Acoustic medium

The gas the sound travels in. Uniform: one density $\rho_0$ and one speed of sound $c_0$ for the whole model, from the Material step. From CFD fields: the solved temperature and absolute pressure of the flow run give a density $\rho(\mathbf{x})$ and a speed of sound $c(\mathbf{x})$ at every point of the acoustic mesh.

Last updated 2026-11-11

Theory

The acoustic model solves the Helmholtz equation for the complex pressure amplitude $p$ at angular frequency $\omega$ , equation (1), with the density and the sound speed allowed to vary in space. With the uniform medium both are constants, equation (2): the gas of the Material step at its temperature and at the ambient pressure, with the ideal-gas constant and heat-capacity ratio of the selected gas.

With the medium from the CFD fields, the flow run comes first. Its last solution is converted to VTK (foamToVTK), the temperature $T$ and the absolute pressure are interpolated onto every node of the acoustic mesh (a node outside the flow mesh takes the nearest flow value), and equation (3) gives $\rho$ and $c$ there, with the same ideal gas the compressible solver used. The acoustic mesh then follows the local wavelength: a hot region gets larger elements than a cold one (Elements per wavelength). Each port uses the mean $\rho$ and $c$ of its own face for its modes and powers.

Only the steady compressible solver solves a temperature and an absolute pressure, so this choice locks the Model step to compressible and steady. The mean velocity of the flow is not part of the acoustic equation unless Mean-flow convection is switched on.

Equations

\nabla\cdot\left(\frac{1}{\rho}\nabla p\right) + \frac{\omega^2}{\rho c^2}\,p = 0

(1)

\rho_0 = \frac{p_{atm} M}{R_u T}, \qquad c_0 = \sqrt{\gamma R_s T}

(2)

\rho(\mathbf{x}) = \frac{p(\mathbf{x})}{R_s T(\mathbf{x})}, \qquad c(\mathbf{x}) = \sqrt{\gamma R_s T(\mathbf{x})}

(3)

where	meaning	unit
$p$	Acoustic pressure amplitude (equation 1), absolute static pressure of the flow (equation 3)	Pa
$\omega$	Angular frequency, $2\pi f$	rad/s
$\rho, c$	Density and speed of sound of the gas	kg/m³, m/s
$p_{atm}$	Ambient pressure of the Material step	Pa
$M$	Molar mass of the gas	kg/kmol
$R_u$	Universal gas constant, 8314.47	J/(kmol K)
$R_s$	Specific gas constant, $R_u/M$	J/(kg K)
$T$	Temperature (Material step, or the solved field)	K
$\gamma$	Ratio of the specific heats of the gas	-

Default and rule

Default: uniform
Rule: Uniform. It needs no flow solution and is exact for a muffler at one temperature.
Source: The mapped medium is validated in two ways. A duct whose temperature rises linearly from 293 to 700 K, solved in 3-D against an exact one-dimensional integration of the same equation, agrees within 0.02 dB at 600-3000 Hz. An expansion chamber with 600 K gas mapped from a real compressible flow run shifts its transmission-loss maxima by the factor $\sqrt{600/293.15} = 1.4306$ within 0.14 % (measured ratios 1.4326 / 1.4316 / 1.4305). The equation is the standard Helmholtz equation for a medium at rest with variable density and sound speed.

Valid range uniform | cfd_fields (needs fluid flow, steady compressible)

Requirements

From CFD fields needs fluid flow, the compressible analysis type and a steady run. A transient run is incompressible and has no temperature field.

Mapping checks

After mapping, the program compares the mass-weighted mean temperature of each port with the flow run's own value (within 0.5 %) and checks that no acoustic node is far outside the flow mesh (fails beyond 2 % of the model size, warns when more than 10 % of the nodes lie outside it).

Medium at rest

The mapped medium changes $\rho$ and $c$ only. The mean flow's convection of sound is a separate option.

Theory

Equations

Default and rule

Valid range uniform | cfd_fields (needs fluid flow, steady compressible)

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