Laminar Pipe Flow

Laminar Pipe Flow Created using ANSYS 13.0. Tutorial instructions work with ANSYS 14.0 and 15.0. There are minor layout changes in ANSYS 15.0. This tutorial has videos. If you are in a computer lab, make sure to have head phones.

Problem Specification

Consider fluid flowing through a circular pipe of constant radius as illustrated above. The figure is not to scale. The pipe diameter D = 0.2 m and length L = 8 m Consider the inlet velocity to be constant over the cross-section and equal to 1 m/s. The pressure at the pipe outlet is 1 atm. Take density  ρ = 1 kg/ m 3 and coefficient of viscosity µ = 2 x 10 -3 kg/(m s). These parameters have been chosen to get a desired Reynolds number of 100 and don't correspond to any real fluid.

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Solve this problem numerically using ANSYS FLUENT. Present the following results: Velocity vectors Velocity magnitude contours Pressure contours Velocity profile at the outlet Skin friction coefficient along the wall Provide comparisons of the results with the full-developed full -developed analytical solution. sol ution. Verify your results. Go to Step 1: Pre-Analysis & Start-Up

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Pre-Analysis & Start-Up P r e lili m i n a r y A n a l y s i s

Start-Up

Prior to opening ANSYS, create a folder called  pipe in a convenient location. 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: S t a rt rt > A l l P r o g r a m s > A n s y s 1 3. 3. 0> 0> W o r k b e n c h  

The

following

figure

shows

the

workbench

window.

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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 two thirds as shown below.

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Start-Up

Prior to opening ANSYS, create a folder called  pipe in a convenient location. 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: S t a rt rt > A l l P r o g r a m s > A n s y s 1 3. 3. 0> 0> W o r k b e n c h  

The

following

figure

shows

the

workbench

window.

Higher Resolution Image Management o f Screen Real Estate 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 two thirds as shown below.

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If the monitor you are using is insufficient in size, you can press the A l t  and Ta b  keys simultaneously to toggle between ANSYS and your internet browser. Go to Step 2: Geometry

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Geometry For users of ANSYS 15.0, please check this link for procedures for turning on the Auto Constraint feature before creating sketches in DesignModeler. 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. (FLUENT)  LUENT) , and drag the icon into the empty space Left click (and hold) on Fluid Flow (F in the Project Schematic . Your ANSYS window should now look comparable to the image below.

Since we selected Fluid Flow (F , each cell of the system corresponds to a step (FLUENT)  LUENT)  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 P r o j e c t S c h e m a t i c  of the Workbench window, right click on G e o m e t r y  and select Properties , as shown below.

The properties menu will then appear to the right of the Workbench window. Under A d v a n c e Ge o m e t r y O p t i o n s  , change the A n a l y s i s T y p e  to 2D as shown in the image below.

Launch Design Modeler

In the P r o j e c t S c h e m a t i c  , double click on G e o m e t r y  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 Outlin e  , select XYPlane  , then click on S k e t c h i n g  right before Details View . This will bring up the S k e t c h i n g . Toolboxes  Click Here for Select Sketching Toolboxes Demo

Click on the +Z axis on the bottom right corner of the G r a p h i c s  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 G r a p h i c s  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 S k e t c h i n g T o o l b o x e s   , select D i m e n s i o n s  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.

Click Here for Higher Resolution Surface Body Creation

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

This will create a new surface SurfaceSK1  . Under Details View , select S k e t c h 1  as the B a s e O b j e c t s by selecting one of the lines of the sketch and by clicking apply. Then select the thickness to be 0.1m and click Generate to generate the surface. Saving

 At this point, you can close the D es i g n M o d e l e r  and go back to W o r k b e n c h P r o j ec t Page . Save the project by clicking on the "Save As.." button, , which is located on the top of the W o r k b e n c h P r o j e c t Pa g e  . 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", 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 and the folder. If you do not have BOTH, you will not be able to access your project.

Go to Step 3: Mesh

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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 W o r k b e n c h P r o j e c t P a g e ,  then (Dou ble 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 (Righ t 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 > can be seen below. Generate Mesh as

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 Mesh ing . In order to incorporate this meshing style (Click) can be seen below. Mesh Control > Mapped Face M e s h i n g  as

Now, the M a p p e d F a c e M e s h i n g     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) A p p l y  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 E d g e   needs to be inserted. First, (Click) Mesh Con trol > Sizing   as shown below. Sizing 

Now, the geometry and the number of divisions need to be specified. First (Click) Ed ge , 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 A p p l y    under the Details as shown below. of Sizing table

Now,

Then,

change T y p e   to N u m b e r

set N u m b e r

of

of

D i v i s i o n s  as

D i v i s i o n s  to

shown

100

in

as

the

image

shown

below.

below.

Follow the same procedure as for the edge sizing in the radial direction, except select the left and right side instead of the top and bottom and set the N u m b e r o f Di v i s i o n   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

expanding Statistics   under the Details o f Mesh   table. In order to get the desired 500 element mesh the B e h a v i o r  needs to be changed from S o f t   to Hard for both E d g e . In order to carry this out first E x p a n d M e s h     in the tree outline then click E d g e Sizing's  Sizing    and then change B e h a v i o r    to Hard   under the Details of Edge Sizing   table, as shown below.

Then set the B e h a v i o r   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) Edg e 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.

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 W o r k b e n c h Project

P a g e  and

click

the Update

Project button,

.

Go to Step 4: Physics Setup

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Physics Setup Your current W o r k b e n c h P r o j e c t Pa g e  should look comparable to the following image. You should have checkmarks to the right of G e o m e t r y   and Mesh .

Next, the mesh and geometry data need to be read into FLUENT. To read in the data (Righ t Click) Setup > Refresh   in the W o r k b e n c h P r o j e c t Pa g e   as shown in the image below. If the refresh option is not available, simply omit this step.

 After you click U p d a t e,  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 W o r k b e n c h P r o j e c t Pa g e  which will bring up the FLUENT L a u n c h e r .  When the F L U E NT L a u n c h e r  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 double-precision 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.

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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 boundary-value problem. On the left-hand side of the FLUENT interface, we see various items listed under P r o b l e m S e t u p   . We will work from top to bottom of the P r o b l e m S e t u p     items to setup the physics of our boundary-value problem. On the right hand side, we have the G r a p h i c s    pane and, below that, the C o m m a n d   pane. Check and Display Mesh

First, the mesh will be checked to verify that it has been properly imported from W o r k b e n c h .  In order to obtain the statistics about the mesh (Click) Mesh > Info > , as shown in the image below. Size 

Then,

you

should

obtain

the

following

output

in

the C o m m a n d    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 C o m m a n d  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 M e s h D i s p l a y     window to open, as shown below. Note that the N a m e d S e l e c t i o n s  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 M e s h D i s p l a y  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 w a l l ,  o u t l e t ,  and centerline  and then click Display  you should then obtain the following output in the graphics window.

Now, make sure all 5 items under Surfaces are selected. The button next to Surfaces selects all of the boundaries while the 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 L e f t Mouse B u t t o n  and then moving the mouse in the desired direction. Zoom In: Hold down the M i d d l e M o u s e B u t t o n     and drag a box from the Upper Left   over the area you want to zoom in on. H a n d C o r n e r   to the L o w e r R ig h t H a n d C o r n e r   Zoom Out: Hold down the M i d d l e M o u s e B u t t o n  and drag a box anywhere from the L o w e r the U p p e r Right Hand C o r n e r  to Left Hand C o r n e r .  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 A x i s y m m e t r i c   as shown in the image below.

Click Here for Higher Resolution Next, the V i s c o u s M o d e l   parameters will be specified. In order to open the Viscous Model Options Models > Visco us - Lam inar > 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 Mod els > 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 E n e r g y E q u a t i o n    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 D e n s i t y  to 1kg/m^3 (constant) and set the V i s c o s i t y  to 2e-3 kg/(ms) (constant) as shown in the image below.

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

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D e f in e B o u n d a r y C o n d i t i o n s

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

In order to start the process (Click) Bou nd ary Cond itions > inlet > Edit... as shown in the following image.

Click Here for Higher Resolution Note that the B o u n d a r y C o n d i t i o n T y p e  should have been automatically set to velocity-inlet . Now, the velocity at the inlet will be specified. In the Velocity   menu set the V e lo c i t y S p e c i f i c at i o n M et h o d   to C o m p o n e n t s ,  and set the A x i a l -   Inlet  Velocity (m/s) to 1 m/s, as shown below.

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

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Outlet Boundary Condition

First,

select outlet in

the B o u n d a r y

C o n d i t i o n s  menu,

as

shown

below.

Click Here for Higher Resolution  As can be seen in the image above the T y p e  should have been automatically set to p r e s s u r e - o u t l e t.  If the T y p e   is not set to p r e s s u r e - o u t l e t,  then set it to p r e s s u r e -   o u t l e t .  Now, no further changes are needed for the outlet  boundary condition. Centerline Boundary Condition

Select centerline in

the B o u n d a r y

C o n d i t i o n s  menu,

as

shown

below.

Click Here for Higher Resolution  As can be seen in the image above the T y p e   has been automatically set to w a l l   which is not correct. Change the T y p e   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 B o u n d a r y

C o n d i t i o n s  menu,

as

shown

below.

Click Here for Higher Resolution  As can be seen in the image above the T y p e  should have been automatically set to w a l l .  If the T y p e   is not set to w a l l ,  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 Projec t   as shown in the image below.

Go to Step 5: Numerical Solution

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Numerical 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 S o l u t i o n M e t h o d s  then click on M o m e n t u m  and select S e c o n d O r d e r U p w i n d  as shown in the image below.

Click Here for Higher Resolution 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 click on Standard Initialization then , Compute select inlet as shown below. Initialization  f r o m  and

Click

Here

Then, click the Initialize button,

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. This completes the initialization.

Set Convergenc e 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) Monito rs > Residu als > Edit... , as shown in the image below.

Click Next,

Here for Higher Resolution Criterion  change the residual under C o n v e r g e n c e  for c o n t i n u i t y , x -  ,and y-velocity , all to 1e-6, as can be seen below. velocity 

Click Here for Higher Lastly, click OK  to close the R e s id u a l M o n i t o r s    menu.

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Monitor Drag

The following video shows you how to monitor the drag coefficient during iterations in addition to the default residuals. The equation for the drag coefficient is given in this pdf file.

Execute Calculation

Prior, to running the calculation the maximum number of iterations must be set. To specify the maximum number of iterations click on R u n C a l c u l a t i o n  then set the N u m b e r 100, as shown in the image below. of I t e r a t i o n s  to

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  At

this

Here point,

for save

the

Higher project

once

Resolution again.

Go to Step 6: Numerical Results

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Numerical Results The results steps shown below are for the CFD-Post postprocessor that is included in  ANSYS Workbench. For instructions to view the results in the traditional FLUENT postprocessor, click here. Velocity Vector s

The following video shows how to visualize velocity vectors. Summary of the above video: 1. 2. 3. 4. a. b. c. 5. a. b.

At the project schematic, double click on Results Click on the Z axis to view the XY plane Click periodic 1 Add velocity vector Click on vector icon between the Location drop down menu and the Contour icon In the Details menu, select periodic 1 for the Location Click Apply To make the vector symbols smaller In the details menu of Velocity vectors, select the Symbol tab Enter 0.1 for the Symbol Size V e lo c i t y M a g n i t u d e C o n t o u r s

The following video shows how to plot velocity magnitude contours. In order to get a better view of the contours, the video also shows how to stretch the domain in the radial direction as well as reflect it about the axis. Summary of the above video: 1. Click on the Contours icon next to the Velocity Vectors icon 2. 3. 4. 5. 6. a. b. 7.

Name it Velocity Magnitude In the Details of Velocity magnitude, selection periodic 1 for Location In the variable dropdown menu, select Velocity Click Apply To get more contours Scroll down the details geometry tab Enter 51 contours in the # of Contours blank To scale the diagram

a. Click on the View tab inside the Details menu b. Check Apply Scale c. Enter 10 in the radial direction (2nd blank) d. Click Apply 8. Turn off the wireframe by unchecking Wireframe under User Locations and Plots in the main tree 9. To reflect the diagram to better represent a pipe a. Scroll down the View tab b. Check Apply Reflection Mirroring c. In the Method dropdown menu, select ZX Plane

In ANSYS version 14.5, only one half of the pipe cross-section is displayed after using the mirroring option. You can work around this by applying the mirroring condition in the "Default transform" setting instead of the "View" Tab from the above video. To do this select "Default Transform" in the left-hand menu, uncheck "Instancing Info from Domain", check "Apply Reflection" and select to mirror about the ZX Plane.

Velocity Pro file at the Outlet

The following video shows how to plot the velocity profile at the outlet. Summary of the above video: 1. a. b. c. d. e. f. 2. 3. a. b. c. d. e. f. g. h.

Create a line at the outlet Click on the Location icon at the toolbar Select Line Name it Pipe Outlet For Point 1, enter 8 0 0 For Point 2, enter 8 .1 0 Click on Apply Uncheck Velocity magnitude and check Wireframe to verify the location of the two points Plot the axial velocity along this line Click on the Chart icon in the toolbar Name it Velocity Profile Click on the 3D viewer by clicking the tab at the bottom Click on the Data Series tab in Details of Velocity Profile In the Location dropdown menu, select Pipe Outlet Click on the X Axis tab In the Variable dropdown menu, select Velocity U Click on the Y Axis tab

i.

In the Variable dropdown menu, select Y (radial distance)

 j. Click Apply and you should see a plot in the Chart Viewer tab to the right 4. To export the data to Excel, in the Details of Velocity Profile, click Export

Tip: You can increase the number of Samples   along the "Pipe Outlet location" to get a smoother curve (though it might not make a difference here since the radial mesh is very coarse). See snapshot below.

Ax ial Variation of Pressure

The following video shows how to plot the pressure variation along the wall and the axis.

Summary of the above video: 1. Go to 3D Viewer tab 2. To plot the pressure along the centerline a. In the toolbar, click on the Location dropdown menu b. Select Line c. d. 3. a.

For Point 1, enter 0 0 0 For Point 2, enter 8 0 0 To plot the pressure along the pipe wall, duplicate Centerline under User Locations and Plots For Point 1, enter 0 0.1 0

b. For Point 2, enter 8 0.1 0 4. Create a Chart by clicking the Chart icon in the toolbar a. Name this Axial Pressure Variation b. c. d. e.

In the Details menu, click on the Data Series tab In the Locatin dropdown menu, select Centerline Click on the X Axis tab For the Variable dropdown menu, select X

f. Click on the Y Axis tab g. For the Variable dropdown menu, leave as pressure h. Go back to Data Series tab i. Add another line by clicking on the New Icon  j. For Location dropdown menu, select Pipe Wall

You can increase the number of S a m p l e s   for "Centerline" and "Pipe Wall" locations to get smoother curves. S k i n F r i c t i o n C o e f f i c i en t

The video below explains how the skin friction coefficient is calculated in FLUENT and the need for setting reference values.

To plot the skin friction coefficient in CFD Post, follow the steps in the video below. Summary of the above video: 1. 2. 3. 4. 5. 6. 7. a.

Go to the Project Schematic page, click on Solution In Fluent, under Reference values, make sure the density and velocity are of value 1 Click on File > Data File Quantities, select Skin Friction Coefficient Click on Run Calculation tab > Calculate Go back to Project Schematic Double click on Results Create a Chart by clicking on the Chart Icon in the toolbar Name it Cf

b. Click on the Data Series tab in Details of Cf window c. For the Location dropdown menu, select Pipe Wall d. For the X Axis tab, select Variable X e. For the Y Axis tab, select Variable Skin Friction Coefficient f. Press Apply 8. To get a smoother plot a. b. c. d.

Go to Pipe Wall in the tree Scroll down in Geometry tab Increase Sample to 100 Press apply

Go to Step 7: Verification & Validation

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Verification & Validation It is v e r y im p o r t a n t  that you take the time to check your solution. This section leads you through some checks on the solution.

Check Boundary Conditions

In the previous step, we already checked that the FLUENT solution satisfies the boundary conditions on velocity. One can check the boundary condition on pressure in a similar fashion.

Check Mass Imbalance

On the menu bar, click on Report > Result Repo rts  . Make sure F l u x e s is highlighted and click Set Up ... . Check that Mass Flow Rate is selected before selecting all the boundaries except i n t e r i o r - s u r f a c e _ b o d y, as shown in the figure below.

Check Momentum Imbalance

The following video shows you how to evaluate the momentum imbalance in the axial direction. This pdf file derives the equation to implement.

Check Discretization Error

Let's repeat the FLUENT solution on a finer mesh. For the finer mesh, we will increase the number of radial divisions from 5 to 10. In the W o r k b e n c h P r o j e c t P ag e  right click on Mesh then click D u p l i c a t e  as shown below.

Higher Resolution Image Rename the duplicate project to L a m i n a r P i p e F l o w ( m e s h 2 )  . You should have the following two projects in your W o r k b e n c h Project P a g e  .

Next, double click on the Mesh cell of the L a m i n a r P i p e F l o w ( m e s h 2 )  project. A new  ANSYS Mesher window will open. Under O u t l i n e  , expand Mesh and click on E d g e as shown below. Sizing ,

Under Details of "Edge Sizing", enter 10 for N u m b e r o f Di v i s i o n s  , as shown below.

Higher

Resolution

Image

Sometimes, you need to turn-off "Advanced Size Function" under "Details of Mesh" to get the mesher to accept the modified settings. That way the Advanced Size Function feature will not over-ride your settings (this feature is useful for meshing complex geometries). Click Mesh in the tree and turn off Advanced Size Function under "Details of Mesh" as shown below.

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 are indeed 1000 elements.

Higher Resolution Image

Compute the Solution

Close the ANSYS Mesher to go back to the W o r k b e n c h P r o j e c t P ag ag e  . Under L a m i n a r Pipe Flow (mesh 2) , right click on Fluid Flow (F (FLUENT)  LUENT) and click on U p d a t e  , 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. It is necessary to check that the solution iterations have converged. Launch FLUENT by double clicking on S o l u t i o n  of the "Laminar Pipe Flow (mesh 2)" project in P a g e  . After FLUENT launches, select M o n i t o r s > R e s i d u a ls ls the W o r k b e n c h P r o j e c t Pa then P l o t  , as shown in the images below. > Edit... and

It looks like my solution hasn't converged, so I need to run more iterations by selecting R u n C a lc lc u l a t i o n  . You may want to increase the number of iterations to, say, 1000. Ensure that you have a converged solution and save the project.

If you double-click on Results for mesh 2 in the project page, you'll see that all results have been updated for the new mesh. Also, you can drag S o l u t i o n  for the original mesh on to Results for mesh 2 in the project page. CFD-Post will automatically add the results from the original mesh to the plots for mesh 2. For instance, you will get the velocity profiles for both meshes in the same plot and you can export that to Excel and compare with the full-developed analytical solution. For instructions to compare results in the traditional FLUENT post-processor, click here and scroll down.

Check Against Hand Calculations

The following figure shows the comparison of the velocity profile at the outlet. Note that the green line represents hand calculated values.

Go to Exercises

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Exercises Exercise 1: Vertical Channel Flow Problem Specification (pdf file)

Exercise 2: Laminar Flow within Two Rotating Concentric Cylinders C o n t r i b u t e d b y P r o f . J o h n C i m b a l a an d M a t th e w E r d m a n , Th e P e n n s y l v a n i a S t at e U n i v e r s i t y

Problem Specification (pdf file) The video below shows how to use ANSYS Fluent to set up and solve a problem like this.

Exercise 3: Laminar Pipe Flow Consider developing flow in a pipe of length L = 8 m, diameter D = 0.2 m, ρ = 1 kg/m3 , µ =2 × 10^−3 kg/m s, and ent rance velocity u_in = 1 m/s (the conditions specified in the Problem Specification section). Use FLUENT with the "second-order upwind"

scheme for momentum to solve for the flowfield on meshes of 100 × 5, 100 × 10 and 100 × 20 (axial divisions × radial divisions). 1. Plot the axial velocity profiles at the exit obtained from the three meshes. Also, plot the corresponding velocity profile obtained from fully -developed pipe analysis. Indicate the equation you used to generate this profile. In all, you should have four curves in a single plot. Use a legend to identify the various curves. Axial velocity u should be on the abscissa and r on the ordinate.

2. Calculate the shear stress Tau_xy at the wall in the fully-developed region for the three meshes. Calculate the corresponding value from fully-developed pipe analysis. For each mesh, calculate the % error relative to the analytical value. Include your results as a table:

3. At the exit of the pipe where the flow is fully -developed, we can define the error in the centerline velocity as

where u_c is the centerline value from FLUENT and u_exact is the corresponding exact (analytical) value. We expect the error to take the form

where the coefficient K and power p depend upon the order of accuracy of the discretization. Using MATLAB, perform a linear least squares fit of 

to obtain the coe fficients p and K. Plot ϵ vs. ∆r (using symbols) on a log -log plot. Add a line corresponding to the least- squares fit to this plot. Hint: In FLUENT, you can write out th e data in any "XY" plot to a file by selecting the "Write to File" option in the Solution XY Plot menu. Then click on Write and enter a filename. You can strip the headers and footers in this file and read this into MATLAB as column data using the load function in MATLAB.

4. Let's see how p changes when using a first -order accurate discretization. In FLUENT, use "first-order upwind" scheme for momentum to solve for the flowfield on the three meshes. Repeat the calculation of coe fficients p and K as above. Add this ϵ vs. ∆r data (using symbols) to the above log-log plot. Add a line corresponding to the least-squares fit to this plot. In all, you should have four curves on this plot (two each for second - and first-order discretization). Make sure you include an appropria te legend in the figure. Contrast the value of p obtained in the two cases and briefly explain your results (2 3sentences). Hint: To interpret your results, you should keep in mind that the first or second -order upwind discretization applies only to the inertia terms in the momentum equation. The discretization of the viscous terms is always second-order accurate. Go to Comments

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Comments Do you have any questions or comments about this tutorial? To post comments and to see all previous discussion posts on this tutorial, please click on the following link: Piazza Discussion - Laminar Pipe Flow First time using our Piazza discussion board? Please click on the following link to enroll in our class: Piazza Sign-Up Tutorial Don't worry, it is quick and easy! After enrollment, you will be able to access the discussion pages for all SimCafe tutorials. Rest assured that you can post anonymously if you wish. Go to all FLUENT Learning Modules

Turbulent Pipe Flow Created using ANSYS 13.0 This tutorial has videos. If you are in a computer lab, make sure to have head phones.

Problem Specification

Let's revisit the pipe flow example considered in t he previous exercise. As before, the inlet 3 velocity is 1 m/s, the fluid exhausts into the ambient atmosphere and density is 1 kg/m . For µ = -5 2 x 10 kg/(ms), the Reynolds no. based on the pipe diameter and average velocity at the inlet is

This change of viscosity has taken us from a Reynolds number of 100 to 10,000. At this Reynolds number, the flow is usually completely turbulent. We'll solve this problem numerically using ANSYS FLUENT. Among the results we'll look at are centerline velocity, skin friction coefficient and the ax ial velocity profile at the outlet. Go to Step 1: Pre-Analysis & Start-Up

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Pre-Analysis & Start-Up Preliminary Analysis

A turbulent flow exhibits small-scale fluctuations in time. It is usually not possible to resolve these fluctuations in a CFD calculation. So the flow variables such as velocity, pressure, etc. are time-averaged. Unfortunately, the time-averaged governing equations are not closed. (i.e. They contain fluctuating quantities which need to be modeled using a turbulence model.) No turbulence model is currently available that is valid for all types of flows and so it is necessary to choose and fine-tune a model for particular classes of flows. In this exercise, you'll be turned loose on variants of the k-ε model. But in the real world, tread with great caution: you should evaluate the validity of your calculations using a turbulence model very carefully (which, ahem, means that there is no getting away from studying fluid dynamics concepts and numerical methods very carefully). FLUENT should not  be used as a  black box. The k-ε models consist of two differential equations: one each for the turbulent kinetic energy k and turbulent dissipation ε. These two equations have to be solved along with the timeaveraged continuity, momentum and energy equations. So turbulent flow calculations are much more difficult and time-consuming than laminar flow calculations. This is an ex ercise to whet your appetite for turbulent flow calculations.

 Start ANSYS FLUENT

Since the flow is axisymmetric, the geometry is a rectangle as in the Laminar Pipe Flow tutorial. We will first use a 100x30 mesh (i.e. 100 divisions in the axial direction and 30 divisions in the radial direction). We could create this mesh from scratch, as in th e Laminar Pipe Flow tutorial, but instead, we will modify the previous 100x5 to get the 100x30 mesh. This will introduce you to the art of modifying meshes in the ANSYS Workbench Mechanical Mesher. Go to Step 2: Geometry

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Geometry For this tutorial we are going to be using the same geometry that we created in the previous tutorial. Once you have completed the Laminar Pipe Flow tutorial, you can open the saved  project and use it as a template for this tutorial. Go to Step 3: Mesh

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Mesh You should have completed the Laminar Pipe Flow tutorial before continuing with this one. The starting point for this tutorial is the ending point of the on e before it. If you bring up the project we have already completed, you can follow the next steps. Right click on Mesh . Then click on Duplicate , which will duplicate the mesh from the previous tutorial. Enter "Turbulent Flow" in the highlighted field to rename it. At this point your project schematic window should appear as below:

 Next, double click on the Mesh cell so we can edit the mesh.

We need to change the edge sizing, as we did in the previous tutorial, to 100 by 30 (instead of 100 by 5). We are also going to need to bias it. This is because we want smaller divisions the closer you get to the wall. First, right click o n Edge Sizing 2  in the Project tree on the left, and click Delete to remove the existing edge sizing on the inlet and outlet.  Next, we'll apply an edge sizing with bias to the inlet, the left end of the pipe. Click Mesh Control > Sizing . Using the edge selection tool, highlight the inlet (left end) of the pipe and click Apply next to Geometry. As in the Laminar Pipe Flow tutorial, change Type to Number of Divisions , and enter 30. Change Behavior  to Hard. Now, let's apply a bias to the edge sizing. Under Bias Type, select the second option, - –  —  ----. Enter a Bias Factor of 10. Your Details of "Edge Sizing 2" should now appear like the image below.

 Now we would like to apply an edge sizing to the outlet, the right end of the pipe. Once again, we'll use 30 divisions, with a bias factor of 1 0 and with the smaller divisions at the top, near the wall. This time, when selecting Bias Type, choose the first option, ---- —  –  -. This will put the smallest divisions at the top. Other than this, the procedure is the same as for the inlet. When complete, your Details of "Edge Sizing 3" should look like this:

Right click on Mesh and select "Generate Mesh". The bias factor generates a finer mesh near the  pipe wall. This is done to compute the small fluctuation in fluid property near the wall.

 Next, close the meshing window to return to the main project view. Recall that we created the following boundary types for the 100x5 mesh in the Laminar Pipe Flow tutorial: Edge Position Name

Type

Left

inlet

VELOCITY_INLET

Right

outlet

PRESSURE_OUTLET

Top

wall

WALL

Bottom

centerline AXIS

Go to Step 4: Physics Setup

Go to all FLUENT Learning Modules Useful Information Click here for the FLUENT 6.3.26 version.

Physics Setup Launch FLUENT

We will be working within ANSYS Workbench. To launch FLUENT, double click on the Setup  cell from the Project view. Make sure the Doubl e Precision  option is selected. This will use 64  bits (rather than 32) per floating point number, decreasing round-off errors.

Once Fluent has opened, select Problem Setup > General > Display... Make sure all 5 items under Surfaces   are selected. Then click Display  . Remember that we can zoom in using the middle mouse button. Zoom in and admire the mesh. How many divisions are there in the radial direction?

Recall that you can look at specific components of the mesh b y choosing the entities you wish to view under Surfaces   (click to select and click again to deselect a specific boundary). Click  again when you have selected your boundaries. Use this feature and make sure that the Display   boundary labels correspond to the correct geometric entities. Define Governing Equations

Problem Setup > General > Solver

Choose Axisymmetric   under 2D Space  . As in the laminar pipe flow tutorial, we'll use the defaults of Pressure-Based Type, Steady flow and Absolute Velocity Formulation. Problem Setup > Models > Energy...

The energy equation can be turned off since this is an incompressible flow and we are not interested in the temperature. Make sure En ergy - Off  appears. Problem Setup > Models > Viscous - Laminar

Click Edit... and choose k-epsilon (2eqn) . Notice that the window expands and additional options are displayed on choosing the k-epsilon turbulence model. Under Near-Wal l Treatment  ,  pick En hanced Wall Tr eatment  . This option uses a blended function to go between a two-layer model and standard wall functions. If the mesh ne ar the wall is fine enough, the two-layer model is used. Otherwise, standard wall functions are used. You cou ld alternately use Standard Wall ; this will work well when 30 < y+ < 100. Refer to the turbulence chapter in the Functions  FLUENT user manual.

Click OK . Problem Setup > Materials

Double click on air  and change Density   to 1.0 kg/m^3 and Viscosity   to 2e-5 kg/(m*s). These are the values in the Problem Specification and are picked to give us a Reynolds number of 10,000. We'll take both as constant.

Click Change/Create   and close the window. Define Boundary Conditions

Problem Setup > Boundary conditions > Operating Conditions...

Recall that for all flows, FLUENT uses the gauge pressure internally. Any time an absolute  pressure is needed, it is generated by adding the operating pressure to the gauge pressure. We'll use the default value of 1 atm (101,325 Pa) as the Oper atin g Pr essur e  . Click Cancel  to leave the default in place. We'll now setup the boundary conditions at the wall, centerline, inlet and outlet. Problem Setup > Boundary conditions

We don't need to set any parameters for the pipewall   zone. FLUENT will automatically detect that this location should be set as a wall based on its name. Verify this by selecting that zone and looking at its type in the drop down menu.  Next, let's look at the centerline. Since we are solving an axisymmetric problem, we will set the centerline as the axis; this will impose symmetry at this boundary. Set centerline   to axis  boundary type, using the drop down menu. Click Yes   and OK  to confirm.

Choose inlet and click on Edit..... This boundary is set to velocity-inlet   type by default which is right in our case. Change the Velocity Specif ication M ethod   to M agni tude, Normal to . This indicates that the fluid is coming in n ormal Boundary. Enter 1 m/sfor Velocity M agni tude  to the inlet at the rate of 1 meter per second. Select I ntensity and H ydraul ic D iameter   next to the . Then enter 1% for Tur bulence I ntensity   and 0.2m for Tu r bul ence Specif icati on M ethod  H ydraul ic D iameter  . Click OK  to set the boundary conditions for the inlet.

The (absolute) pressure at the outlet is 1 atm. Since the operating pressure is set to 1 atm, the outlet gauge pressure = outlet absolute pressure - operating pressure = 0. Choose outlet   under . The Type   of this boundary is pressure-outlet  . Click on Edit. The default value of the Zone   is 0. Click Cancel  to leave the defaults in place. Gauge Pr essur e   Note: Backflow in the Pressure Outlet  menu refers to flow entering  through an outlet boundary. This is not likely to happen in this case. So we don't have to set the backflow parameters. This completes the boundary condition specification. Reference Values

Let's setup the reference values, which will be used later on while viewing non-dimensional results (this setting doesn't affect the numerical solution). Problem Setup > Reference Values Select Compute from > in let  . Go to Step 5: Numerical Solution

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Numerical Solution

We'll use second-order discretization for the momentum equation, as in the laminar pipe flow tutorial, and also for the turbulence kinetic energy equation which is part of the k-epsilon turbulence model. Solution > Solution Methods

Change the Discretization for Momentum  , Turbulence Ki netic Energy   and Turbulence  equations to Second Order U pwind   (if you do not see all of the equations scroll Di ssipati on Rate  down to see them).

The order of discretization that we just set refers to the convective terms in the equations; the discretization of the viscous terms is always second-order accurate in F LUENT. Second-order discretization generally yields better accuracy while first-order discretization yields more robust convergence. If the second-order scheme doesn't converge, you can try starting the iterations with the first-order scheme and switching to the second-order scheme after some iterations.  Set Convergence Criteria

Recall that 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.

Solu ti on > M onit ors > Residu als, Statistic and For ce M oni tors 

Double click on Residuals. Notice that Conver gence Cr iteri on   has to be set for the k  and epsilon equations in addition to the three equations in the last tutorial. Set the Conver gence Cr it eri on   to  be 1e-06 for all five equations being solved. Select Pri nt to Console   and Plot   under Options   (these are the defaults). This will print as well  plot the residuals as they are calculated which you will use to monitor convergence.

Click OK .  Set Initial Guess

We'll use an initial guess that is constant over the entire flow domain and equal to the values at the inlet: Soluti on > Soluti on I ni tiali zation > Standard I ni tiali zation 

In the Solution Initialization menu that comes up, choose inlet   under Compute F rom . The Axial Velocity   for all  cells will be set to 1 m/s, the Radial Velocity   to 0 m/s and the Gauge Pr essur e   to 0 Pa. The Tur bulence Kinetic Energy   and Di ssipati on Rate  (scroll down to see it) values are set from the prescribed values for the Turbulence Intensity and Hydraulic Diameter  at the inlet.

Click Initialize   (this is easy to overlook). This completes the problem specification. Save your project. Iterate Until Convergence

Solve for 700 iterations. Soluti on > Run Calculation 

In the Iterate menu that comes up, change the Number of I terations   to 700. Click Calculate  . The solution converges in a total of about 220 iterations. You may get a different number of iterations to convergence depending on your mesh and software version.

Click here to see a higher resolution image. We need a larger number of iterations for convergence than in the laminar case since we have a finer mesh and are also solving additional equation s from the turbulence model.  Setup Data Export

In addition to the standard data quantities, we would also like to view the results for the Skin Friction Coefficient. This quantity is not transferred to the post-processor by default; so we hav e to do it manually. F il e > Data F il e Quantiti es 

Under Additional Quantiti es  , select Skin F ri ction Coeff icient  , which should be roughly half way down. Your window should now look like this:

Go to Step 6: Numerical Results

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Numerical Results After the solution is complete, close the FLUENT window to return to the Workbench window. Double click Results   in the main Workbench window to open CFD Post, where we will be viewing the results. For a basic orientation on how to use CFD Post, pl. see the videos in the results step of the Laminar Pipe Flow tutorial. The following instructions show only how to view results using the "chart" option. But one should really start by viewing velocity vectors, velocity/pressure/TKE contours etc. and check that the solution looks basically right. The Laminar Pipe Flow tutorial walks you through the steps to view vectors and contours in CFD Post. Locations

Before viewing the results, we need to define the locations in CFD Post where we would like to view the results, namely the wall, centerline, and outlet.

I nsert > L ocation > L ine 

Rename this location "Pipe Wall". Avoid naming locations in CFD Post with identical names to those used in FLUENT, this can cause problems. We will define the line by two points. Enter (0,0.1,0) for Point 1   and (8,0.1,0) for Point 2  . Change Samples   to 100. Repeat the process for the two other locations needed:

 Name

Point 1 Point 2

"Pipe Centerline" (0,0,0) (8,0,0) "Pipe Outlet"

(8,0,0) (8,0.1,0)

 y+

Turbulent flows are significantly affected by the presence of w alls. The k-epsilon turbulence model is primarily valid away from walls and special treatment is required to make it valid near walls. The near-wall model is sensitive to the grid resolution which is assessed in the wall unit  y+(defined in section 10.9.1 of the FLUENT user manual). We'll gloss over the details for now and use the following rule of thumb: select the near-wall resolution such that y+ > 30 or < 5 for the wall-adjacent cell when using the En han ced Wall Tr eatment   option. Look at section 10.9, Grid Considerations for Turbulent Flow Simulations, for details. Let's plot y+ values for wall-adjacent cells to check how it compares with the recommendation mentioned above. I nsert > Chart 

Let's rename the graph "Wall Y plus". Also, change Title   to "Wall Y plus". Data Series Tab Rename the data series to "Y plus". Next, change Location   to Pipe Wall.

X Axis Tab Change Variable   to X . Y Axis Tab Change Variable   to Yplus  .

Click Apply   and our chart should appear.

As we can see, the wall _y+_value is between roughly 1.35 and 2.45. Since this is less than 5, the near-wall grid resolution is acceptable. Export the data to a .csv file ("comma separated values") by clicking on Export  . This file can be opened in Excel.

Centerline Velocity

 Next, we would like to make a graph of the axial velocity along the centerline. We will do this  by creating another chart. Insert > Chart Rename this chart "Centerline Velocity", and change the title of the chart as well. Data Series Change Name   to "Centerline Velocity", and this time set Location   to "Pipe Centerline". X Axis Once again, change Variable   to X .

Y Axis Change Variable   to Velocity u  , which corresponds to the Axial Velocity.

Click Apply   and our chart should appear.

Coefficient of Skin Friction

The definition of the skin friction coefficient was discussed in the laminar pipe flow tutorial. Once again, insert another chart, naming and titling it Coefficient of Skin Friction. Rename the data series and choose Pipe Wall for Location. Plot X on the X Axis and the Skin Friction Coefficient on the Y Axis. When complete, your chart should match the image below:

We can see that the fully-developed value is 0.0085. Compare this with what you'd expect from the Moody chart. Velocity Profile

We'll plot the axial velocity at the outlet as a function of the distance from the center of the pipe. Insert another chart, naming and titling it "Outlet Velocity". Change the name of the data series, and set the Location to Pipe Outlet. This time, put Velocity u on the X Axis and Y on the Y Axis. When complete, your chart should appear as below:

The axial velocity is maximum at the centerline and zero at the wall to satisfy the no-slip  boundary condition for viscous flow. Compare qualitatively the near-wall velocity gradient normal to the wall with the laminar case. Which is larger? From this, what can you say about the relative strengths of near-wall mixing in the laminar and turbulent cases? Non-dimensional Velocity Profile

To create a nondimensional version of the velocity profile, we first create a variable for r/D as shown in the the following video. Summary of the above video: 1. In the right preview window, select Chart Viewer (Outlet Velocity selected in the tree) 2. Go to Expressions tab in the same row as Outline 1. Right click Expressions > New 2. Name "r nondim exp" 3. For Definition 1. Right click > Variables > Y 2. Insert /0.2[m] after Y 3. Apply 3. Go to Variables tab next to Outline 1. Right click on Derived > New 2. Name it r nondim 3. For Expression, select "r nondim exp"

Then we make a plot of r/D vs. u/U using the steps shown below.

Summary of the above video: 1. Go to Outline tab 2. Highlight Outlet Velocity Chart > Right click > Duplicate 1. Name it Outlet Velocity nondim 3. Go to Chart Viewer in the right preview 1. Double click on Outlet Velocity nondim to ensure you are editing this new version 2. Click on the Y Axis 3. Select Variable r nondim 4. Apply

The axis labels and legend can be modified as shown below. Summary of the above video: 1. In the General Table 1. For Title, enter Nondimensional Velocity Profile 2. Apply 2. In the X Axis 1. Scroll down and uncheck Use data for axis labels 2. Enter in Custom Label u/U 3. In the Y Axis 1. Scroll down and uncheck Use data for axis labels 2. Enter in Custom Label r/D 4. In the Line Display 1. Double click on Series 1 (Pipe Outlet) 2. Uncheck Use series name for legend name 3. Rename to Re = 10,000

We add the corresponding laminar profile. The n ecessary csv file can be downloaded here. Summary of the above video: 1. Make sure you are editing Outlet Velocity nondim by double clicking on it 2. Go to Data Series tab 1. In the white space, right click > New 2. Click File 3. Select csv file downloaded from webpage 4. Apply 3. Go to Line Display 1. Double click on the second curve 2. Uncheck Use series name for legend name 3. Name the Legend Name Laminar 4. To save a copy of the chart, click on Save Picture icon in top toolbar

Non-dimensional Turbulent Viscosity Profile

Summary of the above video: 1. Start FLUENT 2. Go to File > Data File Quatntities 1. Make sure Turbulent Velocity is selected, press OK 3. Go back to FLUENT, click on Run C alculation 1. Enter 1 in Number of Iterations 2. Calculate 4. Go back to Project Schematic 1. Right click on Results > Refresh 5. Go to CFD Post 1. Click on Expressions tab 2. Right click on Expressions > New 3. Name it mut nondim exp 4. In Definition white space: 1. Right click > Variables > Eddy Viscosity 2. Insert + 2e-5[kg/m/s] 3. Divide whole thing by molecular viscosity 2e-5[kg/m/s] 5. Apply 6. Go to Variables tab 1. Right click Derived > New 2. Name it mut nondim 3. Click Expression > select mut nondim exp 7. Go to Outline > click on Chart icon in top toolbar 1. Name it mut nondim plot 2. Click on Data series 1. Location Pipe Outlet 3. Click on X Axis 1. Variable mut nondim 4. Click on Y Axis 1. Variable r nondim 5. Apply

Tips on plotting additional derived quantities (such as velocity gradient)

In order to plot additional derived quantities such as the gradient, divergence or curl of the velocity field, you may find these quantities in a pop-up window in CFD post. Look at the illustration below for plotting velocity gradient in x.

Go to Step 7: Verification & Validation

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Verification & Validation Useful Information Click here for the FLUENT 12 version. In order to assess the numerical accuracy of th e results obtained, it is necessary to compare results on different meshes. We'll re-do the calculation on a 100x60 mesh which has twice the number of nodes in the radial direction as the 100x30 mesh. In Workbench, under Tur bulent Fl ow   project, right click on Fluid F low (FL UENT)   and click duplicate. Rename the duplicate project to Tur bulent F low Refi ned M esh  . You should have three project cells in workbench.

Double click on M esh  for Tur bulent F low Refi ned M esh  . The ANSYS Mesher window will open. Under Outline  , expand mesh tree and click on Edge Sizing 2  . Highlight "Edge Sizing 2". Under Details of "Edge Sizing 2", increase Number of D ivisions   to 60. This will refine the mesh in the radial direction at the inlet. Highlight "Edge Sizing 3". Under Details of "Edge Sizing 3", increase Number of D ivisions   to 60. This will refine the mesh in the radial direction at the outlet. Click Update   to generate the new mesh. Close the ANSYS Mesher and go back to Workbench windows. Under Tur bulent Fl ow Refi ned , right click on Fluid Fl ow (FL UENT)   and click Update  . Wait for a few minutes for M esh  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  to Results   cell of Tur bulent Fl ow  . Tur bulent F low Refi ned M esh  Double click the Results   cell of Tur bulent Fl ow  , and after CFD Post opens, we can compare our results by simply selecting the desired chart! Result Comparison

The following images show comparisons of Centerline Velocity, Coefficient of Skin Friction, Outlet Velocity, and Wall Y-plus.

From the first three plots, we can see that the velocity and skin friction coefficient results have remained nearly unchanged. However, the Y-plus results show significant improvement. You may want to experiment with meshes of other granularities and compare their plots with the  plots saved from the 100x30 and 100x60 meshes.