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Chapter 2

The Example Problem. Chapter 2. An Example Problem !!. Flow of Air in a 2D duct…. Objective: Peform laminar analysis of a relatively slow moving flow and then increase the flow rate dramatically. Streamlines. The Geometry. This is Duct which has a smooth transition to a larger area.

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Chapter 2

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  1. The Example Problem Chapter 2

  2. An Example Problem !! • Flow of Air in a 2D duct…. • Objective: Peform laminar analysis of a relatively slow moving flow and then increase the flow rate dramatically. Streamlines 001312 30 Nov 1999 2-2

  3. The 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 001312 30 Nov 1999 2-3

  4. Properties - 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 001312 30 Nov 1999 2-4

  5. Set Preferences • Preferences provides a filter to prevent irrelevant information from being presented…. 001312 30 Nov 1999 2-5

  6. Establish Element Type • Main Menu: Preprocessor-> Element Type->Add/Edit/Delete 2 - Choose 1- Add 4 - Close 3 - OK 001312 30 Nov 1999 2-6

  7. Geometry - 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 001312 30 Nov 1999 2-7

  8. The Two Rectangles 001312 30 Nov 1999 2-8

  9. Transition 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…. 001312 30 Nov 1999 2-9

  10. The Smooth Transition Line • Tangency to two lines requires choosing the proper endpoints….. 001312 30 Nov 1999 2-10

  11. The Transition Area • Preprocessor>Modeling>Create> Area >Arbitrary • Choose 4 keypoints in response to the PICKER, then OK 3 4 1 2 001312 30 Nov 1999 2-11

  12. Geometry is Finished!! Area Plot Line Plot 001312 30 Nov 1999 2-12

  13. Boundary 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 001312 30 Nov 1999 2-13

  14. The Boundary Conditions • These boundary conditions are typical • Proper condition at boundary intersections is determined by FLOTRAN Walls Walls Outlet PRES = 0 Inlet: VX=10,VY=0 001312 30 Nov 1999 2-14

  15. Solid Model Boundary Conditions 4 - Input Values, Do Endpoints of lines…OK • Example for Walls 1-Lines 3-OK 2-Pick These 6 Lines 001312 30 Nov 1999 2-15

  16. Remaining Boundaries. • Note that leaving a blank DOES NOT result in a zero condition being applied.. Inlet Outlet 001312 30 Nov 1999 2-16

  17. Control 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 001312 30 Nov 1999 2-17

  18. Preparation 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…. 001312 30 Nov 1999 2-18

  19. Mesh Tool 2 - Choose Lines Use FLIP if Line Bias is reversed 1 3 - OK 001312 30 Nov 1999 2-19

  20. Element Size Box 001312 30 Nov 1999 2-20

  21. Proper 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!) 001312 30 Nov 1999 2-21

  22. 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 1 3 2 4 5 001312 30 Nov 1999 2-22

  23. Now You Have a Mesh! Picture Made with Reverse Video (PlotCtrls>Style>Color>ReverseVideo 001312 30 Nov 1999 2-23

  24. Now for the FLOTRAN Input • Enter FLOTRAN Setup through PREP7 or Solution • (Depending on Program Setup, you may need to access “Unabridged Menu”) 001312 30 Nov 1999 2-24

  25. FLOTRAN Setup • We will be making changes to these portions of the Menu. NOW - Our Initial Analysis LATER - Follow On Work 001312 30 Nov 1999 2-25

  26. Execution Control • Choose 50 Global Iterations to Start with • We are not relying on the automatic termination criterion based on problem convergence OK! 001312 30 Nov 1999 2-26

  27. Fluid Properties • Choose AIR-IN for the property type for Density and Viscosity using scroll down menu…. • OK 001312 30 Nov 1999 2-27

  28. Resulting Screen (click OK) (Thermal conductivity and Specific Heat not needed) 001312 30 Nov 1999 2-28

  29. Flow Environment • Reference Conditions are found as a subset: • Pressure: 14.7Psi • Nominal Temperature: 70F • Offset Temperature: 460R • OK! 001312 30 Nov 1999 2-29

  30. FLOTRAN 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 001312 30 Nov 1999 2-30

  31. Convergence Monitors 001312 30 Nov 1999 2-31

  32. More Convergence Monitors 001312 30 Nov 1999 2-32

  33. Post-Processing • FLOTRAN Post-Processing is fairly typical of ANSYS • Explicity read in a set of results (not automatically loaded) • Velocity Vectors • Nodal Solution Plots • Solid Color • Line Contours • Path Plots • Particle Traces 001312 30 Nov 1999 2-33

  34. Velocity Vectors • Plot Results>Predefined Vector Plot..OK (Use this for Nodal Solution Plots….) 001312 30 Nov 1999 2-34

  35. Vectors - Typical 50 Global Iterations after 100 Global Iterations 001312 30 Nov 1999 2-35

  36. Nodal 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 001312 30 Nov 1999 2-36

  37. Pressures (50, 100 Global Iterations) 001312 30 Nov 1999 2-37

  38. Results • 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 001312 30 Nov 1999 2-38

  39. Changing Advection • FLOTRAN Setup > Advection OK! 001312 30 Nov 1999 2-39

  40. Convergence with SUPG 001312 30 Nov 1999 2-40

  41. Results • 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. 001312 30 Nov 1999 2-41

  42. Comparison of Vectors at 100, 200 GI Vectors at 200 GI show more extensive recirculation 001312 30 Nov 1999 2-42

  43. Path 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 001312 30 Nov 1999 2-43

  44. Set up the Path Plot 001312 30 Nov 1999 2-44

  45. Path plot • Pick the corner nodes • OK • Name the Path • OK 001312 30 Nov 1999 2-45

  46. Path plot - Still More • Read and dismiss the PDEF (path definition) box • Map Onto Path, Choose VX, Give it a Name, OK 001312 30 Nov 1999 2-46

  47. Path Plot - Almost Done • -Plot Path Item on Graph • Choose DOF, OK • And Then…... 001312 30 Nov 1999 2-47

  48. Path Plot of the Outlet Velocity! 001312 30 Nov 1999 2-48

  49. Some 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 001312 30 Nov 1999 2-49

  50. The 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….) 001312 30 Nov 1999 2-50

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