Skip to main content
NCBI home page
Springer Nature - PMC COVID-19 Collection logoLink to Springer Nature - PMC COVID-19 Collection
. 2021 Oct 31;35(11):5007–5022. doi: 10.1007/s12206-021-1019-9

Pressure drop and optimization meta-models for arbitrary low-height pleated filter shapes and flowrates

Paul Choi 1, Christian Ariane Santos 1, Min-Kun Kim 2, Hyunsook Jung 2, Do-Young Hong 3, Junemo Koo 1,✉
PMCID: PMC8556855

Abstract

This study delivers equations useful for low-height pleated fibrous filter design: two pressure drop equations and one set of optimum design equations applicable to arbitrary pleated filter shapes and flowrates. The pressure drop equations were derived to predict the pressure loss of the pleated filter. They were made through regression analysis with a total of 1024 CFD data. The set of optimum design equations was developed to find the optimum filter shape minimizing pressure drop. All equations were validated through the 8-fold cross-validation method and were accurate enough to replace the CFD simulations. Additionally, novel contour plots were made to describe how optimum filter geometry changes due to flowrate, height, and media permeability. The delivered equations were applied to an actual filter design problem and verified with additional CFD simulations. This study allows filter designers to predict the pressure loss and to design the optimum filter shape without any simulations.

Keywords: Pleated fibrous filter, Pressure drop, Optimization, Regression analysis, Computational fluid dynamics, Latin-hypercube sampling

Acknowledgments

This work was supported by the Agency for Defense Development of Korea (UC190034GD).

Abbreviation

AIC

Akaike information criterion

CBRN

Chemical biological radiological and nuclear

CFD

Computational fluid dynamics

LHS

Latin-hypercube sampling

MAE

Mean absolute error

PAPR

Powered air purifying respirator

RMSE

Root mean square error (= root mean square deviation)

MAPE

Mean absolute percentage error

Symbols

θ

Filter folding angle [rad]

θ¯¯

Dimensionless folding angle for LHS [-]

ΔP

Overall pressure drop across the filter [Pa]

ΔPmedia

Pressure drop due to media resistance [Pa]

ΔPthroat

Pressure drop due to the drag in the pleat spacing [Pa]

μ

Air dynamic viscosity [kg·m−1·s−1]

ρ

Air density [kg·m−3]

h

Filter height [mm]

L

Length of the filter centerline within half-pitch [mm]

W

Filter pitch (= pleat width) [mm]

Woptim

Optimum pitch minimizing pressure drop [mm]

R

Filter folding radius [mm]

Roptim

Optimum folding radius minimizing pressure drop [mm]

Refiber

Fiber Reynolds number [-]

r2

Coefficient of determination [-]

t

Filter media thickness [mm]

U

Upstream velocity (= inlet velocity for CFD simulation) [m·s−1]

Vface

Filtration velocity (= face velocity) [m·s−1]

VR

Media resistance (= reciprocal of media permeability) [m−2]

B

Breadth of narrow passage made by folding radius [mm]

Footnotes

Paul Choi received his Bachelor’s degree in Mechanical Engineering from Kyung Hee University in 2021. He is currently a battery engineer at LG Energy Solution, Ltd. His research is the optimization of the electrode slurry coating process using CFD and programming.

Christian Ariane Santos is a researcher at the Fine Particle Flow Laboratory in Kyung Hee University, Yongin, South Korea. She has a master’s degree in Environmental Engineering.

Min-Kun Kim is a Senior Researcher in the Agency for Defense Development, Daejeon, South Korea. He earned his Ph.D. degree in School of Chemical and Biological Engineering from Seoul National University. His current research field is CBRN protection/decontamination engineering.

Do-Young Hong is a Principal Researcher at the Korea Research Institute of Chemical Technology (KRICT). He joined the faculty there in 2013. He received his Ph.D. (2006) in chemical engineering from Hanyang University. He then conducted postdoctoral studies in the lab of Prof. C.W. Jones at the Georgia Institute of Technology (2007) and the lab of Prof. A. Bhan at the University of Minnesota (2010). His present research areas are in catalysis for biomass and waste plastics and gas sorption based on organic-inorganic hybrid materials.

Hyunsook Jung is a Principal Researcher in the Chem-Bio Technology Center, Agency for Defense Development, Deajeon, South Korea. She earned her Ph.D. degree in Chemistry from Texas A&M University at College Station.

Junemo Koo is a Professor in the Department of Mechanical Engineering, Kyung Hee University, Yongin, South Korea. He earned his Ph.D. degree in Mechanical and Aerospace Engineering from North Carolina State University.

References

  • [1].Saleh A M, Tafreshi H V. A simple semi-numerical model for designing pleated air filters under dust loading. Sep. Purif. Technol. 2014;137:94–108. doi: 10.1016/j.seppur.2014.09.029. [DOI] [Google Scholar]
  • [2].Théron F, Joubert A, Le Coq L. Numerical and experimental investigations of the influence of the pleat geometry on the pressure drop and velocity field of a pleated fibrous filter. Sep. Purif. Technol. 2017;182:69–77. doi: 10.1016/j.seppur.2017.02.034. [DOI] [Google Scholar]
  • [3].M. I. Nazarious, T. Mathanlal, M. P. Zorzano and J. Martin-Torres, Pressure optimized powered respirator (PROPER): a miniaturized wearable cleanroom and biosafety system for aerially transmitted viral infections such as COVID-19, HardwareX, 8 (2020). [DOI] [PMC free article] [PubMed]
  • [4].Li C C. Aerodynamic behavior of a gas mask canister containing two porous media. Chem. Eng. Sci. 2009;64(8):1832–1843. doi: 10.1016/j.ces.2009.01.009. [DOI] [Google Scholar]
  • [5].Wood S G A, Chakraborty N, Smith M W, Summers M J. A computational fluid dynamics analysis of transient flow through a generic chemical biological radiological and nuclear respirator canister. Chem. Eng. Res. Des. 2019;142:13–24. doi: 10.1016/j.cherd.2018.11.028. [DOI] [Google Scholar]
  • [6].Feng Z, Long Z, Chen Q. Assessment of various CFD models for predicting airflow and pressure drop through pleated filter system. Build. Environ. 2014;75:132–141. doi: 10.1016/j.buildenv.2014.01.022. [DOI] [Google Scholar]
  • [7].Chen D R, Pui D Y H, Liu B Y H. Optimization of pleated filter designs using a finite-element numerical model. Aerosol Sci. Technol. 1995;23(4):579–590. doi: 10.1080/02786829508965339. [DOI] [Google Scholar]
  • [8].Wakeman R J, Hanspal N S, Waghode A N, Nassehi V. Analysis of pleat crowding and medium compression in pleated cartridge filters. Chem. Eng. Res. Des. 2005;83(10A):1246–1255. doi: 10.1205/cherd.04183. [DOI] [Google Scholar]
  • [9].Li S, Hu S, Xie B, Jin H, Xin J, Wang F, Zhou F. Influence of pleat geometry on the filtration and cleaning characteristics of filter media. Sep. Purif. Technol. 2019;210(February2018):38–47. doi: 10.1016/j.seppur.2018.05.002. [DOI] [Google Scholar]
  • [10].Rebaï M, Prat M, Meireles M, Schmitz P, Baclet R. A semi-analytical model for gas flow in pleated filters. Chem. Eng. Sci. 2010;65(9):2835–2846. doi: 10.1016/j.ces.2010.01.014. [DOI] [Google Scholar]
  • [11].Tronville P, Sala R. Minimization of resistance in pleated-media air filter designs: empirical and CFD approaches. HVAC R Res. 2003;9(1):95–106. doi: 10.1080/10789669.2003.10391058. [DOI] [Google Scholar]
  • [12].Fotovati S, Hosseini S A, Tafreshi H V, Pourdeyhimi B. Modeling instantaneous pressure drop of pleated thin filter media during dust loading. Chem. Eng. Sci. 2011;66(18):4036–4046. doi: 10.1016/j.ces.2011.05.038. [DOI] [Google Scholar]
  • [13].Fotovati S, Tafreshi H V, Pourdeyhimi B. A macro-scale model for simulating pressure drop and collection efficiency of pleated filters over time. Sep. Purif. Technol. 2012;98:344–355. doi: 10.1016/j.seppur.2012.07.009. [DOI] [Google Scholar]
  • [14].Rebai M, Prat M, Meireles M, Schmitz P, Baclet R. Clogging modeling in pleated filters for gas filtration. Chem. Eng. Res. Des. 2010;88(4):476–486. doi: 10.1016/j.cherd.2009.08.014. [DOI] [Google Scholar]
  • [15].Oxarango L, Schmitz P, Quintard M. Laminar flow in channels with wall suction or injection: a new model to study multi-channel filtration systems. Chem. Eng. Sci. 2004;59(5):1039–1051. doi: 10.1016/j.ces.2003.10.027. [DOI] [Google Scholar]
  • [16].Waghode A N, Hanspal N S, Wakeman R J, Nassehi V. Numerical analysis of medium compression and losses infitration area in pleated membrane cartridge filters. Chem. Eng. Commun. 2007;194(8):1053–1064. doi: 10.1080/00986440701293140. [DOI] [Google Scholar]
  • [17].Cheng Y H, Tsai C J. Factors influencing pressure drop through a dust cake during filtration. Aerosol Sci. Technol. 1998;29(4):315–328. doi: 10.1080/02786829808965572. [DOI] [Google Scholar]
  • [18].Lücke T, Fissan H. The prediction of filtration performance of high efficiency gas filter elements. Chem. Eng. Sci. 1996;51(8):1199–1208. doi: 10.1016/0009-2509(95)00366-5. [DOI] [Google Scholar]
  • [19].Joubert A, Laborde J C, Bouilloux L, Callé-Chazelet S, Thomas D. Influence of humidity on clogging of flat and pleated HEPA filters. Aerosol Sci. Technol. 2010;44(12):1065–1076. doi: 10.1080/02786826.2010.510154. [DOI] [Google Scholar]
  • [20].Li J, Li S, Zhou F. Effect of moisture content in coal dust on filtration and cleaning performance of filters. Physicochem. Probl. Miner. Process. 2016;52(1):365–379. [Google Scholar]
  • [21].Choi J H, Ha S J, Bak Y C, Park Y O. Particle size effect on the filtration drag of fly ash from a coal power plant. Korean J. Chem. Eng. 2002;19(6):1085–1090. doi: 10.1007/BF02707237. [DOI] [Google Scholar]
  • [22].Frising T, Thomas D, Bémer D, Contal P. Clogging of fibrous filters by liquid aerosol particles: experimental and phenomenological modelling study. Chem. Eng. Sci. 2005;60(10):2751–2762. doi: 10.1016/j.ces.2004.12.026. [DOI] [Google Scholar]
  • [23].McKay M D, Beckman R J, Conover W J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics. 1979;21(2):239–245. [Google Scholar]
  • [24].Del Fabbro L, Laborde J C, Merlin P, Ricciardi L. Air flows and pressure drop modelling for different pleated industrial filters. Filtr. Sep. 2002;39(1):34–40. doi: 10.1016/S0015-1882(02)80055-6. [DOI] [Google Scholar]
  • [25].Anderson N J, Cassidy P E, Janssen L L, Dengel D R. Peak inspiratory flows of adults exercising at light, moderate and heavy workloads. J. Int. Soc. Respir. Prot. 2006;23(1943):53–63. [Google Scholar]
  • [26].Kiefer J. Sequential minimax search for a maximum. Proc. Am. Math. Soc. 1953;4(3):502. doi: 10.1090/S0002-9939-1953-0055639-3. [DOI] [Google Scholar]
  • [27].Storn R, Price K. Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 1997;11(4):341–359. doi: 10.1023/A:1008202821328. [DOI] [Google Scholar]
  • [28].Su Y C, Li C C. Computational fluid dynamics simulations and tests for improving industrial-grade gas mask canisters. Adv. Mech. Eng. 2015;7(8):1–14. doi: 10.1177/1687814015596297. [DOI] [Google Scholar]
  • [29].National Institute for Occupational Safety and Health (NIOSH) Statement of Standard for Chemical, Biological, Radiological, and Nuclear (CBRN) Full Facepiece Air Purifying Respirator (APR) Washington, DC: NIOSH; 2003. [Google Scholar]
  • [30].I. P. S. Araújo, D. B. Costa and R. J. B. De Moraes, Identification and characterization of particulate matter concentrations at construction jobsites, Sustainability (2014) 7666–7688.

Articles from Journal of Mechanical Science and Technology are provided here courtesy of Nature Publishing Group

RESOURCES