Devesh Ranjan

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.

Experimental validation of a Richtmyer-Meshkov scaling law over large density ratio and shock strength ranges

A universal scaling law for the Richtmyer–Meshkov instability is validated with experimental results covering a wide range of density ratios and shock strengths. These results include the first membraneless, gas-phase, interface experiments for A>0.5 and M>1.5. The shock-accelerated, sinusoidal interface experiments are conducted in a vertical shock tube with a large square cross section and cover the experimental parameter space: 0.29<A<0.95, 1.1<M<3, and 3.1×104<Re<1.4×107. Results provide growth-rate data for comparison with computational fluid dynamics simulation codes and verify the nondimensional time and amplitude parameters chosen for scaling are the correct ones. Correct scaling is obtained by including a growth-reduction factor that accounts for diffusion at the interface. Planar imaging techniques are used to diagnose the instability development for a nearly single-mode interface, and results are reported for eight scenarios (including three distinct gas pairs) that span the linear and nonlinea...

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.

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.

Non-uniform volumetric structures in Richtmyer-Meshkov flows

We perform an integrated study of volumetric structures in Richtmyer-Meshkov (RM) flows induced by moderate shocks. Experiments, theoretical analyses, Smoothed Particle Hydrodynamics simulations, and ARES Arbitrary Lagrange Eulerian simulations are employed to analyze RM evolution for fluids with contrast densities in case of moderately small amplitude initial perturbation at the fluid interface. After the shock passage the dynamics of the fluids is a superposition of the background motion and the interfacial mixing, and only a small part of the shock energy is available for interfacial mixing. We find that in the fluid bulk the flow fields are non-uniform at small scales, and the heterogeneous volumetric structures include reverse jets, shock-focusing effects, and local hot spots with the temperature substantially higher than that in the ambient.

Investigation of the initial perturbation amplitude for the inclined interface Richtmyer?Meshkov instability

A simulation studying the effects of inclination angle and incident shock Mach number on the inclined interface Richtmyer–Meshkov instability is presented. Interface inclination angle is varied from 30° to 85°, with incident shock Mach numbers of 1.5, 2.0 and 2.5 for an air over SF6 interface. The simulations were performed in support of experiments to be performed in the Texas A&M shock tube facility, and were created with the ARES code developed at Lawrence Livermore National Laboratory. The parametric cases are separated by inclination angle into nonlinear and linear initial perturbation cases. A linear initial perturbation is defined as when the interface amplitude over wavelength is less than 0.1. Density, pressure gradient and vorticity plots are presented for a nonlinear and a linear case to highlight the differences in the flow field evolution. It is shown that the nonlinear case contains strong secondary compressible effects which reverberate through the interface until late times, while in the linear case these waves are almost completely absent. The inclined interface scaling method presented in previous work (McFarland et al 2011 Phys. Rev. E 84 026303) is tested for its ability to scale the mixing width growth rate for linear initial perturbation cases. This model was shown in the previous work to collapse data well for varying Mach numbers and nonlinear inclination angles. The scaled data is presented to show that a regime change occurs in the mixing width growth rate near an inclination angle of 80° which corresponds to the transition from a linear to nonlinear initial perturbation.

Experimental investigation of a twice-shocked spherical density inhomogeneity

Results are presented from a series of experiments investigating the behavior of a twice-shocked spherical density inhomogeneity. The experiments are performed at the Wisconsin Shock Tube Laboratorys (WiSTL) 9?m long vertical shock tube with a square internal cross section, 0.254?m on a side, equipped with a pneumatically retracting bubble injector. Baroclinic vorticity deposition occurs during the interaction of the shock wave with the spherical density inhomogeneity, leading to the formation of a vortex ring. The incident shock wave reflects from the tube end wall and interacts with the translating vortex ring (reshock), resulting in additional vorticity deposition. After reshock, the ambient particle velocity is zero and the subsequent translational motion of the vortex ring is due entirely to the net circulation present. Circulation models are investigated for the reshock scenario and a new model is developed and applied to both once-shocked and reshocked scenarios. Two Atwood numbers (A=0.17,?0.68) and three initial Mach numbers (M=1.35,?2.00,?2.33) are investigated. High-speed cameras at 10?000?fps are used to observe the development of the vortex ring after reshock. An understanding of the shock-induced compression and vortex generation is vital to the future study of turbulent combustion initiated by the shock focusing phenomenon.

Experimental study for ICF-related richtmyer-meshkov instabilities

Abstract Richtmyer-Meshkov experiments for a membrane-less, sinusoidal gas interface are carried out in a vertical shock tube for a pre-shock Atwood number (A = (σ2 – σ1)/(σ1 + σ2)) of approximately 0.68 at M = 1.26 and M = 2.05. The perturbation amplitude is obtained by analyzing a time sequence of pre-shock and post-shock images. The Mikaelian and Dimonte & Schneider models both predict the observed growth in the perturbation amplitude, with better agreement obtained for the data at M = 1.26.

Computations in 3D for shock-induced distortion of a light spherical gas inhomogeneity

Results are presented from a series of 3D numerical simulations for shock-bubble interactions, for a spherical helium bubble in air or nitrogen initially at atmospheric pressure (A≈ -0.75), accelerated by a planar shock wave of Mach number M = 1.45, 2.08, or 2.95. The simulations are carried out using a multifluid, adaptive Eulerian Godunov code at a fine-grid resolution of R 100. The computed solutions clearly resolve well-known shock refraction and vortex formation processes. Further, distinct, counter-rotating secondary vortex rings are observed to form in the flowfield as a result of irregular shock refraction effects. The temporal development of the the bubble’s streamwise dimension and the mixing of bubble and ambient fluid are shown to collapse onto nearly self-similar trends on timescales based on a 1D gasdynamics analysis.