Optimum Sound Attenuation in Flow Ducts Based on the "Exact" Cremer Impedance

Modal filters for mitigation of in-duct sound

“…As a consequence, strongly reflective (and hence low transmissive) systems have high Transmission Losses, even though only little power is actually absorbed inside the silencer. Kabral and Åbom [7] defined a Dissipation Loss, which subtracts reflections from the incident acoustic power in order to correct the Transmission Loss and to show the actual power dissipation inside the silencer. The normalized incident acoustic power is then defined as * + = 1 − |< 8 ' | and the emitted power is* , = |7 89 | ' .…”

“…In this work, silencer designs are presented that are specific for single modes and which can be used in a cascade to realize good dissipation in applications where multi-modal sound is propagating. As this design has not been investigated in the literature, the focus of this paper is on the properties of the so called 'modal filter' which is introduced in more detail in section 2 E. For the plane wave mode, a new type of dissipative silencer proposed by Kabral et al [7,10] with cavity structures covered by perforated plates is suggested, using optimized wall impedance (Cremer wall impedance) for a certain target frequency (section 2 D).…”

“…Kabral and Åbom used an expansion chamber muffler with a micro-perforated cover tube to design silencers with optimal wall impedance (Cremer impedance, [8]) that reduces tonal noise of compressors in turbochargers [7], [10]. In their design strategy, cavity structures are fitted with a micro-perforated cover sheet, so that the wall impedance equals the Cremer value at one target frequency.…”

“…The mitigation strategies are based on micro-perforated plates (MPPs) placed along the propagation path of the sound waves creating surfaces with acoustic resistance. The MPPs are used in two configurations; the first configuration aims at damping the plane wave mode, based on the work of Kabral and Åbom [7], and is designed to realize the so called Cremer impedance at a given target frequency. By adopting a wall impedance for optimal attenuation which was firstly described by Cremer [8] for rectangular ducts and later derived for circular ducts by Tester [9], extremely high damping can be achieved with very compact silencers as shown in Ref.…”

“…At a frequency where the filter impedance matches the Cremer impedance, optimal damping is guaranteed for the plane wave. The drawback, however, is that the design can only realize the optimum Cremer impedance at one single frequency [7]. Furthermore, the impedance is optimized to damp the plane wave whereas other modes experience less damping and can be strongly reflected at the silencer inlet.…”