Physical investigation of 2d free falling wedge

Abstract

Water entry is an important phenomenon for sea-going vessel in terms of planing and slamming. Pressure distribution on the solid surface, at the moment of impact on water is a critical parameter during the initial design and optimization of a vessel, especially on planing vessels, trawlers or free-fall lifeboats and alike. The aim of this study is to create a simple yet accurate method to aid ship designers on the initial process & optimization of the ship design. Porpoising motion of planing hulls or releasing the free-fall lifeboat from the ship during the emergency situation are perfect two examples of this specific design problem. During this specific water impact event, none of the vessels shall suffer any kind of damage which results in either structural failure on the said vessel or injuries/death of persons onboard. It is fair to say that this specific design factor has its importance to this date. Starting from this point of view, for the easiness of the calculations a wedge shape is taken into account for both planing vessels and trawlers & fishing vessels. This wedge shape can be considered as similar to planing hulls, small craft such as trawlers or free-fall lifeboats. Based on Wagner's famous method for calculating pressure distribution and pile-up of water on plates, this study proposes a new method using Schwarz-Christoffel conformal mapping to calculate pressure distribution along the surface as well as pile-up of water and force history. At the beginning, the definition between mapping plane and real plane is presented. By doing this, pile-up coefficients are calculated. Based on the Wagner's flat plate theory, the pile-up coefficients are plotted from 0 degrees of deadrise to 90 degrees deadrise, where 0 degrees deadrise is a flat plate. The results are further compares against Mei's results [17], which are not only improving the Wagner's fixed pile-up coefficient but also found by similar conformal mapping method. Upon calculating the pile-up coefficient, this coefficient incorporated into existing empirical methods for individual usage. Then, conformal mapping calculations are continued to plot pressure distribution along the wedge. The pressure distribution values are compared against Yettou's Experiment [15], Oien's Experiment [54], Sun's Results [36] and Dong's Experiment [20]. These experiments consist of respectively 25 degrees of deadrise, 30 degrees of deadrise, 10 degrees of deadrise and 45 degrees of deadrise. The results are very well matching. Upon completion of comparison, the force history is calculated. The force history is compared against Sun's results, which are consisting of four different impact speeds. It is found some overestimation on the force history, but in general results are satisfactory. As an additional verification, comparison against real ship sections was also examined. This proposed method can be expressed on monotonic sections. Based on this method of application, alternative sections were proposed against real ship sections and comparison for slamming pressure is conducted. Results were discussed accordingly. Lastly, a comparison against CFD application is done. The results are shown as very well matching. By doing this, presented method in this study was compared against drop test experiments, real ship sections and CFD application all together. It is accuracy proved in all aspects. In conclusion, the aim is considered to be achieved by presenting pressure distribution and force history results by making different comparisons. This study provides an easy method to calculate this critical design factor. It is noted that the method is very accurate for initial impact loads and can be used in initial design stage to understand the loads and pressure along the ship section.