The Example Problem Chapter 2. Training Manual May 15, 2001 Inventory #001477 2-2 Flow of Air in a 2D duct. Objective: Perform laminar analysis of a

The Example Problem

Chapter 2

May 15, 2001Inventory

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Training Manual

• Flow of Air in a 2D duct….

• Objective: Perform laminar analysis of a relatively slow moving flow and then increase the flow rate dramatically.

Streamlines

An Example Problem !!


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Training ManualThe Geometry

• This is Duct which has a smooth transition to a larger area.

• Units of Length - Inches– Inlet length 3.0– Inlet height 0.5– Transition length 1.0 – Outlet height 1.0 – Outlet length 4.0


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Training ManualProperties - Conditions

• Use PSI system of units– Property type is AIR-IN– Density will be 1.1214E-7 (lbf-s2/in4)

– Viscosity will be 2.6240E-9 (lbf-s/in2)

• Conditions– Reference Pressure 14.7 psi– Outlet Pressure 0 psi (relative pressure)– Default Temperature used : 293K

• Flow – Velocity of 10 inch/sec -> RE ~ 424 (laminar)– Note in 2D the hydraulic diameter (used in the Reynolds

Number) is twice the inlet height


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Training ManualSet Preferences

• Preferences provides a filter to prevent irrelevant information from being presented….


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Training Manual

1- Add

2 - Choose

3 - OK4 - Close

Establish Element Type

• Main Menu: Preprocessor-> Element Type->Add/Edit/Delete


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Training ManualGeometry - Create Inlet/Outlet Regions

• Preprocessor>Modeling>Create Areas> Rectangle (By Dimensions)

• First– X1=0,X2=3– Y1=0,Y2=0.5– Click Apply

• Second– X1=4,X2=8– Y1=0,Y2=1– Click OK


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Training ManualDisplay Adjustment

• First turn off the background shading– Utilities Menu > Plot Ctrls > Style > Background > Display

Background• By default it is checked. Uncheck it.

• Then reverse the video, creating a white background.– Utilities Menu > Plot Ctrls > Style > Color > Reverse Video


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Training ManualThe Two Rectangles


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Training ManualTransition Region Between Them

• Create a smooth transition line between the two

• Preprocessor>Modeling>Create Lines (Tangent to 2 Lines)

• Follow the Instructions carefully in the resulting PICKERS– There will be four successive choices

• Check your result with the following page….


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Training ManualThe Smooth Transition Line

• Tangency to two lines requires choosing the proper endpoints…..


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Training ManualThe Transition Area

• Preprocessor > Modeling > Create > Area > Arbitrary

• Choose 4 keypoints in response to the PICKER, then OK

1 2

34


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Training ManualGeometry is Finished!!

Area Plot

Line Plot - (after /triad,off)


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Training ManualBoundary Conditions

• Use Solid Model Boundary Conditions– Do not require require re-application upon re-

meshing

Preprocessor > Loads > Apply > Velocity > Lines

• We will apply Velocities and Pressures

– Inlets are Velocity or Pressure– Outlets are Pressure– Walls: Velocities are zero


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Training Manual

Walls

Walls

Inlet:VX=10,VY=0

OutletPRES = 0

The Boundary Conditions

• These boundary conditions are typical

• Proper condition at boundary intersections is determined by FLOTRAN


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Training ManualSolid Model Boundary Conditions

• Walls - Apply Velocity on lines

• Pick the 6 lines below

• Set values to 0, OK


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Training ManualRemaining Boundaries.

• Note that leaving a blank DOES NOT result in a zero condition being applied..

Inlet

Outlet


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Training ManualControl of the Display

This is a line plot after application of the Boundary Conditions

To prevent display of these symbols:Utility Menu: PlotCtrls > Symbols…

Choose NONE and OK


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Training ManualPreparation for Meshing

• Use the Mesh Tool – Size Controls, Lines, Set

• PICKER shows up and you choose the lines,OK– Set the number of divisions and the ratio, OK

• Use these settings for line divisions Line Divisions• Lines NDIV Ratio• Transverse direction 12 -3• Inlet Region - flow direction 16 -2• Transition - flow direction 10 1• Outlet - flow direction 18 2

• See next page for Mesh tool!

SAVE Database Before Meshing….


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Training ManualMesh Tool

1

2 - Choose Lines

3 - OK

Use FLIPif Line Biasis reversed


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Training ManualElement Size Box


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Training ManualProper Line Divisions

• Four Different Groups of Lines must be done for this problem…

• Remember to flip one of the outlet lines

• Generally, Avoid large adjacent element size changes

• The Four lines in the Y direction are the transverse lines

• Inlet Lines Transition Outlet Lines (Flipped!)

TransverseLines


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Training Manual

1

2

3

4

5

Meshing Step

• Use the Mesh Tool– 1: Choose Areas– 2: Mapped– 3: Quad– 4: Mesh

• PICKER comes up– Pick All

• (Meshing Occurs)

• 5: Close Meshtool


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Training ManualNow You Have a Mesh!

Picture Made with Reverse Video(PlotCtrls > Style > Color > Reverse Video)


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Training ManualFLOTRAN Setup

• Enter FLOTRAN Setup through PREP7 or Solution


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Training ManualFLOTRAN Setup

• We will be making changes to these portions of the Menu.

– NOW - Our Initial Analysis

LATER - Follow On Work


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Training Manual

OK!

Execution Control

• Choose 50 Global Iterations to Start with– We are not relying on

the automatic termination criterion based on problem convergence


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Training ManualFluid Properties

• Choose AIR-IN for the property type for Density and Viscosity using scroll down menu….

• OK


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Training ManualResulting Screen (click OK)

(Thermal conductivity and Specific Heat not needed)


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Training ManualFlow Environment

• Reference Conditions are found as a subset:

• Pressure: 14.7Psi

• Nominal Temperature: 70F

• Offset Temperature: 460R

• OK!


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Training ManualFLOTRAN Execution

• Done in SOLUTION:

• Run FLOTRAN

• Execute 50 iterations, look at the results and then run 50 more…

• Convergence monitors indicate the normalized rate of change of the solution


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Training ManualConvergence Monitors


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Training Manual

More Convergence Monitors


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Training ManualPost-Processing

• FLOTRAN Post-Processing is fairly typical of ANSYS– Explicitly read in a set of results (not automatically loaded)

• Velocity Vectors

• Nodal Solution Plots– Solid Color– Line Contours

• Path Plots

• Particle Traces


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Training ManualVelocity Vectors

• Plot Results>Predefined Vector Plot..OK

(Use this for Nodal Solution Plots….)


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Training ManualVectors - Typical

50 Global Iterations

after 100 Global Iterations


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Training ManualNodal Results Plotting

• Show up as solid color plots or lines depending on the device chosen– Utility Menu>Plot Ctrls>Device Options

• Shading or Contours

• Choose DOF

• OK


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Training ManualPressures (50, 100 Global Iterations)


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Training ManualResults

• We can’t tell the difference between the velocity vector plots, but it looks like the pressures have changed slightly.

• We also notice that the Convergence Monitors (Normalized rate of change of each DOF) have leveled off….– This implies solution is slightly oscillatory

• We will modify the input slightly, choosing the SUPG (Streamline Upwind Petrov-Galerkin) formulation for the momentum equations…– The SUPG algorithm is less diffusive and more accurate (but

sometimes less robust) than the default algorithm (MSU - Monotone Streamline Upwind Method)

• Also, set the number of Global Iterations to 100


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Training ManualChanging Advection

• FLOTRAN Setup > Advection

OK!


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Training ManualConvergence with SUPG


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• We could continue, but you get the idea...

• Use of SUPG has given enhanced convergence.

• We should expect a less diffusive solution, and so the re-circulation region may be better defined.


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Training ManualComparison of Vectors at 100, 200 GI

Vectors at 200 GI show more extensive recirculation


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Training ManualPath Plots

• Look at the profile of VX along the outlet

• Procedure -Path Operations– Define Path by Nodes

• Choose Nodes on either corner of the outlet– Map Onto Path

• Choose VX and label it– Plot

• On graph


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Training ManualSet up the Path Plot


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Training ManualPath plot

• Pick the corner nodes

• OK

• Name the Path

• OK


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Training Manual

• Read and dismiss the PDEF (path definition) box

• Map Onto Path, Choose VX, OK

Path plot - Still More


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Training ManualPath Plot - Almost Done

• -Plot Path Item on Graph

• Choose DOF, OK

• And Then…...


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Training ManualPath Plot of the Outlet Velocity!


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Training ManualSome Discussion

• Modify the line colors as needed with the Utility Menu– PlotCtrls>Style>Colors>Graphs

• Modify the plot controls as needed with Utility Menu– PlotCtrls>Style>Graphs

• Result– Fully developed flow would show the outlet velocity profile as a

perfect parabola– Therefore, the problem domain could be lengthened to provide

room for more flow development– Check the Mass Balance


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Training ManualThe Print File

• Use the Utility Menu to Look at the bottom of the jobname.pfl file

• List > Files> Other> (choose jobname.pfl file)• Scan to the bottom• Mass balance looks good!!!• (If you had forgotten to put a No-Slip Boundary condition

somewhere, there would be another outlet listed….)


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Training ManualMassless Particle traces

• Particle traces are based on the velocity field, not the stream function.

• For a steady state, perfectly converged problem on a perfect mesh, the streamlines and particle trace plots would be identical.

• Procedure: Plot Results>Flow Traces– Define trace points with PICKER– Plot Flow Traces

• Optionally color code trace with • the value of a DOF


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Training ManualTrace Points

• The points defined on the Working Plane– Ensure, for 3D models, that the WP is correctly located!

• The resolution of the trace point location is controlled by the currently set Snap Increment (Working plane controls)


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Training ManualParticle Trace

• Color Code According to PRES (or something else!)

• Note Maximum number of loops allowd

• OK


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Training ManualParticle Trace

• The maximum number of loops is exceeded in the recirculation region. Close the box


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Training ManualNew Analysis

• Increase the velocity from 10 to 200 (no other changes)– This makes the Reynolds Number ~8500

• Solve the problem– Very Shortly you will get a message that either the solution has

diverged or that a negative value has been encountered in the coefficient matrix main diagonal.

• This is because the flow is now in the turbulence regime and a laminar solution will be unstable!

• So activate the turbulence model and again solve.

!


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Training ManualFLOTRAN Solution Options

• Activate Turbulence with Scroll Down Menu Option,OK

• SOLVE


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Training ManualTurbulent Flow Results


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Training ManualDiscussion

• Note that the maximum value of pressure is no longer at the inlet. It has moved to the outlet !!!

• Consider Bernoulli’s equation and note that in our new, higher velocity problem the relative importance of the viscosity has decreased.– The recoverable pressure due to the velocity change now

dramatically outweighs the viscous losses.

unrec2c

22

21c

21

1 Pghρg2VPghρ

g2VP


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Training ManualNew Outlet Velocity Profile

• A Fully developed flow would have the maximum value in the center. This implies we should make the problem domain longer….


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Training Manual

Another New Analysis - Extend the Problem• Outline of the steps required

– Add another rectangle to the outlet• Try 15 additional inches• Remember to Merge Keypoints

– Revise boundary conditions• Delete old pressure boundary• Pressure on new boundary• Walls


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Training ManualNew Geometry


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Training Manual

As expected, the meshed line is kept

Completing the New Geometry

• Preprocessor>Numbering Ctrls>Merge Items> Keypoints


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Training ManualNew Boundary Conditions

• Preprocessor>Loads>Delete>


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Training ManualNew Boundary Conditions

• Add the walls as done previously

• Assign Zero pressure to the outlet line as done previously


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Training ManualMesh the New Outlet Area

• Use the Mesh tool to copy the transverse direction assignment to the new outlet boundary.

• PICKER asks for the line to be copied from (pick andOK) and then the line to be copied to (pick and OK).


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Training ManualSet Divisions Along Outlet

• Flip the line after setting (when necessary)

• Then Mesh the New Area as in previous fashion


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Training ManualThe Mesh

• Note that any symbols shown are the previously transferred Nodal Boundary Conditions. It depends whether or not the symbols are turned on. The solid model boundary conditions don’t show up on an element plot.

• The complete mesh with the symbols turned off..


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Training ManualExecute

• Note that if you have not changed the jobname, FLOTRAN will provide a notice to the effect that it has renamed the old results file to jobname.rfo– This occurs because the number of nodes and elements in the

case has changed, and you have not asked for a restart with a modified mesh.

– Other files such as the jobname.pfl are appended to, even though this is a new analysis


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Training Manual

Convergence Monitors - more


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• Two representations of pressure, the second in the vector mode with 128 contours.

• Note that the pressure drop, once the flow has recovered, is very small.

• Window Options used to turn off max/min symbols and legends

• We expect a good outlet velocity profile.


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Training ManualRecirculation Region

• The recirculation region is captured despite the relatively coarse mesh.


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Training ManualBenefits of Extension

• The lines are superimposed onto the new velocity vector plot. It is clear that the flow is continuing to develop past the original boundary of the problem.

Old Outlet


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Training ManualOutlet Velocity Profile


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Training ManualOutlet velocity profile

• PlotCtrls > Style > Colors > Graph colors• Choose black for curve number 1.


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Training Manual Check of Transverse Velocity

• The flow is very close to fully developed. The following plot of the transverse velocities at the outlet provides a measure of how close it is. Note the scale. The maximum transverse velocity is 0.11.


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Training ManualWait! There’s One More Thing!

• Suppose we now want see if a finer mesh affects the recirculation region results.

• We can refine the mesh and FLOTRAN will interpolate the results onto the new mesh and then continue….

• Refine the mesh based on the AREA• Pick this one! OK


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Training ManualRefined mesh in transition region

• Use minimal mesh refinement...

• Use of solid model boundary conditions saves us the trouble of reapplying the wall constraints!


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Training ManualThe Restart….

FLOTRAN Setup > Restart Options > Restart/Iteration

If you are Saving copy of the initial results file, you should also save the database for that results file.


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Training ManualRe-Execution

• Choose the File !!

• Solve


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Training ManualInterpolation results

• The “old” solution interpolated onto the new mesh

• The “new” solution after 10 global iterations


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Training ManualConclusion

• Note that the Global Iteration Numbers start over again.

At Long Last: The Finish Line!

Documents

The Example Problem Chapter 2. Training Manual May 15, 2001 Inventory #001477 2-2 Flow of Air in a 2D duct. Objective: Perform laminar analysis of a