# COMPUTATIONS Acoustic parameters

Sound pressure level (SPL)

ADEM can compute SPL in the frequency spectrum of a one-dimensional source in dB (L, A, B, C), phon or sone units, or in 1/N octave bands (calculation of SPL at a target point requires knowledge of a mathematical model of the acoustic source, as well as that of the path between the source and the target point).

SPL radiated from variable speed fluid machinery intake and exhaust can be computed and 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 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). Thus, IL can be predicted by two SPL calculations. ADEM also computes IL by assuming that the characteristics of the source remain unchanged after the silencer is inserted, and that the silencer replaces a lossless pipe.

Noise Reduction

Noise Reduction (NR) gives the level difference of sound pressures at two different points of a duct system and does not depend on the source characteristics. ADEM can compute NR between two ports of a block diagram, or between the standing pressure wave maxima in the inlet and outlet ducts of a silencer, or between the equivalent source plane and a target point in the exterior environment of the open end of an intake or exhaust system. The latter may provide an estimate of the Insertion Loss under certain conditions (see Duct Acoustics).

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).  TL of silencers with multiple inlet or outlet pipes can be computed.  TL can be computed for multi-modal propagation at the inlet and outlet of a system in 1/N octave bands.

Transfer matrix

ADEM can compute the transfer matrix between inlet and outlet ports of a system in wave or impedance format and as function of frequency or as function specific orders of rotational speed. Sound propagation can be three-dimensional, except at the inlet and outlet of the system, where only one-dimensional waves are assumed to be propagating (measured or FEM based transfer matrices can be imported for use as acoustic elements).

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 can be linked to modal acoustic elements. 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 and can be used as variables in mathematical expressions defining constraints using a simple script notation.

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.