three-phase.h

Three-phase interfacial flows

Three-phase interfacial flows

This file helps setup simulations for flows of three fluids separated by an interface (i.e. immiscible fluids). It is typically used in combination with a Navier–Stokes solver.

The interface between the fluids is tracked with a Volume-Of-Fluid method.
The volume fraction in fluid 2 is f2=1, in fluid 3 is f3=1, and in fluid 1 is f1=(1 -f2 -f3).
The densities and dynamic viscosities for fluid 1, 2, and 3 are rho1, mu1, rho2, mu2, rho3, mu3, respectively.

#include "vof.h"

scalar f2[],f3[],f1[];
scalar * interfaces = {f2,f3,f1};
double rho1 = 1., mu1 = 0., rho2 = 1., mu2 = 0., rho3 = 1., mu3 = 0.;

Auxilliary fields are necessary to define the (variable) specific volume \alpha=1/\rho as well as the cell-centered density.

face vector alphav[];
scalar rhov[];

event defaults (i = 0) {
  alpha = alphav;
  rho = rhov;

If the viscosity is non-zero, we need to allocate the face-centered viscosity field.

  if (mu1 || mu2 || mu3)
    mu = new face vector;
}

Now we define new relations for rho et mu with fields f2, f3, and f1.
note that we must have f1 + f2 + f3 = 1.0

#ifndef rho
// two phases definition was rho(f) (clamp(f,0.,1.)*(rho1 - rho2) + rho2)
// three phases definition
#define rho(f2,f3) (clamp(1.-f2-f3,0,1)*rho1+clamp(f2,0,1)*rho2+clamp(f3,0,1)*rho3)
#endif

#ifndef mu
// two phases definition was mu(f)  (clamp(f,0.,1.)*(mu1 - mu2) + mu2)
// three phases definition
#define mu(f2,f3)  (clamp(1.-f2-f3,0,1)*mu1+clamp(f2,0,1)*mu2+clamp(f3,0,1)*mu3)
#endif

We do not need to use filtered variables

event properties (i++) {

#if TREE
  f1.prolongation = refine_bilinear;
  f2.prolongation = refine_bilinear;
  f3.prolongation = refine_bilinear;
  boundary ({f1,f2,f3});
#endif
  
  foreach_face() {
    double ff2 = (f2[] + f2[-1])/2.;
    double ff3 = (f3[] + f3[-1])/2.;
    alphav.x[] = fm.x[]/rho(ff2,ff3);
    if (mu1 || mu2 || mu3) {
      face vector muv = mu; 
      muv.x[] = fm.x[]*mu(ff2,ff3);
    }
  }  
  foreach()
    rhov[] = cm[]*rho(f2[],f3[]);

#if TREE  
  f1.prolongation = fraction_refine;
  f2.prolongation = fraction_refine;
  f3.prolongation = fraction_refine;
  boundary ({f1,f2,f3});
#endif
}