For citation:
Tukmakov D. A. Numerical study of coagulation of dispersed inclusions during injection of droplet fractions into a flow of dusty medium. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 3, pp. 419-433. DOI: 10.18500/1816-9791-2025-25-3-419-433, EDN: OVRYHI
Numerical study of coagulation of dispersed inclusions during injection of droplet fractions into a flow of dusty medium
The paper presents a numerical solution to the problem of coagulation of solid particles and droplets during the injection of a gas-droplet flow into a gas suspension flow. It was assumed that a dusty medium moves in a flat channel, and a gas-droplet mixture is blown through the side surface of the channel. As a result of the coagulation of solid particles and droplets, the average density of the solid particle fraction decreases and the fractional composition of the droplet mixture changes. The calculations are based on a mathematical model of the dynamics of a polydisperse multi-velocity and multi-temperature gas suspension with a Lagrangian model of particle coagulation with relative velocity sliding. The mathematical model implemented a continuum technique for modeling the dynamics of multiphase media, which makes it possible to take into account the interphase interaction. The dynamics of the carrier medium is described by the Navier – Stokes equations for a compressible heat-conducting gas with interphase heat and momentum exchange. The aerodynamic drag force, the added mass force, and the dynamic Archimedes force were taken into account. The dispersed phase consisted of a number of fractions differing in the size of dispersed inclusions and the density of the particle material. The hydro- and thermodynamics of each dispersed fraction were described by a system of hydrodynamic equations, including the continuity equation, the equations for the conservation of momentum components, and the equation for the conservation of thermal energy, written taking into account the interphase thermal and force interaction. The system of equations for the dynamics of a multi-velocity multi-temperature polydisperse system was integrated by the explicit finite-difference McCormack method. The monotonicity of the solution was ensured by a nonlinear correction scheme. As a result of the calculations, time and space dependencies were obtained that characterize the evolution of the composition of a multi-fraction system when mixing flows of different dispersion.
- Nigmatulin R. I. Osnovy mekhaniki geterogennykh sred [Fundamentals of the mechanics of heterogeneous media]. Moscow, Nauka, 1978. 336 p. (in Russian).
- Deich M. E., Filippov G. A. Gazodinamika dvukhfaznykh sred [The gas dynamics of two-phase media]. Moscow, Energoizdat, 1981. 472 p. (in Russian).
- Voloshchuk V. M. Kineticheskaya teoriya koagulyatsii [Kinetic theory of coagulation]. Leningrad, Gidrometeoizdat, 1984. 283 p. (in Russian).
- Vasenin I. M., Arkhipov V. A., Butov V. G., Gluzunov A. A., Trofimov V. F. Gazovaya dinamika dvukhfaznykh techeniy v soplakh [Gas dynamics of two-phase flows in nozzles]. Tomsk, Tomsk University Publ., 1986. 261 p. (in Russian).
- Kiselev S. P., Ruev G. A., Trunev A. P., Fomin V. M., Shavaleev M. Sh. Udarno-volnovye protsessy v dvukhkomponentnykh i dvukhfaznykh sredakh [Shock wave processes in two-component and two-phase media]. Novosibirsk, Nauka, 1992. 257 p. (in Russian).
- Sternin L. E., Shraiber A. A. Mnogofaznye techeniya gaza s chastitsami [Multiphase gas flows with particles]. Moscow, Mashinostroenie, 1994. 318 p. (in Russian).
- Kutushev A. G. Matematicheskoe modelirovanie volnovykh protsessov v aerodispersnykh i poroshkoobraznykh sredakh [Mathematical modeling of wave processes in aerodispersed and powdery media]. St. Petersburg, Nedra, 2003. 283 p. (in Russian).
- Fedorov A. V., Fomin V. M., Khmel T. A. Volnovye protsessy v gazovzvesyakh chastits metallov [Wave processes in gas suspensions of metal particles]. Novosibirsk, Parallel, 2015. 305 p. (in Russian).
- Shagapov V. S., Galimzyanov M. N., Agisheva U. O. Single waves in a gas-liquid bubble mixture. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 2, pp. 232-240 (in Russian). DOI: https://doi.org/10.18500/1816-9791-2020-20-2-232-240, EDN: NKIQHH
- Galimzyanov M. N. Propagation of pressure waves in finite-size bubbles zones. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2010, vol. 10, iss. 4, pp. 27–35 (in Russian). DOI: https://doi.org/10.18500/1816-9791-2010-10-4-27-35, EDN: NBNMEB
- Kotalczyk G., Kruis F. E. A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging. Journal of Computational Physics, 2017, vol. 340, pp. 276–296. DOI: https://doi.org/10.1016/j.jcp.2017.03.041
- Suresh V., Liu Z., Perry Z., Gopalakrishnan R. Modeling particle-particle binary coagulation rate constants for spherical aerosol particles at high volume fractions using Langevin dynamics simulations. Journal of Aerosol Science, 2022, vol. 164, art. 106001. DOI: https://doi.org/10.2139/ssrn.4058874, EDN: IORMBV
- Zhou D., Liu X., Yang S., Hou Y., Zhong X. Collision dynamics of two liquid nitrogen droplets under a low-temperature condition. Cryogenics, 2022, vol. 124, art. 103478. DOI: https://doi.org/10.1016/j.cryogenics. 2022.103478, EDN: MVZCPH
- Amanbaev T. R., Tilleuov G. E., Zuparbekova A. Mathematical modeling of dispersed media f lows in the presence of nucleation, coagulation and phase transitions. Bulletin of the Karaganda University. Physics Series, 2021, vol. 102, iss. 2, pp. 14–24. DOI: https://doi.org/10.31489/2021Ph2/14-24, EDN: JAJQRV
- Khmelev V. N., Shalunov A. V., Dorovskikh R. S., Nesterov V. A., Golykh R. N. Modeling the process of wet gas purification with the imposition of ultrasonic fields. South Siberian Scientific Bulletin, 2017, iss. 4 (20), pp. 57–63 (in Russian). EDN: YLBKTW
- Timofeeva M. V. The effect of coagulation of water droplets on their size distribution in the operating part of an air-cooler device. Technical Physics, 2019, vol. 64, iss. 4, pp. 449–454. DOI: https://doi.org/10.1134/S1063784219040248, EDN: LEFGAT
- Wang L. P. Coagulation in turbulent particle-laden flows. In: Subramaniam S., SBalachanda S. (eds.) Modeling Approaches and Computational Methods for Particle-Laden Turbulent Flows. Academic Press, 2023, pp. 111–145. DOI: https://doi.org/10.1016/B978-0-32-390133-8.00012-8
- Zaichik L. I., Alipchenkov V. M. The coagulation of aerosol particles in turbulent flow. High Temperature, 2008, vol. 46, iss. 5, pp. 666–674.
- Chen J., Gao P., Gu H., Yu H. Evaluation of the relative deviation for coagulation and gravitational sedimentation model from experimental results of submicron aerosol in water vapor environments. Progress in Nuclear Energy, 2023, vol. 163, art. 104824. DOI: https://doi.org/10.1016/j.pnucene.2023.104824
- Patra P., Roy A. Brownian coagulation of like-charged aerosol particles. Physical Review Fluids, 2022, vol. 7, iss. 6, art. 064308. DOI: 10.1103/PhysRevFluids.7.064308, EDN: WXALQG
- Laptev A. G., Lapteva E. A. Mathematical model and thermohydraulic characteristics of packed scrubbers of condensation cooling of a gas. Journal of Engineering Physics and Thermophysics, 2022, vol. 95, iss. 1, pp. 257–265. DOI: https://doi.org/10.1007/s10891-022-02473-3, EDN: MJPBOU
- Makarov V. N., Ugolnikov A. V., Makarov N. V., Boyarskikh G. A. Dust control efficiency improvement. Gornyi Zhurnal [Mining Journal], 2022, iss. 8, pp. 62–70 (in Russian). DOI: https://doi.org/10.17580/gzh.2022.08.09, EDN: NUAJMF
- Shraiber A. A., Fedinchik I. V., Protasov M. V. On effect of gas flow turbulence on the efficiency of particle collection in a Venturi scrubber. High Temperature, 2015, vol. 53, iss. 1, pp. 80–85. DOI: https://doi.org/10.1134/S0018151X14060145
- Alemasov V. E., Dregalin A. F., Tishin A. P., Khudyakov V. A. Termodinamicheskie i teplofizicheskie svoystva produktov sgoraniya. T. 1. Metody rascheta [Thermodynamic and thermophysical properties of combustion products. Vol. 1. Calculation methods]. Moscow, VINITI, 1971. 267 p. (in Russian).
- Tukmakov A. L. Dynamics of a coagulating polydisperse gas suspension in the nonlinear wave field of an acoustic resonator. Journal of Engineering Physics and Thermophysics, 2015, vol. 88, iss. 1, pp. 9–17. DOI: https://doi.org/10.1007/s10891-015-1162-1, EDN: NOGEWV
- Tukmakov A. L. Program code for modeling the dynamics of homogeneous and dispersed media using the explicit McCormack method in generalized curvilinear coordinates (2D). Certificate of registration of the computer program RU 2018619242, 08/02/2018. Application no. 2018616542 dated 06/19/2018.
- Tukmakov A. L., Tukmakov D. A. Dynamics of a charged gas suspension with an initial spatially nonuniform distribution of the average dispersed phase density during the transition to the equilib rium state. High Temperature, 2017, vol. 55, iss. 4, pp. 491–495. DOI: https://doi.org/10.1134/S0018151X17030221, EDN: XNVGSP
- Tukmakov A. L., Tukmakov D. A. Numerical study of the influence of the parameters of dispersed particles on the deposition of the solid phase of an electrically charged polydisperse gas suspension. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 1, pp. 90-102 (in Russian). DOI: https://doi.org/10.18500/1816-9791-2022-22-1-90-102, EDN: DJLRDK
- Tukmakov D. A. Numerical investigation of the influence of properties of the gas component of a suspension of solid particles on the spreading of a compressed gas-suspension volume in a binary medium. Journal of Engineering Physics and Thermophysics, 2020, vol. 93, iss. 2, pp. 291–297. DOI: https://doi.org/10.1007/s10891-020-02120-9
- Tukmakov D. A. One-dimensional unsteady numerical model of gas suspension flow caused by gravitational sedimentation of particles with a constant velocity. Journal of Applied Mechanics and Technical Physics, 2022, vol. 63, iss. 7, pp. 1218–1226. DOI: https://doi.org/10.1134/S0021894422070148, EDN: KUFPAP
- Tukmakov D. A. Numerical simulation of oscillations of aerosol with a low dispersed phase concentration in a closed tube by the continuum mathematical model. Technical Physics, 2022, vol. 67, pp. 764–770. DOI: https://doi.org/10.1134/S1063784222110032, EDN: ZCTMNH
- Fletcher C. Computation techniques for fluid dynamics. Berlin, Springer-Verlag, 1988. 898 p. (Russ. ed.: Moscow, Mir, 1991. Vol. 2. 551 p.).
- Muzafarov I. F., Utyuzhnikov S. V. Application of compact difference schemes to investigation of unstationary gas flows. Matematicheskoe Modelirovanie [Mathematical Modeling], 1993, vol. 5, iss. 3, pp. 74–83 (in Russian).
- Pirumov U. G., Roslyakov G. S. Gazovaya dinamika sopel [Gas dynamics of nozzles]. Moscow, Nauka, 1990. 364 p. (in Russian).
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