Scaling law for Rayleigh-Taylor instability of aluminum tube under cylindrical implosion

Abstract

The Rayleigh-Taylor instability (RTI) in metals with convergent geometry is of considerable importance in both scientific research and engineering applications, where the key issue is to accurately describe the dynamics of interface perturbation. However, the complex interplay of multiple physical factors has impeded a comprehensive understanding of RTI growth mechanisms. In this study, we investigated the RTI behavior of aluminum tube (liner) under cylindrical implosion by using a combination of dimensional analysis, experiments, and numerical simulations. The essential dimensionless parameters governing the RTI evolution, namely the perturbation amplitude and growth rate, were identified through dimensional analysis, leading to the derivation of the geometrical scaling law for the dimensionless growth rate of RTI. Thereafter, magnetically driven implosion experiments and numerical simulations were carried out to validate the geometrical scaling laws and examine the influence of the dimensionless parameters on the growth rate. By fitting the simulation results, the power-law relationships were established between the dimensionless growth rate and various factors, including loading intensity and duration, initial perturbation amplitude and wavelength, as well as liner radius and thickness. Furthermore, an empirical formula was proposed to predict the dimensionless growth rate of RTI under cylindrical implosion, which shows comparable accuracy to the simulation results. This study provides an effective approach for the analysis of cylindrical RTI in metals, and serves as a valuable guidance for optimizing the design of magnetically driven implosion experiments.