Document pBvnbLrb3XkBEK2nrVK3Z0np6

208 CHAPTER 14 1965 Guide And; Data Book A particularly severe cross transmission problem- exists:in prisons, where ducts could be used for communication between cells. In this case, no credit should be taken for the ratio Sj/8*, as the inmates w21 move close to the outlets to talk and to listen. r.-` T.Iine aO'fah Fiction and dischargeplenums. This.iaa very x-onfimii-al nr to get considerable sound absorption in systems _______ 0_m_ejn dee' ments. 2. lin* ducts with sound absorbing material which also serves as thgrrr.nl insulation. Note: Duet dimensions must be increased to lYimpmuito for area lost due to lining. 3. Locate lined duct sections dose to elbows to take advantage of the interaction of sound absorption and sound reflection. STEP 4--DESIGN OF ACOUSTIC TREATMENT - 4. Introduce large amounts of sound absorbing materials into FOR DUCT SYSTEMS a hrnHjH length of duct as special purpose duct silencers. . , 5. ingtAll prefabricated attenuators which contain specially Selection of the Absorptive Material shaped perforated baffles filled with sound absorbing materiaL When a sound wave impinges on the surface of a porous material the air within the small pores of the material is set' into a vibrating motion. The flow resistance within the pores., Usually, several arrangements are'combined, in order to achieve-the required amount of sound attenuation calculated i Step 3. of the matai-ial converts a portion of the sound energy to heat. The decimal fraction representing the absorbed portion of the Attenuation.of. Lined.Plenums incident sound wave is called the absorption coefficient. Con A sound absorption plenum on the fan discharge, .aa shown siderable absorption may also result, particularly in the low-' "in fig. 17, will often prove the most economical arrangement. frequency range, from the flexural vibrations of duct, walls.; - Based on both experiment and .ray aooustics theory, the In the paWtinn and application of the absorptive material,1. -. followingapproximate expression baa been derived for acoustic . the following points should be considered: plenum attenuation. ' 1. For the absorption of the low-frequencies below 500 epe the-. material be 2 to 12 in. thick. Thin materials, particularly when mounted on hard solid surfaces, will absorb only the high,, frequencies. 2. It him been shown1* that increased attenuation at frequen-..;. des below 700 cpfl may be realised by using a perforated facing in Attenuation (db) 10 logt* I"----- ---------------------- 1 inhere ;(16) which the area of the perforations is surface area. Such fxing*, however, from 3 to 10 decrease the percent of the-t sound absorp " tion at higher frequencies. 3, Any air space behind the material has considerable effect (see Fig. 16). Absorption coefficients should be based-on the par*, titular mounting method intended. a '< absorption coefficieilt of the hning, dimengioTilwn- S4 -- plenum.exit arep, square feet. S* plenum wall area, square feet. d -- distance between entrance and'exit, feet. (See Fig-17.) 0 _ the ngl of incidence at the exit,' ue., 'the angle which Ronqd ^boorbing materials suitable for use in air ducts are available in the form of blankets, semi-rigid boards, and loose ' the direction d degrees: with the normal to the exit opening, fill. Specifications and absorption coefficients for most ma : The ratio represented.by the bracketed term in Equation terials wrn be obtained from the Acoustical Materials Associa-' . : 16 is evaluated by substituting valu6 for the symbols. From tion." The following additional properties should be evaluated in the Bfthytion of acoustical materials: (1) adequate strength to avoid breakage and crumbling, (2) fire resistance and com pliance with national and local code requirements, (3) particles . pbnifld not fray off at the higher air velocities, and (4) freedom from odor when either dry or wet. There are several ways in which Bound absorbing material be arranged in a duct system: 1 this ratio in lower scale of Fig. 1, proceed vertically to the ' intersection with the diagonal and then read the attenuation of the plenum in the left vertical scale. For frequencies sufficiently high so that the wave length is loo than the plenum dimondnnftl Equation 16 is accurate within a few decibels. At lower frequencies. Equation 16 is conservative, and1 the actual attenuation exceeds the calcu lated value -by 5 to 10 db, due to sound reflection by the plenum. ' Attenuation of lined Ducts .. i? Duct iiTMng* may be dawignad for the dual, function of pn> viding sound absorption and thermal insolation. Thicknesses between $ and 2 in', are usually adequate'for thermal insula1 tidn. The Bound absorption of such' relatively thin' lininga however, is limited, especially at low frequencies (see Fig.' 16). The exact mathematics of sound attenuation in lined ducts1? a very yuppie***!-' Empirical formulas,''such' as Equation 17, can be used for design calculations within certain limits. fig. 17.... Diagram of Sound Absorbing Plenum Sound: Control ' .- 209 ; Table 19.... Values of (a)1-?, for Equation 17 AbtotpBeo CetBidvda AyA 0.10 0.04 0.15 0.07 0.20 0.11 0.25 0.14 0.30 0.19 0.35 0.23 0.40 0.28 0.45 0.33 0.5 0.38 0.5 0.49 0.7 0.61 O.S 0.73 0.9 1.0 0.88 | 1.0 .. This equation gives the attenuation due to the lining which then be added to the attenuation of the unlined duct (Table 13). p Attenuation (db) = 12.61 -- a1-4 (17) ichor l " length of lined duct, feet. P_ - perimeter of duct inside the tilling,,inches. S4 * cross eoctionai area of duct, inside the lining, square . . inches. . a .absorption coefficient of lining (a function of frequency). - The' value of edA can.be found from Table 19 for various values of o. The limitation* of Equation 17 art: 1. ,Smallest duct dimension should not exceed 18 in., and not be less than 6 in. 2. Ratio'of duct width to height should not exceed 2/1. 3. The absorption coefficient a should be representative for the entire octave band. A coefficient at 500 cps, for instant, is usually too high for the lower port of the 300-600 cps band. The average of the coefficients at 250 and 500 cps should De used for conserve-; tive results,' if coefficients on an octave band baas are not avail able. . .. 1, 4. Air flow velocities should not exceed 4000 fpm.*1-0 5. Equation 17 does not allow for line-of-eight propagation.of sound which limits high frequency attenuation: In a straight .12 . in. duct, for instance, the attenuation above 4800 cps will be only about 10 db for any lining length over 3 ft.* The attenuation in' the next lower octave band (2400-4800 cps). will be about mid way between 10 db and the value calculated from Equation 17. The frequency above which the 10 db limit applies is inversely proportional to the shortest dimension of the duct. 1. Only the lining on the tides of the duct is involved in thin interaction. .... ' 2. .This attenuation is the effect of the elbow and'should be' added to the attenuation which would be calculated for ihe- lengths of lined duct which are involved. (Equation 17) 3. For best results, the sides of the duct should be lined, both ' before and after', the elbow, for a length, of at least two duct ; -widths. This length is' based bn a lining thickness of at i*t 10 percent of the duct width. 4. If the duct is lined only before or after the elbow, there is still some gain In attenuation, as shown in Rows B and C of Table 15. 1 5. The attenuation which can be credited to the ductliriing'ia; the difference between the total attenuation in Rows B, C,"or D' af Table 15, and the attenuation of the unlined elbow.(Rbw'A).. '6. The listed increases in elbow attenuation are obtained only' with .duct linings, not witheound traps or lined plenums. * ' ' ' Example 6: Calculate the sound attenuation obtained by lining the branch duct shown in Fig. 15, for a length of 10 ft, with 1 in. - sound absorbing blanket insulation. Asume that'the. duct'sue7 can be increased to 14 X 20 in. to permit the same inside dimen sions of 12 X 18 in. ' Solution:. The `perimeter of theduct (inside the lining) is; 12 + 12 + 18 + 18 TM 60 in. The duct area' (made this lining): is 12 X 18 - 216 sq in. - 1' .."""BA, Values of a for the octave frequency bands are found frbmFig., 16 and entered in line 1 of Table 20. Values of * are found from' Table 19 andentered in line 2. .* * From Equation 17, with P 60 in.. 84 - 216 sq in.,,f - 10 ft, and using the values of a1-4 from Line 2 of Table 20, the at-' tarnation due to the lining is found and entered in Line 3. Hanking Transmission Some recent test data for 12 X 12 in. ducts are shown in Fig. 18. In the first 5`ft of the-lining, the sound level in any band in the 850-2400 cycle range was found to drop much faster than calculated from Equation 17. These tests confirm Morse's prediction that lined ducts should have-a rather steep attenuation peak when the duct width is between one and two times the wave length of the sound. Fig. 18 also shows (hat, after the first five feet,:attenuation rates were much lower than those calculated from Equation 17. This is due to the flanking transmission of sound telegraphed along the vibrat ing walls of the sheet metal duct!.'This flanking was the limit ing factor in any frequency band in which the lining attenua tion exceeded 2 db per foot. Practical formulae for calculating these two opposing effects not exist-at this time. It is therefore recommended that Equation 17 be used to estimate the available lining attenua tion arid that flexible vibration breaks be installed for every 25 db of lining attenuation required in any frequency band. Interaction of Duct Lining and Duct Elbows If there is an elbow in a lined duct, the line-of-cdght propa gation of sound rays is interrupted.' This results in a consider ably improved sound attenuation' at frequencies for which the wave length of the sound is shorter than the duct width, (see Fig. 14 and-Table 15)..It should be noted that: fig. 18.... Comparison of Measured and Calculated Attenuation-in 12 in. X-12 in. Duct. Lined with .1 in.:.Thick'i J tb Density Blanket