Equivalent Mechanical Model Utilizing Strip Method and Fast Estimation Formulas for Airship Gas Sloshing

The hull of the stratospheric airship is designed and arranged into multiple independent ballonets. The proportions of buoyancy gas and atmospheric air in independent ballonet control both the lift and the pitching attitude during the ascend and descend process. There is a density difference and interface between the buoyancy gas and the air, causing them to slosh when the airship moves, affecting airship motion characteristics. In this paper, the ballonets are approximated as horizontal cylinder containers. For a cylinder container, it is proposed to divide one into multiple slices in the direction parallel to the fluid movement. The sloshing effect in the cylinder under longitudinal and pitching excitations are approximated as cumulative rectangular slices (tanks) using strip method. Through Computational Fluid Dynamics (i.e., CFD) simulations and existing experimental data, the correctness of the spring-mass-dashpot equivalent model for the basic rectangular tank is confirmed. The strip method of assembling rectangular tank slices into more complex shapes is introduced, and verified through the construction of both upright and horizontal cylinders. Fast estimation formulas are then provided for the tank and horizontal cylinder models. This research provides valuable references for incorporating gas sloshing into the dynamics modeling of the stratospheric airships.