Material Properties
The Acoustics Module includes two material databases: Liquids and Gases, with temperature-dependent fluid dynamic and thermal properties, and a Piezoelectric Materials database with common piezoelectric materials.
Probably, the two most common materials used in acoustics are air and water. In this section we shortly discuss the definition and properties of the built-in Air and Water, liquid materials from the Material Library.
The built-in air and water materials are general and to some extent simplified models. For example, the air represents dry air and the material properties do not depend on moisture. This means that for high-precision absolute-value simulations, detailed material data need to be entered, for example, following the IEC standard for moist air (see Ref. 13). In COMSOL, create your own material and let it depend on the necessary model inputs (pressure, temperature, or relative humidity). Then set up the necessary interpolation functions or analytical expressions and store the material under the User-Defined Library for future use.
The Air and Water, liquid materials were updated for the COMSOL version 5.4 release. Some material data has been added to simplify modeling, and inconsistencies due to rounding have been removed.
To take advantage of the new and updated material data, when opening an existing model (older than version 5.4), delete the material and add it again from the Materials window.
For detailed information about Materials, the Liquids and Gases Materials Database, and the Piezoelectric Materials Database see the COMSOL Multiphysics Reference Manual.
The (Dry) Air Material
The built-in Air material, located both in the Built-In and the Liquids and Gases library, is commonly used in applications and models. The material properties represent those of dry air without the inclusion of moisture.
The air material defines common material parameters and their dependency on the ambient pressure pA and temperature T. The relations are simplified and not all thermodynamic dependencies are taken into account. The speed of sound c and the density ρ are defined through the ideal gas law (assuming adiabatic behavior) following
with the ratio of specific heats γ = 1.4, the gas constant R (COMSOL has a built-in constant called R_const), and the molar mass Mn = 0.02897 kg/mol. This is an idealization of air valid in many cases; see Ref. 2. This means that the speed of sound is not a function of the ambient pressure for this built-in Air material.
Some material properties are only temperature dependent and are given by polynomial fit curves like:
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The dynamic viscosity μ = μ(T)
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The (specific) heat capacity at constant pressure Cp = Cp(T)
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The thermal conductivity k = k(T)
Some properties are defined as constant:
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The ratio of specific heats γ = 1.4
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The molar mass Mn = 0.02897 kg/mol
Furthermore, there are material parameters and properties that are derived from their definitions and the above material data:
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The bulk viscosity μB is defined as μB = 0.6·μ(T) in order to comply with the absorption behavior (see discussion in The Bulk Viscosity section).
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The (isobaric) coefficient of thermal expansion is defined as αp = 1/T, following the ideal gas law.
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The parameter of nonlinearity B/A is also defined for gases following the ideal gas law as B/A = (γ+1)/2 (see Ref. 12).
The (Clean) Water Material
The built-in Water, liquid material, located both in the Built-In and the Liquids and Gases library, is also commonly used in applications and models. These material properties represent those of clean water without the dependency on, for example, salinity or pH value necessary to describe salt water in the ocean.
Specifically for acoustics applications, the water material properties include properties that are temperature dependent like:
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The speed of sound c = c(T)
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The density ρ = ρ(T)
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The dynamic viscosity μ = μ(T)
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Thermal conductivity k = k(T)
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The heat capacity at constant pressure Cp = Cp(T)
Furthermore, there are detailed material parameters that are derived from the above definitions:
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The bulk viscosity is defined as μB = 2.79·μ(T). In order to comply with the absorption behavior, (see the discussion in The Bulk Viscosity section).
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The (isobaric) coefficient of thermal expansion is defined through the thermodynamic definition as
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The ratio of specific heats γ = γ(Τ) is based on the thermodynamic relation
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This definition is necessary in detailed models solving the thermoviscous acoustics or the linearized Navier-Stokes equations in water. The definition ensures that it is not just set to γ = 1.