Hydrodynamic model of a funnel from an explosion of a buried charge

About the authors:

Alexey M. Bubenchikov , Dr. Sci. (Phys.-Math.), Professor, Leading Researcher, Regional Scientific and Educational Mathematical Center, National Research Tomsk State University; bubenchicov_am@mail.ru

Evgeniy B. Brazovskiy , Postgraduate Student, Department of Theoretical Mechanics, National Research Tomsk State University; kondraten.kondraten@mail.ru

Abstract:

The problems of the flow of an ideal fluid with an unknown (free) boundary is known from the theory of jets, which is well developed and widely used to solve problems in the field of hydrodynamics and filtration theory. The methods of this theory can also be successfully applied to calculate the shape of craters during explosions, using the well-developed mathematical apparatus of the theory of potential flows and the theory of analytical functions.

One of the main tasks that arise when using ejection explosions is the task of determining the size and shape of the ejection funnels depending on the geometry of the area, soil properties, energy characteristics of the charge, as well as its shape and location. Explosions are used in the development of minerals, in the excavation of trenches including for laying underground oil and gas pipelines in hard rocks, in the construction of dams, the construction of underground storage facilities, including gas. Camouflage explosions are used in the oil and gas industry for creating underground storage facilities and intensifying oil and gas production. The scope of the explosion in the national economy is constantly expanding.

The aim of the work is the analytical construction of an accurate mapping of the area of the complex potential on the plane of the hodograph, which implements the task of ejecting soil during the explosion of a corded (elongated) buried charge.

The paper uses a solid-liquid explosion model proposed by M. A. Lavrentiev in the middle of the 20th century. Within the framework of this mathematical model, a solution for the problem is obtained and analyzed in detail: the explosion of a point buried charge.

The choice of this problem is due to the fact that it has an exact analytical solution, and in a simple analytical form, in elementary functions. The solution of this problem was known from literary sources, but it was solved anew in a different way.

References:

1. Bolotova Yu. N. 2021. “The influence of the explosive charge design on the formation of seismic and explosive waves”. Explosion Technology, no. 133-90, pp. 149-157. [In Russian]

2. Viktorov S. D., Zakalinsky V. M., Shipovskii I. E., Mingazov R. Ya. 2021. “The concept of development of drilling and blasting works mineral deposits”. Explosion Technology, no. 133-90, pp. 100-112. [In Russian]

3. Gurevich M. I. Theory of jets of an ideal liquid. Moscow: Fizmatgiz, 1961. 496 p. [In Russian]

4. Zakalinsky V. M., Mingazov R. Ya. 2021. “About drilling and blasting operations at large depths”. Explosion Technology, no. 133-90, pp. 113-121. [In Russian]

5. Kuznetsov V. M. 1977. Mathematical models of explosive business. Novosibirsk: Nauka. Pp. 84-127. [In Russian]

6. Lavrentiev M. A., Shabat B. V. 1973. Methods of the theory of functions of a complex variable: study guide for universities. 4^th ed., corrected. Moscow: Science. 736 p. [In Russian]

7. Martynyuk P. A. 1965. “On the shape of the ejection funnel during an explosion in the ground of a cord charge”. National Economic Use of the Explosion, no. 30, pp. 3-9. [In Russian]

8. Milne-Thomson L. M. 1974. Theoretical hydrodynamics. Translated from English by A. A. Petrova et al. Edited by N. N. Moiseeva. Moscow: Mir. 655 p. [In Russian]

9. Norov A. Yu. 2020. “The problem of controlling the explosion energy during the formation of the collapse of the exploded rock mass in quarries”. Explosion Technology, no. 129-86, pp. 85-104. [In Russian]

10. Khokhlov S. V., Bazhenova A. V., Makkoev V. A., Rakhmanov R. A., Alenichev I. A. 2021. “Investigation of the issue of management and control over the displacement of ore contours after the blast”. Explosion Technology, no. 132-89, pp. 59-76. [In Russian]