M UFFLER DESCRIPTION AND CAD MODEL

The system under investigation is a two perforated tube muffler (see Figure 5.2.1) with two expansion chambers and a transition chamber. It equips small engine cars with 0.9-1 liter displacement.

Figure 5.2.1 – The studied commercial muffler.

Each expansion chamber includes a blister containing 50 g of glass wool. The two blisters burn when the muffler reaches a sufficiently high temperature, leaving the wool depositing on the lower walls. In the present work, however, the presence of the insulating material has been neglected.

The muffler is entirely made of aluminized carbon steel P04. The two tubes lie in different horizontal planes and, for this reason, the structure is not symmetrical. Each geometrical length of the muffler has been accurately measured (Figure 5.2.2a) and a CAD model has been obtained, (see Figure 5.2.2b).

In particular, muffler length is about 310 mm plus the length of external portions of the two tubes (100 mm). Axial cross section is not perfectly elliptical with the maximum and minimum length of 216 mm and 133 mm respectively. The two expansion chambers have a length of 110 mm, while the transition chamber of 90 mm. The two tubes have inner diameter of 35mm. External walls thickness is 1.2 mm and tubes and inner diaphragms thickness is 1.5 mm. Diaphragms are only welded to the tubes, with 2 or 3 spot welds, and are free to vibrate with respect to the external walls. Each tube is provided of an ending restriction, highlighted in Figure 2b. Each tube has two perforated portions provided with a variable number of 3 mm diameter holes (from 52 to 77 holes per portion).

Chapter 5 – 1D and 3D BEM analysis of a commercial cross flow muffler

172

a)

b)

Figure 5.2.2 – a) Nominal dimensions of the system; b) CAD model of the muffler.

5.2.2 1D

3D

The 1D and 3D BEM analyses of the previously described muffler have been performed with the commercial software packages GT-Power^TM and VNOISE^TM [2], [4]. These latter, and the integrated equations, have been already widely described in the paragraph 5.1 [10].

Here, in Figure 5.2.3, a 3D rendered model, obtained using the GTMuffler^TM tool, is depicted.

Figure 5.2.3 – 3D rendered model of the muffler derived from GTMuffler^TM tool.

Chapter 5

As previously mentioned, the major advantage related to the use of BEM is that only boundary surfaces must be discretized. Since the geometry under investigation is relatively complicated and includes several thin obstacles within the cavity volume (i.e. baffles), a multi domain approach has been found to be suitable. In this case, the mesh surface, show Figure 5.2.4, consists of 17091 nodes and 32800 shell elements

meshing the CAD surfaces

cavity has been divided into a number of sub the conventional BEM is applied to each sub

The BEM equations for different sub

continuity conditions of pressure and normal velocity at the inte

neighbouring sub-domains (physical continuity BCs). In this case the word ‘interface’

indicates an imaginary surface where the acoustic pressure and normal velocity are imposed to be continuous, or where conditions of porosity are imposed

applied on the other internal and external surfaces [11]. Figure 5.2.6a shows the groups with velocity BCs, while in Figure 5.2.6b the groups with interface BCs are depicted.

a)

Figure 5.2.6 – a) Groups with Velocity B

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As previously mentioned, the major advantage related to the use of BEM is that only s must be discretized. Since the geometry under investigation is relatively complicated and includes several thin obstacles within the cavity volume (i.e. baffles), a multi domain approach has been found to be suitable. In this case, the mesh surface, show

17091 nodes and 32800 shell elements. It has been obtained by meshing the CAD surfaces with the commercial software FEMAP 9.0TM

cavity has been divided into a number of sub-domains, subdivided imaginary sur the conventional BEM is applied to each sub-domain.

Figure 5.2.5 – Surface mesh model.

The BEM equations for different sub-domains are coupled to each other by enforcing the continuity conditions of pressure and normal velocity at the inte

domains (physical continuity BCs). In this case the word ‘interface’

indicates an imaginary surface where the acoustic pressure and normal velocity are imposed to be continuous, or where conditions of porosity are imposed. Furthermore, velocity BCs are applied on the other internal and external surfaces [11]. Figure 5.2.6a shows the groups with velocity BCs, while in Figure 5.2.6b the groups with interface BCs are depicted.

b)

a) Groups with Velocity BCs; b) – Groups with Interfaces BCs.

commercial cross flow muffler

As previously mentioned, the major advantage related to the use of BEM is that only s must be discretized. Since the geometry under investigation is relatively complicated and includes several thin obstacles within the cavity volume (i.e. baffles), a multi domain approach has been found to be suitable. In this case, the mesh surface, shown in . It has been obtained by TM. Thus, the muffler domains, subdivided imaginary surfaces. Hence,

domains are coupled to each other by enforcing the continuity conditions of pressure and normal velocity at the interface between two domains (physical continuity BCs). In this case the word ‘interface’

indicates an imaginary surface where the acoustic pressure and normal velocity are imposed . Furthermore, velocity BCs are applied on the other internal and external surfaces [11]. Figure 5.2.6a shows the groups with velocity BCs, while in Figure 5.2.6b the groups with interface BCs are depicted.

Groups with Interfaces BCs.

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The 3D acoustic analysis requires the specification of the acoustic impedance of perforations.

To this aim, the following semi-empirical expression developed by Sullivan and Crocker [6]

has been employed:

( )

[ ]

ζp ϕ ^h

d t jk 0.75 006

.

0 + +

=

(5.2.1)

where t is the perforated tube wall thickness, dh is the holes diameter, and φ the porosity of the perforation. Through the (6), the holes are not geometrically modeled, and each perforated surface can be described as a simple surface. On the other side, the main disadvantage is that it’s based on a semi-empirical relation which, in some situations, could not ensure an accurate simulation of the physical phenomenon.

As known, eq. (6) is only valid at zero mean flow and with no contact of adsorbent material with the holes. However, since 3D analyses have been performed in absence of mean flow, the application of eq. (5.2.1) can be accepted.