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ENH: Added new function object to compute the Proudman acoustic power

Andrew Heather requested to merge feature-proudmann-fo into develop

@Roger @Prashant - can you confirm this OK to go in? and any test case/updated tutorial that can be provided?

Details of the new function object:

Calculates the acoustic power due to the volume of isotropic turbulence using Proudman's formula

The acoustic power P_A [W/m3] in terms of turbulence k and \epsilon is given as:

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

where alpha_\epsilon is a constant (0.1) 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 is a constant (1e-12 W/m3)

Usage Example of function object specification to calculate the Proudman acoustic power

    type        proudmanAcousticPower;
    libs        ("");

    // Required additional entries for incompressible calculations
    rhoInf      1.225;
    aRef        340;

Where the entries comprise:
    Property     | Description                 | Required   | Default value
    type         | type name: proudmanAcousticPower         | yes        |
    rhoInf       | Freestream density for incompressible cases  | no |
    aRef         | Reference spped of sound for incompressible cases | no |
    alphaEps     | Model coefficient           | no         | 0.1


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

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