Russian Federation
Purpose: When the water movement in the pipeline is stopped in conditions of negative temperatures, its freezing and destruction are possible, which leads to the failure of water supply systems for a long time. For accident-free operation of the water pipeline, it is important to know the time during which its complete or partial freezing occurs. The purpose of this work is to study the physical processes that occur during freezing, to formulate the basic mathematical model and its numerical solution, to build an analytical solution in a quasistationary approximation, to obtain formulas that are convenient for freezing time calculation and to determine the range of parameter values at which they are valid. Methods: The mathematical model of the freezing process relies on the use of energy conservation law. When constructing a difference scheme, the integrointerpolation method is used to numerically solve the nonlinear differential equations of the model. To obtain an approximate analytical solution, the method of separating equations describing processes that occur at different speeds, is used. Results: The mathematical model of pipeline freezing during water movement shutdown under conditions of constant negative temperature of the surrounding atmosphere has been formulated and substantiated. Within the framework of the quasi-stationary approximation, simple formulas for the freezing time of the water pipeline have been obtained. The criteria for the applicability of these formulas have been established. The numerical solution of equations of initial mathematical model is compared with the results obtained within quasi-stationary approximation. Practical significance: The ratios obtained in the work make it possible to estimate the time during which repair work should be carried out and the movement of water in the pipeline should be restored before its destruction due to freezing occurs.
Above-ground water pipeline, internal icing, freezing time, mathematical modeling, quasistationary approximation
1. Bogoslovskiy P. A. Ledovyy rezhim truboprovodov gidroelektricheskih stanciy / P. A. Bogoslovskiy. - M.; L.: Gosenergoizdat, 1950. - 154 s.
2. Zhidkih V. M. Ledovyy rezhim truboprovodov / V. M. Zhidkih, Yu. A. Popov. - L.: Energiya, 1979. - 132 s.
3. Cheng K. C. Freezing and melting heat transfer in engineering: Selected topics on ice-water systems and welding and casting processes / K. C. Cheng, N. Seki. - New York: Hemisphere, 1991. - 815 p.
4. Gordon J. R. An Investigation into Freezing and Bursting Water Pipes in Residential Construction / J. R. Gordon // Research Report, University of Illinois at Urbana-Champaign, Urbana, USA. - 1996. - Iss. 96-1P. - Pp. 1-51. - URL: https://www.ideals.illinois.edu/items/54859.
5. Akyurt M. Freezing phenomena in ice-water systems / M. Akyurt, G. Zaki, B. Habeebullah // Energy Conversion and Management. - 2002. - Vol. 43. - Pp. 1773-1789.
6. Terehov L. D. Tehnologicheskie osnovy energosberezheniya pri podache vody po vodovodam na Severe: diss. ... d-ra tehn. nauk / L. D. Terehov. - Habarovsk: Dal'nevostochnyy gosudarstvennyy universitet putey soobscheniya, 1999. - 275 s.
7. McDonald A. Mathematical simulation of the freezing time of water in small diameter pipes / A. McDonald, B. Bschaden, E. Sullivan et al. // Applied Thermal Engineering. - 2014. - Vol. 73(1). - Pp. 142-153.
8. Hongfei Xu. Modelling ice and wax formation in a pipeline in the Arctic environment / Xu Hongfei, H. Dali, S. Yue et al. // Journal of Loss Prevention in the Process Industries. - 2020. - Vol. 66. - Pp. 104197. - DOI: https://doi.org/10.1016/j.jlp.2020.104197.
9. Terehov L. D. Vnutrennee obledenenie vodovodov v zimniy period / L. D. Terehov, N. V. Tvardovskaya, E. A. Tvardovskaya // III Betankurovskiy mezhdunarodnyy inzhenernyy forum: sbornik trudov, Sankt-Peterburg, 2-3 dekabrya 2021 goda. - SPb: FGBOU VO PGUPS, 2021. - T. 2. - S. 161-164.
10. Miheev M. A. Osnovy teploperedachi / M. A. Miheev, I. M. Miheeva. - M.: Energiya, 1977. - 344 s.
11. Kutateladze S. S. Osnovy teorii teploobmena / S. S. Kutateladze. - M.: Atomizdat, 1979. - 416 s.
12. GOST 21880-2011. Maty iz mineral'noy vaty proshivnye teploizolyacionnye / Redaktor V. N. Kopysov. - M.: Standartinform, 2012. - 10 s.
13. Landau L. D. Teoreticheskaya fizika: Uchebnoe posobie. V 10 t. T. VI. Gidrodinamika / L. D. Landau, E. M. Lifshic. - M.: Nauka, 1986. - 736 s.
14. Lykov A. V. Teoriya teploprovodnosti / A. V. Lykov. - M.: Vysshaya shkola, 1967. - 600 s.
15. Samarskiy A. A. Teoriya raznostnyh shem / A. A. Samarskiy. - M.: Nauka, 1989. - 616 s.
