USING OF NEAR-CRITICAL FLOWS’ THEORY IN PRACTICAL CALCULATIONS

The paper considers the problem of practical using of theory about near-critical flows. It describes the types of immovable and movable near-critical flow phenomena and cases of these phenomena formation during different hydrotechnical constructions operating. The paper gives generalized differential equation of free-surface profile of wavelike near-critical flows. The solution of mentioned generalized differential equation is given as well. The solution of generalized differential equation takes into account possible deviating from hydrostatic pressure in initial cross-section of considered flows. If the specifity of near-critical flows, especially wavelike free-surface profile and deviation of pressure distribution in initial section of considered flows, will not be taken into account, it can put to difference between designed and real hydraulic regimens. This factor can bring to miscalculation during designing, building and exploitation of hydrotechnical constructers. All that shows the issue urgency of near-critical flows characteristics determination and modelling for practical calculations. The equations for determination main depths (maximum and second conjugated) are given. Besides, the paper gives existence conditions of different types of near-critical flows. An objective of this work is to present the comparison between theoretical and experimental data of free-surface profile of cnoidal waves. The comparison shows good convergence of results.

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[1] Riabenko O.A. (2003). Theoretical elements and methods of calculations of near-critical fluid flows with a free surface. Thesis for academic degree of doctor of technical sciences: 05.23.16. Rivne. 393 ps. (in Ukrainian).

[2] State building rulers V.2.4-1-99. (1999) Meliorative systems and structures. Derzhbud of Ukraine. Кyiv. 112 ps. (in Ukraine).

[3] Tursunov A.A. (1969). Near-critical state of gravity water flows, Izvestiya VNIIG. Vol. 90. p. 201–224 (in Russian).

[4] Riabenko O.A. (2011). Problems and paradoxes of near-critical fluid flow. Applied Fluid Mechanics, Vol. 13(85), №4. Kyiv. p. 37–51 (in Ukrainian).

[5] Riabenko O.A., Halych O.O., Poplavskiy D.M. (2013) Using of differential equations to calculate the free-surface profile of undular jump. Georgian Technical University, Hydroengineering, Vol. 1-2(15-16). Tbilisi. p. 36–44 (in Russian).

[6] Klyuha O.O. (2006). Flow hydraulics after single-span regulator sluice with pivot-leaf gates with accounting properties of near-critical flow. Synopsis of a thesis. Rivne, p. 19 (in Ukrainian).

[7] Chernobyl O.Y. (2010). The improvement’s methods of hydraulic calculations and designs of double-span regulator sluice with accounting properties of near-critical flow. Synopsis of a thesis. Rivne, p. 20 (in Ukrainian).

[8] Riabenko O.A., Cherniuk V., Klyuha O.A., Halych O.A., Poplavskiy D.M. Mathematical and hydraulic modeling. XV International Scientific Conference. Current issues of civil and environmental engineering and architecture. Book of abstracts. Rzeszόw – Lviv – Košice. Rzeszόw. Poland. 2015, p. 132–133.