Shevchenko H.O., Cholyshkina О.H., Sukhariev V.V., Kurilov V.S. Mathematical model for determining the hydraulic characteristics of finely dispersed water mineral suspensions

Details

Parent Category: Geo-Technical Mechanics, 2022

Category: Geo-Technical Mechanics, 2022, № 163

Geoteh. meh. 2022, 163, 155-164

https://doi.org/10.15407/geotm2022.163.155

 

MATHEMATICAL MODEL FOR DETERMINING THE HYDRAULIC CHARACTERISTICS  OF FINELY DISPERSED WATER MINERAL SUSPENSIONS

Shevchenko H.O., Cholyshkina О.H., Sukhariev V.V., Kurilov V.S.

Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine

UDC 532.5.011: 622.33: 622.752.3                                

Language: English

Abstract. Hydraulic characteristics of polydisperse mineral suspensions such as viscosity, concentration, porosity, volume and weight content of solid and liquid phases are necessary to calculate the speed of free or constrained deposition and floating of particles of different composition and size. This speed is the basis for the calculation of hydraulic classifiers and separators for the enrichment of mineral pulps. Determination of hydraulic characteristics requires a lot of experimental measurements, taking into account the different composition of suspensions and operating modes of the devices. The known calculation formulas are empirical and semi-empirical. Theoretical formulas are known only for viscosity, but they are limited by the concentration of the solid phase within 2–5%. The aim of the work is to develop a mathematical model for determining hydraulic characteristics depending on only one measured indicator – the density of the suspension (the volume weight of the sample). This indicator is easily measured in practice, at processing plants it serves to monitor the operating mode of the devices. In this work we use a cellular model of a water suspension consisted of discrete particles, and classical definitions of hydraulic characteristics. Based on this, defining formulas were obtained, an algorithm and a program for calculating characteristics were developed. When using the program, the obtained database allows us to establish approximating dependences: for the weight content of the solid phase θ, porosity ε, concentration β, kinematic viscosity v, density of the suspension ρ_s in a wide range. These dependencies allow us to calculate the hydraulic characteristics for any zone of the apparatus and different modes using only one simple measurement of pulp density by the weight method. Based on this, for example, it is possible to calculate the speed of constrained deposition and floating of particles and to build a map of the distribution of speeds and the efficiency of gravitational separation of particles. The developed mathematical model, algorithm and calculation program can be used to evaluate the optimal mode, control the stability of the equipment and design new hydraulic devices.
Keywords: mineral suspension, density, viscosity.

REFERENCES

1. Bogdanov, O.S., Olevsky, V.A., et al. (1972), Spravochnik po Obogascheniju rud [Handbook for ore dressing], Nedra, Moscow, Vol.1, pp. 229–233.

2. Richards, J.F. (1974),"The beginning of fluidization and homogeneous systems" in Davidson and J.F., Harrison D.(ed.), Fluidization, Chemistry, Moscow, pp. 37–69.

3. Einstein, V.G., Zakharov, M.K., Nosov G.A. et al. (1999), General course of processes and apparatuses of chemical technology, Vol.1, Chemistry, Moscow, pp. 213–232.

4. Landau, L.D. and Lifshits, E.M. (1986), Theoretical physics. Hydrodynamics, Nauka, Moscow.

5. Happel, J. and Brenner, H. (1965), Low Reynolds number hydrodynamics, Prentice-Hall, New York University.

6. Pilov, P.I. (1991), "Equation "viscosity-concentration" for polydisperse suspensions", Enrichment of minerals, Mining Institute, Dnepropetrovsk, no. 41, pp. 79–87.

7. Bulat, A. F., Nadutiy, V.P., Chelyshkina, V.V. and Kurilov, V.S. (2020), "A Determination of characteristic properties of mineral suspension for calculating the particle velocity". Geotekhnicheskaya Mekhanika [Geo-Technical Mechanics], vol.152, pp. 172–183. https://doi.org/10.15407/geotm2020.152.172

8. Tarasov, V.I., Tomash, A.A. and Krivenko, S.V. (2000), "Modern research methods and mathematical description of the structure of the granular layer". Vistnik Priazov. derzh. technical University, Mariupil, vol.10, pp. 7–9.

About authors:

Shevchenko Heorhii Oleksandrovych, Doctor of Technical Sciences (D.Sc.), Head of Department of Mechanics of Mineral Processing Machines and Processes, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine (IGTM NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

Cholyshkina Olha Henadiivna, Candidate of Technical Sciences (Ph.D), Associate Professor in Department of Computational Informational System and Technologies, Dean of Faculty of Computational Informational Technologies, Interregional Academy of Personnel Management, Kyiv, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

Sukharіev Vitaliі Vitaliіovych, Candidate of Technical Sciences (Ph.D.), Senior Researcher in Department of Mechanics of Mineral Processing Machines and Processes, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine (IGTM NAS of Ukraine), Dnipro, Ukraine,  This email address is being protected from spambots. You need JavaScript enabled to view it.

Kurilov Vladislav Serhiiovych, Junior Researcher in Department of Mechanics of Mineral Processing Machines and Processes, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine (IGTM NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it.

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