Effect of Atwood number on convergent Richtmyer–Meshkov instability

Acta Mechanica Sinica - Developments of two-dimensional single-mode light/heavy interfaces driven by convergent shock waves are numerically investigated, focusing on the effect of the Atwood number...     

An attempt to reduce the membrane effects in Richtmyer–Meshkov instability shock tube experiments

A new device has been developed to reduce the effects of the initial materialization of the gaseous interface in the context of horizontal shock tube experiments for the Richtmyer–Meshkov instability study. The thin nitrocellulosic membrane deposited on a stereolithographed grid support woven with thin wires is destroyed by thermal effect, through a powerful electrical pulse, just before the arrival of the incident shock wave. We present a first attempt realized in the light/heavy gas configuration (air/SF₆) and compared with the experiments carried out without destruction. We show that the present device allows to reduce the influence of the membrane on the instability development.      

Effect of shock–wave loading on the properties of cryogenic TiNi — a shape–memory alloy

Results of an experimental study of the shock–wave deformation of TiNi and its effect on the crystallographic structure and temperature of austenite–martensite transformations are given. It is found that, for pressures of up to 2 GPa, shock–wave loading changes the defect structure and parameters of the lattice; however, this does not lead to a noticeable change in the temperature of the austenite–martensite transformation and the manifestation of the shapeNdash;memory effect.     

Richtmyer–Meshkov instability on a low Atwood number interface after reshock

The Richtmyer–Meshkov instability after reshock is investigated in shock tube experiments at the Wisconsin Shock Tube Laboratory using planar laser imaging and a new high-speed interface-tracking technique. The interface is a mixture of helium and argon (50% each by volume) stratified over pure argon. This interface has an Atwood number of 0.29 and a near single-mode, two-dimensional, standing wave perturbation with an average amplitude of 0.35?cm and a wavelength of 19.4?cm. The incident shock wave of Mach number 1.92 accelerates the interface before reflecting from the shock tube end wall with M =?1.70 and accelerating the interface in the opposite direction. The amplitude growth after reshock is reported for variations in this initial amplitude, and several amplitude growth rate models are compared to the experimental growth rate after reshock. A new growth model is introduced, based on a model of circulation deposition calculated from one-dimensional gas dynamics parameters. This model compares well with the amplitude growth rate after reshock and the circulation over one-half wavelength of the interface after the first shock wave and after reshock.     

Numerical investigation of turbulence in reshocked Richtmyer–Meshkov unstable curtain of dense gas

Moderate-resolution numerical simulations of the impulsive acceleration of a dense gas curtain in air by a Mach 1.21 planar shock are carried out by solving the 3D compressible multi-species Navier–Stokes equations coupled with localized artificial diffusivity method to capture discontinuities in the flow field. The simulations account for the presence of three species in the flow field: air, $\hbox {SF}_6$ and acetone (used as a tracer species in the experiments). Simulations at different concentration levels of the species are conducted and the temporal evolution of the curtain width is compared with the measured data from the experimental studies by Balakumar et al. (Phys Fluids 20:124103–124113, 2008). The instantaneous density and velocity fields at two different times (prior and after the reshock) are compared with experimental data and show good qualitative agreement. The reshock process is studied by re-impacting the evolving curtain with the reflected shock wave. Reshock causes enhanced mixing and destroys the ordered velocity field causing a chaotic flow. The unsteady flow field is characterized by computing statistics of certain flow variables using two different definitions of the mean flow. The average profiles conditioned on the heavy gas (comprising $\hbox {SF}_6$ and acetone) and the corresponding fluctuating fields provide metrics which are more suitable to comparing with experimentally measured data. Mean profiles (conditioned on the heavy gas) of stream-wise velocity, variance of stream-wise velocity, and turbulent kinetic energy and PDF (probability distribution function) of fluctuating velocity components are computed at two different times along the flow evolution and are seen to show trend towards grid convergence. The spectra of turbulent kinetic energy and scalar energy (of mass fraction of heavy gas) show the existence of more than half decade of inertial sub-range at late times following reshock. The Reynolds stresses in the domain are reported while identifying the term that is dominant in its contribution to the Reynolds stresses.     

Particle image velocimetry study of the shock-induced single mode Richtmyer–Meshkov instability

Full field particle image velocimetry (PIV) measurements are obtained for the first time in Richtmyer–Meshkov instability shock tube experiments. The experiments are carried out in a vertical shock tube in which the light gas (air) and the heavy gas (SF₆) flow from opposite ends of the shock tube driven section and exit through narrow slots at the interface location. A sinusoidal perturbation is given to the interface by oscillating the shock tube in the horizontal direction. Richtmyer–Meshkov instability is then produced by the interaction with a weak shock wave (M _s  = 1.21). PIV measurements are obtained by seeding the flow with 0.30 μm polystyrene Latex spheres which are illuminated using a double-pulsed Nd:YAG laser. PIV measurements indicate the vorticity to be distributed in a sheet-like distribution on the interface immediately after shock interaction and that this distribution quickly rolls up into compact vortices. The integration of the vorticity distribution over one half wave length shows the circulation to increase with time in qualitative agreement with the numerical study of Peng et al. (Phys. Fluids, 15, 3730–3744, 2003).     

Experiments on the Richtmyer–Meshkov instability with an imposed, random initial perturbation

A vertical shock tube is used to perform experiments on the Richtmyer–Meshkov instability with a three-dimensional random initial perturbation. A membraneless flat interface is formed by opposed gas flows in which the light and heavy gases enter the shock tube from the top and from the bottom of the shock tube driven section. An air/SF $_{6}$ gas combination is used and a Mach number $ M = 1.2$ incident shock wave impulsively accelerates the interface. Initial perturbations on the interface are created by vertically oscillating the gas column within the shock tube to produce Faraday waves on the interface resulting in a short wavelength, three-dimensional perturbation. Planar Mie scattering is used to visualize the flow in which light from a laser sheet is scattered by smoke seeded in the air, and image sequences are captured using three high-speed video cameras. Measurements of the integral penetration depth prior to reshock show two growth behaviors, both having power law growth with growth exponents in the range found in previous experiments and simulations. Following reshock, all experiments show very consistent linear growth with a growth rate in good agreement with those found in previous studies.     

The effect of viscosity,surface tension and non-linearity on Richtmyer–Meshkov instability

A weakly non-linear theoretical model of the Richtmyer–Meshkov instability between two viscous fluids with surface tension is proposed. The model is based on the application of singular perturbations techniques to the incompressible Navier–Stokes equations written for two superposed immiscible fluids. A simple analytical law of interface deformation is obtained, in which the effects of viscosity, surface tension and non-linearities appear under the form of independent terms. The model gives also access to the velocity and pressure distribution in the fluids, which can be of interest for estimating vorticity diffusion in the fluids. A comparison with accurate direct numerical simulations confirms the validity of the proposed theory. The interface deformation law is then applied to typical experimental configurations in order to estimate the relative influence of surface tension, viscosity and non-linearities on the growth of perturbations for each of the chosen cases.     

The Richtmyer–Meshkov instability of a 'V' shaped air/helium interface subjected to a weak shock

The Richtmyer–Meshkov instability of a ‘V' shaped air/helium gaseous interface subjected to a weak shock wave is experimentally studied.A soap film technique is adopted to create a ‘V' shaped interface with accurate initial conditions.Five kinds of ‘V' shaped interfaces with different vertex angles are formed to highlight the effects of initial conditions on the flow characteristics.The results show that a spike is generated after the shock impact,and grows constantly with time.As the vertex angle increases,vortices generated on the interface become less noticeable,and the spike develops less pronouncedly.The linear growth rate of interface width after compression phase is estimated by a linear model and a revised linear model,and the latter is proven to be more effective for the interface with high initial amplitudes.The linear growth rate of interface width is,for the first time in a heavy/light interface configuration,found to be a non-monotonous function of the initial perturbation amplitude–wavelength ratio.     

Thermodynamic fluctuations in canonical shock–turbulence interaction: effect of shock strength

In this work, we use numerical simulation and linear inviscid theory to study the thermodynamic field generated by the interaction of a shock wave with homogeneous isotropic turbulence. Fluctuations in density, pressure, temperature and entropy can play an important role in shock-induced mixing, combustion and energy transfer processes. Data from shock-captured direct numerical simulations (scDNS) are used to investigate the variation of thermodynamic fluctuations for varying shock strengths, and the results are compared with linear interaction analysis (LIA). The density, pressure and temperature variances attain large values at the shock, followed by, in general, a rapid decay in the downstream flow. The rapid variation behind the shock makes it difficult to compare numerical results with theoretical predictions. A threshold method based on instantaneous shock dilatation is used to overcome this problem, and it gives excellent match between scDNS and LIA. We find cases with non-monotonic variation with Mach number as well as local peaks in density fluctuations behind the shock. These are explained in terms of the contribution of the post-shock acoustic and entropy modes in the LIA solution and their cross-correlation. Budget of the transport equations reveals interesting insight into the physics governing the thermodynamic field behind the shock wave. It is found that the variances are primarily determined by the competing effects of dilatational and dissipation mechanisms. The dominant mechanisms are identified for a range of conditions, and their implication for developing predictive models is highlighted.     

Generation of polygonal gas interfaces by soap film for Richtmyer–Meshkov instability study

A simple method of generating polygonal gas interfaces is proposed by using the soap film technique. Thin pins are used as angular vertexes to connect the adjacent sides of polygonal soap films in order to avoid the pressure singularities around the vertexes caused by the surface tension. As a demonstration, three polygonal interfaces (i.e., square, equilateral triangle and diamond) are created in the test section of a shock tube. Experiments are then carried out for a planar shock wave (Mach number about 1.2) interacting with air/SF₆ polygonal interfaces. Numerical simulations are also performed to validate the proposed method of the interface formation. Wave systems and interface structures can be clearly identified in experimental schlieren images and agree well with the numerical results. It is also indicated that the presences of thin pins and fine chamfers only have limited effects on the interface evolution and can be ignored at the very early stage. Experimental and numerical results about the movement of the distorted interface, the width and height of the interface structures are further compared and good agreement is achieved. It is then concluded that the polygonal interface formed by the proposed method is applicable for the Richtmyer–Meshkov instability study.     

Special features of the shock‐wave structure in mixtures of gases with disparate molecular masses

Asymptotic solutions are constructed for the problem of the shockwave structure in mixtures of gases with disparate molecular masses. The effect of emergence of a plateau on the density profile of the light component and nonmonotonicity of the temperature profile of the heavy component is described. Based on a comparison with calculations of the full model, the range of applicability of asymptotic solutions is determined.     

Multi-component Reynolds-averaged Navier–Stokes simulations of Richtmyer–Meshkov instability and mixing induced by reshock at different times

Turbulent mixing generated by shock-driven acceleration of a perturbed interface is simulated using a new multi-component Reynolds-averaged Navier–Stokes (RANS) model closed with a two-equation $K$ – $\epsilon $ model. The model is implemented in a hydrodynamics code using a third-order weighted essentially non-oscillatory finite-difference method for the advection terms and a second-order central difference method for the gradients in the source and diffusion terms. In the present reshocked Richtmyer–Meshkov instability and mixing study, an incident shock with Mach number $M\!a_{\mathrm{s}}=1.20$ is generated in air and progresses into a sulfur hexafluoride test section. The time evolution of the predicted mixing layer widths corresponding to six shock tube test section lengths are compared with experimental measurements and three-dimensional multi-mode numerical simulations. The mixing layer widths are also compared with the analytical self-similar power-law solution of the simplified model equations prior to reshock. A set of model coefficients and initial conditions specific to these six experiments is established, for which the widths before and after reshock agree very well with experimental and numerical simulation data. A second set of general coefficients that accommodates a broader range of incident shock Mach numbers, Atwood numbers, and test section lengths is also established by incorporating additional experimental data for $M\!a_{\mathrm{s}}=1.24$ , $1.50$ , and $1.98$ with $At=0.67$ and $M\!a_{\mathrm{s}}=1.45$ with $At=-0.67$ and previous RANS modeling. Terms in the budgets of the turbulent kinetic energy and dissipation rate equations are examined to evaluate the relative importance of turbulence production, dissipation and diffusion mechanisms during mixing. Convergence results for the mixing layer widths, mean fields, and turbulent fields under grid refinement are presented for each of the $M\!a_{\mathrm{s}}=1.20$ cases.     

Three-dimensional magnetohydrodynamic description of the process of collision of a solar wind shock wave and the Earth’s bow shock

The propagation of a solar wind shock wave along the surface of the Earth’s bow shock is investigated within the framework of an ideal magnetohydrodynamic model in the three-dimensional non-plane-polarized formulation. The most characteristic values of the solar wind parameters and the interplanetary magnetic field strength are considered for the plane front of a solar wind shock wave moving at various velocities along the Sun-Earth radius. The global three-dimensional pattern of the interaction is constructed as a function of the angle of inclination of the surface of the bow shock to the solar wind velocity and the azimuthal angle along the curve of intersection of the fronts of the interacting shock waves. The evolution of the flow developed in the neighborhood of the bow shock is investigated and the parameters of the medium and magnetic field are calculated.     

Effect of high-frequency stimulation on nerve pulse propagation in the FitzHugh–Nagumo model

We consider the FitzHugh–Nagumo model axon under action of a homogeneous high-frequency stimulation (HFS) current. Using a multiple scale method and a geometrical singular perturbation theory, we derive analytically the main characteristics of the traveling pulse. We show that the effect of HFS on the axon is determined by a parameter proportional to the ratio of the amplitude to the frequency of the stimulation current. When this parameter is increased, the pulse slows down and shrinks. At some threshold value, the pulse stops and its width becomes zero. The HFS prevents the pulse propagation when the parameter exceeds the threshold value. The analytical results are confirmed by numerical experiments performed with the original system of partial differential equations.     

Effect of prestress on the stability of electrode–electrolyte interfaces during charging in lithium batteries

We formulate a model of the growth of electrode–electrolyte interfaces in lithium batteries in the presence of an elastic prestress. The model accounts for the kinetics of Li⁺ transport through a solid electrolyte and, within the interface, for the kinetics of Li⁺ adsorption by the anode, electrostatics, and the elastic field. We specifically account for the effect of the elastic field through an asymptotic analysis of a nearly flat interface between two semi-infinite elastic bodies. We use the model as a basis for assessing the effect of prestress on the stability of planar growth and the potential of prestress as a means of suppressing the formation of deleterious dendrites. We present a linear stability analysis that results in explicit analytical expressions for the dependence of growth rates, and of the critical unstable wavelength for the interfacial roughening, on the state of prestress and on fundamental parameters such as surface diffusivities, surface energy, deposition kinetics, and elastic moduli. Finally, we examine the model in the light of experimental observations concerned with the effect of applied pressure on a lithium/dioxolane-dimethoxy ethane electrolyte systems. With reasonable choices of parameters and some calibration, the model accounts for the observation that a modest applied pressure indeed results in a substantial reduction in the roughening of the lithium surface during cycling.     

Effect of Evaporation of Liquid Droplets on the Distribution of Parameters in a Two–Species Laminar Flow

A calculation model was developed, and the heat– and mass–transfer characteristics in a laminar air—vapor—droplet flow moving in a round tube were studied numerically. The distributions of parameters of the two–phase flow over the tube radius were obtained for varied initial concentrations of the gas phase. The calculated heat and mass transfer is compared to experimental data and calculations of other authors. It is shown that evaporation of droplets in a vapor—gas flow leads to a more intense heat release as compared to a one–species vapor—droplet flow and one–phase vapor flow     

Effect of Transitional Nonequilibrium on the Molecular–Dissociation Rate in a Hypersonic Shock Wave

The problem of the influence of a nonequilibrium (non–Maxwellian( distribution of translational energy over the degrees of freedom of molecules on the rate of their dissociation in a hypersonic shock wave is considered. An approximate beam—continuous medium model, which was previously applied to describe a hypersonic flow of a perfect gas, was used to study translational nonequilibrium. The degree of dissociation of diatomic molecules inside the shock–wave front, which is caused by the nonequilibrium distribution over the translational degrees of freedom, is evaluated. It is shown that the efficiency of the first inelastic collisions is determined by the dissociation rate exponentially depending on the difference in the kinetic energy of beam molecules and dissociation barrier.     

Influence of nanoprecipitates on the creep strength and ductility of a Fe–Ni–Al alloy

Creep studies of a duplex Fe–Ni–Al intermetallic alloy, in two microstructural states, have been carried out at temperatures between 725 and 800 °C (about 0.6 T_m). In the as-cast state, the alloy contains a large volume fraction of nanoprecipitates (50–100 nm) which confer a very high creep strength with a stress exponent of 3 and an activation energy of 280 kJ/mol. The different microstructure obtained in the second state of the alloy, obtained after annealing at 1000 °C for 24 h, leads to a much lower creep strength with a higher stress exponent as well as a large value of the apparent activation energy. While volume diffusion appears to control creep in the as-cast state, both thermal and athermal processes seem to contribute to the different creep rate of material in the annealed state. The latter also exhibits a much larger ductility (12%) relative to that observed in the as-cast material (3%), due to the presence of large numbers of interfaces between the two phases present where strain incompatibilities can be accommodated.