The Poroacoustics node defines a fluid domain with a porous material modeled in a homogenized way using a so-called equivalent fluid model. Several models exist to define the attenuation and dispersion experienced by the pressure waves as they propagate in the porous domain. The different models are described below.
Select a Poroacoustics model:
Delany-Bazley-Miki (the default),
Zwikker-Kosten,
Attenborough,
Wilson,
Johnson-Champoux-Allard,
Johnson-Champoux-Allard-Lafarge,
Johnson-Champoux-Allard-Pride-Lafarge,
Three-parameter approximation JCAL model,
Williams EDFM, or
Wood.
The following properties are available based on the Poroacoustics model selected above. The default values are taken
From material. For
User defined enter a different value or expression.
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Density ρf (SI unit: kg/m 3) of the saturating fluid (the fluid density).
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If any other than the default Delany-Bazley-Miki is selected, the following properties are also required, depending on the selection. These material parameters are necessary as the more advanced models include the losses associated with viscosity and thermal conduction in a more or less detailed way:
In this section, enter the properties that describe the porous material. By default the Porous elastic material uses the
Domain material (the material defined for the domain). Select another material as needed. For example, create your own material that contains the properties of a given porous material and refer to it here. Here you also select if you want to use a
rigid frame approximation or a
limp frame approximation for the porous material (where applicable). The poroacoustic model defines complex-valued frequency-dependent expressions for both the bulk modulus and the equivalent density.
Based on the Poroacoustics model selected, enter the following settings for the porous matrix.
Select an option from the Constants list:
Delany-Bazley (the default),
Miki,
Qunli,
Mechel, glass fiber, low X,
Mechel, glass fiber, high X,
Mechel, rock fiber, low X,
Mechel, rock fiber, high X,
Komatsu,
Modified Allard and Champoux, or
User defined. For
User defined enter values in the
C1 to
C8 fields. The models are empirical and based on fitting to measured data. This means the models have different regions of applicability with respect to the flow resistivity
Rf, the frequency
f, the material type, and the parameter
X defined as
The exception is the Komatsu model, where
X = 2 − log
10(f/Rf) (which is a completely empirical quantity). All the models are applicable for materials with a porosity
εp close to 1. The model information is listed in
Table 2-2. See also
Ref. 23 and the relevant section in
About the Poroacoustics Models for further details.
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Absorptive Muffler: Application Library path Acoustics_Module/Automotive/absorptive_muffler
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For Zwikker-Kosten, select a
Porous matrix approximation:
Rigid (the default) or
Limp. Then based on your choice, the default value for each of the following parameters is taken
From material. For
User defined, enter another value or expression.
For Attenborough, select a
Porous matrix approximation:
Rigid (the default) or
Limp. Then based on your choice, the default value for most of the following parameters is taken
From material. For
User defined, enter another value or expression.
For Wilson, select a
Porous matrix approximation:
Rigid (the default) or
Limp. Then based on your choice, the default value for the following parameters is taken
From material. For
User defined, enter another value or expression.
The Johnson–Champoux–Allard (or JCA model) is a five-parameter semiempirical model for describing a large range of porous materials with rigid (or limp) frames. As input, the model requires the viscous Lv and thermal
Lth characteristic lengths (sometimes denoted
Λ and
Λ'). These replace the hydraulic radius used in simpler models and account for the thermal and viscous losses that appear at the acoustic boundary layer at pore walls. See
About the Poroacoustics Models for details.
For Johnson-Champoux-Allard, select a
Porous matrix approximation:
Rigid (the default) or
Limp. Then based on your choice, the default value for most of the following parameters is taken
From material. For
User defined, enter another value or expression.
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Select Viscous characteristic length (the default) to directly enter an expression for Lv (SI unit: m). The default expression is sqrt(acpr.mu*acpr.tau*8/(acpr.Rf*acpr.epsilon_p)), which corresponds to s = 1.
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Select Viscous characteristic length parameter to enter a value for s (dimensionless) (the default is 1).
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For Johnson-Champoux-Allard-Lafarge, the settings are the same as for
Johnson–Champoux–Allard with the addition of the
Static thermal permeability κ'0 (SI unit: m
2) setting.
For Johnson-Champoux-Allard-Pride-Lafarge, the settings are the same as for
Johnson–Champoux–Allard plus these additional parameters:
The Three-parameter approximation JCAL model represents an approximation to the JCAL model. Instead of requiring 6 parameters as input for the porous matrix it only requires three. The porosity as well as two parameters that relate to the topology of the pores are needed (their size and distribution). Two different approximation methods exist for the density and bulk modulus. Select the
Density and bulk modulus approximation to either
Johnson-Champoux-Allard-Pride-Lafarge (the default) or
Padé approximation. Then if necessary enter the values for (default is
From material):
Williams EDFM is an
effective density fluid model (EDFM) used to model the propagation of acoustic waves in sediments. The model assumes that the bulk and shear moduli of the frame of the porous material are negligible, meaning that the porous frame is limp. See
Ref. 24 and
About the Poroacoustics Models for further details.
The Porous Matrix Properties (the properties for the sediment) for
Williams EDFM have the default values taken
From material. For
User defined, enter another value or expression:
The Wood model is used for a fluid mixture or a fluid suspension (solid inclusions completely surrounded by fluid). The Woods formula for the sound velocity is determined by using the effective bulk modulus of the suspension and the volume average density. As the Williams EDFM, this model gives effective values for the mixture. This model is exact for low frequencies, when the wavelength is much larger than the size of the inclusions. See
Ref. 25 and
About the Poroacoustics Models for further details.
The Porous Matrix Properties (the properties for the inclusions) for the
Wood model are entered in the
Inclusion properties table. For each
Inclusion (any number of inclusions can be added, the number is automatically incremented) enter the
Volume fraction, the
Bulk modulus, and the
Density. Add a new row (inclusion) by clicking the plus sign below the table. The table may be saved or loaded from a file.