void
StiffenedGasFluidProperties::T_from_v_e(Real v, Real e, Real & T, Real & dT_dv, Real & dT_de) const
{
T = T_from_v_e(v, e);
dT_dv = -_p_inf / _cv;
dT_de = 1.0 / _cv;
}
Real
SinglePhaseFluidProperties::T_from_p_h(Real p, Real h) const
{
const Real s = s_from_h_p(h, p);
const Real rho = rho_from_p_s(p, s);
const Real v = 1. / rho;
const Real e = e_from_v_h(v, h);
return T_from_v_e(v, e);
}
Real
StiffenedGasFluidProperties::s_from_v_e(Real v, Real e) const
{
Real T = T_from_v_e(v, e);
Real p = p_from_v_e(v, e);
Real n = std::pow(T, _gamma) / std::pow(p + _p_inf, _gamma - 1.0);
if (n <= 0.0)
throw MooseException(name() + ": Negative argument in the ln() function.");
return _cv * std::log(n) + _q_prime;
}
Real
StiffenedGasFluidProperties::g_from_v_e(Real v, Real e) const
{
// g(p,T) for SGEOS is given by Equation (37) in the following reference:
//
// Ray A. Berry, Richard Saurel, Olivier LeMetayer
// The discrete equation method (DEM) for fully compressible, two-phase flows in
// ducts of spatially varying cross-section
// Nuclear Engineering and Design 240 (2010) p. 3797-3818
//
const Real p = p_from_v_e(v, e);
const Real T = T_from_v_e(v, e);
return (_gamma * _cv - _q_prime) * T -
_cv * T * std::log(std::pow(T, _gamma) / std::pow(p + _p_inf, _gamma - 1.0)) + _q;
}
void
StiffenedGasFluidProperties::s_from_v_e(Real v, Real e, Real & s, Real & ds_dv, Real & ds_de) const
{
Real T, dT_dv, dT_de;
T_from_v_e(v, e, T, dT_dv, dT_de);
Real p, dp_dv, dp_de;
p_from_v_e(v, e, p, dp_dv, dp_de);
const Real n = std::pow(T, _gamma) / std::pow(p + _p_inf, _gamma - 1.0);
if (n <= 0.0)
throw MooseException(name() + ": Negative argument in the ln() function.");
s = _cv * std::log(n) + _q_prime;
const Real dn_dT = _gamma * std::pow(T, _gamma - 1.0) / std::pow(p + _p_inf, _gamma - 1.0);
const Real dn_dp = std::pow(T, _gamma) * (1.0 - _gamma) * std::pow(p + _p_inf, -_gamma);
const Real dn_dv = dn_dT * dT_dv + dn_dp * dp_dv;
const Real dn_de = dn_dT * dT_de + dn_dp * dp_de;
ds_dv = _cv / n * dn_dv;
ds_de = _cv / n * dn_de;
}
