BEM_tutorial_Chp3_Traveling Wave in a Duct

7/28/2019 BEM_tutorial_Chp3_Traveling Wave in a Duct

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Chapter 3

Example Two: Traveling Wave

in a Duct

The second example (see Figure 1.1.b) is a simple model of a 1D travelingwave in a rigid walled duct.

This problem introduces the concept of impedance by the addition ofabsorption to the downstream end of the duct studied in the first example.The wave is fully absorbed (no reflections), resulting in a traveling wave.

Either the previous example (stand.gid) can be loaded up or a com-pletely new model can be made. To make changes to example one, load upstand.gid and save as trav.gid. To start a new model open up a newproject and save it in your working folder as trav.gid. Follow the samesteps as outlined in the first example up to and including the step wherethe velocity boundary conditions are defined.

Enter the boundary condition environment, either after making changesto example one or starting a new model (after the assignment of unit velocityto mimic the piston but before selecting finish). An absorption boundarycondition needs to be added to the downstream end of the duct. To dothis click on Impedance. Set the real normal impedance to 415.03 (theproduct of the speed of sound in air and the density of air, 343 and 1.21

respectively) and leave the imaginary normal impedance as 0. Click assignand then using the mouse, select the surface at z=10, the far end of the duct(see Figure 3.1). Select finish to complete the assignment of boundaryconditions.

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3. Example Two: Traveling Wave in a Duct

Figure 3.1: Adding an impedance to the duct.

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Select (Data > Problem data). Give the project a title of .

Set the problem data parameters to be exactly the same as for exampleone. In addition, set the Output Points panel to the values shown inFigure 3.2, and select close. This will set evenly spaced output points alongthe centreline of the duct.

Figure 3.2: Problem data output points panel.

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The next step is to mesh the duct. Select (Mesh > Generate). A

dialog box will appear asking you to Enter the size of elements to begenerated. Type in . A dialog box will appear which states that328 triangular elements have been created. Press OK and the mesh willappear, as shown in Figure 3.3.

Figure 3.3: Duct mesh.

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Generate a solution and review the results in exactly the same manner

as for example one. The pressure amplitude pattern obtained should differconsiderably from that of the standing wave (Figure 3.1). This time, theamplitude should approximately constant along the duct length.

Figure 3.4: Pressure amplitude over boundary of duct.

Figure 3.1 may not appear to be constant, however try changing the scale range

to match that of Figure 2.13. Use the Set minimum value and Set maximum value

icons at the left of the screen.

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During the generation of the solution, a file entitled output.fdat2

would have been written to your working folder. This can be opened andread using your preferred text editor. This file gives values associated withthe output points, details of which are given in B.

The analytical pressure at any point in the duct of a traveling planewave is given by the equation:

p(x) = ceikx (3.1)

where x is the distance from the point of excitation along the duct.Using your preferred graphing package try comparing the absolute value

of the traveling wave pressure with the analytical solution. You should

obtain a graph which looks similar to Figure 3.5.

0 2 4 6 8 10500

400

300

200

100

0

100

200

300

400

500

Distance along duct (m)

Absolute

Sound

pressure

(Pa)

BEM

Theory

Figure 3.5: Sound pressure along the centre of duct side.

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BEM_tutorial_Chp3_Traveling Wave in a Duct