# A Numerical Simulation of the Underwater Supersonic Gas Jet Evolution and Its Induced Noise
## 1 Introduction  
Underwater high-speed gas jet technology has broad application prospects in areas such as ocean resource exploitation and the design of underwater weapon systems. The underwater jet propulsion system has a simpler structure and higher propulsion efficiency compared to traditional propeller propulsion methods [1]. However, a profound understanding of the intricate jet flow fields and noise characteristics is indispensable to designing a high-speed, efficient, stable, and low-noise underwater jet propulsion system. The main challenge lies in the complex interaction between the high-temperature, high-pressure gas jet and the significantly denser water. Early underwater high-speed gas jet research focused on experimental measurements and theoretical analyses. Unlike a low-speed jet, where the bubbles break and rise at the nozzle outlet under the action of gravity or density differences [2], an underwater high-speed gas jet usually starts to break up and spray downstream from the jet. [PERSON] et al. [3] experimentally studied the transition of a high-speed underwater jet from bubbles to a jet; [PERSON] et al. [4] observed that the jet changed from bubbles to a jet near the sonic point; and [PERSON] et al. [5] attributed this phenomenon to compressibility effects, surmising that the temporal and spatial growth rates of the disturbance increased with an increase in the subsonic gas velocity. The disturbance growth rate also peaked when it reached the speed of sound, after which it decreased rapidly to zero with increasing gas velocity. [PERSON] et al. [6] established a two-dimensional underwater high-speed gas jet experimental system to study the instability of subsonic and supersonic jets. [PERSON] et al. [7] measured the spatial and temporal changes in the jet boundary directly through high-speed imaging. They found that the large density difference between the gas and water led to the enhancement of turbulent mixing, shortened jet kernel, and a relationship between the jet stability and Mach number. Owing to the challenges of observing the complex underwater high-speed jet processes, traditional experimental methods can be costly, and capturing detailed flow information can be difficult. Consequently, numerical simulations have become increasingly important for their study. However, the numerical simulation of a three-dimensional underwater supersonic jet takes time and has poor stability. Most of the numerical simulations use two-dimensional axisymmetric assumptions, the research content covering the thrust characteristics of the engine [8; 9; 10; 11], the structure of the jet wave system [12], the development of the gas-liquid interface [9; 11; 13; 14; 15], and the jet instability [14; 15; 16], which provides a theoretical basis for the flow process of underwater high-speed jets. Considering that a two-dimensional axisymmetric jet cannot precisely capture the influence of three-dimensional fluid motion on the air-liquid interface, [PERSON] et al. [17] used the delayed detached eddy simulation (DDES) turbulence model to study the effect of different environmental densities on a supersonic jet. They found that the turbulence intensity at the air-liquid interface increased considerably with an increase in fluid density, resulting in poorer jet stability. Regarding the noise characteristics of underwater gas jets, the noise from low-speed jets is primarily caused by bubbles [18; 19; 20; 21; 22]. However, based on the research conducted by [PERSON] et al. [23], who used a large eddy simulation (LES) to analyze the flow structure and noise radiation of underwater supersonic jets, the noise generated by high-speed jets originated primarily from the shockwave structure of the jet. In this study, three-dimensional unsteady numerical simulations of underwater supersonic gas jets were performed using LES. The noise characteristics of the jet were analyzed using the Ffowcs Williams-Hawkings (FW-H) model [24], which was compared with the experimental noise data to validate the accuracy of the numerical method.