Duct Element Sound Attenuation
A major transmission path of noise from mechanical equipment is through air distribution ductwork. Duct elements and concepts covered in this section include plenums, unlined rectangular ducts, acoustically lined rectangular ducts, unlined round ducts, acoustically lined round ducts, elbows, acoustically lined round radiused elbows, duct silencers, duct branch power division, duct end reflection loss, and terminal volume regulation units. Simplified tabular procedures for obtaining the sound attenuation associated with these elements are presented.
Plenums. Plenums are often placed between a fan and main air distribution ducts to smooth turbulent airflow. They are typically lined with acoustically absorbent material to reduce fan and other mechanical noise. Plenums are usually large rectangular enclosures with an inlet and one or more outlets.
Based on experience, ASHRAE-sponsored research (Mouratidis and Becker 2004), and earlier work (Wells 1958), transmission loss associated with a plenum can be expressed using the following considerations:
-
Frequency range (based on the cutoff frequency described in the following paragraphs), which is defined as the upper limit for plane wave sound propagation
-
In-line inlet and outlet openings
-
End-in/end-out versus end-in/side-out orientation (i.e., in-line versus elbow configuration)
At frequencies above the cutoff frequency, as defined by the plenum’s inlet duct dimensions, the wavelength of sound is small compared to the characteristic dimensions of the plenum. Plane wave propagation in a duct exists at frequencies below the cutoff, creating a need to consider two frequency ranges, where
where
| fc = cutoff frequency, Hz |
| c = speed of sound in air, ft/s |
| a = larger cross-sectional dimension of rectangular duct, ft |
| d = diameter of round duct, ft |
The cutoff frequency fc is the frequency above which plane waves no longer propagate in a duct. At these higher frequencies, waves that propagate in the duct create cross or spinning modes. The transmission loss (TL) in this higher frequency range may be predicted using the following relationship:
where
| TL = transmission loss, dB |
| b = 3.505 |
| n = –0.359 |
| Sout = area of plenum outlet, ft2 |
| S = total inside surface area of plenum minus inlet and outlet areas, ft2 |
| r = distance between centers of inlet and outlet of plenum, ft |
| Q = directivity factor; taken as 2 for opening near center of wall, or 4 for opening near corner of plenum |
| αa = average absorption coefficient of plenum lining (see Equation [8]) |
| OAE = offset angle effect; additional attenuation found in Tables 14 and 15, which tabulate frequency-dependent sound transmission properties that are manifested when inlet and outlet of plenum are not in a direct line; 90° angle is referred to as elbow effect |
The average absorption coefficient αa of plenum lining is given by
where
| α1 = sound absorption coefficient of any bare or unlined inside surfaces of plenum |
| S1 = surface area of any bare or unlined inside surfaces of plenum, ft2 |
| α2 = sound absorption coefficient of acoustically lined inside surfaces of plenum |
| S2 = surface area of acoustically lined inside surfaces of plenum, ft2 |
In many situations, inner surfaces of a plenum chamber are lined with a sound-absorbing material. For these situations, αa = α2. Table 12 gives sound absorption coefficients for selected common plenum materials.
Note: transmission loss (TL) of a plenum is the difference between the duct sound power level at the outlet and inlet of the plenum, unlike insertion loss (IL) ratings for silencers, which represent the difference (at a downstream measurement location) between the duct sound pressure levels with the silencer and with no silencer (replaced with an empty duct). For purposes here, both TL and IL are interpreted as attenuation, or the net reduction in propagating duct sound power.
For frequencies that correspond to plane wave propagation in the duct (below the cutoff frequency), the following relationship applies, with a lower frequency limit of 50 Hz:
where
| Af = surface area coefficient, dB/ft2 (see Table 13 for small and large plenum size ranges) |
| We = wall effect, dB (see Table 13 for common HVAC plenum wall types) |
| OAE = offset angle effect |
The maximum TL predicted by Equation (7) should be limited to 20 dB.
For an end-in/end-out plenum configuration, where the openings are not in-line, the offset angle θ must be considered in the TL calculation. The value of θ is obtained from the following relationship:
where (refer to Figure 19)
| θ = offset angle representing r to long axis l of duct |
| l = length of plenum, ft |
| rv = vertical offset between axes of plenum inlet and outlet, ft |
| rh = horizontal offset between axes of plenum inlet and outlet, ft |
For a given offset angle, apply the applicable effects on TL (decibel addition or subtraction) for angles up to 45° (Table 14).
For an end-in/side-out plenum configuration, where openings are perpendicular to each other, the elbow effect must be considered in the TL calculation. For any plenum configuration involving an elbow condition, apply the applicable effects on TL (decibel addition or subtraction) for the two frequency ranges, both above and below the cutoff (Table 15).
For plenum applications within a practical size envelope of 20 to 1100 ft3 volume or 50 to 650 ft2 surface area, using duct sizes in the range 12 < d < 48 in., this model may be applied with an anticipated standard deviation of ±3.5 to 5.0 dB for 50 Hz < f ≤ fc and ±1.5 to 3.0 for fc < f ≤ 5000 Hz. Use caution when applying these prediction methods for plenum configurations where either the width or height dimension is <1.5d. In this case, the plenum may not perform as an expansion chamber, thus changing its broadband TL characteristics significantly.
Example 3.
A small plenum with acoustically lined surfaces is 5.9 ft high, 4.0 ft wide, and 5.9 ft long. The inlet and outlet are each 3.0 ft wide by 2.0 ft high. The horizontal offset between centers of the plenum inlet and outlet is 1.0 ft. The vertical offset is 4.0 ft. The inside of the plenum is completely lined with 1 in. thick fiberglass insulation board, with sound absorption values as shown in Table 8. Determine the transmission loss TL associated with this plenum.
Solution:
The areas of the inlet section, outlet section, and overall surfaces are
with l = 5.9 ft, rv = 4.0 ft, and rh = 1.0 ft,
The cutoff frequency fc is
where 1132 ft/s is the approximate speed of sound in standard air.
Frequency Range #1 (1/3-octave TL in 50 Hz ≤ f ≤ fc range)
(Consult Table 13 for Af and We and Table 14 for offset angle effect.)
Frequency Range #2 (1/3-octave TL in fc < f ≤ 5000 Hz range)
where
| b = 3.505 |
| n = –0.359 |
| Q = 4 (directivity factor for inlet opening close to adjacent wall or bihedral corner of plenum) |
| αa = 1/3-octave average absorption values for 1 in. fiberglass lining (see Table 12) |
| OAE = see Table 14 |
Note: for angles between tabulated values in Table 14, use linear interpolation.
The results are tabulated as follows:
Unlined Rectangular Sheet Metal Ducts. Straight, unlined rectangular sheet metal ducts provide a fairly significant amount of low-frequency sound attenuation. Table 16 shows the results of selected unlined rectangular sheet metal ducts (Cummings 1983; Reynolds and Bledsoe 1989a; Ver 1978; Woods Fan Division 1973). Attenuation values in Table 16 apply only to rectangular sheet metal ducts with the lightest gages allowed by Sheet Metal and Air Conditioning Contractors’ National Association, Inc. (SMACNA) HVAC duct construction standards. Attenuation for lengths greater than 10 ft is not well documented.
Sound energy attenuated at low frequencies in rectangular ducts may manifest itself as breakout noise along the duct. Low-frequency breakout noise should therefore be checked. For additional information on breakout noise, see the section on Sound Radiation Through Duct Walls.
Acoustically Lined Rectangular Sheet Metal Ducts. Internal duct lining for rectangular sheet metal ducts can be used to provide both thermal insulation and sound attenuation. The thickness of duct linings for thermal insulation usually varies from 0.5 to 2 in.; the density of the internal lining usually varies between 1.5 and 3.0 lb/ft3, but may be as low as 0.75 lb/ft3. For duct lining to attenuate sound effectively, it should have a minimum thickness of 1 in. At low frequencies, thicker lining performs slightly better than thinner lining. Tables 17 and 18 give attenuation values of selected rectangular sheet metal ducts for 1 and 2 in. thick glass fiber duct lining, respectively (Herrin et al. 2017; Kuntz 1986; Kuntz and Hoover 1987; Machen and Haines 1983; Reynolds and Albright 2018; Reynolds and Bledsoe 1989a). Note that attenuation values for ducts with a cross-sectional area less than 1 ft2 or greater than 16 ft2 in these tables are taken from previous editions of the ASHRAE Handbook and based on laboratory tests using 10 ft lengths of lined duct. Insertion loss values for all other duct sizes in these tables were obtained in ASHRAE research project RP-1408 (Reynolds et al. 2018). This research project included lengths of uninterrupted straight ducts from 3 to 40 ft with varying sizes and lengths of round and rectangular ducts with fiberglass duct liner, and also captured data at 63 and 8000 Hz not reported in earlier research. The liner used in this testing was 1.5 lb/ft3 for the rectangular ducts.
Though previous editions of this table indicated values of dB/ft, research projects have shown that attenuation does not vary exactly linearly with length. Therefore, these updated tables show attenuation for lengths as actually tested. For interpolation to various duct lengths and cross sections, using the duct liner attenuation spreadsheet (available as an extra feature for the ASHRAE Handbook Online version of this chapter) is recommended. Note that the total attenuated noise will never be below the flow-generated noise level in the duct, and, because of typical flows and flanking noise in practice, attenuation values are capped at 50 dB.
Insertion loss values in Tables 17 and 18 represent the difference in the space-average sound pressure level measured in a reverberation room with sound propagating through a straight section of unlined rectangular duct minus the corresponding sound pressure level measured when the unlined section of rectangular duct is replaced with a similar section of acoustically lined rectangular duct. The net result is the attenuation resulting from adding duct liner to a sheet metal duct.
Insertion loss values discussed in this section apply only to straight rectangular sheet metal ducts made with the lightest gages allowed by the SMACNA HVAC duct construction standards. Insertion loss values for heavier gage ductwork are expected to be slightly less than the tabulated values. Insertion loss values in octave and 1/3-octave bands are available in the online version of the Handbook. Also available in the online version is a calculator which provides octave band and 1/3-octave band insertion loss values for any duct cross section larger than 12 × 12 in. and smaller than 48 × 48 in. in lengths ranging from 3 to 40 ft.
Insertion loss and attenuation values discussed in this section apply only to rectangular sheet metal ducts made with the lightest gages allowed by SMACNA HVAC duct construction standards. Attenuation for lengths greater than 10 ft is not well documented.
Unlined Round Sheet Metal Ducts. As with unlined rectangular ducts, unlined round ducts provide some natural sound attenuation that should be taken into account when designing a duct system. Compared to rectangular ducts, round ducts are much more rigid and thus breakout, especially at low frequencies, is significantly less than that from other shapes. Though this reduces attenuation values for low-frequency sound propagating down the duct, it better protects the surrounding space from breakout noise. Table 19 lists sound attenuation values for unlined round ducts (Kuntz and Hoover 1987; Woods Fan Division 1973).
Acoustically Lined Round Sheet Metal Ducts. ASHRAE research project RP-1408 (Reynolds et al. 2018) measured the insertion loss of round sheet metal ducts with 1 and 2 in. thick glass fiber duct liner and diameters of 12 to 48 in. Tables 20 and 21 present the measured insertion loss of acoustically lined round sheet metal ducts as a function of frequency and length of duct lining for a variety of common duct sizes. Insertion loss values for diameters smaller than 12 in. and larger than 48 in. were taken from previous editions of the ASHRAE Handbook. The liner was 4.0 lb/ft3.
Though previous editions of this table indicated values of dB/ft, research projects have shown that attenuation does not vary exactly linearly with length. Therefore, these updated tables show attenuation for lengths as actually tested. For interpolation to various duct lengths and cross sections, using the duct liner attenuation spreadsheet (available as an extra feature for the ASHRAE Handbook Online version of this chapter) is recommended. Note that the total attenuated noise will never be below the flow-generated noise level in the duct, and, because of typical flows and flanking noise in practice, attenuation values are capped at 50 dB.
Rectangular Sheet Metal Duct Elbows. Table 22 displays insertion loss values for unlined and lined square elbows without turning vanes (Beranek 1960). For lined square elbows, duct lining must extend at least two duct widths w beyond the elbow. Table 22 applies only where the duct is lined before and after the elbow. Table 23 gives insertion loss values for unlined radiused elbows. Table 24 gives insertion loss values for unlined and lined square elbows with turning vanes. The quantity fw in Tables 22 to 24 is the midfrequency of the octave band times the width of the elbow (Figure 20) (Beranek 1960; Ver 1983b).
Nonmetallic Insulated Flexible Ducts. Nonmetallic insulated flexible ducts can significantly reduce airborne noise. Insertion loss values for specified duct diameters and lengths are given in Table 25 and in Appendix D of ARI Standard 885. Recommended duct lengths are normally 3 to 6 ft. Take care to keep flexible ducts straight; bends should have as long a radius as possible. Although an abrupt bend may provide some additional insertion loss, the noise associated with airflow in the bend may be unacceptably high. Because of potentially high breakout sound levels associated with flexible ducts, take care when using flexible ducts above sound-sensitive spaces.
Duct Branch Sound Power Division. When sound traveling in a duct encounters a junction, the sound power contained in the incident sound waves in the main feeder duct is distributed between the branches associated with the junction (Ver 1982, 1983b). This division of sound power is called branch sound power division. The corresponding attenuation of sound power transmitted down each branch of the junction is comprised of two components. The first is associated with reflection of the incident sound wave if the sum of the cross-sectional areas of individual branches ΣSBi differs from the cross-sectional area of the main feeder duct. The second and more dominant component is associated with energy division according to the ratio of the cross-sectional area of an individual branch SBi divided by ΣSBi. Values for the attenuation of sound power ΔLBi are given in Table 26.
Duct Silencers. Silencers, sometimes called sound attenuators, sound traps, or mufflers, are designed to reduce the noise transmitted from a source to a receiver. For HVAC applications, the most common silencers are duct silencers, installed on the intake and/or discharge side of a fan or air handler. Also, they may be used on the receiver side of other noise generators such as terminal boxes, valves, dampers, etc.
Duct silencers are available in varying shapes and sizes to fit project ductwork. Generally, a duct silencer’s outer appearance is similar to a piece of ductwork. It consists of a sheet metal casing with length commonly ranging from 3 to 10 ft. Common shapes include rectangular, round, elbow, tee, and transitional. Figure 21 shows some duct silencer configurations.
All silencers can be rated for (1) insertion loss, (2) dynamic insertion loss, (3) pressure drop, and (4) self-generated noise in accordance with ASTM Standard E477 test standards. As such, the performance is under rather ideal conditions as seen in Figure 22.
Insertion loss is the reduction in the sound power level at the receiver after the silencer is installed (“inserted”) in the system. Insertion loss is measured as a function of frequency and commonly published in full octave bands ranging from 63 to 8000 Hz.
Dynamic insertion loss is insertion loss with given airflow direction and velocity. A silencer’s insertion loss varies depending on whether sound is traveling in the same or opposite direction as airflow. Silencer performance changes with absolute duct velocity. However, airflow velocity generally does not significantly affect silencers giving a pressure drop of 0.35 in. of water or less, including system effects.
Pressure drop is measured across the silencer at a given velocity. Good flow conditions are required for accurate measurements at both the inlet and discharge of the silencer. The measuring points are usually 2.5 to 5 duct diameters upstream and downstream of the silencer to avoid turbulent flow areas near the silencer and to allow for any static pressure regain. For nonideal installations, with duct elbows or transitions closer than 2.5 to 5 duct diameters, the total system effect will be larger than the laboratory test data.
Airflow-generated self noise is the sound power generated on the receiving side by the silencer when quiet air flows through it. This represents the noise floor, or the lowest level achievable regardless of high insertion loss values. A silencer’s self-generated noise is a function of frequency and internal geometry, and is referenced to specific velocities and airflow direction (forward or reverse). The airflow-generated sound power of the silencer is logarithmically proportional to silencer cross-sectional area. Self noise generally does not vary with silencer length.
There are three types of HVAC duct silencers: dissipative (with acoustic media), fiber-free reactive (no media), and active.
Dissipative Silencers. Dissipative silencers use sound-absorptive media such as fiberglass as the primary means of attenuating sound; mineral wool can be used in high-temperature applications but may contain too much contamination (“shot”) for commercial HVAC applications. Usually, the absorptive medium is covered by perforated metal to protect it from erosion by airflow. If internal silencer velocities are high (faster than 4500 fpm), media erosion may be further reduced by a layer of material such as fiberglass cloth or polymer film liner placed between the absorptive media and the perforated metal. Dissipative silencers may be supplied as hospital-grade or as film-lined silencers that include special polymer film linings to prevent contamination of the airstream by acoustical media fibers and prevent particles from the airstream from getting into the media. These silencers are commonly used in hospitals, pharmaceutical facilities, cleanrooms, and other places where indoor air quality is of paramount concern. Consult manufacturers for construction and testing performance details.
Dissipative silencer performance is primarily a function of silencer length; airflow constriction; number, thickness, and shape of splitters or centerbodies; and type and density of absorptive media. The absorptive media allows dissipative silencers to provide significant insertion loss performance over a wide frequency range.
Insertion loss performance does not necessarily increase linearly with silencer length; for a given length, silencer designs can produce varying insertion loss and pressure drop data. Even at the same pressure drop and length, silencers can be configured to provide varying insertion loss performance across the frequency spectrum.
Reactive Silencers. Reactive silencers are constructed only of metal, both solid and perforated, with chambers of specially designed shapes and sizes behind the perforated metal that are tuned as resonators to react with and reduce sound power at certain frequencies. The outward appearance of reactive silencers is similar to that of their dissipative counterparts. However, because of tuning, insertion loss over a wide frequency range is more difficult to achieve. Longer lengths may be required to achieve similar insertion loss performance as dissipative silencers. Airflow generally increases the insertion loss of reactive silencers.
Figure 23 compares insertion loss of dissipative silencers, with and without protective film materials, against that of a reactive silencer for the same pressure drop.
Active Silencers. Active duct silencers, sometimes called noise canceling systems, produce inverse sound waves that cancel noise primarily at low frequencies. An input microphone measures noise in the duct and converts it to electrical signals, which are processed digitally to generate opposite, mirror-image sound signals of equal amplitude. A secondary noise source destructively interferes with the primary noise and cancels a significant portion of it. An error microphone measures residual sound beyond the silencer and provides feedback to adjust the computer model for improved performance.
Because components are mounted outside the airflow, there is no pressure loss or airflow-generated noise. Performance is limited, however, if excessive turbulence is detected by the microphones. Manufacturers recommend using active silencers where duct velocities are less than 1500 fpm and where duct configurations are conducive to smooth, evenly distributed airflow.
Active silencers have significant low-frequency insertion loss, and are self-regulating because, if fan noise levels increase, an active silencer can increase performance to compensate for the increased source noise. Mid- and high-frequency insertion loss is minimal, however, so if required, combinations of active (for low-frequency components) and passive (for mid- and high-frequency components) can be used to achieve insertion loss over a wide frequency range.
Test Standard. Data for dissipative and reactive silencers should be obtained from tests consistent with the procedures outlined in ASTM Standard E477. (This standard has not been verified for determining performance of active silencers.) Because insertion loss measurements use a substitution technique, reasonably precise insertion loss values can be achieved . Airflow-generated noise values can be obtained with similar accuracy. Round-robin tests conducted from 2015 to 2016 from five ASTM E477 participating laboratories have shown that the revised test method (2020 and later) will yield insertion loss and self-generated noise reproducibility standard deviations of less than 3 dB in all eight octave bands. (For normal distribution, uncertainty with a 95% confidence interval is about two standard deviations.)
Silencer Selection Issues. When selecting a duct silencer, consider the following:
-
Insertion loss required to achieve required room sound criteria
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Allowable pressure drop (if no specific requirement, then keep under 0.35 in. of water, including system effects; when system effects are unknown, keep under 0.20 in. of water, excluding system effects) at system duct velocity
-
Silencer location and available space
-
Amount of airflow-generated noise that can be tolerated
-
Indoor air quality concerns
-
Duct configuration
To determine the insertion loss required, analyze the duct system, summing noise-generating mechanisms and subtracting attenuation elements (not including the silencer). The silencer’s required insertion loss is the amount by which the estimated resultant sound pressure level in the space exceeds the room criteria for the space. The user should consider both the sound path through the ductwork and outlets as well as potential locations where sound may break out of the ductwork.
Allowable Pressure Drop Issues
Care should be taken in applying test data to actual project installations. Adverse aerodynamic system effects can significantly affect silencer performance. That is, if the silencer is located where less-than-ideal conditions exists on the inlet and/or the discharge of the silencer (3 to 5 duct diameters of straight duct), then the silencer’s effective pressure drop (PD) is increased (total silencer PD = silencer PD per ASTM Standard E477 + system effect losses). In some situations, the added system effect losses can be greater than the silencer’s pressure drop. Some manufacturers give guidelines for estimated pressure loss increases from varying silencer inlet and discharge configurations (Table 27); these should be considered as general guidelines. Substantial variations can occur depending on the type of silencer, its internal geometry, size of silencer, size of duct, airflow turbulence, etc. For example, an elbow fitting located immediately after a silencer prevents regain of the silencer’s leaving velocity pressure. In addition, local velocities in the elbow fitting are greater than the average duct velocity that produces higher overall static pressure losses.
Silencers should generally be located as close to the noise source as possible but far enough away to allow a uniform flow profile to develop. This helps contain noise at the source and limits potential points where unsilenced noise may break out. However, because turbulent airflow usually exists close to noise sources such as fans, valves, dampers, etc., the user should carefully evaluate aerodynamic system effects.
A straight silencer has a lower first cost than a transitional or elbow silencer. If space limitations prohibit effective use of a straight silencer, or if pressure drop (including system effects) is greater than the loss allowed, use of elbow or transitional silencers should be evaluated. Special fan inlet and discharge silencers, including cone and inlet box silencers, minimize aerodynamic system effects, and contain noise at the source.
Airflow-Generated Noise Issues
In most installations, airflow-generated noise is much less than, and does not contribute to, the reduced noise level on the receiver side of the silencer. This is especially true if the silencer is properly located close to the source. In general, airflow-generated noise should be evaluated if pressure drops exceed 0.35 in. of water (including system effects), the noise criterion is below NC/RC 35, or if the silencer is located very close to or in the occupied space.
To evaluate airflow-generated noise, sum the noise-generating mechanisms (from noise source to silencer) and subtract the attenuation elements (including silencer) in the order they occur to determine the resultant sound power level on the quiet side of the silencer. This resultant level must be summed logarithmically with the silencer’s generated noise (referenced to actual duct velocities, inlet and discharge configurations, and cross-sectional area). If the generated noise is more than 10 dB below the residual sound, then the silencer’s generated noise will have no effect on system noise levels.
Duct End Reflection Loss. When low-frequency sound waves encounter the end of a duct that is terminated into a large room, some of the incident sound energy is reflected back into the duct. Duct end reflection loss (ERL) values for a duct terminated flush with a wall are shown in Table 28.
To use Table 28 for a rectangular duct, calculate the effective duct diameter D by
where A is the cross-sectional area of the rectangular duct (ft2). For the frequency range and duct sizes of interest to HVAC designers, the duct ERL may be accurately computed using a simplified equation (Cunefare and Michaud 2008) of the form
where
| co = speed of sound (dimensionally consistent with D), ft/s |
| f = frequency, Hz |
| a1 and a2 = dimensionless constants determined as follows: |
|
Termination
|
a1
|
a2
|
|
Flush
|
0.7
|
2
|
|
Free space
|
1
|
2
|
ERL varies slightly with the frequency spectrum and measurement bandwidth. The constants apply to a pink spectrum in octave bands, which is representative of HVAC noise. ERLs greater than 20 dB are difficult to confirm in practice. Many test standards, such as AHRI Standard 260 for ducted equipment, limit ERL to 14 dB when reporting equipment sound power levels.
There are many limitations associated with the use of the ERL equation. Free-space conditions may not exist, except for duct terminations of 5D or more from a reflecting plane such as a wall or the floor. Such conditions may exist in test laboratories, but are not typical of HVAC duct applications.
Research (Cunefare and Michaud 2008) has changed our understanding of ERL for ducts terminated with commercial devices. Ducts that terminate with blade-type diffusers and grilles should be treated as having ERL for a flush termination. This includes terminal devices mounted in suspended acoustical ceiling systems. Slot diffusers characterized by high aspect ratios and mounted in a rigid baffle have frequency-independent ERL that may be determined by the analytical expression for the area ratio of the diffuser to duct cross-sectional area. Finally, using flexible duct upstream of diffusers, grilles and other terminal devices reduces ERL to near zero above 63 Hz for all terminal devices. This research suggests that a significant amount of the low-frequency sound that would normally be reflected back into the duct from an open termination is either transmitted through the flexible duct or radiated by the termination. There is however a frequency-independent ERL associated with the area change in the transition to the flexible duct.
Finally, ERL values are based on analytical assumptions and empirical data for long and straight duct sections. Many air distribution systems do not have long straight sections (greater than 3D) before they terminate into a room. Many duct sections between a main feed branch and a diffuser may be curved or short. The effects of these configurations on duct end reflection loss are not known. Table 28 can be used with reasonable accuracy for many diffuser configurations. However, use caution when a diffuser configuration differs from the conditions used to derive these ERL values.
Sound Radiation Through Duct Walls
Duct Rumble. Duct rumble is low-frequency sound generated by vibration of a flat duct surface. The vibration is caused when an HVAC fan and its connected ductwork act as a semiclosed, compressible-fluid pumping system; both acoustic and aerodynamic air pressure fluctuations at the fan are transmitted to other locations in the duct system. Rumbling occurs at the duct’s resonance frequencies (Ebbing et al. 1978), and duct rumble levels of 65 to 95 dB in the 16 to 100 Hz frequency range have been measured in occupied spaces. With belt-driven fans, the rumble sound level fluctuates above and below the mean dB level by 5 to 25 dB at a rate of 2 to 10 “beats” per second (Blazier 1993). The most common beat frequency occurs at the difference between the fan rpm and twice the belt frequency (belt rpm = fan sheave diameter × sheave rpm × π/belt length). As shown in Figure 24, duct rumble is dependent on the level of duct vibration. The very low resonant frequencies at which duct rumble occurs means that the sound wavelengths are very long (10 to 70 ft), and the rumble can exert sound energy over long distances. Lightweight architectural structures such as metal frame and drywall systems near a source of duct rumble can easily vibrate and rattle in sympathy to the rumble.
Case histories indicate that duct vibration is much more prevalent when there is a dramatic change in airflow direction near the fan, and at large, flat, unreinforced duct surfaces (usually greater than 48 in. in any dimension) near the fan. Problems can occur with dimensions as small as 18 in. if high noise levels are present. Figure 25 shows duct configurations near a centrifugal fan. Good to optimum designs of fan discharge transitions minimize potential for duct rumble; however, this may not completely eliminate the potential for duct rumble, which also depends heavily on flow turbulence at the fan wheel, duct stiffness, air velocity in the duct, and duct resonant characteristics.
Duct liner, sound attenuators, and duct lagging with mass-loaded vinyl over fiberglass do not reduce duct rumble. One approach to eliminate or reduce rumble is to alter the fan or motor speed, which changes the frequency of air pressure fluctuations so that they differ from duct wall resonance frequencies. Another method is to apply rigid materials, such as duct reinforcements and drywall, directly to the duct wall to change the wall resonance frequencies (Figure 26). Noise reductions of 5 to 11 dB in the 31.5 and 63 Hz octave frequency bands are possible using this treatment.
Mass-loaded materials applied in combination with absorptive materials do not alleviate duct rumble noise unless both materials are completely decoupled from the duct by a large air separation (preferably greater than 6 in.). The mass-loaded material should have a surface density greater than 4 lb/ft2. An example of this type of construction, using two layers of drywall, is shown in Figure 27. Because the treatment is decoupled from the duct wall, it provides the greatest noise reduction. Mass-loaded/absorptive material directly attached to a round duct can be an effective noise control treatment for high-frequency noise above the duct rumble frequency range of 16 to 100 Hz. In addition, the stiffness of round ductwork prevents flexure of the duct wall. Where space allows, round ductwork is an effective method to prevent duct rumble (Harold 1986). However, unless round ducts are used throughout the primary duct system, duct rumble can be still generated at a remote point where round duct is converted to rectangular or flat oval.
Round ducts can have a resonant ring resonance frequency, which depends on duct material and diameter. The ring frequency is a resonance frequency that occurs where the circumference of the duct is equal to the wavelength of the bending waves in the duct wall. On rare occasions, loud in-duct noise, such as blade-pass frequency noise from a centrifugal or axial fan, can excite this resonance. In all cases, this resonance causes an increase in radiated noise in the frequency region close to the ring frequency.
Sound Breakout and Break-In from Ducts. Breakout is sound associated with fan or airflow noise inside a duct that radiates through duct walls into the surrounding area (Figure 28). Breakout can be a problem if it is not adequately attenuated before the duct runs over an occupied space (Cummings 1983; Lilly 1987). Sound that is transmitted into a duct from the surrounding area is called break-in (Figure 29). The main factors affecting breakout and break-in sound transmission are the transmission loss of the duct, total exposed surface area of the duct, and presence of any acoustical duct liner.
Transmission loss (TL) is the ratio of sound power incident on a partition to the sound power transmitted through a partition. This ratio varies with acoustic frequency as well as duct shape, size, and wall thickness. Higher values of transmission loss result in less noise passing through the duct wall.
Breakout sound transmission from ducts is the sound transmitted through a duct wall and then radiated from the exterior surface of the duct wall. Its sound power level is given by
where
| Lw(out) =sound power level of sound radiated from outer surface of duct walls, dB |
| Lw(in) = sound power level of sound inside duct, dB |
| S = surface area of outer sound-radiating surface of duct, in2 |
| A = cross-section area of inside of duct, in2 |
| TLout = normalized duct breakout transmission loss (independent of S and A), dB |
Equation (13) is a simplified expression that assumes that the sound power level inside the duct does not decrease with distance over the length of the duct. In fact, for very long ducts (when S >> A), the radiated sound power level Lw(out) could become greater than the sound power level inside the duct, which would violate the conservation of energy principle. A more accurate expression for breakout is presented in Equation (20).
Values of TLout for rectangular ducts are given in Table 29, for round ducts in Table 30, and for flat oval ducts in Table 31 (Cummings 1983, 1985; Lilly 1987).
Equations for S and A for rectangular ducts are
where
| a =larger duct cross-section dimension, in. |
| b =smaller duct cross-section dimension, in. |
| L =length of duct sound-radiating surface, ft |
Equations for S and A for round ducts are
where
| d =duct diameter, in. |
| L =length of duct sound-radiating surface, ft |
For flat oval ducts,
where
| a= length of major axis, in. |
| b =length of minor axis, in. |
| L =length of duct sound-radiating surface, ft |
Equation (13) assumes no decrease in the internal sound power level with distance along the length of the duct. Thus, it is valid only for relatively short lengths of unlined duct. For long ducts or ducts that have internal acoustic lining, one approach is to divide the duct into sections, each of which is short enough to be modeled as a section of duct with constant internal sound power level over the length of each section. The recommended maximum length of each section is the length that would result in a 1 dB reduction in the internal sound power level at the frequency of interest. Alternatively, the total sound power radiated from any duct of any length (including an internally lined duct) can be calculated in a single step with a modified version of Equation (13) (Lilly 1987):
where S* is the effective surface area of the duct. S* = PL*, where P = duct perimeter, and L* = effective length. The effective length L* is calculated as
where
where α = duct attenuation rate, dB/ft (see Tables 16 to 21). For lined rectangular ducts, Tables 17 and 18 do not have data at 63 Hz. For rough approximations, use Table 16 values.
In most rooms where the listener is close to the duct, an estimate of the breakout sound pressure level can be obtained from
where
| Lp = sound pressure level at a specified point in the space, dB |
| Lw(out) = sound power level of sound radiated from outer surface of duct walls, given by Equation (13) or Equation (20), dB |
| r = distance between duct and position for which Lp is calculated, ft |
| L = length of the duct sound-radiating surface, ft |
Note that Equation (23) gives sound pressure from a duct that is in a wide-open ceiling plenum space. If the duct is in a tight space between floor slab and ceiling, it may be up to 6 dB louder.
Example 4..
A 24 in. by 24 in. by 25 ft long unlined rectangular supply duct is constructed of 22 ga sheet metal. Given the following sound power levels in the duct, what are the breakout sound pressure levels 5 ft from the surface of the duct?
Solution: Using Equations (13) and (23),
Using Equations (21) to (23),
Example 6..
Repeat Example 5 using 24 in. diameter spiral round duct, with 24 ga, 25 ft long with 1 in. thick acoustical duct lining.
Solution: Using Equations (21) and (23),
Using Equations (21) to (23) yields
Using round duct eliminates the low-frequency rumble present with rectangular ducts but introduces some mid- and high-frequency noise that can be reduced by adding duct liner as shown.
When sound is not transmitted through the wall of a round duct, it propagates down the duct and may become a problem at another point in the duct system. Round flexible and rigid fiberglass ducts do not have high transmission loss properties because they lack the mass or stiffness associated with round sheet metal ducts.
Whenever duct sound breakout is a concern, fiberglass or flexible round duct should not be used; these ducts have little or no transmission loss, and are essentially transparent to sound.
Break-in sound transmission into ducts is sound transmitted into a duct through the duct walls from the space outside the duct. Its sound power level is given by
where
| Lw(in) = sound power level of sound transmitted into duct and then transmitted upstream or downstream of point of entry, dB |
| Lw(out) = sound power level of sound incident on outside of duct walls, dB |
| TLin = duct break-in transmission loss, dB |
Values for TLin for rectangular ducts are given in Table 32, for round ducts in Table 33, and for flat oval ducts in Table 34 (Cummings 1983, 1985).