noise_control.valves_hydrodynamic

Control valve hydrodynamic noise (IEC 60534-8-4:2005).

Water carries sound at 1 400 m/s and is far too stiff to choke the way a gas does, so a control valve on a water line cannot make the shock cells that IEC 60534-8-3 spends five regimes on. It makes two things instead, and the whole of this part is the sum of them:

• turbulence in the jet leaving the vena contracta, whose acoustical efficiency is a straight line in the jet velocity, Equation (8);
• cavitation, once the differential pressure passes the point where the liquid flashes to vapour in the vena contracta and the bubbles collapse again downstream. Equation (9) gives that its own efficiency, and it is a steep function of how far past the threshold the valve is: a fifth power of $x_F/x_{Fzp1}$ multiplied by an exponential.

The threshold is the characteristic pressure ratio $x_{Fz}$, a measured property of the valve (IEC 60534-8-2) that Equations (3a) and (3b) estimate when no measurement exists, corrected to the working inlet pressure by Equation (3c). Everything in the method turns on where the operating ratio $x_F$ of Equation (1) sits with respect to it, which is why Annex A’s third example perturbs $x_{Fz}$ by 0,1 and watches the answer move 14 dB.

After the source, the chain is the same shape as the aerodynamic one: an internal level at the pipe wall, Equation (10); a transmission loss through the wall, negative by construction and anchored at the ring frequency, Equations (14) and (15); and a level 1 m outside, Equations (18a) and (18b). The band-by-band route of 5.4 spreads the internal level around the peak frequency with Equations (20a) and (20b) and gives the wall a frequency-dependent loss with Equations (22a) and (22b).

Six defects of the printed document, all confirmed on the page and all recorded in docs/ERRATA.md:

• Equation (12) is printed twice, differently: Clause 5.1 gives the Strouhal number a leading 0,02 and no valve style modifier, Annex A’s Table A.1 gives it 0,036 and a factor $F_d^{0,75}$. Only the annex form reproduces the annex’s own printed $N_{Str}$, which is why STROUHAL_CONSTANTS carries both and the default is "annex".
• Table A.1 prints the band transmission loss as TL(8 000 Hz) = 51,76 dB, positive, where its own two inputs sum to $-51,763$ dB.
• The seat diameter formula of 6.3.2 b), $d_o=5,2\sqrt{N_{34}{C}_n}$, returns millimetres for a symbol Clause 3 declares in metres, which is why last_stage_seat_diameter_mm carries the unit in its name.
• Equation (23b) computes each stage’s inlet pressure from the next stage’s, which contradicts Equation (23a) and runs the pressure the wrong way along the trim.
• Equations (18a) and (18b) are printed with conditions on two different thresholds, $x_F\le x_{Fz}$ and $x_{Fzp1}<x_F\le 1$, which divide the domain between them only at the one inlet pressure where those two are equal. Every other regime statement in the document tests the corrected ratio, and so does this module.
• Three intermediates of Table A.1 do not follow from the intermediates printed beside them, by up to 0,08 dB.

Clause 6, the multistage trim, is the same method with per-stage inputs: stage_conditions splits the differential, and either the stages are summed in energy by Equation (27) or, for a fixed device with increasing flow areas, only the last stage is calculated at all.

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

Constant (mapping).

ACOUSTIC_POWER_RATIOS = {'globe parabolic plug': 0.25, 'globe 3 V-port plug': 0.25, 'globe 4 V-port plug': 0.25, 'globe 6 V-port plug': 0.25, 'globe 60 hole drilled cage': 0.25, 'globe 120 hole drilled cage': 0.25, 'butterfly swing-through': 0.5, 'butterfly fluted vane': 0.5, 'butterfly 60 deg flat disk': 0.5, 'eccentric rotary plug': 0.25, 'segmented ball 90 deg': 0.25, 'expander': 1.0}

Constant (float).

AIR_DENSITY_KG_M3 = 1.293

band_internal_levels(
    frequency: ArrayLike,
    internal_level: float,
    *,
    turbulent_peak: float,
    cavitation_peak: float | None = None,
    cavitation_fraction: float = 0.0,
) -> NDArray[np.float64]

Equations (19a) and (19b): the internal level, band by band.

The cavitating form is the turbulent and the cavitating spectra added in energy, each weighted by the share of the sound power its own efficiency accounts for. Since the two peak frequencies differ by a factor of a few, the sum is a two-humped spectrum, and which hump is taller is decided by ${\eta }_{cav}/({\eta }_{turb}+{\eta }_{cav})$ alone.

Parameters

Returns: $L_{pi}(f_i)$, in dB, one value per band.

Raises

Constant (mapping).

CAPACITY_SCALE_CONSTANTS = {'Cv': 1.17, 'Kv': 1.0}

cavitation_differential(
    *,
    inlet_pressure_pa: float,
    outlet_pressure_pa: float,
    vapour_pressure_pa: float,
    pressure_recovery: float,
) -> float

Equation (2): the differential the jet velocity is computed from.

The second candidate is where the flow chokes. Past it the valve cannot turn any more differential into velocity, so $\Delta p_c$ stops following $p_1-p_2$ and Equation (5) stops accelerating the jet, even though the noise keeps rising because cavitation takes over.

The printed equation says “lower than … or …”, with no min operator and no inequality; the minimum is what it means.

Parameters

Returns: $\Delta p_c$, in Pa.

Raises

cavitation_distribution(
    frequency: ArrayLike,
    peak: float,
) -> NDArray[np.float64]

Equation (20b): how cavitation noise spreads over the bands.

The same shape as Equation (20a) with every numeral changed. Both exponents are $\pm 1,5$ instead of 3 and −1, so both flanks fall at the same 4,5 dB per octave and the hump is symmetric, but about $\sqrt[3]{4}{f}_{p,cav}$, two thirds of an octave above the frequency Equation (13) names, because the quarter in front of the rising branch shifts the maximum up. Against Equation (20a)‘s 3 dB up and 9 dB down that is a far broader spectrum: cavitation is heard as a wide band of gravel where turbulence is heard as a hiss around one frequency.

Parameters

Returns: $F_{cav}(f_i)$, in dB.

Raises

cavitation_efficiency(
    *,
    turbulent: float,
    differential: float,
    choked_differential: float,
    pressure_ratio: float,
    corrected_ratio: float,
) -> float

Equation (9): what the collapsing bubbles add.

Three of those factors are what makes cavitation noise behave the way it does. $(x_F-x_{Fzp1}{)}^{1,5}$ starts the term at exactly zero on the threshold, so the two regimes meet without a step; $(x_F/x_{Fzp1}{)}^5$ then makes it climb almost vertically once the threshold is passed; and $(1-x_F{)}^{-0,5}$ sends it towards infinity as the valve approaches flashing, which is where the method stops.

Parameters

Returns: ${\eta }_{cav}$, dimensionless, and exactly zero on the threshold.

Raises

Constant (float).

CAVITATION_FLOOR_WIDTH = 0.1

cavitation_peak_frequency(
    turbulent_peak: float,
    pressure_ratio: float,
    corrected_ratio: float,
) -> float

Equation (13): the peak frequency of the cavitation noise.

Both brackets are the reciprocals of the ones in Equation (9), and that is deliberate rather than a misprint: the same factors that make the cavitation level rise as the valve is opened further into cavitation make its peak frequency fall, because the bubbles grow larger and take longer to collapse. Just past the threshold the collapse is fast and the noise is hissy, six times the turbulent peak; deep into cavitation it drops back down into a rumble.

Parameters

Returns: $f_{p,cav}$, in Hz.

Raises

cavitation_transmission_loss(
    turbulent_loss: float,
    *,
    turbulent_peak: float,
    cavitation_peak: float,
    efficiency_ratio: float,
    pressure_ratio: float | None = None,
    corrected_ratio: float | None = None,
) -> float

Equation (17): the transmission loss once the valve cavitates.

Cavitation noise peaks higher in frequency than turbulent noise, and the pipe wall passes high frequencies better, so the correction is normally positive: the wall becomes less effective when the valve cavitates, which is one reason cavitating valves are heard from far away.

The NOTE to the equation floors the efficiency ratio at $f_{p,turb}^2/(250f_{p,cav}^{1,5})$ while $x_F$ is within 0,1 of the threshold, which is exactly the value that makes the bracket equal 1. Just above incipient cavitation, where the cavitating efficiency is still a small fraction of the total, the floor therefore keeps the cavitating transmission loss from falling below the turbulent one. Pass both ratios to apply it; leave them out to evaluate the equation as printed.

Parameters

Returns: $T{L}_{cav}$, in dB, negative.

Raises

combine_stage_levels(*levels: float) -> float

Equation (27): the stages of a multistage trim, added.

6.3.1 calculates each stage as if it were a valve of its own and sums them in energy here. That is the branch for a trim whose stages all radiate into the pipe, Figures 1 and 3; the fixed device of 6.3.2 with increasing flow areas does not use it, because everything but the last stage is absorbed inside the trim.

Parameters

Returns: Their energy sum, in dB.

Raises

corrected_incipient_ratio(
    incipient_ratio: float,
    inlet_pressure_pa: float,
) -> float

Equation (3c): the threshold moved to the working inlet pressure.

Equation (3a) and the charts of Figures 4 to 9 are drawn at 6 × 10⁵ Pa. Raising the inlet pressure lowers the threshold, because the same differential ratio now means a larger absolute pressure drop and a livelier vena contracta, but the eighth-power root makes it a slow correction: ten times the inlet pressure moves the threshold by a quarter.

Below 6 × 10⁵ Pa the correction works the other way and raises the threshold, and with an $x_{Fz}$ near the 0,90 ceiling of Equation (3a) it can carry it to or past 1. That pair is outside the method: a threshold of 1 is the flashing point, so it is not a ratio at which cavitation could be detected, and Equations (9) and (13) divide by $1-x_{Fzp1}$. It is rejected here rather than several steps later.

Parameters

Returns: $x_{Fzp1}$, dimensionless.

Raises

differential_pressure_ratio(
    *,
    inlet_pressure_pa: float,
    outlet_pressure_pa: float,
    vapour_pressure_pa: float,
) -> float

Equation (1): the differential pressure ratio.

The denominator is the differential the valve would need to take the liquid all the way down to its vapour pressure, so $x_F$ says how far towards flashing this operating point is, and 1 is the whole way.

Parameters

Returns: $x_F$, dimensionless.

Raises

HydrodynamicValveNoise(
    regime: str,
    pressure_ratio: float,
    differential: float,
    cavitation_differential: float,
    incipient_ratio: float,
    corrected_ratio: float,
    jet_diameter_m: float,
    velocity: float,
    stream_power: float,
    turbulent_efficiency: float,
    cavitation_efficiency: float | None,
    sound_power: float,
    internal_level: float,
    strouhal_number: float,
    turbulent_peak: float,
    cavitation_peak: float | None,
    pipe_ring_frequency: float,
    reference_transmission_loss: float,
    turbulent_transmission_loss: float,
    cavitation_transmission_loss: float | None,
    transmission_loss: float,
    external_level: float,
    frequencies: NDArray[np.float64],
    band_internal_level: NDArray[np.float64],
    band_transmission_loss: NDArray[np.float64],
    band_external_level: NDArray[np.float64],
)

What IEC 60534-8-4 says about one operating point on a liquid line.

Attributes

incipient_cavitation_ratio(
    flow_coefficient: float,
    style_modifier: float,
    pressure_recovery: float,
    *,
    coefficient: str = 'Cv',
) -> float

Equation (3a): where cavitation becomes audible, estimated.

4.2 asks for a measured $x_{Fz}$ (IEC 60534-8-2) and offers this only as an estimate, warning that a prediction built on it “can create uncertainties as illustrated in Annex A”. Annex A’s third example is exactly that illustration: 0,1 on this number moves the answer 14 dB.

The nesting is worth reading twice. The outer radical covers the whole of $1+3F_d\sqrt{\cdots }$; the inner one covers only the capacity group. A valve with a small style modifier, a cage full of small holes, keeps $x_{Fz}$ high and stays quiet longer.

Parameters

Returns: $x_{Fz}$ at an inlet pressure of 6 × 10⁵ Pa, dimensionless.

Raises

internal_sound_pressure_level(
    *,
    sound_power: float,
    density: float,
    speed_of_sound: float,
    internal_diameter_m: float,
) -> float

Equation (10): the level inside, at the pipe wall.

The sound power is spread over the pipe cross-section and turned into a pressure through the impedance of the liquid, which is why the density and the speed of sound multiply rather than divide: water’s impedance is 3 400 times air’s, so the same acoustic power makes a level some 35 dB higher inside a water line than inside an air line. Levels of 150 dB in the pipe are ordinary here, and it is the transmission loss, not the source, that makes the outside habitable.

In the printed equation the density has lost its Greek base glyph and reads as a bare subscript; Table A.1 prints the same equation with ${\rho }_L$ intact, which settles it.

Parameters

Returns: $L_{pi}$, in dB re 2 × 10⁻⁵ Pa.

Raises

jet_strouhal_number(
    *,
    flow_coefficient: float,
    style_modifier: float,
    pressure_recovery: float,
    corrected_ratio: float,
    valve_diameter_m: float,
    seat_diameter_m: float,
    inlet_pressure_pa: float,
    vapour_pressure_pa: float,
    coefficient: str = 'Cv',
    form: str = 'annex',
) -> float

Equation (12): the Strouhal number of the jet.

This is the one place where the two printings of the standard disagree with each other. The form above is Table A.1’s; Clause 5.1 prints the same equation with a leading 0,02 and no $F_d^{0,75}$. Only the annex form reproduces the annex’s own $N_{Str}=0,399$, so it is the default here; pass form="clause" for the normative text’s version and see docs/ERRATA.md.

Unlike the Strouhal number of a free jet, which is a constant near 0,2, this one is a fitted group that carries the whole geometry of the valve and comes out anywhere between about 0,2 and 0,5.

Parameters

Returns: $N_{STR}$, dimensionless.

Raises

last_stage_differential(
    *,
    inlet_pressure_pa: float,
    outlet_pressure_pa: float,
    vapour_pressure_pa: float,
    corrected_ratio: float,
) -> float

Equation (28): the differential of the last stage of a fixed device.

This is not Equation (2) with different symbols. Equation (2) caps the differential at the choking point, $F_L^2(p_1-p_v)$; this one caps it at the cavitation threshold of the last stage, $x_{Fzp1,n}(p_{1,n}-p_v)$, which is a smaller number. A fixed multistage device is designed so that the last stage never cavitates, and the cap says so.

Parameters

Returns: $\Delta p_c$, in Pa.

Raises

last_stage_seat_diameter_mm(
    flow_coefficient: float,
    *,
    coefficient: str = 'Cv',
) -> float

6.3.2 b): the seat diameter of the last stage, estimated.

The one display formula in the standard that carries no equation number, and the one whose unit does not survive its own arithmetic: Clause 3 declares $d_o$ in metres, and for any real last stage this returns tens. It is millimetres, which is why the unit is in the name of this function; see docs/ERRATA.md. Equation (12) then wants the result in metres, so divide by 1 000 before passing it on.

Parameters

Returns: $d_o$, in millimetres.

Raises

LiquidPipe(
    internal_diameter_m: float,
    wall_thickness: float,
    density: float,
    speed_of_sound: float = 5000.0,
    air_density: float = 1.293,
    air_sound_speed: float = 343.0,
)

The pipe the noise comes out of, and the air around it.

Attributes

LiquidStream(
    mass_flow: float,
    inlet_pressure_pa: float,
    outlet_pressure_pa: float,
    vapour_pressure_pa: float,
    density: float,
    speed_of_sound: float,
)

The liquid and the operating point, which Clause 4.1 reads first.

Attributes

LiquidTrim(
    flow_coefficient: float,
    style_modifier: float,
    pressure_recovery: float,
    incipient_ratio: float,
    power_ratio: float,
    valve_diameter_m: float,
    seat_diameter_m: float,
    coefficient: str = 'Cv',
)

The valve, at the travel being examined.

Attributes

mechanical_stream_power(
    mass_flow: float,
    velocity: float,
    pressure_recovery: float,
) -> float

Equation (6): the stream power the valve dissipates.

The kinetic power of the jet, $\dot{m}{U}_{vc}^2/2$, scaled back by $F_L^2$ to the part of it that is actually thrown away rather than recovered as pressure downstream. Equation (7a) then takes a part in $10^{-6}$ of this and calls it sound.

Parameters

Returns: $W_m$, in W.

Raises

multihole_incipient_cavitation_ratio(
    passages: int,
    hole_diameter_m: float,
    pressure_recovery: float,
) -> float

Equation (3b): the same threshold for a multihole trim.

A multihole trim is not described by its capacity and style modifier but by how many holes it has and how big they are, which is what this form takes. The group $N_o{d}_H^2$ is the total hole area to within $\pi /4$, so two trims with the same open area and different hole counts get the same threshold here.

Parameters

Returns: $x_{Fz}$ at an inlet pressure of 6 × 10⁵ Pa, dimensionless.

Raises

pipe_ring_frequency(
    internal_diameter_m: float,
    *,
    pipe_sound_speed: float = 5000.0,
) -> float

Equation (14): the ring frequency of the pipe.

The frequency at which one wavelength of a compressional wave in the wall material wraps exactly once around the circumference. The wall is at its most transparent there, so the transmission loss of Equation (15) is anchored at this frequency and Equations (16b) and (22b) only ever make it worse.

Parameters

Returns: $f_r$, in Hz.

Raises

Constant (float).

REFERENCE_INLET_PRESSURE_PA = 600000.0

reference_transmission_loss(
    internal_diameter_m: float,
    wall_thickness: float,
    *,
    pipe_density: float,
    pipe_sound_speed: float = 5000.0,
    air_density: float = 1.293,
    air_sound_speed: float = 343.0,
) -> float

Equation (15): the transmission loss at the ring frequency.

A mass law written as a ratio of two impedances: the wall’s, per unit area, against the air’s, scaled by how much wall there is per unit bore. Both terms are negative, and the standard keeps them that way, so this quantity is a negative number that is added to the internal level all the way to Equation (18). A DN 100 steel pipe with a 3,6 mm wall comes out at −44,7 dB.

Parameters

Returns: $T{L}_{fr}$, in dB, negative.

Raises

stage_conditions(
    *,
    inlet_pressure_pa: float,
    outlet_pressure_pa: float,
    vapour_pressure_pa: float,
    stage_coefficients: Sequence[float],
    flow_coefficient: float,
) -> tuple[StageConditions, ...]

Equations (23a) to (24b) and (26): the differential, stage by stage.

Each stage takes a share of the total differential in inverse proportion to the square of its own capacity, which is the series law for flow resistances: $1/C^2={\sum }_{i}1/C_i^2$. A trim whose stages all have the same $C_i$ splits the drop evenly; one with an increasing flow area, the device of 6.3.2 and Figure 2, puts most of the drop in the first stages and leaves the last one working at a differential small enough not to cavitate.

Equation (23b) is printed with $p_{1,i+1}$ on the right, which would compute each stage’s inlet from the next stage’s and run the pressure backwards along the trim, contradicting (23a). The recursion implemented here is the forward one the index $C_{i-1}$ calls for; see docs/ERRATA.md.

Parameters

Returns: One StageConditions per stage, in flow order.

Raises

StageConditions(
    inlet_pressure_pa: float,
    outlet_pressure_pa: float,
    pressure_ratio: float,
)

What one throttling stage of a multistage trim sees.

Attributes

Constant (mapping).

STROUHAL_CONSTANTS = {'annex': 0.036, 'clause': 0.02}

transmission_loss_correction(
    frequency: ArrayLike,
    ring: float,
) -> NDArray[np.float64]

Equations (16b) and (22b): how far the wall is from its ring.

One expression covers both printed equations: (16b) evaluates it at the turbulent peak frequency and (22b) at each band. The bracket is a sum of two branches, one falling as $1/f$ and one rising as $f^{1,5}$, so the correction is worst far from the ring frequency on either side. It is never zero: where the two branches together are smallest, at $(2/3{)}^{0,4}{f}_r=0,85f_r$, the bracket is still 1,96 and the correction still costs 5,85 dB, and at $f_r$ itself it costs 6,02.

Parameters

Returns: $\Delta TL$, in dB, one value per frequency, and always negative: the correction is worth at least 5,85 dB even where it is smallest.

Raises

turbulent_distribution(
    frequency: ArrayLike,
    peak: float,
) -> NDArray[np.float64]

Equation (20a): how turbulent noise spreads over the bands.

A band correction, in dB, that adds to the overall internal level. The two terms in the bracket are the two sides of the peak: below it the $f^{-1}$ term dominates and the level rises at 3 dB per octave; above it the $f^3$ term takes over and the level falls at 9 dB per octave. The trailing 3,1 dB is a printed offset and not a normalisation: over the band set of 5.4.1 these corrections do not sum back to $L_{pi}$, they sum about 5 dB above it, so the band route and the overall route of Equation (18a) are two answers and not one answer twice. The maximum is not exactly at $f_{p,turb}$ either: the quarter in front of the rising branch puts it at $(4/3{)}^{1/4}{f}_{p,turb}$, a few per cent above.

The negative exponent is easy to lose. Text extracted from the printed page renders it as a bare 1, which flattens the low-frequency side.

Parameters

Returns: $F_{turb}(f_i)$, in dB.

Raises

turbulent_efficiency(velocity: float, speed_of_sound: float) -> float

Equation (8): the acoustical efficiency of the turbulent jet.

5.1 argues the case: at these velocities the jet is slow enough to be a monopole, and a monopole’s efficiency rises with the first power of the Mach number, reaching $10^{-4}$ when the jet reaches the speed of sound in the liquid. Water carries sound at about 1 400 m/s and a control valve jet runs at tens of metres per second, so the efficiency comes out in the $10^{-6}$ range: one part in a million of the stream power.

Parameters

Returns: ${\eta }_{turb}$, dimensionless.

Raises

turbulent_peak_frequency(
    strouhal_number: float,
    velocity: float,
    jet: float,
) -> float

Equation (11): the peak frequency of the turbulent noise.

A jet radiates around the frequency at which its own eddies pass a fixed point, which is the velocity divided by the size of the eddies. The jet diameter of Equation (4) stands for that size.

Parameters

Returns: $f_{p,turb}$, in Hz.

Raises

uniform_passage_style_modifier(passages: int) -> float

Equation (29): the style modifier of a last stage full of openings.

IEC 60534-8-3 defines $F_d$ as the hydraulic diameter of one passage over the diameter of the single orifice of the same total area. For $N_o$ identical round openings that ratio collapses to $1/\sqrt{N_o}$, which is what this equation prints. Sixteen openings therefore give a quarter of the jet diameter, a sixteenth of the jet area, and a peak frequency four times higher.

Parameters

Returns: $F_d$, dimensionless.

Raises

valve_hydrodynamic_noise(
    stream: LiquidStream,
    valve: LiquidTrim,
    pipe: LiquidPipe,
    *,
    strouhal_form: str = 'annex',
    frequency: ArrayLike | None = None,
) -> HydrodynamicValveNoise

The whole of Clauses 4 and 5, from the operating point to 1 m.

The chain is the standard’s own: the pressure ratios of 4.1 and 4.2, the geometry and the stream power of 4.4 to 4.6, the regime test and the two efficiencies of 5.1, the pipe transmission loss of 5.2, the external level of 5.3, and the band route of 5.4 alongside it.

Which regime the valve is in is decided once, on $p_1-p_2$ against $x_{Fzp1}(p_1-p_v)$, and it selects the sound power of Equation (7a) or (7b), the transmission loss of (16a) or (17), the external level of (18a) or (18b), and the band spectrum of (19a) or (19b) together. On the threshold itself Equation (9) returns exactly zero, so the two branches meet without a step.

Parameters

Returns: A HydrodynamicValveNoise carrying every printed intermediate as well as the level at 1 m.

Raises

vena_contracta_velocity(
    differential: float,
    density: float,
    pressure_recovery: float,
) -> float

Equation (5): the jet velocity.

Bernoulli’s velocity for the differential of Equation (2), divided by the recovery factor because $F_L$ is defined as the fraction of the ideal velocity head the valve actually reaches at the vena contracta.

Parameters

Returns: $U_{vc}$, in m/s.

Raises