Deployment of Lobed Super-Pressure Balloons
Large balloons have an important role in atmospheric research, astrophysics, astronomy, etc. NASA's development of a large payload, high altitude and long duration balloon, the so called Super-Pressure Balloon, centers on a pumpkin shaped design. The lobed shape that has been chosen for structural efficiency has led to complications during deployment: several balloons have not deployed into the expected, cyclically symmetrical equilibrium configuration, but have settled into unexpected asymmetric shapes. This puzzling shape anomaly consists of a single non-meridional cleft spanning from top to bottom of the balloon and involving several lobes. Our particular interest in this research is in clefts that remain once a balloon has reached its float altitude and is fully pressurized.
One attempt has focused on the overall geometric stability of a fully deployed balloon subject to increasing uniform internal pressure. Pagitz (2007) exploited the high degree of symmetry of the unclefted balloon by adopting a closed form expression for a symmetry-adapted coordinate system that provided the tangent stiffness matrix in an efficient block-diagonal form. It was found that for any chosen balloon there is a power law relation between the critical pressure and the number of lobes. Xu (2007)Â seeded the eigenmodes as geometric imperfections into the balloon geometry to trigger a post-buckling analysis by using the finite element package ABAQUS/Standard. It was found that by using the single critical eigenmode as imperfection, the balloon deformed into a globally buckled shape whereas a more localized deformed shape was obtained by introducing the combined eigenmodes. Unfortunately, noneof these analyses produced deformed shapes that resemble the S-cleft that had been observed experimentally.
In my research I use fully three-dimensional finite-element model that incorporates wrinkling and frictionless contact to simulate the shapes taken up by a balloon during the final stages of ascent and pressurization. The loading on the balloon is a non-uniform differential pressure with constant gradient along the height. The three-dimensional solutions are obtained with ABAQUS/Explicit, with a user-defined material subroutine for elastic isotropic wrinkling that implements a mixed stress-strain criterion. Using the Rand-Schapery model for this film, experimental tests on StratoFilm 420 under simple shear, in comparison with ABAQUS/Explicit simulations, had shown that StratoFilm 420 has only weak anisotropy and viscoelastic behavior is a significant source of energy dissipation.
Two different methods have been considered to predict the clefts: (i) deflation & inflation method and (ii) constraint shift method. The design of superpressure balloon is investigated: a hybrid design balloon where the lobe cutting pattern combines a constant bulge angle with a constant bulge radius approach, with maximum bulge angle of 98.1 deg and maximum bulge radius of 0.284 m. In method I, the starting configuration for the deflation simulation is obtained by deflating an initially symmetric balloon subject to uniform pressure. The deflation simulation is continued until the differential pressure at the bottom of the balloon has become negative, at which point the balloon is extensively clefted. The balloon is then inflated by increasing the bottom pressure while maintaining a uniform vertical pressure gradient, and the evolution of the shape and stress distributions in the balloon are studied and shown as follows.
Although the deflation & inflation method can produce detailed pictures of the loading paths for better understanding of the behavior of clefting, it is less computationally efficient for the requirement of multiple case studies. Assuming that material dissipation can be ignored, a method of artificially breaking the symmetry, constraint shift method, has been developed and will be published in future.
- Deng, X., and Pellegrino, S. (2010) Wrinkling of orthotropic viscoelastic membranes. 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 12-15 April 2010, Orlando, FL, AIAA-2010-2670.
- Deng, X., and Pellegrino, S. (2009) Finite element simulations of clefting in lobed super-pressure balloons. AIAA Balloon Systems Conference. 4-7 May 2009, Seattle, WA, AIAA-2009-2816.
- Deng, X., and Pellegrino, S. (2008) Computation of partially inflated shapes of stratospheric balloon structures. 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. 7-10 April 2008, Schaumburg, Illinois, AIAA-2008-2133.
- Pagitz, M., and Pellegrino, S. (2006). Computation of buckling pressure of pumpkin balloons. 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 1-4 May 2006, Newport, RI, AIAA-2006-1803.
- Pagitz, M., Xu, Y., and Pellegrino, S. (2005). Buckling of pumpkin balloons. In: Ramm, E. Wall, W.A. Bletzinger, K.-U. Bischoff, M., editors: Computation of Shell and Spatial Structures, June 1-4, 2005, Salzburg, Austria.
- Pagitz, M., Xu, Y., and Pellegrino, S. (2005). Stability of lobed balloons. Advances in Space Research.