## 5 Influence of Angular Velocity on Hydrodynamic Ram Effect
### Influence of Angular Velocity Direction on Hydrodynamic Ram Effect  
Numerical simulations were carried out in which the translation velocity of 7000 m/s in the \(x\) direction remained unchanged. The angular velocities of \(w_{x}=5\) rad/us, \(w_{y}=5\) rad/us, and \(w_{z}=5\) rad/us  
Figure 11: Stress–time curves of element H on the front wall with liquid-filling ratios of 70%, 80%, 90%, and 100%. Figure 12: Stress–time curves of element I on the back wall with liquid-filling ratios of 70%, 80%, 90%, and 100%. were applied to the debris, respectively, and the influence of angular velocity direction on the hydrodynamic ram effect was studied. Front and back perforations caused by the debris impacting satellite tank with angular velocities were compared with those caused by the debris impacting the satellite tank without angular velocities, which are illustrated in Figure 13. When the debris impacted the satellite tank at the angular velocity of \(w_{x}=5\) rad/\(\upmu\)s, the front perforation was close to a quadrilateral, and the periphery was serrated. The absence of the back perforation indicates that the velocity declined to zero before the debris reached the back wall. When the debris impacted the satellite tank at the angular velocity of \(w_{y}=5\) rad/\(\upmu\)s, the front perforation was elliptical, and the back perforation deviated from the initial impact point in the negative direction of the \(z\) axis. When the debris impacted the satellite tank at the angular velocity of \(w_{z}=5\) rad/\(\upmu\)s, the front perforation was elliptical, and the back perforation deviated from the initial impact point in the negative direction of the \(y\) axis. Moreover, the front and back perforations caused by the impact of debris with angular velocities of \(w_{x}=5\) rad/\(\upmu\)s, \(w_{y}=5\) rad/\(\upmu\)s and \(w_{z}=5\) rad/\(\upmu\)s were larger than those caused by the impact of debris without angular velocities, which indicates that the damage caused by the impact of debris with angular velocities is more serious. When the debris impacted the satellite tank with the angular velocities in the \(y\) and \(z\) direction, the back perforation deviated from the initial impact point, demonstrating that the direction of angular velocity has a significant effect on the debris trajectory. When the debris penetrated the satellite tank with the angular velocity of \(w_{x}=5\) rad/\(\upmu\)s, the debris trajectory is shown in Figure 14. The debris moved in the liquid hydrazine, and the liquid hydrazine flowed around the debris. The debris rotated around the \(x\) axis, and the surrounding liquid hydrazine produced a clockwise vortex around the \(x\) axis. The rotational direction of the vortex was perpendicular to the flow direction of the liquid hydrazine, no Magnus force was formed. The debris was only subject to liquid resistance, and the direction of translational velocity was not deflected. Under the action of viscous shear force, the velocity of the fluid layer around the debris decreased. Finally, the fluid layer adhered to the debris to form a boundary layer. The boundary layer enlarged the effective cross-sectional area of debris, leading to an increase in the liquid resistance, and a decrease in the debris velocity. As a result, the translation velocity decreased to zero at \(x=35\) m, and the debris could not pass through the back wall. Figure 13: Front and back perforations caused by the debris impacting the satellite tank with angular velocities of \(w_{x}=5\) rad/\(\upmu\)s, \(w_{y}=5\) rad/\(\upmu\)s, and \(w_{z}=5\) rad/\(\upmu\)s.  
When the debris moves in liquid hydrazine, a boundary layer is formed around the debris and the turbulent wake is generated at the tail of the debris [23]. As the liquid flows back along the boundary layer, the kinetic energy in the boundary layer is dissipated by the viscosity. The velocity of the liquid decreases, which leads to an adverse pressure gradient in the boundary layer. Under the action of the adverse pressure gradient, the liquid slows down further.