# COMPUTATIONS Acoustic parameters

Sound pressure level (SPL)

ADEM calculates the SPL at a target point due to given ducted source in dB(L,A,B,C), phon or sone units as function of frequency, or in proportional or fixed frequency bands. SPL radiated from fluid machinery intake and exhaust can also be computed as function of the rotational speed of the fluid machine and can be plotted in the form of a Campbell diagram (Figure 1). Horizontal cuts of the Campbell diagram showing the variations of SPL with the frequency at specific rotational speeds, and inclined cuts (Figure 2) showing the variation of SPL with the rotational speed for any harmonic order of the rotational speed can also be produced. Figure 2  Some order cuts of the Campbell diagram in Figure 1.

Insertion loss

The difference in SPL at a target point before and after a silencer is mounted on a duct system is called Insertion Loss (IL). IL can be predicted by two SPL calculations. However, it is customary to assume that the characteristics of the source remain unchanged after the silencer is inserted. Then IL depends only on the impedance of the source and can be calculated directly. Calculations are often simplified further by envisaging that the silencer replaces a lossless pipe.

Noise Reduction

Noise Reduction (NR) gives the level difference between the sound pressures at two different points of a duct system. In travelling microphone days of sound pressure measurements, they were usually taken, in anticipation of validation tests, at the points of standing wave maxima in the inlet and outlet ducts of a silencer. When the reference points are taken at the equivalent source plane and a microphone position outside the open end of the system, NR may provide an estimate of the Insertion Loss (see Duct Acoustics), even though it does not depend on the source characteristics.

Attenuation

Attenuation is defined as the level difference between the incident sound pressures at two different points, which are usually taken at the equivalent source plane and the open end, of an intake or exhaust system. Calculation of Attenuation does not require information about the source characteristics. Under certain conditions, Attenuation may be used to estimate Insertion Loss (see Duct Acoustics).

Transmission Loss

This classical parameter (TL) gives the level difference between the incident acoustic power at the inlet and outlet of a muffler or silencer, assuming outlet(s) is anechoic (non-reflecting or an infinitely long duct).  Silencers with multiple inlet pipes can be modeled.  TL can be computed for multi-modal propagation at the inlet and outlet of a system in 1/N octave bands.

Transfer matrix

Two-port transfer matrices can be computed in wave or impedance format and as function of frequency or as function specific orders of rotational speed. Sound propagation can be 3-D, except at the inlet and outlet of the system, where only 1-D waves are assumed to be  propagating . Measured or FEM based transfer matrices can be imported for use as acoustic elements and, conversely, transfer matrices computed in ADEM can be exported for use as acoustic elements elsewhere.

Acoustic path index

This index may be used for the assessment of the likelihood of meeting a specified SPL target with a given silencer prototype.   See Duct Acoustics for the definition of this parameter.

Equivalent one-port source

Figure 4 shows the block of a system which consists of four one-port sources (element 11) on a network converging to single duct.  This can be envisaged as the acoustic model of a four-cylinder engine manifold or as four pressure drivers mounted on a duct.  Such multiple-source networks can be reduced to an active one-port element, which can be saved with a name and invoked, implicitly or explicitly, as a one-port spectral source element when required.

Sectional parameters

The parameters can be calculated at the nodes of a block diagram model of a duct system: Acoustic Power, Reflection coefficient, Acoustic impedance.

Transverse duct modes

Three-dimensional effects on sound propagation in ducts are represented by the transverse duct modes which are characterized by their eigenvalues and eigenfunctions. ADEM  has an easy-to-use modal analysis interface for calculation of any number of transverse eigenvalues and eigenfunctions of hard-walled ducts of any connected geometry.  Duct boundary can be circular, rectangular, elliptical, oval or any simply connected curve consisting of linear and circular segments.

The finite element mesh required for modal calculations is generated automatically and the computed transverse modes are linked also to the appropriate acoustic elements simply  inputting a section id number. Cut-outs can be circular, rectangular or elliptical.   Figure 3 shows the finite element meshes generated for some sections.  The eigenvalues and the corresponding nodal lines can be viewed on the user interface.

## Optimization

ADEM has several tools that equip the user with the ability to  determine systematically the details of muffler or silencer concepts that meet a given target performance.

Firstly, acoustic parameters can be computed as functions system parameters, enabling design of experiment (DOE) simulations.  The parameters are activated directly from element datasheets by simple mouse actions and can be used as variables to form mathematical expressions defining constraints using a simple script.

Secondly, provided are systematic direct search algorithms for accelerated searching of local optima under arbitrary number of equality and inequality constraints.  The search process is followed on-line on the graphical output interface and the speed of convergence can be monitored by the user.

Thirdly, acoustic performance parameters can be computed in stochastic intervals corresponding to variations of selected system parameters in given intervals. This is of particular importance when uncertainty exists about the values of some element parameters and the designer wants to know the sensitivity of the system to possible variations.

For example, Figure 5 shows the sensitivity of a silencer to the value of the end-correction applied at a sudden are-change. Heuristic (experimental or theoretical) values are often proposed as end correction to account for the higher order mode effects at such discontinuity,  but these are strongly dependent on the actual system geometry.  Interval plots such as Figure 5 provide better assessment of the effects of variations due to the fuzziness of the end-correction.