The motion of the free-surface separation point during the initial stage of horizontal impulsive displacement of a floating circular cylinder
- 132 Downloads
The initial stage of unsteady two-dimensional flow caused by the impulsive horizontal motion of a floating circular cylinder is investigated by using methods of asymptotic analysis. Initially the cylinder is half-submerged and the liquid free surface is flat and horizontal. The liquid is of infinite depth. Then the cylinder suddenly starts to move horizontally with a speed given as a function of time. The liquid is assumed ideal and incompressible and its flow potential. The initial flow is provided by pressure-impulse theory, with an account of a possible separation of the liquid free surface from the trailing face of the rigid surface of the cylinder. The initial position of the separation point on the surface of the moving body is determined by using the condition that the fluid velocity is finite at the separation point (Kutta condition). The motion of the separation point along the surface of the cylinder is numerically determined with the help of the second-order outer solution of the problem and the Kutta condition at the moving separation point. It is shown that the length of the wetted part of the cylinder surface increases at a rate proportional to the speed of the cylinder. The speed of the separation point depends on the Froude number. The pressure on the wetted part of the cylinder can be below the atmospheric pressure for relatively high speed.
KeywordsAsymptotic analysis Free-surface flows Hydrodynamic impact Sedov’s model Separation effects
Unable to display preview. Download preview PDF.
- 1.Sedov LI (1965) Two-dimensional problems of hydrodynamics and aerodynamics. Interscience Publications, New YorkGoogle Scholar
- 2.Kudryavtseva NA (1960) Horizontal impact of a floating ellipse on an incompressible fluid. Prikl Mat Mekh 24: 258–261Google Scholar
- 3.Korchagin VS (1978) Separation impact on a cylinder semi-submerged in a fluid. Izv Sev-Kavkaz Nauchn Tsentr Vyssh Shkoly Estestv Nauki 4: 25–27Google Scholar
- 4.Korchagin VS (1989) Separation impact of a body on an incompressible fluid. Izv Sev-Kavkaz Nauchn Tsentr Vyssh Shkoly Estestv Nauki 3: 30–33Google Scholar
- 5.Dvorak AV, Teselkin DA (1986) Numerical solution of two-dimensional problems of pulsed motion of floating bodies. Zh Vychisl Mat Mat Fiz 26(1): 144–150Google Scholar
- 10.Norkin MV (2009) Separation impact of an elliptic cylinder floating on the surface of an inhomogeneous incompressible fluid. Izvestia Vusov Severo-Kavkazskii Region, Special Issue “Actual problems of mathematical hydrodynamics”. Nat Sci 168–173Google Scholar
- 14.Aleksandrov VM, Pozharskii DA (1998) Nonclassical three dimensional problems of mechanics of contact interaction between elastic bodies. Faktorial, Moscow [in Russian]Google Scholar
- 15.Aleksandrov VM, Chebakov MI (2004) Analytical methods in contact problems of the elasticity theory. Fizmatlit, Moscow [in Russian]Google Scholar
- 17.Gazzola T, Korobkin AA, Malenica S (2006) Hydro-elastic Wagner impact using variational inequalities. In: Proceedings of 21th international workshop on water waves and floating bodies, Loughborough, UK, pp 57–60Google Scholar
- 18.Korobkin AA (1993) Low-pressure zones under a liquid–solid impact. In: Blake JR, Boulton-Stone JM, Thomas NH (eds) Bubble dynamics and interface phenomena: proceedings of the IUTAM symposium, held in Birmingham, UK, 6–9 September, 1993. Kluwer, Dordrecht, pp 375–381Google Scholar
- 19.Korobkin AA (2003) Cavitation in liquid impact problem. In: Proceedings of the 5th international congress on cavitation, Osaka, Japan, 6 ppGoogle Scholar