Real
IdealRealGasMixtureFluidProperties::v_from_p_T(Real p, Real T, const std::vector<Real> & x) const
{
const Real x_primary = primaryMassFraction(x);
Real M_primary = _fp_primary->molarMass();
Real sum = x_primary / M_primary;
for (unsigned int i = 0; i < _n_secondary_vapors; i++)
sum += x[i] / _fp_secondary[i]->molarMass();
Real M_star = 1. / sum;
Real v_ideal = R_molar * T / (M_star * p);
// check range of validity for primary (condensable) component
static const Real Tc = _fp_primary->criticalTemperature();
static const Real vc = 1. / _fp_primary->criticalDensity();
Real v_spndl, e_spndl;
if (T < Tc)
_fp_primary->v_e_spndl_from_T(T, v_spndl, e_spndl);
else
v_spndl = vc;
Real lower_spec_volume = v_spndl * x_primary;
Real upper_spec_volume = v_ideal; // p*v/(RT) <= 1
// Initial estimate of a bracketing interval for the temperature
Real p_max = p_from_T_v(T, lower_spec_volume, x);
if (p > p_max || upper_spec_volume < lower_spec_volume)
return getNaN();
// Use BrentsMethod to find temperature
auto pressure_diff = [&T, &p, &x, this](Real v) { return this->p_from_T_v(T, v, x) - p; };
BrentsMethod::bracket(pressure_diff, lower_spec_volume, upper_spec_volume);
Real v = BrentsMethod::root(pressure_diff, lower_spec_volume, upper_spec_volume);
return v;
}
StackSegment::StackSegment()
:min(getNaN())
,max(getNaN())
{
}
Real
IdealRealGasMixtureFluidProperties::xs_prim_from_p_T(Real p,
Real T,
const std::vector<Real> & x) const
{
Real T_c = _fp_primary->criticalTemperature();
Real xs;
if (T > T_c)
// return 1. to indicate that no water would condense for
// given (p,T)
xs = 1.;
else
{
Real pp_sat = _fp_primary->pp_sat_from_p_T(p, T);
if (pp_sat < 0.)
{
// return 1. to indicate that no water would condense for
// given (p,T)
xs = 1.;
return xs;
}
Real v_primary = _fp_primary->v_from_p_T(pp_sat, T);
Real pp_sat_secondary = p - pp_sat;
Real v_secondary;
if (_n_secondary_vapors == 1)
v_secondary = _fp_secondary[0]->v_from_p_T(pp_sat_secondary, T);
else
{
std::vector<Real> x_sec(_n_secondary_vapors);
const Real x_primary = primaryMassFraction(x);
Real sum = 0.;
for (unsigned int i = 0; i < _n_secondary_vapors; i++)
{
x_sec[i] = x[i] / (1. - x_primary);
sum += x_sec[i] / _fp_secondary[i]->molarMass();
}
Real M_star = 1. / sum;
v_secondary = R_molar * T / (M_star * pp_sat_secondary);
int it = 0;
double f = 1., df_dvs, pp_sec, p_sec, dp_dT_sec, dp_dv_sec, dp_dT, dp_dv;
double tol_p = 1.e-8;
while (std::fabs(f / pp_sat_secondary) > tol_p)
{
pp_sec = 0.;
dp_dT = 0.;
dp_dv = 0.;
for (unsigned int i = 0; i < _n_secondary_vapors; i++)
{
_fp_secondary[i]->p_from_T_v(T, v_secondary / x_sec[i], p_sec, dp_dT_sec, dp_dv_sec);
pp_sec += p_sec;
dp_dT += dp_dT_sec;
dp_dv += dp_dv_sec / x_sec[i];
}
f = pp_sec - pp_sat_secondary;
df_dvs = dp_dv;
v_secondary -= f / df_dvs;
if (it++ > 15)
return getNaN();
}
}
xs = v_secondary / (v_primary + v_secondary);
}
return xs;
}
