Low-Order Mechanical Modeling of Liquid Fuel Sloshing

Since the space launch vehicle undergoes not only external disturbances such as aerodynamic force or solar wind pressure but also internal dynamic influences such as the bending mode vibration of the vehicle and the sloshing of the liquid propellant, it is essential to reflect these disturbances when designing a precise flight controller. The sloshing phenomenon refers to the vibration of a fluid having a free surface and occurs in the liquid fuel and oxidant tanks due to the accelerated motion of the vehicle. Since the propellant’s sloshing natural frequencies may overlap with the frequency band of the attitude control device. For this reason, the sloshing mode of the propellant may resonate with the actuation of the TVC (thrust vector control) device or the bending mode of the vehicle, which can cause severe damage of the vehicle or instability of the attitude control (Healy, Development of the Rocket Engine for the Jupiter Missile. Rocketdyne, 1958). Among the solutions to mitigate the sloshing problem, there is a method of installing baffles that provides damping in the sloshing, but in the case of a space vehicle, the baffle design causes an increase in mass and cost, so there is a limit to its use. Therefore, it is necessary to accurately capture the dynamic characteristics of the sloshing and to apply the low-order equivalent mechanical model to the attitude controller using a simple mechanical mass-spring model or pendulum model as shown in Fig. 16.1.