Thermoviscous Acoustics Model
Use the Thermoviscous Acoustics Model node to define the model inputs (the background equilibrium temperature and pressure) and the material properties of the fluid (dynamic viscosity, bulk viscosity, thermal conductivity, heat capacity at constant pressure, and equilibrium density) necessary to model the propagation of acoustic compressible waves in a thermoviscous acoustic context. Extended inputs are available for the coefficient of thermal expansion and the compressibility, which enables modeling of any constitutive relation for the fluid.
Model Inputs
This section contains field variables that appear as model inputs. The fields for the Equilibrium pressure p0 and the Equilibrium temperature T0 are always active as they enter the governing equations explicitly. If material properties depend on other model inputs they will automatically appear in this section.
Select User defined (the default), Common model input, or an existing variable from another physics interface.
The Equilibrium pressure p0 (SI unit: Pa) has the default value set to 1 atm. The Equilibrium temperature T0 (SI unit: K) has the default value set to 293.15 K (that is, 20oC).
Details about the Model Input and the Default Model Inputs are found in the Global and Local Definitions chapter of the COMSOL Multiphysics Reference Manual.
Fluid Properties
Define the material properties of the fluid by selecting an Equilibrium density — Ideal gas, From material, or User defined.
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If From material is selected (the default), the equilibrium density, and its dependence on the equilibrium pressure p0 and temperature T0, is taken from the defined material. Make sure that the Thermal Expansion and Compressibility settings are correct.
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For Ideal gas also select the Gas constant type — select Specific gas constant Rs (SI unit: J/(kg·K) or Mean molar mass Mn (SI unit: kg/mol)
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For User defined enter a value or expression for the Equilibrium density ρ0(p0, T0) (SI unit: kg/m3). The default is ta.p0/(287[J/kg/K]*ta.T0), which is the ideal gas law.
The other thermoviscous acoustic model parameters defaults use values From material. For User defined enter another value or expression for:
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Dynamic viscosity μ (SI unit: Pa·s).
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Bulk viscosity μB (SI unit: Pa·s). The bulk viscosity parameter describes the difference between the mechanical and thermodynamic pressures. It is associated with losses due to expansion and compression.
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Thermal conductivity k (SI unit: W/(m·K)).
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Heat capacity at constant pressure Cp (SI unit: J/(kg·K)). This is the specific heat capacity or heat capacity per unit mass.
For a discussion about the air and water materials as commonly used in acoustics and other material properties, such as the bulk viscosity, see the Acoustic Properties of Fluids chapter of this manual.
Thermal Expansion and Compressibility
One of the main characteristics of an acoustic wave is that it is a compressional wave. In the detailed thermoviscous acoustic description, this property is closely related to the constitutive relation between the density, the pressure, and the temperature. This results in the important (linear) relation for the acoustic density variation
where ρt is the total density variation, pt is the total acoustic pressure, Tt is the total acoustic temperature variation, βT is the (isothermal) compressibility of the fluid, and αp the (isobaric) coefficient of thermal expansion (sometimes named α0). If this constitutive relation is not correct, then no waves propagate or possibly they propagate at an erroneous speed of sound. The default behavior is to define both quantities from the speed of sound and the ratio of specific heats (using the From speed of sound option) which are material properties often more readily available.
Note that when the Adiabatic formulation option is selected, under the Thermoviscous Acoustics Equation Settings section, the equation of state reduces to
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When the From equilibrium density option is selected for the coefficient of thermal expansion and the compressibility, both values are derived from the equilibrium density ρ0(p0,T0) using their defining relations
If the equilibrium density ρ0 is a user-defined constant value, is picked up from another physics interface, or the material model does not define both a pressure and temperature dependence for ρ0, the coefficient of thermal expansion and/or the compressibility will evaluate to 0. Then the default From speed of sound option or the User defined options should be used.
If the material is air, the From equilibrium density option works well as the equilibrium density ρ0 = ρ0(p0,T0) is defined as a function of both pressure and temperature.
For the water material the coefficient of thermal expansion is well defined as ρ0 = ρ0(T0), while the compressibility should be defined using the default From speed of sound option.
The Thermal Expansion and Compressibility section is displayed if From material or User defined is selected as the Equilibrium density under Thermoviscous Acoustics Model. For the Ideal gas option, the parameters are readily defined.
Select an option from the Coefficient of thermal expansion αp list — From material, From equilibrium density, From speed of sound (the default), or User defined. For User defined enter a value for αp (SI unit: 1/K = K-1).
Select an option from the Isothermal compressibility βT list — From equilibrium density, From isentropic compressibility, From speed of sound (the default), or User defined. For User defined, enter a value for βT (SI unit: 1/Pa = Pa-1).
The different options for defining the coefficient of thermal expansion and the compressibility stem from their thermodynamic definitions:
For each of the following, and based on the above selection, the default is taken From material. For User defined enter another value or expression in the text field.
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Speed of sound c (SI unit: m/s).
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Ratio of specific heats γ (dimensionless). The default is 1.
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Isentropic compressibility βs (SI unit: 1/Pa = Pa-1).
See the Theory Background for the Thermoviscous Acoustics Branch section for a detailed description of the governing equations and the constitutive relations.
To visualize the dissipated energy due to viscosity and thermal conduction in postprocessing, three postprocessing variables exist:
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The viscous power dissipation density ta.diss_visc.
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The thermal power dissipation density ta.diss_therm.
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The total thermo-viscous power dissipation density ta.diss_tot.
In certain cases, it can be interesting not to include thermal conduction in the model and treat all processes as adiabatic (isentropic). This is, for example, relevant for most liquids where the thermal boundary layer is much thinner than the viscous. Not solving for the temperature field T also saves some degrees of freedom (DOFs). This is achieved by selecting the Adiabatic formulation option under the Thermoviscous Acoustics Equation Settings section.
See also Solver Suggestions for Large Thermoviscous Acoustics Models for suggestions on how to select an iterative solver for large problems.