Federal Educational and MethodologicalAssociation in the System of Higher Education «Technospheric Safety and Environmental Management» (Associate Professor)
Moskva, Moscow, Russian Federation
The possibility of applying the probabilistic-statistical method for theoretical calculation of characteristics related to suspensions separation in self-cleaning hydrodynamic filters with a rotating filter element has been demonstrated. It has been shown that the change in characteristics of the suspensions separation in hydrodynamic filters with a rotating filter element can be satisfactorily described based on equations of diffusion type, in particular, using the Fokker–Planck–Kolmogorov equation. The main parameters of the separation process in hydrodynamic filters with a rotating filter element have been determined.
self-cleaning filter, hydrodynamic filter, suspensions separation, equations of diffuse type, Fokker-Planck-Kolmogorov equations
1. Finkel'shtejn 3.L. Primenenie i ochistka rabochih zhidkostej dlja gornyh mashin [Application and cleaning of working fluids for mining machines]. Moscow: Nedra Publ., 1986. 232 p. (in Russian).
2. Devisilov V., Sharai E. Hydrodynamic filters in hydraulic fluid cleaning system of hydraulic drive. IOP Conference Series: Materials Science and Engineering. Vol. 492. I. 1. 2019. DOI:https://doi.org/10.1088/1757-899X/492/1/012025
3. Sivuhin D.V. Obshhij kurs fiziki. T.I. Mehanika [General course of physics]. Moscow: FIZMATLIT Publ., MFTI Publ., 2002. 560 p. (in Russian).
4. Protod'jakonov I.O., Bogdanov S.R. Statisticheskaja teorija javlenij perenosa v processah himicheskoj tehnologii [Statistical theory of transport phenomena in the processes of chemical technology]. Leningrad: Himija Publ., 1983. 400 p. (in Russian).
5. Spravochnik po teorii verojatnostej i matematicheskoj statistike [Handbook on the theory of probability and mathematical statistics]. Moscow: Nauka Publ., 1985. 640 p. (in Russian).
6. Kholpanov L.P., Ibyatov R.I., Akhmadiev F.G., Fazylzyanov R.R. Mathematical Modeling of the Hydrodynamics over Permeable Surfaces // Teoretical Foundations of Chemical Engineering. - 2003. - Vol. 37, No. 3. - R. 207
7. Kholpanov L.P., Ibyatov R.I. Mathematical Modeling of the Dispersed Phase // Teoretical Foundations of ChemicaltEngineering. - 2005. - Vol. 39, No. 2. - P. 190
8. Schutyser M., Belfort G. Dean vortex membrane microfltration non-Newtonian viscosity effects // Ind. Eng. Chem. Res. - 2002. - Vol. 41, I. 3. - P. 494.
9. Testik F., Voropaev S. On the case when steady converging/diverging flow of a non-Newtonian fluid in a round cone permits an exact solution // Mesh. Res. Commun. - 2004. - Vol. 31, I. 4. - P. 477.
10. Krokhina A. V., Lvov V. A., Fatova A. V. Asymptotic Properties of a Probabilistic-Statistical Model of Particle Classification in Hydrocyclones //Chemical Engineering & Technology. - 2019. - V. 42. - I. 1. - S. 209-214. https://doi.org/10.1002/ceat.201800370
11. Krokhina A. V., Lvov V. A., Fatova A. V. Practical Application of the Probabilistic-Statistical Model of the Suspension Separation in Hydrocyclones // Chemical Engineering and Technology. 2019. V. 42. I. 4. pp. 774-779. DOIhttps://doi.org/10.1002/CEAT.201800599
12. Devisilov V.A., L'vov V.A., Sharaj E.Ju., Mjagkov I.A. Analiticheskaja model' processa razdelenija suspenzij v gidrodinamicheskom fil'tre s vrashhajushhejsja perforirovannoj peregorodkoj [Analytical model of the process of separating suspensions in a hydrodynamic filter with a rotating perforated baffle]. Bezopasnost' v tehnosfere [Safety in the technosphere]. 2014, V. 3, I. 5, pp. 32-41. DOI:https://doi.org/10.12737/6022. (in Russian).
13. Pavlihin G.P., Krohina A.V., L'vov V.A. Verojatnostno-statisticheskaja model' processa razdelenija suspenzij v gidrociklonah s dopolnitel'noj inzhekciej [Probabilistic-statistical model of the process of separating suspensions in hydrocyclones with additional injection]. Bezopasnost' v tehnosfere [Safety in the technosphere]. 2012, V. 1, I. 2, pp. 46-51. (in Russian).
14. Cronin K., Catak M., Bour J., Collins A. Stochastic modelling of particle motion along a rotary drum // Powder technology. 2011. - V. 213. - I. 1-3. - p. 79-91. https://doi.org/10.1016/j.powtec.2011.07.009
15. Tjakra J. D., Bao J., Hudon N., Yang R Studies of particulate system dynamics in rotating drums using Markov chains //IFAC Proceedings Volumes. 2012. - V. 45. - I. 15. - p. 487-492. https://doi.org/10.3182/20120710-4-SG-2026.00083
16. Reshetnjak S.A., Sheljapin L.A. Kvazistacionarnye raspredelenija v kinetike [Quasi-stationary distributions in kinetics.]. Moscow: Avtor Publ., 1996. 296 p. (in Russian).
17. Berthiaux H., Mizonov V. Applications of Markov chains in particulate process engineering: a review // The Canadian Journal of Chemical Engineering. - 2004. - V. 82. - I. 6. - p. 1143-1168. https://doi.org/10.1002/cjce.5450820602
18. Yaming Zhuang, Xiaoping Chen and Daoyin Liu. Stochastic bubble developing model combined with Markov process of particles for bubbling fluidized beds // Chemical Engineering Journal. - 2016. V. 291 (206).
19. Ternovskij I.G., Kutepov A.M. Gidrociklonirovanie [Hydrocycloning]. Moscow: Nauka Publ., 1994. 350 p. (in Russian).
20. Levitan B. M., Sargsjan I. S. Operatory Shturma - Liuvillja i Diraka [Operators of Sturm - Liouville and Dirac]. Moscow: Nauka. Gl. red. fiz.-mat. lit. Publ., 1988. 432 p. (in Russian).
21. Marchenko V. A. The Sturm-Liouville Equation and Transformation Operators //Sturm-Liouville Operators and Applications. - Birkhäuser, Basel, 1986. - S. 1-100. (in Russian).
22. Ahtjamov A.M., Sadovnichij V.A., Sultanaev Ja.T. Obratnye zadachi Shturma - Liuvillja s neraspadajushhimisja kraevymi uslovijami [Inverse Sturm - Liouville problems with non-decaying boundary conditions]. Moscow: Moskovskii universitet Publ., 2009. 184 p. (in Russian).
23. Landau L.D., Lifshic E.M. Fizicheskaja kinetika [Physical kinetics]. Moscow: FIZMATLIT Publ., 2001. 536 p. (in Russian).
24. Tihonov A.I., Samarskij A.A. Uravnenija matematicheskoj fiziki [Equations of mathematical physics]. Moscow: Nauka Publ. 1977. 736 p. (in Russian).
25. Korn G., Korn T. Spravochnik po matematike [Handbook of mathematics]. Moscow: Nauka Publ., 1977. 832 p. (in Russian).
