Silencers Practical silencers are complex devices, which operate reducing pressure oscillations before they reach the atmosphere, producing the minimum possible loss of engine performance. However they are composed of many simple elements based on only two basic principles: absorption and/or reflection of sound waves. The most common simple elements of silencers are: a) sound absorbing element: a chamber filled with sound absorbing material, through which a perforated exhaust pipe passes. Then part of the acoustic energy, carried by the flowing waves, is absorbed and dissipated as heat by the elastic material. b) expansion box: is an enlargement of the exhaust pipe, which modifies the system impedance, in order to mismatch the box inlet duct from the outlet pipe. The result is that only a part of the acoustic power, carried by the incident pressure wave, is transmitted toward the exhaust system exit. c) side resonator: is a separate closed chamber communicating with the main exhaust pipe through holes or short side branches. Then intense attenuations of the pressure levels are obtained for noise components with the same frequency of the natural resonance of the lateral chamber. d) perforated element: is formed by ducts, with many small holes on their lateral surface, which go through cavities. When the pressure inside the perforated duct is larger than in the surrounding volume, exhaust gases pass from the duct to the cavity and vice versa, when the pressure difference is reversed. Since flows through the holes dissipate acoustic energy, this element produces reduction of sound oscillations both by viscous dissipation and by ware reflection. In the first element the absorption and dissipation of the sound energy is clearly dominant, while the other three are called reactive silencers since they use the mechanism of reflection and transmission of the acoustic waves at geometrical discontinuities of the systems, to reflect back most of the incident sound power and so to control the part transmitted downstream, toward the exit. Transmission and Insertion Loss The insertion of a silencer in an intake or exhaust system clearly involves a modification of the system itself. Actually the inserted muffler produces some reduction of sound pressure fluctuations, but on the other hand it changes the whole wave pattern in the system. To take into account this system reaction, the designer con follow a two-stage approach. At first, on the basis of the noise spectrum measured or predicted for the un-silenced engine, a silencer theoretically able to produce the sedated action, is selected. Then the silencer design can be modified to correct the effects of its insertion in the system. Therefore it is important to introduce the definition of insolated silencer as that one excited by a sound source, which is not affected by reflections from the muffler and connected (at the other end) to a completely absorbing outlet, so that no reflection return to it. Transmission loss, for a given frequency, is hence defined the reduction (in db) of a transmitted acoustic power Pt, reported to the incident acoustic power Pi: If the pressure fluctuation are not too large (relative to their mean value), their acoustic power levels are reduced by a fraction independent of the incident level. The performance parameter TL is therefore a function only of the frequency and of the silencer geometry, which is so fully characterized. The parameter TL can be easily predicted by computer models, since it does not involve the knowledge of the source impedance and the calculations of Pi and Pt are not influenced by reflection. However, the
measurement of the two acoustic powers Pi and Pt is difficult since both fluid pressure and velocity have to be measured. When a silencer is inserted into a complex plant, it reacts upon the system modifying its characteristics. In the same time reflections from other elements react upon the silencer. Therefore the reduction of intensity level, at any given frequency, produced by inserting the muffler in the system, is not equal to its TL at that frequency. To take into account this different results, another performance parameter is introduced, called Insertion Loss. This is defined as difference between the sound intensity, measured in a given point of the space, before the insertion of the silencer pe0 and that measured after its insertion pes. The insertion loss clearly represents the true performance of the muffler, since it measures the drop in the radiated power level, consequent to its insertion in the system. But it requires prior knowledge or measurement of the internal impedance of the source, which is an important complexity, when it is necessary to predict its value. Hence, on the contrary of the parameter TL, the insertion loss is difficult to be computed, since it requires a model able to predict the source reactions to the system changes, but IL is easy to be measured by means of a simple microphone. TL of an Expansion Box Expansion box It is an enlargement in series with the exhaust pipe, whose main geometric parameters are: its length L and the ratio between the silencer cross section Ss and the pipe cross section Sp. As the frequency of the incident sound wave varies, the gas mass included in the box (axial entry/exit) resonates whenever an integral number of half wave lengths fits the box length L. Since the system is open at box ends, the basic theory states that its resonance frequency are the fundamental f0: together with its integral multiples (f0, 2 f0, 3 f0,..., n f0). Since at these frequency the gases mass resonates, sound pressure waves are integrally transferred from the inlet to the outlet box duct. Thus for the resonant frequencies (called pass bands) the expansion box cannot reduce the sound pressure level and its TL is zero. As the incident frequency increase their difference from resonances, the reaction of the silencer grow, reflecting back to the source most of the sound energy. Then the maximum of TL is reached at the anti-resonances frequencies, that are the ones in the middle of two consecutive resonances. Moreover, increasing the section Ss/Sp, the TL curves grow up since larger is the muffler reaction on incident pressure waves. The cross section shape of the box does not influence the basic TL curve, therefore the elliptical cross section are often used, to reduce the vertical dimension of the silencer. To obtain an higher TL, two or more boxes of different length can be placed in series. Moreover, if each length is chosen in a proper way, an excellent TL curve can be achieved over a wide frequency range. A good TL is also given by two equal boxes in series, connected by a pipe of the same length, which removes the common pass band f0.
TL of a Side-Resonator Side-resonator element It is a box of volume Vs, connected to the main pipe through an opening, which can assume different configurations: one or more circular holes, a pipe or neck, a rectangular slit parallel to the pipe axis, or a peripheral slit along its circumference till to obtain two facing pipes, etc... The opening conductivity k has the dimension of length and is a function of its geometry only, provided its dimensions are small compared with the wave-length of sound considered. For a circular hole of radius R in a pipe of thin wall, k = 2*R can be assumed, while for a neck of length L and radius R, k value is: which takes the previous value for L = 0. Side-resonator is also called Helmholtz resonator and its unique natural resonance frequency is: When the side volume is in resonance, it absorbs the frequency f0 from the pressure oscillations of the gas flowing in the main pipe, with a TL very high in a narrow band around f0. For frequencies different from f0, TL is controlled by the parameter sqrt(kvs)/(2*sp) and for high values of this ratio, a good TL is obtained for a wide frequency range around f0. A good TL curve can be achieved over a wide frequency range, placing in series two or more side-resonator of different natural frequencies, obtained changing the side volume Vs, or the conductivity k of the connection with the cavity imposing more passages in the same volume with pipes of different conductivity. TL of a Side Column Resonator Side column resonator It is a pipe parallel with the main duct, whose cross section is comparable. The gas inside the pipe resonates whenever a pressure peak is formed at the closed end and the pressure is zero at the open end. Thus its resonance frequencies are the fundamental f0: together with its odd multiples (f0, 3 f0, 5 f0,...). Since at these frequency the gas mass resonates, the side volume should absorb the resonance frequency from the pressure oscillations of the gas flowing in the main pipe, with a TL very high (theoretically infinite) in a narrow band around them. Only the first few resonance are effective and TL is good just in a narrow band around f0. However the side column resonator often offers a helpful solution, when a noisy low frequency must be cut. In this case, a quite long column is needed. It is possible to limit the column axial extension, using more concentric pipes of constant annular cross sections, connected to each other at their endings. TL of Absorbing Silencer Absorbing element It is obtained filling the chamber of a perforated element with sound absorbing material, which dissipates as viscous drag and heat the acoustic energy, especially of the higher frequency sound waves. The attenuation action is proportional to the contact area between gases and absorbing material, to its
thickness and to the filling density, strongly depending on sound frequency and on elastic characteristics of the material. The specific TL of a typical absorption silencer with axial extension shows that: 1) the sound attenuation is small at low frequency, but it rapidly increases with frequency. 2) at low frequencies, TL is small and strongly influenced by the absorption coefficient of the material, which in turn depends on its thickness around the pipe, on elastic characteristic and on density of the material; 3) at high frequencies TL becomes quite high and nearly independent on the elastic characteristics of the absorbing material. Absorbing silencers present the advantages of a definitely larger TL at high frequencies and lower pressure drops, but they are more expensive and they see their characteristics worsen with time, since the absorbing material deteriorates because of pressure oscillations, acid condensations and gradual exportation by flowing gases. TL of Perforated Silencer Perforated silencers Perforates consists of one or more perforated ducts surrounded by a cylindrical cavity. When pressure waves propagates through the gases moving inside the ducts, the continuously varying pressure difference across the pipe holes forces the gas to flow through the holes, dissipating acoustic energy by viscous drag. In the same time, the gases inside the cavity reacts to pressure oscillations, travelling along the ducts, with continuous compression and expansions, so reducing the pressure waves amplitude. The results is that perforates produce reduction of sound oscillations both by viscous dissipation (flows through holes) and by wave reflection (reaction of cavity). Usually the holes are uniformly distributed along the lateral surface of the duct and they are characterized by a geometric parameter, called porosity σ, defined as the ratio between the total flow area offered by the holes and the lateral surface of the relative cylinder part. If on the surface of a pipe of diameter dp there is a series of nh holes of diameter dh with an axial spacing p, the porosity is: 1) For small values of σ TL is low, since the gas flowing in the main pipe does not feel much either the viscous dissipation through the holes, nor the reaction of the surrounding cavity. Actually, when σ goes to zero, the perforated pipe becomes a simple duct without any section variation, thus unable of sound attenuation. 2) For proper intermediate values of σ to the cavity performance as expansion box is added another con as side resonator with a narrow frequency band of high TL, which is usually increased over the hole frequency range. 3) For large values of σ the perforated TL curve progressively approaches the TL curve of the corresponding
expansion box, since the presence of the perforated duct becomes un-influential. Higher TL can be obtained increasing the number of chambers and/or the number of perforated ducts, so that the mail flow crosses the same cavity many times. Moreover a large acoustic reduction is reached closing the perforated ducts at their ending, so forcing the whole main flow go through the holes. However, in this case, the large value of TL, due to the increase of the friction drag through the holes, is paid with an high pressure drop. If TL curves of an expansion box, an absorbing element and a simple perforated silencer, all with cavities of the same geometry, it is evident that the perforated performance is in between of that one of the expansion box and on the absorbing element, with a larger TL of the last one at low frequencies, but a quite smaller TL at high frequencies. The better performance at low frequencies, together with lower costs and longer lives justifies actual trend to replace absorbing elements with perforated ones, unless a strong reduction of high frequency tones is required.