emission.sound_power_in_duct

Sound power radiated into a duct by a fan, in-duct method: ISO 5136:2003.

A ducted fan does not radiate into a room: what leaves it travels down the duct, so ISO 5136 measures it inside the duct. The fan is connected to an anechoically terminated test duct on its inlet and/or outlet side, and a microphone in that duct samples the one-third-octave sound pressure level at three circumferential positions (clause 6.2.2), by multiplexing, or over one continuous revolution (clauses 7.2.3 and 7.2.4). Three things stand between that reading and the sound power. The microphone sits in a mean flow that adds turbulent pressure fluctuations, so it is shielded by a sampling tube, a nose cone or a foam ball; the shield has a frequency response of its own; and above the first cut-on the duct carries higher-order modes to which a sampling tube does not respond as it does to a plane wave. Clause 8 gathers the three into one combined correction $C$ on the averaged level (equations (9), (10) and (11)):

where $C_1$ is the microphone free-field correction from the manufacturer’s data, $C_2$ the frequency response correction of the shield measured per clause 5.3.3.2 c) or 5.3.4.2, and $C_{3,4}$ the combined mean flow velocity and modal correction. For a level already averaged by multiplexing or a traverse, $\overline{L_p}=\overline{L_{pm}}+C$ (equation (11)). The sound power then follows from the plane-wave relation of clause 8.2:

$C_{3,4}$ is the part of the standard that is not arithmetic. For the sampling tube it is a polynomial in the mean flow velocity $U$, in metres per second, negative on the inlet side and positive on the outlet side (clause 5.3.3.4, equation (7)):

whose coefficients $a_i$ Annex A tabulates per one-third-octave band and per range of test-duct diameter (Tables A.1 to A.6, 0,15 m to 2 m), an empty cell being zero. The coefficients are normative for 50 Hz to 10 kHz and $|U|\le 40$ m/s. The footnote of every table then adds two informative extensions which do not combine: within 50 Hz to 10 kHz the rows also hold for $40<|U|\le 60$ m/s, while the rows for 12,5 kHz to 20 kHz are given for $|U|\le 40$ m/s only, and carry their own ”$|U|\le 40$ m/s” band header in the print. A velocity beyond 40 m/s is therefore refused as soon as a band above 10 kHz is asked for. For the omni-directional nose cone and foam ball no modal data exist, and clause 5.3.4.3 replaces the polynomial by the frequency-independent convective term (equation (8)):

with $c$ the speed of sound, which clause 5.3.4.3 prints as 340 m/s “under normal conditions”. A whole determination knows the duct air, so sound_power_in_duct evaluates Eq. (8) with the $c$ its temperature gives, the “speed of sound in the test duct” of Table 1; the 340 m/s is the default of flow_modal_correction called on its own.

The A-weighted sound power level is the energy sum of the band levels with the $C_j$ of Table C.1 (Annex C, equation (C.1)), and the uncertainty to be recorded is the reproducibility of Table 2, ${\sigma }_R$ per band for the sampling tube, expanded to $2{\sigma }_R$ at 95 % coverage (clause 9.2). Above 10 kHz the standard suggests the extrapolated values of Table 3 without making them part of itself.

What is not a term of $L_W$, and is therefore not computed here, is the qualification of the facility and the instrument: the reflection coefficient of the anechoic termination (Table 5, Annex F), the directivity of the sampling tube (equation (6), Table 6), the signal-to-noise ratio against turbulence (Annex B) and the duct geometry (clause 5.2). The informative Annexes H and I extend the coefficient tables below 0,15 m and above 2 m; the standard’s own scope stops at those diameters and so does this module.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

flow_modal_correction(
    frequencies: ArrayLike,
    flow_velocity: float,
    duct_diameter: float,
    *,
    shield: MicrophoneShield = 'sampling-tube',
    speed_of_sound: float = 340.0,
) -> np.ndarray

Combined mean flow velocity and modal correction $C_{3,4}$.

For the sampling tube, the polynomial of clause 5.3.3.4 with the coefficients of Annex A for the band and the test-duct diameter, an empty cell of the print counting as zero (Eq. (7)):

For the omni-directional nose cone and foam ball, the frequency-independent convective term of clause 5.3.4.3 (Eq. (8)):

$U$ is signed: negative for an inlet-side measurement, positive on the outlet side (Table 1 NOTE 2), so the same speed reads as a different correction on the two sides of the fan.

One cell of Annex A is not legible, the $a_3$ of the 5 000 Hz row of the table that serves 0,8 m to 1,25 m, and asking for that band and that diameter emits a SoundPowerWarning saying the coefficient is a reading rather than a transcription (see docs/ERRATA.md). Every other coefficient in the annex is transcribed and none of them warns.

Parameters

Returns: $C_{3,4}$ per band, in decibels.

Raises

in_duct_reproducibility(frequencies: ArrayLike) -> np.ndarray

Standard deviation of reproducibility ${\sigma }_R$ per band.

Table 2 of ISO 5136:2003 for the sampling tube, 50 Hz to 10 kHz, which is what clause 9.2 doubles into the expanded uncertainty to be recorded at 95 % coverage. For 12,5 kHz, 16 kHz and 20 kHz the extrapolated values of Table 3 are returned; clause 4 suggests them while saying that measurements above 10 kHz are not part of the standard, so a result that carries those bands says so in information_only_band.

Parameters

Returns: ${\sigma }_R$ per band, in decibels.

Raises

InDuctSoundPowerResult(
    frequencies: np.ndarray,
    sound_power_level: np.ndarray,
    mean_pressure_level: np.ndarray,
    corrected_pressure_level: np.ndarray,
    microphone_correction: np.ndarray,
    shield_correction: np.ndarray,
    flow_modal_correction: np.ndarray,
    combined_correction: np.ndarray,
    reproducibility_standard_deviation: np.ndarray,
    expanded_uncertainty: np.ndarray,
    information_only_band: np.ndarray,
    duct_diameter: float,
    duct_area: float,
    characteristic_impedance: float,
    speed_of_sound: float,
    flow_velocity: float,
    shield: str,
    sound_power_level_a: float,
)

Result of an ISO 5136:2003 in-duct sound power determination.

sound_power_level is the per-band $L_W$ of Eq. (12), and sound_power_level_a the A-weighted total of Annex C, Eq. (C.1), over the bands supplied. mean_pressure_level is the spatially averaged level before any correction, the bracket of Eq. (9) or the $\overline{L_{pm}}$ of Eq. (11); corrected_pressure_level is $\overline{L_p}$ after the combined correction. The three corrections are kept apart so the record clause 9.1 f) asks for can be made: microphone_correction ($C_1$), shield_correction ($C_2$) and flow_modal_correction ($C_{3,4}$), with combined_correction their sum (Eq. 10).

reproducibility_standard_deviation is ${\sigma }_R$ of Table 2 per band (Table 3 above 10 kHz) and expanded_uncertainty is twice it, the 95 % figure clause 9.2 says to record. information_only_band marks the bands the standard gives for information rather than as part of itself: those above 10 kHz, and every band when the sampling tube is used between 40 m/s and 60 m/s (5.3.3.4 NOTE, clause 4). Table 2 is stated for the sampling tube; clause 4 NOTE 5 expects the figures to grow for the other shields and gives no others, so the same values are reported for them.

duct_diameter and duct_area are $d$ and $S$, characteristic_impedance is the $\rho c$ of the duct air and speed_of_sound its $c$, flow_velocity is the signed $U$ (negative on the inlet side) and shield names the microphone shield.

InDuctSoundPowerResult.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the in-duct sound power spectrum with the A-weighted total.

One bar per one-third-octave band of sound_power_level, the $L_{W\mathrm{A}}$ of Annex C in the title. Requires matplotlib (pip install phonometry[plot]); returns the Axes.

Parameters

Returns: The axes.

Raises

sound_power_in_duct(
    levels: ArrayLike,
    frequencies: ArrayLike,
    duct_diameter: float,
    flow_velocity: float,
    *,
    shield: MicrophoneShield = 'sampling-tube',
    microphone_correction: ArrayLike = 0.0,
    shield_correction: ArrayLike = 0.0,
    temperature: float = 20.0,
    static_pressure: float = 101.325,
) -> InDuctSoundPowerResult

Sound power radiated into a test duct, in-duct method (ISO 5136:2003).

levels is either a (positions, bands) array of the time-averaged sound pressure level at each circumferential microphone position, energy- averaged by Eq. (9), or a (bands,) spectrum already averaged by multiplexing or a continuous traverse (Eq. (11)). The combined correction $C=C_1+C_2+C_{3,4}$ of Eq. (10) is added to the average, with $C_1$ and $C_2$ supplied per band or as a scalar and $C_{3,4}$ from flow_modal_correction, and the plane-wave relation of Eq. (12) gives the sound power in each band:

The A-weighted total follows Annex C over the bands supplied, and the uncertainty statement of clause 9.2, twice the reproducibility of Table 2, is carried per band.

Parameters

Returns: InDuctSoundPowerResult.

Raises