On the Threshold of Drop Fragmentation under Impulsive Acceleration

We examine the complete landscape of parameters which affect secondary breakup of a Newtonian droplet under impulsive acceleration. A Buckingham-Pi analysis reveals that the critical Weber number $\mathit{We}_\mathit{cr}$ for a non-vibrational breakup depends on the density ratio $(\rho)$, the drop $(\mathit{Oh}_d)$ and the ambient $(\mathit{Oh}_o)$ Ohnesorge numbers. Volume of fluid (VOF) multiphase flow simulations are performed using Basilisk to conduct a reasonably complete parametric sweep of the non-dimensional parameters involved. It is found that, contrary to current consensus, even for $\mathit{Oh}_d \leq 0.1$, a decrease in $\mathit{Oh}_d$ has a substantial impact on the breakup morphology, motivating plume formation. In addition to $\rho$, $\mathit{Oh}_o$ also affects the balance between pressure differences between a droplet's pole and its periphery, and the shear stresses on its upstream surface, which ultimately dictates the flow inside the droplet. This behavior manifests in simulations through the observed pancake shapes and ultimately the breakup morphology (forward or backward bag). All these factors affecting droplet deformation process are specified and theories explaining the observed results are provided. A $\mathit{We}_\mathit{cr}-\mathit{Oh}_d$ plot is provided to summarize all variations in $\mathit{We}_\mathit{cr}$ observed due to changes in the involved non-dimensional parameters. All observed critical pancake and breakup morphologies are summarized using a phase diagram illustrating all deformation paths a droplet might take under impulsive acceleration. Finally, based on the understanding of process of bag breakup gained from this work, a non-dimensional parameter to predict droplet breakup threshold is derived and tested on all simulation data obtained from this work and all experimental data gathered from existing literature

Study of the growth and development of a particle-laden richtmyer-meshkov instability using high order methods

La inestabilidad de Richtmyer-Meshkov (RM) ocurre cuando dos fluidos de distintas densidades son sometidos a una gran aceleración en una dirección opuesta al gradiente de densidades. Para resolver las ecuaciones de Navier-Stokes suponemos un flujo compresible en un dominio cerrado en dos dimensiones. Por un lado, iniciamos el código con una nube de partículas simulando un 4% en volumen y con velocidad inicial nula. Por otro lado, inicializamos la fase gaseosa de acuerdo con una onda de choque con un valor de Mach de 2.8. En el flujo acelerado tras el paso de la onda de choque, parecen dos tipos de inestabilidades de RM: una de ellas es gobernada por los fenómenos de baroclinidad, relacionada con los gradientes de presión y densidad; la otra se encuentra en la fase de partículas, en la cual, al no tener un gradiente de presión, no debería seguir la baroclinidad. En este trabajo mostramos los efectos y similitudes tanto cuantitativas como cualitativas del desarrollo de la fase no baroclínica de la inestabilidad de RM en la fase gaseosa. Palabras clave: Richtmyer-Meshkov, Inestabilidad, partículas, CFD, baroclinidad.Departamento de Ingeniería Energética y FluidomecánicaMáster en Ingeniería Industria

Study of magnetohydrodynamic effects for the richtmyer-meshkov instability

This work presents experimental and computational studies of the Richtmyer-Meshkov (RM) instability with Magnetohydrodynamic (MHD) effects. The experimental work does not consider the instability or its growth, but rather developes an atmospheric plasma jet for use in future magnetohydrodynamic experiments. The operating conditions of the torch are explored to optimize the ionized length of the plasma jet by varying the voltage-current characteristics and the gas low rates. Probe, spectral, and visual diagnostics are also developed in an effort to characterize the plasma. The probe diagnostics were unsuccessful but discussions are included to help improve the technique. The visual Mie-Scattering like technique is able to capture qualitative images of the plasma flow field and are ready for use in future hydrodynamic experiments where the qualitative growth is of interest. Simulations utilized the hydrocode FLAG, developed at Los Alamos National Laboratory, are performed on a 2D shock cylinder plasma-air interface where MHD effects work to remove vorticity from the interface and suppress RM growth. To study this magnetic field orientation, magnetic field strength, and incident Mach number are all varied in this study. It was found that the orientation of the magnetic fi eld relative to the shock wave direction causes different morphology and can effect the amount of observable RM suppression. Similarly, increasing the magnetic field strength reduces the effects of the baroclinic vorticity, responsible for RM growth, by generating strong MHD waves which carry the vorticity away from the interface quicker. Increasing the Mach number can also cause varying qualitative effects, with greater Mach numbers showing greater interfacial compression. But comparing the MHD RM to the RM instability at a single Mach number still shows suppresion of the instability. Finally a 3D cylindrical interface is simulated using the hydrocode ARES. These simulations compare the cylindrical Richtmyer-Meshkov to two cases of the MHD-RM instability; one with a parallel and one with a perpendicular magnetic fi eld of 500 Guass. As per literature, the magnetic cases exhibit suppression through decreased enstrophy, vorticity, and mixedness with respect to time in addition to the clear morphological differences.Includes bibliographical reference

From Perturbation to Ejecta: An Exploration of Mixing Regimes in the Blast-Driven Instability using High-speed Experiments and Hydrocode Simulations.

The fluid mixing caused by variable-density instabilities is important in a wide variety of scenarios from ocean mixing and astrophysical phenomena to nuclear fusion techniques and atomic weapons. This thesis explores the mixing resulting from a specific instability known as the Blast-Driven Instability (BDI). A novel experimental platform was designed and built with the intention of studying the BDI for this thesis. Using high speed experimental techniques, the first fully time-resolved observations of the BDI are made. An understanding of the general dynamics caused by the BDI are established. Analytical models used successfully in the literature are also shown to need modifications in order to capture the BDI behavior. These observations are then used to test two common mixing models (RANS and LES) in a digital-twin simulation designed to precisely match the novel facility used in the high-speed experiments. Simulation results are analyzed against the data and reasons for their agreement, or lack thereof, are explored in detail. The RANS and LES simulation are shown to capture the BDI development to the 0th order, at the least. The LES simulations are also shown to be crucially dependent upon the characterization of initial conditions. The experimental data is used in conjunction with the simulation results to explore the BDI's sensitivity to two key governing parameters. How changes in the governing parameters create qualitative and quantitative changes in the BDI's behavior is explored extensively. Incident blast-wave strength is shown to change the hydrodynamic time scale, while changes in density difference cause much more non-linear effects. Finally, various scaling attempts are investigated in an attempt to decipher how the mixing induced by the BDI can be explicitly linked to the governing parameters.Ph.D

Part I: The Equations of Plasma Physics and the Richtmyer-Meshkov Instability in Magnetohydrodynamics. Part II: Evolution of Perturbed Planar Shockwaves.

Part I: Mitigating the Richtmyer-Meshkov instability (RMI) is critical for energy production in inertial confinement fusion. Suitable plasma models are required to study the hydrodynamic and electromagnetic interactions associated with the RMI in a conducting medium. First, a sequence of asymptotic expansions in several small parameters, as formal limits of the non-dissipative and non-resistive two-fluid plasma equations, leads to five simplified plasma/magnetohydrodynamics (MHD) systems. Each system is characterized by its own physical range of validity and dispersion relations, and includes the widely used magnetohydrodynamic (MHD) and Hall-MHD equations. Next we focus on the RMI in MHD. Using ideal MHD, it has been shown that the RMI is suppressed by the presence of an external magnetic field. We utilize the incompressible, Hall-MHD model to investigate the stabilization mechanism when the plasma ion skin depth and Larmor radius are nonzero. The evolution of an impulsively accelerated, sinusoidally perturbed density interface between two conducting fluids is solved as a linearized initial-value problem. An initially uniform background magnetic field of arbitrary orientation is applied. The incipient RMI is found suppressed through oscillatory motions of the interface due to the ion cyclotron effect. This suppression is most effective for near tangential magnetic fields but becomes less effective with increasing plasma length scales. The vorticity dynamics that facilitates the stabilization is discussed. Part II: We consider the evolution of a planar gas-dynamic shock wave subject to smooth initial perturbations in both Mach number and shock shape profile. A complex variable formulation for the general shock motion is developed based on an expansion of the Euler equations proposed by Best [Shock Waves, {1}: 251-273, (1991)]. The zeroth-order truncation of Best's system is related to the well-known geometrical shock dynamics (GSD) equations while higher-order corrections provide a hierarchy of closed systems, as detailed initial flow conditions immediately behind the shock are prescribed. Solutions to Best's generalized GSD system for the evolution of two-dimensional perturbations are explored numerically up to second order in the weak and strong shock limits. Two specific problems are investigated: a shock generated by an impulsively accelerated piston with a corrugated surface, and a shock traversing a density gradient. For the piston-driven flow, it is shown that this approach allows full determination of derivative jump conditions across the shock required to specify initial conditions for the retained, higher-order correction equations. In both cases, spontaneous development of curvature singularity in the shock shape is detected. The critical time at which a singularity occurs follows a scaling inversely proportional to the initial perturbation size. This result agrees with the weakly nonlinear GSD analysis of Mostert et al. [J. Fluid Mech., {846}: 536-562, (2018)].</p