void
SinglePhaseFluidProperties::e_dpT(Real p, Real T, Real & e, Real & de_dp, Real & de_dT) const
{
mooseDeprecated(name(), ": e_dpT() is deprecated. Use e_from_p_T() instead");
e_from_p_T(p, T, e, de_dp, de_dT);
}
void
StiffenedGasFluidProperties::e_from_p_T(Real p, Real T, Real & e, Real & de_dp, Real & de_dT) const
{
e = e_from_p_T(p, T);
de_dp = (1. - _gamma) * _p_inf / (p + _p_inf) / (p + _p_inf) * _cv * T;
de_dT = (p + _gamma * _p_inf) / (p + _p_inf) * _cv;
}
Real
SinglePhaseFluidProperties::e(Real p, Real T) const
{
mooseDeprecated(name(), ": e() is deprecated. Use e_from_p_T() instead");
return e_from_p_T(p, T);
}
void
SinglePhaseFluidProperties::rho_e_from_p_T(Real p,
Real T,
Real & rho,
Real & drho_dp,
Real & drho_dT,
Real & e,
Real & de_dp,
Real & de_dT) const
{
rho_from_p_T(p, T, rho, drho_dp, drho_dT);
e_from_p_T(p, T, e, de_dp, de_dT);
}
void
NaClFluidProperties::rho_e_dpT(Real pressure,
Real temperature,
Real & rho,
Real & drho_dp,
Real & drho_dT,
Real & e,
Real & de_dp,
Real & de_dT) const
{
rho_from_p_T(pressure, temperature, rho, drho_dp, drho_dT);
e_from_p_T(pressure, temperature, e, de_dp, de_dT);
}
DualReal
SinglePhaseFluidProperties::e_from_p_T(const DualReal & p, const DualReal & T) const
{
Real e = 0.0;
Real pressure = p.value();
Real temperature = T.value();
Real de_dp = 0.0;
Real de_dT = 0.0;
e_from_p_T(pressure, temperature, e, de_dp, de_dT);
DualReal result = e;
for (size_t i = 0; i < p.derivatives().size(); ++i)
result.derivatives()[i] = p.derivatives()[i] * de_dp + T.derivatives()[i] * de_dT;
return result;
}
void
GeneralVaporMixtureFluidProperties::p_T_from_v_e(Real v,
Real e,
std::vector<Real> x,
Real & p,
Real & dp_dv,
Real & dp_de,
std::vector<Real> & dp_dx,
Real & T,
Real & dT_dv,
Real & dT_de,
std::vector<Real> & dT_dx) const
{
p_T_from_v_e(v, e, x, p, T);
// specific volume residual and Jacobians from primary vapor and mixture
Real v_unused, dv_dp, dv_dT;
std::vector<Real> dv_dx;
v_from_p_T(p, T, x, v_unused, dv_dp, dv_dT, dv_dx);
// specific internal energy residual and Jacobians from primary vapor and mixture
Real e_unused, de_dp, de_dT;
std::vector<Real> de_dx;
e_from_p_T(p, T, x, e_unused, de_dp, de_dT, de_dx);
// Compute derivatives using the following rules:
// * Reciprocity: da/db|_c = (db/da|_c)^{-1}
// * Chain rule: da/db|_c = da/dc|_b * dc/db|_a
// * Triple product rule: da/db|_c * db/dc|_a * dc/da|_b = -1
dp_dv = de_dT / (dv_dp * de_dT - dv_dT * de_dp);
dp_de = dv_dT / (de_dp * dv_dT - de_dT * dv_dp);
dT_dv = de_dp / (dv_dT * de_dp - dv_dp * de_dT);
dT_de = dv_dp / (de_dT * dv_dp - de_dp * dv_dT);
// Derivatives with respect to mass fractions are more complicated, so a
// finite difference approximation is used (this is expensive of course).
for (unsigned int i = 0; i < _n_secondary_vapors; ++i)
{
Real p_perturbed, T_perturbed;
std::vector<Real> x_perturbed(x);
x_perturbed[i] += 1e-6;
p_T_from_v_e(v, e, x_perturbed, p_perturbed, T_perturbed);
dp_dx[i] = (p_perturbed - p) / 1e-6;
dT_dx[i] = (T_perturbed - T) / 1e-6;
}
}
void
IdealGasFluidPropertiesPT::rho_e_dpT(Real pressure,
Real temperature,
Real & rho,
Real & drho_dp,
Real & drho_dT,
Real & e,
Real & de_dp,
Real & de_dT) const
{
Real density, ddensity_dp, ddensity_dT;
rho_from_p_T(pressure, temperature, density, ddensity_dp, ddensity_dT);
rho = density;
drho_dp = ddensity_dp;
drho_dT = ddensity_dT;
Real energy, denergy_dp, denergy_dT;
e_from_p_T(pressure, temperature, energy, denergy_dp, denergy_dT);
e = energy;
de_dp = denergy_dp;
de_dT = denergy_dT;
}
Real
SimpleFluidProperties::h_from_p_T(Real pressure, Real temperature) const
{
return e_from_p_T(pressure, temperature) +
_pp_coeff * pressure / rho_from_p_T(pressure, temperature);
}
void
GeneralVaporMixtureFluidProperties::p_T_from_v_e(
Real v, Real e, std::vector<Real> x, Real & p, Real & T) const
{
// The residuals are the following:
// residual[0] = v(p,T,x) - v
// residual[1] = e(p,T,x) - e
std::vector<Real> residual(2);
// The Jacobian columns are the following:
// 0: pressure
// 1: temperature
std::vector<std::vector<Real>> jacobian(2);
jacobian[0].resize(2);
jacobian[1].resize(2);
std::vector<Real> dv_dx(_n_secondary_vapors);
std::vector<Real> de_dx(_n_secondary_vapors);
p = _p_guess;
T = _T_guess;
bool converged = false;
std::stringstream err_ss;
err_ss << name() << ": The nonlinear solve for p and T did not converge:\n";
err_ss << " v = " << v << ", e = " << e;
for (unsigned int i = 0; i < _n_secondary_vapors; ++i)
err_ss << ", x[" << i << "] = " << x[i];
err_ss << "\n";
for (unsigned int l = 0; l < _newton_max_its; ++l)
{
// specific volume residual and Jacobians from primary vapor and mixture
Real v_it, dv_it_dp, dv_it_dT;
std::vector<Real> dv_it_dx;
v_from_p_T(p, T, x, v_it, dv_it_dp, dv_it_dT, dv_it_dx);
residual[0] = v_it - v;
jacobian[0][0] = dv_it_dp;
jacobian[0][1] = dv_it_dT;
// specific internal energy residual and Jacobians from primary vapor and mixture
Real e_it, de_it_dp, de_it_dT;
std::vector<Real> de_it_dx;
e_from_p_T(p, T, x, e_it, de_it_dp, de_it_dT, de_it_dx);
residual[1] = e_it - e;
jacobian[1][0] = de_it_dp;
jacobian[1][1] = de_it_dT;
// compute scaled errors
const Real scaled_residual_v = residual[0] / std::abs(v);
const Real scaled_residual_e = residual[1] / std::abs(e);
// check for convergence
const Real l2_error =
std::sqrt(std::pow(scaled_residual_v, 2) + std::pow(scaled_residual_e, 2));
err_ss << " Iteration " << l << ": p = " << p << ", T = " << T << ": l2 error = " << l2_error
<< "\n";
if (l2_error < _newton_rel_tol)
{
converged = true;
break;
}
// take Newton step: dx = -J^{-1} r
const Real elim = jacobian[1][0] / jacobian[0][0];
const Real T_step =
(residual[1] - elim * residual[0]) / (jacobian[1][1] - elim * jacobian[0][1]);
const Real p_step = (residual[0] - jacobian[0][1] * T_step) / jacobian[0][0];
p -= p_step * _newton_damping;
T -= T_step * _newton_damping;
}
if (converged)
{
if (_update_guesses)
{
_p_guess = p;
_T_guess = T;
}
}
else
{
err_ss << "\nTry setting the parameters 'p_initial_guess' and 'T_initial_guess'.";
mooseWarning(err_ss.str());
p = std::nan("");
T = std::nan("");
}
}
void
SinglePhaseFluidProperties::e_dpT(
Real pressure, Real temperature, Real & e, Real & de_dp, Real & de_dT) const
{
e_from_p_T(pressure, temperature, e, de_dp, de_dT);
}
Real
SinglePhaseFluidProperties::e(Real p, Real T) const
{
return e_from_p_T(p, T);
}
Real
NaClFluidProperties::cv_from_p_T(Real pressure, Real temperature) const
{
return e_from_p_T(pressure, temperature) / temperature;
}
