Analytical Models for Particulate Filter Backpressure Prediction

Tim  Watling, Johnson Matthey

One-dimensional models of Particulate Filters (PF) typically involve the numeric solution of the mass, momentum and energy balance equations for the gas in the inlet and outlet channels. However, for isothermal conditions and uniform soot- and ash-deposits, the mass and momentum balance equations can be solved analytically. Analytical models have the advantage over numeric models of faster solution and that they make the identification of general trends easier.

The first analytical PF model was published by Konstandopoulos and Johnson (SAE 890405). Since then, several other analytical PF models have been published. This presentation reports an improved analytical PF model that for the first time includes all the following features: i) compressible flow; ii) soot-loaded PFs; iii) momentum flux correction factors; iv) asymmetric PFs; and v) the friction factor and momentum flux correction factor being different for the inlet and outlet channels when these have a different shape, e.g. with octo-square PFs. Predictions of the analytical model will be compared with those of a numeric model. The analytical model can predict backpressure across the PF, as well as velocity and pressure profiles along the channels.

In addition to their analytical PF model, Konstandopoulos and Johnson (SAE 890405) also published a simplified model valid for low flow rates. However, this model was not derived, but rather obtained by fitting a function to the low-velocity predictions of the analytical model. This presentation will show how that simplified model can be derived from the detailed analytical model. This enables the limitations and assumptions behind the model to be better understood. An extension of the simplified model to include asymmetric PFs is also presented.

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