noise_control.hvac

HVAC duct acoustics: fan power, duct losses, plenums and flow-generated noise.

A ventilation duct network attenuates fan noise through several mechanisms that add up along the path, and it regenerates noise wherever the airflow is disturbed. This module gathers the element models that a duct-borne noise calculation needs, from two engineering references that are kept side by side rather than merged:

• Bies, Hansen & Howard, Engineering Noise Control 5th ed., Chapter 8, for the duct end reflection (§8.13, Table 8.14), the bends/elbows (§8.11, Table 8.11), the plenum chambers (§8.17, Wells’ method) and the flow-generated (self) noise of straight ducts and bends (§8.15).
• Long, Architectural Acoustics 2nd ed., Chapters 13 and 14, for the fan sound power from the operating point (Eq. 13.1 with the ASHRAE Tables 13.5-13.7), the straight-duct attenuation of unlined and lined rectangular and circular ducts (Eqs. 14.9-14.13 with Tables 14.1-14.3, the Reynolds regressions), the lined flexible duct insertion loss (Table 14.4), the branch split loss (Eq. 14.17), the closed-form end reflection (Eqs. 14.14-14.16), the silencer self-noise (Eq. 14.31 with Table 14.8) and the room effect that turns the sound power arriving at the terminal device into a sound pressure level in the room.

Both references trace back to the same ASHRAE data for the elbows: Bies Table 8.11 is indexed by $W/\lambda$ and Long Tables 14.5-14.7 by the frequency-width product f w (kHz times inches), and the two indexings agree band by band ($W/\lambda =0.074fw$), so elbow_insertion_loss serves both. Where they genuinely differ — the end reflection, tabulated by Bies and given in closed form by Long — both are selectable (method="bies" or method="long") and neither replaces the other.

phonometry.noise_control.duct_path chains these elements into the end-to-end fan-to-room calculation.

.. warning:: Long’s worked duct-borne sheet (Table 14.9) was produced by a commercial computer program, not by hand from the tables printed alongside it, and several of its element rows do not follow from the book’s own data. The functions here implement the printed equations and tables, so they reproduce some rows of that sheet and not others. Verified band by band:

• split_loss reproduces the 25 per cent split row (-6 dB) exactly, and elbow_insertion_loss reproduces the unlined-elbow row exactly when the elbow is read as round (Table 14.7) at $w=24$ in;
• lined_rectangular_duct_attenuation with include_unlined=True reproduces the 18 x 12 in run from 500 Hz up (11/25/22/16/13 dB) and the 36 x 24 in run at 500 Hz and 8 kHz, but is 1-2 dB low at 63-250 Hz on one run and 2 dB high on the other;
• the fan row (90/86/82/79/77/75/71/61 dB) is not reproducible from Eq. 13.1 with the Table 13.5 forward-curved constants, which give 99/99/89/84/82/77/72/67 dB at the same duty; the printed spectrum is not a level shift of the tabulated one, so it comes from other data;
• the flexible-duct row (14/14/16/15/17/22/16/13 dB) is not the Table 14.4 entry for 12 in by 6 ft (3/5/10/15/17/16/9 dB);
• diffuser_sound_power reproduces the supply diffuser row (33/32/29/23/15/4/0/0 dB) to better than 1 dB in five of the six bands that carry it (+0.4/+0.4/+0.2/+0.7/+0.9 dB from 63 Hz to 1 kHz) and to 1.9 dB in the sixth (2 kHz), reading the device as a 24 x 24 in rectangular diffuser;
• the silencer and grille rows are manufacturer data, which is what a real sheet uses and what DuctElement accepts.

The cascade arithmetic of that sheet is reproduced exactly (see the duct-path tests, which feed it its own printed element rows), and the sheet’s own internal rounding is 1 dB.

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

air_terminal_damper_correction(
    pressure_ratio: float,
    *,
    location: str = 'diffuser_neck',
) -> float

Level to add to a diffuser sound rating for a throttled volume damper.

ASHRAE (2019) HVAC Applications Handbook Chapter 49, Table 10. A balancing damper throttled in the neck of a diffuser turns the pressure it drops into noise right at the outlet, where the room hears it: at a damper pressure ratio of 3 the published penalty is 15 dB in the neck, 5 dB in the inlet plenum and 2 dB when the damper sits at least 1.5 m back in the supply duct. That ordering is the whole design rule: throttle far from the outlet, or balance the system with duct sizing instead.

The table is interpolated linearly between its tabulated pressure ratios (1.5 to 6) and held flat outside them.

Parameters

Returns: The level to add to the diffuser’s rated sound power, dB.

Raises

air_terminal_velocity_limit(
    design_criterion: float,
    *,
    opening: str = 'supply',
) -> float

Maximum recommended neck velocity of a diffuser or register.

ASHRAE (2019) HVAC Applications Handbook Chapter 49, Table 9: the “free” opening airflow velocity not to be exceeded if the room is to reach a given design RC(N), for use when no sound data is available for the selected device. It is a screening check, not a spectrum: the sound power of a real grille, register or diffuser comes from manufacturer data measured to ASHRAE Standard 70, and diffuser_sound_power estimates it when that data is not to hand. Several devices in the same room, or a damper throttled in the neck, raise the level further and the allowable velocity has to be reduced accordingly.

Parameters

Returns: The maximum recommended neck velocity, m/s.

Raises

blade_passing_frequency(rotational_speed: float, blades: int) -> float

Blade passing frequency (Long Eq. 13.4).

$f_{bp}=\mathrm{rpm}\times \mathrm{blades}/60$.

Parameters

Returns: The blade passing frequency, Hz.

Raises

diffuser_sound_power(
    frequencies: ArrayLike | None,
    face_area: float,
    volume_flow: float,
    pressure_drop: float,
    *,
    shape: str = 'rectangular',
    count: int = 1,
) -> HvacSpectrumResult

Regenerated (self) noise of a grille, register or diffuser.

Reynolds’s estimate as Long Eqs. 13.27 to 13.33, for when the manufacturer’s ASHRAE Standard 70 data is not to hand. The overall sound power level is Eq. 13.27:

with S_\mathrm{G} the face area of the device (ft2), $U_{\mathrm{G}}=Q/(60S_{\mathrm{G}})$ the approach velocity (ft/s) and $\xi =334.9dP/({\rho }_0{U}_{\mathrm{G}}^2)$ the normalised pressure-drop coefficient of Eq. 13.28 (dP in inches of water gauge, ${\rho }_0=0.075$ lb/ft3); this function takes and returns SI and converts internally.

The octave-band spectrum follows from Eq. 13.29, $L_{W,\mathrm{oct}}=L_W+C_{\mathrm{D}}$, with the shape functions of Eqs. 13.30 and 13.31:

normalised to the peak frequency $f_P=48.8U_{\mathrm{G}}$ of Eq. 13.32, where $A=N_B(f_P)-N_B(f)$ is the distance in octaves from the peak band (Eq. 13.33) counted on Long’s band numbering, 0 at 32 Hz.

The sixth power of velocity in Eq. 13.27 is the design message: the level rises about 18 dB for every doubling of the approach velocity, and for a given air volume doubling the face area buys about 15 dB. Nothing downstream can take that noise back out, because there is no ductwork left, which is why the terminal device usually sets the room criterion in the mid and high bands.

Several identical devices serving the same room add $10{\log }_{10}n$, which is what count applies.

Parameters

Returns: An HvacSpectrumResult of the band sound power level, dB re 1e-12 W.

Raises

elbow_insertion_loss(
    frequencies: ArrayLike,
    width: float,
    *,
    bend_type: str = 'square',
    vanes: bool = False,
    lined: bool = False,
    speed_of_sound: float = 343.0,
    model: str = 'ashrae',
    lined_side: str = 'both',
) -> HvacSpectrumResult

Duct bend/elbow insertion loss per bend, by either method.

Indexed by the frequency-to-width ratio $W/\lambda$ ($\lambda =c/f$). Lined bends assume the lining extends at least three duct diameters up- and downstream. Round bends are treated as unlined with no vanes.

model="vdi2081" reads Table 7 of VDI 2081 Part 1 Section 6.2, which is printed once, for a 1250 mm side, and carried along the frequency axis for every other size. The duct’s limit frequency comes from Equation (33), c / (2 a), or Equation (34), 0,586 c / d; the octave holding it takes the place of the table’s own 125 Hz column, and the whole row moves with it. Below the shifted row the loss is nought, which is the guideline’s statement that a bend reflects nothing while only plane waves run.

The two methods index the same physics on the same ratio, but they do not tabulate the same bends: Table 7 distinguishes lining before, after, or on both sides of the corner, which the ASHRAE table does not, and width is read there as the largest side of a rectangular duct or the bore of a round one rather than as the width in the plane of the bend.

Parameters

Returns: A HvacSpectrumResult of the insertion loss, dB per bend.

end_reflection_loss(
    frequencies: ArrayLike,
    diameter: float,
    *,
    termination: str = 'flush',
    method: str = 'bies',
    speed_of_sound: float = 343.0,
    aspect_ratio: float = 1.0,
    maximum_reduction_db: float | None = 15.0,
) -> HvacSpectrumResult

Duct end reflection loss (Bies Table 8.14, ASHRAE; or Long’s closed form).

The low-frequency reflection of sound back up a duct at its open termination into a room. Two published methods are offered and neither replaces the other:

• method="bies" (default) interpolates the ASHRAE look-up of Bies Table 8.14 over log diameter and log frequency, passing exactly through the tabulated (diameter, octave band) nodes. The table covers 63 Hz to 2 kHz and 150 mm to 1830 mm.
• method="long" evaluates Reynolds’ closed form as given by Long (Eqs. 14.14-14.15), end_reflection_loss_closed_form, which has no frequency or diameter range limit.

The two agree within a couple of decibels over the bands both cover.

Parameters

Returns: A HvacSpectrumResult of the reflection loss, dB.

end_reflection_loss_closed_form(
    frequencies: ArrayLike,
    diameter: float,
    *,
    termination: str = 'flush',
    speed_of_sound: float = 343.0,
) -> HvacSpectrumResult

Duct end reflection loss in closed form (Long Eqs. 14.14-14.15, Reynolds).

$R=10{\log }_{10}[1+(c/(\pi fd){)}^{1.88}]$ for a duct terminated in free space and $R=10{\log }_{10}[1+(0.8c/(\pi fd){)}^{1.88}]$ for one terminated flush with a wall, d being the duct diameter (use the equivalent diameter equivalent_diameter for a rectangular duct, Eq. 14.16). The exponent 1.88 is Reynolds’ empirical fit: the plane-wave area-change result over-predicts at high frequency, where the sound leaves the duct as a beam and never sees the expansion. This is the closed-form alternative to the Bies/ASHRAE table look-up of end_reflection_loss; the two agree within a couple of decibels over the bands where both are defined.

End-reflection loss does not occur when the duct terminates in a diffuser, whose flare smooths the impedance transition into the room.

Parameters

Returns: An HvacSpectrumResult of the reflection loss, dB.

equivalent_diameter(area: float) -> float

Equivalent duct diameter $d=\sqrt{4S/\pi }$ (Long Eq. 14.16).

Parameters

Returns: The equivalent diameter, m.

fan_casing_attenuation(
    frequencies: ArrayLike | None = None,
) -> HvacSpectrumResult

Fan-housing (casing) attenuation of the radiated power (Long Table 13.8).

Subtracted from the sound power level of fan_sound_power to estimate what the fan radiates through its housing into the plant room rather than into the duct. The values assume no separate enclosure and no absorption inside the housing, but a silencer or a lining in the ductwork close to the fan; at low frequency the vibrating casing radiates as much as the unhoused fan would, hence the zeroes. Miller (1980) states them as approximate: real values depend strongly on the gauge and construction of the housing.

Parameters

Returns: An HvacSpectrumResult of the attenuation, dB.

fan_efficiency_correction(*, relative_efficiency_percent: float) -> float

Off-peak efficiency correction C_EFF (Long Table 13.6).

A fan running away from its peak static efficiency is noisier at the same duty. The correction is a step function of the static efficiency expressed as a percentage of the peak (Long Eq. 13.3): 90 per cent of peak and above adds nothing, and anything below 50 per cent adds 16 dB. When the peak efficiency is unknown Long recommends assuming 80 per cent, which lands in the 6 dB step.

Parameters

Returns: The correction C_EFF, dB.

Raises

fan_sound_power(
    volume_flow: float,
    *,
    fan_static_pressure_pa: float,
    model: Literal['ashrae'] = ...,
    fan_type: str = ...,
    relative_efficiency_percent: float = ...,
    blade_frequency: float | None = ...,
    frequencies: ArrayLike | None = ...,
) -> HvacSpectrumResult

fan_sound_power(
    volume_flow: float,
    *,
    model: Literal['vdi2081'],
    fan_total_pressure_pa: float,
    assembly: str,
    fan_speed_rpm: float,
    specific_sound_power_level: float | None = ...,
    blade_count: int | None = ...,
    relative_flow: float = ...,
    frequencies: ArrayLike | None = ...,
) -> HvacSpectrumResult

Octave-band fan sound power from the operating point, by either method.

Two schools of calculation answer the same question and do not agree on how. model="ashrae" (the default) is the scaling law below; model="vdi2081" is the German method, described after it. Each takes the arguments its own standard is written on, so neither can be handed the other’s: the ASHRAE law scales the static pressure, VDI 2081 the total pressure rise, and confusing them is worth 20 log of the ratio.

The ASHRAE (1987) scaling law, originally due to Beranek and published by Graham (1975):

with the spectral constant K_\mathrm{F} of Long Table 13.5 (one row per fan type), the off-peak efficiency correction C_EFF of Table 13.6 (fan_efficiency_correction) and the blade frequency increment C_BFI of Table 13.7, added to the single octave band that contains the blade passing frequency. In SI the reference volume flow is $Q_{\mathrm{REF}}=0.472$ L/s and the reference pressure $P_{\mathrm{REF}}=249$ Pa, so the two logarithmic terms take the same values as the foot-pound form in cfm and inches of water gauge.

The law assumes ideal inlet and outlet flow conditions and gives the power radiated into the duct; the fan radiates the same power from its intake and from its discharge. Manufacturer data measured to AMCA 300 should be preferred wherever it exists: this model is the early-design fallback, and ASHRAE’s own current guidance (2019 HVAC Applications Handbook, Ch. 49) is that a fan’s sound power “is best obtained from manufacturers’ test data” to AMCA Standard 300 or ASHRAE Standard 68. Long’s worked sheet (Table 14.9) prints a forward-curved row that this equation does not reproduce; see the module warning.

VDI 2081 Part 1:2001-07, Section 4.3. The German method describes a fan by its assembly type rather than by a per-type band table:

Equation (13) and Equation (15). The factor 20 on the pressure is the general $5(\gamma -1)$ of Equation (11) with the Mach number exponent taken as 5, which Section 4.3.2 does for every ventilation fan. The Strouhal number carries no diameter: it cancels between the tip speed and the impeller circumference, so the impeller size a nomogram gives is not an input here. Section 4.3.3 sets the specific level and the spectral parameter for each of the three assemblies of VDI 3731 Part 2, and Figures 13 and 14 add a cubic allowance for running away from the best duty point, worth 0,1 dB at the optimum itself.

Parameters

Returns: An HvacSpectrumResult of the band sound power level, dB re 1e-12 W.

flexible_duct_insertion_loss(
    frequencies: ArrayLike | None,
    diameter: float,
    length: float,
) -> HvacSpectrumResult

Insertion loss of a lined round flexible duct (Long Table 14.4, ASHRAE 1995).

The last run of a supply branch is usually flexible duct: a fabric liner inside a lightweight fibreglass fill inside a plastic membrane. Its published insertion loss is remarkably high, 2 to 3 dB per foot in the mid bands, partly because the test replaces a length of sheet-metal duct and so credits the flexible duct’s breakout as well as its dissipation. That same property makes a serpentine run of flexible duct in an attic or a joist space work as an improvised breakout silencer. The table is interpolated linearly over length and over log diameter; it stops at 4 kHz, so no 8 kHz value is returned.

Parameters

Returns: An HvacSpectrumResult of the insertion loss, dB.

flow_noise_bend(
    frequencies: ArrayLike,
    flow_velocity: float,
    area: float,
    height: float,
    *,
    density: float = 1.206,
    model: str = 'ashrae',
    branch_diameter: float | None = None,
    approach_velocity: float | None = None,
    rounding_ratio: float | None = None,
) -> HvacSpectrumResult

Flow-generated octave-band sound power of a bend or junction, by either method.

with the stream power level $L_{W\mathrm{s}}$ (Bies Eq. (8.252)) and the Strouhal number $N_{\mathrm{s}}=fH/U$ (H the duct height in the plane of the bend). The radiated sound power grows as the sixth power of the stream speed at low N_\mathrm{s} (the inner-corner drag dipole) and the eighth power at high N_\mathrm{s} (the outer-corner shear quadrupole); equivalently, the efficiency referenced to the stream power grows as $U^3$ and $U^5$ respectively.

model="vdi2081" is Equation (18) of VDI 2081 Part 1 Section 5.2.2, which covers a junction and a bend with one law:

with the normalised level of Figure 17, $L_W^{\ast }=12-21,5(\lg St{)}^{1,268}+(32+13\lg St)\lg (v_{\mathrm{h}}/v_{\mathrm{a}})$, the rounding correction of Figure 18, $K=13,9(3,43-\lg St)(0,15-r/d_{\mathrm{a}})$, and $St=f{d}_{\mathrm{a}}/v_{\mathrm{a}}$. A bend is the same law with the two velocities equal, which sends the second term of $L_W^{\ast }$ and the velocity ratio to nought.

Both figures state that they hold only for $St>1$, so a band below that returns negative infinity, the level of no contribution at all, rather than an extrapolation: the fit turns over there and its fractional power of $\lg St$ is not real below one.

Parameters

Returns: A HvacSpectrumResult of the band sound power level, dB re 1e-12 W.

flow_noise_straight_duct(
    frequencies: ArrayLike,
    flow_velocity: float,
    area: float,
) -> HvacSpectrumResult

Flow-generated octave-band sound power of a straight duct (Bies Eq. (8.251)).

in dB re 1e-12 W (VDI 2081-1), for airflow speed U in a duct of area S.

Parameters

Returns: A HvacSpectrumResult of the band sound power level, dB re 1e-12 W.

HvacSpectrumResult(
    frequencies: np.ndarray,
    values: np.ndarray,
    quantity: HvacQuantity,
    label: str,
)

A per-frequency HVAC quantity (attenuation or regenerated power level).

Attributes

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

Plot the quantity against a continuous log-frequency axis.

Requires matplotlib (pip install phonometry[plot]).

HvacSpectrumResult.report(
    path: str,
    *,
    metadata: ReportMetadata | None = None,
    engine: str = 'reportlab',
    verbose: bool = False,
    language: str = 'en',
) -> str

Render an HVAC duct-noise-spectrum fiche to path.

Writes a one-page HVAC-noise sheet: the method-basis line naming the reported quantity and the Bies, Hansen & Howard chapter (Engineering Noise Control 5th ed., Chapter 8), an optional metadata header (client, duct element, test environment, instrumentation, climate, date), a per-band table (nominal frequency and the reported quantity) beside the spectrum, the boxed single-number result (for a regenerated-noise spectrum the A-weighted sound power level L_WA re 1 pW with the overall unweighted total; for an attenuation spectrum the mean attenuation with its band range), an optional verdict row against a declared limit, and a method-basis strip stating the reported quantity’s relation.

Parameters

Returns: The written path as a str.

Raises

An HVAC input outside the span the table it feeds was tabulated from.

lined_circular_duct_attenuation(
    frequencies: ArrayLike | None,
    diameter: float,
    length: float,
    lining_thickness: float,
) -> HvacSpectrumResult

Insertion loss of a lined circular duct (Long Eq. 14.13, Table 14.3).

The Reynolds (1990) third-order regression $R=(A+Bt+C{t}^2+Dd+E{d}^2+F{d}^3)l$, with the lining thickness t and the internal diameter d in inches and the length l in feet. It was developed for spiral ducts with a 12 kg/m3 fibreglass lining 25 mm to 76 mm thick behind a 25 per cent open perforated facing, over internal diameters from 150 mm to 1.5 m. Negative regression values are clipped to zero and, as for rectangular ducts, flanking limits the run to 40 dB. The unlined contribution is so small for circular ducts that Long ignores it.

Parameters

Returns: An HvacSpectrumResult of the attenuation, dB.

lined_rectangular_duct_attenuation(
    frequencies: ArrayLike | None,
    width: float,
    height: float,
    length: float,
    lining_thickness: float,
    *,
    include_unlined: bool = False,
) -> HvacSpectrumResult

Insertion loss of a lined rectangular duct (Long Eq. 14.12, Table 14.2).

The Reynolds (1990) regression $R=B(P/S{)}^C{t}^{D}l$, with the duct perimeter P in feet, its area S in square feet, the lining thickness t in inches and the run length l in feet. It was fitted to 25 mm to 52 mm linings of 24 to 48 kg/m3 density over P / S from 1.1667 to 6 ft^-1; linings thinner than 25 mm are generally ineffective. The insertion loss is measured by substituting the lined section for an unlined one of the same face size, so the unlined attenuation may be added on top (include_unlined=True, which Long recommends for rectangular ducts). Flanking limits the total to 40 dB.

Parameters

Returns: An HvacSpectrumResult of the attenuation, dB.

octave_band_limits(
    a_weighted_limit_db: float,
    frequencies: ArrayLike | None = None,
) -> HvacSpectrumResult

Octave limits from an A-weighted room requirement (VDI 2081 Part 2 Eq. (1)).

with the correction VDI2081_SPECTRAL_CORRECTION, which is the inverse A-weighting less 5 dB. The 5 dB is what Section 1.1 allows for summing eight octave bands: a spectrum flat in A-weighted terms would earn 9 dB, and the guideline takes 5 because the noise of an air-conditioning system does not follow the inverse A curve.

The result is the unweighted octave level each band may reach. The same requirement can be read the other way round, which is what the guideline’s own worked example does: add the A-weighting to the computed spectrum and compare every band against the flat L_A - 5. The two are the same test, since K_A = -A - 5.

Parameters

Returns: An HvacSpectrumResult of the per-band limit, dB.

plenum_attenuation(
    exit_area: float,
    line_of_sight: float,
    wall_area: float,
    mean_absorption: ArrayLike,
    *,
    angle: float = 0.0,
) -> np.ndarray | float

Plenum-chamber transmission loss by Wells’ method (Bies Eq. (8.275)).

where the reverberant term uses the plenum room constant $R=S_{\mathrm{w}}\alpha /(1-\alpha )$ (phonometry.room.room_constant). The method holds above the inlet cut-on and when the plenum is large compared with the wavelength; it underpredicts the low-frequency loss by 5-10 dB.

Parameters

Returns: The transmission loss, dB (float for scalar absorption, else a per-band array).

Raises

plot_plenum_geometry(
    exit_area: float,
    line_of_sight: float,
    wall_area: float,
    ax: Axes | None = None,
    *,
    angle: float = 0.0,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw the plenum-chamber section honouring the acoustic geometry.

The two truly geometric parameters of plenum_attenuation are drawn exactly: the inlet-to-outlet line of sight r and its angle off the inlet axis fix the box; the exit area sets the drawn outlet mouth (square-duct side sqrt(S_out)) and the wall area is annotated.

Parameters

Returns: The axes.

Raises

room_effect(
    distance: float,
    room_constant: ArrayLike,
    *,
    directivity: ArrayLike = ...,
) -> np.ndarray | float

room_effect(
    distance: float,
    *,
    absorption_area: ArrayLike,
    directivity: ArrayLike = ...,
) -> np.ndarray | float

Room effect: the drop from the terminal sound power to the room level.

The last step of a duct-path calculation turns the sound power arriving at the terminal device into a sound pressure level at the listener, through the steady-state room relation $L_p=L_W+10{\log }_{10}[Q/(4\pi r^2)+4/R]$ (Long Eq. 14.40; Bies Eq. (6.43), phonometry.room.steady_state_spl). This function returns the attenuation, the positive number $-10{\log }_{10}[Q/(4\pi r^2)+4/R]$, so it drops into a duct-path cascade beside every other loss; Long’s worked sheets print it as the negative level change. A ceiling diffuser radiates into a half space, hence the default $Q=2$.

VDI 2081 Blatt 1 Section 6.7.3 closes its own chain with the same expression, written in the equivalent absorption area A rather than the room constant R (Equation (36)), and prints the result as the Raumdämpfung $L_W-L_p$, which is what this returns. The two measures are not interchangeable, so each has its own argument; and the guideline’s directivity comes from a chart against frequency, which is why Q may be given one value per band.

Parameters

Returns: The room effect as a positive attenuation, dB (a float when every input is scalar, otherwise a per-band array).

Raises

section_change_loss(
    frequencies: ArrayLike,
    upstream_area: float,
    downstream_area: float,
    *,
    shape: str = 'rectangular',
    upstream_size: float | None = None,
    speed_of_sound: float = 343.0,
    cap: float = 5.0,
) -> HvacSpectrumResult

Reflection at a sudden change of duct section (VDI 2081 Part 1, 6.3).

Figure 26 gives the reduction of the internal sound power level in closed form, for the area ratio $r=S_1/S_2$:

and it applies differently on the two sides of unity. A sudden reduction ($r>1$) reflects at every frequency; the figure’s own column says the frequency has no effect. A sudden increase ($r<1$) reflects only below the limit frequency of the upstream duct, Equation (33) or (34), and above it the figure gives nought: past that frequency the duct carries more than plane waves and the mismatch stops behaving as one.

A gradual change is not this: 6.3 says that where the transition is smooth, through a tapered adapter long compared with the wavelength, the reduction is negligibly small.

The reduction is reached only with the duct anechoically terminated at both ends, which practice rarely is, so VDI 3733 recommends taking no more than 5 dB from it. That is the default cap, and it binds from an area ratio of about 10,5 upwards, or 0,095 downwards.

There is no ASHRAE counterpart to call through model=: Long folds the reflection from a change of total section into the junction itself, which is what split_loss implements for model="ashrae", while VDI 2081 treats the two as separate elements of the chain.

Parameters

Returns: An HvacSpectrumResult of the reflection loss, dB.

Raises

silencer_self_noise(
    frequencies: ArrayLike | None,
    airway_velocity: float,
    passages: int,
    height: float,
    *,
    model: str = 'ashrae',
    pressure_drop_pa: float | None = None,
    approach_area: float | None = None,
    airway_width: float | None = None,
) -> HvacSpectrumResult

Regenerated (self) noise of a splitter silencer (Long Eq. 14.31).

Fry’s (1988) estimate, for when manufacturer self-noise data is not available:

with V the velocity in the splitter airway ($V_0=1$ m/s), N the number of air passages and H the silencer height or, for a round unit, its circumference ($H_0=1$ mm). The octave-band spectrum follows by subtracting the corrections of Table 14.8, which fall steeply above 500 Hz.

The fifth-and-a-half power of the airway velocity is the practical message: doubling the face velocity of a silencer adds about 17 dB, which is how a silencer ends up making the noise it was bought to remove.

Manufacturer self-noise data is measured on a 600 x 600 mm face, so a published spectrum has to be corrected by $10{\log }_{10}(S/S_0)$ for the actual face area before it is used; this estimate needs no such correction because the face size enters through N and H.

Parameters

Returns: An HvacSpectrumResult of the band sound power level, dB re 1e-12 W.

Raises

split_loss(
    main_area: float,
    branch_areas: ArrayLike,
    *,
    branch: int = 0,
    model: str = 'ashrae',
) -> float

Power split loss into one branch of a duct division (Long Eq. 14.17).

Where a duct divides, the sound power is shared between the branches in proportion to their areas, and a further reflection occurs when the total branch area does not match the feeder area:

Long prints this as a negative level change (a 25 per cent area split shows as -6 dB in his worked sheet); this function returns it as a positive attenuation, like every other loss in the module.

model="vdi2081" keeps only the second term, which is Equation (35) of VDI 2081 Part 1 Section 6.4:

The two standards divide the same physics differently rather than disagreeing about it. Long folds the reflection from a change of total section into the junction; VDI 2081 treats a junction and a change of section as two elements of the chain, the second in Section 6.3, and its junction is the area split alone. Where the branches happen to sum to the feeder area the two agree; where they do not, the difference is exactly the reflection term, half a decibel in the guideline’s own Table 1 for the junction whose branch areas sum to twice its feeder.

The split is the same in every octave. The German text says so (“frequenzunabhängig”) and Figure 27 has no frequency axis; the English column of the same page says the opposite, which docs/ERRATA.md records.

Parameters

Returns: The split loss, dB (positive).

Raises

splitter_silencer_insertion_loss(
    frequencies: ArrayLike | None,
    height: float,
    length: float,
    airway_widths: ArrayLike,
    splitter_thickness: float,
) -> HvacSpectrumResult

Insertion loss of a parallel-splitter (dissipative) silencer.

A splitter silencer divides the duct into parallel airways separated by absorbent baffles. Bies, Hansen & Howard (§8.10.5) reduce it to a lined duct: each airway is calculated as a lined duct whose liner thickness is half the splitter thickness, because each face of a splitter lines the airway beside it, and the insertion losses of the airways combine as

which is the energy average over the airways: when they are identical the total equals the loss of a single passage, and when they differ the leakiest airway dominates, exactly as a real unit does. The airway loss itself comes from the Reynolds (1990) lined-rectangular-duct regression of lined_rectangular_duct_attenuation (Long Eq. 14.12), so the same validity envelope applies: linings of 25 mm to 52 mm at 24 to 48 kg/m3 and a perimeter-to-area ratio of the airway between 1.1667 and 6 ft^-1.

Published dynamic insertion loss (DIL) from the silencer manufacturer, measured with the design airflow and in the design direction, should be preferred wherever it exists; this estimate is the early-design fallback and ignores the entrance and exit losses of the unit. The unit’s regenerated noise is a separate quantity, silencer_self_noise.

Parameters

Returns: An HvacSpectrumResult of the insertion loss, dB.

Raises

unlined_circular_duct_attenuation(
    frequencies: ArrayLike | None,
    length: float,
    *,
    diameter: float | None = None,
    model: str = 'ashrae',
) -> HvacSpectrumResult

Attenuation of an unlined circular sheet-metal duct (Long Table 14.1).

A circular duct is far stiffer than a rectangular one in its breathing mode, so the sound field can hardly excite it: the loss is about a tenth of the rectangular value and is tabulated as a length rate alone, 0.03 dB/ft up to 250 Hz and 0.05 to 0.07 dB/ft above. The published table stops at 4 kHz; the 4 kHz rate is held for the 8 kHz band.

model="vdi2081" reads Table 5 of VDI 2081 Part 1 Section 6.1, which does depend on the diameter: a wide round duct is stiffer still and its tabulated loss falls to nothing at 63 Hz above 400 mm, where the table prints a dash. That is the substantive difference between the two accounts of this element, and it is why diameter is required there and not here.

Parameters

Returns: An HvacSpectrumResult of the attenuation, dB.

unlined_rectangular_duct_attenuation(
    frequencies: ArrayLike,
    width: float,
    height: float,
    length: float,
    *,
    wrapped: bool = False,
    model: str = 'ashrae',
) -> HvacSpectrumResult

Attenuation of an unlined rectangular sheet-metal duct (Long Eqs. 14.9-14.11).

Sound running down an unlined duct loses energy into the induced motion of the duct walls, so the loss grows with the perimeter-to-area ratio P / S (a wide, shallow duct has floppier side walls). Reynolds (1990) fits the 63 Hz to 250 Hz bands with $R=17.0(P/S{)}^{0.25}{f}^{-0.85}l$ for $P/S\ge 3$ ft^-1 and $R=1.64(P/S{)}^{0.73}{f}^{-0.58}l$ below it, and everything above 250 Hz with $R=0.02(P/S{)}^{0.8}l$. An external fibreglass blanket adds surface mass and doubles the low-frequency loss (wrapped=True).

model="vdi2081" reads Table 5 of VDI 2081 Part 1 Section 6.1 instead: a step table in dB per metre, keyed on the largest clear side length and on five frequency columns, 63, 125, 250, 500 and above 1000 Hz. It is a different account of the same loss, not a restatement of this one: Reynolds fits a continuous power law of the perimeter-to-area ratio, VDI 2081 tabulates four size bands of 1 mm steel sheet, and where the two overlap they differ by a decibel or two per metre. wrapped has no meaning there and is refused.

Parameters

Returns: An HvacSpectrumResult of the attenuation, dB.

Constant (numpy.ndarray, shape (8,)).