# Науковий вісник НГУ

## Theoretical bases of pulp suction process in the shallow dredge underwater face

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Abstract:

Purpose. To develop a mathematical model of the process of interaction of the shallow dredge suction pipe with solid particles and formation of the underwater face.

Methodology. To describe the motion of a fluid flow involving solid particles in the underwater face of a single suction pipe, the continuity equation for an ideal fluid in polar coordinates is applied. The solution of the differential equation in general form is fulfilled. The motion of solid particles and the formation of an underwater face of the suction pipe are considered as a result of the difference in pressures below and above the particle.

Findings. A mathematical description of the process of movement of a carrier flow carrying solid particles in the underwater surface suction zone of a single suction pipe is performed, using the continuity equation for an ideal fluid, written in polar coordinates. The interaction of the suction pipe with the pulp flow is described in the form of an axisymmetric process with a function of the medium density constant in time. The motion of a solid particle in an underwater face of a suction pipe is considered as a function of the difference in pressures below and above the particle. Based on the fact of low velocities of the suction flow moving, an expression is obtained for calculating the suction radius of solid particles and determining the boundary of the erosion zone when the soil is sucked in the underwater face of the suction pipe. The determining effect of the radial motion of the suction flow and the centrifugal force insignificance is taken into account. The construction of an underwater surface erosion zone of a single suction pipe in the form of surfaces of the erosion zone boundary and the boundary of the suction zone of the suspended soil composed of quartz particles by the size 0.16 mm at a suction efficiency of 800 m3/h is constructed.

Originality. As a result of the development of a mathematical model on the basis of the equation of continuity written in polar coordinates, it is established that the radius of absorption of suspended quartz particles by the size d  0.15...5 mm in the underwater face of a single suction pipe is directly proportional to the root of the fourth ratio of the square of the productivity of the pulp in the suction pipe to the solid particle diameter and the cosine of the inclination angle of forming of the suction zone.

Practical value. The analytical dependencies obtained in the work allow us to perform the construction of the boundaries of the underwater surface face and determine the volume of granular soils excavation by the shallow dredge working member. That allows substantiating the rational design parameters of the mining machine and the technological parameters of the process of mineral resources underwater mining.

References.

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2. Volker Patzold, Gunter Gruhn and Carsten Drebenstedt, 2008. Der Nassabbau. Erkundung, Gewinnung, Aufbereitung, Bewertung/Springer-Verlag Berlin Heidelberg. Available at: <https://books.google.com.ua/books?id=CqsfBAAAQBAJ&printsec=frontcover&dq=Der+Nassabbau.+Erkundung,+Gewinnung,+Aufbereitung,+Bewertung&hl=ru&sa=X&ved=0ahUKEwiYofyy88PaAhWI8ywKHWcCDVAQ6AEIJjAA#v=onepage&q=Der%20Nassabbau.%20Erkundung%2C%20Gewinnung%2C%20Aufbereitung%2C%20Bewertung&f=false> [Accessed 12 February 2017].

3. Bray, R. N., 2009. A guide to cost standards for dredging equipment. London: CIRIA. Available at: <https://books.google.com.ua/books?id= EWyygK_T-FAC&
printsec=frontcover&hl=ru#v=onepage&q&f= false> [Accessed 2 February 2017].

4. R. N. Bray, ed., Environmental Aspects of dredging. Taylor & Francis/Balkema. Leiden. Available at: <https://books.google.com.ua/books?id=7xYzciM42YC&printsec=frontcover&dq=Environmental+Aspects+of+dredging&hl=ru&sa=X&ved=0ahUKEwjUoLDn88PaAhWDDywKHYnaADMQ6AEIJjAA#v=onepage&q=Environmental%20Aspects%20of%20dredging& f=false> [Accessed 5 April 2017].

5. Pavol Rybar, Henrich Hamrak, Jan Kosco, Lucia Domaracka, Dusan Domaracky and Maria Rybarova, 2011. Polymetalicke konkrecie bohatstvo na dne mori a oceanov/Kosice. TU v Kosiciach, Fakulta BERG, Deka­nat-Edicne pracovisko. Available at: <https://www.martinus.sk/?uItem=119306> [Accessed 13 March 2017].

6. Gaydіn, A. M., Sobko, B. Yu. and Laznіkov, O. M., 2016. Mining of flooded deposits of titanium ores. Dnipropetrovsk: Lіtograf.

7. Bondarenko, A. A., 2012. Mathematical modeling of soil dredger absorption processes in the underwater bottomhole. Metallurgical and Mining Industry, 3, рр. 79‒81.

8. Bondarenko, A. A. and Zapara, Ye. S., 2012. Laws of determination of fine materials suction limits in submarine suction dredge face. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 4, рр. 59‒64.

9. Bashtovoy, V. G., Rex, A. G. and Chorny, A. D., 2012. Fluid Mechanics. Minsk: National Technical University. Available at: <https://rep.bntu.by/handle/data/ 24252> [Accessed 27 February 2017].

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ISSN (print) 2071-2227,
ISSN (online) 2223-2362.
Journal was registered by Ministry of Justice of Ukraine.
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