Confined Rayleigh–Plesset equation for Hydrodynamic Ram analysis in thin-walled containers under ballistic impacts

Fourest, Thomas; Laurens, Jean-Marc; Deletombe, E.; Dupas, Jacques; Арригони, М.

doi:10.1016/j.tws.2014.10.003

Cited by 33 publications

(11 citation statements)

References 20 publications

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“…We consider a spherical bubble of radius R in a liquid; the liquid and the bubble are confined in a spherical cavity of radius R c within a solid (figure 1(b)). This 3-layer geometry (bubble-liquid-solid) has similarities with previous studies that have considered bubble-liquid-air (Obreschkow et al 2006), bubble-solid shell-liquid (Church 1995) or bubble-liquid-soild shell (Fourest et al 2015). The case of Fourest et al (2015) is closest to the case considered here, however these authors considered a situation where the liquid is incompressible and all variations of bubble volume were accommodated by modifications of the shell radius.…”

Section: Framework Hypotheses and Definitionssupporting

confidence: 61%

“…This 3-layer geometry (bubble-liquid-solid) has similarities with previous studies that have considered bubble-liquid-air (Obreschkow et al 2006), bubble-solid shell-liquid (Church 1995) or bubble-liquid-soild shell (Fourest et al 2015). The case of Fourest et al (2015) is closest to the case considered here, however these authors considered a situation where the liquid is incompressible and all variations of bubble volume were accommodated by modifications of the shell radius. Here, we consider a more general situation where both the liquid volume and the cavity size may vary, and where the confinement geometry can be an extended elastic solid or an elastic shell.…”

Section: Framework Hypotheses and Definitionssupporting

confidence: 61%

“…where G is the shear modulus of the solid (Landau & Lifshitz 1986). The parameter K c allows taking into account other confinement geometries, such as solid shells of thickness d (Fourest et al 2015). In the case of thin shells this parameters is…”

Section: Free Energy Of a Fully Confined Bubblementioning

confidence: 99%

“…Rocks contain trapped fluid inclusions and the study of the quasi-static behavior of bubbles in these inclusions is used by geologists to extract past thermodynamic conditions (Roedder 1980;Marti et al 2012). Impact of projectiles into liquid-filled tanks can generate cavitation bubbles with disastrous consequences for the solid structure (Fourest et al 2015). Water status in plants or in soils is also typically measured by tensiometers where an isolated pocket of liquid is put in equilibrium with the material, and the unwanted appearance of bubbles can disrupt the function of these devices (Tarantino & Mongiovì 2001;Pagay et al 2014).…”

Section: Introductionmentioning

confidence: 99%

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On the statics and dynamics of fully confined bubbles

Vincent

Marmottant

2017

J. Fluid Mech.

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We investigate theoretically the statics and dynamics of bubbles in fully confined liquids, i.e. in liquids surrounded by solid walls in all directions of space. This situation is found in various natural and technological contexts (geological fluid inclusions, plant cells and vessels, soil tensiometers, etc.), where such bubbles can pre-exist in the trapped liquid or appear by nucleation (cavitation). We focus on volumetric deformations and first establish the potential energy of fully confined bubbles as a function of their radius, including contributions from gas compressibility, surface tension, liquid compressibility and elastic deformation of the surrounding solid. We evaluate how the Blake threshold of unstable bubble growth is modified by confinement and we also obtain an original bubble stability phase diagram with a regime of liquid superstability (spontaneous bubble collapse) for strong confinements. We then calculate the liquid velocity field associated with radial deformations of the bubble and strain in the solid, and we predict large deviations in the kinematics compared to bubbles in extended liquids. Finally, we derive the equations governing the natural oscillation dynamics of fully confined bubbles, extending Minnaert’s formula and the Rayleigh–Plesset equation, and we show that the compressibility of the liquid as well as the elasticity of the walls can result in ultra-fast bubble radial oscillations and unusually quick damping. We find excellent agreement between the predictions of our model and recent experimental results.

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Section: Framework Hypotheses and Definitionssupporting

confidence: 61%

Section: Framework Hypotheses and Definitionssupporting

confidence: 61%

Section: Free Energy Of a Fully Confined Bubblementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the statics and dynamics of fully confined bubbles

Vincent

Marmottant

2017

J. Fluid Mech.

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“…The agreement is better for the pool test, in which the bubble created in the experiment is more spherical (Deletombe et al [2]). The application of the confined Rayleigh-Plesset equation is here presented with a calibration of the structure response, but it has been shown in Fourest et al [12] that the value of the confinement parameter can be reasonably well approximated using analytical models on the plates of the container.…”

Section: Presentation Of the Confined Rayleigh-plesset Equationmentioning

confidence: 99%

Prediction of thermal effects of magnitude for HRAM event in fuel-filled tank using the rayleigh-plesset equation

Fourest¹,

Арригони²,

Deletombe³

et al. 2016

Int. J. CMEM

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To reduce the vulnerability of both civilian and military aircraft, it is important to take the hydrodynamic ram (HRAM) effect into account when designing their fuel tanks. HRAM is especially dangerous for liquid-filled thin walled lightweight structures that cannot be armoured due to weight penalty reasons. However, the response of the tank structure during HRAM events depends on a coupling model between fluid and structure. Water is generally used as a liquid candidate for experimental observations of HRAM, since it is a safe and affordable solution. However, its characteristics in thermal transfers are far different from the ones of hydrocarbons, and it may influence the bubble behaviour and thus its resulting loading on the tank walls. A good understanding of all these aspects is still needed to enhance the tank designs. Similarities in bubble behaviour between HRAM and underwater explosion situations were observed in recent high-speed tank penetration/water entry experiments. A confined version of the Rayleigh-Plesset equation-which is classically used for bubble dynamics analysis (including underwater explosion)-has been previously proposed to simulate a bubble created by an HRAM event. The work the presented work is a first attempt to the estimation of the influence of thermal effects in HRAM processes, by using the Rayleigh-Plesset equation in confined regime.

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