# Application of a Coupled Eulerian-Lagrangian Approach to the Shape and Force of Scientific Balloons
## 4 Dynamic Fluid-Structure Coupling Shape and Force Analysis
### Dynamic Mushroom-Shaped Configuration Solving  
In actual launches, a certain amount of helium gas is initially filled into the scientific balloon on the ground. Once the balloon stabilizes, the bottom restraint is released at the appropriate moment, allowing the balloon to be launched. After launching, the balloon undergoes rapid deformation into a mushroom shape due to buoyancy, gravity, membrane tension, atmospheric pressure, and air resistance. It then gradually recovers to its stable pre-launching state and begins to rise. At this point, the internal helium pressure does not maintain a linear hydrostatic pressure gradient but rather a nonlinear distribution, causing the balloon shape to change [28]. To investigate the shape characteristics of balloon launching, a ground test simulating the unsteady balloon shape was conducted in a balloon storage facility, as shown in Figure 8. The balloon was initially fixed to a small launching vehicle using a rope. After the rope was released, the balloon ascended vertically. As the balloon lost its bottom force and the upper part of the balloon was influenced by air resistance, the helium in the lower section quickly moved upward, compressing the upper helium section and expanding the balloon's cross-sectional size. At this point, the moving helium at the bottom impacted the upper membrane, disrupting the originally stable hydrostatic pressure gradient distribution. As the helium at the bottom decreased, the negative pressure increased. The helium in the upper section increased as well, leading to a larger pressure differential, and a rapid increase in pressure occurred at the zero-pressure point. The division between the two pressure regions became more pronounced, with a rapid transition at the balloon's waist. This section uses the CEL method in Abaqus/Explicit to simulate the process. The model of the zero-pressure balloon from the static shape solver is imported. We add an analysis step and expand the Euler domain to simulate the dynamic launching process. Figure 8: The mushroom shape of a zero-pressure balloon when it is launched from the ground. Unlike the actual launching of a zero-pressure balloon, the simulation needs to divide the process into two distinct analysis steps. The first analysis step provides enough time for the internal and external fluids to fully interact with the balloon membrane and reach a stable state, forming a physical model identical to the pre-launching state in reality. In the second analysis step, the fixed bottom point of the balloon is released to simulate the launching moment and subsequent ascent process of the balloon's shape. After expanding the Euler domain to 40 \(\times\) 40 \(\times\) 90 dimensions, the zero-pressure balloon is embedded within. We use the volume fraction tool to redefine the regions of helium gas and air in the expanded Euler domain. The corresponding material properties are then assigned. Due to the modeling and post-processing software settings in Abaqus, the fluid part between the solid and Euler boundaries cannot be visualized. Therefore, a circular barrel is added between the balloon membrane and the Euler boundary, as shown in the schematic diagram in Figure 9a, to facilitate the observation of the pressure gradient and the external flow field around the balloon membrane, as shown in Figure 9b. It is important to ensure that the barrel, balloon membrane, and Euler boundaries are sufficiently meshed. If the spacing between the elements is smaller than a single minimum unit mesh, the computational results may not converge. Before launching, the buoyancy, gravity, and the tensile force from the fixed point of the balloon form a balance. The force at the fixed point is transmitted through the middle and lower sections of the balloon membrane to the entire balloon. At the moment of launching, when the constraint at the fixed end is removed, the tensile force on the balloon membrane becomes zero. Since the buoyancy is much greater than the gravity, the balloon accelerates upward, gaining upward velocity.