The proudmanAcousticPower function object computes the acoustic power due to the volume of isotropic turbulence using Proudman’s formula.

The acoustic power, i.e. \(P_A\) [W/m^3] in terms of turbulent kinetic energy, i.e. \(k\), and turbulent kinetic energy dissipation rate, i.e. \(\epsilon\) is given as:

\[P_A = \alpha_\epsilon \rho \epsilon M_t^5\]

where \(\alpha_\epsilon = 0.1\) is a constant and

\[M_t = \frac{\sqrt{2 k}}{a_0}\]

with \(a_0\) the speed of sound.

The acoustic power is also output in dB using:

\[L_P = 10 \log \frac{P_A}{P_{\ref}}\]

where \(P_{\ref} = 1e^{-12}\) [W/m^3] is a constant.


Operand Type Location
input volScalarField $FOAM_CASE/<time>/<inpField>
output file - -
output field volScalarField $FOAM_CASE/<time>/<outField>


Example of the proudmanAcousticPower function object by using functions sub-dictionary in system/controlDict file:

    // Mandatory entries (unmodifiable)
    type            proudmanAcousticPower;
    libs            (fieldFunctionObjects);

    // Optional entries (runtime modifiable)
    alphaEps    0.1;
    // For incompressible flow simulations
    rhoInf      1.225;
    aRef        340;

    // Optional (inherited) entries
    region          region0;
    enabled         true;
    log             true;
    timeStart       0;
    timeEnd         1000;
    executeControl  timeStep;
    executeInterval 1;
    writeControl    timeStep;
    writeInterval   1;

where the entries mean:

Property Description Type Required Default
type Type name: proudmanAcousticPower word yes -
libs Library name: fieldFunctionObjects word yes -
rhoInf Freestream density (for incompressible) scalar conditional -
aRef Speed of sound (incompressible) scalar conditional -
alphaEps Empirical model coefficient scalar no 0.1

The inherited entries are elaborated in:

Usage by the postProcess utility is not available.

Notes on entries

The freestream density and reference speed of sound are only necessary when a thermodynamics package is unavailable, typically for incompressible cases.

Further information


Source code:



  • Introduced in version v1912