MODELING

OF

 MUFFLERS AND SILENCERS BY BLOCK DIAGRAMS

Block diagrams Source Element database Data input

Genuine block diagram models of flow ducts, mufflers, silencers and resonators are constructed by the user on the System Model Interface (SMI) by simple mouse actions.  SMI has several layers.  The complete block diagram model is drawn in layer 1. Figure 1 is a snapshot of layer 1 displaying a block diagram model of the cold end of an exhaust line of a passenger car, a schematic of which is shown in Fig.2. 

Figure 2 A snapshot of the System Drawing Interface (SDI) displaying a sketch of the system corresponding to the block diagram in Fig. 1. Sections of such a sketch or drawing can be linked to the ports of the block diagram. The pipes in dark gray are represented in the block diagram by element 2 and the parts in dark and bright green are represented by element 45 (parts in dark green are packed with sound absorbing material).
Figure 1 A snapshot of the System Model Interface  (SMI). Rectangular blocks represent acoustic elements. Modeling actions such as creating, deleting. joining, moving, etc., are selected by clicking on toolbar buttons or drop-down list items.  Acoustic elements are characterized by their ports, represented by the small circles on sides of blocks, and are connected by dragging the mouse from one port to the other with a compatible positive acoustic flow direction (displayed at the port). These directions can be changed by the user by clicking on the nodes so that the continuity of flow is maintained.

Block diagram strategy

The network strategy of ADEM  is based, conceptually and mathematically, on giving users the freedom of constructing their own acoustic models in 1-D and 3-D, by using the element database of the software, without being involved in any mathematics or programming, simply by drawing block diagrams.  The process of generating a mathematical model from a block diagram is carried out by the computer. This involves complex mathematical operations, which are often published as research articles in scientific journals.  

For example,  in Figure 1, the elements numbered 45, which are generically called UsedMacro, are formulated by the user and represent the green regions of the oval and circular mufflers.  A UserMacro can be saved with a special name so that it can be used later as an acoustic two-port element.  Thus, however complex  the actual system configuration may be, its block diagram model may always be represented in layer 1 of SMI as a cascade of two-port elements,  This strategy simplifies the reading of complex block diagrams and it is ideally suited for teamwork and customization for specific projects. 

Block diagrams of UserMacros (1-D or 3-D) are constructed in sublayers of  SMI.  For example, Figure 3 is a block-diagram of the oval muffler in Figure 2. Sub-layers may have different UserMacos, but only the one linked to a specific UserMacro in layer 1 is used in assembling the system model. When a UserMacro is linked to a sublayer, the color of its sides turns bright-green.  The linked sublayer number can be input as a parameter of a UserMacro. Then several different prototypes can be run in batch.

Figure 3 Acoustic model of an element formulated by the user

Sound source

The acoustic source driving a duct system can be defined in ADEM explicitly or implicitly.

The explicit method: SourceMacro

Any multiple-input-single-output duct system with spectral sources (defined subsequently) is represented by the generic one-port element called SourceMacro. This is connected as the terminal element on the source side of the block diagram in layer 1. For example, Fig. 4a is a schematic of a laboratory setup, where the acoustic field in a duct system is generated by two pressure drivers in tandem, for the measurement of some acoustic parameters of the system. The SourceMacro is used to model the upstream side of the (equivalent) source plane as shown in Fig. 4b. A SourceMacro is similar to a UserMacro, in that, it must be linked to a sub-layer of SMI, where its block diagram model is drawn. Fig 4c is a block diagram of the SourceMacro in Fig. 4b.

Two-port acoustic source are applied by using the element SOURCEL, the characteristics of which may be based on actuator-disk models or measurements. This may co-exist with a SourceMacro or an implicitly defined one-port source, or may be the primary source.

The implicit method

If a duct system is driven by a one-port source, the program assumes that it is applied at the inlet node of the system, which is defined as the unconnected inlet node on the source side of the block diagram in layer 1. For example, in Figure 1 the source is applied by the implicit method at the inlet node of element 2, which corresponds to the inlet of the circular muffler in Figure 2.

Fig. 4a An expansion chamber driven by two pressure drivers in tandem. Upstream of the source plane is modeled by a SourceMacro.
Fig. 4b A block diagram model of the system in Fig. 4a. Element 13 is the SourceMacro and the green color indicates that it is linked to a su-layer where its block diagram is drawn (Fig. 4c). Element 1 models a generic expansion chamber in 1-D or 3-D. The source plane corresponds to the inlet node of the duct element 2 on the source side.
Fig. 4c Acoustic block diagram of the source side of the system shown in Fig. 4a. Element 11 represents an arbitrary spectral source, element 6 models the acoustic boundary on the source side and element 55 models duct junctions. This model is drawn in a sublayer of SMI, which is linked to the SourceMacro in layer 1.
Video 1

The type of an implicit source is selected from the main menu and the source data are input in respective datasheets (see Video 1). The following source types can be applied implicitly:

Piston

Rigid piston driven by arbitrary velocity or displacement signal.

Spectral

One-port source with frequency dependent impedance and pressure strength. Simple tools are provided for calculating crisp spectral source characteristics of loudspeakers and the crisp or fuzzy equivalent source characteristics of engine exhausts and intakes. There is also a tool for moving multiple crisp spectral sources to an equivalent source plane. Steady and non-steady spectral one-port sources, the characteristics of which are determined from the microphone signals in source measurements can be applied implicitly and Campbell diagrams can be produced in case of non-steady sources.

Orders

This is a non-steady spectral source. Its datasheet, which is designed for automobile engine applications, allows input of the equivalent intake or exhaust source characteristics corresponding to the important  harmonic orders of the engine rotational speed.

Power

Applies a given acoustic power spectrum at the source plane, irrespectively of the load.

Undefined

This option is chosen when calculating an acoustic parameter that do not depend on the source characteristics (e.g., transmission loss of a 1-D system).

Acoustic element database

The following table summarizes the categories of the over 60 acoustic elements contained in the database of the software. Each category includes one-dimensional and three-dimensional elements with mean flow. Using this database, users can create an infinity of new elements. 

CategorySome features
Perforated pipe packs Any number of perforated pipes enclosed in hard- or soft-walled casing in any communication topology; mean cross-flow or grazing flow configuration; sound absorbent material application; discrete or continuous perforate models.
Area changes Open or closed; through flow or flow reversing; multiple inlets or outlets; side-inlet or side-outlet
Junctions With any number of connecting ducts including branch and splitter configurations
Pipes  and ducts  Uniform or non-uniform; mean temperature and pressure gradients; narrow viscothermal; lined; open or porous walls; distensible walls.
Macros (user formulated)Generic passive two port (based on ADEM database): generic passive two-port (measured or FEM or BEM based); generic active one-port (equivalent of arbitrary miso system)
Sources 1-port: 2-port
BoundaryOpen (flanged or unflanged, intake or exhaust with mean flow); closed; pressure-release, anechoic; measured; multi-mode cut-on
Open end radiationFree-field; fractional free-field; diffuse field.
CompoundsSeveral common mufflers, chambers and resonators
BafflesPerforated uniformly or over regions
After treatmentCatalytic converter; Diesel particulate filter

Input datasheets

Element data are entered in element datasheets, which open when you click within the area of a block. Element datasheets have formula input capability and error filters for number input format.  A typical input datasheet is shown in Figure 4.  Detailed definitions of the input parameters on each datasheet are accessed on-line by clicking on the Help button.  The input fields accept algebraic formulas in APL language and are checked for syntax. The mean temperature and the mean pressure in elements are input only for a reference operational point and no input is required for the mean flow velocity.

Figure 4 The element datasheet of a one-dimensional multi-port junction block, element 55. The number of pipes are selected by the user . The pipe numbering corresponds to the port numbering on the block.
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