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This rather long cylindrical shell subjected to an underwater explosion collapses in a 2-lobed pattern. (n = 2 circumferential waves.)
FROM:
Kamran, Kazern, Oñate Ibáñez de Navarra, Eugenio, Idelsohn, Barg, Sergio Rodolfo and Rossi, Riccardo, “A compressible Lagrangian framework for the simulation of underwater implosion problems”, Barcelona, Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), 2013. Also see the Ph.D. dissertation by Kazem Kamran on which this paper is based: Ph.D. dissertation submitted to: Departamento de Resistència de Materials i Estructures a l’Enginyeria Escola Tècnica Superior d’Enginyers de Camins, Canals i Ports de Barcelona Universitat Politècnica de Catalunya, Barcelona Octobre 2012. This is one of the pictures in Kamran’s Ph.D. dissertation.
ABSTRACT: The development of efficient algorithms to understand implosion dynamics presents a number of challenges. The foremost challenge is to efficiently represent the coupled compressible fluid dynamics of internal air and surrounding water. Secondly, the method must allow one to accurately detect or follow the interface between the phases. Finally, it must be capable of resolving any shock waves which may be created in air or water during the final stage of the collapse. We present a fully Lagrangian compressible numerical framework for the simulation of underwater implosion. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method. A nodally perfect matched definition of the interface is used and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm), and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in addition to the shock waves traveling in the fluid domains are among the phenomena that are observed in the simulation. We then extend our framework to model the underwater implosion of a cylindrical aluminum container considering a monolithic fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data.
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