Impact parameters in case of an emergency fall of a body onto a liquid

Introduction. In a number of applied engineering problems, questions related to the impact of massive bodies on water and their motion in the water after the impact often arise. Renowned Russian and international scientists, including L.I. Sedov, M.V. Keldysh, G. Wagner, T. Karman, and others, conducted theoretical and practical research in this area of hydrodynamics.
Problems involving determining the dynamic loads arising in liquid-filled containers when various large objects fall into them often arise during the investigation or prediction of emergency situations. This paper examines the problem of an emergency involving the transportation of a container containing radioactive waste over a spent fuel pool, which is found at all nuclear power plants. The container’s attachment breaks, and it falls into the pool. Determining the loads arising in such a scenario is a mandatory task for all nuclear power plants.

Materials and methods. This paper describes in detail the physical processes accompanying the impact of a heavy, flat-bottomed body on a water surface and formulates general principles for the formation and calculation of hydrodynamic loads arising in a fluid. The feasibility of using the concept of “added mass” in the physical interpretation of this phenomenon is analyzed. The limits of its validity in considering various problems of unsteady hydrodynamics are indicated. The results of model experimental studies aimed at studying the impact pressure arising in water when a heavy, flat-bottomed body falls into it are presented. The well-known Godunov method, based on the problem of the decay of an arbitrary discontinuity, was used in the mathematical description of the hydrodynamic phenomena under consideration. This method allows one to determine the dynamic parameters of pressure and velocity of a fluid in the presence of significant discontinuities in the initial and boundary conditions.

Results. Based on data from model experiments and the results of numerical calculations, the authors identified four main phases of a body’s motion as it falls into a liquid. A series of computational experiments was used to formulate a methodology for determining the time dependence of the added mass involved in the impact. It was shown that when a body impacts water contained in a confined pool, there is a time dependence of the added mass, which is determined by the geometric parameters of the pool. As an example, the paper presents several instantaneous impact pressure profiles generated in a pool when a flat body impacts water. Examples of maximum pressure fields generated in a pool when a massive body impacts water are also given.

Conclusions. Model experiments revealed that the shock pressure generated when a flat body impacts water is significantly lower than predicted by the solution to the problem of the decay of an arbitrary discontinuity. The maximum pressure obtained through calculations is 3–4 times greater than that obtained experimentally. The significant reduction in shock load is caused by the presence of an air gap between the flat bottom of the body and the free surface of the water. The presence of an air bubble (air gap) beneath the body leads to an increased time for the formation of a stable hydrodynamic flow around the body and, consequently, a decrease in the intensity of the shock wave.

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