Initial stage of plate lifting from a water surface

Abstract

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.

Experimental investigation of the water entry and/or exit of axisymmetric bodies

“…Following the theoretical work of Korobkin et al (2017b) who showed that the quantity 1 − c(t)/c 0 was proportional to [h(t)/c 0 ] 2/3 during the water exit of a flat plate at constant acceleration, the experimental results obtained in Froude similarity are depicted in figure 28 in terms of the quantity 1 − c(t)/c 0 . One can see that the results compare very well with the power law predicted by Korobkin et al (2017b) (but with a different coefficient) for h(t)/c 0 ranging from 0.1 to 0.7. This agreement is somewhat surprising given the influence of gravity in our experiments (see figure 17) and the rather different motion imposed to the cone.…”

Hydroelastic effects during the fast lifting of a disc from a water surface

“…At longer times, when the contact line detaches from the edge and recoils, its position can be related to the instantaneous displacement of the plate edge, h e (t), using the ideas of Korobkin et al (2017b). In that paper, the authors found a self-similar solution to describe the dynamics of the free surface close to the edge of a plate lifted from the water surface at a large constant acceleration.…”

“…The model was developed further to be included in the two-dimensions-plus-time analysis of aircraft ditching. Korobkin et al (2017b) presented another model of water exit, which is based on a small-time asymptotic solution of the two-dimensional problem of a plate lifted suddenly from the water surface and the method of matched asymptotic expansions. A similar model was developed by Iafrati & Korobkin (2008) for water impact problems.…”

“…In section 3, the relation between the measured force and acceleration is compared to that predicted by the linearised theory of water exit of Korobkin (2013). Furthermore, the motion of the contact line is used to validate some results reported in Korobkin et al (2017b). In section 4, we present a generalised linear theory of water exit that takes into account elastic effects in the motion of the plate.…”

Preface to the sixth special issue on “Practical Asymptotics”

“…The cost of computational studies may prohibit numerical simulations at a number of parameter values which limits, for example, the optimization of prototypes. There still exists a number of practical problems which are tractable for approximate analytical methods but inaccessible to computation.The special issue invites research articles addressing the following problems: drag coefficients in low Reynolds number flow [6], ice formation on a cold surface due to the impact of a supercooled water droplet [7], droplet impacts with a porous medium [8], the propagation of fronts in a discrete reaction-diffusion equation [9], fluidsolid interactions [10] and geothermal heat exchangers [11]. The analyses comprise a range of perturbation methods, including a hybrid asymptotic-numerical method, matched asymptotic expansion and WKBJ methods, all of which demonstrate the importance of asymptotics in real-world applications.…”