Impedance
The Impedance node adds an impedance boundary condition with the option to select between several built in impedance models. The impedance condition is a generalization of the sound-hard and sound-soft boundary conditions:
In the Pressure Acoustics, Transient interface using a Time Dependent study, the impedance boundary condition is the following:
Here Zi is the specific acoustic input impedance of the external domain and it has the SI unit Pa·s/m — a pressure divided by a velocity. From a physical point of view, the acoustic input impedance is the ratio between the local pressure and local normal particle velocity. The specific acoustic impedance Zi is related to the acoustic impedance Zac (ratio of pressure and flow rate) and the mechanical impedance Zmech (ratio of force and velocity) via the area A of the boundary, according to
The Impedance boundary condition is a good approximation of a locally reacting surface — a surface for which the normal velocity at any point depends only on the pressure at that exact point.
Most impedance models only exist in the frequency domain. The only exception is the User defined impedance which can be applied also in the time domain.
In the two opposite limits Zi → ∞ and Zi → 0, this boundary condition is identical to the Sound Hard Boundary (Wall) condition and the Sound Soft Boundary condition, respectively.
Impedance
A number of different types of impedance boundary conditions are included to address standard situations in many typical applications of pressure acoustics.
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Simple RCL models to define lumped-parameter circuits describing, for example, the mechanical response of a microphone diaphragm.
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A set of physiological models enable easy modeling of the surface impedance of human skin and the acoustic loads of the human ear and eardrum.
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The waveguide end impedances define simplified models of the acoustic losses at the end of pipes and ducts.
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A porous layer backed by a sound-hard wall model can be defined.
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Simple wave-type specific characteristic impedance model exist to address open boundaries in a simplified way.
The ear impedance, skin impedance, and RCL models provide a tool for engineers to add realistic acoustic loads when, for example, developing and simulating headphones, hearing aids, head sets, and other mobile devices.
Choose an Impedance model — User defined, RCL, Physiological, Waveguide end impedance, Porous layer, or Characteristic specific impedance.
User defined
Allows the user to enter any expression and is the only impedance model which applies to time-dependent models. It is advantageous to enter complicated user-defined models as a variable under the Definitions node or use an interpolation function for measured data.
Enter the value of the Impedance Zi (SI unit: Pa·s/m). The default value is set to the characteristic specific impedance of air 1.2 kg/m3·343 m/s.
RCL
The RCL model includes all possible circuits involving a source of damping (a resistor Rac), an acoustic mass or inertance (an inductor Lac), and a source of acoustic compliance (a capacitor Cac). The circuit elements are entered in acoustic units. These can be used as a simple model of, for example, the input impedance of a microphone, a loudspeaker cone, or other electromechanical applications. Other applications include general transmission line/circuit models with applications in materials with exotic acoustic properties. More advanced circuit models may be entered manually in the User defined option or by coupling to an Electric Circuit model (this requires the AC/DC Module).
Choose an option from the list: Serial coupling RCL, Parallel coupling RCL, Parallel LC in series with R, Parallel RC in series with L, Parallel RL in series with C, Serial RC in parallel with L, Serial LC in parallel with R, or Serial RL in parallel with C.
Notice the matching diagram and Equation section information for each choice. Then enter the following:
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Equivalent acoustic resistance Rac (SI unit: kg/(m4·s)).
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Equivalent acoustic compliance Cac (SI unit: m4·s2/kg).
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Equivalent acoustic inertance Lac (SI unit: kg/m4).
Generic 711 Coupler—An Occluded Ear-Canal Simulator: Application Library path Acoustics_Module/Electroacosutic_Transducers/generic_711_coupler
Physiological
This is a set of simple models to address applications involving interactions of acoustics with the human body. The models comprise human skin, the impedance of the entire human ear including or excluding the pinna, the outward radiation impedance caused by the pinna, and the inward impedance experienced at the ear drum comprising the drum and the entire inner ear. For the two models of the human ear (with/without pinna), the pressure at the ear drum is automatically calculated. The variable has the form acpr.imp1.p_ear_drum and can be plotted in postprocessing.
The whole ear models are based on the geometry of the ear canal and pinna of a specific ear (see Ref. 28-30), but person-to-person variations of these are to be expected. For applications where a specific ear canal geometry can be obtained, better results are expected by explicitly modeling this and applying the eardrum impedance at the end.
Choose an option from the list: Human skin, Outward human ear radiation, Human ear drum, Human ear without pinna, or Human ear, full. Then select either From material (the default) or User defined for the following, as required:
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Ratio of specific heats γ (SI unit: 1).
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Heat capacity at constant pressure Cp (SI unit: J/(kg·K)).
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Thermal conductivity k (SI unit: W/(m·K)).
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Dynamic viscosity μ (SI unit: Pa·s).
When the From material option is selected, remember to add a material under the Materials node and assign it to the specific boundary. The boundary will not automatically assume the physical properties of the domain.
Waveguide end impedance
This is a set of idealized models for the acoustic losses at the end of pipes opening into vast domains. The models consider both square and circular cross sections, as well as flanged and unflanged pipe ends. These models are based on a plane wave assumption (propagation below the cut-off frequency).
Choose an option from the list: Flanged pipe, circular (the default), Flanged pipe, rectangular, Unflanged pipe, circular (low ka limit), or Unflanged pipe, circular. Then enter the following as required:
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Inner radius a (SI unit: m) or
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Inner width wi (SI unit: m) and Inner height hi (SI unit: m).
Open Pipe: Application Library path Acoustics_Module/Verification_Examples/open_pipe
Porous layer
This choice models the acoustic losses of a normally incident field on a porous layer of user-defined thickness d backed by a sound-hard wall. Use this boundary condition as an alternative to modeling the porous layer explicitly using the Poroacoustics feature. All material models from Poroacoustics are implemented in this feature.
Enter the Thickness of porous layer d (Si unit: m) and select a Poroacoustic model. The rest of the settings are the same as for Poroacoustics.
Characteristic specific impedance
This is a set of models describing the characteristic impedance associated with three basic wave types: plane wave, cylindrical wave, and spherical wave. Although mostly of academic interest, these serve as good first-order and wave-type specific boundary-condition models of infinite domains (open boundaries). They can be applied to all cases where the tangential components of the acoustic field at the boundary may be ignored. Use the radiation conditions (Plane Wave Radiation, Spherical Wave Radiation, or Cylindrical Wave Radiation) if a nonreflecting open boundary is modeled.
Select a Wave type: Plane wave (the default), Cylindrical wave, or Spherical wave. Then enter the Source location x0 (SI unit: m) and for the Cylindrical wave, the Source axis esa (SI unit: m).
The theory for the impedance models is discussed in detail in Theory for the Boundary Impedance Models.