The development of analytical theory and experimental methods for understanding the correlation between the explosive properties and bubble dynamic characteristics in underwater explosions has important engineering application value for underwater weapons and ships. Based on the assumption of an instantaneous explosive detonation, we introduced the Jones–Wilkins–Lee equation of state to describe the high-pressure state in an explosion bubble and established the initial conditions for the bubble dynamics calculations. Considering the high-Mach-number flow and high pressure at the initial boundary of the explosion bubble, the Lezzi–Prosperetti equation with second-order Mach accuracy was used. Thus, an analytical model and a calculation method of the explosion bubble dynamics for an explosive detonation were established. This direct link between the detonation parameters and the bubble features is significant for the subtle design, selection, and optimization of explosives' properties. A micro-equivalent explosive bubble pulsation experiment was carried out in a water tank using a customized experimental system, which can offer nearly boundary-free condition to mitigate the reflective wave effects on bubbles. Three types of explosives were used in the experiment: the Research Department explosive (RDX), the Pentaerythritol tetranitrate (PETN), and the Hexanitrohexaazaisowurtzitane (CL20). Finally, the experimental results and the practicability of the experimental system were analyzed. The influence of the explosive type on the dynamic characteristics of the explosion bubbles and the differences between the theoretical and experimental results were compared. The results showed that the proposed explosion bubble dynamics model and calculation method have high accuracy and practicability. The proposed model can be used for explosives with known detonation parameters and equation of state parameters. The detonation parameters, velocity, and pressure are linked to the bubble features pulsation period and the maximum radius directly. The designed experimental system, which is capable of simulating an infinite water for the explosion of micro-equivalent explosives, was stable and easy to use. The work is significant for the subtle design, selection, and optimization of explosives' properties.

The dynamic behaviors of underwater explosion bubbles differ for different explosives. The explosive characteristic parameters will result in a greater impact on the motion characteristics of the bubbles. Based on the bubble dynamics equation established by Prosperetti and Lezzi [“Bubble dynamics in a compressible liquid. Part 1. First-order theory,” J. Fluid Mech. 168, 457âĂŞ-478 (1986); “Bubble dynamics in a compressible liquid. Part 2. Second-order theory,” J. Fluid Mech. 185, 289âĂŞ-321 (1987)], we proposed an initial condition and an equation of state (EOS) form applicable for calculating the underwater explosion bubble dynamics of different explosives. With the assumption of instantaneous detonation and initial shock wave formation at the gas–liquid boundary, we calculated the initial state of the bubble boundary and established the initial condition for calculating explosion bubbles. Using the Jones–Wilkins–Lee EOS for different explosives, we constructed an isentropic EOS with a polytropic exponent that varied with density. We calculated and analyzed the differences in the initial expansions and the subsequent oscillations of underwater explosion bubbles with different explosives as well as the effects of different explosive parameters on the explosion bubble dynamics. This study showed that the proposed initial condition and the EOS form with a polytropic exponent that varied with density yielded good calculation accuracy and achieve close association of the underwater explosion bubbles with the properties of the explosive detonation and the characteristics of the detonation products. In addition, the explosion bubbles differed in the initial expansion, where the bubbles produced by explosives with higher densities and greater detonation velocities expanded more rapidly.

In this paper, the effects of the water depth on the overpressure (pressure difference between positive shock pressure and hydrostatic pressure) peak and energy of underwater explosion shock waves were analyzed. Two quantitative calculation models were established that accounted for the effect of the water depth, which have theoretical and practical engineering value. A simulated deepwater explosion tank test was first conducted to obtain experimental data of the overpressure peaks and energies of the explosion shock waves generated by 10 and 30 g trinitrotoluene (TNT) explosives in a simulated environment at water depths of 400, 500, and 600 m. A one-dimensional wedge-shaped Euler grid numerical model was established to simulate the underwater explosion using the Autodyn software. The simulation model was validated by the experimental data to prove its accuracy and rationality. Then, numerical simulations were carried out at 13 operating conditions with 30 g of TNT in a full water depth range of 0–5000 m. Based on the simulation data analysis, the calculation models of the overpressure peak and energy flow density of the underwater explosion shock wave were obtained, which contain water depth correction functions. The results show that both the overpressure peak and the shock wave energy decreased with increase in the water depth, but the reduction percentage of the overpressure peak with the water depth was very small. The overpressure peak and energy flow density of the shock wave agreed with the explosion similarity law at all fixed water depths. The proposed calculation models have practical engineering value and generalization ability.

To calculate the near-field shockwave propagation of underwater explosions for different explosives quickly and accurately, an improved calculation model, based on the Kirkwood–Bethe theory, is proposed. Based on the detonation theory and shock jump conditions, the model establishes initial equilibrium conditions and an initial shockwave-front state of the explosion bubble interface. By incorporating a second-order Mach-precision bubble dynamics equation, the model determines the physical parameters and enthalpy change functions at the initial expanding stage in real time. By solving the isentropic flow of the enthalpy change function G at varying delay times, a functional relation was established between the enthalpy change function and the pressure at arbitrary flow points and times. The model obtained the near-field shockwave-front peak-pressure spatial distributions of underwater explosions and the pressure decay time constants at arbitrary flow points. The results indicated that the proposed method can quickly and accurately determine the near-field shockwave propagation of underwater explosions for different explosives, with satisfactory agreement with experimental data. The proposed method relates the explosive detonation, explosion bubble expansion, and shockwave propagation, thus connecting the explosive parameters with the shockwave front state parameters.

Traditional computational fluid dynamics (CFD) techniques deduce the dynamic variations in flow fields by using finite elements or finite differences to solve partial differential equations. CFD usually involves several tens of thousands of grid nodes, which entail long computation times and significant computational resources. Fluid data are usually irregular data, and there will be turbulence in the flow field where the physical quantities between adjacent grid nodes are extremely nonequilibrium. We use a graph attention neural network to build a fluid simulation model (GAFM). GAFM assigns weights to adjacent node-pairs through a graph attention mechanism. In this way, it is not only possible to directly calculate the fluid data but also to adjust for nonequilibrium in vortices, especially turbulent flows. The GAFM deductively predicts the dynamic variations in flow fields by using spatiotemporally continuous sample data. A validation of the proposed GAFM against the two-dimensional (2D) flow around a cylinder confirms its high prediction accuracy. In addition, the GAFM achieves faster computation speeds than traditional CFD solvers by two to three orders of magnitude. The GAFM provides a new idea for the rapid optimization and design of fluid mechanics models and the real-time control of intelligent fluid mechanisms.