Simplified Analytic Particulate Filter Backpressure Models, including the Additive Flow Resistance Model

• Published in: Emission control science and technology (Online) 2022-12, Vol.8 (3-4), p.138-153
• Main Author: Watling, Timothy C.
• Format: Article
• Language: English
• Subjects: Computer simulation; Earth and Environmental Science; Earth Sciences; Energy balance; Environmental Science and Engineering; Flow resistance; Fluid filters; Industrial Chemistry/Chemical Engineering; Inertia; Mathematical analysis; Mathematical models; Momentum; One dimensional models; Permeability; Predictions; Pressure drop; Soot; Surfaces and Interfaces; Technical papers; Thin Films; Trends; Viscosity
• ISSN: 2199-3629; 2199-3637
• DOI: 10.1007/s40825-022-00213-w

One-dimensional models of particulate filters (PF) typically involve numeric solution of the mass, momentum and energy balance equations. However, for isothermal conditions and axially uniform soot deposits, the mass and momentum balance equations can be solved analytically. Analytic models have the advantage of faster solution and easier identification of trends. Analytic models fall into two types; some aim to include all the features of an isothermal numeric model, while others take a more approximate approach, using simpler equations at the expense of a lower range of applicability. The latter is the subject of this work. This class of models also includes correlations obtained by fitting a function to the predictions of a detailed model, the first such model being an “additive flow resistance” (AFR) model by Konstandopoulos and Johnson (SAE Technical Paper 890405). Three simplified analytic models are derived with different assumptions/approximations, viz. a model neglecting inertial contributions to backpressure (“low-inertia”), a model additionally assuming the pressure drop across the PF wall and soot cake is large compared with that along the channels (“low-α”), and a generalised AFR model. All models apply to symmetric and asymmetric PFs including octo-squares. The predictions of these analytic models are compared with each other and a full/detailed numeric model to understand the range of validity and limitations of these model. Under favourable conditions, the AFR model can give a good backpressure prediction, despite its less than rigorous derivation. However, the low-inertia model is valid over a wider range of conditions. The low-α model consistently under predicts backpressure.