Shock-driven mixing: Experimental design and initial conditions

Journal of Fluid Mechanics, 2015

Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long enough times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late time behaviour of single-shocked Richtmyer-Meshkov Instability (RMI) and associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible-incompressible solver that removes the low-Mach number limitations of the compressible solvers, thus allowing numerical simulations of late time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

Shock Waves, 1999

We present an overview of the diagnostic methods used in shock-tube investigations of mixing induced by Richtmyer-Meshkov instability. The different diagnostic techniques are first briefly presented, and then reviewed in a simple single table, which lists their advantages and disadvantages, their technological characteristics and domain of validity, the physical parameters measured, the laboratory in which they were developed and an assessment of their mean cost.

OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information), 2007

Turbulent transport and mixing in the reshocked multi-mode Richtmyer-Meshkov instability is investigated using three-dimensional ninth-order weighted essentially non-oscillatory simulations. A two-mode initial perturbation with superposed random noise is used to model the Mach 1.5 air/SF 6 Vetter-Sturtevant [1] experiment. The mass fraction isosurfaces and density cross-sections show the detailed structure before, during, and after reshock. The effects of reshock are quantified using the baroclinic enstrophy production, buoyancy production, and shear production terms. The mixing layer growth agrees well with the experimental growth rate. The post-reshock growth is in good agreement with the Mikaelian reshock model [2].

2011

In the large eddy simulation ͑LES͒ approach, large-scale energy-containing structures are resolved, smaller structures are filtered out, and unresolved subgrid effects are modeled. Extensive recent work has demonstrated that predictive under-resolved simulations of the velocity fields in turbulent flows are possible without resorting to explicit subgrid models when using a class of physics-capturing high-resolution finite-volume numerical algorithms. This strategy is denoted as implicit LES ͑ILES͒. Tests in fundamental applications ranging from canonical to complex flows indicate that ILES is competitive with conventional LES in the LES realm proper-flows driven by large-scale features. The performance of ILES in the substantially more difficult problem of under-resolved material mixing driven by under-resolved velocity fields and initial conditions is a focus of the present work. Progress in addressing relevant resolution issues in studies of mixing driven by Richtmyer-Meshkov instabilities in planar shock-tube laboratory experiments is reported. Our particular focus is devoted to the initial material interface characterization and modeling difficulties, and effects of initial condition specifics ͑resolved spectral content͒ on transitional and late-time turbulent mixing-which were not previously addressed.

Physics of Fluids, 2015

We measure two-dimensional velocity and density fluctuations in a shock-driven heavy gas curtain for three different incident Mach numbers (M = 1.21, 1.36, and 1.50) and a fixed initial perturbation. We study the time evolution of the velocity and density fields and observe two different mixing transitions in this unsteady flow. The first transition is caused by small-scale mixing in vortex cores, while the second transition is related to increased homogenization across the mixing layer and a drive towards isotropy. By measuring the anisotropy of the velocity fluctuations and the evolution of the turbulent kinetic energy, we are able to assess the anisotropy of the flow. For the first time in Richtmyer-Meshkov (RM) flows, we measure and compare turbulent length scales derived from both the density and velocity field measurements, and we find ratios of Liepmann-Taylor to inner-viscous scales (λ L /λ ν) that are inconsistent with those found using Reynolds number scaling based on circulation, Re Γ , or based on turbulent kinetic energy, Re K. At late times, Re K better reflects the decay of the mixing field than Reynolds numbers that are based upon mixing width or circulation. We also estimate the time evolution of dissipation and Kolmogorov scales for the first time in RM flows. When we estimate the Taylor microscale (λ T) for our experiments using both density and velocity, the density microscale agrees well with the relationship λ T = √ 10δRe −1/2 where Re = Re K and δ is the mixing layer width, but the velocity-based Taylor microscale follows a new scaling of λ T = 10δRe −1/2 .

Physical Review Fluids, 2020

This paper provides insights into the process driving the fast transition of an impulsively accelerated, then decelerated interface between gases of different densities, such as the one produced by the Richtmyer-Meshkov instability, when the timescale of this transitional process is of the same order as the characteristic timescales representative of the resulting turbulence. In this context, a new experimental approach is exposed. For the first time, it allows to design well-defined initial gaseous interfaces in a multiparametric and controlled way, giving access to a precise statistical analysis of the flow. An overview of the main results obtained by means of strioscopic, particle image velocimetry and tomoscopic measurements is provided. They unravel the fast transition of the mixing zone to a turbulent state, as the imprint of the initial condition is lost and the dynamical spectral content covers a wide range of scales, compatible with the achievement of a self-similar trend on very short timescales.

Shock Waves, 2007

An attempt to extract velocity and molar fraction from a single hot-wire trace within a turbulent mixing zone induced by a shock accelerated gaseous interface has been proposed. Experiments have been conducted for negative and positive density jumps across the interface. The hot-wire signals clearly show interfaces between mixed and unmixed regions and the locations of incident and reflected shocks. With some hypotheses on the temperature, velocity and molar fraction profiles within the turbulent mixing zone have been obtained solving an inverse problem. Results show that if the molar fraction profiles follow physically coherent evolutions, those of the local velocity are strongly correlated with the choice of its variation range. So, we reasonably think that the results obtained from single wire have to remain limited to interface and shock locations. And it is only by coupling the present technique with the laser Doppler velocimetry, which we will be able to possibly obtain reliable estimates of the variations of quantities in the turbulent mixing zone.

Physical Review E, 2007

The ninth-order weighted essentially nonoscillatory ͑WENO͒ shock-capturing method is used to investigate the physics of reshock and mixing in two-dimensional single-mode Richtmyer-Meshkov instability to late times. The initial conditions and computational domain were adapted from the Mach 1.21 air ͑acetone͒/SF 6 shock tube experiment of Collins and Jacobs ͓J. Fluid Mech. 464, 113 ͑2002͔͒: the growth of the bubble and spike amplitudes from fifth-and ninth-order WENO simulations of this experiment were compared to the predictions of linear and nonlinear amplitude growth models, and were shown to be in very good agreement with the experimental data prior to reshock by Latini, Schilling, and Don ͓Phys. Fluids 19, 024104 ͑2007͔͒. In the present investigation, the density, vorticity, baroclinic vorticity production, and simulated density Schlieren fields are first presented to qualitatively describe the reshock process. The baroclinic circulation deposition on the interface is shown to agree with the predictions of the Samtaney-Zabusky model and with linear instability theory. The time evolution of the positive and negative circulation on the interface is considered before and after reshock: it is shown that the magnitudes of the circulations are equal before as well as after reshock, until the interaction of the reflected rarefaction with the layer induces flow symmetry breaking and different evolutions of the magnitude of the positive and negative circulation. The post-reshock mixing layer growth is shown to be in generally good agreement with three models predicting linear growth for a short time following reshock. Next, a comprehensive investigation of local and global mixing properties as a function of time is performed. The distribution and amount of mixed fluid along the shock propagation direction is characterized using averaged mole fraction profiles, a fast kinetic reaction model, and mixing fractions. The modal distribution of energy in the mixing layer is quantified using the spectra of the fluctuating kinetic energy, fluctuating enstrophy, pressure variance, density variance, and baroclinic vorticity production variance. It is shown that a broad range of scales already exists prior to reshock, indicating that the single-mode Richtmyer-Meshkov instability develops nontrivial spectral content from its inception. The comparison of the spectra to the predictions of classical inertial subrange scalings in two-dimensional turbulence shows that the post-reshock spectra may be consistent with many of these scalings over wave number ranges less than a decade. At reshock, fluctuations in all fields ͑except for the density͒ are amplified across all scales. Reshock strongly amplifies the circulation, profiles, and mixing fractions, as well as the energy spectra and statistics, leading to enhanced mixing followed by a decay. The mole and mixing fraction profiles become nearly self-similar at late times following reshock; the mixing fraction exhibits an approach toward unity across the layer at the latest time, signifying nearly complete mixing of the gases. To directly quantify the amplification of fluctuations by reshock, the previously considered quantities are compared immediately after and before reshock. Finally, to investigate the decay of fluctuations in the absence of additional waves interacting with the mixing layer following reshock, the boundary condition at the end of the computational domain is changed from reflecting to outflow to allow the reflected rarefaction wave to exit the domain. It is demonstrated that the reflected rarefaction has an important role in breaking symmetry and achieving late-time statistical isotropy of the velocity field.

Journal of Fluid Mechanics, 2014

Experiments in Fluids, 2000

We describe a highly-detailed experimental characterization of the Richtmyer-Meshkov instability (the impulsively driven Rayleigh-Taylor instability) . In our experiment, a vertical curtain of heavy gas (SF 6 )¯ows into the test section of an air-®lled, horizontal shock tube. The instability evolves after a Mach 1.2 shock passes through the curtain. For visualization, we pre-mix the SF 6 with a small ($10 )5 ) volume fraction of sub-micron-sized glycol/water droplets. A horizontal section of the¯ow is illuminated by a light sheet produced by a combination of a customized, burst-mode Nd:YAG laser and a commercial pulsed laser. Three CCD cameras are employed in visualization. The``dynamic imaging camera'' images the entire test section, but does not detect the individual droplets. It produces a sequence of instantaneous images of local droplet concentration, which in the post-shock¯ow is proportional to density. The gas curtain is convected out of the test section about 1 ms after the shock passes through the curtain. A second camera images the initial conditions with high resolution, since the initial conditions vary from test to test. The third camera,``PIV camera,'' has a spatial resolution suf®cient to detect the individual droplets in the light sheet. Images from this camera are interrogated using Particle Image Velocimetry (PIV) to recover instantaneous snapshots of the velocity ®eld in a small (19´14 mm) ®eld of view. The ®delity of the¯ow-seeding technique for density-®eld acquisition and the reliability of the PIV technique are both quanti®ed in this paper. In combination with wide-®eld density data, PIV measurements give us additional physical insight into the evolution of the Richtmyer-Meshkov instability in a problem which serves as an excellent test case for general transition-to-turbulence studies.