.. 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.