Viscous effects on the non-classical Rayleigh–Taylor instability of spherical material interfaces

The viscous and conductivity effects on the instability of a rapidly expanding material interface produced by a spherical shock tube are investigated through the employment of a high-order WENO scheme. The instability is influenced by various mechanisms, which include (a) classical Rayleigh–Taylor (RT) effects, (b) Bell–Plesset or geometry/curvature effects, (c) the effects of impulsively accelerating the interface, (d) compressibility effects, (e) finite thickness effects, and (f) viscous effects. Henceforth, the present instability studied is more appropriately referred to as non-classical RT instability to distinguish it from classical RT instability. The linear regime is examined and the development of the viscous three-dimensional perturbations is obtained by solving a one-dimensional system of partial differential equations. Numerical simulations are performed to illustrate the viscous effects on the growth of the disturbances for various conditions. The inviscid analysis does not show the existence of a maximum amplification rate. The present viscous analysis, however, shows that the growth rate increases with increasing the wave number, but there exists a peak wavenumber beyond which the growth rate decreases with increasing the wave number due to viscous effects.     

Comparison between Kelvin–Helmholtz instability experiments on OMEGA and simulation results using the CRASH code

The Center for Radiative Shock Hydrodynamics (CRASH) at the University of Michigan has developed a Eulerian radiation-hydrodynamics code with dynamic adaptive mesh refinement, CRASH, which can model high-energy-density laser-driven experiments. One of these experiments, performed previously on the OMEGA laser facility, was designed to produce and observe the Kelvin–Helmholtz instability. The target design included low-density carbonized-resorcinol-formaldehyde (CRF) foam layered on top of polyamide–imide plastic, with a sinusoidal perturbation on the interface and with the assembled materials encased in beryllium. The results of a series of CRASH simulations of these Kelvin–Helmholtz instability experiments are presented. These simulation results show good agreement both quantitatively and qualitatively with the experimental data.     

Rayleigh–Taylor instability of high-velocity condensed-matter liners

A review of publications on the Rayleigh–Taylor instability arising during high-velocity implosion of liners is presented. Papers that describe experimental testing and numerical simulation of the development and suppression of this instability are also considered.     

Discrete particle modeling of granular Rayleigh–Taylor instability

The gravitational air–grain Rayleigh–Taylor (RT) flow instability in a Hele-Shaw cell was studied using a parallel three-dimensional discrete particle model (DPM). The onset of flow instability and the development of fingering flow structures were well captured by the model. Power spectra analysis of solid volume fraction field indicated the non-linear coarsening process of the fingering flow structures. The sensitivity of the flow patterns to the initial porosity, the Atwood number, and the ratio of particle size to the Hele-Shaw cell width was also demonstrated. The excellent agreement of DPM simulation results with the reported experimental observations proved the robustness and reliability of the numerical approach to model complex multiphase flows such as granular RT instability.     

Rayleigh–Taylor instability of immiscible fluids in porous media

The time development of an interface separating two immiscible fluids of different densities in heterogeneous two-dimensional porous media is studied. The governing equations are simplified with the help of approximate Green’s functions which allow computation of the shape of the interface directly without resolving the fluid flow in the entire domain. The new formulation is amenable to numerical approximation, and the reduction in dimension leads to a significant gain in efficiency in the numerical simulation of the interfacial dynamics. Several test cases are investigated, and the numerical solutions are compared to known exact solutions and experimental data.     

Deforming static fluid interfaces with magnetic fields: application to the Rayleigh–Taylor instability

Shaping arbitrary fluid interfaces opens interesting perspectives for fluid-based processes and experiments. We demonstrate an experimental method to create non-planar static interfaces of almost arbitrary shape between two fluids, one of which is made highly magnetically permeable by the addition of a magnetic compound. By relying on spatially modulated magnetic fields, a non-homogeneous magnetic force is added to Earth's gravitational force, and a non-planar static interface can be stabilized. Precision experimental measurements are possible because we have developed a general method that allows us to predict numerically the shape of the interface, thereby facilitating the optimal experimental design before actually implementing it. As a first example, we apply this method to the Rayleigh–Taylor instability between two immiscible fluids. The results we obtain demonstrate the feasibility of the experimental method and the accuracy of the numerical predictions.     

Design and implementation plan for indirect-drive highly nonlinear ablative Rayleigh–Taylor instability experiments on the National Ignition Facility

In the context of National Ignition Facility Basic Science program we propose to study on the NIF ablative Rayleigh–Taylor (RT) instability in transition from weakly nonlinear to highly nonlinear regimes. Based on the analogy between flame front and ablation front, highly nonlinear RT instability measurements at the ablation front can provide important insights into the initial deflagration stage of thermonuclear supernovae of type Ia. NIF provides a unique platform to study the rich physics of nonlinear and turbulent mixing flows in High Energy Density plasmas because it can accelerate targets over much larger distances and longer time periods than previously achieved on the NOVA and OMEGA lasers. In one shot, growth of RT modulations can be measured from the weakly nonlinear stage near nonlinear saturation levels to the highly nonlinear bubble-competition, bubble-merger regimes and perhaps into a turbulent-like regime. The role of ablation on highly-nonlinear RT instability evolution will be comprehensively studied by varying ablation velocity using indirect and direct-drive platforms. We present a detailed hydrocode design of the indirect-drive platform and discuss the implementation plan for these experiments which only use NIF diagnostics already qualified.     

Non-linear characteristics of Rayleigh–Taylor instable perturbations

The direct numerical simulation method is adopted to study the non-linear characteristics of Rayleigh-Taylor instable perturbations at the ablation front of a 200 μm planar CH ablation target. In the simulation, the classical electrical thermal conductivity is included, and NND difference scheme is used. The linear growth rates obtained from the simulation agree with the Takabe formula. The ampli- tude distribution of the density perturbation at the ablation front is obtained for the linear growth case. The non-linear characteristics of Rayleigh-Taylor instable perturbations are analyzed and the numerical results show that the amplitude distributions of the compulsive harmonics are very different from that of the fundamental perturbation. The characteristics of the amplitude distributions of the harmonics and their fast growth explain why spikes occur at the ablation front. The numerical results also show that non-linear effects have relations with the phase differences of double mode initial perturbations, and different phase differences lead to varied spikes.     

Coriolis effects on the stability of pulsed flows in a Taylor–Couette geometry

Results steming from the linear stability of time-periodic flows in a Taylor–Couette geometry with cylinders oscillating in phase or out-of-phase are presented. Our analysis takes into account the gap size effects and investigates the influence of a superimposed mean angular rotation of the whole system.In case of no mean rotation, the finite gap geometry is found to affect the shape of the stability diagrams (critical Taylor number versus the frequency parameter) which consist of two distinct branches as opposed to being continuous in the narrow gap approximation. In particular, in the out-of-phase configuration a new branch for low frequencies was found, thus enabling better agreement with available experimental results.When cylinders are co-rotating and subject to rotation effects, our calculations provide the evolution of the critical Taylor number versus the rotation number for two values of the frequency. The stability curves are found to be in qualitative agreement with available experimental data revealing a maximum of instability for a rotation number of about 0.3.In the high rotation regime, enhancement of the critical Taylor number is investigated through an asymptotic analysis and the value of the rotation number at which restabilization occurs is found to depend on the frequency parameter.A restabilization of the flow also occurs when the rotation number and the gap size are of the same order, a phenomenon already pointed out in the case of steady flows and attributed to the near cancellation of Coriolis and centrifugal effects. Our investigation proves that the same mechanism still holds for time-periodic flows.     

The Braginskii model of the Rayleigh–Taylor instability. I. Effects of self-generated magnetic fields and thermal conduction in two dimensions

There exists a substantial disagreement between computer simulation results and high-energy density laboratory experiments of the Rayleigh–Taylor instability [1]. Motivated by the observed discrepancies in morphology and growth rates, we attempt to bring simulations and experiments into better agreement by extending the classic purely hydrodynamic model to include self-generation of magnetic fields and anisotropic thermal conduction.We adopt the Braginskii formulation for transport in hot, dense plasma, implement and verify the additional physics modules, and conduct a computational study of a single-mode RTI in two dimensions with various combinations of the newly implemented modules. We analyze physics effects on the RTI mixing and flow morphology, the effects of mutual physics interactions, and the evolution of magnetic fields.We find that magnetic fields reach levels on the order of 11 MG (plasma β ≈ 9.1 × 10^?2) in the absence of thermal conduction. These fields do not affect the growth of the mixed layer but substantially modify its internal structure on smaller scales. In particular, we observe denting of the RT spike tip and generation of additional higher order modes as a result of these fields. Contrary to interpretation presented in earlier work [2], the additional mode is not generated due to modified anisotropic heat transport effects but due to dynamical effect of self-generated magnetic fields. The overall flow morphology in self-magnetized, non-conducting models is qualitatively different from models with a pre-existing uniform field oriented perpendicular to the interface. This puts the usefulness of simple MHD models for interpreting the evolution of self-magnetizing HED systems with zero-field initial conditions into doubt.The main effects of thermal conduction are a reduction of the RT instability growth rate (by about 20% for conditions considered here) and inhibited mixing on small scales. In this case, the maximum self-generated magnetic fields are weaker (approximately 1.7 MG; plasma β ≈ 49). This is due to reduction of temperature and density gradients due to conduction. These self-generated magnetic fields are of very similar strength compared to magnetic fields observed recently in HED laboratory experiments [3].We find that thermal conduction plays the dominant role in the evolution of the model RTI system considered. It smears out small-scale structure and reduces the RTI growth rate. This may account for the relatively featureless RT spikes seen in experiments, but does not explain mass extensions observed in experiments.Resistivity, related heat source terms and the thermo-electric contribution to the heat flow were not included in the present work. We estimate their impact on RTI as modest and not affecting our main conclusions. These effects will be discussed in detail in the next paper in the series.     

Taylor–Dean instability of yield-stress fluids at large gaps

Centrifugal instability of Bingham fluids is investigated in Taylor–Dean flow when the gap size is large compared to the cylinders radii. To determine conditions for the onset of instability, an infinitesimal axisymmetric disturbance was introduced to the basic flow and its evolution in time was monitored using a normal-mode linear stability analysis. To avoid the problem with the stress discontinuity at the location of the yield surface(s), use was made of the Papanastasiou’s regularized variation of the Bingham model in order to obtain the basic flow velocity profiles. An eigenvalue problem was obtained for the exact Bingham fluid which was solved numerically using the collocation method. A plot of the neutral instability curve at different Bingham numbers suggests that the yield stress can have a stabilizing or destabilizing effect on Taylor–Dean flow depending on the sign and magnitude of the pressure gradient, and also on the sense of rotation of the two cylinders with respect to each other.     

Modeling the mechanics of HMX detonation using a Taylor–Galerkin scheme

Design of energetic materials is an exciting area in mechanics and materials science. Energetic composite materials are used as propellants, explosives, and fuel cell components. Energy release in these materials are accompanied by extreme events: shock waves travel at typical speeds of several thousand meters per second and the peak pressures can reach hundreds of gigapascals. In this paper, we develop a reactive dynamics code for modeling detonation wave features in one such material. The key contribution in this paper is an integrated algorithm to incorporate equations of state, Arrhenius kinetics, and mixing rules for particle detonation in a Taylor–Galerkin finite element simulation. We show that the scheme captures the distinct features of detonation waves, and the detonation velocity compares well with experiments reported in literature.     

Simulations of granular flow along an inclined plane using the Savage–Hutter model

In this work a velocity-dependent friction is introduced into a depth-averaged Savage–Hutter dynamical model for shallow granular flows. The process of granular material flowing along an inclined plane and then depositing on a horizontal plane is simulated. The surface profiles and evolution of various types of energy are investigated and compared when using the standard Coulomb-type friction versus velocity-dependent friction. Interestingly, there is a small difference between the two different types of friction.     

Assessment of added mass effects on flutter boundaries using the Leishman–Beddoes dynamic stall model

We consider the dynamics of a typical airfoil section both in forced and free oscillations and investigate the importance of the added mass terms, i.e. the second derivatives in time of the pitch angle and plunge displacement. The structural behaviour is modelled by linear springs in pitch and plunge and the aerodynamic loading represented by our interpretation of the state-space version of the Leishman–Beddoes semi-empirical model. The added mass terms are often neglected since this leads to an explicit system of ODEs amenable for solution using standard ODE solvers. We analyse the effect of neglecting the added mass terms in forced oscillations about a set of mean angles of incidence by comparing the solutions obtained with the explicit and implicit systems of ODEs and conclude that their differences amount to a time lag that increases at a constant rate with increases of the reduced frequency. To determine the effect of the added mass terms in free oscillations, we introduce a spring offset angle to obtain static equilibrium positions at various degrees of incidence. We analyse the stability of the explicit and implicit aeroelastic systems about those positions and compare the locations of the respective flutter points calculated as Hopf bifurcation points. For low values of the spring offset angle, added mass effects are significant for low values of the mass ratio, or the ratio of natural frequencies, of the aeroelastic system. For high values of the spring offset angle, corresponding to stall flutter, we observe that their effect is greater for large values of the mass ratio.     

Numerical study of Saffman–Taylor instability in immiscible nonlinear viscoelastic flows

In this paper, a numerical solution for Saffman–Taylor instability of immiscible nonlinear viscoelastic-Newtonian displacement in a Hele–Shaw cell is presented. Here, a nonlinear viscoelastic fluid pushes a Newtonian fluid and the volume of fluid method is applied to predict the formation of two phases. The Giesekus model is considered as the constitutive equation to describe the nonlinear viscoelastic behavior. The simulation is performed by a parallelized finite volume method (FVM) using second order in both the spatial and the temporal discretization. The effect of rheological properties and surface tension on the immiscible Saffman–Taylor instability are studied in detail. The destabilizing effect of shear-thinning behavior of nonlinear viscoelastic fluid on the instability is studied by changing the mobility factor of Giesekus model. Results indicate that the fluid elasticity and capillary number decrease the intensity of Saffman–Taylor instability.     

On hot-wire diagnostics in Rayleigh–Taylor mixing layers

Two hot-wire flow diagnostics have been developed to measure a variety of turbulence statistics in the buoyancy driven, air-helium Rayleigh–Taylor mixing layer. The first diagnostic uses a multi-position, multi-overheat (MPMO) single wire technique that is based on evaluating the wire response function to variations in density, velocity and orientation, and gives time-averaged statistics inside the mixing layer. The second diagnostic utilizes the concept of temperature as a fluid marker, and employs a simultaneous three-wire/cold-wire anemometry technique (S3WCA) to measure instantaneous statistics. Both of these diagnostics have been validated in a low Atwood number (A _t  ≤ 0.04), small density difference regime, that allowed validation of the diagnostics with similar experiments done in a hot-water/cold-water water channel facility. Good agreement is found for the measured growth parameters for the mixing layer, velocity fluctuation anisotropy, velocity fluctuation p.d.f behavior, and measurements of molecular mixing. We describe in detail the MPMO and S3WCA diagnostics, and the validation measurements in the low Atwood number regime (A _t  ≤ 0.04). We also outline the advantages of each technique for measurement of turbulence statistics in fluid mixtures with large density differences.