Nonlinear mathematical model of hydrodynamics of a rigid bearing surface gliding on an incompressible weightless fluid with oscillations
- Authors
-
-
- Keywords:
- Array, Array, Array, Array, Array, Array, Array
- Abstract
-
The paper presents a nonlinear mathematical model for studying the hydrodynamics of a rigid bearing surface gliding on an incompressible weightless liquid with oscillations in the process of gradual motion. The mathematical model was developed for further studies to assess the loads on the wetted surface of the fuselage of transport category aircraft in contact with a water surface during an emergency landing. The problem is to be solved in a nonlinear steady-state formulation using the wing analogy and will allow, along with the total loads, to obtain distributed loads to assess the strength of the structure in the investigated mode. The basic mathematical relations for obtaining the desired values, the general methodology and features of the numerical implementation of the proposed mathematical model are presented. The presented methodology allows studying hydrodynamic characteristics in the presence of flow asymmetry and angular velocities. As an example, numerical calculations are carried out and the obtained hydrodynamic characteristics of a gliding bearing surface at low subsonic speeds in the presence of an angular pitching speed are presented.
- Author Biography
- References
-
Sedov, L.I. (1981). Plane problems of hydrodynamics and aerodynamics. M.: Nauka. 384 p.
Kosourov, K.F. (1961). Theoretical foundations of hydroaviation (hydromechanics of a seaplane). M.: Voenizdat. 600 p.
Calculation of the airfoil of an arbitrary shape in plan view in a wide range of angles of attack. Izv. AN USSR. Fluid and Gas Mechanics. 1968. No. 4.
Belotserkovskiy, S.M. & Nisht, M.I. (1978). Detachable and non-detachable flow of thin wings by an ideal fluid. M.: Nauka. 362 p.
Belotserkovskiy, O.M. (1994). Numerical modelling in the mechanics of solid media. M.: Fizmatlit. 442 p.
Belotserkovskiy, O.M. (1999). Turbulence and instabilities. Moscow Inst. of Physics and Technology, 348 p.
Dvorak, A.V. & Lomov, S.M. (1980). Investigation of the convergence of the iterative process in nonlinear problems of stationary flow. Scientific and methodological materials on aerodynamics of aircraft. P. 2. M.: Zhukovsky Aircraft Research Inst.
Aubakirov, T.O., Belotserkovsky, S.M., Zhelannikov, A.I. & Nisht, M.I. (1997). Nonlinear wing theory and its applications. Almaty: Gylym. 448p.
Belotserkovskiy, S.M. (1965). Wing in a subsonic gas flow. M.: Nauka. 682 p.
Belotserkovskiy, S.M. & Skripach, B.K. (1975). Aerodynamic derivatives of an aircraft and a wing at subsonic speeds. M.: Nauka. 439 p.
Corjon, A.Q., Risso, F., Stoessel, F. & Poinsot, T. (1996). Tree-dimensional direct numerical simulations of wake vortices: atmosphere turbulence effect and rebound with crosswind. AGARD Conf. Proc. Vol. 584. Pp. 28-1-28-21.
Belotserkovskiy, S.M. & Ginevskiy, A.S. (1995). Modelling of turbulent jets and wakes on the basis of the method of discrete vortices. M.: Fizmatlit. 368 p.
Gaifullin, A.M. (2006). Investigation of vortex structures formed by the flow of bodies by liquid or gas. TsAGI. 138 p.
Darracq, D., Corjon, A. & Dueros, F. (2000). Simulation of wake vortex detection of airborne Doppler lidar J. Aircraf. Vol. 37. № 6.
Moin, P. (1997). Progress in large eddy simulation of turbulent flows. AIAA. Paper 97-0749.
Belotserkovskiy, S.M. & Ginevskiy, A.S. (1995). Computer concept of vortex turbulence. Izv. vuzov. Applied Nonlinear Dynamics. No. 2. Pp. 72—93.
Belotserkovskiy, Al.S. & Ginevskiy, A.S. (2002). Numerical modelling of a long-range vortex wake on take-off and landing modes (in russian). Doklady RAN. Vol. 380. № 6. Pp. 761—764.
Belotserkovskiy, Al.S., Ginevskiy, A.S., Pogrebnaya, T.V. & Shipilov, S.D. (2003). Modelling of the long-range vortex wake of mainline aircraft during take-off and landing (in russian). Udachy mekhaniki. Vol. 2. № 4. Pp. 106—127.
Belotserkovskiy, S.M., Shipilov, S.D. & Pogrebnaya, T.V. (1995). Investigation of aerodynamic derivatives of aircraft on a computer (in russian). Doklady RAN. Vol. 341.
Belotserkovskiy, S.M., Kotovskiy, V.N., Nisht, M.I. & Fedorov, R.M. (1988). Mathematical modelling of the detachable streamlining of bodies. M.: Nauka. 232 p.
Winckelmans, G., Code, R., Dufresne, L. & Capart, R. Vortex methods and their application to trailing wake vortex simulations Comptes Rendus Physique (2005)6 (4/5). Special iss. on Aircraft trailing vortices. Pp. 467—486.
Winckelmans, G., Cottin, C., Daeninck, G. & Leweke, T. Experimental and numerical study of counter-rotating vortex pair dynamics in large defect. 18e Congres Franqais de Mecanique. 27-31 August 2007. Grenoble, France. Paper CFM2007-1131.
Winckelmans, G., Bricteux, L., Code, R., Duponcheel, M. & Georges, L. Assessment of multiscale models for LES: spectral behaviour in very high Reynolds number turbulence and cases with aircraft wakes vortices. Proc. 5th Intern. Symposium on Turbulence and Shear Flow Phenomena (TSFP-5), 27-29 August 2007, Garching, Germany. Vol. I. P. 327—331.
Aparinov, V.A. (1980). Calculation of nonlinear unsteady aerodynamic characteristics of a bearing surface at oscillations and angular rotations in an incompressible fluid flow. Scientific and Methodological Mater. on Aerodynamics of Aircraft. Nonlinear characteristics. P. 1. M.: Zhukovsky Aircraft Research Inst. Pp. 56—64.
Dvorak, A.V. (1981). To the calculation of aerodynamic loads in non-stationary nonlinear problems. Scientific and methodological material on aerodynamics of aircraft. Nonlinear characteristics. M.: Zhukovsky Aircraft Research Inst. Pp. 84—92.
Fundamentals of military-technical research. Theory and applications. Synthesis of weapons systems and military equipment. (Monograph edited by O.P. Kovtunenko). 2011. K.: NAU. Vol. 1. 500 p.
Rastryhin, O.O., Varsiegov, A.S. & Kanishchev, V.V. (2024). Methods for calculating the hydrodynamic loads on the wetted area of the fuselage of a military transport aircraft during an emergency landing on water. Coll. of scientific works. K.: Central Research Institute of Aircraft. Iss. № 4(95). Pp. 278—293, inv. 6172.
Aviation rules. P. 25. Airworthiness standards for transport category aircraft. Interstate Aviation Committee. 1994. 368 p.
Kanishchev, V., Rasstrygin, O., Varsegov, A., & Isaienko, O. (2025). METHOD FOR CALCULATING THE HYDRODYNAMIC CHARACTERISTICS OF A CIRCUIT PLANNING ON THE UNDISTURBED SURFACE OF AN INCOMPRESSIBLE, WEIGHTLESS FLUID AT LOW SUBSONIC SPEEDS. Weapons and Military Equipment, 46(2), 22–28.
- Downloads
- Published
- 2025-09-30
- Section
- NAVY ARMAMENT & EQUIPMENT
- License
-
Copyright (c) 2026 Олександр Расстригін,Вадим Каніщев

This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
Most read articles by the same author(s)
- Andrii Zirka , Olexandr Rasstrygin, Substantiation of scientifi c and methodological apparatus for calculating the aerodynamic characteristics of unmanned aerial vehicle during fl ight at supersonic speeds in its conceptual design , Weapons and military equipment: Vol. 41 No. 1 (2024): Weapons and military equipment
- Vadym Kanishchev, Olexandr Rasstrygin, Scientific and methodological apparatus for assessing loads on the fuselage of a transport category aircraft during an emergency landing on a wavy water surface , Weapons and military equipment: Vol. 48 No. 4 (2025): Weapons and military equipment
- Vadym Kanishchev, Oleksandr Rasstrygin, Andrii Varsegov, Olena Isaienko, METHOD FOR CALCULATING THE HYDRODYNAMIC CHARACTERISTICS OF A CIRCUIT PLANNING ON THE UNDISTURBED SURFACE OF AN INCOMPRESSIBLE, WEIGHTLESS FLUID AT LOW SUBSONIC SPEEDS , Weapons and military equipment: Vol. 46 No. 2 (2025): Weapons and military equipment
