# Application of a Coupled Eulerian-Lagrangian Approach to the Shape and Force of Scientific Balloons
## 5 Conclusions  
This study utilized the Coupled Eulerian-Lagrangian (CEL) method in Abaqus to systematically investigate the mechanical behavior of scientific balloons during launching and ascent. First, we simulated the static ascent model. Under varying pressure conditions, the helium within the balloon expanded to different volumes. Multiple volumes of helium were enclosed by the balloon membrane for simulation, and the results were compared with numerical solutions of balloon shapes under corresponding pressures. This comparison validated the reliability and feasibility of the CEL method in addressing the coupling problem between flexible materials and dual flow fields. Next, we applied the CEL method to simulate the dynamic mushroom-shaped deformation of the balloon during launching. Upon launching, the tension in the lower-middle portion of the membrane dropped to zero, causing it to accelerate upward. Meanwhile, the upper membrane, influenced by inertia and air resistance, exhibited slower acceleration, resulting in the lateral expansion of the lower-middle membrane. Subsequently, the upper membrane, driven by helium's buoyancy, ascended and pulled the circumferentially expanded lower-middle membrane upward. This motion gradually restored the balloon to its initial shape and enabled its upward ascent. This study revealed that the upper membrane experienced the maximum stress at the moment of launching, while the velocity of the membrane at the bottom point rapidly increased initially. As the mushroom shape developed, the velocity gradually decreased until it stabilized and aligned with the overall ascent speed. Additionally, this study simulated the motion of the balloon in a wind field to replicate the deployment conditions in an actual windy environment. The results showed that the balloon shifted in the downwind direction and exhibited rotational motion around its axis. The windward side of the balloon displayed a pronounced indentation at its bottom, while two stress concentration points appeared symmetrically on either side of the most prominent point on the upper membrane. On the leeward side, the most prominent point became the area of maximum stress on the membrane. While the CEL method effectively simulates the balloon's ascent process, the simplified simulation model still deviates from the actual physical system. The current model omits various structural details present in real scientific balloons, such as strengthening bands,  
Figure 19: Wind-scooping shape of a scientific balloon during ground launching. multi-layered head structures, flanges, exhaust tubes, and gondolas. These components significantly impact the balloon's ascent, expansion, and formation processes. For instance, strengthening bands and multi-layered head structures provide additional support under varying atmospheric pressures, while flanges and exhaust tubes play crucial roles in controlling the gas flow and pressure distribution. The payload capsule also influences the stability and buoyancy distribution of the balloon. Future simulations should incorporate these features to better approximate the actual conditions, thereby enhancing the accuracy and relevance of the simulation results. Using the CEL method in Abaqus/Explicit, the mechanical behavior of the scientific balloon membrane under the coupling of internal and external flow fields was simulated. This successfully solved the coupling problem between the fluid and flexible materials in the dual-flow field, providing an important reference for the optimized design of actual deployment missions. This simulation method is highly applicable, as it can not only accurately predict the release and deployment processes of scientific balloons but also be extended to the study of the mechanical behavior of other large flexible structures, offering an efficient and universal solution for related fields. Conceptualization, L.K. and H.Z. ; methodology, L.K. ; software, L.K. ; validation, L.K., Y.Y. and H.Z. ; formal analysis, L.K. ; investigation, H.Z. ; resources, W.L.