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Natural Science Forum / Physics / Acoustics / February 2005Expansion Chamber
Hey all, I'm helping someone with an industrial dust collector. The collector is generating a 40 Hz tone that we're trying to eliminate. We've traced the tone to the exhaust duct (which kind of makes sense since the duct is 31 feet long). Since this is a narrow tone, it looks like the insertion of an expansion chamber may help here. I have a set of application notes that says the cross-sectional area of the chamber should be 4 to 6 times the area of the duct, and the length should be 1/4 the wavelength of the lowest frequency of concern (~7.5 ft in this case). Other than adding absorption, is that all there is to it? This sounds way to easy. I will try to look up some of the relevant ASHRAE standards, but am I missing something? Herb  SignatureHerb Singleton usenet3@ross-specrtrum.com Sound & Vibration Measurements http://www.cross-spectrum.com > I'm helping someone with an industrial dust collector. The collector is > generating a 40 Hz tone that we're trying to eliminate. We've traced the [quoted text clipped - 10 lines] > way to easy. I will try to look up some of the relevant ASHRAE > standards, but am I missing something? The primary mode of cancellation here is the impedance mismatch so the absorption is relatively unimportant for the fundamental tone. The bigger the expansion ratio the better the attenuation. There will be a tradeoff between the number of mufflers and their length, I am not sure that a single quarter wave box is optimal. Position of the muffler along the length of the pipe is important. You may find that a Helmholtz resonator (or less likely a quarter wave sidepipe) is a more efficient attenuator at just one frequency. But basically, yes, expansion chambers are pretty straightforward. Cheers Greg Locock Thanks Ang & Greg, I'll go with the Helmholtz resonator method, since it seems as straightforward as the expansion chamber, and I have a better idea of the underlying mathematic principles. Herb SignatureHerb Singleton usenet3@ross-specrtrum.com Sound & Vibration Measurements http://www.cross-spectrum.com > I'm helping someone with an industrial dust collector. The collector is > generating a 40 Hz tone that we're trying to eliminate. We've traced the [quoted text clipped - 6 lines] > the duct, and the length should be 1/4 the wavelength of the lowest > frequency of concern (~7.5 ft in this case). A Helmholtz "Branch Resonator" may work for you as it did for me years ago. That amounted to a stiff 4'cube box (64 ft^3 or any volume shape of the same value) with two 7" round holes cut into the duct, with the box attached directly to it (actually, it wa a stiffened 4' thick sheet metal cubic box with stiffeners added, assembled around a 21" diameter chimney pipe). See Helmholtz resonator formulae for applying to you job. Mine was a 40 Hz problem also. This acts as a notch attenuator at and near (few Hz) 40 Hz. Angelo Campanella > A Helmholtz "Branch Resonator" may work for you as it did for me years > ago. That amounted to a stiff 4'cube box (64 ft^3 or any volume shape of [quoted text clipped - 4 lines] > Mine was a 40 Hz problem also. This acts as a notch attenuator at and > near (few Hz) 40 Hz. Angelo, Are these values approximate? Or was the gas not air or not at STP? When I stick your values into the appropriate Helmholtz equation (specifically w_o = c * (S/L'V)^0.5 where c=343m/s, S=area, L' equals effective length for circular hole in a thin wall, and V is the volume), I get a resonance frequency of 24 Hz. Equation from Kinsler & Frey, 4th edition. Herb SignatureHerb Singleton usenet3@ross-specrtrum.com Sound & Vibration Measurements http://www.cross-spectrum.com > Are these values approximate? Or was the gas not air or not at STP? When > I stick your values into the appropriate Helmholtz equation > (specifically w_o = c * (S/L'V)^0.5 where c=343m/s, S=area, L' equals > effective length for circular hole in a thin wall, and V is the volume), > I get a resonance frequency of 24 Hz. Touche`! It was the exhaust of a large gas furnace. Probably 900F?... Angelo Campanella >> Are these values approximate? Or was the gas not air or not at STP? >> When I stick your values into the appropriate Helmholtz equation [quoted text clipped - 4 lines] > Touche`! It was the exhaust of a large gas furnace. Probably > 900F?... You need the end correction as well, Your formula doesn't directly include it. I /think/ the effective length of the resistive channel L' is L+0.6*D Cheers Greg Locock > You need the end correction as well, Your formula doesn't directly include > it. I /think/ the effective length of the resistive channel L' is L+0.6*D It was the "royal" L' :) K&F actually has L'=L+0.6*r Herb SignatureHerb Singleton usenet3@ross-specrtrum.com Sound & Vibration Measurements http://www.cross-spectrum.com >> You need the end correction as well, Your formula doesn't directly >> include it. I /think/ the effective length of the resistive channel [quoted text clipped - 3 lines] > > K&F actually has L'=L+0.6*r Hey, what's a factor of 2? Sounds like you've got everything you need now. Good luck. Cheers Greg > Hey, what's a factor of 2? It depends - are we talking about my billings? ;) > Sounds like you've got everything you need now. > Good luck. Thanks for the help. Herb SignatureHerb Singleton usenet3@ross-specrtrum.com Sound & Vibration Measurements http://www.cross-spectrum.com |
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