.. _Chap:QB:mehrdad:

Mehrdad's Bed
=============

Typically, bubbling fluidized beds are produced by uniformily--in space and
time--driving a gas flow through a particle bed. Slightly different bubbling
patterns are observed depending largely on the Geldart classification [G73]_
of the particles and the size of the bed. Like gas bubbles in a liquid bed,
the dynamics are almost always highly irregular and chaotic in nature.
However, by periodically driving the gas flow, chaotic bubbling can be
suppressed yielding quasi-regular periodic bubbling [PB98]_. Studying bubble
control methods, Coppens and coworkers [Cv03]_ realized that periodic bubbling
produces starkly regular patterns in thin beds, which may be useful for code
validation [WdLC16]_. Shahnam and coworkers took the problem even further and
reducing the latteral dimension to produce an oscillating Left-Right single
bubble pattern in a setup affectionately referred to as *Mehrdad's bed* [S18]_.


Mehrdad's bed is a rectangular geometry of width :math:`L_x` =  50 mm,
height :math:`L_y` = 160 mm, and depth :math:`L_z` =   5 mm. The domain is
resolved by a uniform CFD grid of :math:`80 \times 256 \times 8`. No-slip walls
are applied on the vertical domain extents with a mass inflow at the bottom and
a pressure outflow at the top of the domain. The mass inflow is defined in
`usr1.f90` as:

.. code:: fortran

  real(rt),   intent(in ) :: time
  real(rt) :: usr_pi, usr_umf

  usr_pi  = 4.0d0*ATAN(1.0d0)
  usr_umf = MIN(0.15d0, 0.1d0*time)

  bc_u_g(1) = usr_umf*(1.3d0 + 0.7d0*DSIN(10.0d0*usr_pi*time))

The bed consists of 188500 particles which are assumed to be monodisperse with
constant diameter and density of :math:`d_p = 400` microns and
:math:`\rho_p = 2500` kg/m\ :sup:`3` \, respectively.


.. figure:: figs/mehrdad_1908_small.png
   :width: 16cm
   :align: center
   :alt: Sim comparison to Mehrdad's experiment

   Comparison of the experiment (middle two rows) to the MFIX-Exa simulation
   (top and bottom rows).

The bed is simulated using MFIX-Exa 19.08 for an initial transient period of
10 s before an observation window of an additional 5 s. The desired left-right
pattern is seen as shown in the figure above.
