Pooya Movahed

A solution-adaptive method for efficient compressible multifluid simulations, with application to the Richtmyer-Meshkov instability

The evolution of high-speed initially laminar multicomponent flows into a turbulent multi-material mixing entity, e.g., in the Richtmyer-Meshkov instability, poses significant challenges for high-fidelity numerical simulations. Although high-order shock- and interface-capturing schemes represent such flows well at early times, the excessive numerical dissipation thereby introduced and the resulting computational cost prevent the resolution of small-scale features. Furthermore, unless special care is taken, shock-capturing schemes generate spurious pressure oscillations at material interfaces where the specific heats ratio varies. To remedy these problems, a solution-adaptive high-order central/shock-capturing finite difference scheme is presented for efficient computations of compressible multi-material flows, including turbulence. A new discontinuity sensor discriminates between smooth and discontinuous regions. The appropriate split form of (energy preserving) central schemes is derived for flows of smoothly varying specific heats ratio, such that spurious pressure oscillations are prevented. High-order accurate weighted essentially non-oscillatory (WENO) schemes are applied only at discontinuities; the standard approach is followed for shocks and contacts, but material discontinuities are treated by interpolating the primitive variables. The hybrid nature of the method allows for efficient and accurate computations of shocks and broadband motions, and is shown to prevent pressure oscillations for varying specific heats ratios. The method is assessed through one-dimensional problems with shocks, sharp interfaces and smooth distributions of specific heats ratio, and the two-dimensional single-mode inviscid and viscous Richtmyer-Meshkov instability with re-shock.

Cavitation-induced damage of soft materials by focused ultrasound bursts: A fracture-based bubble dynamics model.

A generalized Rayleigh-Plesset-type bubble dynamics model with a damage mechanism is developed for cavitation and damage of soft materials by focused ultrasound bursts. This study is linked to recent experimental observations in tissue-mimicking polyacrylamide and agar gel phantoms subjected to bursts of a kind being considered specifically for lithotripsy. These show bubble activation at multiple sites during the initial pulses. More cavities appear continuously through the course of the observations, similar to what is deduced in pig kidney tissues in shock-wave lithotripsy. Two different material models are used to represent the distinct properties of the two gel materials. The polyacrylamide gel is represented with a neo-Hookean elastic model and damaged based upon a maximum-strain criterion; the agar gel is represented with a strain-hardening Fung model and damaged according to the strain-energy-based Griffiths fracture criterion. Estimates based upon independently determined elasticity and viscosity of the two gel materials suggest that bubble confinement should be sufficient to prevent damage in the gels, and presumably injury in some tissues. Damage accumulation is therefore proposed to occur via a material fatigue, which is shown to be consistent with observed delays in widespread cavitation activity.

Numerical simulations of the Richtmyer-Meshkov instability with reshock

Two-dimensional simulations of the Richtmyer-Meshkov instability with re-shock are carried out based on the single-mode Mach 1.21 air/SF6 shock tube experiments of Collins and Jacobs. A second-order accurate MUSCL-Hancock scheme and several high-order WENO schemes are used for shock capturing along with a gamma-based model for interface capturing to allow for the stable and accurate representation of fluids of different ratios of specific heats. The present results are compared qualitatively and quantitatively with existing theoretical models, experimental data and computational results. Good quantitative agreement with the observed amplitude growth, interface velocity and time of reshock are achieved. The amount and role of numerical dissipation of different schemes on the physical properties of the flow such as the circulation, enstrophy, mixing and kinetic energy of the small scales are also investigated.

Ultrasound-Induced Bubble Clusters in Tissue-Mimicking Agar Phantoms

Therapeutic ultrasound can drive bubble activity that damages soft tissues. To study the potential mechanisms of such injury, transparent agar tissue-mimicking phantoms were subjected to multiple pressure wave bursts of the kind being considered specifically for burst wave lithotripsy. A high-speed camera recorded bubble activity during each pulse. Various agar concentrations were used to alter the phantoms mechanical properties, especially its stiffness, which was varied by a factor of 3.5. However, the maximum observed bubble radius was insensitive to stiffness. During 1000 wave bursts of a candidate burst wave lithotripsy treatment, bubbles appeared continuously in a region that expanded slowly, primarily toward the transducer. Denser bubble clouds are formed at higher pulse repetition frequency. The specific observations are used to inform the incorporation of damage mechanisms into cavitation models for soft materials.

On the formation of bubble clusters and tunnels in tissue-mimicking agarose phantoms by focused ultrasound bursts

Formation of bubble clusters in soft tissues is a potential injury mechanism in therapeutic ultrasound treatments. To study this phenomenon, transparent tissue-mimicking agarose phantoms were subjected to a series of multiple-cycle ultrasound bursts, using a burst wave lithotripsy (BWL) protocol, and simultaneously imaged with a high-speed camera. The negative pressure in the initial bursts causes preexisting sub-micron bubbles to expand sufficiently to become visible in images (~200 microns). Additional bubbles appear continuously during the subsequent bursts. A Rayleigh-Plesset-type bubble dynamics model, which is generalized to include elastic resistance and damage mechanisms, is developed and used to explain key observations. It is proposed that material fatigue leads eventually to irreversible fracture-like failure. In addition to isolated, approximately spherical bubbles, long tunnel-like features are observed, which seemingly comprise lines of joined bubbles along a possible fracture or defect. Sta...

Investigating the Multi-layered Richtmyer-Meshkov Instability with High-Order Accurate Numerical Methods

The Richtmyer-Meshkov instability (RMI) occurs in flows where a shock interacts with a perturbed interface between two different fluids. At the interface, the interacting shock deposits baroclinic vorticity that drives the perturbation growth [1]. Conducting theoretical and experimental analysis is important to understand the physics of the RMI and its role in the context of high-energy-density physics [3], particularly inertial confinement fusion [8] and supernova collapse [6]. In these latter problems, the geometry is such that the shock interacts with multiple layers of materials. Thus, the multi-layered RMI is particularly relevant in these multi-material problems, where an accurate characterization of the level of mixing is important. Although the single interface RMI has been studied extensively in the past, through both experiments [2] and numerical simulations [5, 7], little attention has been given to the multi-layered RMI.

A numerical study of turbulence in boxes with no-slip walls and of varying volume-to-surface ratios

We use scaling analysis and direct numerical simulation (DNS) to investigate the decay of initially isotropic turbulence in rectangular boxes with solid no-slip walls and of different aspect ratios. The problem under consideration is initialized with an initially isotropic turbulent field, from which volumes of different aspect ratios are extracted and along whose boundaries solid walls are placed. Depending on the aspect ratio, we observe different rates of kinetic energy decay. Using simple theoretical arguments, we develop a scaling law for the kinetic energy with respect to time based on dissipation at the wall, in which the relevant length scale is the volume to surface ratio. We verify this scaling using the DNS results.

Turbulence diffusion effects at material interfaces, with application to the Rayleigh-Taylor instability

A new set-up is proposed to numerically investigate turbulent multi-material mixing in the presence and in the absence of a gravitational field. The set-up consists of an initial unperturbed interface that separates two fluids in an existing isotropic velocity field. The initial unperturbed interface evolves into a turbulent multi-material mixing region due to the fluctuating velocity field. For simulations without gravity, the initial velocity field decays, while the simulations with gravity are Rayleigh-Taylor unstable, such that the misalignment of the pressure and the density gradients generates baroclinic vorticity feeding the instability. The flow parameters are chosen such that the density fields are different, but that the kinetic energy decays at the same rate in both fluids. Direct numerical simulations are performed using a high-order accurate minimally dissipative kinetic-energy preserving and interface-capturing scheme. Results with and without gravity are compared to investigate flow isotropy and intermittency. The current results suggest that the initial anisotropy in the composition is not sufficient to make the initial isotropic field anisotropic in the absence of gravity.

Parametric Study of Mixed Convection in Channels with a Convex Surface

In this paper a numerical investigation has been carried out to define average Nusselt number on a convex heated curved surface entry of an adiabatic channel. For channels with a convex heated surface, where the increase in flow cross sectional area decelerates the flow (adverse pressure gradient) while buoyancy accelerates the flow, separation is observed near the heated surface. The effects of Reynolds number, Grashof number, and separation on average Nusselt number is discussed for a fixed value of R/L.