A One-Dimensional Model for Square and Octo-Square Asymmetric Particulate Filters with Correct Description of the Channel and Wall Geometry

摘要

Asymmetric particulate filters (PF), where the inlet channel is wider than the outlet channel, are commonly used because of their greater capacity for ash. Somewhat surprisingly, very few models for asymmetric PFs have been published and none of these gives a correct/detailed description of the geometry. For example, octahedral channels may be treated as if they were square or the tapering walls between the inlet and outlet channels treated as if they were rectangular in cross section. Alternatively, the equations may be presented in generic form in terms of channel cross-sectional areas and perimeters, but without giving any indication of how to calculate these. This paper aims to address these deficiencies with a model that correctly describes the geometry of square and octo-square asymmetric PFs. Expressions for the solid fraction of the PF (which affects thermal mass) and channel cross section and perimeter (both when clean and soot/ash loaded) are presented. The error introduced by assuming the inlet channels are square rather than octahedral depends on the substrate, but can be significant. Expressions for the pressure drop across the wall and soot cake are also given. While other things depend on channel geometry, the rate of soot of oxidation by NO_2 and O_2 is shown to be the same irrespective of channel geometry, depending only on contact time (provided the gas flow through the soot cake remains uniform or is well mixed). The tapered shape of the filter wall results in an increase in gas velocity as the gas passes from the inlet channel to the outlet channel. This impacts filtration efficiency. Particulate capture by interception is unaffected by the gas velocity as the capture probability is purely a geometric effect. Capture by Brownian diffusion, on the other hand, depends on residence time and so varies through the wall.