# Acoustic Power¶

## Description¶

Compute the acoustic power in Watt across a surface $$S$$ defined as

$P = \iint_S \vec{I} \cdot \vec{n} \, dS$

where $$\vec{I} = p' \vec{v'}$$ is the acoustic intensity, with $$p'$$ the acoustic pressure (or pressure fluctuation), $$\vec{v'}$$ the velocity fluctuations, and $$\vec{n}$$ the unit vector normal to the surface.

Compute also the Sound Power Level in dB and the Sound Pressure Level in dB.

Two formulations are considered:

• For a plane acoustic wave as a duct mode, or a progressive acoustic wave at infinity in a stagnant uniform fluid, the component of the acoustic intensity in the direction of propagation is

$I = p'^2/(\rho_0 c_0)$

with $$p'$$ the acoustic pressure, $$\rho_0$$ the density and $$c_0$$ the sound speed at infinity.

It can be shown for a stagnant uniform fluid that $$I_x$$ is given by

$I_x = p'u'$

with $$u'$$ the axial component of the velocity disturbances.

• For homentropic non-uniform fluid, the acoustic intensity is expressed as

$\vec{I} = \left( \frac{p'}{\rho_0} + \vec{v_0} \cdot \vec{v'} \right) \left( \rho_0 \vec{v'} + \rho' \vec{v_0} \right)$

with the mean velocity $$\vec{v_0} = (U_0,V_0,W_0)$$ and the velocity disturbances $$\vec{v'} = (u',v',w')$$.

Frequential formulations of previous definitions are also implemented to evaluate the contribution of each frequency to the total acoustic power.

For more details on aeroacoustics, you may refer to

[HIRSCHBERG]

Hirschberg, A. and Rienstra, S.W. “An Introduction to Aeroacoustics”, Instituut Wiskundige Dienstverlening (Eindhoven) (2004).

## Parameters¶

• base: Base

The input base.

• dtype_in: str, default= ‘re’

If dtype_in is ‘re’, then the base is real. If dtype_in is in [‘mod/phi’, ‘im/re’], the base is complex (modulus/phase or imaginary/real part decomposition respectively). If the signal is complex, a suffix must be added to the name of the variable depending on the decomposition (_im and _re for im/re, _mod and _phi for mod/phi). If given, the phase must be expressed in radians.

• flow: str, default= ‘stagnant’

The state of the medium: ‘stagnant’ or ‘non-uniform’.

• variables: list(str)

The variable names.

• rho_ref: float, default= 1.18

The value of the ambient density. The default value is $$\rho=1.18$$ kg/m3, i.e. for a medium at an ambient temperature and pressure of T=298 K and P=101325 Pa, respectively.

• c_ref: float, default= 346.0

The value of the ambient sound velocity, only for real data. The default value is c=346 m/s, i.e. for a medium at an ambient temperature of T=298 K.

• mach_ref: float, default= 0.0

Mach number.

## Preconditions¶

Zones may be either structured or unstructured.

Stagnant uniform fluid:

1. the required variables is the mean square of the acoustic pressure fluctuation $$p'$$, i.e. $$<p'p'>$$

2. the reference uniform density $$\rho_0$$ and uniform sound velocity $$c_0$$

Homentropic non-uniform fluid:

1. the required variables are:

• the mean velocity vector $$\vec{v_0} = (U_0,V_0,W_0)$$

• the fluctuating velocity vector $$\vec{v'} = (u',v',w')$$

• the mean density field $$\rho_0$$

• the fluctuating pressure field $$p'$$

## Postconditions¶

The output base contains a single zone with a single instant with 3 or 4 scalar variables depending on dtype_in:

• “Power (Watt)”: the acoustic power (Watt)

or

• “Power_re(Watt)”: the real part of the acoustic power (Watt)

• “Power_im(Watt)”: the imaginary part of the acoustic power (Watt)

and

• “Sound Power Level (dB)”: the Sound Power Level (dB)

• “Sound Pressure Level (dB)”: the Sound Pressure Level (dB)

## Example¶

import antares
myt = antares.Treatment('acousticpower')
myt['base'] = base
myt['dtype_in'] = 're'
myt['flow'] = 'stagnant'
myt['rho_ref'] = rho
myt['c_ref'] = c
power = myt.execute()


## Main functions¶

class antares.treatment.TreatmentAcousticPower.TreatmentAcousticPower
execute()

Compute the acoustic power across a surface.