Effect of Pleat Angle on Pressure Drop in H14 HEPA Filters: A Mathematical Analysis with Corrections for Real Filter Behaviour

Abstract

Abstract

The influence of pleat angle on the pressure drop of H14 HEPA filters was investigated through a mathematical model that represents the filter as a system of converging–diverging channels coupled with porous filtration media. The analysis was conducted for pleat angles ranging from 1° to 20° under a constant laminar airflow rate of 0.167 m3/s and 0.45 m/s velocity. The model combines Darcy–Forchheimer flow through the filtration media with laminar channel flow theory, enabling the total pressure drop to be expressed as a function of pleat geometry and subsequently optimised through analytical differentiation. The results show that the pressure drop contribution of the filtration media increases with the pleat angle, from 10.57 Pa at 1° to 213.49 Pa at 20°, whereas channel losses decrease sharply from 1121.71 Pa to 2.75 Pa over the same interval. The competing behaviour of these two mechanisms generates a minimum total pressure drop of 94.56 Pa at a pleat angle of approximately 6°, compared with 120 Pa for the current industrial configuration operating at 3.73°. This represents a pressure drop reduction of approximately 21.2%, implying a corresponding decrease in fan energy consumption without compromising filtration performance. The analysis further demonstrates that very small pleat angles (1–2°) are highly unfavourable, producing total pressure drops between 301 and 1132 Pa due to severe channel constriction, while for angles above 13–14°, the channel contribution becomes negligible, and the overall pressure drop is governed almost entirely by the filtration media. These findings provide quantitative design criteria for optimising HEPA, EPA, and ULPA filter geometries, highlighting pleat angle as a critical parameter for improving aerodynamic performance, flow uniformity, and energy efficiency in high-purity environments. The proposed model was further assessed using a commercially available H14 HEPA filter with 188 pleats, an effective filtration area of 10.618 m2, and a nominal airflow rate of 600 m3/h, demonstrating its applicability to real industrial filter configurations.