## 1 Introduction  
Collisions between satellites and space debris are likely to occur given the rapid increase in space debris [1]. The satellite tank is filled with liquid hydrazine, which accounts for a large part of the total mass, and is one of the most vulnerable components to debris impact. When the debris impacts the satellite tank, a shock wave is generated in the liquid hydrazine. Debris penetration and shock wave pressure act on the tank walls, causing catastrophic damage to the tank structure. This phenomenon is known as the hydrodynamic ram effect. Since the 1970s, the hydrodynamic ram effect has been the subject of many investigations. Scholars have focused on the hydrodynamic ram effect caused by the fragment impact on aircraft fuel tanks [2, 3]or ship defensive cabins [4]. The deformation of tank walls, the shock wave pressure, and the velocity attenuation of the fragment have been studied. As the hydrodynamic ram effect involves the shock stage, drag stage, cavity stage, and exit stage [5], it can be complicated to describe each stage in theory. Tests and numerical simulation are the main research methods. [PERSON]. [6] performed a series of tests where a tungsten projectile, steel projectile, and aluminum projectile were shot into a liquid-filled tank at the velocities of 341 m/s, 389 m/s, and 455 m/s. The shock wave pressures at different positions were measured. [PERSON] et al. [7] carried out tests in which projectiles weighting 3.5 g and 7 g were accelerated to velocities between 1000 m/s and 3000 m/s to impact water-filled tanks and the movement of the projectiles and the plastic deformation of the tank walls were recorded. [PERSON] et al. [8] conducted tests in which spherical projectiles were launched at velocities from 40 m/s to 200 m/s against an aluminum square tube filled with water to explore the relationship between the square tube perforation, material strength, and projectile diameter. [PERSON] et al. [9] used the steel projectiles with the diameter of 12.5 mm moving at velocities of 600 m/s and 900 m/s to impact an aluminum vessel filled with water. The effects of the liquid filling ratio and impact velocity on wall deformation were investigated. [PERSON] et al. [10] performed a test where a steel projectile with the diameter of 9.5 mm was shot into an aluminum vessel filled with water at the velocity of 686 m/s and the length and diameter of the cavity were recorded by a high-speed camera. With the advantages of low cost, good repeatability, and easy access to intermediate quantities, numerical simulation has been widely used. Based on the smoothed particle hydrodynamics (SPH) algorithm in AUTODYN software, [PERSON] et al. [11] conducted numerical simulation where two fragments impacted the liquid-filled cabin at the velocity of 2000 m/s simultaneously. The influence of the interval between two fragments on the superposition of shock waves was investigated. [PERSON] et al. [12] carried out a numerical simulation where the projectile impacted the water-filled tank at the velocity of 972 m/s using the coupling algorithm of finite element method (FEM) and SPH. The pressure-time curve obtained by the simulation agreed well with the test results. [PERSON] et al. [13] simulated projectiles impacting the water-filled tank at the velocity of 250 m/s and 300 m/s based on the MSC/Dytran program, and analyzed the dynamic response of the entry wall and the exit wall. [PERSON] et al. [5; 14] used the arbitrary Lagrangian-Eulerian (ALE) algorithm and SPH algorithm to reproduce the projectiles impacting the 60%, 75%, and 100% water-filled tank at the velocity of 600 m/s and 900 m/s. Results showed that the shock wave pressure calculated by the ALE algorithm was more accurate than the SPH algorithm. [PERSON] et al. [15] simulated the impact of fragments on an aircraft fuel tank based on ANSYS/LS-DYNA software. The influence of the velocity, mass, shape, and incident angle of the fragment on the hydrodynamic ram effect were analyzed.