materials.airflow_resistance

Airflow resistance of porous materials: ISO 9053-1 and ISO 9053-2.

Two standardised measurement methods share the same three quantities and units (ISO 9053-1:2018, Clause 3; ISO 9053-2:2020, Clause 3):

• Airflow resistance R = dp / q_v in Pa*s/m3, with dp the air pressure difference across the specimen (Pa) and q_v the volumetric airflow rate through it (m3/s) (ISO 9053-1:2018, 3.1).
• Specific airflow resistance R_s = R * A in Pa*s/m (not Pa*s/m2), with A the cross-sectional area of the specimen perpendicular to the flow (m2) (ISO 9053-1:2018, 3.2). Equivalently R_s = dp / u with u the linear airflow velocity, since u = q_v / A.
• Airflow resistivity sigma = R_s / d in Pa*s/m2, with d the specimen thickness in the flow direction (m), for homogeneous materials (ISO 9053-1:2018, 3.3). Equivalently sigma = R * A / d.

The linear airflow velocity is u = q_v / A (ISO 9053-1:2018, 3.4).

Static (DC) method, ISO 9053-1:2018. A steady unidirectional flow in the laminar regime is used. The recommended reference linear airflow velocity is u = 0.5e-3 m/s (0.5 mm/s, clause 7.5); if measured stepwise the highest velocity shall not exceed 15e-3 m/s (15 mm/s), beyond which the flow may be non-linear. When measured stepwise the pressure difference is plotted against u and fitted with a regression of at least second order constrained through the origin, dp = a*u + b*u**2; dp and R_s are then evaluated at u = 0.5e-3 m/s (clause 7.5). Because R_s = dp / u = a + b*u, the linear coefficient a is the zero-velocity specific airflow resistance.

Alternating (AC) method, ISO 9053-2:2020. A sinusoidally moving piston (frequency 1 Hz to 4 Hz, typically 2 Hz; clause 6.2) drives an alternating volume flow into an air cavity terminated either by the specimen or by an airtight termination. The airflow resistance follows from the sound-pressure-level difference between the two terminations (ISO 9053-2:2020, Formula (2), 8.7):

R = kappa' * P_S / (2*pi*f*V) * (h_t/h_s) * 10**((L_ps - L_pt)/20)

with kappa' the effective ratio of specific heats for air (Annex A), P_S the static (atmospheric) pressure (Pa), f the piston frequency (Hz), V the cavity volume with the airtight termination (m3), h_t/h_s the piston stroke amplitudes with the airtight termination / specimen cell, and L_ps/L_pt the cavity sound pressure levels with the specimen / airtight termination (dB). Only the level difference enters, so the sound level device needs no absolute calibration (clause 8.7). The RMS piston volume flow is q_v = 2*pi*f*h*A_P (ISO 9053-2:2020, 6.2), with h the stroke amplitude and A_P the piston cross-sectional area.

The effective ratio of specific heats kappa' accounts for heat conduction between the oscillating air and the cavity walls, which makes the compression not fully adiabatic. ISO 9053-2:2020 Annex A (normative) gives its evaluation from the cavity geometry and air properties (effective_kappa, Formula (A.7)); the Annex A.3 worked example yields kappa' = 1.370 (about 2 % below the adiabatic kappa = 1.4008). When no cavity/air data are supplied, alternating_airflow_resistance falls back to the uncorrected adiabatic value kappa = 1.4 (Formula (A.1)); for a conforming result compute kappa' per Annex A and pass it explicitly.

Neither part defines a temperature/atmospheric normalisation of the result.

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airflow_resistance

airflow_resistance(pressure_drop: float, volume_flow_rate: float) -> float

Airflow resistance R = dp / q_v (ISO 9053-1:2018, 3.1).

pressure_drop is the pressure difference dp across the specimen (Pa) and volume_flow_rate is the volumetric airflow rate q_v (m3/s). Returns R in Pa*s/m3.

airflow_resistivity

airflow_resistivity(specific_resistance: float, thickness: float) -> float

Airflow resistivity sigma = R_s / d in Pa*s/m2 (ISO 9053-1:2018, 3.3).

specific_resistance is R_s (Pa*s/m) and thickness is d (m), the specimen thickness in the flow direction. Returns sigma in Pa*s/m2.

AirflowResistanceWarning

Advisory for out-of-range or non-conforming ISO 9053 airflow inputs.

alternating_airflow_resistance

alternating_airflow_resistance(
    level_specimen: float,
    level_termination: float,
    *,
    piston_stroke_specimen: float,
    piston_stroke_termination: float,
    frequency: float,
    cavity_volume: float,
    static_pressure: float = 101325.0,
    kappa_prime: float = 1.4,
    background_level: float | None = None,
) -> float

Alternating-method airflow resistance (ISO 9053-2:2020, Formula (2), 8.7).

Implements:

R = kappa' * P_S / (2*pi*f*V) * (h_t/h_s) * 10**((L_ps - L_pt)/20)

level_specimen (L_ps) and level_termination (L_pt) are the cavity sound pressure levels (dB) with the specimen cell and the airtight termination; piston_stroke_specimen (h_s) and piston_stroke_termination (h_t) the corresponding stroke amplitudes (m); frequency the piston frequency f (Hz, 1-4 Hz); cavity_volume the airtight-termination cavity volume V (m3); static_pressure the atmospheric pressure P_S (Pa, default 101325); kappa_prime the effective ratio of specific heats kappa'; background_level the optional cavity background level L_pb (dB) for the Formula (4) check. Returns R in Pa*s/m3.

kappa_prime defaults to the uncorrected adiabatic kappa = 1.4 (Formula (A.1)). For a result conforming to the normative Annex A, compute the heat-conduction-corrected kappa' with effective_kappa from the cavity geometry and pass it here (the Annex A.3 example gives kappa' = 1.370).

Emits AirflowResistanceWarning when the piston frequency is outside 1-4 Hz or when the Formula (3)/(4) validity criteria are not met.

effective_kappa

effective_kappa(
    cavity_surface: float,
    cavity_volume: float,
    frequency: float,
    *,
    speed_of_sound: float = 345.9,
    air_density: float = 1.186,
    specific_heat_ratio: float = 1.4008,
    specific_heat_cp: float = 938.7,
    thermal_conductivity: float = 0.02355,
) -> float

Effective ratio of specific heats kappa' (ISO 9053-2:2020, Annex A, Formula (A.7)).

Heat conduction between the oscillating air and the cavity walls makes the compression not fully adiabatic, lowering kappa to:

kappa' = kappa / sqrt(1 + (kappa-1)*(S/V)*b + 0.5*((kappa-1)*(S/V)*b)**2)   (A.7)

with b the thermal boundary-layer thickness (Formulae (A.4)/(A.5), thermal_boundary_layer_thickness), S the total internal surface area of the air cavity (m2) and V its volume (m3).

cavity_surface is S (m2), cavity_volume V (m3) and frequency the piston frequency f (Hz); specific_heat_ratio kappa (adiabatic) and the remaining air properties default to the ISO 9053-2:2020 Annex A.3 values. Returns the dimensionless kappa' for use in alternating_airflow_resistance; the Annex A.3 worked example (S = 0.0471 m2, V = 7.854e-4 m3, f = 2 Hz) yields kappa' = 1.370.

linear_airflow_velocity

linear_airflow_velocity(volume_flow_rate: float, area: float) -> float

Linear airflow velocity u = q_v / A (ISO 9053-1:2018, 3.4).

volume_flow_rate is q_v (m3/s) and area is A (m2); returns u in m/s.

piston_volume_flow_rate

piston_volume_flow_rate(
    frequency: float,
    stroke_amplitude: float,
    piston_area: float,
) -> float

RMS piston volume flow q_v = 2*pi*f*h*A_P (ISO 9053-2:2020, 6.2).

frequency is the piston frequency f (Hz), stroke_amplitude the stroke amplitude h (m) and piston_area the piston cross-section A_P (m2). Returns q_v in m3/s.

specific_airflow_resistance

specific_airflow_resistance(
    resistance: float | None = None,
    area: float | None = None,
    *,
    pressure_drop: float | None = None,
    velocity: float | None = None,
) -> float

Specific airflow resistance R_s in Pa*s/m (ISO 9053-1:2018, 3.2).

Two equivalent routes are accepted; supply exactly one:

• resistance (R, Pa*s/m3) and area (A, m2): R_s = R * A.
• pressure_drop (dp, Pa) and velocity (u, m/s): R_s = dp/u (from R_s = R*A with u = q_v/A).

The unit is pascal second per metre (Pa*s/m), not Pa*s/m2.

static_airflow_resistance

static_airflow_resistance(
    velocities: ArrayLike,
    pressure_drops: ArrayLike,
    area: float,
    thickness: float | None = None,
    *,
    evaluation_velocity: float = 0.0005,
) -> StaticAirflowResult

Stepwise static-method airflow resistance (ISO 9053-1:2018, clause 7.5).

Fits the measured pressure difference against the linear airflow velocity with a second-order regression constrained through the origin, dp = a*u + b*u**2, and evaluates the resistances at evaluation_velocity (the clause 7.5 reference 0.5e-3 m/s by default).

velocities are the linear airflow velocities u (m/s) and pressure_drops the matching pressure differences dp (Pa) of at least two measurement steps; area is the cross-section A (m2) and thickness the specimen thickness d (m, optional, enabling sigma).

Because R_s = dp/u = a + b*u, the returned linear_coefficient a is the zero-velocity specific airflow resistance. A velocity above the clause 7.5 upper limit (15 mm/s) raises AirflowResistanceWarning.

StaticAirflowResult

StaticAirflowResult(
    resistance: float,
    specific_resistance: float,
    resistivity: float | None,
    evaluation_velocity: float,
    pressure_drop: float,
    linear_coefficient: float,
    quadratic_coefficient: float,
)

Result of an ISO 9053-1:2018 stepwise (static-method) determination.

resistance (R, Pa*s/m3), specific_resistance (R_s, Pa*s/m) and resistivity (sigma, Pa*s/m2; None when no thickness is supplied) are evaluated at evaluation_velocity (m/s, the ISO 9053-1 clause 7.5 reference 0.5 mm/s by default). linear_coefficient (a) and quadratic_coefficient (b) are the through-origin fit dp = a*u + b*u**2 (clause 7.5); a is the zero-velocity specific airflow resistance (Pa*s/m). pressure_drop is the fitted dp at evaluation_velocity (Pa).

StaticAirflowResult.plot()

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

Plot the fitted dp(u) curve with the evaluation point.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

StaticAirflowResult.report()

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

Render an ISO 9053-1 static airflow-resistance test-report fiche to a PDF.

Writes a one-page accredited airflow-resistance report (ISO 9053-1:2018, static/direct airflow method): the standard-basis line, an optional metadata header block (client, manufacturer, specimen, the specimen thickness d, test facility, date, climate …), a two-panel body with a compact metrics table (the evaluation velocity, the fitted pressure difference dp, the airflow resistance R, the specific airflow resistance R_s, the airflow resistivity sigma when a thickness is available, and the through-origin fit coefficients a and b) beside the fitted dp(u) curve, a boxed specific airflow resistance R_s with the airflow resistance R and the resistivity sigma alongside, and a footer with the fixed disclaimer. ISO 9053-1 is a material characterisation, so there is no pass/fail verdict.

The clause 7.5 stepwise procedure fits dp = a*u + b*u**2 through the origin and evaluates the resistances at the reference velocity u = 0.5 mm/s; the linear coefficient a is the zero-velocity specific airflow resistance. Resistance quantities are printed to the nearest whole Pa*s unit and the evaluation velocity to one decimal place (mm/s).

Parameters

Name	Description
path	Destination path of the PDF file.
metadata	Optional ReportMetadata; None produces a body-and-disclaimer fiche. The applicable descriptive fields are client, manufacturer, specimen, thickness (the specimen thickness d, in metres, shown in millimetres), test_room, test_date, temperature, relative_humidity, measurement_standard, laboratory, operator, report_id and notes. The requirement field is ignored (ISO 9053-1 has no verdict).
engine	Rendering back end; only "reportlab" is supported.
verbose	Accepted for a uniform .report() signature; the airflow-resistance fiche has a single body layout, so it has no effect.
language	Fiche language: "en" (default, English, decimal point) or "es" (Spanish, decimal comma).

Returns: The written path as a str.

Raises

Exception	When
ValueError	If engine is not "reportlab".
ImportError	If reportlab or matplotlib is not installed. The fiche always embeds the fitted dp(u) curve, so both are required (pip install "phonometry[report,plot]").

thermal_boundary_layer_thickness

thermal_boundary_layer_thickness(
    frequency: float,
    *,
    speed_of_sound: float = 345.9,
    air_density: float = 1.186,
    specific_heat_cp: float = 938.7,
    thermal_conductivity: float = 0.02355,
) -> float

Thermal boundary-layer thickness b (ISO 9053-2:2020, Formulae (A.4)/(A.5)).

l_h = k_a / (rho0 * c0 * C_P)              (A.5)
b   = sqrt(2 * c0 * l_h / omega)           (A.4),  omega = 2*pi*f

frequency is the piston frequency f (Hz); speed_of_sound c0 (m/s), air_density rho0 (kg/m3), specific_heat_cp C_P (J/(kg*K)) and thermal_conductivity k_a (J/(s*m*K)) are air properties, defaulting to the IEC 61094-2:2009 values used in ISO 9053-2:2020 Annex A.3. Returns b in metres; with the Annex A.3 example (f = 2 Hz) this is 1.83e-3 m.