Vitesse_derive_Spelt_Biesheuvel.cpp

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#include <Frottement_interfacial_base.h>
#include <Dispersion_bulles_base.h>
#include <Vitesse_derive_Spelt_Biesheuvel.h>
#include <Pb_Multiphase.h>
#include <cmath>
 
Implemente_instanciable(Vitesse_derive_Spelt_Biesheuvel, "Vitesse_relative_derive_Spelt_Biesheuvel", Vitesse_derive_base);
 
Sortie& Vitesse_derive_Spelt_Biesheuvel::printOn(Sortie& os) const
{
  return os;
}
 
Entree& Vitesse_derive_Spelt_Biesheuvel::readOn(Entree& is)
{
  Vitesse_derive_base::readOn(is);
  return is;
}
 
void Vitesse_derive_Spelt_Biesheuvel::completer()
{
  const Pb_Multiphase& pbm = ref_cast(Pb_Multiphase, pb_.valeur());
  if (!pbm.has_correlation("frottement_interfacial"))
    Process::exit(que_suis_je() + " : there must be an interfacial friction correlation in the problem !");
 
  if (pbm.has_correlation("dispersion_bulles"))
    needs_grad_alpha_ = 1;
}
 
void Vitesse_derive_Spelt_Biesheuvel::evaluate_C0_vg0(const input_t& in) const
{
  const Pb_Multiphase& pbm = ref_cast(Pb_Multiphase, pb_.valeur());
  const int D = dimension;
  const int N = in.alpha.dimension(0);
  const double norm_g = sqrt(local_carre_norme_vect(in.g));
 
  // Newton method to determine dv along gravity
  double dv0 = 0.2, epsilon = 1.e-4; // Initialize dv at random
  int step = 1, iter_max = 20;
  DoubleTab p, T, dv(N, N), coeff(N, N, 2), alpha_l(N);
  const Frottement_interfacial_base& correlation_fi = ref_cast(Frottement_interfacial_base, pbm.get_correlation("frottement_interfacial"));
  for (int n=0; n<N ; n++) alpha_l(n)= std::max(in.alpha(n), 1.e-3);
 
  do
    {
      dv(n_g, n_l) = dv0;
      dv(n_l, n_g) = dv0;
      correlation_fi.coefficient(alpha_l, p, T, in.rho, in.mu, in.sigma, in.dh, dv, in.d_bulles, coeff);
      dv0 = dv0 - (coeff(n_l, n_g, 0)*dv0 - norm_g*alpha_l(n_g)*(in.rho[n_l]*in.alpha[n_l]+in.rho[n_g]*in.alpha[n_g] - in.rho[n_g])) / (coeff(n_l, n_g, 1)*dv0 + coeff(n_l, n_g, 0));
      step = step + 1;
      if(step > iter_max)
        Process::exit(que_suis_je() + " : Newton algorithm not converging to find relative velocity !");
    }
  while(std::abs(coeff(n_l, n_g, 0)*dv0 - norm_g*alpha_l(n_g)*(in.rho[n_l]*in.alpha[n_l]+in.rho[n_g]*in.alpha[n_g]- in.rho[n_g])) > epsilon);
 
  /* distribution parameter */
  C0 = 1;
 
  /* drift velocity along gravity */
  for (int d = 0; d < D; d++)
    vg0(d) = - dv0 * in.g(d) / norm_g;
 
  /* Turbulent diffusion ; possible stability issues in the future... */
  const double u_turb = std::pow(0.09, 0.25) * std::sqrt(in.k[n_l]) ;
  const double beta = u_turb / dv0 ;
  const double epsilon_turb = 0.09 * in.k[n_l]*in.k[n_l] /in.nut[n_l] ;
  const double L = std::pow(0.09, 0.75)  * std::pow(in.k[n_l], 1.5) / epsilon_turb ;
  const double tau_rel = dv0/(2*norm_g);
  const double lambda_turb = std::sqrt(10*in.mu[n_l]/in.rho[n_l]*in.k[n_l]/epsilon_turb);
  const double mu_turb = lambda_turb/tau_rel ;
  const double diffu_Spelt_Biesheuvel = 0.5*beta*u_turb*L + 3./8.*beta*u_turb*L*(tau_rel/mu_turb)*(tau_rel/mu_turb)*lambda_turb/L;
 
  for (int d = 0; d < D; d++)
    vg0(d) +=  - diffu_Spelt_Biesheuvel * in.gradAlpha(n_g, d)/std::max(in.alpha[n_g], 1.e-4) ;
 
  for (int d = 0; d < D; d++)
    vg0(d) *=  (1.0 - C0*in.alpha[n_g]) ;
}