Development of a generalized scaling law for underwater explosions using a numerical and experimental parametric study

In order to reduce enormous cost of real-scale underwater explosion experiments on ships, the mechanical response of the ships have been analyzed by combining scaled-down experiments and Hopkinson's scaling law. However, the Hopkinson's scaling law is applicable only if all variables vary in an identical ratio; for example, thickness of ship, size of explosive, and distance between the explosive and the ship should vary with same ratio. Unfortunately, it is infeasible to meet such uniform scaling requirement because of environmental conditions and limitations in manufacturing scaled model systems. For the facile application of the scaling analysis, we propose a generalized scaling law that is applicable for non-uniform scaling cases in which different parts of the experiments are scaled in different ratios compared to the real-scale experiments. In order to establish such a generalized scaling law, we conducted a parametric study based on numerical simulations, and validated it with experiments and simulations. This study confirms that the initial peak value of response variables in a real-scale experiment can be predicted even when we perform a scaled experiment composed of different scaling ratios for each experimental variable.