ANSYS

Problem Specification

Consider fluid flowing through a circular pipe of constant radius as illustrated D  = 0.2 m and length L = 8 m. The inlet velocity Ū z  above. The pipe diameter D = z  = 1 m/s. Consider the velocity to be constant over the inlet cross-section. The fluid exhausts into the ambient atmosphere which is at a pressure of 1 atm. Take density  ρ = 1 kg/ m 3  and coefficient of viscosity µ = 2 x 10 -3  kg/(ms). The Reynolds number Re  based on the pipe diameter is

where Ū z  z  is the average velocity at the inlet, which is 1 m/s in this case. Solve this problem using FLUENT via ANSYS Workbench. W orkbench. Plot the centerline velocity, wall skin-friction coefficient, and velocity profile at the outlet. Validate your results. Note: The values used for the inlet velocity and flow properties are chosen for convenience rather than to reflect reality. The key parameter value to focus on is the Reynolds number.

Step 1: Pre-Analysis & Start-up Preliminary Analysis  We expect the viscous boundary layer to grow along the pipe starting at the inlet. It will eventually grow to fill the pipe completely (provided that the pipe is long enough). When this happens, the flow becomes fully-developed and there x  (see figure below). is no variation of the velocity profile in the axial direction, x (see One can obtain a closed-form solution to the governing equations in the fullydeveloped region. You should have seen this in the Introduction to Fluid  Mechanics course. Mechanics  course. We will compare the numerical results in the fully-

developed region with the corresponding analytical results. So it's a good idea for you to go back to your textbook in the Intro course and review the fullydeveloped flow analysis. What values would you expect for the centerline velocity and the friction factor in the fully-developed region based on the analytical solution? What is the solution for the velocity profile?

We'll create the geometry and mesh in ANSYS 12.1 which is the preprocessor for FLUENT, and then read the mesh into FLUENT and solve for the flow solution.

Start ANSYS FLUENT  pipe in a convenient location. Prior to opening ANSYS, create a folder called pipe in We'll use this as the working folder in which files created during the session will be stored. For this simulation Fluent will be run within the ANSYS Workbench Interface. Start ANSYS workbench: Start> All Programs> Ansys 12.1> Workbench  The following figure shows the workbench window.

Higher Resolution Image

Management of Screen Real Estate  This tutorial is specially configured, so the user can have both the tutorial and ANSYS open at the same time as shown below. It will be beneficial to have both ANSYS and your internet browser displayed on your monitor simultaneously. Your internet browser should consume approximately one third of the screen width while ANSYS should take the other ot her two thirds as shown below.

Click Here for Higher Resolution If the monitor you are using is insufficient in size, you can press t and b keys the Al t  and Ta b  keys simultaneously to toggle between ANSYS and your internet browser.

Saving  It would be of best interest, to save the project at this point. Click on the "Save As.." button,

, which is located on the top of the Workbench 

Project Page . Save the project as "LaminarPipeFlow" in your working directory. When you save in ANSYS a file and a folder will be created. For instance if you save as "LaminarPipeFlow", " LaminarPipeFlow", a "LaminarPipeFlow" file and a folder called "LaminarPipeFlow_files" will appear. In order to reopen the ANSYS files in the future you will need both the ".wbpj" file f ile and the folder. If you do not have BOTH, you will not be able to access your project.

Fluid Flow(FLUENT) Project Selection  On the left hand side of the workbench window, you will see a toolbox full of various analysis systems. To the right, you see an empty work space. This is the place where you will organize your project. At the bottom of the window, you see messages from ANSYS. Left click (and hold) on Fluid Flow (FLUENT) , and drag the icon into the empty space in the Project Schematic . Your ANSYS window should now look comparable to the image below.

Since we selected Fluid Flow(FLUENT), each cell of the system corresponds to a step in the process of performing CFD analysis using FLUENT. Rename the project to Laminar Pipe. We will work through each step from top down to obtain the solution to our problem.

Analysis Type  In the Project Schematic of the Workbench window, right click on Geometry and select Properties , as shown below.

The properties menu will then appear to the right of the Workbench window. Under Advance Geometry Options , change the Analysis Type to 2D as shown in the image below.

Launch Design Modeler  In the Project Schematic , double click on Geometry to start preparing the geometry. At this point, a new window, ANSYS Design Modeler will be opened. You will be asked to select desired length unit. Use the default meter unit and click OK .

Creating a Sketch  Start by creating a sketch on the XYPlane . Under Tree Outline , select XYPlane , then click on Sketching right before Details View . This will bring up the Sketching Toolboxes . Click Here for Select Sketching Toolboxes Demo

Click on the +Z  axis on the bottom right corner of the Graphics window to have a normal look of the XY Plane. Click Here for Select Normal View Demo In the Sketching toolboxes, select Rectangle . In the Graphics window, create a rough Rectangle by clicking once on the origin and then by clicking once somewhere in the positive XY plane. (Make sure that you see a letter P at the origin before you click. The P implies that the cursor is directly over a point of intersection.) At this point you should have something comparable to the image below.

Dimensions  At this point the rectangle will be properly dimensioned. Under Sketching Toolboxes , select Dimensions tab, use the default dimensioning tools. Dimension the geometry as shown in the following image.

Click Here for Higher Resolution Under the Details View table (located in the lower left corner), set V1=0.1m and set H2=8m, as shown in the image below.

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Surface Body Creation  In order to create the surface body, first (Click )Concept > Surface From  Sketches as shown in the image below.

This will create a new surface SurfaceSK1. Under Details View , select Sketch1 as Base Objects and then under Surface body select the thickness to 0.1m and click Apply . Finally click Generate to generate the surface. At this point, you can close the Design Modeler and go back to Workbench  Project Page . Save your work thus far in the Workbench Project Page .

Step 3: Mesh

In this section the geometry will be meshed with 500 elements. That is, the pipe will be divided into 100 elements in the axial direction and 5 elements in the radial direction.

Launch Mesher  In order to begin the meshing process, go to the Workbench Project Page , then (Double Click) Mesh .

Default Mesh  In this section the default mesh will be generated. This can be carried out two ways. The first way is to (Right Click) Mesh > Generate Mesh , as shown in the image below.

The second way in which the default mesh can be generated is to (Click)  Mesh > Generate Mesh as can be seen below.

Either method should give you the same results. The default mesh that you generate should look comparable to the image below.

Note that in Workbench there is generally at least two ways to implement actions as has been shown above. For, simplicity's sake the "menu" method of implementing actions will be solely used for the rest of the tutorial.

Mapped Face Meshing  As can be seen above, the default mesh has irregular elements. We are interested in creating a grid style of mesh that can be mapped to a rectangular domain. This meshing style is called Mapped Face Meshing . In order to incorporate this meshing style (Click) Mesh Control > Mapped Face  Meshing as can be seen below.

Now, the Mapped Face Meshing still must be applied to the pipe geometry. In order to do so, first click on the pipe body which should then highlight green. Next, (Click) Apply in the Details of Mapped Face Meshing table, as shown below.

This process is shown here Now, generate the mesh by using either method from the "Default Mesh" section above. You should obtain a mesh comparable to the following image.

Edge Sizing  The desired mesh has specific number of divisions along the radial and the axial direction. In order to obtain the specified number of divisions Edge  Sizing must be used. The divisions along the axial direction will be specified first. Now, an Edge Sizing needs to be inserted. First, (Click) Mesh  Control > Sizing as shown below.

Now, the geometry and the number of divisions need to be specified. First (Click) Edge Selection Filter ,

. Then hold down the "Control"

button and then click the bottom and top edge of the rectangle. Both sides should highlight green. Next, hit Apply under the Details of Sizing table as shown below.

Now, change Type to Number of Divisions as shown in the image below.

Then, set Number of Divisions to 100 as shown below.

At this point, the edge sizing in the the radial direction will be specified. Follow the same procedure as for the edge sizing in the axial direction, except select the left and right side instead of the top and bottom and set the number of division to 5. Then, generate the mesh by using either method from the "Default Mesh" section above. You should obtain the following mesh.

As it turns out, in the mesh above there are 540 elements, when there should be only 500. Mesh statistics can be found by clicking on Mesh in the Tree and then by expandingStatistics under the Details of Mesh table. In order to get the desired 500 element mesh the Behavior needs to be changed from Soft to Hard for both Edge Sizing's . In order to carry this out first Expand Mesh in the tree outline then click Edge Sizing and then change Behavior to Hard under the Details of Edge Sizing table, as shown below.

Then set the Behavior to Hard for Edge Sizing 2 . Next, generate the mesh

using either method from the "Default Mesh" section above. You should then obtain the following 500 element mesh.

Radial Sizing

Create Named Selections  Here, the edges of the geometry will be given names so one can assign boundary conditions in Fluent in later steps. The left side of the pipe will be called "Inlet" and the right side will be called "Outlet". The top side of the rectangle will be called "PipeWall" and the bottom side of the rectangle will be called "CenterLine" as shown in the image below.

In order to create a named selections first (Click) Edge Selection  Filter ,

. Then click on the left side of the rectangle and it should highlight

green. Next, right click the left side of the rectangle and choose Create  Named Selection as shown below.

Select the left edge and right click and select Create Named Selection . Enter Inlet and click OK , as shown below.

Now, create named selections for the remaining three sides and name them according to the diagram.

Save, Exit & Update  First save the project. Next, close the Mesher window. Then, go to the Workbench Project Page and click the Update  Project button,

.

Step 4: Setup (Physics) Your current Workbench Project Page should look comparable to the following image. Regardless of whether you downloaded the mesh and geometry files or if you created them yourself, you should have checkmarks to the right of Geometry and Mesh .

Next, the mesh and geometry data need to be read into FLUENT. To read in the data (Right Click) Setup > Refresh in the Workbench Project Page as shown in the image below.

After you click Update , a question mark should appear to the right of the Setup cell. This indicates that the Setup process has not yet been completed.

Launch Fluent  Double click on Setup in the Workbench Project Page which will bring up the FLUENT Launcher . When the FLUENT Launcher appears change the options to "Double Precision", and then click OK as shown below.The Double Precision option is used to select the double-precision solver. In the doubleprecision solver, each floating point number is represented using 64 bits in contrast to the single-precision solver which uses 32 bits. The extra bits increase not only the precision, but also the range of magnitudes that can be represented. The downside of using double precision is that it requires more memory.

Click Here for Higher Resolution Twiddle your thumbs a bit while the FLUENT interface starts up. This is where we'll specify the governing equations and boundary conditions for our boundaryvalue problem. On the left-hand side of the FLUENT interface, we see various items listed under Problem Setup . We will work from top to bottom of the Problem Setup items to setup the physics of our boundary-value problem. On the right hand side, we have the Graphics pane and, below that, the Command pane.

Check and Display Mesh  First, the mesh will be checked to verify that it has been properly imported from Workbench . In order to obtain the statistics about the mesh (Click)  Mesh > Info > Size , as shown in the image below.

Then, you should obtain the following output in the Command pane.

The mesh that was created earlier has 500 elements(5 Radial x 100 Axial). Note that in FLUENT elements are called cells. The output states that there are 500 cells, which is a good sign. Next, FLUENT will be asked to check the mesh for errors. In order to carry out the mesh checking procedure (Click) Mesh >  Check as shown in the image below.

You should see no errors in the Command Pane. Now, that the mesh has been verified, the mesh display options will be discussed. In order to bring up the display options (Click) General > Mesh > Display as shown in the image below.

The previous step should cause the Mesh Display window to open, as shown below. Note that the Named Selections created in the meshing steps now appear.

Click Here for Higher Resolution You should have all the surfaces shown in the above snapshot. Clicking on a surface name in the Mesh Display menu will toggle between select and unselect. Clicking Display will show all the currently selected surface entities in the graphics pane. Unselect all surfaces and then select each one in turn to see which part of the domain or boundary the particular surface entity corresponds to (you will need to zoom in/out and translate the model as you do this). For instance, if you select wall , outlet , and centerline and then clickDisplay you should then obtain the following output in the graphics window.

Now, make sure all 5 items under Surfaces are selected. The to Surfaces selects all of the boundaries while the

button next

button deselects all of

the boundaries at once. Once, all the 5 boundaries have been selected

click Display , then close the Mesh Display window. The long, skinny rectangle displayed in the graphics window corresponds to our solution domain. Some of the operations available in the graphics window to interrogate the geometry and mesh are: Translation: The model can be translated in any direction by holding down the Left Mouse Button and then moving the mouse in the desired direction. Zoom In: Hold down the Middle Mouse Button and drag a box from the Upper Left Hand Corner to the Lower Right Hand Corner over the area you want to zoom in on. Zoom Out: Hold down the Middle Mouse Button and drag a box anywhere from the Lower Right Hand Corner to the Upper Left Hand Corner . Use these operations to zoom in and interrogate the mesh.

Define Solver Properties  In this section the various solver properties will be specified in order to obtain the proper solution for the laminar pipe flow. First, the axisymmetric nature of the geometry must be specified. Under General > Solver > 2D  Space select Axisymmetric as shown in the image below.

Click Here for Higher Resolution Next, the Viscous Model parameters will be specified. In order to open the

Viscous Model Options Models > Viscous - Laminar > Edit.... By default, the Viscous Model options are set to laminar, so no changes are needed. Click Cancel to exit the menu. Now, the Energy Model parameters will be specified. In order to open the Energy Model Options Models > Energy-Off > Edit.... For incompressible flow, the energy equation is decoupled from the continuity and momentum equations. We need to solve the energy equation only if we are interested in determining the temperature distribution. We will not deal with temperature in this example. So leave the Energy Equation set to off and click Cancel to exit the menu.

Define Material Properties  Now, the properties of the fluid that is being modeled will be specified. The properties of the fluid were specified in the Problem Specification section. In order to create a new fluid(Click) Materials > Fluid > Create/Edit... as shown in the image below.

In the Create/Edit Materials menu set the Density to 1kg/m^3 (constant) and set the Viscosity to 2e-3 kg/(ms) (constant) as shown in the image

below.

Click Here for Higher Resolution Click Change/Create . Close the window.

Define Boundary Conditions  Selections will be At this point the boundary conditions for the four Named Selections will inlet will be specified first. specified. The boundary condition for the inlet will Inlet Boundary Condition

In order to start the process (Click) Boundary Conditions > inlet >  Edit... as shown in the following f ollowing image.

Click Here for Higher Resolution Note that the Boundary Condition Type should Type  should have been automatically inlet will be specified. In set to velocity-inlet . Now, the velocity at the inlet will the Velocity Inlet menu Inlet menu set the Velocity Specification  Method to Method  (m/s) to to Components , and set the Axial-Velocity (m/s)  to 1 m/s, as shown below.

Click Here for Higher Resolution Inlet menu. Then, click OK  to close the Velocity Inlet menu.

Outlet Boundary Condition

outlet  in the Boundary Conditions menu, First, select outlet in Conditions  menu, as shown below.

Click Here for Higher Resolution As can be seen in the image above the Type  should have been automatically Type should Type is set to pressure-outlet . If the Type  is not set to pressure-outlet , then set it to pressure-outlet . Now, no further changes are needed for outlet boundary condition. the outlet boundary Centerline Boundary Condition

centerline  in the Boundary Conditions menu, Conditions menu, as shown below. Select centerline in

Click Here for Higher Resolution As can be seen in the image above the Type has been automatically set to wall which is not correct. Change the Type to axis , as shown below.

Click Here for Higher Resolution When the dialog boxes appear click Yes  to change the boundary type. Then click OK  to accept "centerline" as the zone name. Pipe Wall Boundary Condition

First, select pipe_wall in the Boundary Conditions menu, as shown below.

Click Here for Higher Resolution As can be seen in the image above the Type should have been automatically set to wall . If the Type is not set to wall , then set it to wall . Now, no further changes are needed for the pipe_wall boundary condition.

Save 

In order to save your work (Click)File > Save Project as shown in the image below.

Step 5: Solution Second Order Scheme  A second-order discretization scheme will be used to approximate the solution. In order to implement the second order scheme click on Solution  Methods then click onMomentum and select Second Order Upwind as shown in the image below.

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Set Initial Guess  Here, the flow field will be initialized to the values at the inlet. In order to carry out the initialization click on Solution Initialization then click on Compute  from and select inlet as shown below.

Click Here for Higher Resolution Then, click the Initialize button,

. This completes the initialization.

Set Convergence Criteria  FLUENT reports a residual for each governing equation being solved. The residual is a measure of how well the current solution satisfies the discrete form of each governing equation. We'll iterate the solution until the residual for each equation falls below 1e-6. In order to specify the residual criteria (Click)  Monitors > Residuals > Edit..., as shown in the image below.

Click Here for Higher Resolution Next, change the residual under Convergence Criterion for continuity , x-  velocity ,and y-velocity , all to 1e-6, as can be seen below.

Click Here for Higher Resolution Lastly, click OK to close the Residual Monitors menu.

Execute Calculation  Prior, to running the calculation the maximum number of iterations must be set. To specify the maximum number of iterations click on Run Calculation then set the Number of Iterations to 100, as shown in the image below.

Click Here for Higher Resolution As a safeguard save the project now. Now, click on Calculate two times in order to run the calculation. The residuals for each iteration are printed out as well as plotted in the graphics window as they are calculated. After running the calculation, you should obtain the following residual plot.

Click Here for Higher Resolution The residuals fall below the specified convergence criterion of 1e-6 in about 48 iterations, as shown below. Actual number of convergence steps may vary slightly.

Click Here for Higher Resolution At this point, save the project once again.

Step 6: Results

Velocity Vectors  One can plot vectors in the entire domain, or on selected surfaces. Let us plot the velocity vectors for the entire domain to see how the flow develops downstream of the inlet. First, click on Graphics & Animations . Next, double click on Vectors which is located under Graphics . Then, click on Display . Zoom into the region near the inlet. (Click here to review the zoom functionality discussion in step 4.) The length and color of the arrows represent the velocity magnitude. The vector display is more intelligible if one makes the arrows shorter as follows: Change Scale to 0.4 in the Vectors menu and click Display . The laminar pipe flow was modeled asymmetrically; however, the plot can be reflected about the axial axis to get an expanded sectional view. In order to carry this out (Click) Display > Views... as shown below.

Higher Resolution Image Under Mirror Planes , only the axis (or centerline) surface is listed since that is the only symmetry boundary in the present case. Select axis (or  centerline) and clickApply , as shown below.

Then click Close to exit the Views menu. Your vector field should have been reflected across the axially axis as, shown below.

Higher Resolution Image The velocity vectors provide a picture of how the flow develops downstream of the inlet. As the boundary layer grows, the flow near the wall is retarded by viscous friction. Note the sloping arrows in the near wall region close to the inlet. This indicates that the slowing of the flow in the near-wall region results in an injection of fluid into the region away from the wall to satisfy mass conservation. Thus, the velocity outside the boundary layer increases. By default, one vector is drawn at the center of each cell. This can be seen by turning on the grid in the vector plot: Select Draw Grid in the Vectors menu and then click Display in the Grid Display as well as the Vectors menus. Velocity vectors are the default, but you can also plot other vector quantities. See section 27.1.3 of the user manual for more details about the vector plot functionality.

Centerline Velocity  Here, we'll plot the variation of the axial velocity along the centerline. In order to start the process (Click) Results > Plots > XY Plot... > Set Up.. as shown below.

Higher Resolution Image In the Solution XY Plot menu make sure that Position on X Axis is selected , and X is set to 1 and Y is set to 0. This tells FLUENT to plot the xcoordinate value on the abscissa of the graph. Next, select Velocity... for the first box underneath Y Axis Function and select Axial Velocity for the second box. Please note that X Axis Function and Y Axis  Function describe the x and y axes of the graph , which should not be confused with the x and y directions of the pipe. Finally, select centerline under Surfaces since we are plotting the axial velocity along the centerline. This finishes setting up the plotting parameters. Your Solution XY Plot should look exactly the same as the following image.

Higher Resolution Image Now, click Plot . The plot of the axial velocity as a function of distance along the centerline now appears.

Higher Resolution Image In the graph that comes up, we can see that the velocity reaches a constant value beyond a certain distance from the inlet. This is the fully-developed flow region. At this point the graph will be modified such that the fully developed regions results are truncated. That is, the range of the axes will be reconfigured. Open the Solution XY Plot menu, then click onAxes..., as shown below.

Higher Resolution Image Then, deselect Auto Range , which is located under Options . The boxes under Range should now be accessible. Next, select X , which is located under Axis . Enter 1 forMinimum and 3 for Maximum under Range . At this point the grid lines will be turned on in order to help estimate where the flow becomes fully developed. Check the boxes next to Major Rules and Minor  Rules under Options . At this point your Axes - Solution XY Plot menu should look exactly the same as the image below.

Higher Resolution Image Lastly, click Apply . Now, that the X axis has been formatted, we will move on to formatting the Y axis. Select Y under Axis and once again deselect Auto  Range under Options . Then, enter 1.8 for Minimum and

2.0

for Maximum under Range . Also

select Major Rules and Minor Rules to turn on the grid lines in the direction. At this point your Axes - Solution XY Plot menu should look exactly the same as the image below.

Higher Resolution Image We have now finished specifying the range for each axis, so click Apply and then Close . At this point, the graph can be replotted. Go to the Solution XY  Plot menu and clickPlot to plot the graph again with the new axes extents.

Higher Resolution Image From the image above, one can see that the fully-developed region starts at around x =3m and the centerline velocity in this region is 1.93 m/s .

Saving the Plot  In this section, we will save the data from the plot and a picture of the plot. The data from the plot will be saved first. In order to save the plot data open the Solution XY Plot menu and then select Write to File , which is located under Options . The Plot button should have changed to Write.... Click on Write..., and then enter

vel.xy

as the XY  File Name. Next, click OK .

Check that this file has been created in your FLUENT working directory. Lastly, close the Solution XY Plot menu. At this point, we'll save a picture of the plot. First click on File then click Save  Picture , as shown below.

Under Format , choose one of the following three options: EPS - if you have a postscript viewer, this is the best choice. EPS  allows you to save the file in vector mode, which will offer the best viewable image quality. After selecting EP S , choose Vector from under File Type . TIFF - this will offer a high resolution image of your graph. However, the image file generated will be rather large, so this is not recommended if you do not have a lot of room on your storage device. JPG - this is small in size and viewable from all browsers. However, the quality of the image is not particularly good. After selecting your desired image format and associated options, click on Save... Enter vel.eps, vel.tif, or vel.jpg depending on your format choice and click OK . Verify that the image file has been created in your working directory. You can now copy this file onto a disk or print it out for your records.

Coefficient of Skin Friction  FLUENT provides a large amount of useful information in the online help that comes with the software. Let's probe the online help for information on calculating the coefficient of skin friction. In order to access the online help first (click) Help > Users Guide Index as shown in the following image.

Click on S in the links on top and scroll down to skin friction coefficient . Click on the first link (normally, you would have to go through each of the links until you find what you are looking for). There you can see the following excerpt on the skin friction coefficient as well as the equation for calculating it.

Click on the link for Reference Values panel, which tells us how to set the reference values used in calculating the skin coefficient. In order to set the reference values, click onReference Values , as shown below.

Then, set Compute From to inlet , to tell FLUENT to calculate the reference values from the values at inlet. Check that density is 1 kg/m 3 and velocity is 1 m/ s . (Alternately, you could have just typed in the appropriate values). Your Reference Values should look the same as the following screen snapshot.

Higher Resolution Image Now, reopen the Solution XY Plot menu. Uncheck the Write to File check

box under Options , since we want to plot to the window. The Options and Plot Direction can be left as is since we are still plotting against the x distance along the pipe. Under the Y Axis Function , pick Wall  Fluxes... , and then Skin Friction Coefficient in the box under that. Under Surfaces , only select pipe_wall . At this point, your Solution XY  Plot menu should look exactly like the following image.

Higher Resolution Image Now, the ranges of each axis will be specified. Click on Axes... within the Solution XY Plot menu and re-select Auto-Range for the Y axis. Click Apply . Set the range of the X axis from 1to 8 by selecting X under Axis , entering 1 under Minimum , and 8 under Maximum in the box (remember to deselect Range Auto-Range first if it is checked). ClickApply , then click Close . Lastly, click Plot in the Solution XY Plot menu. You should obtain the following plot.

Higher Resolution Image We can see that the fully developed region is reached at around x=3.0m and the skin friction coefficient in this region is around 1.54. In order to save the data from this plot, first reopen the Solution XY 

Plot menu. Then, select Write to File under Options and click Write.... Enter cf.xy for XY File and clickOK .

Velocity Profile  In this section we will plot the velocity at the outlet as a function of the distance from the center of the pipe. In order to start the process (Click) Results >  Plots > XY Plot... > Set Up.. as shown below.

Higher Resolution Image For this graph, the y axis of the graph will have to be set to the y axis of the pipe (radial direction). To plot the position variable on the y axis of the graph, uncheck Position on X Axis under Options and choose Position on Y  Axis instead. To make the position variable the radial distance from the centerline, under Plot Direction , change X to 0 andY to 1. To plot the axial velocity on the x axis of the graph, select Velocity... for the first box underneath X Axis Function , and select Axial Velocity for the second box. Next, select outlet , which is located under Surfaces . Then, uncheck the Write to File check box under Options , so the graph will plot. Your Solution XY Plot , should look exactly like the image below.

Higher Resolution Image Next, click on Axes in the Solution XY Plot menu. Then, change both the x and y axes to Auto-Range . (Don't forget to click apply before selecting a different axis). Click Close in the Axes - Solution XY Plot menu. It is of interest to compare the velocity profile with the theoretical parabolic profile. In order to plot the theoretical results, first click here to download the necessary file. Save the file to your working directory. Next, go to the Solution  XY Plot menu and click Load File... and select the file that you just downloaded, profile_fdev.xy . Lastly, click Plot in theSolution XY  Plot menu. You should then obtain the following figure.

Higher Resolution Image Notice, how results compare relatively well with the theoretical parabolic profile. In order to save the data from this plot, first reopen the Solution XY  Plot menu. Then, select Write to File under Options and click Write.... Enter profile.xy for XY File and click OK . To see how the velocity profile changes in the developing region, we will add profiles at x=0.6m (x/D=3) and x=0.12m (x/D=6) to the previous plot. In order to create the profiles, we must first create vertical lines using the Line/Rake tool. First, (Click) Surface < Line/Rake as shown in the following image.

We'll create a straight line from (x0,y0)=(0.6,0) to (x1,y1)=(0.6,0.1). Select Line  Tool under Options . Enter x0 =0.6, y0 =0,x1 =0.6, y1 =0.1. Enter line1 under New Surface Name . Click Create .

To see the line that you just created,(Click) Display > Mesh . Note that line1appears in the list of surfaces. Select all surfaces except default-  interior . Click Display . This displays all surfaces but not the mesh cells. Zoom into the region near the inlet to see the line created at x=0.6m. (Click here to review the zoom functionality discussion in step 4.) The white vertical line appearing to the right is line1, as shown in the image below.

Similarly, create a vertical line called line2 at x=1.2; (x0,y0)=(1.2,0) to (x1,y1)=(1.2,0.1). Display it in the graphics window to check that it has been created correctly. Now, we can plot the velocity profiles at x=0.6m (x/D=3) and x=0.12m (x/D=6) along with the outlet profile. First, open the Solution XY  Plot menu. Under Surfaces , in addition to outlet , selectline1 and line2 . Make sure Node Values is selected under Options . Now, your Solution  XY Plot menu should look exactly like the following image.

Higher Resolution Image Lastly, click Plot and you should obtain the following output. Your symbols might be different from the ones below. You can change the symbols and line styles under the Curves...button. Click on Help in the Curves menu if you have problems figuring out how to change these settings.

Higher Resolution Image

The profile three diameters downstream is fairly close to the fully-developed profile at the outlet. If you redo this plot using the fine grid results in the next step, you'll see that this is not actually the case. The coarse grid used here doesn't capture the boundary layer development properly and under predicts the development length. In FLUENT, you can choose to display the computed cell-center values or values that have been interpolated to the nodes. By default, the Node Values option is turned on, and the interpolated values are displayed. Node-averaged data curves may be somewhat smoother than curves for cell values.

Step 7: Verification & Validation It is very important that you take the time to check the validity of your solution. This section leads you through some of the steps you can take to validate your solution.

Refine Mesh  Let's repeat the solution on a finer mesh. For the finer mesh, we will use increase the radial divisions from 5 to 10. In the Workbench Project  Page right click on Mesh then clickDuplicate as shown below.

Higher Resolution Image Rename the duplicate project to Laminar Pipe Flow (mesh 2) . You should

have the following two projects in your Workbench Project Page .

Next, double click on the Mesh cell of the Laminar Pipe Flow (mesh  2) project. A new ANSYS Mesher window will open. Under Outline , expand Mesh and click on Edge Sizing , as shown below.

Under Details of "Edge Sizing", enter 10 for Number of Divisions , as shown below.

Higher Resolution Image Then, click Update to generate the new mesh.

The mesh should now have 1000 elements (10 x 100). A quick glance of the mesh statistics reveals that there is indeed 1000 elements.

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Compute the Solution  Close the ANSYS Mesher to go back to the Workbench Project Page . Under Laminar Pipe Flow (mesh 2) , right click on Fluid Flow  (FLUENT) and click on Update , as shown below.

Higher Resolution Image Now, wait a few minutes for FLUENT to obtain the solution for the refined mesh. After FLUENT obtains the solution, save your project.

Velocity Profile  In order to launch FLUENT double click on the Solution of the "Laminar Pipe Flow (mesh 2)" project in the Workbench Project Page . After, FLUENT launches (Click) Plots > XY Plot > SetUp... as shown in the image below.

For this graph, the y axis of the graph will have to be set to the y axis of the pipe (radial direction). To plot the position variable on the y axis of the graph, uncheck Position on X Axis under Options and choose Position on Y  Axis instead. To make the position variable the radial distance from the centerline, under Plot Direction , change X to 0 andY to 1. To plot the axial velocity on the x axis of the graph, select Velocity... for the first box underneath X Axis Function , and select Axial Velocity for the second box. Next, select outlet , which is located under Surfaces . Then, uncheck the Write to File check box under Options , so the graph will plot. Now, your Solution XY Plot menu should look exactly like the following image.

Higher Resolution Image Since we would like to see how the results compare to the courser mesh and the theoretical solution, we will load the profile.xy file, which was created in the previous step. In order to do so, click Load File... in the Solution XY  Plot menu, then select the profile.xy file. Click OK , then click Plot in the Solution XY Plot menu. You should then obtain the following plot.

Higher Resolution Image In the plot above the green dots correspond to the theoretical solution, the red dots correspond to the rough mesh ( 5 x 100 ), and the white dots correspond to the refined mesh ( 10 x 100 ). Note how the refined mesh results resemble the theory signicantly more than the rough mesh.

Further Verification  The plot below shows the results of a further refined mesh ( 20 radial x 100 axial ) and the theoretical results.

Higher Resolution Image Notice that for the further refined mesh, the results are almost indistinguishable from theory.

Problem Specification

Consider the unsteady state case of a fluid flowing past a cylinder, as illustrated above. For this tutorial we will use a Reynolds Number of 120. In order to simplify the computation, the diameter of the pipe is set to 1 m, the x component of the velocity is set to 1 m/s and the density of the fluid is set to 1 kg/m^3. Thus, the dynamic viscosity must be set to 8.333x10^-3 kg/m*s in order to obtain the desired Reynolds number. For this Unsteady Case, the governing equation becomes non linear due to the addition of a time derivative term:

The methods implemented by FLUENT to solve a time dependent system are very similar to those used in a steady-state case. In this case, the domain and boundary conditions will be the same as the Steady Flow Past a Cylinder. However, because this is a transient system, initial conditions at t=0 are required. To solve the system, we need to input the desired time range and time step into FLUENT. The program will then compute a solution for the first time step, iterating until convergence or a limit of iterations is reached, then will proceed to the next time step, "marching" through time until the end time is reached.

1. Pre-Analysis & Start-Up Prior to opening FLUENT, we must answer a couple of questions. We must determine what our solution domain is and what the boundary conditions are.

Solution Domain  For an external flow problem like this, one needs to determine where to place the outer boundary. A circular domain will be used for this simulation. The effects that the cylinder has on the flow extend far. Thus, the outer boundary will be set to be 64 times as large as the diameter of the cylinder. That is, the outer boundary will be a circle with a diameter of 64 m. The solution domain discussed here is illustrated below.

Boundary Conditions  First, we will specify a velocity inlet boundary condition. We will set the left half of the outer boundary as a velocity inlet with a velocity of 1 m/s in the x direction. Next, we will use a pressure outlet boundary condition for the left half of the outer boundary with a gauge pressure of 0 Pa. Lastly, we will apply a no slip boundary condition to the cylinder wall. The aforementioned boundary conditions are illustrated below.

2. Geometry Strategy for Geometry Creation  In order to create the desired geometry we will first create a surface body for the cylinder. Next, we will create a surface body for the outer boundary as a frozen, so that it doesn't merge with the first surface body. Then, we will use a boolean operation to subtract the small surface body from the large surface body. At this point, we will have the surface body of the outer boundary with a hole in the middle where the cylinder is. Lastly, we will project a vertical line on to the geometry, so that radial edge sizing can be implemented in the meshing process.

Fluid Flow(FLUENT) Project Selection  Drag Fluid Flow(FLUENT) into the Project Schematic window.

Analysis Type  (Right Click) Geometry > Properties  Set Analysis Type to 2D 

Launch Design Modeler  (Double Click) Geometry 

Create Inner Circle and Dimension  Create a circle, centered around the origin in the xy plane. Set the diameter of the circle to 1m.

Inner Circle Surface Body Creation  Concept > Surfaces From Sketches . Set the Base Object to Sketch 1 (located underneath XYPlane in the Tree). Click Generate 

Create New Sketch in the XY Plane  In this step we will create a new sketch in the XY Plane. This step is required for the boolean operation that we will carry out later in the geometry process. It allows us to create two distinguishable geometries, in the xy plane. Click on XYPlane in the Tree Outline and it should highlight blue. Then click on the New Sketch button,

.

Create Outer Circle and Dimension  Now, create a circle centered around the origin in Sketch 2 . Set the diameter of the circle to 64m.

Outer Circle Surface Body Creation  In this step the Surface Body will be created as a frozen, such that it does not merge with the inner circle surface body. Concept > Surfaces From Sketches . Set the Base Object to Sketch 2 (located underneath XYPlane in the Tree). Then set Operation to Add Frozen as shown in the image below.

 \  Then, click Generate 

Carry Out Boolean Operation: Subtraction  In this step, the inner circle will be subtracted from the outer circle in order to obtain the desired geometry. Create > Boolean . First, set Operation to Subtract . Next, use the face selection filter,

, to

apply the outer circle surface body as the Target Body . Then, use the face selection filter,

, to apply the inner circle surface body as the Tool Body .

Lastly, click Generate . At this point if you zoom into the center of the circle you

should see the 1m diameter hole, as shown below.

Create a Bisecting Line  The purpose of this step and the following two steps is to imprint a line onto the geometry that will, allow for radial edge sizing in the meshing step. Click on XYPlane in the tree and it should highlight blue. Then, click the new sketch button,

. In the new sketch draw a line on the y axis that goes through

both of the concentric circles. Make sure that it is coincident to the y axis. Then trim the line segments that lay inside of the inner circle and the line segments that lay outside of the outer circle. This, is carried out by using the Trim feature located in the Modify portion of Sketching .

Line Body Creation  Concept > Lines From Sketches . Set the Base Object to Sketch 3. (located underneath XYPlane in the Tree). Click Generate 

Projection  Tools > Projection . Apply the two lines that you created to edge and apply the surface body to target. You must do these steps by using the line selection filter and the surface

selection filter. For the two lines hold down control to select them both. Click Generate .

Save Project and Close Design Modeler 

3. Mesh In this section the geometry will be meshed with 18,432 elements. The geometry will be given 192 circumferential divisions and 96 radial divisions. Mapped face meshing will be used and biasing will be used in order to significantly increase the number of elements located close to the cylinder.

Launch Mesher  (Double Click) Mesh 

Mapped Face Meshing  (Right Click) Mesh > Insert > Mapped Face Meshing  Set Geometry to both portions of the surface body. You will have to hold down control in the selection process in order to highlight both halves. Click Update .

Circumferential Edge Sizing  (Right Click) Mesh > Insert > Sizing  Set Geometry to both edges of the surface body. You will have to use the edge selection filter and you will have to hold down control in the selection process in order to highlight both halves. Set Type to Number of Divisions , set Number of Divisions to 96 and set Behavior to Hard . Click Update to generate the new mesh.

Radial Edge Sizing 1 (Top Half)  (Right Click) Mesh > Insert > Sizing  Set Geometry to the top half of the bisecting line. Set Type to Number of  Divisions , set Number of Divisions to 96 and set Behavior to Hard . Then, set Bias Type to the first option and set Bias Factor to 460. These

selections are shown in the image below.

Radial Edge Sizing 2 (Bottom Half)  (Right Click) Mesh > Insert > Sizing  Set Geometry to the top half of the bisecting line. Set Type to Number of  Divisions , set Number of Divisions to 96 and set Behavior to Hard . Then, set Bias Type to the second option and set Bias Factor to 460. These selections are shown in the image below.

Then, click Update to generate the new mesh. You should obtain the mesh, that is shown below.

Click Here For Higher Resolution

Verify Mesh Size  (Click) Mesh > (Expand) Statistics  You should have 18,624 nodes and 18,432 elements.

Create Named Selections  In this section the various parts of the geometry will be named according to the image below. First create a named selection for the left half of the outer boundary and call it "farfield1". Next, create a named selection for the right half of the outer boundary and call it "farfield2". Lastly, create a named selection for both sides of the inner circle(cylinder) and call it "cylinderwall". When creating the third named selection, make sure that you included both halves of the circle. You will have to hold down control to select both edges.

Save Project 

4. Setup (Physics) Launch Fluent  (Double Click) Setup in the Workbench Project Page .

Double Precision  Select Double Precision .

Parallel Processing  If you are using a computer that has more than one core, it is advantageous to turn on the parallel processing feature of FLUENT. This feature will divide the solution domain amongst the number of cores that you specify. The maximum number of cores that you can specify is 4 for the standard FLUENT package. The Swanson Lab at Cornell University has dual core machines. In order to use both cores, set Processing Options to Parallel (Local Machine) and set the Number of Processes to 2. These selections are shown below.

If you have more cores set Number of Processes to the number of cores you have ( 4 is the limit). Now, when you run your calculations in FLUENT you will have more than one core working for you, which will significantly reduce your computation time. Lastly, click OK .

Check Mesh  (Click) Mesh > Info > Size  You should now have an output in the command pane stating that there are 18,432 cells. (Click) Mesh > Check  You should see no errors in the command pane.

Specify Material Properties  Problem Setup > Materials > Fluid > Create/Edit.... Then set the Density to 1 kg/m^3 and set Viscosity to 0.05 kg/m*s. Click Change/Create then click Close .

Boundary Conditions  FarField1

Problem Setup > Boundary Conditions > farfield1. Set Type to velocity-inlet . Click Edit.... Set Velocity Specification 

Method to Components , set X-Velocity to 1 m/s, and set Y-Velocity to 0 m/s. FarField2

Problem Setup > Boundary Conditions > farfield2.. Set Type to pressure-outlet . Cylinder Wall 

Problem Setup > Boundary Conditions > cylinderwall . Set Type to wall .

Reference Values  Problem Setup > Reference Values . Set the Density to 1 kg/m^3. The other default values will work for the purposes of this simulation.

Save Project 

5. Solution Second Order Upwind Momentum Scheme  Solution > Solution Methods > Spatial Discretization . Set Momentum to Second Order Upwind 

Convergence Criterion  Solution > Monitors > Residuals > Edit.... Set the Absolute Criteria for , x-velocity and y-velocity all to 1e-6. Click ok  Solution > Monitors > Drag > Edit.... Then check Print to Console and Plot . Next, click cylinderwall , which is located under Wall Zones . Lastly, click ok 

Initial Guess  Solution > Solution Initialization . Set Compute From to farfield1. Alternately, you can simply set X  Velocity to 1 m/s. Then, click Initialize .

Iterate Until Convergence  Solution > Run Calculation . Set the Number of Iterations to 2000. Then, click Calculate . (You may have to hit Calculate twice.) Now, have a cup of coffee. The solution should converge after approximately 1647 iterations.

Save Project 

6. Results Velocity Vectors  Results > Graphics and Animations > Vectors > Set Up... Then click Display . The Scale was set to 2 in the plot below.

Higher Resolution Image

Stream Lines  Results > Graphics and Animations > Contours > Set Up... Set Contours of to Velocity.. and set the box below to Stream Function . Make sure Filled is not selected and click Display . The plots below were created by settinglevels to 40, deselecting Auto Range , setting Mi n  (kg/s) to 31 and setting Max (kg/s) to 33.

Higher Resolution Image

Vorticity  Results > Graphics and Animations > Contours > Set Up... Set Contours of to Velocity.. and set the box below to Vorticity  Magnitude . Then click Display . The plot below was created by by setting levels to 60, deselecting Auto Range , setting Min (1/s) to 0.25 and setting Max (1/s) to 9.

Higher Resolution Image

Drag Coefficient  Reports > Result Reports > Forces > Setup  Then, click Print . The command pane will now display the following results: the pressure force, the viscous force, the total force, the pressure force coefficient, the viscous force coefficient and the drag force coefficient. As one can see from the following image link, FLUENT yields 2.04 for the value of the drag coefficient. Drag Coefficient

Problem Specification

This tutorial shows you how to simulate forced convection in a pipe using ANSYS FLUENT 12. The simulation corresponds to the forced convection experiment in MAE 4272 at Cornell University. The diagram shows a pipe with a heated section in the middle where constant heat flux is added at the wall. The ambient air is flowing into the pipe from the left with a uniform velocity. We'll use FLUENT to solve the relevant boundary-value problem and obtain the velocity, temperature, pressure and density distribution in the pipe. Inputs necessary for the simulation, such as the velocity at the pipe inlet and heat flux added at the wall, are obtained from one particular experimental run. Results from the simulation will be compared with corresponding experimental values. Background information is provided in this presentation from MAE 4272 at Cornell University. Your fingers might be itching to launch FLUENT and get busy with the mouse and keyboard. Nevertheless, you will be wellserved by reviewing the presentation before proceeding. That way, you will be better able to apply the solution procedure to new problems. Note to Cornell students enrolled in MAE 4272, Fall 2011: It is best to run FLUENT in the ACCEL lab in the Engineering Library. The CIT labs in B7 Upson and 318 Phillips also have FLUENT. However, there is a video card incompatibility on the CIT computers that appears in the post-processing step. As a result, the temperature contours can look weird. Everything else works fine in the CIT labs. So, alternately, you can go through the simulation in the CIT labs, save your files and load them on to the ACCEL computers to obtain the correct temperature contours.

Simulation Inputs Obtained from Experiment  The following inputs are necessary to specify the domain, boundary conditions and material properties for the Boundary Value Problem (BVP) that we'll solve using FLUENT. The relevant BVP is discussed in presentation mentioned above.

Pipe Geometry: Circular cross-section Pipe radius = 2.94e-2 m Pipe length = 6.045 m Material Properties: Coeff. of viscosity = 1.787e-5 kg/(m s) Cp = 1005 J/(kg K) Thermal conductivity = 0.0266 W/(m K) Molecular weight = 28.97 g/mole Inlet: • u = 25.05 m/s • v = 0 m/s • T = 298.15 K • k = 0.09 m2/s2; epsilon = 16 m2/s3 (These are not measured and are rough

guess values) Outlet: • Pressure = 97225.9 Pa

Wall: • Heating between x = 1.83 m and x = 4.27 m • Wall heat flux = 3473.9 W /m2 • Wall roughness: 0 (assume smooth) • Wall thickness: 0 (assume negligible)

Ambient conditions: • Ambient pressure = 98338.2 Pa

Experimental Data for Comparison with Simulation Results 

Links are provided later to download these .csv files and make comparisons with corresponding simulation results.

Step 1: Pre-Analysis & Start-Up Since the pipe cross-section is circular and heat is applied in an axisymmetric manner, we'll assume that the flow is axisymmetric. In cylindrical polar coordinates, this means that the flow variables depend only on the axial coordinate x and radial coordinate r, and are independent of the azimuthal coordinate θ. Hence we can model the pipe problem with a rectangular domain.

Here R = radius of the pipe, and L = length of the pipe. Rotating the above rectangle 360 degrees about the axis will recover the full pipe geometry.

Start ANSYS FLUENT  This tutorial is specially configured, so the user can have both the tutorial and ANSYS open at the same time as shown below. It will be beneficial to have both ANSYS and your internet browser displayed on your monitor. Your internet browser should consume approximately one third of the screen width while ANSYS should take the other two thirds. We'll run FLUENT within the ANSYS Workbench interface. Start ANSYS workbench: Start > All Programs > ANSYS 13.0 > Workbench The following figure shows the workbench window.

Higher Resolution Image

On the left hand side of the workbench window, you will see a toolbox full of various analysis systems. To the right, you see an empty work space. This is the place where you will organize your project. At the bottom of the window, you see messages from ANSYS. Note to Cornell students enrolled in MAE 4272: You can skip the geometry and mesh steps. Download the mesh by right clicking here and saving the zip file to a convenient location. Unzip the downloaded file (you cannot read in the zip file directly). After unzipping, you should see a file called pipe_flow.wbpj and a folder called pipe_flow_files . Read the mesh into Workbench using File > Open. Browse to the pipe_flow.wbpj file and select it. Then skip to Step 4: Setup (Physics).

Step 2: Geometry Since our problem involves fluid flow, we will select the FLUENT component on the left panel. Left click (and hold) on Fluid Flow (FLUENT) , and drag the icon to the empty space in the Project Schematic . Here's what you get:

Since we selected Fluid Flow (FLUENT), each cell of the system corresponds to a step in the process of performing CFD analysis using FLUENT. Rename the project to Forced Convection. We will work through each step from top down to get to obtain the solution to our problem.

In the Project Schematic of Workbench window, right click on Geometry and select Properties . You will see the properties menu on the right of the Workbench window. UnderAdvance Geometry Options , change the Analysis Type to 2D.

In the Project Schematic , double left click on Geometry to start preparing the geometry. After you launch the web tutorials and FLUENT, you will have to drag the browser window to the width of the largest image (about 350 pixels). To make best use of screen real estate, move the windows around and resize them so that you approximate this screen arrangement

At this point, a new window, ANSYS Design Modeler will be opened. You will be asked to select desired length unit. Use the default meter unit and click OK .

Creating a Sketch  Start by creating a sketch on the XYPlane . Under Tree Outline , select XYPlane , then click on Sketching right before Details View . This will bring up the Sketching Toolboxes . Click Here for Select Sketching Toolboxes Demo

Click on the +Z  axis on the bottom right corner of the Graphics window to have a normal look of the XY Plane. Click Here for Select Normal View Demo

In the Sketching toolboxes, select Rectangle . In the Graphics window, create a rough Rectangle from starting from the origin in the positive XY direction (Make sure that you see a letter P at the origin before you start dragging the rectangle. The letter P at the origin means the geometry is constrained at the origin.) You should have something like this:

Note: You do not have to worry about geometry for now, we can dimension them properly in the later step.

Modify the Sketch  Since we have a heated section in the middle of the pipe, we need to split the geometry appropriately. Click Modify tab and select Split . Select two points at the top of the rectangle, where there will be a heated section. Then select two points at the bottom of the rectangle. Now we can constraint the lower rectangle with the top of the rectangle. Click Constraints tab, select Equal Length . Click the appropriate top and bottom edge and set them to be of equal length. This is shown below:

Dimensions  Under Sketching Toolboxes , select Dimensions tab, use the default dimensioning tools. Then click on the lines and drag upwards or sideways as the case may be to place the dimensions (V1, H2, H3, H4). Note: For horizontal dimensioning (shown in H2, H3 and H4), click first on the horizontal dimension tab under the dimensions tab and then click (turns yellow) on the end points of the split section lines (H2, H3 and H4). Then click on any point on the y-axis and drag up. For the vertical dimensioning (V1), click on the vertical dimension tab under the dimensions tab. Then click on the any point on the x-axis then click on V1 (turns yellow). Then drag V1 to the left side. Dimensioning of the geometry is shown below:

Under Details View on the lower left corner, input the value for dimension appropriately. Then hit enter each time each dimension is entered. V1: 0.0294 m H2: 1.83 m H3: 4.27 m H4: 6.045 m At this point, you should see something like this for your sketch:

Now that we have the sketch done, we can create a surface for this sketch. Then click on Concept tab in the Design modeler window, then click on Surface from sketches . This will create a new surface SurfaceSK1. Under the Tree Outline , click on the X-Y Plane  and select Sketch1 as Base Objects and under Details  View , click Apply . Finally click Generate to generate the surface. Click Here for Create Surface Demo

You can close the Design Modeler and go back to Workbench (Don't worry, it will auto save).

Step 3: Mesh Save your work in Workbench window. In the Workbench window, right click on Mesh , and click Edit . A new ANSYS Mesher window will open. We will create a mesh with 200x30 elements along the pipe. This means that we will divide the pipe with 200 elements in axial direction and 30 elements along the radial direction. In ANSYS Mesher , make sure that the unit we are working on is meter Metric unit. On the top menu, click on Units and make sure that Metric (m, kg, N, s, V, A) is selected. Since we are going to manually specify meshing type and element size, we should turn off ANSYS build-in advanced sizing function. Under Details of  "Mesh" , expand Sizing , select Of f next to Use Advanced Size  Function . Turn off advanced size demo

Meshing Method  We would also like to create a structured mesh where the opposite edges correspond with each other. Let's insert a Mapped Face mesh. Under Outline , right click on Mesh , move cursor to Insert , and select Mapped Face  Meshing . Alternatively, you can click on Mesh Control on the third menu and select Mapped Face Meshing . Finally select the pipe surface body in the Graphics window and click Apply next to Geometry . Mapped Face Demo

Edge Sizing  Now let us move on to specify the element sizing along the pipe radial direction. Outline > Mesh > Insert > Sizing In the Graphics window, select both the left and right edge of the geometry (click on the Edge tab on the Fluid flow Fluent - Mesh window and then press Ctrl + mouse click to multiple select). Under Details of "Edge Sizing" , click Apply next to Geometry . Change the edge sizing definition Type to Number of Divisions . Enter 30 for Number of  Divisions . Radial Sizing

Now continue with the sizing in the axial direction. Outline > Mesh > Insert > Sizing In the Graphics window, select all the top and bottom edge of the geometry (press Ctrl + mouse click to multiple select). Under Details of "Edge  Sizing" , click Apply next toGeometry . Enter 0.03 for Element Size (this will give us roughly 200 divisions). Next to Behaviour , change Soft to Hard (This is to overwrite the sizing function employed by ANSYS Mesher. Try meshing with soft behavior and see what you get). Axial Sizing Demo

We have specified all the meshing conditions. Click Update on the third menu to see the mesh. Mesh and Click on Mesh  and look under Details of "Mesh" , next to Statistics , you Elements for should see that we have 6120 Elements  for our mesh.

Create Named Selection  Next, we will name the edges accordingly so that we can specify the appropriate boundary conditions in the later step. We W e know the bottom edges of the geometry are the centerline of the pipe, the left edge is the inlet of the pipe, the right edge is the outlet of the pipe, top side edges are wall and the top middle edge is the heated wall section. Let's name the edges according to the Edge tab diagram below. Remember to click on the Edge  tab on the Fluid flow Fluent Mesh window and then press Ctrl + mouse click to multiple select the 3 line sections that make up the center line before naming it.

Select the left edge and right click and select Create Named Selection . Enter Inlet and click O K . Under Outline , you will see the Inlet under name Inlet  under Named Selections . Named Selection Demo

Finish naming rest of the edges. Finally, click Update 

.

Step 4: Setup (Physics) Workbench window, In the Workbench  window, this is what you should see currently in the Project Schematic space. Schematic space.

Setup which Double click on Setup  which will bring up the FLUENT Launcher . Click OK  to select the default options in the FLUENT Launcher . Twiddle your thumbs a bit while the FLUENT interface comes up. This is where we'll specify the governing equations and boundary conditions for our boundary-value problem. On the left-hand side of the FLUENT interface, we see various items listed under Problem Setup . We will work from fr om top to bottom of the Problem  Setup items Setup  items to setup the physics of our boundary-value problem. On the right ri ght Graphics pane hand side, we have the Graphics  pane and, below that, Command pane. the Command  pane.

Display Mesh  Let's first display the mesh that was created in the previous step. Problem Setup > General > Mesh > Display...

The long, skinny rectangle displayed in the graphics window corresponds to our

solution domain. Some of the operations available in the graphics window to interrogate the geometry and mesh are: Translation: The model can be translated in any direction by holding down Button and then moving the mouse in the desired direction. the Left Mouse Button and Button and drag a box from Zoom In: Hold down the Middle Mouse Button and Corner to the Lower Right Hand Corner over Corner  over the the Upper Left Hand Corner to area you want to zoom in on. Button and drag a box anywhere Zoom Out: Hold down the Middle Mouse Button and from the Lower Right Hand Corner to Corner  to the Upper Left Hand Corner . Use these operations to zoom in and interrogate our mesh. You should have all the surfaces surfaces shown in the above above snapshot. Clicking on a Display  menu will toggle between select and surface name in the Mesh Display menu unselect. Clicking Display will will show all the currently selected surface entities in the graphics pane. Unselect all surfaces and then select each one in turn to see which part of the domain or boundary the particular surface entity corresponds to (you will need to zoom in/out and translate the model as you do this). For heated_section  should correspond to the part of instance, the surface labeled heated_section should the wall where heating occurs.

Specify Governing Equations  We ask FLUENT to solve the axisymmetric form of the governing equations. General > Solver > 2D Space > Axisymmetric

The energy equation is turned off by default. Turn on the energy equation. Models > Energy - Off > Edit... Turn on the Energy Equation and click OK . By default, FLUENT will assume the flow is laminar. Let's tell it that our flow is turbulent rather than laminar and that we want to use the k-epsilon turbulence model to simulate our turbulent flow. This means FLUENT will solve for mean (i.e. Reynolds-averaged) quantities at every point in the domain. It will add the k and epsilon equations to the governing equations to calculate the effect of the turbulent fluctuations on the mean, as discussed in the powerpoint presentation. Models > Viscous - Laminar > Edit... Under Model , select k-epsilon (2 eqn) . Since we'll use the default settings for the k-epsilon turbulence model, click OK .

This is what you should currently see under Models .

Now let's set the "material properties" i.e. properties of air that appear in our boundary value problem. Materials > Fluid air > Create/Edit... Since variations in absolute pressure are small in our pipe, we'll use a constant absolute pressure in the ideal gas law as discussed in the powerpoint presentation. This is called the "Incompressible ideal gas" model in FLUENT (it's non-standard nomenclature). Change the Density  (kg/m3) from constant to incompressible-ideal-gas . The constant absolute pressure to be used in the ideal gas equation is specified later as Operating Pressure . The other properties are also functions of temperature. However, we'll use constant values equal to the average values over temperature range obtained in the experiment. Enter the following constant values: Cp (Specific Heat) (j/kg-k): 1005 Thermal Conductivity (w/m-k): 0.0266 Viscosity (kg/m-s): 1.787e-5 Molecular Weight (kg/kgmol): 28.97

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Click Change/Create and Close the Create/Edit Materials window.

Specify Boundary Conditions  FLUENT uses gauge pressure internally in order to minimize round-off errors stemming from small differences of big numbers. Any time an absolute pressure is needed, it is generated by adding the so-called "operating pressure" to the gauge pressure: absolute pressure = gauge pressure + "operating pressure" This "operating pressure" is also used in the "incompressible ideal gas" model as mentioned above. We will specify the "operating pressure" as equal to the measured ambient pressure since the absolute pressure in the pipe varies only slightly from this (you do get significant variations in gauge pressures though). Boundary Conditions > Operating Conditions... Enter 98338.2 under Operating Pressure and click OK . Next we will specify the boundary condition for the centerline. Boundary Conditions > centerline Change the Type to axis and click OK . FLUENT will set the flow gradients at this boundary in accordance with the axisymmetric assumption.

Now let's specify the boundary condition at the walls. By default, FLUENT correctly picks the Wall boundary type for these boundaries. It will impose the no-slip condition for velocity at these boundaries. Additionally, for the heated wall section, we need to specify the heat flux into the flow. Boundary Conditions > heated_section > Edit... A new Wall window will open. Click on Thermal tab and enter 3473.9 next to Heat Flux (w/m2) and click OK .

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As discussed in the powerpoint presentation, we need to set: 

velocity and temperature (plus k and epsilon for the turbulence model equations) at the inlet



pressure at the outlet

For incompressible flow, the flow adjusts to the pressure at the outlet (consider this as a signal you are sending the flow about what it needs to do inside the pipe). Select: Boundary Conditions > inlet Note that the boundary Type is automatically set to velocity-inlet . FLUENT has an automatic mechanism to pick a boundary type according to the name you give and settings that you have selected previously (this could be

dangerous if FLUENT selects the wrong boundary type and a lackadaisical user doesn't change it.). In this case, it gets it right. Click Edit... to set up the correct inlet parameters. The Velocity Inlet window pops up. Enter 25.05 next to Velocity Magnitude (m/s) . For Turbulent  Kinetic Energy (m2/s2) , enter value 0.09. For Turbulent Dissipation  Rate (m2/s3) , enter value 16. Note that k and epsilon are not measured and are rough guess values. The results should not be sensitive to these inputs since most of the turbulence is generated in the boundary layers (ideally, you should check the sensitivity of your calculation to this setting).

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Now click on Thermal tab and enter 298.15K for Temperature. Click OK  to close the window. Finally, set up the outlet boundary condition: Boundary Conditions > Outlet FLUENT selects the pressure-outlet boundary type and its guess turns out to be right. Click Edit... to specify the gauge pressure at the outlet. Enter -1112.3 for Gauge Pressure and click Ok . (From experiment, measured outlet pressure is 97225.9 Pa. Corresponding gauge pressure = 97225.9 Pa operating pressure = -1112.3 Pa)

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Now FLUENT knows all necessary elements of our beloved BVP (domain, governing equations and boundary conditions). In the Solution step, we'll prod the beast to obtain an approximate numerical solution to our BVP.

Step 5: Solution FLUENT incorporates advanced algorithms for numerically solving our nonlinear BVP. There are lots of knobs in the Solution menu that you can twiddle to improve your numerical solution to the BVP. We'll not mess with most of these since the default settings yield an adequate numerical solution for our problem. We could get a slight improvement in accuracy by fiddling various knobs which we'll refrain from doing. Let's now investigate how we can achieve a numerical solution in FLUENT. One must keep in mind that the governing equations we are attempting to find an approximate solution to are non-linear. This means that in order for a CFD program, such as FLUENT to solve it, it must go through an iterative process. This process is briefly described in the flow-chart below.

From the flow chart, we see that we need to provide FLUENT with an initial guess for the flow variables (velocity, pressure etc.) to start the iterations. We'll also specify the convergence criterion to let the beast know when to consider the iterative process to have converged to a solution. Let's take a peek under: Solution > Solution Methods In this case, we are using the first order solvers. (If time permits, try using second order solvers and determine what kind of difference it makes to the convergence time and the final solution. This is the one of the first knobs that one twiddles). To set the convergence criterion identified in the flowchart above , select: Solution > Monitors > Residuals - Print, Plot > Edit... We see that we need to provide a convergence criterion for each PDE that is being solved. For this example, we will use the default values. Also make sure Plot box is checked. This will help you monitor how/whether the solution is proceeding to convergence. Click OK .

Next, we set the initial guess indicated in the flowchart. The initial guess can be entered using: Solution > Solution Initialization For this example, we know the conditions at the inlet of the pipe (except for pressure which is set to zero gauge by default). Initialize the entire flowfield to the specified values at the inlet: Under Compute from , select Inlet and click Initialize . To prevent the computer from iterating indefinitely, we need to set an iterations limit. Solution > Run Calculation Enter 500 for Number of Iterations and click Calculate . You will see a window message saying Calculating the solution... Wait for FLUENT to finish the calculation. You should see a residual plot on screen as the computation is being performed. It should look something like this:

Now that the computation is completed, we can go check out the results!

Step 6: Results Please make sure your project is saved in Workbench. Double click on Results in the Project Schematic window. This will open CFD-Post (the program used to analyze results from FLUENT computation.)

Overview  You may have noticed in previous sections, that the pipe looks extremely long and thin on the screen. In fact, due to the axisymmetric assumption, we have

only modeled half of a 2D section through the pipe in our analysis. To be able to make full use of the results, we must: 1) Generate the results for the parameter investigated (e.g. temperature, pressure, velocity). 2) Mirror the result to reflect the result of the full pipe section. 3) Stretch the pipe in the radial direction to better view contours. The results shown below were obtained with a pipe length of 6.096 which is slightly different from the current length of 6.045. So your results might be slightly different from those shown below.

Temperature Contour  Our first challenge is the temperature contour. On the top menu, click on contour

. We will be calling this contour "Temperature Contour", OK  when

done. On the left hand side, Details of Temperature Contour will allow you to select parameters relevant to the results we're looking for. In this example, the Locations is periodic 1, the Variable isTemperature . The number of contours is a personal preference, in this example, we have selected 100. This step tells CFD-Post we are looking to plot contours of temperature.

The next step is to mirror the image, this will make the results more intuitive and easier to understand. From the previous screen, select the View tab. This tab will allow us to adjust the appearance of the contour plot we have just generated. Check Apply Reflection/Mirroring . Select ZX  Plane for Method . Choosing this option reflects the current model in the ZX

plane and allows us to view the "full" pipe section.

Finally, we stretch the pipe in the radial direction. Select Apply Scale . Enter 30 for y-axis. This will stretch our model in the y (radial) direction by a factor of 30. Click Apply . After you click Apply , you will see that under Outline > User Locations and Plots, Temperature Contour is created. You will also see that the Temperature Contour is plotted in the Graphics window on the right.

Under Outline > User Locations and Plots, uncheck Wireframe to see just the Temperature Contour in the Graphics window.

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In developing the experiment, it was assumed that by the end of the adiabatic mixing stage, the flow will be well mixed. Do the results from the numerical solution simulation support this assumption?

Velocity Vectors  Our next challenge is to produce velocity vectors. This is a very similar process to creating the temperature contours above. On the top menu, click on vector

. Name it "Velocity Vector" and click OK . Under Details of 

Velocity Vector , select periodic 1 for Locations . Select Velocity for Variable . This tells CFD-post we are looking for vector plots of velocity. In the next step, we will specify the appearance of vector arrows. Select the Symbol tab. Enter 0.05 for Symbol Size . This again is dependent on personal preference.

Finally click Apply . You will see that under Outline > User Locations and Plots, Velocity Vector is created. Un-check Temperature Contour so that Graphics window shows just the Velocity Vector plot. You can mirror the plot about the axis as before. You can translate the model to look at flow development near the entrance. There is a toolbar option at top that puts you in translate mode. You can click on the z-axis to restore our original view. Does the flow become fully developed at the end of the first section?

Centerline Temperature Plot  Now let's look at the temperature variation along the center-line of the pipe. To do this we need to first create a center-line: Insert > Location > Line Name it "Centerline" and click OK . On the lower left panel, you will see Details  of Centerline . Enter the following coordinates. Point 1 (0,0,0) Point 2 (6.045,0,0) Enter 50 for Samples . (This will be the number of sample points used when plotting data) Click Apply .

You will see centerline created under User Locations and Plots . In the experiment, we are only able to measure the temperature at two points. First, at the inlet of the pipe and second, after the adiabatic mixing stage. The simulation can show us the variation of temperature in between these two points. To create the desired plot: Insert > Chart Please name this chart "Centerline Temperature". You will see Details of  Centerline Temperature appear on the lower left panel. Select the General tab and name the chart "Temperature Variation along Pipe Axis".

Moving on, please select the Data Series tab. This tab will help us specify the source of the chart data. Change the name of the first data series from Series  1 to FLUENT . Under Data Source , specify Centerline as Location . Click Apply . On top of this would would also like to plot the experimental data, which can be downloaded here. Download it to a directory of your choice. Now, click a new data series

. Name it "Experiment". Under Data Source ,

select File and browse for the downloaded experimental data.

Now that we have our data sources, we will proceed by specifying the axes. We want to see the variation of temperature with the length of the pipe. Therefore, temperature will be on the y axis of the chart and x-position on the x axis of the chart. We will start by defining the X-axis: Click on X Axis tab. Next to Variable , choose X .

Now the y axis: Click on Y Axis tab. Next to Variable , choose Temperature .

Now that the chart specifications are defined, we want to customize the display. The default setting is to display all data series using line charts, but since we only have very few experimental points, it would be more logical to display the experimental data using data points: Click on Line Display tab. Select "Experimental" . Next to Line Style , changeAutomatic to None . Next to Symbols , change None to Diamond . Change the color to red. Click Apply .We are now displaying experimental data using data points denoted by red diamonds.

You will see Centerline Temperature created under Report in the Outline tab. This is what you should see in the Graphics window.

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From this it is obvious the experimental data compares quite well to simulation results. This would be more accurate if we had more experimental data points to work with, but as it is not the case, we can only assume that the in between stages match just as well as the inlet and outlet temperatures.

Wall Temperature Plot  We will now investigate the temperature variation along the wall. To do this we need to create a new line on the simulation. It needs to be a horizontal line correponding to the wall. Insert > Location > Line Please name this line "Wall" . On the lower left panel, you will see Details of  Wall . Enter the following coordinates. Point 1 (0,0.0294,0) Point 2 (6.045,0.0294,0) Again 50 for the sample size Click Apply . You will see wall created under User Locations and Plots . Next, we will repeat the previous process, but using this new line as source data. Insert > Chart You will see Details of Wall Temperature appear on the lower left panel. Under General tab, please name the chart "Wall Temperature". Now click on Data Series tab to specify the location of the chart data. Change the name of the first data series from Series 1 to FLUENT . Under Data  Source , specify Wall asLocation . As before, we would also like to compare our simulation result with experimental data. Experimental data can be downloaded here. Now, click a new data series

. Name itExperiment . Under Data Source ,

select File and browse for the downloaded experimental data.

Again in this case, the x-axis is the x-position along the pipe and the y-axis denotes temperature. As previously shown, we will specify how the chart should be displayed. The default setting is to display the data series in lines. Since we only have a few experimental points, we want them to be displayed in data points. Click on Line Display. Then click on experimental tab. Next to Line Style , change Automatic to None . Next to Symbols , changeNone to Diamond . Change the color to red. Click Apply . This is what you should see in the Graphics window.

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The experimental data are a fairly good match for what the simulation has predicted. The wall temperature in the experiment seems to be consistently higher than the simulation in the heated section. We will later check if refining the mesh improves this agreement.

Pressure Plot  Now let's us look at the pressure variation at the centerline. We can use the center-line we created earlier. Next, we will create a chart using this Location data. Insert > Chart Enter "Axial Pressure" as Name . You will see Details of Axial  Pressure appear on the lower left panel. Under General , name the chart "Pressure Variation along Pipe Axis". Now click on Data Series tap to specify the location of the chart data. Change the name of the first data series from Series 1 to FLUENT . Under Data  Source , specifyCenterline as Location . The centerline was already created while doing the temperature variation along the center-line. If that chart was skipped please refer to that section on how to create a centerline. We would also like to compare our simulation result with experimental data. Experimental data is can be downloaded here. Download it to the directory that you like. Now, click a new data series

. Name it Experiment . Under Data 

Source , select File and browse for the downloaded experimental data. Our purpose in this exercise is to study the pressure variation along the length of the pipe. Therefore our chart should show pressure in the y-axis and xposition in the x-axis. In this case, our x-axis variable is x and our y-axis variable is pressure. We want to the chart to be displayed exactly the same way as for wall temperature and centerline temperature plots. This is what you should see in the Graphics window.

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The simulation results follow the experimental data quite closely, the general trend is that pressure decreases (almost linearly) as we move from the inlet towards the outlet of the pipe.

Axial Velocity Profile  Now, let's investigate the velocity profile at different lengths along the pipe. We are especially interested in the flow development before it enters the heated section. Then please divert your attention to the difference heat addition has on flow development.  Axial Velocity Profile before Heated Section

The heated section is from x-positions of 1.83m to 4.27m. To allow us insight into flow development before the heated section, we will begin by creating 4 lines of x-position less than 1.83m. Insert > Location > Line The first line will be to define the inlet. Accordingly, please name this line "Inlet" and click OK . On the lower left panel, you will see Details of Inlet . Enter the following coordinates. The coordinates are entered in terms of (x,y,z). Point 1 (0,0,0) Point 2 (0,0.0294,0)

We want to create a vertical line, parallel to the y axis, so check to make sure that the x and z coordinates are the same for both points. Enter 50 for Samples . Click Apply . Please repeat the process for Preheat 1 (x = 0.6) Preheat 2 (x=1.2) and 3 (x=1.8) To double check, the coordinates for the 4 lines should be: Point 1

Inlet

(0,0,0)

Point 2

(0,0.0294,0)

Preheat1 (0.6,0,0)

(0.6,0.0294,0)

Preheat2 (1.2,0,0)

(1.2,0.0294,0)

Preheat3 (1.8,0,0)

(1.8,0.0294,0)

Check that you have the following under Outline.

Now that we have enough intervals to understand the flow development before the heating. We should create a chart of the velocity profile at these lines. Insert > Chart Enter "First Section Axial Velocity Profile" as Name . Again, Details of First 

Section Axial Velocity Profile will appear and please name the chart "Axial Velocity Profile". Select the Data Series tab to specify the location of the chart data. Change the name of the first data series to Inlet. Under Data Source , specify Inlet as Location . Continue adding Data Source until we added all Inlet, Preheat 1, Preheat 2 , and Preheat 3 . Name them according to the figure shown below.

Now we will specify the X Axis parameter. Click on X Axis tab. Next to Variable , choose Velocity u . Next we will specify the Y Axis parameter. Click on Y Axis tab. Next toVariable , choose Y . Click Apply . You will see First Section Axial Velocity Profile created under Report in the Outline tab.

This is what you should see in the Graphics window.

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Notice preheat 2 and preheat 3 lines yield almost the same velocity profile. This tells us that after preheat 2, the flow his almost fully developed.  Axial Velocity Profile before and after Heated Section

To make things more interesting, let's now compare the velocity profiles before and after the heated section. To do this, we need to first create lines after heated section Insert > Location > Line Name it "Postheat 1" and click OK . On the lower left panel, you will see Details of Postheat 1. Enter the following coordinates. Point 1 (4.27,0,0) Point 2 (4.27,0.0294,0) Enter 50 for Samples . (This will be the number of sample points used when plotting data) Click Apply . Create Postheat 2. Insert > Location > Line Name it "Postheat 2" and click OK . On the lower left panel, you will see Details of Postheat 2 . Enter the following coordinates. Point 1 (5,0,0)

Point 2 (5,0.0294,0) Enter 50 for Samples . Click Apply . Continue the same step for creating line Outlet (x=6.045m). Now we will have enough interval to look at the flow development before and after the heating. Let's create a chart to investigate this. Insert > Chart Enter "Second Section Axial Velocity Profile" as Name. You will see Details of  Second Section Axial Velocity Profile appear on the lower left panel. Under General , give the chart Title as "Axial Velocity Profile". Now click on Data Series tap to specify the location of the chart data. Under Data Source , specify Preheat 3 as Location for the first data series. Change the name to x=1.8m. Continue adding Data Source until we added all Preheat 3, Postheat 1, Postheat 2 , and Outlet . Name them according to the figure shown below.

Now we will specify the X Axis parameter. Click on X Axis tab. Next to Variable , choose Velocity u . Next we will specify the Y Axis parameter. Click on Y Axis tab. Next toVariable , choose Y . Click Apply . You will

see First Section Axial Velocity Profile created under Report in the Outline tab. This is what you should see in the Graphics window.

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What we notice when comparing fully developed flow before and after heated section is that the flow increases in velocity after the heated section. As air is heated, the density decreases. So the velocity has to increase to maintain the same mass flow rate.

Temperature Profile  Now let's us look at the temperature profile before and after the heating section. Insert > Chart Enter "Temperature Profile" as Name. Details of Temperature  Profile appears on the lower left panel, so please name the chart "Temperature Profile". Now click on Data Series tab to specify the location of the chart data. Under Data Source , specify Preheat 3 as Location for the first data series. Change the name to x=1.8m. Similarly, add the locations: Preheat 3, Postheat 1, Postheat 2 , and Outlet . Name them according to the figure shown below.

Now we will specify the X Axis parameter. Click on X Axis tab. Next to Variable , choose Temperature . Next we will specify the Y Axis parameter. Click on Y Axis tab. Next toVariable , choose Y . Click Apply . You will see Temperature Profile created under Report in the Outline tab.This is what you should see in the Graphics window.

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The plot shows temperature is nearly uniform at the outlet (end of mixing section).

Step 7: Verification & Validation

Verification and validation is a formal process for checking results. Each of these terms has a specific meaning which we won't get into here. We'll act like consultants and do the bare minimum: we'll refine the mesh and make sure that the results are nearly independent of the mesh. We will also repeat the comparison with experiment which is a very important way to check simulation results.

Refine Mesh  Let's repeat the solution on a finer mesh with smaller cells. In workbench, under Forced Convection project, right click on Fluid Flow  (FLUENT) and click duplicate. Rename the duplicate project to Force  Convection Refined Mesh . You should have two project cells in workbench.

Double click on Mesh for Forced Convection Refined Mesh . The ANSYS Mesher window will open. Under Outline , expand mesh tree and click on Edge Sizing .

Highlight "Edge Sizing". Under Details of "Edge Sizing", increase Number of  Divisions to 50. This will refine the mesh in the radial direction. Highlight "Edge Sizing 2". Under Details of "Edge Sizing 2", decrease element size to be 0.02. This will refine the mesh in the axial direction. Click Update 

to generate the new mesh. If you refer back to the

mesh details and expand statistics, you will notice that the number of elements has increased to 15300, compared to 5508 of the original mesh.

Close the ANSYS Mesher and go back to Workbench windows. Under Forced  Convection Refined Mesh , right click on Fluid Flow (FLUENT) and click Update . Wait for a few minutes for FLUENT to obtain a solution and update all the results. We would want to compare the solution on the two meshes. To do that, drag the Solution cell of Forced Convection Refined Mesh to Results cell of Forced Convection .

Finally, double click on Results cell of Forced Convection to compare. Under Outline tab, click on the results of interest to analyze (pretty sweet, huh?).

Centerline Temperature 

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Wall Temperature 

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Axial Pressure 

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First Section Axial Velocity Profile 

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Second Section Axial Velocity Profile 

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Temperature Profile 

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Comparison of Results  We can see from the charts comparing the results from the original and refined meshes that the results have changed very little and still compare well with actual simulation results. From this, we can say that our results have meshconverged, refining the mesh further will not improve results. See and rate the complete Learning Module