Performance of Asymmetric Particulate Filter with Soot and Ash Deposits: Analytical Solution and Its Application

With ever-tightening emission regulations, particulate filters are critical for internal combustion engines to meet the stringent particulate matter emission standards. A fast way to predict the filter performance, instead of numerically solving the governing differential equations, is needed for filter design and selection, real-time control, malfunction detection, and deposit load sensing. Approximate analytical solutions for wall flow filters, considering asymmetric channels and arbitrary deposit amounts, are derived by a technique of successive approximation. The analytical predictions of filter pressure drop have been validated against both steady state and transient experimental measurements. Moreover, over a broad range of filter operating conditions, the accuracy of the second-order analytical solution is validated by comparisons with the numerical predictions. The derivation also provides analytical expressions for channel and wall velocity profiles along the filter length. This study reveals the necessity of considering the nonlinear term of the governing equations when the actual open widths of inlet and outlet channels are quite different.