Underwater explosion poses a significant threat to the structural integrity of ocean vehicles and platforms. Accurate prediction of the dynamic loads from an explosion and the resulting structural response is crucial to ensuring safety without overconservative design. When the distance between the explosive charge and the structure is relatively small (i.e., near-field explosion), the dynamics of the gaseous explosion product, i.e., the “bubble”, comes into play, rendering a multiphysics problem that features the interaction of the bubble, the surrounding liquid water, and the solid structure. The problem is highly nonlinear, as it involves shock waves, large deformation, yielding, contact, and possibly fracture. This paper investigates the two-way interaction between the cyclic expansion and collapse of an explosion bubble and the deformation of a thin-walled elastoplastic cylindrical shell in its vicinity. Intuitively, when a shock wave impinges on a thin cylindrical shell, the shell would collapse in the direction of shock propagation. However, some recent laboratory experiments have shown that under certain conditions the shell collapsed in a counter-intuitive mode in which the direction of collapse is perpendicular to that of shock propagation. In other words, the nearest point on the structural surface moved towards the explosion charge, despite being impacted by a compressive shock. This paper focuses on replicating this phenomenon through numerical simulation and elucidating the underlying mechanisms. A recently developed computational framework (“FIVER”) coupling a nonlinear finite element structural dynamics solver and a finite volume compressible fluid dynamics solver is used to complete this study. The solver utilizes an embedded boundary method to track the wetted surface of the structure (i.e. the fluid-structure interface), which is capable of handling large structural deformation and topological changes (e.g., fracture). The solver also adopts the level set method for tracking the bubble surface (i.e. the liquid-gas interface). The fluid-structure and liquid-gas interface conditions are enforced by constructing and solving one-dimensional multi-material Riemann problems, which naturally accommodates the propagation of shock waves across the interfaces. In this paper, mesh refinement study is made to examine the sensitivity of the results to various meshing parameters. The results show that the intermediate level of refinement is appropriate in terms of both the accuracy and the computation costs. Next, the deformation history of both the bubble and the structure are presented and analyzed to provide a detailed view of the counter-intuitive collapse mode mentioned above. We show that timewise, the structural collapse spans multiple cycles of bubble oscillation. Additional details about the time-histories of fluid pressure, structure displacement, and bubble size are presented to elucidate this dynamic bubble-structure interaction and the resulting structural failure.
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Shock-induced bubble collapse near solid materials: effect of acoustic impedance
The fluid dynamics of a bubble collapsing near an elastic or viscoelastic material is coupled with the mechanical response of the material. We apply a multiphase fluid–solid coupled computational model to simulate the collapse of an air bubble in water induced by an ultrasound shock wave, near different types of materials including metals (e.g. aluminium), polymers (e.g. polyurea), minerals (e.g. gypsum), glass and foams. We characterize the two-way fluid–material interaction by examining the fluid pressure and velocity fields, the time history of bubble shape and volume and the maximum tensile and shear stresses produced in the material. We show that the ratio of the longitudinal acoustic impedance of the material compared to that of the ambient fluid, $Z/Z_0$ , plays a significant role. When $Z/Z_0<1$ , the material reflects the compressive front of the incident shock into a tensile wave. The reflected tensile wave impinges on the bubble and decelerates its collapse. As a result, the collapse produces a liquid jet, but not necessarily a shock wave. When $Z/Z_0>1$ , the reflected wave is compressive and accelerates the bubble's collapse, leading to the emission of a shock wave whose amplitude increases linearly with $\log (Z/Z_0)$ , and can be much higher than the amplitude of the incident shock. The reflection of this emitted shock wave impinges on the bubble during its rebound. It reduces the speed of the bubble's rebound and the velocity of the liquid jet. Furthermore, we show that, for a set of materials with $Z/Z_0\in [0.04, 10.8]$ , the effect of acoustic impedance on the bubble's collapse time and minimum volume can be captured using phenomenological models constructed based on the solution of Rayleigh–Plesset equation.
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- NSF-PAR ID:
- 10202720
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 907
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Shock waves from underwater and air explosions are significant threats to surface and underwater vehicles and structures. Recent studies on the mechanical and thermal properties of various phase-separated elastomers indicate the possibility of applying these materials as a coating to mitigate shock-induced structural failures. To demonstrate this approach and investigate its efficacy, this paper presents a fluid-structure coupled computational model capable of predicting the dynamic response of air-backed bilayer (i.e. elastomer coating – metal substrate) structures submerged in water to hydrostatic and underwater explosion loads. The model couples a three-dimensional multiphase finite volume computational fluid dynamics model with a nonlinear finite element computational solid dynamics model using the FIVER (FInite Volume method with Exact multi-material Riemann solvers) method. The kinematic boundary condition at the fluid-structure interface is enforced using an embedded boundary method that is capable of handling large structural deformation and topological changes. The dynamic interface condition is enforced by formulating and solving local, one-dimensional fluid-solid Riemann problems, which is well-suited for transferring shock and impulsive loads. The capability of this computational model is demonstrated through a numerical investigation of hydrostatic and shock-induced collapse of aluminum tubes with polyurea coating on its inner surface. The thickness of the structure is resolved explicitly by the finite element mesh. The nonlinear material behavior of polyurea is accounted for using a hyper-viscoelastic constitutive model featuring a modified Mooney-Rivlin equation and a stress relaxation function in the form of prony series. Three numerical experiments are conducted to simulate and compare the collapse of the structure in different loading conditions, including a constant pressure, a fluid environment initially in hydrostatic equilibrium, and a two-phase fluid flow created by a near-field underwater explosion.
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Recent studies indicate that cavitation may play a vital role in laser lithotripsy. However, the underlying bubble dynamics and associated damage mechanisms are largely unknown. In this study, we use ultra-high-speed shadowgraph imaging, hydrophone measurements, three-dimensional passive cavitation mapping (3D-PCM), and phantom test to investigate the transient dynamics of vapor bubbles induced by a holmium:yttrium aluminum garnet laser and their correlation with solid damage. We vary the standoff distance ( SD) between the fiber tip and solid boundary under parallel fiber alignment and observe several distinctive features in bubble dynamics. First, long pulsed laser irradiation and solid boundary interaction create an elongated “pear-shaped” bubble that collapses asymmetrically and forms multiple jets in sequence. Second, unlike nanosecond laser-induced cavitation bubbles, jet impact on solid boundary generates negligible pressure transients and causes no direct damage. A non-circular toroidal bubble forms, particularly following the primary and secondary bubble collapses at SD = 1.0 and 3.0 mm, respectively. We observe three intensified bubble collapses with strong shock wave emissions: the intensified bubble collapse by shock wave, the ensuing reflected shock wave from the solid boundary, and self-intensified collapse of an inverted “triangle-shaped” or “horseshoe-shaped” bubble. Third, high-speed shadowgraph imaging and 3D-PCM confirm that the shock origins from the distinctive bubble collapse form either two discrete spots or a “smiling-face” shape. The spatial collapse pattern is consistent with the similar BegoStone surface damage, suggesting that the shockwave emissions during the intensified asymmetric collapse of the pear-shaped bubble are decisive for the solid damage.more » « less
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ABSTRACT A core-collapse supernova is generated by the passage of a shock wave through the envelope of a massive star, where the shock wave is initially launched from the ‘bounce’ of the neutron star formed during the collapse of the stellar core. Instead of successfully exploding the star, however, numerical investigations of core-collapse supernovae find that this shock tends to ‘stall’ at small radii (≲10 neutron star radii), with stellar material accreting on to the central object through the standing shock. Here, we present time-steady, adiabatic solutions for the density, pressure, and velocity of the shocked fluid that accretes on to the compact object through the stalled shock, and we include the effects of general relativity in the Schwarzschild metric. Similar to previous works that were carried out in the Newtonian limit, we find that the gas ‘settles’ interior to the stalled shock; in the relativistic regime analysed here, the velocity asymptotically approaches zero near the Schwarzschild radius. These solutions can represent accretion on to a material surface if the radius of the compact object is outside of its event horizon, such as a neutron star; we also discuss the possibility that these solutions can approximately represent the accretion of gas on to a newly formed black hole following a core-collapse event. Our findings and solutions are particularly relevant in weak and failed supernovae, where the shock is pushed to small radii and relativistic effects are large.
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2020.810
