309 research outputs found
Startup process in the Richtmyer-Meshkov instability
An analytical model for the initial growth period of the planar Richtmyer–Meshkov instability is presented for the case of a reflected shock, which corresponds in general to light-to-heavy interactions. The model captures the main features of the interfacial perturbation growth before the regime with linear growth in time is attained. The analysis provides a characteristic time scale τ for the startup phase of the instability, expressed explicitly as a function of the perturbation wavenumber k, the algebraic transmitted and reflected shock speeds U_(S1) 0 (defined in the frame of the accelerated interface), and the postshock Atwood number A^+: τ=[(1-A^+)/U_(S2)+(1+A^+)/(-U_(s1))]/(2k). Results are compared with computations obtained from two-dimensional highly resolved numerical simulations over a wide range of incident shock strengths S and preshock Atwood ratios A. An interesting observation shows that, within this model, the amplitude of small perturbations across a light-to-heavy interface evolves quadratically in time (and not linearly) in the limit A→1^−
Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer–Meshkov instability
We first study the linear stability of an interface between two fluids following the passage of an imploding or exploding shock wave. Assuming incompressible flow between the refracted waves following shock impact, we derive an expression for the asymptotic growth rate for a three-dimensional combination of azimuthal and axial perturbations as a function of the Atwood ratio, the axial and azimuthal wave numbers, the initial radial position and perturbation amplitude of the interface, and the interface velocity gain due to the shock interaction. From the linearized theory, a unified expression for the impulsive asymptotic growth rate in plane, cylindrical, and spherical geometries is obtained which clearly delineates the effects of perturbation growth due to both geometry and baroclinic vorticity deposition. Several different limit cases are investigated, allowing recovery of Mikaelian's purely azimuthal theory and Richtmyer's plane model. We discuss the existence of three-dimensional perturbations with zero growth, typical of curvilinear geometries, as first observed by Mikaelian. The effect of shock proximity on the interface growth rate is studied in the case of a reflected shock. Analytical predictions of the effect of the incident shock strength and the perturbation wave numbers are then compared with results obtained from highly resolved numerical simulations of cylindrical imploding Richtmyer–Meshkov instability for ideal gases. A parallel is made with the instability growth in spherical and plane geometry. In particular, we propose a representation of the perturbation growth by considering the volume of the perturbed layer. This volume is found to grow faster in the plane case than in the imploding cylindrical geometry, among other results
Converging shocks in elastic-plastic solids
We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e = e_(s)(I_1)+e_(h)(ρ,ς), where e_(s) accounts for shear through the first invariant of the Cauchy–Green tensor, and e_(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e_(h) = e_(h)(ρ), with a power-law dependence e_(h) ∝ ρ_(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M ∝ [log(1/R)]^α, independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M ∝ R^(−(s−1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part eh is that of an ideal gas, is also tested, recovering the strong-shock limit M∝R^(−(s−1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ−1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the hydrostatic part of the energy essentially commands the strong-shock behavior, the shear modulus and yield stress modify the compression ratio and velocity of the shock far from the axis or origin. A characterization of the elastic-plastic transition in converging shocks, which involves an elastic precursor and a plastic compression region, is finally exposed
Atwood ratio dependence of Richtmyer-Meshkov flows under reshock conditions using large-eddy simulations
We study the shock-driven turbulent mixing that occurs when a perturbed planar density interface is impacted by a planar shock wave of moderate strength and subsequently reshocked. The present work is a systematic study of the influence of the relative molecular weights of the gases in the form of the initial Atwood ratio A. We investigate the cases A = ± 0.21, ±0.67 and ±0.87 that correspond to the realistic gas combinations air–CO_2, air–SF_6 and H_2–air. A canonical, three-dimensional numerical experiment, using the large-eddy simulation technique with an explicit subgrid model, reproduces the interaction within a shock tube with an endwall where the incident shock Mach number is ~1.5 and the initial interface perturbation has a fixed dominant wavelength and a fixed amplitude-to-wavelength ratio ~0.1. For positive Atwood configurations, the reshock is followed by secondary waves in the form of alternate expansion and compression waves travelling between the endwall and the mixing zone. These reverberations are shown to intensify turbulent kinetic energy and dissipation across the mixing zone. In contrast, negative Atwood number configurations produce multiple secondary reshocks following the primary reshock, and their effect on the mixing region is less pronounced. As the magnitude of A is increased, the mixing zone tends to evolve less symmetrically. The mixing zone growth rate following the primary reshock approaches a linear evolution prior to the secondary wave interactions. When considering the full range of examined Atwood numbers, measurements of this growth rate do not agree well with predictions of existing analytic reshock models such as the model by Mikaelian (Physica D, vol. 36, 1989, p. 343). Accordingly, we propose an empirical formula and also a semi-analytical, impulsive model based on a diffuse-interface approach to describe the A-dependence of the post-reshock growth rate
Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth
We present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number ≈1.2, the density ratio (precisely |A_0|≈0.67) and the perturbation shape (dominant spherical wavenumber ℓ_0=40 and amplitude-to-initial radius of 3%): the incident shock travels from the lighter fluid to the heavy fluid or, inversely, from the heavy to the light fluid. After describing the computational problem we present results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. Turbulent statistics are developed in Part 2 (Lombardini, M., Pullin, D. I. & Meiron, D. I. J. Fluid Mech., vol. 748, 2014, pp. 113–142). A wave-diagram analysis of the radially symmetric flow highlights that the light–heavy mixing layer is processed by consecutive reshocks, and not by reverberating rarefaction waves as is usually observed in planar geometry. Less surprisingly, reshocks process the heavy–light mixing layer as in the planar case. In both configurations, the incident imploding shock and the reshocks induce Richtmyer–Meshkov (RM) instabilities at the density layer. However, we observe differences in the mixing-layer growth because the RM instability occurrences, Rayleigh–Taylor (RT) unstable scenarios (due to the radially accelerated motion of the layer) and phase inversion events are different. A small-amplitude stability analysis along the lines of Bell (Los Alamos Scientific Laboratory Report, LA-1321, 1951) and Plesset (J. Appl. Phys., vol. 25, 1954, pp. 96–98) helps quantify the effects of the mean flow on the mixing-layer growth by decoupling the effects of RT/RM instabilities from Bell–Plesset effects associated with geometric convergence and compressibility for arbitrary convergence ratios. The analysis indicates that baroclinic instabilities are the dominant effect, considering the low convergence ratio (≈2) and rather high (ℓ>10) mode numbers considered
Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics
We present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number ≈ 1.2, the density ratio (precisely |A_0| ≈ 0.67) and the perturbation shape (dominant spherical wavenumber ℓ_0=40 and amplitude-to-initial radius of 3 %): the incident shock travels from the lighter fluid to the heavy one, or inversely, from the heavy to the light fluid. In Part 1 (Lombardini, M., Pullin, D. I. & Meiron, D. I., J. Fluid Mech., vol. 748, 2014, pp. 85-112), we described the computational problem and presented results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. In particular, it was shown that both configurations reach similar convergence ratios ≈2. Here, turbulent mixing is studied through various turbulence statistics. The mixing activity is first measured through two mixing parameters, the mixing fraction parameter Theta and the effective Atwood ratio A(e), which reach similar late time values in both light-heavy and heavy-light configurations. The Taylor-scale Reynolds numbers attained at late times are estimated ≈2000 in the light-heavy case and 1000 in the heavy-light case. An analysis of the density self-correlation b, a fundamental quantity in the study of variable-density turbulence, shows asymmetries in the mixing layer and non-Boussinesq effects generally observed in high-Reynolds-number Rayleigh-Taylor (RT) turbulence. These traits are more pronounced in the light-heavy mixing layer, as a result of its flow history, in particular because of RT-unstable phases (see Part 1). Another measure distinguishing light-heavy from heavy-light mixing is the velocity-to-scalar Taylor microscales ratio. In particular, at late times, larger values of this ratio are reported in the heavy-light case. The late-time mixing displays the traits some of the traits of the decaying turbulence observed in planar Richtmyer-Meshkov (RM) flows. Only partial isotropization of the flow (in the sense of turbulent kinetic energy (TKE) and dissipation) is observed at late times, the Reynolds normal stresses (and, thus, the directional Taylor microscales) being anisotropic while the directional Kolmogorov microscales approach isotropy. A spectral analysis is developed for the general study of statistically isotropic turbulent fields on a spherical surface, and applied to the present flow. The resulting angular power spectra show the development of an inertial subrange approaching a Kolmogorov-like -5/3 power law at high wavenumbers, similarly to the scaling obtained in planar geometry. It confirms the findings of Thomas & Kares (Phys. Rev. Lett., vol. 109, 2012, 075004) at higher convergence ratios and indicates that the turbulent scales do not seem to feel the effect of the spherical mixing-layer curvature
Numerical simulations of the Richtmyer-Meshkov instability in solid-vacuum interfaces using calibrated plasticity laws
The Richtmyer-Meshkov instability of interfaces separating elastic-plastic materials from vacuum (heavy-light configuration) is studied by means of computational techniques. A fully Eulerian multimaterial algorithm that solves consistently the Euler equations and the time evolution of the deformations in the material is applied to three distinct materials (copper, aluminum, and stainless steel). If a perfectly plastic constitutive relation is considered, an empirical law is computed that relates the long-term perturbation amplitude of the interface, its maximum growth rate, the initial density, and the yield stress of the material. It is shown that this linear relation can be extended to materials that follow more complex plastic behavior which can account for rate dependency, hardening, and thermal softening, and to situations in which small-perturbation theory is no longer valid. In effect, the yield stress computed from measurements of the long-term amplitude and maximum growth rate closely matches the von Mises stress found at the interface of solid materials for a wide range of cases with different initial parameters
Psychometric Evaluation of the Care Transition Measures in a Sample of ACS Patients: Results from Transitions, Risks, and Actions in Coronary Events – Center for Outcomes Research and Education (TRACE-CORE)
Background: Quality of transitional care is associated with important health outcomes such as rehospitalization and costs. A widely used measure of the construct, the Care Transitions Measure (CTM-15), was developed with classical test theory approach. Its short version (CTM-3) was included in the CAHPS® Hospital Survey.
Methods: As part of TRACE-CORE 1545 participants were interviewed during hospitalization for ACS providing information on general health status (SF-36). At 1 month post-discharge, patients completed CTM-15, health utilization and care process questions. We evaluated the psychometric properties of the CTM using classical and item response theory analyses. We compared the measurement precision of CTM-15, CTM-3, and a CTM-IRT based score using relative validity (RV).
Results: Participants were 79% non-Hispanic white, 67% male, 27% with a college education or higher (27%) and average age of 62 years. The CTM scale had good internal consistency (Cronbach’s alpha=0.95), but demonstrated strong acquiescence bias (8.7% participants responded “Strongly agree”, 19% “Agree” to all 15 items) and limited score variability. IRT based item parameters were estimated for all items. The CTM-15 differentiated between groups of patients defined by self-reported health status, health care utilization, and care transition process indicators. Differences between groups were small (2-3 points). There was no gain in measurement precision for the scale from IRT scoring. The CTM-3 was not significantly lower for patients reporting rehospitalization or emergency department visits.
Conclusion: We identified psychometric challenges of the CTM, which may limit its value in research and practice. The strong acquiescence bias in the measure leads to highly skewed, clustered scores with restricted score variance. In the absence of guidelines on meaningfully important differences, it is hard to determine whether detected statistically significant differences in CTM are important. These results are in line with emerging evidence of gaps in the validity of the measure
Stimulatory Effect of Taurine on Calcium Ion Uptake in Rod Outer Segments of the Rat Retina Is Independent of Taurine Uptake 1
ABSTRACT Taurine stimulates ATP-dependent Ca 2ϩ uptake in the rat rod outer segments (ROS). This stimulation has been linked to the function of the cyclic nucleotide-gated cation channel, implying an important physiologic role for taurine in visual signal transduction. Calmodulin (CaM) has been reported to affect taurine transport in the choroid plexus and also to inhibit the cyclic nucleotide-gated channel; thus, the effects of the competitive CaM inhibitors trifluoperazine (TFP) and N-(8-aminooctyl)-5-iodonaphthalene-1-sulfonamide (J-8) were studied on Ca 2ϩ and taurine uptake in the rat ROS. Pretreatment of the ROS preparation with TFP and J-8 for 5 min before measurement of Ca 2ϩ -uptake activity produced inhibition of the effects of taurine on ATP-dependent Ca 2ϩ uptake. Both TFP and J-8 also were effective in inhibiting high-affinity taurine uptake. In both uptake systems, inhibition by TFP was noncompetitive. These data initially suggested that the stimulatory effects of taurine on ATP-dependent Ca 2ϩ uptake are dependent on taurine uptake. However, competitive inhibition of taurine uptake by guanidinoethane sulfonate did not produce any effect on the stimulatory effects of taurine. Previous studies have proposed that taurine binds directly to the plasma membrane, and our study demonstrated that TFP inhibits taurine binding to the ROS. In addition, our study demonstrated that taurine uptake is unaffected by varying the concentration of Ca 2ϩ and that the effects of TFP are independent of Ca 2ϩ , suggesting that TFP acts through a CaM-independent mechanism
Transition to turbulence in shock-driven mixing: a Mach number study
Large-eddy simulations of single-shock-driven mixing suggest that, for sufficiently high incident Mach numbers, a two-gas mixing layer ultimately evolves to a late-time,
fully developed turbulent flow, with Kolmogorov-like inertial subrange following a -5/3 power law. After estimating the kinetic energy injected into the diffuse density layer during the initial shock–interface interaction, we propose a semi-empirical characterization of fully developed turbulence in such flows, based on scale separation, as a function of the initial parameter space, as (η_(0^+)Δu/ν)(η_(0^+)/L_ρ)A^+/√(1-A^(+)^2) ≳ 1.53 × 10^4/C^2, which corresponds to late-time Taylor-scale Reynolds numbers ≳250. In this expression, η_(0^+) represents the post-shock perturbation amplitude, Δu the change in interface velocity induced by the shock refraction, ν the characteristic kinematic viscosity of the mixture, L_ρ the inner diffuse thickness of the initial density profile, A^+ the post-shock Atwood ratio, and C(A^+, η_(0^+)/λ_0)≈0.3 for the gas combination and post-shock perturbation amplitude considered. The initially perturbed interface separating air and SF_6 (pre-shock Atwood ratio A ≈ 0.67) was impacted in a heavy–light configuration by a shock wave of Mach number M_I = 1.05, 1.25, 1.56, 3.0 or 5.0, for which η_(0^+) is fixed at about 25% of the dominant wavelength λ_0 of an initial, Gaussian perturbation spectrum. Only partial isotropization of the flow (in the sense of turbulent kinetic energy and dissipation) is observed during the late-time evolution of the mixing zone. For all Mach numbers considered, the late-time flow resembles homogeneous decaying turbulence of Batchelor type, with a turbulent kinetic energy decay exponent n ≈ 1.4 and large-scale (k⟶0) energy spectrum ~k^4, and a molecular mixing fraction parameter, Θ ≈ 0.85. An appropriate time scale characterizing the Taylor-scale Reynolds number decay, as well as the evolution of mixing parameters such as Θ and the effective Atwood ratio A_e, seem to indicate the existence of low- and high-Mach-number regimes
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