Abstract: Sound attenuation in absorptive silencers has been analyzed in this paper. The structure of such devices is as follows. When the rigid duct of an expansion chamber has been lined by a packed absorptive material under a perforated membrane, incident sound waves will be dissipated by the absorptive liners. This kind of silencer, usually are applicable for medium to high frequency ranges. Several conditions for different absorptive materials, variety in their thicknesses, and different shapes of the expansion chambers have been studied in this paper. Also, graphs of sound attenuation have been compared between empty expansion chamber and duct of silencer with applying liner. Plane waves have been assumed in inlet and outlet regions of the silencer. Presented results that have been achieved by applying finite element method (FEM), have shown the dependence of the sound attenuation spectrum to flow resistivity and the thicknesses of the absorptive materials, and geometries of the cross section (configuration of the silencer). As flow resistivity and thickness of absorptive materials increase, sound attenuation improves. In this paper, diagrams of the transmission loss (TL) for absorptive silencers in five different cross sections (rectangle, circle, ellipse, square, and rounded rectangle as the main geometry) have been presented. Also, TL graphs for silencers using different absorptive material (glass wool, wood fiber, and kind of spongy materials) as liner with three different thicknesses of 5 mm, 15 mm, and 30 mm for glass wool liner have been exhibited. At first, the effect of substances of the absorptive materials with the specific flow resistivity and densities on the TL spectrum, then the effect of the thicknesses of the glass wool, and at last the efficacy of the shape of the cross section of the silencer have been investigated.
Abstract: This is a study on numerical simulation of the convection-diffusion transport of a chemical species in steady flow through a small-diameter tube, which is lined with a very thin layer made up of retentive and absorptive materials. The species may be subject to a first-order kinetic reversible phase exchange with the wall material and irreversible absorption into the tube wall. Owing to the velocity shear across the tube section, the chemical species may spread out axially along the tube at a rate much larger than that given by the molecular diffusion; this process is known as dispersion. While the long-time dispersion behavior, well described by the Taylor model, has been extensively studied in the literature, the early development of the dispersion process is by contrast much less investigated. By early development, that means a span of time, after the release of the chemical into the flow, that is shorter than or comparable to the diffusion time scale across the tube section. To understand the early development of the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Flux Corrected Transport Algorithm (FCTA). The computation has enabled us to investigate the combined effects on the early development of the dispersion coefficient due to the reversible and irreversible wall reactions. One of the results is shown that the dispersion coefficient may approach its steady-state limit in a short time under the following conditions: (i) a high value of Damkohler number (say Da ≥ 10); (ii) a small but non-zero value of absorption rate (say Γ* ≤ 0.5).