Circulation around the ends
3.3 Example of a Circular Duct
We will now consider a specific example of circular duct shown in Figure 3.2.
z
Schematic of a circular duct of radius a, length L, u1 and u2 velocities of the face at each end of the duct.
3.3. Example of a Circular Duct 107 The analyses that will be conducted are the calculation of the:
• natural frequencies,
• sound pressure distribution along the duct for a harmonic volume velocity excitation at one end of a duct with a finite length,
• pressure distribution along an infinitely long duct, and
• pressure distribution along a duct with a finite length that has a frequency-varying impedance at one end to simulate the end of the duct radiating into free space.
The parameters used in the example are listed in Table 3.2.
TABLE 3.2
Parameters Used in the Analysis of a Circular Duct Description Parameter Value Units
Diameter 2a 0.1 m
Length L 3 m
Speed of sound c0 343 m/s
Density ρ0 1.21 kg/m3
Velocity at piston u2 0.0 m/s
Velocity at rigid end u1 0.0 m/s
3.3.1 ANSYS Workbench
This section describes instructions for modeling a circular rigid duct, with a diameter of 0.1 m and a length of 3 m. A modal analysis will be conducted using ANSYS Workbench.
The completed ANSYS Workbench archive file called res freqs duct.
wbpz , which contains the .wbpj project file, is included with this book.
Instructions
• Start ANSYS Workbench.
• In theToolbox window, under the Analysis Systems, left-click and hold the mouse button down on the Modal icon and then drag it into the Project Schematic window.
108 3. Ducts
• Double-click on row3 Geometry to start DesignModeler.
• SelectMeter as the desired length unit, and click the OK button.
• Click on theXYPlane icon in the Tree Outline window.
• Click on theNew Sketch icon.
• Click on theSketch1 icon.
• Click on theSketching tab.
• Before we start to create a circular area for the duct, theAuto Constraint Cursor must be turned on to ensure that the cursor will “snap” to points and edges. In theSketching Toolbox window, click on the Constraints tab.
To scroll through the Constraint menu options, click on the downward-pointing triangle next to the Setting tab until the Auto Constraints
3.3. Example of a Circular Duct 109 option is visible, then left-click on it. Click in the box next to Cursor:
to activate the generation of automatic constraints.
• The next step is to create a circular area to represent the duct. Click on the Draw tab in the Sketching Toolbox window and select the Circle tool.
• Move the cursor so that it is over the origin of the axes, and make sure that the origin point changes to red and that the letter P is shown at the cursor (to indicate that the cursor will snap to a coincident point at the origin), then left-click the mouse button to start drawing the circle. It is very important that the center of the circle is selected to be at the origin. In later steps, the circular area will be divided into 4 sectors about theXZ and YZ planes, and if the center of the circle is not coincident with the origin, then the areas for each of the quadrants of the circle will differ, and there will also be issues when trying to use symmetry to model a quarter section of the duct.
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• Move the mouse cursor away from the origin so that a circle appears. Notice that in the status bar at the bottom of the screen, the dimension of the radius is shown. Left-click the mouse button to complete drawing a circle at any radius. The correct dimension for the diameter of the circle will be assigned in a later step.
• Click on theDimension tab in the Sketching Toolboxes window.
• Click on theDiameter tool.
3.3. Example of a Circular Duct 111
• In theGraphics window, left-click once on the perimeter of the circle to start drawing the dimension. Move the cursor away from the perimeter and left-click again to indicate the location for the diameter dimension. A diameter D1 will be shown.
D1
• In the windowDetails View, click the mouse in the square box next to the label D1.
• The letterD will appear in the square box, and a dialog window will open. In the text area forParameter Name: type duct_diam, then click the OK button.
• The next step is to extrude the circle along the Z axis to create a volume for the circular duct. Click theModeling tab.
• Click on theSketch1 icon.
• Click on theExtrude icon.
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• The geometry that is to be extruded was already selected as Sketch1, so click the Apply button next to the row Geometry. After pressing the Apply button, Sketch1 should appear in the Geometry row.
• Click in the square box next toFD1, to parameterize the depth of the extru-sion.
• In the dialog window that appears, in the text entry area next toParameter Name: type duct_length. The correct length of the duct will be assigned in a later step.
3.3. Example of a Circular Duct 113
• Notice that there is a lightning bolt next to theExtrude1 icon in the Tree Outline window. Click on the Generate icon to create the extrusion.
• An extruded shape will be created in theGraphics window.
• You might be feeling uneasy that the extruded shape does not resemble a duct. Although it is not necessary to fix this issue at the moment, we will update the parameters so that the model resembles a duct. First, in the menu bar, click on File | Save Project, and give your project a filename such as res freqs duct.wbpj.
• Return to theProject Schematic window and double-click on the Parameter Set box. Several tables will appear with the parameter names that were de-fined earlier. We will return to the Parameter Set window several times to insert new variables and calculated expressions.
• Click in cell C4 for the value of the duct_diam and type in the value 0.1, then press the <Enter> key on the keyboard.
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• Repeat this step to assign theParameter Name duct_length a value of 3.
• Click on theRefresh Project icon.
• The solid model in DesignModeler will have been updated with the new values for the parameters. Return to the DesignModeler window. The model might not be visible, so click on the Zoom to Fit icon.
• The solid model should now resemble the shape of a duct. It is likely that the placement of the dimension text will be awkward. Although it not necessary to fix this, if you wish to move the placement of the dimension text, click on theSketching tab, click on the Dimensions tab, and click on the Move icon.
If you cannot see the Move icon, you might need to click on the triangles
3.3. Example of a Circular Duct 115 to the right of Constraints or Dimensions to scroll the window to reveal theMove icon. Click on the diameter dimension to select it, move the mouse cursor to where you would like to place the dimension text, and then click the mouse cursor again.
• The full model of the duct will be dissected into 4 slices to create a quarter model. SelectCreate | Slice from the menu bar.
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• You need to select the plane that will be used to slice the model. Click on the icon for theYZPlane and then click the Apply button in the row for Base Plane.
• Make sure that the row forSlice Targets says All Bodies, then click the Generate icon. The cylinder will be split into two halves.
• Repeat these steps to slice all the bodies along theZXPlane, so that there are 4 bodies.
• Check that each of the 4 bodies have the sameVolume and Surface Area by clicking on the first Solid body in the tree beneath 4 Parts, 4 Bodies.
3.3. Example of a Circular Duct 117
In the window Details View, note the values for the Volume and Surface Area and then click on the other 3 Solid bodies and ensure that the values are identical. If the values are not the same, then you should consider fixing this issue as the results from the simulation will be different from those shown in this book.
• The next step involves merging the 4 parts and 4 bodies into a single part.
The reason for doing this is to ensure that the nodes on the faces between parts are shared and hence there is continuity of pressure between two con-nected volumes. In theTree Outline window, click on the plus sign next to the 4 Parts, 4 Bodies branch to expand the list. Click on the first Solid body.
• Hold down the Shift key on the keyboard and click on the Solid body icon at the bottom of the list, so that all 4 Solid bodies are highlighted.
Right-click the mouse button to open a context menu and select Form New Part.
118 3. Ducts
• The 4 separate parts will have been merged into a single part, which will be indicated by the tree branch showing1 Part, 4 Bodies.
• Save the model again by selectingFile | Save Project.
• We will create 3Named Selections of features of this solid model for the faces on the inlet and outlet of the duct, and the edge along the center axis of the duct. This will make it easier in the later steps when defining the loads and boundary conditions on the model, where the Named Selections can be used. Click on the Faces selection filter icon or press <Ctrl> f on the keyboard so that theFaces icon appears depressed.
• Select the 4 faces on the end of the cylinder by holding down the <Ctrl>
key and left-clicking on each face.
• In the menu bar, click onTools | Named Selection.
3.3. Example of a Circular Duct 119
• Make sure the 4 faces are still selected, which will be highlighted in green and the status bar at the bottom of the screen will say 4 Faces. Click the Apply button in the Geometry row in the Details View window.
• In the cell next to Named Selection, type NS_outlet. Click the Generate icon.
• Repeat these steps to define a named selection for the 4 faces on the opposite end of the cylinder at theXY Plane, and call it NS_inlet.
Y Z X
• Click on theEdges selection filter icon. Select the edge along the axis of the cylinder, which is also along the Z axis.
120 3. Ducts
• Create aNamed Selection for this edge and call it NS_duct_axis. Click on theGenerate icon.
• The completedTree Outline should be similar to the list below.
• Click onFile | Save Project.
That completes the creation of the solid model. The next stage is to develop the finite element model using ANSYS Mechanical.
• This example (along with most examples in this book using ANSYS Work-bench) will make use of the ACT Acoustic extension. Make sure that it is loaded by clicking on Extensions | Manage Extensions from the Project Schematic window.
3.3. Example of a Circular Duct 121
• Make sure there is a tick in the columnLoad for the row ExtAcoustics. Click on theClose button when completed.
• In the Project Schematic window, double-click on row 4 Model to start Mechanical. You may be presented with a dialog box to “Read Upstream Data”; you should click on theYes button.
• The solid model from DesignModeler should be transferred to Mechan-ical, and under the Geometry branch there should be 1 Part, and 4 Solid bodies listed underModel (A4) in the Outline window.
• Make sure that the tabGeometry is selected so that the model is displayed in the window. The other two tabs for Print Preview and Report Preview are not discussed in this book.
• The next steps will involve selecting the method that will be used to mesh the bodies. TheSweep method will generate a mesh pattern that is repeated along the axis of the duct. Right-click on theMesh branch and select Insert
| Method.
• For the geometry selection, right-click in theGeometry window and from the context menu, left-click on Select All, which will highlight all the solid bodies in green.
122 3. Ducts
Click on the Apply button in the Geometry row and the cell should have written that4 Bodies have been selected.
• In the window Details of "Automatic Method" - Method, change the Method from Automatic to Sweep.
• Some further options will be presented for the Sweep method. Change the row labeledType from Number of Divisions to Element Size.
3.3. Example of a Circular Duct 123
• Click on the square cell next to Sweep Element Size and the letter P will appear in the cell to indicate that this value will be defined in theParameter Set.
• Right-click on theMesh branch and select Insert | Sizing.
• Change the filter selection to Edges. Change the selection method from Single Select to Box Select. Select all 16 edges on the faces on both ends of the cylinder, and then click theApply button in the Geometry row.
• Change theType from Element Size to Number of Divisions. Change the value in the row forNumber of Divisions to 6. Change the Behavior from Soft to Hard. When trying to mesh bodies, there can be multiple constraints that have been applied and the meshing algorithm may adjust some of the constraints. By selecting Hard means that this meshing constraint will not be over-ridden.
124 3. Ducts
• For this model theFLUID30 acoustic elements will be used that do not have mid-side nodes. Left-click on theMesh branch, click in the Details of "Mesh"
window, and click on the plus sign next toAdvanced. In the row for Element Midside Nodes, change the value from Program Controlled to Dropped.
• Before the model is meshed, it is necessary to define the size of the elements.
At a later time we will explore the effect of changing the size of the elements on the results. To make it easier to change the size of elements, we will define size as a parameter in theParameter Set window. Return to the Workbench Project Schematic window and double-click on the box for Parameter Set.
• Click on the cell that is labeledNew name, type c_speed_sound, and then press the <Tab> key to move to the cell to the right.
• The cursor should be in the cell for the Value of c_speed_sound, so type 343 and press the <Enter> key on the keyboard, which assigns the Input Parameter ID P4.
• Repeat these steps to define newParameter Name entries for n_index = 1 for the mode index and epw = 12 for the number of elements per wavelength, which will be assigned Input Parameter IDs P5 and P6, respectively.
3.3. Example of a Circular Duct 125
• Create a new Parameter Name called max_freq. In the cell, to define its value, we will enter a mathematical expression for the natural frequency of a rigid–rigid duct, which is fn = nc0/(2L). Type in the cell to define its Value as P5*P4/2/P2. After you press the <Enter> key, it will evaluate to 57.167.
• Repeat this process to define a newParameter Name called esize, which will represent the element size for the acoustic elements. The element size will be defined as
esize = λ epw=c0
f × 1 epw= P4
P7× 1
P6, (3.22)
where λ is the acoustic wavelength, c0 is the speed of sound, and f is the frequency of interest. Hence, in theValue cell, enter the expression P4/P7/P6 and press the <Enter> key, which will evaluate to 0.5.
• Click in the Value cell for P3 Sweep Method Sweep Element Size. In the lower window labeled Properties of Outline C6: P3, click in the cell next toExpression and type P8*1[m], which will set the element size to the value that was calculated previously. Note that it is necessary to define the parameter with units by typing*1[m] at the end of the expression to assign the units of meters. Press the <Enter> key on the keyboard and the Value should evaluate to 0.5, the same as esize.
126 3. Ducts
• Click on theRefresh Project icon, which will transfer the calculated values from the Parameter Set into Mechanical.
• Click on theSave icon to save the project.
• Click on theWorkbench Mechanical window.
• Click on theSweep Method in the Mesh branch and you should notice that the row labeledSweep Element Size has been updated from Please Define to 0.5m.
• Now that the element sizes have been defined, the solid bodies can be meshed. However, before doing so, always save your model by clicking on File | Save Project from the menu bar. Right-click on the Mesh branch and selectGenerate Mesh.
• Once the meshing has been completed, you should notice that there are only 6 elements along the axis of the cylinder. If you zoom to show the mesh at the end of the cylinder, you will see that there are 6 elements on each of the edges, as was defined. The peculiar feature of this mesh is that the patterns in the quadrants are not the same. In ANSYS Release 14.5, it is not easy to create a repeated mesh pattern in ANSYS Workbench compared to using Mechanical APDL. The mesh has resulted in very elongated brick elements, which is usually not advisable. However for this analysis, where acoustic plane wave conditions will exist, the elements with poor aspect ratio will still provide accurate results.
• Up to this point, ANSYS Workbench has meshed the solid model with the default structuralSOLID186 elements. However, we want to conduct an acoustic analysis using acoustic elementsFLUID30. By using the ACT Acous-tics extensions toolbox, it is easy to make the conversion from the structural to acoustic element types. In the ACT Acoustics extension toolbar, select Acoustic Body | Acoustic Body.
3.3. Example of a Circular Duct 127
• In the Graphics window, right-click with the mouse and click on Select All, so that all 4 bodies are highlighted.
• In the window forDetails of "Acoustic Body", click in the cell next to Geometry and click on the Apply button.
• In the window forDetails of "Acoustic Body", change the Mass Density to 1.21, change the Sound Speed to 343, and leave the rest of the entries unaltered. Note this step requires that the units are set to MKS in ANSYS Mechanical.
• Click on the Analysis Settings branch. In the window Details of
"Analysis Settings", click on the plus sign next to Output Controls.
Change the rows for Nodal Forces, Calculate Reactions, General Miscellaneous to Yes.
• Click on the plus sign next to the row for Analysis Data Management, and changeSave MAPDL db to Yes. This step is important because the finite
• Click on the plus sign next to the row for Analysis Data Management, and changeSave MAPDL db to Yes. This step is important because the finite