Construction of Dimensionless Parameters and Similarity Analysis for Confined Cavities Induced by Hydrodynamic Ram

High-velocity fragment penetration into a liquid-filled container induces hydrodynamic ram (HRAM) and produces an elongated cavity that expands and contracts within the liquid. Container confinement strongly affects cavity evolution, whereas dimensional variables alone cannot clearly distinguish the effect of container size from that of the confinement condition. A dimensionless framework was therefore developed to characterize the peak features of confined cavities in containers of different sizes. A cylindrical-cavity cross-sectional model was adopted, and the fragment kinetic-energy loss per unit penetration length was used to represent the initial energy input. Liquid compression and elastic container expansion were treated as two volume springs connected in series, and a system equivalent bulk modulus was introduced to describe their combined resistance to cavity expansion. The initial inner radius of the container, liquid density, and system equivalent bulk modulus were selected as repeating variables. The fragment energy input, initial pressure difference, elastic volume partitioning, wall inertia, and initial geometric scale were then organized into a dimensionless parameter group. Fragment-impact experiments were conducted using three structurally similar water-filled containers of different sizes. Cavity contours were extracted from high-speed images, and a pixel-slice method was used to obtain the radius history, maximum radius, and time to maximum radius at selected valid cross-sections in the central region of each container. The square cross-sections were converted into equal-area circular cross-sections. The container equivalent bulk modulus was identified by matching the calculated and measured radius histories, and the system equivalent bulk modulus was then determined from the liquid and container moduli. The experimental confined-cavity results were also compared with reference values obtained from an unconfined cylindrical-cavity model. The results show that the dimensionless maximum radius increases approximately linearly with the dimensionless kinetic-energy input. A larger initial pressure-difference ratio produces a smaller dimensionless maximum radius under a comparable energy input because the relative contribution of the initial pressure difference to the total pressure difference increases. The sensitivity of the maximum radius to energy input, represented by the slopes of the grouped linear fits, decreases rapidly at first and then approaches a relatively stable level as the initial pressure-difference ratio increases. In contrast, the dimensionless time to maximum radius exhibits substantially greater dispersion and does not form a stable monotonic relation with energy input. Its variation depends not only on the maximum radius but also on the radial-velocity decay history, including the effects of pressure evolution, wall inertia, and geometric scale. Comparison with the unconfined reference shows that confinement reduces both the maximum radius and the time to maximum radius, but the relative reduction in time is greater. Consequently, the dimensionless average expansion rate is higher under confined conditions, and the difference becomes more pronounced as the container size decreases. The proposed dimensionless framework provides a consistent basis for comparing peak cavity characteristics under different container sizes and confinement conditions and supports similarity analysis of hydrodynamic ram and damage assessment of liquid-filled structures.