc,2))*powInt(rho,2)/powInt(0.6*rhoc_visc,2);
}
else
{
DELTA_lambda=DELTA_lambda_id*(X_T*X_T)/(X_T*X_T+powInt(rho-0.96*rhoc_visc,2));
}
}
else
{
DELTA_lambda=0.0;
}
return lambda_0+lambda_tilde+DELTA_lambda;
}
