Initial stage of flat plate impact onto liquid free surface

Iafrati, Alessandro; Korobkin, A.A.

doi:10.1063/1.1714667

Cited by 50 publications

(63 citation statements)

References 6 publications

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“…Inspecting all shapes in figure 9(a-d ), we see that indeed we find self similar solutions for a large range of Weber numbers, that only depend on We. Figure 10 shows that for We → ∞ the solution becomes independent of We, confirming the results of Iafrati & Korobkin (2004).…”

Section: Self Similaritysupporting

confidence: 79%

“…In this section we will provide a theoretical description for the formation of the splash neglecting the effect of air density, which is in part analogous to Iafrati & Korobkin (2004). Let us first notice from figures 1-2 that there exist two well-differentiated spatial regions after a solid impacts a free surface.…”

Section: Theoretical Description Of the Splashmentioning

confidence: 99%

“…Self-similar solutions for the case without surface tension (We → ∞) have been found by Iafrati & Korobkin (2004) for the initial stage after impact, whose scaling exponents were already noticed by Yakimov (1973). Later, this analysis was expanded in order to calculate the hydrodynamic load on a flat surface close to impact by Iafrati & Korobkin (2008.…”

Section: Introductionmentioning

confidence: 99%

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Splash wave and crown breakup after disc impact on a liquid surface

2013

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In this paper we analyze the impact of a circular disc on a free surface using experiments, potential flow numerical simulations and theory. We focus our attention both on the study of the generation and possible breakup of the splash wave created after the impact and on the calculation of the force on the disc. We have experimentally found that drops are only ejected from the rim located at the top part of the splash -giving rise to what is known as the crown splash-if the impact Weber number exceeds a threshold value We crit ≃ 140. We explain this threshold by defining a local Bond number Bo tip based on the rim deceleration and its radius of curvature, with which we show using both numerical simulations and experiments that a crown splash only occurs when Bo tip 1, revealing that the rim disrupts due to a Rayleigh-Taylor instability. Neglecting the effect of air, we show that the flow in the region close to the disc edge possesses a Weber-numberdependent self-similar structure for every Weber number. From this we demonstrate that Bo tip ∝ We, explaining both why the transition to crown splash can be characterized in terms of the impact Weber number and why this transition occurs for W e crit ≃ 140.Next, including the effect of air, we have developed a theory which predicts the timevarying thickness of the very thin air cushion that is entrapped between the impacting solid and the liquid. Our analysis reveals that gas critically affect the velocity of propagation of the splash wave as well as the time-varying force on the disc, F D . The existence of the air layer also limits the range of times in which the self-similar solution is valid and, accordingly, the maximum deceleration experienced by the liquid rim, what sets the length scale of the splash drops ejected when W e > We crit .

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Section: Self Similaritysupporting

confidence: 79%

Section: Theoretical Description Of the Splashmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Splash wave and crown breakup after disc impact on a liquid surface

2013

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“…Asymptotic methods are used to obtain a uniformly valid initial asymptotic solution. The approach is similar to that developed by Iafrati and Korobkin [17,18] for the problem of initial flow caused by sudden motion of a floating body. In this approach, the flow region is divided into the main flow region, where the solution can be obtained by the small-time expansion method, and the immediate vicinities of the plate edges, where the inner leading-order solution is obtained numerically.…”

mentioning

confidence: 94%

Initial stage of plate lifting from a water surface

2015

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This study deals with the flow induced by a rigid flat plate of finite length, initially touching a horizontal water surface, when it starts to move upwards with constant acceleration. In the present model, negative hydrodynamic pressures on the lower (wetted) surface of the plate are allowed, and thus, the water follows the plate due to the resulting suction force. The acceleration of the plate and the plate length are such that gravity, surface tension and viscous effects can be neglected during the early stages of the motion. Under these assumptions, the initial two-dimensional, potential flow caused by the plate lifting is obtained by using the small-time expansion of the velocity potential. This small-time solution is not valid close to the plate edges, as it predicts there singular flow velocities and unbounded displacements of the water-free surface. It is shown that close to the plate edges the flow is nonlinear and self-similar to leading order. This nonlinear flow is computed by the boundary-element method combined with a time-marching scheme. The numerical time-dependent solution approaches the self-similar local solution with time.

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“…All these methods are based on the theory of complex variables and reduce the problem to one or two integral equations, which are then solved by a numerical method. The solution of this kind of problem with emphasis on blunt bodies was also considered in the framework of matched asymptotic expansions in recent studies [12][13][14][15][16]. In this method, the order of magnitude of the deadrise angle between the body and the x-axis is used as a small parameter of expansion.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric impact between liquid and solid wedges

Semënov

2013

Proc. R. Soc. A.

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The hydrodynamic problem of impact between a solid wedge and a liquid wedge is analysed. The liquid is assumed to be ideal and incompressible; gravity and surface tension effects are ignored. The flow generated by the impact is assumed to be irrotational and therefore can be described by the velocity potential theory. The solution procedure is based on the analytical derivation of the complexvelocity potential in a parameter plane and the function mapping conformally the parameter plane onto the similarity plane. The mapping function is found as a combination of the derivatives of the complex potential in the similarity and parameter planes, through the integral equations for mixed and homogeneous boundary-value problems in terms of the velocity modulus and the velocity angle with the fluid boundary, together with the dynamic and kinematic boundary conditions. These equations are solved through a numerical method. The procedure is first verified through comparisons with some known results. Simulations are then made for a variety of cases, and detailed results are presented in terms of the free surface shape, streamlines, pressure distribution on the wetted solid surface, and contact angles between the free surface and the body surface.

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Initial stage of flat plate impact onto liquid free surface

Cited by 50 publications

References 6 publications

Splash wave and crown breakup after disc impact on a liquid surface

Splash wave and crown breakup after disc impact on a liquid surface

Initial stage of plate lifting from a water surface

Asymmetric impact between liquid and solid wedges

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