565 research outputs found

    Numerical Simulations of Cavitating Bubbles in Elastic and Viscoelastic Materials for Biomedical Applications

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    The interactions of cavitating bubbles with elastic and viscoelastic materials play a central role in many biomedical applications. This thesis makes use of numerical modeling and data-driven approaches to characterize soft biomaterials at high strain rates via observation of bubble dynamics, and to model burst-wave lithotripsy, a focused ultrasound therapy to break kidney stones. In the first part of the thesis, a data assimilation framework is developed for cavitation rheometry, a technique that uses bubble dynamics to characterize soft, viscoelastic materials at high strain-rates. This framework aims to determine material properties that best fit observed cavitating bubble dynamics. We propose ensemble-based data assimilation methods to solve this inverse problem. This approach is validated with surrogate data generated by adding random noise to simulated bubble radius time histories, and we show that we can confidently and efficiently estimate parameters of interest within 5% given an iterative Kalman smoother approach and an ensemble- based 4D-Var hybrid technique. The developed framework is applied to experimental data in three distinct settings, with varying bubble nucleation methods, cavitation media, and using different material constitutive models. We demonstrate that the mechanical properties of gels used in each experiment can be estimated quickly and accurately despite experimental inconsistencies, model error, and noisy data. The framework is used to further our understanding of the underlying physics and identify limitations of our bubble dynamics model for violent bubble collapse. In the second part of the thesis, we simulate burst-wave lithotripsy (BWL), a non- invasive treatment for kidney stones that relies on repeated short bursts of focused ultrasound. Numerical approaches to study BWL require simulation of acoustic waves interacting with solid stones as well as bubble clouds which can nucleate ahead of the stone. We implement and validate a hypoelastic material model, which, with the addition of a continuum damage model and calibration of a spherically- focused transducer array, enables us to determine how effective various treatment strategies are with arbitrary stones. We present a preliminary investigation of the bubble dynamics occurring during treatment, and their impact on damage to the stone. Finally, we propose a strategy to reduce shielding by collapsing bubbles ahead of the stone via introduction of a secondary, low-frequency ultrasound pulse during treatment.</p

    Flow reconstruction and particle characterization from inertial Lagrangian tracks

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    This text describes a method to simultaneously reconstruct flow states and determine particle properties from Lagrangian particle tracking (LPT) data. LPT is a popular measurement strategy for fluids in which particles in a flow are illuminated, imaged (typically with multiple cameras), localized in 3D, and then tracked across a series of frames. The resultant "tracks" are spatially sparse, and a reconstruction algorithm is commonly employed to determine dense Eulerian velocity and pressure fields that are consistent with the data as well as the equations governing fluid dynamics. Existing LPT reconstruction algorithms presume that the particles perfectly follow the flow, but this assumption breaks down for inertial particles, which can exhibit lag or ballistic motion and may impart significant momentum to the surrounding fluid. We report an LPT reconstruction strategy that incorporates the transport physics of both the carrier fluid and particle phases, which may be parameterized to account for unknown particle properties like size and density. Our method enables the reconstruction of unsteady flow states and determination of particle properties from LPT data and the coupled governing equations for both phases. We use a neural solver to represent flow states and data-constrained polynomials to represent the tracks (though we note that our technique is compatible with a variety of solvers). Numerical tests are performed to demonstrate the reconstruction of forced isotropic turbulence and a cone-cylinder shock structure from inertial tracks that exhibit significant lag, streamline crossing, and preferential sampling

    Vanishing dissipation limit for non-isentropic Navier-Stokes equations with shock data

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    This paper is concerned with the vanishing dissipation limiting problem of one-dimensional non-isentropic Navier-Stokes equations with shock data. The limiting problem was solved in 1989 by Hoff-Liu in [13] for isentropic gas with single shock, but was left open for non-isentropic case. In this paper, we solve the non-isentropic case, i.e., we first establish the global existence of solutions to the non-isentropic Navier-Stokes equations with initial discontinuous shock data, and then show these solutions converge in L∞L^{\infty} norm to a single shock wave of the corresponding Euler equations away from the shock curve in any finite time interval, as both the viscosity and heat-conductivity tend to zero. Different from [13] in which an integrated system was essentially used, motivated by [21,22], we introduce a time-dependent shift Xε(t)\mathbf{X}^\varepsilon(t) to the viscous shock so that a weighted Poincar\'{e} inequality can be applied to overcome the difficulty generated from the ``bad" sign of the derivative of viscous shock velocity, and the anti-derivative technique is not needed. We also obtain an intrinsic property of non-isentropic viscous shock, see Lemma 2.2 below. With the help of Lemma 2.2, we can derive the desired uniform a priori estimates of solutions, which can be shown to converge in L∞L^{\infty} norm to a single inviscid shock in any given finite time interval away from the shock, as the vanishing dissipation limit. Moreover, the shift Xε(t)\mathbf{X}^\varepsilon(t) tends to zero in any finite time as viscosity tends to zero. The proof consists of a scaling argument, L2L^2-contraction technique with time-dependent shift to the shock, and relative entropy method.Comment: All comments are welcome

    Time-asymptotic stability of generic Riemann solutions for compressible Navier-Stokes-Fourier equations

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    We establish the time-asymptotic stability of solutions to the one-dimensional compressible Navier-Stokes-Fourier equations, with initial data perturbed from Riemann data that forms a generic Riemann solution. The Riemann solution under consideration is composed of a viscous shock, a viscous contact wave, and a rarefaction wave. We prove that the perturbed solution of Navier-Stokes-Fourier converges, uniformly in space as time goes to infinity, to a viscous ansatz composed of viscous shock with time-dependent shift, a viscous contact wave and an inviscid rarefaction wave. This is a first resolution of the challenging open problem associated with the generic Riemann solution. Our approach relies on the method of a-contraction with shifts, specifically applied to both the shock wave and the contact discontinuity wave. It enables the application of a global energy method for the generic combination of three waves.Comment: arXiv admin note: text overlap with arXiv:2104.0659

    Study of supersonic nozzle flows in low-pressure environments: starting jets and lunar plume-surface interactions

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    Supersonic nozzle flows play an important role in aerospace engineering, e.g. controlling motions, attitudes, and orbits of space vehicles using various propulsion systems. Supersonic nozzle flows include free nozzle flows and restricted nozzle flows, such as plume-surface interactions if a surface obstructs the flow propagation. When compressed gas is discharged from a nozzle into a low-pressure environment in the case of free nozzle flows, the shock wave diffracts around the nozzle lip and a vortex loop forms. These phenomena have attracted much attention in the continuum flow regime, but how the shock diffraction and vortex behave under rarefied flow conditions has received less attention. Understanding transient flow in rarefied conditions is helpful for increasing thrust vector control and avoiding potential contamination and erosion of spacecraft surfaces. Furthermore, comprehending plume-surface interactions is critical for the design of lander modules and future bases on bodies such as the moon, as it is necessary to anticipate surface erosion patterns and the transport of displaced regolith material. Extraterrestrial conditions are difficult to recreate experimentally (e.g. the effects of low gravity, strong radiation and extreme temperature difference). Available numerical techniques for modelling regolith entrainment and subsequent movement suffer from limited accessibility and different levels of sophistication. In this thesis, a design for an open-ended shock tube connected to a vacuum chamber is presented. This is used to release a shockwave into a low-pressure environment and study the subsequent vortex ring formation as the gas diffracts around the shocktube exit. Schlieren visualisation and pressure measurements of the vortex ring formation are conducted. The flow structure degenerates through a decrease in the strength of the embedded shock waves and an increase in their thickness, and the counter-rotating vortex ring when the environmental pressure decreases. The existence of the vortex ring is confirmed through spectral analysis when the environmental pressure is as low as 1.0kPa. Due to limitations with experimental measurement equipment and techniques, the shock wave diffraction problem should be complemented with numerical techniques. A program to generate ensemble-averaged direct simulation Monte Carlo (DSMC) results is designed. Computational fluid dynamics (CFD) and ensemble-averaged DSMC methods are implemented to simulate the formation of a two-dimensional vortex loop due to shock wave diffraction around a 90◦ corner. The influence of the Mach number and rarefaction on the development and growth of the vortex loop are studied. A concept, called rorticity, was used to investigate the transient structures of vortex loops. The simplification of the internal structure of vortex loops and postponement of the vortex loop formation due to the increase of the rarefaction level are confirmed. Two properties from the decomposition equation of vorticity to quantify the vortex strength; rorticity flux (i.e. representing the vortex rotational strength), and the shear vector flux (i.e. representing the vortex shear movement strength), are derived. A mutual transformation relationship between the rorticity and shear vectors has been identified, suggesting that this concept can be employed to better explain vortex flow phenomena. It is found that the increase of the Knudsen number thickens the Knudsen layer, causing the failure of the generation of the vortex sheet and the subsequent formation of vortex loops. A new solver based on dsmcFoamPlus – rarefiedMultiphaseFoam, is developed for solving rarefied multiphase flows. The solver is extended to include a two-way coupling model and a particle phase change model. Additionally, the solid stochastic collison model and the multiphase nparticle-in-cell (MPPIC) method for solving dilute and dense granular flows, respectively, have been implemented in the new solver. The models mentioned are rigorously benchmarked against analytical solutions and previous results in the literature. The benchmarking results of the two-way coupling method show excellent agreement with analytical results. The results of a reproduced uniform gas-solid flow and a purely gravity-controlled granular flow sedimentation agree well with previous numerical results in the literature. A solid particle is allowed to experience a physical and continuous phase change and diameter variation using the updated phase change model. Finally, the rarefiedMultiphaseFoam solver is used to simulate two lunar plume-surface interaction (PSI) cases using the stochastic collision model and the MPPIC method, respectively. Both methods are applied to a scaled down version of the Apollo era lunar module descent engine and comparisons are made between the two simulation results. The results show that the transient effects are essential to both the gas and solid phase evolution and the entrained dust particles significantly influence the evolution of the gas flow. In the PSI simulations, the MPPIC method is more reliable than the stochastic collision method because it takes enduring contacts and the close-packing limit into account. Furthermore, it is identified that the breakdown of the locally free-molecular flow assumption has a significant impact on the solid particle temperatures

    Synchrotron radiography of Richtmyer–Meshkov instability driven by exploding wire arrays

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    We present a new technique for the investigation of shock-driven hydrodynamic phenomena in gases, liquids, and solids in arbitrary geometries. The technique consists of a pulsed power-driven resistive wire array explosion in combination with multi-MHz synchrotron radiography. Compared to commonly used techniques, it offers multiple advantages: (1) the shockwave geometry can be shaped to the requirements of the experiment, (2) the pressure (P > 300 MPa) generated by the exploding wires enables the use of liquid and solid hydrodynamic targets with well-characterized initial conditions (ICs), (3) the multi-MHz radiography enables data acquisition to occur within a single experiment, eliminating uncertainties regarding repeatability of the ICs and subsequent dynamics, and (4) the radiographic measurements enable estimation of compression ratios from the x-ray attenuation. In addition, the use of a synchrotron x-ray source allows the hydrodynamic samples to be volumetrically characterized at a high spatial resolution with synchrotron-based microtomography. This experimental technique is demonstrated by performing a planar Richtmyer–Meshkov instability (RMI) experiment on an aerogel–water interface characterized by Atwood number A 0 ∼ − 0.8 and Mach number M ∼ 1.5. The qualitative and quantitative features of the experiment are discussed, including the energy deposition into the exploding wires, shockwave generation, compression of the interface, startup phase of the instability, and asymptotic growth consistent with Richtmyer's impulsive theory. Additional effects unique to liquids and solids—such as cavitation bubbles caused by rarefaction flows or initial jetting due to small perturbations—are observed. It is also demonstrated that the technique is not shape dependent by driving a cylindrically convergent RMI experiment

    The Magnetic Field of Protostar-Disk-Outflow Systems

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    Recent observations of protostellar cores reveal complex magnetic field configurations that are distorted in the innermost disk region. Unlike the prestellar phase, where the magnetic field geometry is simpler with an hourglass configuration, magnetic fields in the protostellar phase are sculpted by the formation of outflows and rapid rotation. This gives rise to a significant azimuthal (or toroidal) component that has not yet been analytically modelled in the literature. Moreover, the onset of outflows, which act as angular momentum transport mechanisms, have received considerable attention in the past few decades. Two mechanisms: 1) the driving by the gradient of a twisted magnetic field (magnetic pressure gradient force or MPGF); and 2) the driving by magneto-centrifugal winds (MCW), are invoked in the literature and sometimes applied to different launch regions. The former arises when the toroidal component is dominant whereas the latter arises when the poloidal component is dominant near the surface of the accretion disk. By employing three-dimensional resistive non-ideal magnetohydronamics (MHD), the magnetic field of the disk-outflow system has been modelled and analyzed. A mathematical model for the azimuthal component is constructed via a pseudo-Fourier approach, while the poloidal component is an extension of the previous work done by Ewertowski \& Basu (2013). After fitting to simulation data, our results show that the full model is within reasonable agreement with the MHD data with a combined root mean squared error of ~10^{-4}. In addition, by generating a series of azimuthally averaged heat-maps, the driving mechanisms of the wide-angle outflow region is investigated. The heat-maps reveal not one single driver, but a hybrid driving mechanism arising from the MPGF or MCW mechanism in different regions, and extending well beyond the confines of the protostellar disk itself. A flow that is launched along field lines that are very inclined from the vertical is initially MCW-driven until it surpasses the Alfven surface, where it becomes MPGF-driven

    Nonlinear asymptotic stability of compressible vortex sheets with viscosity effects

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    This paper concerns the stabilizing effect of viscosity on the vortex sheets. It is found that although a vortex sheet is not a time-asymptotic attractor for the compressible Navier-Stokes equations, a viscous wave that approximates the vortex sheet on any finite time interval can be constructed explicitly, which is shown to be time-asymptotically stable in the L∞ L^\infty -space with small perturbations, regardless of the amplitude of the vortex sheet. The result shows that the viscosity has a strong stabilizing effect on the vortex sheets, which are generally unstable for the ideal compressible Euler equations even for short time [26,8,1]. The proof is based on the L2 L^2 -energy method.In particular, the asymptotic stability of the vortex sheet under small spatially periodic perturbations is proved by studying the dynamics of these spatial oscillations. The first key point in our analysis is to construct an ansatz to cancel these oscillations. Then using the Galilean transformation, we are able to find a shift function of the vortex sheet such that an anti-derivative technique works, which plays an important role in the energy estimates. Moreover, by introducing a new variable and using the intrinsic properties of the vortex sheet, we can achieve the optimal decay rates to the viscous wave.Comment: In the second version, a new remark is added behind the Theorems and some typos in the proof are correcte

    Plasma Waves and Rayleigh–Taylor Instability: Theory and Application

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    The presence of plasma density gradient is one of the main sources of Rayleigh–Taylor instability (RTI). The Rayleigh–Taylor instability has application in meteorology to explain cloud formations and in astrophysics to explain finger formation. It has wide applications in the inertial confinement fusion to determine the yield of the reaction. The aim of the chapter is to discuss the current status of the research related to RTI. The current research related to RTI has been reviewed, and general dispersion relation has been derived under the thermal motion of electron. The perturbed densities of ions and electrons are determined using two fluid approach under the small amplitude of oscillations. The dispersion equation is derived with the help of Poisson’s equation and solved numerically to investigate the effect of various parameters on the growth rate and real frequency. It has been shown that the real frequency increases with plasma density gradient, electron temperature and the wavenumber, but magnetic field has opposite effect on it. On the other hand, the growth rate of instability increases with magnetic field and density gradient, but it decreases with electron temperature and wave number
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