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 (speed of sound, density, heat capacity at constant pressure, ratio of specific heats, thermal conductivity, dynamic viscosity, and bulk viscosity) necessary to model the propagation of acoustic compressible waves in a thermoviscous acoustic context using the SLNS approach.
The model sets up the three Helmholtz equations that result from a Helmholtz decomposition of the full thermoviscous acoustic governing equations. The three equations are solved sequentially, and represent the viscous and thermal incompressible waves and the compressible acoustic wave. The main assumption for the decomposition is that the acoustical wavelength is much larger than the thickness of the viscous and thermal boundary layers.
The three equations solved are for the viscous scaling function Ψv, the thermal scaling function Ψth, and the total acoustic pressure pt. The equations are
(6-2)
where kv is the viscous wave number, kth is the thermal wave number, and k is the wave number of the compressional acoustic wave. is the modified thermal scaling function. For the adiabatic formulation, the modified thermal scaling function is set equal to 1 and is not solved for. The bulk thermal and viscous losses are always included through the complex-valued density ρc and speed of sound cc, for details see the Thermally Conducting and/or Viscous Fluid Model for the The Pressure Acoustics, Frequency Domain Interface. Note that for notational purposes in the equation display, the thermal conductivity is denoted kcond, as to not confuse the symbol with the wave number k. The condition for the validity of the Equation 6-2 reads
where δv is the viscous boundary layer thickness and δth is the thermal boundary layer thickness.
The two equations for the scaling functions depend only on the geometry, frequency, and material properties, as well as the choice of No slip and Slip (perfect) condition at the Wall. The equations can be solved sequentially with the equation for the acoustic pressure last. When the default solver is generated, the equations are solved sequentially, which gives the desired performance.
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 visible. If material properties depend on these, they are automatically used. Select User defined (the default), Common model input, or an existing variable from another physics interface.
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
For each of the following material properties the default values are taken From material. For User defined, enter other values or expressions for any or all options.
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Speed of sound c (SI unit: m/s).
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Density ρ (SI unit: kg/m3).
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Heat capacity at constant pressure Cp (SI unit: J/(kg·K)).
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Ratio of specific heats γ (dimensionless).
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Thermal conductivity k (SI unit: W/(m·K)). Note that the quantity is called kcond in the equation display.
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Dynamic viscosity μ (SI unit: Pa·s).
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Bulk viscosity μB (SI unit: Pa·s).