A semi-analytical model for gas flow in pleated filters

A semi-analytical model of gas flow in pleated fibrous filters is developed for large filtration velocities. This case presents two main new and distinguishing features compared to the low filtration velocity situations studied in previous works: the velocity profiles are not parabolic within the pleat channels and the filtration velocity is not uniform along the pleated filter element and this has a great impact on the filter loading. The model relies on similarity solutions to the Navier–Stokes equations in the channels formed by pleating the filter medium. After validation by comparison with direct CFD simulations and experimental data, the model is used to determine the optimal pleat density, i.e. the pleat density minimizing the overall pressure drop across the filter for given flow rate, pleat length and given filter medium properties. As illustrated in the paper, this model greatly facilitates the study of flow within the pleated filter compared to a standard CFD approach. It represents an excellent basis for the more involved problem of filter loading computation. In particular, no remeshing across the width of the pleated filter entrance channels is needed when a filtration cake forms at the channel walls.