# Numerical Simulation of Vacuum Leak Jet and Jet Noise
## 1 Introduction  
On April 19, 1971, the world's first space station, Salyut 1, was successfully launched into orbit, marking the arrival of space age. In the following decades, the U.S. Skylab, the Mir Space Station, and the International Space Station (ISS) were successively built and continuously developed, becoming the base of deep space exploration. However, continuously growing space debris increases collision probability among space debris and spacecrafts, which has caused widespread international concerns [1]. It was reported that many leak accidents occurred on the ISS [2], leading to an urgent demand of on-orbit leak detection. The differential pressure method [3] has been widely used on the pressure vessels of spacecrafts to detect the occurrence of leak. However, it cannot give the leak location. In order to locate the leak-induced noise source, on-orbit sensing technology based onacoustic emission has drawn widespread attention due to its low resource occupancy, little structural constraints and real-time monitoring [4]. In order to verify the effectiveness of the acoustic emission technology, the European Space Agency (ESA) conducted verification tests on the experimental cabin of the ISS [5]. Furthermore, a handheld ultrasonic leak detector developed by National Aeronautics and Space Administration (NASA) has been successfully applied to leak detection in orbit [6]. The current acoustic emission leak detection method is to detect and analyze the 40 KHz ultrasonic signals generated by the vortex structures downstream the leak-induced jet [7]. However, because the leak jet enters the vacuum directly, the acoustic emission signal propagating backwards into the pressure vessels is very weak. Therefore, the focus of the acoustic emission research is mainly concentrated on the characteristics of the structure-borne ultrasonic signals in the pressure vessel skin and the improvement of signal manipulations. [PERSON] and [PERSON] [8] reported propagation characteristics of stress waves in a thin aluminum plate and honeycomb sandwich panel, and then used a sensor network with positioning algorithm to locate high-speed impact sources. [PERSON] et al. [9] studied propagation and reflection mechanisms of low-order Lamb waves in stiffener components and constructed a generalized impedance model, which had good agreement with numerical simulation results. The above researches focused on the propagation mechanism of the leak noise in the cabin skin to provide theoretical supports for leak location. However, neglecting generation mechanisms of the leak noise makes it unable to evaluate and classify the leak source. Physically speaking, the spacecraft's leak noise is a flow-induced noise excited by jet's instability waves. In the research of vacuum jet, [PERSON] and [PERSON] [10] proposed an approximate analytical method to predict the external jet density field in vacuum, with the results agreeing well with the traditional characteristic method. [PERSON] et al. [11] imposed two approximate models to improve the accuracy of solving the parameter distribution, such as density, Mach number. [PERSON] and [PERSON] [12] applied direct simulation of Monte Carlo (DSMC) method for plume impingement and obtained good agreements with experimental data. There are few studies on jet noise in vacuum environment, but the research on jet noise in conventional environment on the ground is more mature. For subsonic jet noise, [PERSON] [13] is a pioneer of aeroacoustic who proposed the theory of acoustic analogy and V\({}^{8}\) law to predict jet noise, which inspires many improved models [14; 15; 16; 17]. [PERSON] and [PERSON] [18] proposed a similarity spectra method. Furthermore, [PERSON] and [PERSON] [19] reported two components of the similarity spectra, one from fine-scale turbulence and the other from large-scale turbulence.