Session T32: Flow Instability: Interfacial & Richtmyer-Meshkov

Studying the Interaction of Shocks and Turbulence in a Variable-Density Experiment

Inertial confinement fusion (ICF) capsules are often driven by multiple shocks. As the first shock travels across the ablator-fuel interface, imperfections in the interface give rise to the Richtmyer-Meshkov instability. Additionally, as the capsule accelerates and collapses, the density disparity between the ablator and fuel also creates the Rayleigh-Taylor instability. While questions remain to the nature of this mixing region, i.e., is it turbulent or not, a second shock crossing the layer will drive the mixture turbulent. Any additional shocks will then be crossing a variable-density turbulent mixing layer. Some single fluids studies have previously shown that shocks amplify the turbulence, increasing the velocity fluctuations and decreasing the length scales, while others have observed opposing effects. DNS simulations of shocks interacting with variable-density turbulence indicate an increase in the turbulence is expected. We seek to experimentally study the effect of shocks on variable density turbulence using the Vertical Shock Tube at Los Alamos National Laboratory. We have captured simultaneous velocity and density fields for an Air-SF6 turbulent layer and initial results have found that the turbulent intensity increases while the Taylor microscale decreases, suggesting an increasing in the mixing. We will discuss the results to date, including a comparison on the effects on the vorticity, the turbulent kinetic energy and the mixedness across different Reynolds number flows.

    

Turbulent mixing in multifluid vortex rings before & after shock interaction

In the intermediate stages of Richtmyer-Meshkov instability development, prior to the development of turbulence, vortical flow structures are commonly observed at the outer extents of the mixing region. The behavior of these structures and their evolution upon reshock may play an important role in the tails of the mixedness distribution, but they are difficult to repeatably study because of the inherently unstable mixing process. 

To capture these vortex-shock interaction events in isolation, an ensemble of simultaneous planar laser-induced fluorescence/particle image velocimetry measurements were acquired following the firing of a small, open-ended shock tube filled with either argon, CF₄, or SF₆ upwards into ambient nitrogen. The density mismatch between the initially unmixed light and heavy gases corresponds to Atwood numbers of 0.19, 0.51, and 0.67, respectively. The measurements capture the initial propagation of the heavy-gas vortex ring as well as its perturbation upon M=1.8 shock interaction.   

Experiments on the Richtmyer-Meshkov instability in a dual-driver vertical shock tube with variable shock-to-reshock times

Experiments on the Richtmyer-Meshkov Instability (RMI) using Particle Image Velocimetry (PIV) in a dual driver vertical shock tube are presented. Two shock waves generated at opposite ends of a vertical shock tube travel in opposing directions, impacting a perturbed interface formed between Air and Sulfur Hexaflouride (SF6). Perturbations are formed using a pair of voice coil driven pistons that generate Faraday waves on the interface. Shock strengths are chosen to result in halted interface motion after passage of the second shock wave, permitting a long observational window in which the instability can develop. The dual driver configuration allows for the order of arrival of the two shock waves, as well as the temporal spacing of their arrival, to be controlled. This permits a wide range of shock-to-reshock timings to be studied in both the incident and reshocked instability growth regimes. Light shock first and heavy shock first configurations are examined. Information on the growth of the RMI, including measurements of the growth exponent, θ, anisotropy, and turbulent kinetic energy decay are presented. The influence of the shock-to-reshock time on these parameters is discussed.   

Wall Vortices Induced by Re-Shock in RMI Shock Tube Experiments

The Richtmyer-Meshkov Instability (RMI) is frequently studied in shock tubes, where the walls and relatively narrow cross sections introduce boundary layers that influence the development of the RMI. Traditional RMI analysis assumes statistically two-dimensional flow and sufficient distance from wall effects; however, previous work has shown that vortices form in the boundary layer upon re-shock due to baroclinic vorticity deposition.  Experiments investigating this phenomenon were conducted in the Wisconsin Shock Tube Laboratory at UW-Madison using planar laser-induced florescence and particle image velocimetry for the case of a Mach 1.8 shock wave and an interface with an Atwood number of 0.75. Concurrently, a preliminary simulation using the LLNL hydrodynamics code Miranda was performed to further quantify the impact of the wall vortex on the interface evolution.  

    

Numerical simulation of Richtmyer-Meshkov instabilities in non-Newtonian fluids at positive and negative Atwood numbers

The development of Richtmyer-Meshkov instabilities in non-Newtonian fluids is studied using numerical simulations. These simulations are conducted using the open-source CFD code BlastFoam, which we have further developed to capture shear-thinning flows. This study reveals the influence of non-Newtonian effects on the characteristics of Richtmyer-Meshkov instability-driven structures and, in turn, the influence of these structures on the mixing process. This work is conducted with positive and negative Atwood numbers at low to high Mach numbers. Liquid deuterium and melted polymer are used and treated as Newtonian and non-Newtonian fluids, respectively. The results are compared with simulation cases where both fluids are treated as Newtonian fluids. This research aims to highlight a correlation between non-Newtonian viscosity and energy distribution at conditions relevant to planar shock-induced, inertially-confined nuclear fusion experiments.   

Richtmyer-Meshkov instability in an ion-electron multi-fluid plasma: the planar shock case in 3D and cylindrical converging shock case in 2D

The Richtmyer-Meshkov instability (RMI) results from the impulsive acceleration of a perturbed or planar (with perturbed flow field) density interface.

The RMI is ubiquitous in shock environments, inlcuding inertial confinement fusion (ICF), and may arise due to an interface of fluid species, isotopes, and temperature.

The plasma RMI is significantly affected by electromagnetic effects and can be modelled more accurately by a multifluid plasma (MFP) model rather than conventional magnetohydrodynamics.

We present MFP simulation results of a 3D ideal single-mode double-sine perturbation with a planar shock-wave, and 2D single-mode sine perturbation with a cylindrically converging shock-wave and elastic collisions.

The addition of elastic collisions and more complicated geometry/dimensionality is vital for understanding the plasma RMI and ICF fuel capsule dynamics.

The elastic collisions are modelled by Braginskii transport coefficients, representing the physical processes of thermal equilibration, inter-species drag, viscous momentum- and energy-transfers, and thermal conductivity.

The 3D results show strong symmetry and introduce large and small scale secondary perturbations along the primary density interface not previously seen in the 2D analogue.

The 2D simulations show the key effects of elastic collisions are: reduction of relative motion between the ion and electron fluids (consequently affecting the self-generated electromagnetic fields), introduction of momentum and energy anisotropy, and damping of high frequency plasma waves.

The net result is a general suppression of: the secondary electromagnetically driven Rayleigh-Taylor instability, Kelvin-Helmholtz instability, and small scale interface perturbations.   

Controlling the breakup of spiralling jets: results from experiments, non-linear simulations and linear stability analysis

We experimentally and numerically study the dynamics of a liquid jet issued from a rotating orifice, whose breakup is regulated by a vibrating piezo element. The helical trajectory of the spiralling jet yields fictitious forces varying along the jet whose longitudinal projections stretch and thin the jet, affecting the growth of perturbations. We show that by quantifying these fictitious forces, one can estimate the jet intact length and size distribution of drops formed at jet breakup. The presence of the locally varying fictitious forces may render high-frequency perturbations, that would otherwise be stable in the abscence of stretching, unstable, as observed similarly in the case of straight jets stretching under gravity. The perturbation amplitude then dictates how strong the perturbation is coupled to the jet compared to random noise that is inherently present in any experimental setup. In the present study, we exploit the slenderness of the jet to separate the calculation of the base flow and the growth of perturbations. The fictitious forces calculated from the base flow trajectory are then used in a nonlinear slender jet model, which treats the spiralling jet as a quasi-straight jet with locally varying body forces. We show both experimentally and numerically that jet breakup characteristics (e.g., intact length and drop size distribution) can be controlled by finite amplitude perturbations created by mechanically induced pressure modulations. Finally, we revisit the integrated net gain approach developed for straight jets under gravity and we provide simple analogous relations for spiralling jets.   

Three-dimensional visualization of surface waves and flow instability of liquid film flow on a spinning disk

Liquid film flow over a spinning disk is a common phenomenon in the industry, such as cleaning wafers. Despite its generality, previous studies have only revealed a simple shape of surface waves without exact information. Perhaps, the scientific complexity of this flow regarding surface tension, centrifugal, and Coriolis forces are due to the fact that there has been a general lack of direct experimental visualization. In this study, we provide a direct high spatiotemporal resolution visualization of thin film flow on the spinning disk using a fluorescent imaging method. With a good agreement of surface waves from circular to turbulent patterns along with inlet flow rates and spin speeds, we identify the existence of capillary ripples and wave amplitude (i.e., film thickness) that have not been reported in previous studies. In detail, if an inertia effect becomes dominant as flow rate and/or spin speed increases, we observed the shape of the main hump becomes unsymmetric. In this case, capillary ripples were found in front of it, which show a small amplitude and multiple crests. On the other hand, if the capillary effect becomes dominant, the main hump retains a symmetric shape, and a capillary ripple was not shown.   

Drop Detachment from Liquid/Liquid Interfaces in Vortex-Induced Waves

The dynamics of drop detachment from the interface during the pipe flow of two immiscible liquids are investigated experimentally and numerically. The experiments were carried out with 5 CST Silicone oil and tap water in a 26 mm ID pipe. We employ a transverse cylinder of 5.5mm diameter for generating vortex-induced waves in the stratified regime. It was found that as flow velocity increases in a stratified flow, the interface becomes wavy until eventually drops detach and entrain into the opposite phase; this marks the onset of the transition to dual continuous and then dispersed flows.  We observed that the wave crests or troughs deform to ligaments which elongate inside the other phase. The relative motion of the two phases stretches the ligament further until it becomes very thin and finally ruptures to form a droplet. We performed a parametric study to reveal the role of surface tension with numerical simulations.

    

Shock tube experiments of Richtmyer-Meshkov turbulence with reshock

Shock-driven turbulence may arise when a shock wave interacts multiple times with an interface separating two fluids of different densities and is important in many applications such as inertial confinement fusion. In this work, we perform Richtmyer-Meshkov experiments in a vertical shock tube containing a light fluid (air) sitting on top of a heavy fluid (SF6), and in which an initial single mode perturbation is imposed by a controlled flapping motion. A shock wave traveling from air to SF6 interacts a first time with the interface before reflecting off the bottom of the shock tube to interact with the interface a second time. Simultaneous planar laser-induced fluorescence and particle image velocimetry measurements are taken for three different shock Mach numbers (1.1 < Ms < 1.5), which allows us to access both the density and velocity fields. The high repetition rate of the experiments allows us to obtain second-order turbulence statistics, which are used to compare to and validate a variable-density turbulence model (BHR).   

Combined effect of ambient relative humidity and evaporation on the demixing of a binary mixture

As per known data, hexane and Diethylene Glycol Monoethyl Ether (DGME) are miscible at temperatures above ~7°C (critical solution temperature, CST), manifesting a miscibility gap at lower temperatures. Yet, if we depose a hexane-DGME layer or sessile droplet, we observe, quite unexpectedly, demixing already at room temperature. As hexane is volatile, one might think this was due to evaporative cooling, bringing the temperature down to CST. However, estimations and direct measurements reveal the associated temperature decrease is by far less drastic. Then, we hypothesize that such an anomalous demixing could be caused by moisture in the ambient atmosphere. After all, even if hexane is practically immiscible with water, DGME is hygroscopic. To verify the conjecture, a series of experiments were carried out in a chamber with well controlled temperature and relative humidity (RH), where a layer of hexane-DGME mixture was observed by reflective shadowgraphy. In this way, we were able to measure the 'apparent' CST as a function of RH, which indeed tends to ~7°C in the limit of small RH. Our picture of the phenomenon is also well backed up with an heuristic model of ternary mixture (also including water) based on regular-solution and van Laar fits of the known binary-pair properties.   

Formation of the cavity on a planar interface subjected to a perturbed shock wave

We report the mechanism and modeling for the formation of cavity-like structures on a planar interface subjected to a perturbed shock wave, which are distinguished from bubbles and spikes formed in the regular Richtmyer-Meshkov instability (RMI). The two-dimensional direct numerical simulation is conducted at a range of shock Mach numbers and Atwood numbers. We elucidate the effects of the interfacial vorticity and the shock-induced vorticity on the cavity formation. The interfacial vorticity, which is important in the regular RMI, only has a very minor influence on the cavity width in the linear stage. Alternatively, the cavity width is determined by the Mach-stem height when the shock accelerates the interface. A pair of vorticity patches connecting the Mach stem, as a part of the shock-induced vorticity, penetrate the interface to form the cavity via strong shear layers generated by slipstreams during shock propagation. Inspired by this mechanism, we develop a model of the Mach-stem height to estimate the cavity width. This model captures the cavity width well at various Mach numbers.