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Tutorial 7. Modeling Flow Through Porous MediaIntroductionMany industrial applications involve the modeling of ow through porous media, such as _lters, catalyst beds, and packing. This tutorial illustrates how to set up and solve a problem involving gas ow through porous media.The industrial problem solved here involves gas ow through a catalytic converter. Catalytic converters are commonly used to purify emissions from gasoline and diesel engines by converting environmentally hazardous exhaust emissions to acceptable substances.Examples of such emissions include carbon monoxide (CO), nitrogen oxides (NOx), and unburned hydrocarbon fuels. These exhaust gas emissions are forced through a substrate, which is a ceramic structure coated with a metal catalyst such as platinum or palladium.The nature of the exhaust gas ow is a very important factor in determining the performance of the catalytic converter. Of particular importance is the pressure gradient and velocity distribution through the substrate. Hence CFD analysis is used to designe_cient catalytic converters: by modeling the exhaust gas ow, the pressure drop and the uniformity of ow through the substrate can be determined. In this tutorial, FLUENTis used to model the ow of nitrogen gas through a catalytic converter geometry, so that the ow _eld structure may be analyzed.This tutorial demonstrates how to do the following:_ Set up a porous zone for the substrate with appropriate resistances._ Calculate a solution for gas ow through the catalytic converter using the pressurebased solver._ Plot pressure and velocity distribution on speci_ed planes of the geometry._ Determine the pressure drop through the substrate and the degree of non-uniformityof ow through cross sections of the geometry using X-Y plots and numerical reports.许多工业应用都涉及通过多孔介质(如过滤器,催化剂床和填料)的流动模型。本教程说明如何建立和解决涉及气体通过多孔介质的问题。这里解决的工业问题涉及通过催化转换器的气体流量。催化转化器通常用于通过将对环境有害的废气排放物转化为可接受的物质来净化汽油和柴油发动机的排放物。这种排放的例子包括一氧化碳(CO),氮氧化物(NOx)和未燃烧的碳氢化合物燃料。这些废气排放物被迫通过衬底,该衬底是涂覆有诸如铂或钯的金属催化剂的陶瓷结构。排气流量的性质是决定催化转化器性能的一个非常重要的因素。特别重要的是通过基底的压力梯度和速度分布。因此,使用CFD分析来设计催化转换器:通过对排气流量进行建模,可以确定通过基板的流量的压降和流量的均匀性。在本教程中,FLUENT用于模拟通过催化转化器几何形状的氮气流量,从而可以分析流量结构。本教程演示了如何执行以下操作:_设置具有适当阻力的基材的多孔区域。_使用基于压力的解算器计算通过催化转化器的气体流量的解决方案。_绘制几何体特定平面上的压力和速度分布。_确定通过基材的压降和不均匀的程度通过使用X-Y图和数字报告的几何横截面的流量。PrerequisitesThis tutorial assumes that you are familiar with the menu structure in FLUENT and thatyou have completed Tutorial 1. Some steps in the setup and solution procedure will notbe shown explicitly.本教程假设您熟悉FLUENT中的菜单结构您已完成教程1.设置和解决方案过程中的某些步骤不会明确显示。Problem DescriptionThe catalytic converter modeled here is shown in Figure 7.1. The nitrogen ows inthrough the inlet with a uniform velocity of 22.6 m/s, passes through a ceramic monolithsubstrate with square shaped channels, and then exits through the outlet.图7.1所示为这里建模的催化转化器。氮流入以22.6m / s的均匀速度通过入口,穿过陶瓷整体具有方形通道的基底,然后通过出口离开。While the ow in the inlet and outlet sections is turbulent, the ow through the substrate is laminar and is characterized by inertial and viscous loss coe_cients in the ow (X) direction. The substrate is impermeable in other directions, which is modeled using losscoe_cients whose values are three orders of magnitude higher than in the X direction.当入口和出口段的湍流是湍流时,通过基底的流动是层流的,并且在流动(X)方向上具有惯性和粘性损失系数。 基材在其他方向上是不透水的,其使用的损失系数比在X方向上高三个数量级。Setup and SolutionPreparation1. Download porous.zip from the Fluent Inc. User Services Center or copy it fromthe FLUENT documentation CD to your working folder (as described in Tutorial 1).2. Unzip porous.zip.catalytic converter.msh can be found in the porous folder created after unzippingthe _le.3. Start the 3D (3d) version of FLUENT.1.从Fluent Inc.用户服务中心下载porous.zip或从中复制FLUENT文档光盘放到您的工作文件夹中(如教程1所述)。2.解压多孔.zip。催化转换器.msh可以在解压后形成的多孔文件夹中找到。3.启动FLUENT的3D(3D)版本。Step 1: Grid1. Read the mesh _le (catalytic converter.msh).File ! Read !Case.2. Check the grid.Grid !CheckFLUENT will perform various checks on the mesh and report the progress in the console. Make sure that the minimum volume reported is a positive number.3. Scale the grid.Grid !Scale. (a) Select mm from the Grid Was Created In drop-down list.(b) Click the Change Length Units button. All dimensions will now be shown in millimeters.(c) Click Scale and close the Scale Grid panel.4. Display the mesh. Display !Grid.(a) Make sure that inlet, outlet, substrate-wall, and wall are selected in the Surfaces selection list.(b) Click Display.(c) Rotate the view and zoom in to get the display shown in Figure 7.2.(d) Close the Grid Display panel.The hex mesh on the geometry contains a total of 34,580 cells.Step 2: Models1. Retain the default solver settings. De_ne ! Models !Solver.2. Select the standard k-_ turbulence model.De_ne ! Models !Viscous.Step 3: Materials1. Add nitrogen to the list of uid materials by copying it from the Fluent Databasefor materials. De_ne !Materials.(a) Click the Fluent Database. button to open the Fluent Database Materials panel.i. Select nitrogen (n2) from the list of Fluent Fluid Materials.ii. Click Copy to copy the information for nitrogen to your list of uid materials.iii. Close the Fluent Database Materials panel.(b) Close the Materials panel.Step 4: Boundary Conditions De_ne !Boundary Conditions.1. Set the boundary conditions for the uid (uid).(a) Select nitrogen from the Material Name drop-down list.(b) Click OK to close the Fluid panel.2. Set the boundary conditions for the substrate (substrate).(a) Select nitrogen from the Material Name drop-down list.(b) Enable the Porous Zone option to activate the porous zone model.(c) Enable the Laminar Zone option to solve the ow in the porous zone withoutturbulence.(d) Click the Porous Zone tab.i. Make sure that the principal direction vectors are set as shown in Table7.1.Use the scroll bar to access the _elds that are not initially visible in thepanel.ii. Enter the values in Table 7.2 for the Viscous Resistance and Inertial Resistance.Scroll down to access the _elds that are not initially visible in the panel.(e) Click OK to close the Fluid panel.3. Set the velocity and turbulence boundary conditions at the inlet (inlet).(a) Enter 22.6 m/s for the Velocity Magnitude.(b) Select Intensity and Hydraulic Diameter from the Speci_cation Method dropdownlist in the Turbulence group box.(c) Retain the default value of 10% for the Turbulent Intensity.(d) Enter 42 mm for the Hydraulic Diameter.(e) Click OK to close the Velocity Inlet panel.4. Set the boundary conditions at the outlet (outlet).(a) Retain the default setting of 0 for Gauge Pressure.(b) Select Intensity and Hydraulic Diameter from the Speci_cation Method dropdown list in the Turbulence group box.(c) Enter 5% for the Backow Turbulent Intensity.(d) Enter 42 mm for the Backow Hydraulic Diameter.(e) Click OK to close the Pressure Outlet panel.5. Retain the default boundary conditions for the walls (substrate-wall and wall) andclose the Boundary Conditions panel.Step 5: Solution1. Set the solution parameters. Solve ! Controls !Solution.(a) Retain the default settings for Under-Relaxation Factors.(b) Select Second Order Upwind from the Momentum drop-down list in the Discretizationgroup box.(c) Click OK to close the Solution Controls panel.2. Enable the plotting of residuals during the calculation. Solve ! Monitors !Residual.(a) Enable Plot in the Options group box.(b) Click OK to close the Residual Monitors panel.3. Enable the plotting of the mass ow rate at the outlet.Solve ! Monitors !Surface.(a) Set the Surface Monitors to 1.(b) Enable the Plot and Write options for monitor-1, and click the De_ne. button to open the De_ne Surface Monitor panel.i. Select Mass Flow Rate from the Report Type drop-down list.ii. Select outlet from the Surfaces selection list.iii. Click OK to close the De_ne Surface Monitors panel.(c) Click OK to close the Surface Monitors panel.4. Initialize the solution from the inlet. Solve ! Initialize !Initialize.(a) Select inlet from the Compute From drop-down list.(b) Click Init and close the Solution Initialization panel.5. Save the case _le (catalytic converter.cas). File ! Write !Case.6. Run the calculation by requesting 100 iterations. Solve !Iterate.(a) Enter 100 for the Number of Iterations.(b) Click Iterate.The FLUENT calculation will converge in approximately 70 iterations. By this point the mass ow rate monitor has attened out, as seen in Figure 7.3.(c) Close the Iterate panel.7. Save the case and data _les (catalytic converter.cas and catalytic converter.dat).File ! Write !Case & Data.Note: If you choose a _le name that already exists in the current folder, FLUENTwill prompt you for con_rmation to overwrite the _le.Step 6: Postprocessing1. Create a surface passing through the centerline for postprocessing purposes.Surface !Iso-Surface.(a) Select Grid. and Y-Coordinate from the Surface of Constant drop-down lists.(b) Click Compute to calculate the Min and Max values.(c) Retain the default value of 0 for the Iso-Values.(d) Enter y=0 for the New Surface Name.(e) Click Create.2. Create cross-sectional surfaces at locations on either side of the substrate, as wellas at its center. Surface !Iso-Surface.(a) Select Grid. and X-Coordinate from the Surface of Constant drop-down lists.(b) Click Compute to calculate the Min and Max values.(c) Enter 95 for Iso-Values.(d) Enter x=95 for the New Surface Name.(e) Click Create.(f) In a similar manner, create surfaces named x=130 and x=165 with Iso-Values of 130 and 165, respectively. Close the Iso-Surface panel after all the surfaces have been created.3. Create a line surface for the centerline of the porous media.Surface !Line/Rake.(a) Enter the coordinates of the line under End Points, using the starting coordinate of (95, 0, 0) and an ending coordinate of (165, 0, 0), as shown.(b) Enter porous-cl for the New Surface Name.(c) Click Create to create the surface.(d) Close the Line/Rake Surface panel.4. Display the two wall zones (substrate-wall and wall). Display !Grid.(a) Disable the Edges option.(b) Enable the Faces option.(c) Deselect inlet and outlet in the list under Surfaces, and make sure that only substrate-wall and wall are selected.(d) Click Display and close the Grid Display panel.(e) Rotate the view and zoom so that the display is similar to Figure 7.2.5. Set the lighting for the display. Display !Options.(a) Enable the Lights On option in the Lighting Attributes group box.(b) Retain the default selection of Gourand in the Lighting drop-down list.(c) Click Apply and close the Display Options panel.6. Set the transparency parameter for the wall zones (substrate-wall and wall).Display !Scene.(a) Select substrate-wall and wall in the Names selection list.(b) Click the Display. button under Geometry Attributes to open the Display Properties panel.i. Set the Transparency slider to 70.ii. Click Apply and close the Display Properties panel.(c) Click Apply and then close the Scene Description panel.7. Display velocity vectors on the y=0 surface.Display !Vectors.(a) Enable the Draw Grid option. The Grid Display panel will open.i. Make sure that substrate-wall and wall are selected in the list under Surfaces.ii. Click Display and close the Display Grid panel.(b) Enter 5 for the Scale.(c) Set Skip to 1.(d) Select y=0 from the Surfaces selection list.(e) Click Display and close the Vectors panel.The ow pattern shows that the ow enters the catalytic converter as a jet, withrecirculation on either side of the jet. As it passes through the porous substrate, itdecelerates and straightens out, and exhibits a more uniform velocity distribution.This allows the metal catalyst present in the substrate to be more effective.Figure 7.4: Velocity Vectors on the y=0 Plane8. Display _lled contours of static pressure on the y=0 plane.Display !Contours.(a) Enable the Filled option.(b) Enable the Draw Grid option to open the Display Grid panel.i. Make sure that substrate-wall and wall are selected in the list under Surfaces.ii. Click Display and close the Display Grid panel.(c) Make sure that Pressure. and Static Pressure are selected from the Contoursof drop-down lists.(d) Select y=0 from the Surfaces selection list.(e) Click Display and close the Contours panel.Figure 7.5: Contours of the Static Pressure on the y=0 planeThe pressure changes rapidly in the middle section, where the uid velocity changesas it passes through the porous substrate. The pressure drop can be high, due to theinertial and viscous resistance of the porous media. Determining this pressure dropis a goal of CFD analysis. In the next step, you will learn how to plot the pressuredrop along the centerline of the substrate.9. Plot the static pressure across the line surface porous-cl.Plot !XY Plot.(a) Make sure that the Pressure. and Static Pressure are selected from the Y Axis Function drop-down lists.(b) Select porous-cl from the Surfaces selection list.(c) Click Plot and close the Solution XY Plot panel.Figure 7.6: Plot of the Static Pressure on the porous-cl Line SurfaceIn Figure 7.6, the pressure drop across the porous substrate can be seen to be roughly 300 Pa.10. Display _lled contours of the velocity in the X direction on the x=95, x=130 and x=165 surfaces.Display !Contours.(a) Disable the Global Range option.(b) Select Velocity. and X Velocity from the Contours of drop-down lists.(c) Select x=130, x=165, and x=95 from the Surfaces selection list, and deselecty=0.(d) Click Display and close the Contours panel.The velocity pro_le becomes more uniform as the uid passes through the porous media. The velocity is very high at the center (the area in red) just before the nitrogen enters the substrate and then decreases as it passes through and exits thesubstrate. The area in green, which corresponds to a moderate velocity, increasesin extent.Figure 7.7: Contours of the X Velocity on the x=95, x=130, and x=165 Surfaces11. Use numerical reports to determine the average, minimum, and maximum of thevelocity distribution before and after the porous substrate.Report !Surface Integrals.(a) Select Mass-Weighted Average from the Report Type drop-down list.(b) Select Velocity and X Velocity from the Field Variable drop-down lists.(c) Select x=165 and x=95 from the Surfaces selection list.(d) Click Compute.(e) Select Facet Minimum from the Report Type drop-down list and click Compute again.(f) Select Facet Maximum from the Report Type drop-down list and click Compute again.(g) Close the Surface Integrals panel.The numerical report of average, maximum and minimum velocity can be seen inthe main FLUENT console, as shown in the following example:The spread between the average, maximum, and minimum values for X velocity gives the degree to which the velocity distribution is non-uniform. You can also use these numbers to calculate the velocity ratio (i.e., the maximum velocity divided by the mean velocity) and the space velocity (i.e., the product of the mean velocity and the substrate length).Custom _eld functions and UDFs can be also used to calculate more complex measures of non-uniformity, such as the standard deviation and the gamma uniformityindex.SummaryIn this tutorial, you learned how to set up and solve a problem involving gas ow through porous media in FLUENT. You also learned how to perform appropriate postprocessing to investigate the ow _eld, determine the pressure drop across the porous media and non-uniformity of the velocity distribution as the uid goes through the porous media.See Section 7.19 of the Users Guide for additional details about modeling ow through porous media (including heat transfer and reaction modeling).Further ImprovementsThis tutorial guides you through the steps to reach an initial

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