1. Training Manual Chapter 2 The Example Problem

2. Training Manual 001312 30 Nov 1999 2-2 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 An Example Problem !!

3. Training Manual 001312 30 Nov 1999 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 height0.5 –Transition length1.0 –Outlet height 1.0 –Outlet length4.0

4. Training Manual 001312 30 Nov 1999 2-4 Properties - Conditions Use PSI system of units –Property type is AIR-IN –Density will be 1.1214E-7 (lb f -s 2 /in 4 ) –Viscosity will be 2.6240E-9 (lb f -s/in 2 ) 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

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

6. Training Manual 001312 30 Nov 1999 2-6 1- Add 2 - Choose 3 - OK4 - Close Establish Element Type Main Menu: Preprocessor-> Element Type->Add/Edit/Delete

7. Training Manual 001312 30 Nov 1999 2-7 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

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

9. Training Manual 001312 30 Nov 1999 2-9 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….

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

11. Training Manual 001312 30 Nov 1999 2-11 The Transition Area Preprocessor>Modeling>Create> Area >Arbitrary Choose 4 keypoints in response to the PICKER, then OK 12 3 4

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

13. Training Manual 001312 30 Nov 1999 2-13 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

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

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

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

17. Training Manual 001312 30 Nov 1999 2-17 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

18. Training Manual 001312 30 Nov 1999 2-18 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 LinesNDIVRatio Transverse direction12-3 Inlet Region - flow direction16-2 Transition - flow direction101 Outlet - flow direction182 See next page for Mesh tool! SAVE Database Before Meshing….

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

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

21. Training Manual 001312 30 Nov 1999 2-21 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 LinesTransitionOutlet Lines (Flipped!)

22. Training Manual 001312 30 Nov 1999 2-22 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

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

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

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

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

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

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

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

30. Training Manual 001312 30 Nov 1999 2-30 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

31. Training Manual 001312 30 Nov 1999 2-31 Convergence Monitors

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

33. Training Manual 001312 30 Nov 1999 2-33 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

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

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

36. Training Manual 001312 30 Nov 1999 2-36 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

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

38. Training Manual 001312 30 Nov 1999 2-38 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

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

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

41. Training Manual 001312 30 Nov 1999 2-41 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.

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

43. Training Manual 001312 30 Nov 1999 2-43 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

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

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

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

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

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

49. Training Manual 001312 30 Nov 1999 2-49 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

50. Training Manual 001312 30 Nov 1999 2-50 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….)

51. Training Manual 001312 30 Nov 1999 2-51 Massless 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

52. Training Manual 001312 30 Nov 1999 2-52 Trace 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)

53. Training Manual 001312 30 Nov 1999 2-53 Particle Trace Color Code According to PRES (or something else!) Note Maximum number of loops allowd OK

54. Training Manual 001312 30 Nov 1999 2-54 Particle Trace The maximum number of loops is exceeded in the recirculation region. Close the box

55. Training Manual 001312 30 Nov 1999 2-55 New 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.

56. Training Manual 001312 30 Nov 1999 2-56 FLOTRAN Solution Options Activate Turbulence with Scroll Down Menu Option,OK SOLVE

57. Training Manual 001312 30 Nov 1999 2-57 Convergence Monitors

58. Training Manual 001312 30 Nov 1999 2-58 Turbulent Flow Results

59. Training Manual 001312 30 Nov 1999 2-59 Discussion 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.

60. Training Manual 001312 30 Nov 1999 2-60 New Outlet Velocity Profile A Fully developed flow would have the maximum value in the center. This implies we should make the problem domain longer….

61. Training Manual 001312 30 Nov 1999 2-61 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

62. Training Manual 001312 30 Nov 1999 2-62 New Geometry

63. Training Manual 001312 30 Nov 1999 2-63 As expected, the meshed line is kept Completing the New Geometry Preprocessor>Numbering Ctrls>Merge Items> Keypoints

64. Training Manual 001312 30 Nov 1999 2-64 New Boundary Conditions Preprocessor>Loads>Delete>

65. Training Manual 001312 30 Nov 1999 2-65 New Boundary Conditions Add the walls as done previously Assign Zero pressure to the outlet line as done previously

66. Training Manual 001312 30 Nov 1999 2-66 Mesh 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).

67. Training Manual 001312 30 Nov 1999 2-67 Set Divisions Along Outlet Flip the line after setting (when necessary) Then Mesh the New Area as in previous fashion

68. Training Manual 001312 30 Nov 1999 2-68 The Mesh Note that the symbols shown are the previously transferred Nodal Boundary Conditions. The solid model boundary conditions don’t show up on an element plot. The complete mesh with the symbols turned off..

69. Training Manual 001312 30 Nov 1999 2-69 Execute 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. –Other files such as the jobname.pfl are appended to, even though this is a new analysis

70. Training Manual 001312 30 Nov 1999 2-70 Convergence Monitors

71. Training Manual 001312 30 Nov 1999 2-71 Convergence Monitors - more

72. Training Manual 001312 30 Nov 1999 2-72 Results 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. We expect a good outlet velocity profile.

73. Training Manual 001312 30 Nov 1999 2-73 Recirculation Region The recirculation region is captured despite the relatively coarse mesh.

74. Training Manual 001312 30 Nov 1999 2-74 Benefits 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

75. Training Manual 001312 30 Nov 1999 2-75 Outlet Velocity Profile

76. Training Manual 001312 30 Nov 1999 2-76 Final 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. End of Problem!