Ratnesh Shukla

An interface capturing method for the simulation of multi-phase compressible flows

A novel finite-volume interface (contact) capturing method is presented for simulation of multi-component compressible flows with high density ratios and strong shocks. In addition, the materials on the two sides of interfaces can have significantly different equations of state. Material boundaries are identified through an interface function, which is solved in concert with the governing equations on the same mesh. For long simulations, the method relies on an interface compression technique that constrains the thickness of the diffused interface to a few grid cells throughout the simulation. This is done in the spirit of shock-capturing schemes, for which numerical dissipation effectively preserves a sharp but mesh-representable shock profile. For contact capturing, the formulation is modified so that interface representations remain sharp like captured shocks, countering their tendency to diffuse via the same numerical diffusion needed for shock-capturing. Special techniques for accurate and robust computation of interface normals and derivatives of the interface function are developed. The interface compression method is coupled to a shock-capturing compressible flow solver in a way that avoids the spurious oscillations that typically develop at material boundaries. Convergence to weak solutions of the governing equations is proved for the new contact capturing approach. Comparisons with exact Riemann problems for model one-dimensional multi-material flows show that the interface compression technique is accurate. The method employs Cartesian product stencils and, therefore, there is no inherent obstacles in multiple dimensions. Examples of two- and three-dimensional flows are also presented, including a demonstration with significantly disparate equations of state: a shock induced collapse of three-dimensional van der Waals bubbles (air) in a stiffened equation of state liquid (water) adjacent to a Mie-Gruneisen equation of state wall (copper).

Effect of Loading Wave Profile on Hydrodynamic Void Collapse in Detonation Initiation

We experimentally and numerically investigate void collapse as a mechanism for detonation initiation in porous energetic materials under a stress-wave loading condition, representative of accidental mechanical insult. In contrast to the step loading of a shock, a stress wave induces a ramp loading, where length scales of the wave may be comparable to the void size. Using an inert and transparent polymer material, we decouple the reactive and material aspects of void collapse, and focus instead on the hydrodynamic process of interactive void collapse. Diagnostic techniques include high speed shadowgraph movies of the collapsing voids and particle image velocimetry in the surrounding material. Two dimensional finite volume simulations compare the interaction of a single void undergoing ramp and shock wave loading. Voids exhibit asymmetric collapse, with formation of a high speed jet that originates from proximal wall of the void. Data obtained, including internal volume histories and collapse times of current experiments and simulations, are reported and compared with shock-induced cavity collapse data from the literature.

Interface capturing simulations of acoustically driven bubble dynamics in and near tissue.

Tissue injury during therapeutic ultrasound or lithotripsy is thought, in cases, to be due to the action of cavitation bubbles. Assessing this and mitigating it is challenging since bubble dynamics in the complex confinement of tissues or in small blood vessels are challenging to predict. Simulations tools require specialized algorithms to simultaneously represent strong acoustic waves and shocks, topologically complex liquid‐vapor phase boundaries, and the complex viscoelastic material dynamics of tissue. We discuss advances in a simulation tool for such situations. A single‐mesh Eulerian solver is used to solve the governing equations. Special sharpening terms maintain the liquid‐vapor interface in face of the finite numerical dissipation included in the scheme to accurately capture shocks. A recent enhancement to this formulation has significantly improved this interface capturing procedure, which is demonstrated for simulation of the Rayleigh collapse of a bubble. The solver also transports elastic stresses and can thus be used to assess the effects of elastic properties on bubble dynamics. A shock‐induced bubble collapse adjacent to a model elastic tissue is used to demonstrate this and draw some conclusions regarding the injury suppressing role that tissue elasticity might play.

Bubble dynamics with tissue confinement in shock‐wave lithotripsy.

Estimates are made of the effect of confinement by tissues on the action of small bubbles when subjected to strong pressure waves. The applications of interest are biomedical procedures involving short strong ultrasound bursts or weak shocks of the kind delivered in shock‐wave lithotripsy. Confinement is anticipated to be important in suppressing mechanical injury and slowing the rate of its spread. We consider bubbles in a liquid such as blood within a small vessel in the tissue. A generalization of the Rayleigh–Plesset equation allows us to estimate the effect of the elasticity and viscosity of the surrounding tissue. Ranges of soft‐tissue properties are estimated from a variety of different measurements available in literature. Solutions suggest that elasticity is insufficient to significantly alter bubble dynamics, but that viscosities from the mid‐to‐high range of those suggested might play a significant role in suppressing bubble action. Simulations in two space dimensions of a shocked bubble in a w...

Shock induced detonations in composite heterogeneous energetic materials

Solid energetic materials are used in a wide variety of applications, including solid rocket motors, munitions, explosives for construction and demolition, automotive airbags, and pyrotechnic fasteners and actuators for space applications. An understanding of their potential for initiation and explosion is vital for their safe storage, handling, and transportation. Because of the rich phenomenology associate with microstructural geometric features, such pack as morphology, the presence of voids, and the type of binder, one-dimensional empirical models will be limited in predicting the shock sensitivity of energetic materials for a wide variety of insults. Therefore, the goal of our research is to develop a multidimensional shock-sensitivity model that accounts for microstructural geometric features. Here, we report a novel shock capturing multi-phase flow solver, which combines the features of a level-set method and a time dependent mesh redistribution technique. Numerical simulations of multi-material inert shock problems and detonation initiation through localized thermal energy deposition are used to demonstrate the method. Shock capturing methods are widely used in simulation of compressible multi-fluid reacting flows. A major drawback of these methods is that field representations of multi-material interfaces suffer from numerical smearing even though shocks are captured within a few grid cells. 1, 2 In our approach, special attention is