Hibiki_Ishii_nucleation_site_density.cpp

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// Hibiki, Ishii, "Active nucleation site density in boiling systems", IJHMT, 2003
 
#include <Hibiki_Ishii_nucleation_site_density.h>
#include <algorithm>
#include <cmath>
 
// Physical constants for the Hibiki-Ishii correlation
static constexpr double N_bar = 4.72e5;             // Maximum site density [sites/m^2]
static constexpr double mu_angle = 0.722 * 180 / M_PI; // Mean cavity half-cone angle parameter [degrees]
static constexpr double mu2 = mu_angle * mu_angle;  // Squared mean angle
static constexpr double lambda_prime = 2.5e-6;      // Characteristic length for cavity size distribution [m]
static constexpr double R_gas_universal = 8.314462618; // Universal gas constant [J/(mol.K)]
 
// Computes the intermediate quantities shared by the function and its derivative
static void compute_intermediates(double rho_v, double rho_l, double T_ref, double p,
                                  double L_vap, double T_sat, double sigma,
                                  double theta, double molar_mass,
                                  double& f_rho_plus, double& inv_Rc, double& theta_factor)
{
  const double R = R_gas_universal / molar_mass;
 
  const double rho_p = std::log((rho_l - rho_v) / rho_v);
  f_rho_plus = -0.01064 + 0.48246 * rho_p - 0.22712 * rho_p * rho_p + 0.05468 * rho_p * rho_p * rho_p;
 
  inv_Rc = p * (-1 + std::exp(L_vap * std::max(T_ref - T_sat, 0.) / (R * T_ref * T_sat))) / (2. * sigma * (1 + rho_v / rho_l));
 
  theta_factor = 1 - std::exp(-theta * theta / (8. * mu2));
}
 
double Hibiki_Ishii_site_density(double rho_v, double rho_l, double T_ref, double p,
                                 double L_vap, double T_sat, double sigma,
                                 double theta, double molar_mass)
{
  double f_rho_plus, inv_Rc, theta_factor;
  compute_intermediates(rho_v, rho_l, T_ref, p, L_vap, T_sat, sigma, theta, molar_mass,
                        f_rho_plus, inv_Rc, theta_factor);
 
  return N_bar * theta_factor * (-1. + std::exp(f_rho_plus * lambda_prime * inv_Rc));
}
 
double dT_ref_Hibiki_Ishii_site_density(double rho_v, double rho_l, double T_ref, double p,
                                        double L_vap, double T_sat, double sigma,
                                        double theta, double molar_mass)
{
  double f_rho_plus, inv_Rc, theta_factor;
  compute_intermediates(rho_v, rho_l, T_ref, p, L_vap, T_sat, sigma, theta, molar_mass,
                        f_rho_plus, inv_Rc, theta_factor);
 
  double dT_ref_inv_Rc = 0.;
  if (T_ref - T_sat > 0.)
    {
      const double R = R_gas_universal / molar_mass;
      dT_ref_inv_Rc = p * L_vap / (R * T_ref * T_ref) * std::exp(L_vap * (T_ref - T_sat) / (R * T_ref * T_sat)) / (2. * sigma * (1 + rho_v / rho_l));
    }
 
  return N_bar * theta_factor * f_rho_plus * lambda_prime * dT_ref_inv_Rc * std::exp(f_rho_plus * lambda_prime * inv_Rc);
}