Interphase Coupling
===================

Drag
----

The following inputs must be preceded by "mfix."

+-------------------+-----------------------------------------------------------------------+-------------+-----------+
|                   | Description                                                           |   Type      | Default   |
+===================+=======================================================================+=============+===========+
| drag_type         | Which drag model to use                                               | String      | None      |
+-------------------+-----------------------------------------------------------------------+-------------+-----------+

The options currently supported in mfix are :cpp:`WenYu`, :cpp:`Gidaspow`, :cpp:`BVK2`, or :cpp:`UserDrag`.

If one of these is not specified, the code will abort with

.. highlight:: c++

::

   amrex::Abort::0::"Don't know this drag type!!!

The drag models are defined in src/src_des/des_drag_K.H

If the user wishes to use their own drag model, they must

  * specify :cpp:`mfix.drag_type = UserDrag` in the inputs file

  * provide the code in the ComputeDragUser routine in a local usr_drag.cpp file.
    An example can be found in tests/DEM06-x.

With the variables defined as follows:

   .. code:: shell

    /*
     *  \brief Returns: the calculated drag coefficient.
     *
     *  Inputs:
     *    EPg     - gas volume fraction
     *    Mug     - gas laminar viscosity
     *    ROpg    - gas density * EP_g
     *    vrel    - magnitude of gas-solids relative velocity
     *    DPM     - particle diameter of solids phase M
     *    DPA     - average particle diameter
     *    PHIS    - solids volume fraction of solids phases
     *    fvelx   - x component of the fluid velocity at the particle position
     *    fvely   - y component of the fluid velocity at the particle position
     *    fvelz   - z component of the fluid velocity at the particle position
     *    i, j, k - particle cell indices
     *    pid     - particle id number
     */

The WenYu model is defined as

   .. code:: shell

      RE = (Mug > 0.0) ? DPM*vrel*ROPg/Mug : DEMParams::large_number;

     if (RE <= 1000.0)
     {
         C_d = (24.0/(RE+DEMParams::small_number)) * (1.0 + 0.15*std::pow(RE, 0.687));
     }
     else
     {
         C_d = 0.44;
     }

     if (RE < DEMParams::eps) return 0.0;
     return 0.75 * C_d * vrel * ROPg * std::pow(EPg, -2.65) / DPM;

The Gidaspow model is defined as

   .. code:: shell

      ROg = ROPg / EPg;

      RE = (Mug > 0.0) ? DPM*vrel*ROPg/Mug : DEMParams::large_number;

      // Dense phase - EPg <= 0.8
      Ergun = 150.0*(1.0 - EPg)*Mug / (EPg*DPM*DPM) + 1.75*ROg*vrel/DPM;

      // Dilute phase - EPg > 0.8
      if (RE <= 1000.0)
      {
          C_d = (24.0/(RE+DEMParams::small_number)) * (1.0 + 0.15*std::pow(RE, 0.687));
      }
      else
      {
          C_d = 0.44;
      }

      WenYu = 0.75*C_d*vrel*ROPg*std::pow(EPg, -2.65) / DPM;

      // switch function
      PHI_gs = atan(150.0*1.75*(EPg - 0.8))/M_PI / DPM;

      // blend the models
      if (RE < DEMParams::eps) return 0.0;
      return (1.0 - PHI_gs)*Ergun + PHI_gs*WenYu;

The Gidaspow model is defined as

   .. code:: shell

      amrex::Real RE = (Mug > 0.0) ? DPA*vrel*ROPg/Mug : DEMParams::large_number;

      if (RE > DEMParams::eps)
      {
          oEPgfour = 1.0 / EPg / EPg / EPg / EPg;

          // eq(9) BVK J. fluid. Mech. 528, 2005
          // (this F_Stokes is /= of Koch_Hill by a factor of ep_g)
          F_Stokes = 18.0*Mug*EPg/DPM/DPM;

          F = 10.0*PHIS/EPg/EPg + EPg*EPg*(1.0 + 1.5*sqrt(PHIS));

          F += RE*(0.11*PHIS*(1.0+PHIS) - 4.56e-3*oEPgfour +
               std::pow(RE, -0.343)*(0.169*EPg + 6.44e-2*oEPgfour));

          // F += 0.413*RE/(24.0*EPg*EPg) *
          //     (1.0/EPg + 3.0*EPg*PHIS + 8.4/std::pow(RE, 0.343)) /
          //     (1.0 + std::pow(10.0, 3.0*PHIS)/std::pow(RE, 0.5 + 2.0*PHIS));

          return F*F_Stokes;
      }
      else
      {
          return 0.0;
      }



Heat Transfer Coefficient
-------------------------


The following inputs must be preceded by "mfix."

+-------------------+---------------------------------+-------------+--------------+
|                   | Description                     |   Type      | Default      |
+===================+=================================+=============+==============+
| convection_type   | Which HTC model to use          | String      | RanzMarshall |
+-------------------+---------------------------------+-------------+--------------+

The options currently supported in mfix are :cpp:`RanzMarshall` (default) and :cpp:`Gunn`. 
In both models the HTC is determined from a Nusslet number corelation. 

The RanzMarshall Nusselt number correlation is defined as: 

   .. code:: shell

      amrex::Real N_Nu = 2.0 + 0.6 * std::sqrt(N_Re) * std::pow(N_Pr, 0.333);


The Gunn Nusselt number correlation is defined as: 

   .. code:: shell

      amrex::Real N_Nu =
          (7 - 10*EPg + 5*EPg*EPg)*(1 + .7*std::pow(N_Re, 0.2)*std::cbrt(N_Pr))
          + (1.33 - 2.4*EPg + 1.2*EPg*EPg)*std::pow(N_Re, 0.7)*std::cbrt(N_Pr);


