Scaling law of deep-sea trinitrotoluene (TNT) explosion

Understanding the dynamic characteristics of deep-sea explosions is essential to improve the survivability and combat capability of deep-sea equipment. In this paper, by considering the practical underwater conditions, we investigated the mechanical effects of the deep-sea 1-kg-trinitrotoluene (TNT) explosion with charge depths ranging from 1 to 10 km through numerical simulation and dimensional analysis. The shock wave overpressure, the positive overpressure pulse, the bubble pulse, and the energy distribution for various depth explosions were analyzed systematically. The simulation results showed that the charge depth was negligible for the peak overpressure of the shock wave. However, the positive overpressure pulse, the shock wave energy, the maximum bubble radius, the bubble energy, and the bubble period decrease significantly with increasing the charge depth. Then, the dimensional analysis for deep-sea TNT explosion was performed to reveal the key dimensionless parameters, from which the scaling laws of the shock wave overpressure and the overpressure pulse were obtained. By fitting the simulation results, the dimensionless equations were proposed, providing an effective method for predicting the peak overpressure and the positive overpressure pulse of shock wave for underwater TNT explosion over a wide range of water depths.