A high precision instantaneous detonation model (hp-IDM) for condensed energetic materials and its application in underwater explosions

• Published in: Journal of applied physics 2024-07, Vol.136 (4)
• Main Authors: Yu, Jun, Wang, Jun, Zhang, Xian-pi, Hao, Yi, Jiang, Xiong-wen, Shen, Chao
• Format: Article
• Language: English
• Subjects: Accuracy; Curve fitting; Detonation waves; Discretization; Dynamic structural analysis; Energetic materials; Exact solutions; Image reconstruction; Polynomials; Rarefaction; Runge-Kutta method; Self-similarity; Shaped charges; Structured grids (mathematics); Underwater explosions; Wave propagation
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/5.0220493

The utilization of underwater explosion prediction programs incorporating explosives is not widespread in engineering at present, primarily due to the complexity associated with the detonation reaction process. The instantaneous detonation model (IDM) serves as a valuable tool for simulating underwater explosions due to its efficiency in engineering applications, disregarding the detonation reaction process. However, existing analytical solutions for the distribution of detonation gaseous products, based on the assumption of 1D isentropic flow, have limitations in accuracy. Moreover, alternative IDM approaches have not gained widespread recognition. In this study, we present a novel IDM, termed hp-IDM, which predicts fluid structure in the detonation zone using high-order solutions derived from the Detonation Shock Dynamics (DSD) model. The spatial aspect of the DSD model is discretized using fifth-order weighted essentially non-oscillatory reconstruction in characteristic space and Lax–Friedrich's splitting, while temporal terms are discretized via a third-order total variation diminishing Runge–Kutta scheme. Interface motion is captured using the level-set method combined with the modified ghost fluid method model, and a programmed burn model describes the generation and propagation of the detonation wave. We validate the self-similarity of detonation wave propagation using the DSD model and derive quantitative calculation formulas for the IDM by averaging or curve fitting dimensionless results. Subsequently, the hp-IDM model is established through high-order polynomial approximation of the Taylor rarefaction zone and the constant static zone for 1D planar, cylindrical, and spherical TNT charges. The application of the hp-IDM model involves direct mapping from the radial direction to spatial structured grids for 1D planar, 2D cylindrical, and 3D spherical shaped charges. Numerical results demonstrate that the hp-IDM model proposed in this paper achieves both high accuracy and computational efficiency.