Problem description. An enclosure is bounded by rigid walls and a flexible hemispherical dome, as shown:

Transcription

1 Problem 39: Thermal FS analysis of a heated hemispherical dome Problem description An enclosure is bounded by rigid walls and a flexible hemispherical dome, as shown: z x y 0.05 m A A Air: = N-s/m 2 =1.2 kg/m 3 c p =1006 J/kg- o k =0.025 W/m- o g =-9.8 m/s 2 o -1 = m Walls marked with A: zero temperature, no slip Other walls, top and base: insulated, no slip Hemispherical dome: shell with thermo-isotropic material = N/m 2 =0.33 = o -1 t = m Radius=0.025 m k =204 W/m- o Q=100 W/m 2 The enclosure contains air, which flows due to natural convection caused by the heating of the air near the dome. For analysis purposes, we analyze one quarter of the domain, with symmetric boundary conditions, as shown in the figure on the next page. First we analyze the model using the F fluid element, then we analyze the model using the F- fluid element. ADNA R & D, nc. 39-1

2 Problem 39: Thermal FS analysis of a heated hemispherical dome Face 6, no-slip Face 7, no flow in y direction Face 3, no flow in x direction Face 4, FS and shell-thermal boundary conditions Face 5, no-slip Face 1, no-slip, zero temperature Face 2, no-slip n this problem solution, we will demonstrate the following topics that have not been presented in previous problems: $ Defining a shell thermal boundary condition $ Using a boundary layer table to control meshing $ Plotting a boundary of the model along with the velocities within the model. efore you begin Please refer to the con Locator Tables chapter of the Primer for the locations of all of the AU icons. Please refer to the Hints chapter of the Primer for useful hints. Note that you must have an ADNA-M/PS license to do this problem. This problem cannot be solved with the 900 nodes version of the ADNA System because the model contains too many nodes. Much of the input for this problem is stored in files prob39_1.in, prob39_2.in and prob39_3.in. ou need to copy files prob39_1.in, prob39_2.in and prob39_3.in from the folder samples\primer into a working directory or folder before beginning this analysis. nvoke the AU and set the Program Module drop-down list to ADNA FD ADNA Primer

3 Solution using the F element ADNA FD model Problem 39: Thermal FS analysis of a heated hemispherical dome Defining model control data, geometry, material and boundary conditions We have prepared a batch file (prob39_1.in) that performs the following operations: Defines the geometry bodies Defines most of the analysis control parameters Defines the material properties for the air Defines the zero velocity boundary conditions Defines the temperature boundary condition Defines a time function Defines time stepping information Plots the model hoose File Open atch, navigate to the working directory or folder, select the file prob39_1.in and click Open. The graphics window should look something like this: TM D PRSRD TMPRATUR TM D D D V V V P - - D Selecting thermal FS analysis hoose Model Flow Assumptions, then, in the Fluid-Structure nteraction (FS) box, set "Thermal oupling" to "Through Solid Domain in Fluid Model" and click OK. ADNA R & D, nc. 39-3

4 Problem 39: Thermal FS analysis of a heated hemispherical dome Defining the FS and shell-thermal boundary conditions FS boundary condition: lick the Special oundary onditions icon, add condition number 1 and set the Type to Fluid-Structure nterface. Set the Face # to 4 and the ody # to 2 in the first row of the table and click Save (do not close the dialog box yet). Shell-thermal boundary condition: Add condition number 2, set the Type to Shell Thermal, set the Sub-Type to Heat Flux, the Thickness of oundary to and the Heat onductivity Value to n the Heat Flux box, set the Value to and the Time Function # to 2. Set the Associated Fluid-Structure nterface oundary ondition # to 1, then set the Face # to 4 and the ody # to 2 in the first row of the table. lick OK. When you click the Redraw icon, the graphics window should look something like this: TM PRSRD TMPRATUR TM D F V V V P - D F FS TSH D F - - Defining the element group, creating the mesh We have prepared a batch file (prob39_2.in) that performs the following operations: Defines an element group Subdivides the geometry Replots the mesh 39-4 ADNA Primer

5 Problem 39: Thermal FS analysis of a heated hemispherical dome hoose File Open atch, navigate to the working directory or folder, select the file prob39_2.in and click Open. The graphics window should look something like this: TM D PRSRD TMPRATUR TM F V V V P - D F FS TSH D F - - We anticipate that large velocity gradients exist near the walls, therefore we prefer to have layers of small elements near all of the faces, except for the symmetry faces 3 and 7, as shown in the following figure: Face 6, no-slip, fluid flows radially outwards, fine mesh required Face 7, no flow in y direction, fluid slips along face, coarse mesh is OK Face 3, no flow in x direction, fluid slips along face, coarse mesh is OK Face 4, FS and shell-thermal boundary conditions, fluid rises near this face, fine mesh required Face 5, no-slip, fine mesh required Face 1, no-slip, zero temperature, fluid falls near this face, fine mesh required Face 2, no-slip, fluid flows radially inwards, fine mesh required ADNA R & D, nc. 39-5

6 Problem 39: Thermal FS analysis of a heated hemispherical dome 39-6 ADNA Primer oundary layers: To obtain layers of small elements, click the Mesh odies icon and set the Nodes per lement to 8. lick the... button to the right of the "oundary Layer Table" field and add table number 1. Set the Progression to Geometric, the Number of Layers to 4, the Thickness of First Layer to and the Total Thickness to Now fill in the table as follows and click OK to close the Define oundary Layer Table for Meshing dialog box. Face # ody # 1 st Layer Thickness Total Thickness n the Mesh odies dialog box, set the "oundary Layer Table" to 1 if necessary. nter 2 in the first row of the table and click OK. After you click the Hidden Surfaces Removed icon, the graphics window should look something like this: K K V 1 V 2 V 3 P - D - - F - G - - H J K FS TSH D F 1 2 G - - H J 1 2 K - - TM PRSRD TMPRATUR TM Generating the ADNA FD data file, saving the ADNA-N database lick the Data File/Solution icon, set the file name to prob39_f.dat, make sure that the Run Solution button is unchecked and click Save. Save the database file to file prob39_f.idb.

7 ADNA Structures model Problem 39: Thermal FS analysis of a heated hemispherical dome lick the New icon to begin a new model. We have prepared a batch file (prob39_3.in) that creates the entire ADNA Structures model. hoose File Open atch, navigate to the working directory or folder, select the file prob39_3.in and click Open. The graphics window should look something like this: TM D U U U D To display the mesh without the yellow FS boundary lines, click the Show Fluid Structure oundary icon. The graphics window should look something like the figure on the next page. ADNA R & D, nc. 39-7

8 Problem 39: Thermal FS analysis of a heated hemispherical dome TM D U U U D Generating the ADNA Structures data file, saving the ADNA-N database lick the Data File/Solution icon, set the file name to prob39_a.dat, make sure that the Run Solution button is unchecked and click Save. Save the database file to file prob39_a.idb. Running ADNA-FS hoose Solution Run ADNA-FS, click the Start button, select file prob39_f, then hold down the trl key and select file prob39_a. The File name field should display both file names in quotes. Set the Maximum Memory for Solution to at least 100 M (and preferably to at least 500 M). Then click Start. The ADNA-FS solution takes 2 steps. When ADNA-FS finishes, close all open dialog boxes. Set the Program Module drop-down list to Post-Processing (you can discard all changes), click the Open icon and open porthole file prob39_f. The graphics window should look something like the figure on the next page ADNA Primer

9 Problem 39: Thermal FS analysis of a heated hemispherical dome TM Post-processing Plotting the velocities: lick the Shading icon, the No Mesh Lines icon and the Quick Vector Plot icon. ou don t see any velocity vectors because we are only looking at the vectors on the outside of the model, and the visible elements all have no-slip boundary conditions. Use the Pick icon and the mouse to rotate the model until the graphics window looks something like the top figure on the next page. ADNA R & D, nc. 39-9

10 Problem 39: Thermal FS analysis of a heated hemispherical dome TM VLOT TM This plot shows that there is slip on the symmetric faces of the model. Now click the ull Front Faces icon and rotate the model with the mouse until the graphics window looks something like this: TM VLOT TM ADNA Primer

11 Problem 39: Thermal FS analysis of a heated hemispherical dome vidently the fluid rises near the shell dome, and falls near the zero temperature boundary condition, as expected. (our solution may be slightly different than ours, because free meshing produces different meshes on different platforms.) We can also plot just the dome boundary as an element face-set. First, click the ull Front Faces icon and rotate the model until the dome boundary is visible. Now choose Definitions lement/node Set lement Face Set, add lement Face Set Number 1 and set the Method to Auto-hain lement Faces. Now double-click in the Face {p} column of the table, select one or more of the faces on the dome boundary, then press the sc key. lick Save to create the face-set. Move the dialog box out of the way of the mesh plot and notice that the element faces on the dome boundary are highlighted. lick OK to close the dialog box., set the lement Face Set to 1 and click OK. The Now click the Modify Mesh Plot icon dome boundary is plotted, but no velocities are plotted. This is because the velocities at the dome boundary are zero (no-slip). To see the velocities within the fluid domain, click the Modify Vector Plot icon, click the Grid button, set the Vector Location to Within 3D lements and click OK twice to close both dialog boxes. Rotate the mesh plot with the mouse until the graphics window looks something like this: TM VLOT TM ADNA R & D, nc

12 Problem 39: Thermal FS analysis of a heated hemispherical dome Plotting the temperatures: lick the lear icon, the Mesh Plot icon, then click the reate and Plot icon, set the and Plot Variable to (Temperature: TMPRATUR) and click OK. The graphic window should look something like this: TM TMPRATUR TM MAMUM NOD 1 MNMUM NOD 105 (0.000) Now we use a cutting plane to visualize the temperatures within the model. lick the ut Surface icon, set the Type to utting Plane, set the Defined by field to Origin and Normal, set the Outwards Normal to (1.0, -1.0, 0.0) and click OK. Then click the Model Outline icon to remove the plotted lines on the cutting plane intersection. Use the Pick icon and the mouse to rotate the mesh until the graphics window looks something like the top figure on the next page ADNA Primer

13 Problem 39: Thermal FS analysis of a heated hemispherical dome TM TMPRATUR TM MAMUM NOD 1 MNMUM NOD 107 We can also plot the temperatures at the dome boundary. lick the ut Surface icon the Type to None and click OK. Then click the Modify Mesh Plot icon, set the lement Face Set to 1 and click OK. Use the mouse to scale and rotate the mesh until the graphics window looks something like this:, set TM TMPRATUR TM MAMUM NOD 1 MNMUM NOD 4 ADNA R & D, nc

14 Problem 39: Thermal FS analysis of a heated hemispherical dome Solution using the F- element ADNA Structures model The structural model is unchanged. We only need to save it with a different name. Set the Program Module drop-down list to ADNA Structures (you can discard all changes), then choose file prob39_a.idb from the recent file list at the bottom of the File menu. lick the Data File/Solution icon, set the file name to prob39_c_a.dat, make sure that the Run Solution button is unchecked and click Save. hoose File Save As to save the database file to prob39_c_a.idb. ADNA FD model n the fluid model, the element will be changed from F to F-. lick the New icon (you can discard all changes) and choose file prob39_f.idb from the recent file list at the bottom of the File menu. Selecting the F- element, outer iteration tolerances and FS iteration setting hoose ontrol Solution Process, set the "Flow-ondition-ased interpolation lements" to F- and click OK. Now choose ontrol Solution Process, click the Outer teration... button, then click the Advanced Settings... button. n the Outer teration Advanced Settings dialog box, set the quation Residual Use to All and the Tolerance to , and set the Variable Residual Use to All and the Tolerance to Also set the "nterpolation Scheme for Pressure" to Linear. lick OK three times to close all three dialog boxes. lick the oupling Options icon click OK., make sure the FS Solution oupling is terative, and Generating the data file, running ADNA FD hoose File Save As to save the database to file prob39_c_f. lick the Data File/Solution icon, set the file name to prob39_c_f, make sure that the Run Solution button is unchecked and click Save ADNA Primer

15 Problem 39: Thermal FS analysis of a heated hemispherical dome Running ADNA-FS hoose Solution Run ADNA-FS, click the Start button, select file prob39_c_f, then hold down the trl key and select file prob39_c_a. The File name field should display both file names in quotes. Make sure that the Maximum Memory for Solution is set to at least 100 M. Then click Start. The ADNA-FS solution takes 2 steps. When ADNA-FS finishes, close all open dialog boxes. Set the Program Module drop-down list to Post-Processing (you can discard all changes), click the Open icon porthole file prob39_c_f. and open Post-processing Follow the instructions given above to plot the velocities and temperatures. t can be observed that the solutions of the F- element are very close to those of the F element. Some sample plots are given below. TM VLOT TM ADNA R & D, nc

16 Problem 39: Thermal FS analysis of a heated hemispherical dome TM TMPRATUR TM MAMUM NOD 1 MNMUM NOD 1775 xiting the AU: hoose File xit (you can discard all changes). Notes: 1) The fluid solution process associated with the F- element uses an iterative method. All fluid governing equations are solved one by one in a certain order. Therefore the FS coupling associated with the F- element must also be iterative (and not direct) ADNA Primer