Isotropic Porous Media Tutorial

Transcription

1 STAR-CCM+ User Guide 3927 Isotropic Porous Media Tutorial This tutorial models flow through the catalyst geometry described in the introductory section. In the porous region, the theoretical pressure drop per unit length can be determined using the equation Δp = ( P L i v + P v )v (2) where v is the superficial velocity through the medium and P i, P v are coefficients defining the porous resistance, known as the inertial resistance and viscous resistance, respectively. Values for the resistance coefficients can be measured experimentally or derived using various empirical relationships, depending on the exact nature of the problem. In this case, P = 25 kg/m 4 and = 1500 kg/m 3 i P v s. These values are roughly what we would expect from an isotropic porous catalyst. Importing the Mesh and Naming the Simulation Start up STAR-CCM+ in a manner that is appropriate to your working environment and select the New Simulation option from the menu bar. Continue by importing the mesh and naming the simulation. A polyhedral cell mesh has been prepared for this analysis and is stored in a.ccm format file. Select File > Import... from the menus In the Open dialog, simply navigate to the doc/tutorials/porousmedia subdirectory of your STAR-CCM+

2 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3928 installation directory and select the file catalyst.ccm. Click the Open button to start the import. The Import Mesh Options dialog will appear. Select the following options: Run mesh diagnostics after import Open geometry scene after import Ensure that the Don t show this dialog during import option is not selected and then click OK. STAR-CCM+ will provide feedback on the import process, which will take a few seconds, in the Output window. Two mesh regions named Cells and Cells_1 will be created under the Regions node to represent the two parts of the solution domain. A geometry scene will also be created in the Graphics window. Finally, save the new simulation to disk under file name isotropicporousmedia.sim Visualizing the Imported Geometry Examine the Geometry Scene 1 display in the Graphics window. Initially all parts of the mesh are shown as solid, colored surfaces. Click on one of the parts. The boundary selected is highlighted and a

3 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3931 The geometry display will be re-oriented, as shown below. Defining and Renaming Regions and Boundaries Initially, all regions and boundaries have generic names. We will now give them more suitable labels.

4 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3935 This part of the simulation tree should look as shown below when you are done. Scaling the Mesh The original mesh was not built to scale and therefore requires scaling so that the dimensions of the porous region are 0.1 x 0.03 x 0.1 meters. Select the Mesh > Diagnostics... menu item to determine the current dimensions of the porous region Use the Mesh Diagnostics dialog to select only the Porous region and

5 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3937 in the Selected list box. Enter a value of 0.1 for the scale factor. Click Apply to scale the domain and then click Close. When the Apply button is clicked, the mesh region will be reduced in size. Click on the (Reset View) button in the visualization toolbar to restore the previous viewing distance for the scaled domain in the display To verify that scaling has in fact been applied, you may perform the mesh diagnostics check again and review the output values. Setting Up the Models Models define the primary variables of the simulation, including pressure, temperature and velocity, and what mathematical formulation will be used to generate the solution. In this example, the flow is turbulent and incompressible. The Segregated Flow model will be used together with the standard K-Epsilon turbulence model. The default continuum is automatically named Physics 1 when the mesh is imported. To give the continuum a more appropriate name: Open the Continua node, right-click on the Physics 1 node and select

6 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3941 Setting Material Properties The default material properties for air need to be changed so that it now has a density of kg/m^3 and a dynamic viscosity of 1.81e-5 PaS. Select the Air > Models > Gas > Air > Material Properties > Density > Constant node. In the Properties window, set the Value property to kg/m^3. Still within the Air node, open the Dynamic Viscosity node and select the Constant node Set the Value property to 1.81e-5 Pa-s. Save the simulation. Creating Interfaces All regions in STAR-CCM+ require the creation of interfaces between them that will allow transfer of the appropriate quantities of mass and energy calculated during the simulation. For this example, we will need to create two interfaces between the fluid and porous regions.

7 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3944 Set the Value property to Open the Turbulence Length Scale node and select the Constant node Set the Value property to m Open the Velocity Magnitude node and select the Constant node Set the Value property to 20 m/s. The boundary conditions are now set. Save the simulation. Specifying Porosity Coefficients As discussed in the introduction to this tutorial, the porous region is defined by its inertial and viscous resistance coefficients, which are 25 kg/m 4 and 1500 kg/m 3 s, respectively. As the porous region is isotropic, these values hold in all directions. The coefficients, along with the turbulence parameters in the porous region, must now be specified. To start with, the Porous region must be defined as a porous medium. Select the Porous node under the Regions node and, in the Properties window, change the Type property to Porous Region. Select the Porous > Physics Conditions > Turbulence Specification node Change the Method property to Intensity + Length Scale

8 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3947 Open the Porous Viscous Resistance > Principal Tensor node. Using the same method as for the inertial resistance, specify each of the three components of the viscous resistance to be 1500 kg/m 3 -s. Select the Turbulence Intensity node and change the Value property to 0.1. The default turbulent length scale of 0.01 m is suitable for this case so it does not need changing. Monitoring the Run Progress As part of the post-processing operations, we will check that the calculated pressure drop across the porous region is close to the theoretical drop given by Eqn. (2). To help us do this, we will monitor the average pressure on both fluid-porous interfaces and the mass flow rate through the porous region

9 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3953 Selected list. Right-click on the Average Downstream Pressure Monitor Plot node and select Rename... Change its name to Pressure Drop Monitor Plot. To preview the plot set-ups, double-click on the Mass Flow Rate Monitor Plot and Pressure Drop Monitor Plot nodes. Setting Stopping Criteria Rather than arranging for the analysis to run for a set number of iterations, it is often useful to specify stopping criteria based on residual values and monitored quantities. For this case, we will define a stopping criterion that checks whether the average upstream pressure monitor has reached a steady value. Right-click on the Average Upstream Pressure Monitor node and select

10 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3955 of 100 Pa, this should only occur when the solution has practically reached convergence. Visualizing the Solution We will view the velocity vector field as the solution develops on a plane bisecting the fluid and porous regions. Start by creating a new vector scene: Right-clicking on the Scenes node and then select New Scene > Vector.

11 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3961 Open the Outline 1 displayer node and select the Parts node. Click on the right half of the Parts property in the Properties window. Deselect all the current parts, then select the plane section part only. The vector scene is now ready. Save the simulation. Running the Simulation To run the simulation, click on the (Run) button in the top toolbar. If you do not see this button, use the Solution > Run menu item. You could also show the Solution toolbar by selecting Tools > Toolbars > Solution and then clicking the toolbar button. The Residuals display will be created automatically and will show the progress being made by the solver. If necessary, click on the Residuals tab to bring the Residuals plot into view. An example of a residual plot is shown in a separate part of the User Guide. This example will look different from your residuals, since the plot depends on the models selected. The two monitor plots created in the Monitoring the Run Progress section and the vector scene should also be displayed. The tabs at the top of the Graphics window make it possible to select any one of the active displays for viewing. They can also be rearranged and multiple scenes can even be

12 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3965 location, such as that shown below. Note that as a result of the isotropy of the porous region the vectors are not aligned in any particular direction. Save the simulation. Validating the Results As discussed at the start of the tutorial, the calculated pressure drop across the porous region can be compared to the theoretical pressure drop derived from the mass flow rate. Open the Reports node and right-click on the Average Upstream Pressure node

13 STAR-CCM+ User Guide Isotropic Porous Media Tutorial 3967 medium. In the above comparison, we have used instead an average velocity value based upon the mass flow rate, implying that the theoretical value is only an approximation to the actual pressure drop. Summary This tutorial illustrates the following STAR-CCM+ features: Importing the mesh and saving the simulation. Visualizing the geometry. Defining and renaming regions and boundaries. Scaling the mesh. Defining physical models. Defining material properties required for the selected models. Creating region interfaces. Defining boundary conditions. Specifying porosity coefficients. Monitoring the solution progress. Setting up stopping criteria. Initializing and running the solver until monitored values approach an asymptotic solution. Evaluating the solution results using STAR-CCM+ s visualization and reporting facilities.