.. include:: /images.rst
FLD06: Steady, 2D multi-component species transport
---------------------------------------------------
.. _description-14:
Description
~~~~~~~~~~~
The 2D multi-component species problem investigates the transport of three non-reacting fluid phase species that follow ideal gas behavior. Illustrated in :numref:`fld06fig1`, three separate mass inflows are used to inject three distinct gas species into the system. The species mix as the fluid passes through the domain such that they are well-mixed when the fluid reaches the outlet. The resulting species mass fractions, :math:`X_{\text{gi}}`, for the well-mixed flow are given analytically by,
.. math::
X_{\text{gi}} = \frac{\text{MW}_{\text{gi}}}{\sum_{k}^{}\text{MW}_{\text{gk}}}
:label: fld06eq1
where :math:`\text{MW}_{\text{gi}}` is the molecular weight of the :math:`i^{\text{th}}` gas phase species.
.. _fld06fig1:
.. figure:: ../media/fld06-setup.png
:align: center
Multicomponent species transport.
.. _setup-14:
Setup
~~~~~
.. literalinclude:: /subprojects/mfix/tests/fluid/FLD06/mfix.dat
:language: fortran
.. .. _fld06table1:
.. .. csv-table:: FLD-06 Setup, Initial and Boundary Conditions.
.. :widths: auto
.. :header: "Computational/Physical model", " ", " "
..
.. "2D, Unsteady, incompressible", " ", " "
.. "Single-phase with three species", " ", " "
.. "No gravity", " ", " "
.. "Thermal energy equation is not solved", " ", " "
.. "Turbulence equations are not solved", " ", " "
.. "Uniform mesh", " ", " "
.. "SMART discretization scheme", " ", " "
.. "*χ* correction is used", " ", " "
.. "Time step: 0.01 s (fixed)", " ", " "
.. " ", " ", " "
.. "**Geometry**", " ", " "
.. "Coordinate system", "Cartesian", " ", "Grid partitions"
.. "x-length", "2.00", "\(m\)", "200"
.. "y-length", "0.03", "\(m\)", "3"
.. " ", " ", " "
.. "**Material**", " ", " "
.. "Fluid density, :math:`\rho_{g}`", "*Ideal gas law*", "(kg·m\ :sup:`-3`)"
.. "Fluid viscosity, :math:`\mu_{g}`", "*Sutherland's law*", "(Pa·s)"
.. " ", " ", " "
.. "**Species Molecular Weight**", " ", " "
.. "Species A", "1.0", "\(kg·kmol\ :sup:`-1`\)"
.. "Species B", "5.0", "\(kg·kmol\ :sup:`-1`\)"
.. "Species C", "25.0", "\(kg·kmol\ :sup:`-1`\)"
.. " ", " ", " "
.. "**Initial Conditions**", " ", " "
.. "x-velocity, :math:`u_{g}`", "0.00", "\(m·s\ :sup:`-1`)"
.. "y-velocity, :math:`v_{g}`", "0.00", "\(m·s\ :sup:`-1`)"
.. "Species A mass fraction, :math:`X_{\text{gA}}`", "0.03", "( )"
.. "Species B mass fraction, :math:`X_{\text{gA}}`", "0.27", "( )"
.. "Species C mass fraction, :math:`X_{\text{gA}}`", "0.70", "( )"
.. " ", " ", " "
.. "**Boundary Conditions** :sup:`‡`", " ", " ", " "
.. "West wall mass inflow 1", "0.25", "\(m·s\ :sup:`-1`\)", "Specified velocity"
.. " Location", "\[ 0, H/3 \]", \(m\)
.. " Species A, :math:`X_{\text{gA}}`", "1.0", "( )"
.. " Species B, :math:`X_{\text{gB}}`", "0.0", "( )"
.. " Species C, :math:`X_{\text{gC}}`", "0.0", "( )"
.. "West wall mass inflow 2", "0.25", "\(m·s\ :sup:`-1`\)", "Specified velocity"
.. " Location", "\[ H/3, 2H/3 \]", "\( m \)"
.. " Species A, :math:`X_{\text{gA}}`", "0.0", "( )"
.. " Species B, :math:`X_{\text{gB}}`", "1.0", "( )"
.. " Species C, :math:`X_{\text{gC}}`", "0.0", "( )"
.. "West wall mass inflow 1", "0.25", "\(m·s\ :sup:`-1`\)", "Specified velocity"
.. " Location", "\[ 2H/3, H \]", "\( m \)"
.. " Species A, :math:`X_{\text{gA}}`", "0.0", "( )"
.. " Species B, :math:`X_{\text{gB}}`", "0.0", "( )"
.. " Species C, :math:`X_{\text{gC}}`", "1.0", "( )"
.. "North and South walls", "Cyclic"
.. "East wall", "Pressure outflow"
.. _results-14:
Results
~~~~~~~
The simulation was performed using the SMART discretization scheme with the *χ* correction to ensure species conservation. The average L\ :sub:`2` norm for the three species mass fractions were calculated for consecutive time steps. The simulation was considered converged when all three norms were less than 10\ :sup:`-8`. The species mass fractions at the outflow plane and the L\ :sub:`2` norm between the MFIX and analytical solution are shown in :numref:`fld06table2`. Two additional simulations were carried out where the solution order of the species equations was varied (e.g., ABC, BCA, CAB). No dependence was found on the solution order of the species equations (results not shown).
.. _fld06table2:
.. csv-table:: Average species mass fractions at the outflow and average L\ :sub:`2` Norms between the analytical and MFIX species mass fraction for the well-mixed fluid.
:widths: auto
:header: "Species", "MFiX", "L\ :sub:`2` norm"
"A", "0.027778", "5.86e-7"
"B", "0.277776", "2.07e-6"
"C", "0.694446", "1.48e-6"