Estimation of Filtration Efficiency – from Simple Correlations to Digital Fluid Dynamics

• Autorzy: Przekop R.

Identyfikatory

DOI

10.1515/cpe-2017-0004

• Języki publikacji: EN

Abstrakty

EN

Aerosol filtration in fibrous filters is one of the principal methods of accurate removal of particulate matter from a stream of gas. The classical theory of depth filtration of aerosol particles in fibrous structures is based on the assumption of existing single fibre efficiency, which may be used to recalculate the overall efficiency of entire filter. Using “classical theory” of filtration one may introduce some errors, leading finally to a discrepancy between theory and experiment. There are several reasons for inappropriate estimation of the single fibre efficiency: i) neglecting of shortrange interactions, ii) separation of inertial and Brownian effects, ii) perfect adhesion of particles to the fibre, iv) assumption of perfect mixing of aerosol particles in the gas stream, v) assumption of negligible effect of the presence of neighbouring fibres and vi) assumption of perpendicular orientation of homogenous fibres in the filtration structure. Generally speaking, “classical theory” of filtration was used for characterization of the steady - state filtration process (filtration in a clean filter, at the beginning of the process) without deeper investigation of the influence of the nternal structure of the filter on its performance. The aim of this review is to outline and discuss the progress of deep-bed filtration modelling from the use of simple empirical correlations to advanced techniques of Computational Fluid Dynamics and Digital Fluid Dynamics.

Słowa kluczowe

EN

filtration; lattice Boltzmann; Brownian dynamics; multiphase flows; porous media

PL

filtrowanie; krata Boltzmanna; dynamika Browna; przepływy wielofazowe

• Wydawca: Komitet Inżynierii Chemicznej i Procesowej Polskiej Akademii Nauk
• Czasopismo: Chemical and Process Engineering
• Rocznik: 2017
• Tom: Vol. 38, nr 1
• Strony: 31--50
• Opis fizyczny: Bibliogr. 71 poz.

Twórcy

autor

Przekop R.

• Warsaw University of Technology, Faculty of Che mical and Process Engineering, u l. Waryńskiego 1, 00-645 Warsaw, Poland

Bibliografia

• 1. Albrecht F., 1931. Theoretische Untersuchungen über die Ablagerung von Staub aus der Luft und ihre Anwendung auf die Theorie der Staubfilter. Physik. Zeits., 32, 48-68.
• 2. Bałazy A., Podgórski A., 2007. Deposition efficiency of fractal-like aggregates in fibrous filters calculated using
• 3. Brownian dynamics method. J. Colloid Interface Sci., 311, 323–337. DOI: 10.1016/j.jcis.2007.03.008.
• 4. Banks D.O., Kurowski G.J., 1990. Electrical enhancement of filters with randomly oriented fibres. Aerosol. Sci. Tech., 12, 256-269. DOI: 10.1080/02786829008959344.
• 5. Benarie M., 1969. Einfluss der Porenstruktur auf den Abscheidegrad in Faserfiltern. Staub-Reinhalt. Luft, 29, 74-78.
• 6. Biggs M.J., Humby S.J., Buts A., Tuzun U., 2003. Explicit numerical simulation of suspension flow with deposition in porous media; influence of local flow field on deposition processes predicted by trajectory methods. Chem. Eng. Sci., 58, 1271-1288. DOI: 10.1016/S0009-2509(02)00103-3.
• 7. Brown R.C., 1993. Air filtration: An integrated approach to the theory and applications of fibrous filters. Pergamon Press, Oxford.
• 8. Cai J., 1992. Fibrous filters with non-ideal conditions. PhD Thesis, The Royal Institute of Technology, Stockholm.
• 9. Chandrasekhar S., 1943. Stochastic problems in physics and astronomy. Rev. Mod. Phys., 15, 1-89. DOI: 10.1103/RevModPhys.15.1.
• 10. Clement C.F., Dunnett. S.J., 2000. The use of random variables in fibrous filtration theory. J. Aerosol. Sci., 31 (Suppl. 1), 200-201. DOI: 10.1016/S0021-8502(00)90207-6.
• 11. Derjaguin B.V., Muller V.M., Toporov Y.P., 1975. Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53, 314-326. DOI: 10.1016/0021-9797(75)90018-1.
• 12. Dhaniyala S., Liu B.Y.H., 2001. Theoretical modeling of filtration by non-uniform fibrous filters. Aerosl. Sci. Technol. 34, 161-169. DOI: 10.1080/027868201300034763.
• 13. Dunnett S.J., Clement C.F., 2006. A numerical study of the effects of loading from diffusive deposition on the efficiency of fibrous filters. J. Aerosol Sci., 37, 1116-1139. DOI: 10.1016/j.jaerosci.2005.08.001.
• 14. Dunnett S.J., Clement C.F., 2012. Numerical investigation into the loading behaviour of filters operating in the diffusional and interception deposition regimes. J. Aerosol Sci., 53, 85-99. DOI: 1016/j.jaerosci.2012.06.008.
• 15. Filippova O., Hänel D., 1997. Lattice-Boltzmann simulation of gas-particle flow in filters. Comp. Fluids, 26, 697- 712. DOI: 10.1016/S0045-7930(97)00009-1.
• 16. Happel J., 1959. Viscous flow relative to arrays of cylinders. AIChE J., 5, 174-177. DOI: 10.1002/aic.690050211.
• 17. Henry F., Ariman T., 1981. Cell model of aerosol collection by fibrous filters in an electrostatic field. J. Aerosol Sci. 12, 91-103. DOI: 10.1016/0021-8502(81)90041-0.
• 18. Hertz H., 1896. Miscellaneous Papers. Macmillan, London.
• 19. Hinds W.C., 1999. Aerosol Technology. Wiley & Sons, New York.
• 20. Imai I., 1951. On the asymptotic behaviour of viscous fluid flow at a great distance from a cylindrical body, with special reference to Filon's paradox. Proc. Roy. Soc. London. Ser. A., 208, 487–516. DOI: 10.1098/rspa.1951.0176.
• 21. Johnson K.L., Kendall K., Roberts A.D., 1971. Surface energy and the contact of elastic solids. Proc. R. Soc. London Ser. A, 324, 301-313. DOI: 10.1098/rspa.1971.0141.
• 22. Karadimos A., Ocone R., 2003. The effect of the flow field recalculation on fibrous filter loading: a numerical simulation. Powder Techn., 137, 109-119. DOI: 10.1016/S0032-5910(03)00132-3.
• 23. Kasper, G., Schollmeier, S., Meyer, J., 2010. Structure and density of deposits formed on filter fibers by inertial particle deposition and bounce. J. Aerosol Sci., 41, 1167-1182. DOI: 10.1016/j.aerosci.2010.08.006
• 24. Kirsch A.A., Fuchs N.A., 1967. Studies on fibrous aerosol filters. II. Pressure drops in systems of paralel cylinders. Ann. Occup. Hyg., 10, 23-30. DOI: 10.1093/annhyg/10.1.23.
• 25. Kirsch A.A., Fuchs N.A., 1968. Studies on fibrous aerosol filters. III. Diffusional deposition of aerosols in fibrous filters. Ann. Occup. Hyg. 11, 299-304. DOI: 10.1093/annhyg/11.4.299.
• 26. Kirsch A.A., Stechkina I.B., 1977. Inertial deposition of aerosol particles in model filters at low Reynolds numbers. J. Aerosol Sci., 8, 301-307. DOI: 10.1016/0021-8502(77)90016-7.
• 27. Kuwabara S., 1959. The forces experienced by randomly distributed parallel circular cylinders or spheres in viscous flow at small Reynolds number. J. Phys. Soc. Jpn., 14, 527-532. DOI: 10.1143/JPSJ.14.527.
• 28. Lamb H., 1932. Hydrodynamics. Cambridge University Press, Cambridge.
• 29. Lastow O., Podgórski A., 1998. Single fibre collection efficiency. In: Spurny K.R. (Ed.), Advances in Aerosol Filtration. Lewis Publishers, Boca Raton, 25-52.
• 30. Lee K.W., Ramamurthi M., 1993. Filter collection. In: Willeke K., Baron M. (Eds.) Aerosol Measurements: Principles, Techniques and Applications. Van Nostrand Reinhold, New York, 188.
• 31. Lennard-Jones J.E., 1924. On the determination of molecular fields. II. from the equation of state of a gas. Proc. Royal Soc. London A, 106, 463-477. DOI: 10.1098/rspa.1924.0082.
• 32. Long W., Hilpert M., 2009. A correlation for the collection efficiency of Brownian particles in clean bed filtration in sphere packings by a lattice-Boltzmann method. Eniornm. Sci. Techn., 35, 205-218. DOI: 10.1021/es8024275.
• 33. Marshall H.; Sahraoui M.; Kaviany M., 1994. An improved analytic solution for analysis of particle trajectories in fibrous, two-dimensional filters. Phys. Fluids, 6, 507-520. DOI: 10.1063/1.868346.
• 34. Masselot A., 2000. A new numerical approach to snow transport and deposition by wind: A parallel lattice gas model. PhD Thesis, Geneve University, 2000.
• 35. Maus R., Umhauer H., 1997. Single fibre collection and adhesion efficiency for biological particles. Part. Part. Syst. Charact., 14, 250-256.
• 36. Moskal A., Payatakes A.C., 2006. Estimation of the diffusion coefficient of aerosol particle aggregates using Brownian simulation in the continuum regime. J. Aerosol Sci., 37, 1081–1101. DOI: 10.1016/j.jaerosci.2005.10.005.
• 37. Muller V.M., Yushchenko B.V. Toporov Y.P., 1980. On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. J. Colloid Interface Sci. 77, 91-101. DOI: 10.1016/0021-9797(80)90419-1.
• 38. Oseen C.W., 1927. Neuere Methoden und Ergebnisse in der Hydrodynamik. Akademische Verlagsgesellschaft, Leipzig.
• 39. Payatakes A.C., Gradoń L., 1980a. Dendritic deposition of aerosols by convective Brownian motion diffusion for small, intermediate and large Knudsen numbers. AIChE J., 26, 443-454. DOI: 10.1002/aic.690260316.
• 40. Payatakes A.C., Gradoń L., 1980b. Dendritic deposition of aerosol particles in fibrous media by inertial impaction and interception. Chem. Eng. Sci., 35, 1083-1096. DOI: 10.1016/0009-2509(80)85097-4.
• 41. Pich J.,1966. Theory of aerosol filtration by fibrous and membrane filters. In: Davies C.N. (Ed.) Aerosol Science, Academic Press, London, 223-285.
• 42. Podgórski A., Gradoń L., 1992. Shadow and ordering effects in fibrous electret filters. J. Aersol Sci., 23 (Suppl. 1), 753-756. DOI: 10.1016/0021-8502(92)90521-V.
• 43. Podgórski A., 1993. Analytical description of gas flow around a fibre for modelling of aerosol filtration. J. Aersol Sci., 24 (Suppl. 1), S277-S278. DOI: 10.1016/0021-8502(93)90231-W.
• 44. Podgórski A., Gradoń L., Grzybowski P., 1995. Theoretical study on deposition of flexible and stiff fibrous
• 45. aerosol particles on a cylindrical collector. Chem. Eng. J., 58, 109–121.
• 46. Podgórski A., Luckner H.J., Gradoń L., Wertejuk Z., 1998. Aerosol particle filtration in the fibrous filters at the presence of external electric field I. Theoretical model. Chem. Process Eng., 19, 865-889.
• 47. Podgórski A., Moskal A., 2001. Dispersion of submicron aerosol particles in fibrous filters. Chem. Process Eng., 22, 1139-1144.
• 48. Podgórski A., 2002. On the transport, deposition and filtration of aerosol particles in fibrous filters: Selected problems. Oficyna Wydawnicza Politechniki Warszawskiej, Warsaw.
• 49. Przekop R., Moskal A., Gradoń L., 2003. Lattice-Boltzmann approach for description of the structure of deposited particulate matter in fibrous filters. J. Aerosol Sci., 34, 133-147. DOI: 10.1016/S0021-8502(02)00153-2.
• 50. Przekop R., Grzybowski K., Gradoń L., 2004. Energy-balanced oscillatory model for description of particles deposition and reentrainment on fibre collector. Aerosol Sci. Techn., 38, 330-337. DOI: 10.1080/02786820490427669.
• 51. Przekop R., Podgórski A., 2004. Effect of shadowing on deposition efficiency and dendrites morphology in fibrous filters. Chem. Proc. Eng., 25, 1563-1568.
• 52. Przekop R., Gradoń L., 2008. Deposition and filtration of nanoparticles in the composites of nano- and microsized fibres. Aerosol Sci. Technol., 42, 483-493. DOI: 10.1080/02786820802187077.
• 53. Przekop R., Gradoń L., 2014. Effect of particle and fibre size on the morphology of deposits in fibrous filters. Int. J. Num. Meth. Fluids, 76, 779-788. DOI: 10.1002/fld.3952.
• 54. Przekop R., Jackiewicz A., 2016. Effect of filter inhomogenity on deep bed filtration process. 22nd Polish Conference of Chemical Engineering, Spała, Poland, 5-9 September 2016, 1152-1159.
• 55. Qian Y.H., d’Humieres D., Lallemand P., 1992. Lattice-BGK models for Navier-Stokes equation. EPL, 17, 479– 484. DOI: 10.1209/0295-5075/17/6/001. Reeks M.W., Reed J., Hall D., 1988. On the resuspension of small particles by turbulent flow. J. Phys. D: Appl. Phys., 21, 574-589. DOI: 10.1088/0022-3727/21/4/006.
• 56. Ross R.F., Klingenberg D.J., 1996. Dynamic simulation of flexible fibres composed of linked rigid bodies. J. Chem. Phys., 106, 2949–2960. DOI: 10.1063/1.473067.
• 57. Schweers E., Löffler F., 1994. Realistic modelling of the behaviour of fibrous filters through consideration of filter structure. Powder Technol., 80, 191-206. DOI: 10.1016/0032-5910(94)02850-8.
• 58. Sell W., 1931. Staubabscheidung an einfachen Körpern und Luftfiltren. VDI Forschungs Heft., 347, 1-14.
• 59. Switzer L.H., Klingenberg, D.J., 2004. Flocculation in simulations of sheared fibre suspensions. International J. Multiphase Flow, 30, 67–87. DOI: 10.1016/j.ijmultiphaseflow.2003.10.005. Succi S., 2002. Mesoscopic modelling of slip motion at solid-fluid interfaces with heterogeneous catalysis. Phys. Rev. Lett., 89, 64502. DOI: 10.1103/PhysRevLett.89.064502.
• 60. Sztuk E., Przekop R., Gradoń L., 2012. Brownian dynamics for calculation of the single fibre deposition efficiency of submicron particles. Chem. Process Eng., 33, 279-290. DOI: 10.2478/v10176-012-0025-y.
• 61. Tamada K., Fujikawa H., 1957. The steady two-dimensional flow of viscous fluid At low Reynolds numer passing through an infinite row of equal parallel circular cylinders. Q. J. Mech. Appl. Math., 10, 425-432. DOI: 10.1093/qjmam/10.4.425.
• 62. Tomotika S., Aoi T., 1950. The steady flow of viscous fluid past a sphere and circular cylinder at small Reynolds numbers. Q. J. Mechanics Appl. Math., 3, 141–161. DOI: 10.1093/qjmam/3.2.141.
• 63. Ulam S., 1952. Random processes and transformations. In: Proceedings of the International Congress of Mathematicians (Cambridge, Massachusetts, August30-September 6, 1950), American Mathematical Society, Providence, Rhode Island, 264-275.
• 64. Wang H.C., John W., 1987. Comparative bounce properties of particle materials. Aerosol Sci. Technol., 7, 285-299. DOI: 10.1080/02786828708959165.
• 65. Wang G., Yu W., Zhou Ch., 2006. Optimization of the rod chain model to simulate the motions of long flexible in a simple shear flows. Euro. J. Mech. B/Fluids, 25, 337–347. DOI: 10.1016/j.euromechflu.2005.09.004.
• 66. Yamamoto S., Matsuoka T., 1992. A method for dynamic simulation of rigid and flexible fibres in a flow field. J. Chem. Phys., 98, 644–650. DOI: 10.1063/1.464607.
• 67. Yamamoto S., Matsuoka T., 1999. Dynamic simulation of rod-like and plate-like particle dispersed systems. Comp. Materials Sci., 14, 169–176. DOI: 10.1016/S0927-0256(98)00103-7.
• 68. Yamanoi M., Maia J.M., 2011. Stokesian dynamics simulations of the role of hydrodynamics interactions on the behaviour of a single particle suspending in a Newtonian fluid. Part 1. 1D flexible and rigid fibres. J. Non-Newtonian Fluid Mech., 166, 457–468. DOI: 10.1016/j.jnnfm.2011.02.001.
• 69. Yeh H.C., Liu B.Y.H., 1974. Aerosol filtration by fibrous filters - I. Theoretical. Aerosol Sci., 5, 191-204. DOI:10.1016/0021-8502(74)90049-4.
• 70. Ziskind G., Fichman M., Gutfinger C., 2000. Particle behavior on surfaces subjected to external excitations. J. Aerosol Sci., 26, 703-720. DOI: 10.1016/S0021-8502(99)00554-6.
• 71. Żywczyk Ł., Moskal A., 2015. Modelling of deposition of flexible fractal-like aggregates on cylindrical fibre in continuum regime. J. Aerosol Sci., 81, 75-89. DOI: 10.1016/j.jaerosci.2014.12.002.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)