Carnegie Mellon

Mechanical Engineering

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FEM/ANSYS

T6 Wok

Thermal #6: 3D Heat Conduction within a Solid

Introduction:

In this example you will test your 3D heat transfer skills by modeling an object subjected to varying boundary conditions.  Using ANSYS will allow you to output the temperature distribution in an extremely simple and accurate way.

Problem Description:

·         We assume that our pan is a wok made entirely of steel.

·         All units are S.I.

·         Boundary Conditions:

1) The top has a convective boundary layer (h = 44 W/m2-K and TB = 293 K).
2) The sides are insulated.
3) The bottom side has constant heat flux over only a portion of the area because the wok is not centered over the stove coils/flames.

·         Material Properties: (Approximate the Rice and Vegetables with the values of water for simplicity)

 Material Conductivity (W/m-K) Specific Heat (J/kg-K) Density (kg/m3) Water .61 4190 962 Steel 20 450 8000 Air .023 1000 1

·         Objective: To determine the nodal temperature distribution and create a contour plot of the temperature gradient within the rice and vegetables.

·         Figure:

Starting ANSYS:

·         Click on ANSYS 6.1 in the programs menu.

·         Select Interactive.

·         The following menu comes up. Enter the working directory. All your files will be stored in this directory. Also under Use Default Memory Model make sure the values 64 for Total Workspace, and 32 for Database are entered.  To change these values unclick Use Default Memory Model.

·         Click RUN

Modeling the Structure:

·         Go to the ANSYS Utility Menu (the top bar)

·         Click Workplane>WP Settings…

·         The following widow comes up:

·         Check the Cartesian and Grid Only buttons

·         Enter the values shown in the figure above and then click OK.

·         Go to the ANSYS Main Menu (on the left hand side of the screen) and click Preprocessor>Modeling>Create>Volumes>Sphere>Solid Sphere

·         Enter the dimensions of the sphere that will constitute the food, so we can truncate it before moving onto the wok itself. (Radius = .17 m)

·         Offset the WP by .17 in the X and Z directions and also by -.1125 in the Y direction. This will enable you to create the block to subtract the extraneous portion of the sphere away. Create a square block will dimensions equal to the diameter of the sphere, .34 m.

·         With the block created, use Preprocessor>Modeling>Operate>Booleans>Subtract>Volumes to subtract the chunk away. Choose the sphere first, hit OK then the block. Hit OK

·         Now you have created the volume that makes up the rice and vegetables in the wok.  If at any time you cannot see the complete Workplace then go to Utility Menu>Plot Controls>Pan Zoom Rotate and zoom out to see the entire Workplace. If you want to see the grid itself, go to

Utility Menu>Workplane>Display Working Plane

·         Move the WP (offset it) back to the orginal location (move it .17+X, .17+Z and .075+Y)

·         The model should look like this now:

·         Now use the same process to create the bowl. If you would like (you don’t have to), you can move the piece of food out of the way while you make the rest of the model. Simply change the WP snap settings to something you will remember (like 1m) and then use Preprocessor>Modeling>Move/Modify>Volumes and move the volume -1 in each direction. You will still be able to see it in ISO mode, because you moved it along that line of sight. Remember to move it back when you are finished.

·         Remember that this time, you need to create a solid sphere of radius .175, a second solid sphere of radius .17, and a block of lengths .35m. Subtract the block from the big sphere and then subtract the small sphere from what is left of the big sphere.

·         Lastly, we want to create an area to apply heat generation to. Offset the WP .175m in the –Y direction (to the bottom of the bowl) and rotate the WP by 90 degrees in the –X direction. The WP will appear as follows.

·         Now create the cylinder as follows: (note that the cylinder was created with a length shorter than either radius of the spheres. The program did not subtract volumes correctly when I originally modeled the cylinder with length = .1)

·         Create a new sphere to use in subtracting, select .175 for the radius (remember to offset the WP back to where it started again!)

·         Use Preprocessor>Modeling>Operate>Booleans>Subtract>Volumes to subtract the part of the rod that sticks into the wok.

·         The last step is to glue each piece together. Glue the cylinder to the bowl and the food to the bowl.

·         (recall that glue is found under Preprocessor>Modeling>Operate>Booleans>Glue)

·         The modeling is finished. See below for the general appearance of the model:

Material Properties:

·         Now that we have built the model, material properties need to be defined such that ANSYS understands how heat travels through the “solid” made of rice and vegatables.

·         Go to the ANSYS Main Menu and click Preprocessor>Material Props>Material Models.

·         A pop-up window that looks like this will now appear:

·         In this window, choose Thermal>Density. Enter 962 for the density of water.  Click OK.  Now, from the Define Material Model Behavior window choose Thermal>Specific Heat and enter 4190 for the Specific Heat of water.  Again, click OK, and from the Define Material Model Behavior window choose Thermal>Conductivity>Isotropic and enter 0.61 for the thermal conductivity value.  The windows that appear as result of the last sequence of commands appear as follows:

·         Choose Material>New Model and for the steel and air, use the properties listed at the top of the tutorial. Repeat the processed as it was done for the rice and vegetables above.

·         Now exit the “Define Material Model Behavior” Window

Element Properties:

·         Now that we’ve defined what material ANSYS will be analyzing, we have to define how ANSYS should analyze our block.

·         Click Preprocessor>Element Type>Add/Edit/Delete... In the 'Element Types' window that opens click on Add... The following window opens:

·         Type 1 in the Element Type reference number.

·         Click on Thermal Mass Solid and select Tet 10node 87. Click OK. Close the 'Element types' window.

·         Now we have selected Element Type 1 to be a Thermal Solid 10node Element. This finishes the section defining how the part is to be analyzed.

Meshing:

·         This section is responsible for telling ANSYS how to divide the block such that it has enough nodes, or points, to analyze to make an accurate enough analysis.

·         Go to Preprocessor>Meshing>Size Controls>Manual Size>Lines>All Lines. In the menu that comes up type 0.025 in the field for ”Element edge length”.

·         Click on OK. Now when you mesh the figure ANSYS will automatically create square meshes that have an edge length of 0.025m along the lines you selected.

·         Now go to Preprocessor>Meshing>Mesh Attributes>Default Attributes. The window is shown below:

·         This window appears to select the element type and the material model. Check that you have selected Solid and material 1 to mesh (selected by the Element Type Number), and the right Material Number (1, as defined in the Material Properties section)Once this has been verified, Click OK and proceed to Preprocessor>Meshing>Mesh>Volumes>Free

·         A popup window will appear on the left hand side of the screen.  This window allows you to select the volume to be meshed.

·         Click anywhere within food (you can tell if you picked right) and then click OK in the pop-up window.

·         Go to Mesh Attributes>Default Attributes again and this time choose Material Number 2. Mesh the bowl this time.

·         Finally, change the default attributes to material number three and then return to ManualSize>Lines>All Lines and change the element length to 0.0125m. Finally, mesh the small volume that constitutes the offset burner on the stove.

·         The block should now look like this:

Boundary Conditions and Constraints:

·         Now that we have modeled the block and defined how ANSYS is to analyze the block we will apply the appropriate Boundary Conditions.  ANSYS refers to all Thermal Boundary Conditions as Loads, so be aware that Load and Boundary Condition mean the same thing within the software…

·         Go to Preprocessor>Loads>Define Loads>Apply>Thermal (from here one can apply any of the loads, or Boundary Conditions, offered by ANSYS.)

Apply Convection (Top)

·         First we’ll apply the Convection Boundary layer at the top of the plate.  For this click Convection>On Areas within the Thermal Load category.

·         A popup window will appear on the left hand side of the screen.  This window allows you to select the areas you wish the load to be applied.

·         Select the top rim of the wok and the inside walls of the wok. hit OKThe following window will appear:

·         Fill in the h value in the Film Coefficient blank and the Air temperature in the Bulk Temperature blank.  Click OK when finished.

Apply Temperature (Bottom Area of Cylinder)

·         Now to apply the Heat Flux into the bottom of the plate...

·         Within the Thermal Load category again, select Temperature>On Areas and click OK.

·         This window will now appear:

·         Then enter 1000 into the blank and Click OK.

Solution:

 Go to ANSYS Main Menu>Solution>Analysis Type>New Analysis. Select Steady State. Hit OK
 Now go to Solution>Solve>Current LS. Wait for the solution to get done.

Post-Processing:

 Plotting the temperature field after 50 secs.
 Now go to General Postprocessing>Plot Results>Contour Plot>Nodal Solution. The following window comes up. Enter the values as shown and click OK.

 The temperature distribution looks something like the plot below. (rotated)

 Animating the development of the temperature field Go to Utility Menu>Plot Controls>Animate>IsoSurfaces. The following window comes up. Enter the values as shown and click OK:

Check here for the animated file

 You can also animate slices of the contour: Choose Utility Menu>PlotCtrls>Style>Hidden Line Options…

 To animate this, follow further: Choose Utility Menu>PlotCrtls>Animate>Q-Slice Contours
 Pick the following options and then inspect the image afterward to see where to pick points. Also, use Pan Zoom Rotate and hit the ISO button, so that your model is lined up as the one in the image.

 Pick the three points as explained and the program should begin animating. See the output file

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