Numerical study of the influence of coagulation on the dynamics of a two-fraction gas suspension

A. L. Tukmakov   ; D. A. Tukmakov

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 4, pp. 66-81

Résumé

The work is devoted to mathematical modeling of the dynamics of solid or liquid dispersed inclusions suspended in gas-gas suspensions. The study numerically simulated the dynamics of a gas suspension in a channel with and without taking into account the effect of coagulation of dispersed inclusions. It was assumed that a dusty medium is moving in the channel, and droplet fractions are blown through the side surface of the channel, coagulating with dispersed inclusions of the dusty medium. The paper presents a mathematical model that implements a continuum technique for modeling the dynamics of multiphase media, which involves solving a complete system of dynamic equations for each of the phases of the mixture. The carrier medium was described as a viscous, compressible and thermally conductive gas. Interfacial momentum exchange and interfacial heat transfer were also taken into account. At the boundaries of the computational domain, modeled as solid surfaces, homogeneous Dirichlet boundary conditions were specified for the velocity components of the carrier medium and the dispersed phase. The dispersed phase of a gas suspension was described as multifractional, the fractions of which differ in the size of dispersed inclusions and the density of the particle material. The mathematical model assumed taking into account the interaction between particles, through the absorption of smaller particles by larger particles due to collisional coagulation. A comparison of the results with and without taking into account the effect of coagulation of the droplet and dust fractions of a gas suspension demonstrates that failure to take into account the coagulation effect has a significant impact on both the distribution of concentrations of gas suspension fractions and on the physical fields of the fractions and the carrier medium.

Détail

Keywords: numerical modelling, continuum model of the dynamics of a multiphase medium, interphase interaction, polydisperse gas suspension.

Bibliographie

[1] Nigmatulin R.I., Fundamentals of Mechanics of Heterogeneous Media, Nauka, M., 1978 | MR

[2] Deitch M.E., Filippov G.A., Gas Dynamics of Two-Phase Media, Energoizdat, M., 1981

[3] Kiselev S.P., Ruev G.A., Trunev A.P., Fomin V.M., Shavaleev M.Sh., Shock-Wave Processes in Two-Component and Two-Phase Media, Nauka, Novosibirsk, 1992

[4] Kutushev A.G., Mathematical Modeling of Wave Processes in Aerodispersed and Powdery Media, Nedra, St. Petersburg, 2003

[5] Fedorov A.V., Fomin V.M., Khmel T.A., Wave Processes in Gas Suspensions of Metal Particles, Parallel, Novosibirsk, 2015

[6] Kildibaeva S.R., Kharisov E.I., “Three-Dimensional Visualization of a Flow Model of a Multiphase Submerged Jet”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 16:1 (2023), 69–80 | DOI

[7] Kraiko A.N., “Mathematical Models for Describing the Flow of Gas and Foreign Particles and Unsteady Filtration of Liquid and Gas in Porous Media”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 7:1 (2014), 34–48 | DOI | Zbl

[8] Sadin D.V., “Modification of the Large Particle Method to a Scheme of Second Order Accuracy in Space and Time for Shock-Wave Flows of a Gas Suspension”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 12:2 (2019), 112–122 | DOI | Zbl

[9] Kovalev Yu.M., Pigasov E.E., “Mathematical Model of a Gas Suspension with Chemical Transformations in the Approximation of Pair Interactions”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 7:3 (2014), 40–49 | DOI | Zbl

[10] Bolotnova R.Kh., Gainullina E.F., “Modeling the Dynamics of a Shock Pulse in a Pipe with an Internal Layer of Aqueous Foam”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 14:1 (2021), 118–125 | DOI | Zbl

[11] Klinacheva N.L., Kovalev Yu.M., “Attenuation of Spherical Shock Waves in Heterogeneous Media”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 10:4 (2017), 35–45 | DOI

[12] Magazov F.G., Shestakovskaya E.S., “Mathematical Modeling of Possible Mechanisms for the Formation of Hot Spots”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 11:4 (2018), 154–160 | DOI | Zbl

[13] Surov V.S., “Towards the Calculation by the Godunov Method of Multidimensional Flows of a Multi-Velocity Heterogeneous Medium”, Mathematical Modeling, 29:3 (2017), 29–41 | DOI | Zbl

[14] Pakhomov M.A., Terekhov V.I., “Application of the Eulerian Approach to Simulating the Structure of an Upward Monodisperse Bubbly Flow in a Tube”, Journal of Applied Mechanics and Technical Physics, 57:3 (2016), 432–440 | DOI

[15] 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, 64:4 (2019), 449–454 | DOI

[16] Varaksin A.Y., Protasov M.V., “The Effect of Gas Injection on the Protection of Body Surfaces streamlined by a Two-Phase Flow”, High Temperature, 55:6 (2017), 945–948 | DOI

[17] 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, 95:1 (2022), 257–265 | DOI

[18] Makarov V.N., Ugolnikov A.V., Makarov N.V., Boyarskikh G.A., “Increasing the Efficiency of Dust Collection”, Mining Journal, 2022, no. 8, 62–70 (in Russian) | DOI

[19] S. Ahmed, M. Hassan, Q. Kamran, S. Ajmal, S. Waseem, W. Khalid, I. Naseem, A. Masroor, F. Amjad, “Investigation of Dust Particle Removal Efficiency of Self-Priming Venturi Scrubber Using Computational Fluid Dynamics”, Nuclear Engineering and Technology, 50:5 (2018), 665–672 | DOI

[20] I. Safdar, K. Abdullah, A. Majid, M. Ammar, “Numerical Simulation of Particulate Removal Efficiency in Venturi Scrubber”, 2017 – 13th International Conference on Emerging Technologies (ICET) (Islamabad), 2017, 1–6 | DOI

[21] N. Horiguchi, H. Yoshida, Y. Abe, “Numerical Simulation of Two-Phase Flow Behavior in Venturi Scrubber by Interface Tracking Method”, Nuclear Engineering and Design, 310 (2016), 580–586 | DOI

[22] N. Othmana, S. Dhalywalab, “Simulation Study on Liquid Droplet Size Measurement inside Venturi Scrubber”, Journal of Engineering, 32:2 (2020), 239–246 | DOI

[23] M. Bal, I. Behera, U. Kumari, S. Biswas, B. Meikap, “Hydrodynamic Study and Particulate Matter Removal in a Self Priming Venturi Scrubber”, Environmental Technology and Innovation, 20 (2020), 101167, 20 pp. | DOI

[24] Khmelev V.N., Shalunov A.V., Dorovskikh R.S., Nesterov V.A., Golykh R.N., “Modeling the Process of Wet Gas Purification with the Application of Ultrasonic Fields”, South Siberian Scientific Bulletin, 20:4 (2017), 57–63 (in Russian)

[25] Alemasov V.E., Dregalin A.F., Tishin A.P., Khudyakov V.A., Thermodynamic and Thermophysical Properties of Combustion Products, Publishing House VINITI, M., 1971

[26] Tukmakov A.L., “Dynamics of a Coagulating Polydisperse Gas Suspension in a Nonlinear Wave Field of an Acoustic Resonator”, Journal of engineering physics and thermophysics, 88:1 (2015), 11–19 (in Russian)

[27] Nigmatulin R.I., Gubaidullin D.A., Tukmakov D.A., “Shock Wave Dispersion of Gas-Particle Mixtures”, Doklady Physics, 61:2 (2016), 70–73

[28] D.A. Tukmakov, “Numerical Simulation of Oscillations of Aerosol with a Low Dispersed Phase Concentration in a Closed Tube by the Continuum Mathematical Model”, Technical Physics, 67:12 (2023), 764–770 | DOI

[29] Gubaidulina D.A., Tukmakov D.A., “Numerical Investigation of the Evolution of a Shock Wave in a Gas Suspension with Consideration for the Nonuniform Distribution of the Particles”, Mathematical Models and Computer Simulations, 7:3 (2015), 246–253 | DOI | Zbl

[30] Tukmakov A.L., Bayanov R.I., Tukmakov D.A., “Flow of Polydisperse Gas-Particle Mixture in a Duct Followed by Coagulation in a Nonlinear Wave Field”, Thermophysics and Aeromechanics, 22:3 (2015), 305–311

[31] D.A. Tukmakov, “Investigation of the Grid Convergence of a Finite-Difference Model of the Dynamics of an Electrically Charged Gas Suspension”, 2024 – 6th International Youth Conference on Radio Electronics, Electrical and Power Engineering (REEPE), M., 2024, 1–6 | DOI

[32] Fletcher C.A., Computation Techniques for Fluid Dynamics, Springer, Berlin, 1988

[33] Muzafarov I.F., Utyuzhnikov S.V., “Application of Compact Difference Schemes to the Study of Unsteady Flows of Compressible Gas”, Mathematical Modeling, 5:3 (1993), 74–83 (in Russian) | Zbl

[34] Tukmakov A.L., “Numerical Simulation of the Process of Wave Separation of Solid Particles in Resonance Gas Vibrations in the Closed Pipe”, Acoustical Physics, 55:3 (2009), 345–352 | DOI