Water entry of a wedge with rolled-up vortex sheet

Semënov, Yu. A.; Wu, G.X.

doi:10.1017/jfm.2017.766

Cited by 8 publications

(5 citation statements)

References 27 publications

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“…From Bernoulli's equation (or, in the unsteady cases, the Cauchy-Lagrange integral) in the bulk, this implies that the pressure must be bounded as well. When t > 0, in the problem of a plate suddenly moving in its normal direction, the vortex will be shed from the edge, which leaves the plate tangentially (Jones 2003;Semenov & Wu 2018) provided the KJ condition is satisfied. In the water entry problem, on the other hand, it is directly assumed (e.g.…”

Section: The Kutta-joukowsky Conditionmentioning

confidence: 99%

Flat plate impact on water

Mayer

Krechetnikov

2018

J. Fluid Mech.

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While the classical problem of a flat plate impact on a water surface at zero dead-rise angle has been studied for a long time both theoretically and experimentally, it still presents a number of challenges and unsolved questions. Hitherto, the details of the flow field – especially at early times and close to the plate edge, where the classical inviscid theory predicts a singularity in the velocity field and thus in the free surface deflection, so-called ejecta – have not been studied experimentally, which led to mutually contradicting suppositions in the literature. On one hand, it motivated Yakimov’s self-similar scaling near the plate edge. On the other hand, a removal of the singularity was previously suggested with the help of the Kutta–Joukowsky condition at the plate edge, i.e. enforcing the free surface to depart tangentially to the plate. In the present experimental study we were able to overcome challenges with optical access and investigate, for moderate Reynolds ($0.5<Re<25\,000$) and Weber ($1<We<800$) numbers, both the flow fields and the free surface dynamics at the early stage of the water impact, when the penetration depth is small compared to the plate size, thus allowing us to compare to the classical water impact theory valid in the short time limit. This, in particular, enabled us to uncover the effects of viscosity and surface tension on the velocity field and ejecta evolution usually neglected in theoretical studies. While we were able to confirm the far-field inviscid and the near-edge Stokes theoretical scalings of the free surface profiles, Yakimov’s scaling of the velocity field proved to be inapplicable and the Kutta–Joukowsky condition not satisfied universally in the studied range of Reynolds and Weber numbers. Since the local near-edge phenomena cannot be considered independently of the complete water impact event, the experiments were also set up to study the entirety of the water impact phenomena under realistic conditions – presence of air phase and finite depth of penetration. This allowed us to obtain insights also into other key aspects of the water impact phenomena such as air entrapment and pocketing at the later stage when the impactor bottoms out. In our experiments the volume of trapped air proved not to decrease necessarily with the impact speed, an effect that has not been reported before. The observed fast initial retraction of the trapped air film along the plate bottom turned out to be a consequence of a negative pressure impulse generated upon the abrupt deceleration of the plate. This abrupt deceleration is also the cause of the subsequent air pocketing. Quantitative measurements are complemented with basic scaling models explaining the nature of both retraction of the trapped air and air pocket formation.

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Section: The Kutta-joukowsky Conditionmentioning

confidence: 99%

Flat plate impact on water

Mayer

Krechetnikov

2018

J. Fluid Mech.

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“…Experiments performed by Judge, Troesch & Perlin (2004) on the vertical/oblique impact of a tilted wedge on a water surface illustrated the effects of the wedge's initial velocity ratio and the level of asymmetry from the vertical axis at its vertex on the symmetry of the spray root propagation as well as on the flow separation from the wedge's surface. Mathematical models for the water entry of an asymmetric wedge are developed in studies such as Semenov & Iafrati (2006) and Semenov & Wu (2018). Breton, Tassin & Jacques (2020) performed an experimental study on the vertical water entry/exit of axisymmetric bodies.…”

Section: Introductionmentioning

confidence: 99%

The controlled impact of elastic plates on a quiescent water surface

Wang

Wong

et al. 2022

J. Fluid Mech.

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The impact of flexible rectangular aluminum plates on a quiescent water surface is studied experimentally. The plates are mounted via pinned supports at the leading and trailing edges to an instrument carriage that drives the plates at constant velocity and various angles relative to horizontal into the water surface. Time-resolved measurements of the hydrodynamic normal force ( $F_n$ ) and transverse moment ( $M_{to}$ ), the spray root position ( $\xi _r$ ) and the plate deflection ( $\delta$ ) are collected during plate impacts at 25 experimental conditions for each plate. These conditions comprise a matrix of impact Froude numbers ${Fr} = V_n(gL)^{-0.5}$ , plate stiffness ratios $R_D= \rho _w V_n^2 L^3D^{-1}$ and submergence time ratios $R_T= T_sT_{1w}^{-1}$ . It is found that $R_D$ is the primary dimensionless ratio controlling the role of flexibility during the impact. At conditions with low $R_D$ , maximum plate deflections on the order of $1$ mm occur and the records of the dimensionless form of $F_n$ , $M_{to}$ , $\xi _r$ and $\delta _c$ are nearly identical when plotted vs $tT_s^{-1}$ . In these cases, the impact occurs over time scales substantially greater than the plate's natural period, and a quasi-static response ensues with the maximum deflection occurring approximately midway through the impact. For conditions with higher $R_D$ ( $\gtrsim 1.0$ ), the above-mentioned dimensionless quantities depend strongly on $R_D$ . These response features indicate a dynamic plate response and a two-way fluid–structure interaction in which the deformation of the plate causes significant changes in the hydrodynamic force and moment.

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“…It is shown in Barjasteh et al [25] that the numerical results without vortex shedding by Xu et al [7] are in good agreement with the experimental data for the water entry of asymmetric wedges. Semenov and Wu [26] did include the vortex sheet from the tip of a wedge in their mathematical model. It was found that the effect of vortex was confined in a small local region, and the overall pressure distribution in other places is not significantly affected and the effect on the free surface is hardly visible.…”

Section: Introductionmentioning

confidence: 99%

Free fall water entry of a wedge tank into calm water in three degrees of freedom

Sun

2019

Applied Ocean Research

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The hydrodynamic problem of a two dimensional wedge tank filled with liquid entering a calm water surface is analysed based on the incompressible velocity potential theory. The motion effect of inner liquid on the entry process is investigated through comparison with the result containing equivalent solid mass or the liquid being frozen. The problem is solved through the boundary element method in the time domain. Two separated computational regions are constructed. One is the inner domain for the internal liquid, and the other is the outer open domain for the open water. The former is solved in the physical coordinate system, and the latter is solved in a stretched coordinate system. The solutions of two separated domains are connected through the motion of the body. The auxiliary function method is extended to decouple the nonlinear mutual dependence between fluid loads from two separated domains and the body motion. Detailed results for wedge motion, external impact pressure and free surface, and for internal pressure, free surface deformation and liquid motion are provided. Through comparison with the results of a wedge tank with frozen ice, in-depth discussion on the effect of the inner liquid is provided.

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Water entry of a wedge with rolled-up vortex sheet

Cited by 8 publications

References 27 publications

Flat plate impact on water

Flat plate impact on water

The controlled impact of elastic plates on a quiescent water surface

Free fall water entry of a wedge tank into calm water in three degrees of freedom

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