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Cylindrical Packed Bed
==================================

It is strongly recommended to visit `DEM parameters <../../../parameters/dem/dem.html>`_ and `CFD-DEM parameters <../../../parameters/unresolved-cfd-dem/unresolved-cfd-dem.html>`_ for more detailed information on the concepts and physical meaning of the parameters ind DEM and CFD-DEM.
It is strongly recommended to visit `DEM parameters <../../../parameters/dem/dem.html>`_ and `CFD-DEM parameters <../../../parameters/unresolved-cfd-dem/unresolved-cfd-dem.html>`_ for more detailed information on the concepts and physical meaning of the parameters in DEM and CFD-DEM.


----------------------------------
Expand All @@ -16,7 +16,7 @@ Features


---------------------------
Files Used in This Example
Files Used in this Example
---------------------------

Both files mentioned below are located in the example's folder (``examples/unresolved-cfd-dem/cylindrical-packed-bed``).
Expand Down Expand Up @@ -51,7 +51,7 @@ The ``mesh`` subsection specifies the computational grid:
set type = dealii
set grid type = subdivided_cylinder
set grid arguments = 16:0.01:0.1
set initial refinement = 1
set initial refinement = 2
end
Simulation Control
Expand Down Expand Up @@ -95,7 +95,6 @@ The section on model parameters is explained in the DEM examples. We show the ch
subsection model parameters
set contact detection method = dynamic
set contact detection frequency = 10
set neighborhood threshold = 1.3
set particle particle contact force method = hertz_mindlin_limit_overlap
set particle wall contact force method = nonlinear
Expand Down Expand Up @@ -227,9 +226,8 @@ The simulation is run in steady state. The simulation control section is shown:
.. code-block:: text
subsection simulation control
set method = bdf1
set output name = result
set output path = ./output/
set method = bdf1
set output path = ./output/
end
Physical Properties
Expand Down Expand Up @@ -263,7 +261,7 @@ For the initial conditions, we choose zero initial conditions for the velocity.
Boundary Conditions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For the boundary conditions, we choose a slip boundary condition on the walls of the cylinder (ID = 0) and an inlet velocity of 0.2 m/s at the lower face of the cylinder (ID = 1).
For the boundary conditions, we set a slip boundary condition on the walls of the cylinder (ID = 0), an inlet velocity of 0.2 m/s at the lower face of the cylinder (ID = 1) and an outlet at the upper face of the cylinder (ID = 2).

.. code-block:: text
Expand All @@ -286,6 +284,10 @@ For the boundary conditions, we choose a slip boundary condition on the walls of
set Function expression = 0
end
end
subsection bc 2
set id = 2
set type = outlet
end
end
Expand Down Expand Up @@ -351,12 +353,13 @@ Linear Solver
subsection linear solver
subsection fluid dynamics
set method = gmres
set max iters = 5000
set max iters = 2000
set max krylov vectors = 2000
set relative residual = 1e-3
set minimum residual = 1e-11
set minimum residual = 1e-10
set preconditioner = ilu
set ilu preconditioner fill = 1
set ilu preconditioner absolute tolerance = 1e-14
set ilu preconditioner fill = 4
set ilu preconditioner absolute tolerance = 1e-12
set ilu preconditioner relative tolerance = 1.00
set verbosity = verbose
end
Expand All @@ -372,18 +375,18 @@ The simulation is run using the ``lethe-fluid-vans`` application. Assuming that
.. code-block:: text
:class: copy-button
lethe-fluid-vans parameter_file.prm
mpirun -np 8 lethe-fluid-vans flow-in-bed.prm
-------------
Results VANS
-------------
The results are shown in the plots below. We visualise the velocity of the fluid, the void fraction calculated using the particles' locations, and the pressure drop resulting from the particle-fluid interactions (drag). The plots to the right show the local distribution of the quantities at the center-line of the cylinder.
The results are shown in the plots below. The first plot visualises the velocity of the fluid and the void fraction along the center axis of the cylinder. We see that the fluid rapidly accelerates in as the void fraction decreases to ensure mass conservation. The second plot displays the pressure drop resulting from the particle-fluid interactions. The quasi totality of the pressure drop occurs within the bed of particles.

.. image:: images/packed-bed-vel.png
.. image:: images/velocity_void_fraction.png
:alt: velocity and void fraction distribution
:align: center

.. image:: images/packed-bed-p.png
.. image:: images/pressure_drop_void_fraction.png
:alt: pressure drop in packed bed
:align: center
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<article role="main">
<section id="cylindrical-packed-bed">
<h1>Cylindrical Packed Bed<a class="headerlink" href="#cylindrical-packed-bed" title="Link to this heading">#</a></h1>
<p>It is strongly recommended to visit <a class="reference external" href="../../../parameters/dem/dem.html">DEM parameters</a> and <a class="reference external" href="../../../parameters/unresolved-cfd-dem/unresolved-cfd-dem.html">CFD-DEM parameters</a> for more detailed information on the concepts and physical meaning of the parameters ind DEM and CFD-DEM.</p>
<p>It is strongly recommended to visit <a class="reference external" href="../../../parameters/dem/dem.html">DEM parameters</a> and <a class="reference external" href="../../../parameters/unresolved-cfd-dem/unresolved-cfd-dem.html">CFD-DEM parameters</a> for more detailed information on the concepts and physical meaning of the parameters in DEM and CFD-DEM.</p>
<section id="features">
<h2>Features<a class="headerlink" href="#features" title="Link to this heading">#</a></h2>
<ul class="simple">
Expand All @@ -445,7 +445,7 @@ <h2>Features<a class="headerlink" href="#features" title="Link to this heading">
</ul>
</section>
<section id="files-used-in-this-example">
<h2>Files Used in This Example<a class="headerlink" href="#files-used-in-this-example" title="Link to this heading">#</a></h2>
<h2>Files Used in this Example<a class="headerlink" href="#files-used-in-this-example" title="Link to this heading">#</a></h2>
<p>Both files mentioned below are located in the example’s folder (<code class="docutils literal notranslate"><span class="pre">examples/unresolved-cfd-dem/cylindrical-packed-bed</span></code>).</p>
<ul class="simple">
<li><p>Parameter file for particle generation and packing: <code class="docutils literal notranslate"><span class="pre">packing-particles.prm</span></code></p></li>
Expand All @@ -467,7 +467,7 @@ <h3>Mesh<a class="headerlink" href="#mesh" title="Link to this heading">#</a></h
set type = dealii
set grid type = subdivided_cylinder
set grid arguments = 16:0.01:0.1
set initial refinement = 1
set initial refinement = 2
end
</pre></div>
</div>
Expand Down Expand Up @@ -505,7 +505,6 @@ <h3>Model Parameters<a class="headerlink" href="#model-parameters" title="Link t
<p>The section on model parameters is explained in the DEM examples. We show the chosen parameters for this section:</p>
<div class="highlight-text notranslate"><div class="highlight"><pre><span></span>subsection model parameters
set contact detection method = dynamic
set contact detection frequency = 10
set neighborhood threshold = 1.3
set particle particle contact force method = hertz_mindlin_limit_overlap
set particle wall contact force method = nonlinear
Expand Down Expand Up @@ -609,9 +608,8 @@ <h2>VANS Parameter File<a class="headerlink" href="#vans-parameter-file" title="
<h3>Simulation Control<a class="headerlink" href="#id1" title="Link to this heading">#</a></h3>
<p>The simulation is run in steady state. The simulation control section is shown:</p>
<div class="highlight-text notranslate"><div class="highlight"><pre><span></span>subsection simulation control
set method = bdf1
set output name = result
set output path = ./output/
set method = bdf1
set output path = ./output/
end
</pre></div>
</div>
Expand Down Expand Up @@ -642,7 +640,7 @@ <h3>Initial Conditions<a class="headerlink" href="#initial-conditions" title="Li
</section>
<section id="boundary-conditions">
<h3>Boundary Conditions<a class="headerlink" href="#boundary-conditions" title="Link to this heading">#</a></h3>
<p>For the boundary conditions, we choose a slip boundary condition on the walls of the cylinder (ID = 0) and an inlet velocity of 0.2 m/s at the lower face of the cylinder (ID = 1).</p>
<p>For the boundary conditions, we set a slip boundary condition on the walls of the cylinder (ID = 0), an inlet velocity of 0.2 m/s at the lower face of the cylinder (ID = 1) and an outlet at the upper face of the cylinder (ID = 2).</p>
<div class="highlight-text notranslate"><div class="highlight"><pre><span></span>subsection boundary conditions
set number = 2
subsection bc 0
Expand All @@ -662,6 +660,10 @@ <h3>Boundary Conditions<a class="headerlink" href="#boundary-conditions" title="
set Function expression = 0
end
end
subsection bc 2
set id = 2
set type = outlet
end
end
</pre></div>
</div>
Expand Down Expand Up @@ -718,12 +720,13 @@ <h3>Linear Solver<a class="headerlink" href="#linear-solver" title="Link to this
<div class="highlight-text notranslate"><div class="highlight"><pre><span></span>subsection linear solver
subsection fluid dynamics
set method = gmres
set max iters = 5000
set max iters = 2000
set max krylov vectors = 2000
set relative residual = 1e-3
set minimum residual = 1e-11
set minimum residual = 1e-10
set preconditioner = ilu
set ilu preconditioner fill = 1
set ilu preconditioner absolute tolerance = 1e-14
set ilu preconditioner fill = 4
set ilu preconditioner absolute tolerance = 1e-12
set ilu preconditioner relative tolerance = 1.00
set verbosity = verbose
end
Expand All @@ -735,15 +738,15 @@ <h3>Linear Solver<a class="headerlink" href="#linear-solver" title="Link to this
<section id="running-the-vans-simulation">
<h2>Running the VANS Simulation<a class="headerlink" href="#running-the-vans-simulation" title="Link to this heading">#</a></h2>
<p>The simulation is run using the <code class="docutils literal notranslate"><span class="pre">lethe-fluid-vans</span></code> application. Assuming that the <code class="docutils literal notranslate"><span class="pre">lethe-fluid-vans</span></code> executable is within your path, the simulation can be launched as per the following command:</p>
<div class="copy-button highlight-text notranslate"><div class="highlight"><pre><span></span>lethe-fluid-vans parameter_file.prm
<div class="copy-button highlight-text notranslate"><div class="highlight"><pre><span></span>mpirun -np 8 lethe-fluid-vans flow-in-bed.prm
</pre></div>
</div>
</section>
<section id="results-vans">
<h2>Results VANS<a class="headerlink" href="#results-vans" title="Link to this heading">#</a></h2>
<p>The results are shown in the plots below. We visualise the velocity of the fluid, the void fraction calculated using the particles’ locations, and the pressure drop resulting from the particle-fluid interactions (drag). The plots to the right show the local distribution of the quantities at the center-line of the cylinder.</p>
<img alt="velocity and void fraction distribution" class="align-center" src="../../../_images/packed-bed-vel.png" />
<img alt="pressure drop in packed bed" class="align-center" src="../../../_images/packed-bed-p.png" />
<p>The results are shown in the plots below. The first plot visualises the velocity of the fluid and the void fraction along the center axis of the cylinder. We see that the fluid rapidly accelerates in as the void fraction decreases to ensure mass conservation. The second plot displays the pressure drop resulting from the particle-fluid interactions. The quasi totality of the pressure drop occurs within the bed of particles.</p>
<img alt="velocity and void fraction distribution" class="align-center" src="../../../_images/velocity_void_fraction.png" />
<img alt="pressure drop in packed bed" class="align-center" src="../../../_images/pressure_drop_void_fraction.png" />
</section>
</section>

Expand Down Expand Up @@ -804,7 +807,7 @@ <h2>Results VANS<a class="headerlink" href="#results-vans" title="Link to this h
<ul>
<li><a class="reference internal" href="#">Cylindrical Packed Bed</a><ul>
<li><a class="reference internal" href="#features">Features</a></li>
<li><a class="reference internal" href="#files-used-in-this-example">Files Used in This Example</a></li>
<li><a class="reference internal" href="#files-used-in-this-example">Files Used in this Example</a></li>
<li><a class="reference internal" href="#description-of-the-case">Description of the Case</a></li>
<li><a class="reference internal" href="#dem-parameter-file">DEM Parameter File</a><ul>
<li><a class="reference internal" href="#mesh">Mesh</a></li>
Expand Down
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