.. include:: /images.rst
PIC05: Evaporation
------------------
.. _description-pic05:
Description
~~~~~~~~~~~
This case is used to verify the transport equations governing energy and species conservation. The setup consists of a single parcel representing a droplet suspended in a humidified air stream. This reflects the wet bulb phenomenon, where evaporation from the droplet results in a lowered humidified air temperature. The following reaction represents species transfer from the suspended droplet:
.. math::
:label: pic05eq1
H_{2} O (l) \rightarrow H_{2} O (g)
Fifteen seconds of physical time is simulated to ensure the droplet achieves a steady-state (SS) temperature. The SS temperature should then compare with the theoretical wet-bulb temperature.
.. _setup-pic05:
Setup
~~~~~
.. _pic05table1:
.. csv-table:: PIC-05 Setup, Initial and Boundary Conditions.
:widths: auto
:header: "Computational/Physical model", " ", " "
"3D, Transient", " ", " "
"Multiphase", " ", " "
"Gravity", " ", " "
"Turbulence equations are not solved", " ", " "
"Uniform mesh", " ", " "
"First order upqind discritization scheme", " ", " "
" ", " ", " "
"**Geometry**", " ", " "
"Coordinate system", "Cartesian", " ", "Grid partitions"
"x-length", "0.01", "\(m\)", "1"
"y-length", "0.01", "\(m\)", "1"
"z-length", "0.01", "\(m\)", "1"
" ", " ", " "
"**Material**", " ", " "
"Gas density, :math:`\rho_{g}`", "Ideal gas law", "(kg·m\ :sup:`-3`)"
" ", " ", " "
"**Solids Type**", "PIC,DEM", " "
"Diameter, :math:`d_{p}`", "0.2", "\(mm\)"
"Density, :math:`\rho_{s}`", "958.6", "(kg·m\ :sup:`-3`)"
" ", " ", " "
"**Solids Properties (PIC)**", " ", " "
"Pressure linear scale factor, :math:`P_{s}`", "0.0", "(Pa)"
"Exponential scale factor, :math:`\gamma`", "1.0", "(-)"
"Statistical weight", "25", "(-)"
" ", " ", " "
"**Solids Properties (DEM)**", " ", " "
"Coefficient of friction, :math:`\mu_{pp},\mu_{pw}`", "0.0", "(-)"
"Coefficient of restitution, :math:`e_{pp},e_{pw}`", "1.0", "(-)"
"Spring constant, :math:`k_{pp},k_{pw}`", "0.1", "(kg·m\ :sup:`-1`)"
" ", " ", " "
"**Initial Conditions**", " ", " ", " "
"x-velocity, :math:`u_{g}`", "3.0", "(m·s\ :sup:`-1`)"
"y-velocity, :math:`v_{g}`", "0.0", "(m·s\ :sup:`-1`)"
"z-velocity, :math:`w_{g}`", "0.0", "(m·s\ :sup:`-1`)"
"Gas volume fraction, :math:`\epsilon_{g}`", "0.999894", "(-)"
"Gas volume fraction at packing, :math:`\epsilon_{g}^{*}`", "0.4", "(-)"
"Pressure, :math:`P_{g}`", "101,325", "(Pa)"
"Gas temperature, :math:`T_{g}`", "303.15", "\(K\)"
"Solid temperature, :math:`T_{s}`", "303.15", "\(K\)"
"Species fraction of air, :math:`X_{g1}`", "Varied", "(-)"
"Species fraction of water vapor, :math:`X_{g2}`", "Varied", "(-)"
" ", " ", " "
"**Boundary Conditions**", " ", " ", " "
"West boundary", ":math:`u_{g}` Varied", "(kg·s\ :sup:`-1`)", "Mass inflow"
" ", ":math:`X_{g1},X_{g2}` Varied", "(-)", " "
"East boundary", "101,325", "(Pa)", "Pressure outflow"
"North and South boundaries", " ", " ", "Free-slip walls"
"Top and Bottom boundaries", " ", " ", "Free-slip walls"
.. _results-pic05:
Results
~~~~~~~
MFiX-PIC and MFiX-DEM simulations are performed by varying the relative humidity of surrounding air. :numref:`pic04table2` summarizes the different settings of relative humidity and the corresponding wet bulb temperatures. Based on the comparison of the data from :cite:`Mills1999` it can be concluded that the predictions from MFiX-PIC simulations are accurate :numref:`pic04table2`. Also, the results are consistent with the predictions from MFiX-DEM.
.. _pic05table2:
.. csv-table:: Location of Filling Wave Moving in the Direction of Gravity (m).
:widths: auto
"Rel. Humidity (\%)",":math:`X_{g1}`",":math:`X_{g2}`","Mass Flow Rate (g/s)","Wet Bulb T (°C)"
"0 ","1.000000 ","0.000000 ","0.349315 ","10.5 "
"10 ","0.997390 ","0.002610 ","0.348762 ","13.2 "
"20 ","0.994771 ","0.005229 ","0.348208 ","15.7 "
"30 ","0.992144 ","0.007856 ","0.347655 ","18.0 "
"40 ","0.989509 ","0.010491 ","0.347102 ","20.1 "
"50 ","0.986865 ","0.013135 ","0.346548 ","22.0 "
"60 ","0.984212 ","0.015788 ","0.345995 ","23.8 "
"70 ","0.981552 ","0.018448 ","0.345442 ","25.5 "
"80 ","0.978882 ","0.021118 ","0.344888 ","27.1 "
"90 ","0.976204 ","0.023796 ","0.344335 ","28.6 "
"100 ","0.973518 ","0.026482 ","0.343281 ","30.0 "
.. _pic05fig1:
.. figure:: ../media/pic05-1.png
:align: center
:width: 450px
:height: 400px
Comparison of wet bulb temperatures between data, MFiX-DEM and MFiX-PIC.