A.A. Korobkin

Hydroelastic behaviour of compound floating plate in waves

The paper deals with the plane problem of the hydroelastic behaviour of floating plates under the influence of periodic surface water waves. Analysis of this problem is based on hydroelasticity, in which the coupled hydrodynamics and structural dynamics problems are solved simultaneously. The plate is modeled by an Euler beam. The method of numerical solution of the floating-beam problem is based on expansions of the hydrodynamic pressure and the beam deflection with respect to different basic functions. This makes it possible to simplify the treatment of the hydrodynamic part of the problem and at the same time to satisfy accurately the beam boundary conditions. Two approaches aimed to reduce the beam vibrations are described. In the first approach, an auxiliary floating plate is added to the main structure. The size of the auxiliary plate and its elastic characteristics can be chosen in such a way that deflections of the main structure for a given frequency of incident wave are reduced. Within the second approach the floating beam is connected to the sea bottom with a spring, the rigidity of which can be selected in such a way that deflections in the main part of the floating beam are very small. The effect of the vibration reduction is quite pronounced and can be utilized at the design stage.

Trapping of air in impact between a body and shallow water

Near-impact behaviour is investigated for a solid body approaching another solid body with two immiscible incompressible viscous fluids occupying the gap in between. The fluids have viscosity and density ratios which are extreme, the most notable combination being water and air, such that either or both of the bodies are covered by a thin film of water. Air-water interaction and the commonly observed phenomenon of air trapping are of concern in the presence of the two or three thin layers and one or two interfaces. The subcritical regime is of most practical significance here and it leads physically to the effect of inviscid water dynamics Coupling With a viscous-dominated air response locally. This physical mechanism induces touchdown (or an approach to touchdown), which IS found to occur in the sense that the scaled air-gap thickness shrinks towards zero within a finite scaled time according to analysis performed hand in hand with computation. A global influence oil the local touchdown properties is also identified. Comparisons With computations prove favourable. Air trapping is produced between two touchdown positions, at each of which there is a pressure peak; an oblique approach Would not affect the finding unless the approach itself Is extremely shallow. The mechanism of air-water interaction leading to air trapping is suggested as a quite wide-ranging result.

Shallow-water impact problems

Impact by a box-like structure onto shallow water is analysed with the help of asymptotic methods. The analysis is based on both the asymptotic approach by Korobkin [1], which was derived originally for blunt-body impact, and the experimental results by Bukreev [2]. The flow region is divided into six parts: the region beneath the entering body, the region close to the bottom edge, the region of inertial flow of the liquid, the jet root, the splash jet and outer region. The flows inside each of the subdomains have their own peculiarities and are analysed separately. The matching conditions make it possible to obtain a uniformly valid asymptotic solution of the impact problem. The main attention is paid to the flow patterns and pressure distributions. It was found that the pressure inside the jet root can be comparable with the pressure beneath the entering body and can even exceed it. The effects of the shape of the body bottom and of the body flexibility on the liquid flow and the pressure distribution are investigated.

Asymptotic theory of liquid–solid impact

The liquid–solid impact problem is analysed with the help of the method of matched asymptotic expansions. This method allows us to estimate the roles of different effects (viscosity of the liquid, surface tension, compressibility, nonlinearity, geometry) on the impact, to distinguish the regions of the flow and the stages of the impact, where and when each of these effects is of major significance, to present a complete picture of the flow, and describe approximately such phenomena as jetting, escape of the shock onto the liquid–free surface and cavitation. Five stages of the impact are distinguished: supersonic stage, transonic stage, subsonic stage, inertia stage and the stage of developed liquid flow. The asymptotic analysis of each stage is based on general principles of hydrodynamics and will be helpful to design experiments on liquid impact and to develop an adequate computational algorithm, as well as to understand the dynamics of the process.

Blunt-body impact on a compressible liquid surface

In this paper we are concerned with the unsteady plane liquid motion due to the penetration of a blunt undeformable contour through the free surface. Initially the liquid is at rest, and the contour touches its free surface at a single point. At the initial stage of the process the liquid motion is described within the framework of the acoustic approximation. It is known that, just behind the shock front which is generated under the impact, the liquid motion does not depend on the presence of the free surface for all time

Initial stage of flat plate impact onto liquid free surface

The liquid flow and the free surface shape during the initial stage of flat plate impact onto liquid half-space are investigated. Method of matched asymptotic expansions is used to derive equations of motion and boundary conditions in the main flow region and in small vicinities of the plate edges. Asymptotic analysis is performed within the ideal and incompressible liquid model. The liquid flow is assumed potential and two dimensional. The ratio of the plate displacement to the plate width plays the role of a small parameter. In the main region the flow is given in the leading order by the pressure-impulse theory. This theory provides the flow field around the plate after a short acoustic stage and predicts unbounded velocity of the liquid at the plate edges. In order to resolve the singular flow caused by the normal impact of a flat plate, the fine pattern of the flow in small vicinities of the plate edges is studied. It is shown that the initial flow close to the plate edges is self-similar in the lead...

Impact of two bodies one of which is covered by a thin layer of liquid

The paper deals with the plane unsteady problem of the collision of two rigid undeformable and shallow surfaces, one of which is covered by a thin layer of an ideal incompressible liquid. At the initial instant of time, a dry surface touches the liquid free boundary at a single point and then starts to penetrate the liquid layer. The flow region is divided into four parts : the region beneath the entering surface, the jet root, the spray jet and outer region. Inside each of those subdomains the flow patterns have their own peculiarities and are analysed separately. The matching conditions allow us to obtain the uniformly valid asymptotic solution of the original problem. The relative body motion and the characteristics of the spray jets generated under the impact are determined. The condition on the shapes of the bodies, under which the velocity of the impact of the rigid surfaces is non-zero, is derived. The plane unsteady problem of the collision of two rigid shallow surfaces one of which is covered by a liquid is considered. Examples of processes of this kind can be found in machinery engineering where impacted surfaces (for example, driving wheels) are usually covered by a thin layer of oil, and in the problem of crane operation in a dock. Another example is connected with the natural catastrophe of a huge solid mass falling into a lake from an adjacent mountain. Dr E. Baba (1994, personal communication) reported ‘About 200 years ago in Shimabara of Nagasaki (Japan) a hugh solid mass, which was a part of mountain (Mau-yama) fell into shallow bay (Ariake-bay) due to an earthquake. As a result, many people living at opposite coast of the bay were killed due to tsunami (soliton)’. The closely related problem of large water waves generated by landslides was analysed numerically by Harbitz, Pedersen & Gjevik (1993). A review of a large number of Norwegian events associated with rock slides into fjords and lakes is given by J~rstad (1968). The wave generated by the fall can be very dangerous, especially for dams and power stations. The possibility of this catastrophe has to be taken into account by designers. A sketch of the flow is shown in figure 1. Initially the liquid is at rest and occupies a region -h-f,(x) = 0 andfl(x) > 0 where x += 0. A shallow rigid surface (y =fi(x)) touches the free liquid boundary (y = -f;(x)) at a single point taken as the origin of the Cartesian coordinate system xOy. At some instant of time, taken as the initial one (t = 0), the body begins to penetrate the liquid, the initial impact velocity being V,. The position of the entering body at an instant t is given by y =fi(x)-s(t), where s(t) is the penetration depth. We shall determine the liquid flow, its boundary geometry and the body motion up to the moment T of the contact between the solid surfaces under the following assumptions : (i) the solid

Energy distribution from vertical impact of a three-dimensional solid body onto the flat free surface of an ideal fluid

Abstract Hydrodynamic impact phenomena are three dimensional in nature and naval architects need more advanced tools than a simple strip theory to calculate impact loads at the preliminary design stage. Three-dimensional analytical solutions have been obtained with the help of the so-called inverse Wagner problem as discussed by Scolan and Korobkin in 2001. The approach by Wagner provides a consistent way to evaluate the flow caused by a blunt body entering liquid through its free surface. However, this approach does not account for the spray jets and gives no idea regarding the energy evacuated from the main flow by the jets. Clear insight into the jet formation is required. Wagner provided certain elements of the answer for two-dimensional configurations. On the basis of those results, the energy distribution pattern is analysed for three-dimensional configurations in the present paper.

Hydrodynamic loads during early stage of flat plate impact onto water surface

The hydrodynamic loads during the water entry of a flat plate are investigated. Initially the water is at rest and the plate is floating on the water surface. Then the plate starts suddenly its vertical motion. The analysis is focused on the early stage during which the highest hydrodynamic loads are generated. The liquid is assumed ideal and incompressible; gravity and surface tension effects are not taken into account. The flow generated by the impact is two dimensional and potential. The penetration depth is either a given function of time or calculated by using the equation of the body motion. A theoretical estimate of the loads during the early stage of the water impact is derived with the help of the method of matched asymptotic expansions. The ratio of the plate displacement to the plate half-width plays the role of a small parameter. The second-order uniformly valid solution of the problem is derived. In order to evaluate the hydrodynamic loads, the second-order pressure distribution is asymptotic...

Wave impact on the center of an Euler beam

The problem of a symmetric wave impact on the Euler beam is solved by the normal modes method. The liquid is supposed to be ideal and incompressible. The initial stage of impact when hydrodynamic loads are very high and the beam is wetted only partially is considered. The flow of a liquid and the size of the wetted part of the body are determined by the Wagner approach with a simultaneous calculation of the beam deflection. The specific features of the developed numerical algorithm are demonstrated and the criterion of its stability is specified. In addition to a direct solution of the problem, two approximate approaches within the framework of which the dimension of the contact region is found ignoring the deformations of the plate are considered.