Jeffrey Greenough

A computational parameter study for the three-dimensional shock-bubble interaction

The morphology and time-dependent integral properties of the multifluid compressible flow resulting from the shock–bubble interaction in a gas environment are investigated using a series of three-dimensional multifluid-Eulerian simulations. The bubble consists of a spherical gas volume of radius 2.54 cm (128 grid points), which is accelerated by a planar shock wave. Fourteen scenarios are considered: four gas pairings, including Atwood numbers −0.8 A M ≤ 5.0. The data are queried at closely spaced time intervals to obtain the time-dependent volumetric compression, mean bubble fluid velocity, circulation and extent of mixing in the shocked-bubble flow. Scaling arguments based on various properties computed from one-dimensional gasdynamics are found to collapse the trends in these quantities successfully for fixed A . However, complex changes in the shock-wave refraction pattern introduce effects that do not scale across differing gas pairings, and for some scenarios with A > 0.2, three-dimensional (non-axisymmetric) effects become particularly significant in the total enstrophy at late times. A new model for the total velocity circulation is proposed, also based on properties derived from one-dimensional gasdynamics, which compares favourably with circulation data obtained from calculations, relative to existing models. The action of nonlinear-acoustic effects and primary and secondary vorticity production is depicted in sequenced visualizations of the density and vorticity fields, which indicate the significance of both secondary vorticity generation and turbulent effects, particularly for M > 2 and A > 0.2. Movies are available with the online version of the paper.

Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations

The last 20 years have seen a wide variety of high-resolution methods that can compute sharp, oscillation-free compressible flows. Here, we combine a complementary set of these methods together in a nonlinear (hybridized) fashion. Our base method is built on a monotone high-resolution Godunov method, the piece-wise parabolic method (PPM). PPM is combined with WENO methods, which reduce the damping of extrema. We find that the relative efficiency of the WENO methods is enhanced by coupling them with the relatively inexpensive Godunov methods. We accomplish our hybridizations through the use of a bounding principle: the approximation used is bounded by two nonlinearly stable approximations. The essential aspect of the method is to have high-order accurate approximations bounded by two non-oscillatory (nonlinearly stable) approximations. The end result is an accuracy-, monotonicity- and extrema-preserving method. These methods are demonstrated on a variety of flows, with quantitative analysis of the solutions with shocks.

Shock tube experiments and numerical simulation of the single-mode, three-dimensional Richtmyer–Meshkov instability

A vertical shock tube is used to perform experiments on the single-mode three-dimensional Richtmyer-Meshkov Instability. The interface is formed using apposed flows of air and SF6 and the perturbation is created by the periodic motion of the gases within the shock tube. Planar laser induced fluorescence is used for flow visualization. Experimental results were obtained with a shock Mach number of 1.2. A three-dimensional numerical simulation of this experiment was conducted the results of which are compared with the experimental images and measurements.

Radiation diffusion for multi-fluid Eulerian hydrodynamics with adaptive mesh refinement

Block-structured meshes provide the ability to concentrate grid points and computational effort in interesting regions of a flow field, without sacrificing the efficiency and low memory requirements of a regular grid. We describe an algorithm for simulating radiation diffusion on such a mesh, coupled to multi-fluid gasdynamics. Conservation laws are enforced by using locally conservative difference schemes along with explicit synchronization operations between different levels of refinement. In unsteady calculations each refinement level is advanced at its own optimal timestep. Particular attention is given to the appropriate coupling between the fluid energy and the radiation field, the behavior of the discretization at sharp interfaces, and the form of synchronization between levels required for energy conservation in the diffusion process. Two- and three-dimensional examples are presented, including parallel calculations performed on an IBM SP-2.

Shock-bubble interactions : Features of divergent shock-refraction geometry observed in experiments and simulations

The interaction of a planar shock wave with a spherical bubble in divergent shock-refraction geometry is studied here using shock tube experiments and numerical simulations. The particular case of a helium bubble in ambient air or nitrogen (A≈−0.8) is considered, for 1.4<M<3.0. Experimental planar laser diagnostics and three-dimensional multifluid Eulerian simulations clearly resolve features arising as a consequence of divergent shock refraction, including the formation of a long-lived primary vortex ring, as well as counter-rotating secondary and tertiary upstream vortex rings that appear at late times for M⩾2. Remarkable correspondence between experimental and numerical results is observed, which improves with increasing M, and three-dimensional effects are found to be relatively insignificant. Shocked-bubble velocities, length scales, and circulations extracted from simulations and experiments are used successfully to evaluate the usefulness of various analytical models, and characteristic dimensionle...

Experimental and numerical investigation of shock-induced distortion of a spherical gas inhomogeneity

Results are presented from a series of experiments and simulations, studying the interaction of a planar shock wave (2.0≤M≤5.0) with a discrete gas inhomogeneity. Experiments and computations confirm that the phenomenology of shock–bubble interactions is fundamentally altered by the changes in the Atwood number. In the case of a low Atwood number, the late time flow field is dominated by coherent vortical structures, whereas in the case of a high Atwood number, the shocked bubble is effectively reduced to a small core of compressed fluid, which trails behind a plume-like structure indicative of a well-developed mixing region.

Large eddy simulation requirements for the Richtmyer-Meshkov instability

The shock induced mixing of two gases separated by a perturbed interface is investigated through Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). In a simulation, physical dissipation of the velocity field and species mass fraction often compete with numerical dissipation arising from the errors of the numerical method. In a DNS, the computational mesh resolves all physical gradients of the flow and the relative effect of numerical dissipation is small. In LES, unresolved scales are present and numerical dissipation can have a large impact on the flow, depending on the computational mesh. A suite of simulations explores the space between these two extremes by studying the effects of grid resolution, Reynolds number, and numerical method on the mixing process. Results from a DNS are shown using two different codes that use a high- and low-order numerical method and show convergence in the temporal and spectral dependent quantities associated with mixing. Data from an unresolved, high Reyn...

An adaptive multifluid interface-capturing method for compressible flow in complex geometries

We present a numerical method for solving the multifluid equations of gas dynamics using an operator-split second-order Godunov method for flow in complex geometries in two and three dimensions. The multifluid system treats the fluid components as thermodynamically distinct entities and correctly models fluids with different compressibilities. This treatment allows a general equation-of-state (EOS) specification and the method is implemented so that the EOS references are minimized. The current method is complementary to volume-of-fluid (VOF) methods in the sense that a VOF representation is used, but no interface reconstruction is performed. The Godunov integrator captures the interface during the solution process. The basic multifluid integrator is coupled to a Cartesian grid algorithm that also uses a VOF representation of the fluid-body interface. This representation of the fluid-body interface allows the algorithm to easily accommodate arbitrarily complex geometries. The resulting single grid multifluid-Cartesian grid integration scheme is coupled to a local adaptive mesh refinement algorithm that dynamically refines selected regions of the computational grid to achieve a desired level of accuracy. The overall method is fully conservative with respect to the total mixture. The method will be used for a simple nozzle problem in two-dimensional axisymmetric coordinates.

Comparison of two- and three-dimensional simulations of miscible Richtmyer-Meshkov instability with multimode initial conditions

A comparison between two- and three-dimensional large-eddy simulations of the planar Richtmyer-Meshkov instability with multimode initial conditions is made. The three-dimensional calculation achieves a turbulent state where an inertial range of length scales is present after the second shock wave impacts the interface. Grid independence of the mixing width up until the time of reshock is demonstrated through mesh refinement in both two and three dimensions. Quantitative measures of mixing are compared including the mixing width, mixedness, mixed mass, and spectra of velocity and density. A proposed approximate relation for the mixed mass is evaluated in one, two, and three dimensions and is proportional to the product of the mixing width and the mass fraction variance in the layer. The variance of the velocity field and the scalar mass fraction are compared in two and three dimensions and demonstrate large differences in behavior.

Simulations and Analysis of the Reshocked Inclined Interface Richtmyer–Meshkov Instability for Linear and Nonlinear Interface Perturbations

A computational study of the Richtmyer–Meshkov instability (RMI) is presented for an inclined interface perturbation in support of experiments being performed at the Texas A&M shock tube facility. The study is comprised of 2D, viscous, diffusive, compressible simulations performed using the arbitrary Lagrange Eulerian code, ARES, developed at Lawrence Livermore National Laboratory. These simulations were performed to late times after reshock with two initial interface perturbations, in the linear and nonlinear regimes each, prescribed by the interface inclination angle. The interaction of the interface with the reshock wave produced a complex 2D set of compressible wave interactions including expansion waves, which also interacted with the interface. Distinct differences in the interface growth rates prior to reshock were found in previous work. The current work provides in-depth analysis of the vorticity and enstrophy fields to elucidate the physics of reshock for the inclined interface RMI. After reshock, the two cases exhibit some similarities in integral measurements despite their disparate initial conditions but also show different vorticity decay trends, power law decay for the nonlinear and linear decay for the linear perturbation case.