Shear Instability Mechanism Research Articles

Mass log-stable distribution of fragments in liquid–liquid jet fragmentation based on a two-step cascade between viscous shear instability and Rayleigh–Taylor instability

This work is devoted to the study of liquid-liquid fragmentation. It contains both an experimental part and a theoretical part. In the experimental part, a low-melting point liquid metal jet is injected into a water pool. High-speed shadowgraph method is used to measure the jet velocity and to observe the dynamics of the fragmentation. Thereafter, the solidified fragments are sieved and weighted allowing to measure their mass distribution according to their size. The mass Probability Density Function (PDF) is then fitted using log-stable laws, generalization of log-normal laws. In the theoretical part, it is shown how it is possible to compute the shift parameter of the stable law considering that the droplets are mainly generated by a boundary layer stripping mechanism. Actually the computation relies on a viscous shear instability mechanism (different from classical Kelvin–Helmholtz instability) sometime called “gradient instability”. The width of the distribution (or more precisely its scale parameter) is computed assuming a cascade mechanism between this first wave instability and a secondary Rayleigh–Taylor mechanism applied on the generated wave. The model is then compared to present experimental results and previously published results obtained in the field of nuclear safety studies (Fuel-Coolant Interaction or FCI). Two fitting parameters are then identified. The agreement is good when phase change and solidification effects can be neglected and qualitatively good (i.e. fitting parameters need to be modified) when these effects cannot be neglected.

Experimental study on the irreversible displacement evolution and energy dissipation characteristics of disturbance instability of regular joints

AbstractTo investigate the disturbance‐induced shear instability mechanism of structural catastrophe in the deep rock mass, MTS 815 material testing machine was used to carry out quasi‐static loading tests and disturbance shear tests on symmetrical regular dentate joints of two materials at three undulation angles under specific initial static stress, disturbance frequency, and peak value. The test results indicate that: (i) the total ultimate instability displacement is only related to the intrinsic properties of the joints but not to the initial static stress and disturbance parameters; (ii) the cumulative irreversible displacement required for the disturbance instability conforms to the logistic inverse function relationship with the number of disturbances, displaying the variation trend of “rapid increase in the front, stable in the middle, and sudden increase in the rear”; (iii) the accumulation of plastic deformation energy is consistent with the evolution law of irreversible displacement of joints and the overall proportion of hysteretic energy is not large; (iv) the dissipated energy required for the instability of each group of joints is basically the same under various disturbance conditions, and this energy is mainly controlled by the initial shear stress and has no connection with the disturbance parameters. The stability of the total disturbance deformation and the disturbance energy law of the joints revealed in the tests provide data support for reasonably determining the disturbance instability criterion of joints.

Componentwise influence of upstream turbulence on the far-wake dynamics of wind turbines

Wake meandering and turbulent kinetic energy (TKE) generation in the far-wake region of wind turbines significantly affect the power production and aerodynamic loads of wind farms. This work thus aims at understanding the componentwise influence of upstream turbulence and roles of different mechanisms on the far-wake dynamics to guide the development of wind-farm wake models. We find that the wake meandering is mainly caused by the upstream spanwise (v′) and vertical (w′) velocity fluctuations, supporting the passive wake meandering mechanism. However, our results also show a scale-dependence of the wake meandering that should be accounted in wake models. We find that v′ and w′ cause greater TKE generation than the streamwise velocity fluctuations (u′). We then use simulation- and resolvent-based componentwise input–output analyses to explain that this is because the shear instability in turbine wakes is more receptive to the transverse forcing relative to the streamwise forcing. This highlights the importance of implementing the shear instability mechanism in wake models for accurate TKE estimations. Finally, we find that u′ cause the thrust fluctuations, which can lead to near-wake corrections and hence influence the far-wake evolution.

Dynamic plastic instability of ring-shaped aluminum alloy with different interface behaviors

Unveiling the rate-dependent shear instability mechanism is essential in evaluating the reliability and safety of materials under dynamic loadings. Herein, the strain rate-dependent plastic instability behaviors of 2A12 aluminum alloy with ring-shaped structure and different surface states were systematically investigated and analyzed. The stress softening was displayed in the stress-strain curves as the loading rate increased to a high level. The lubricated interface will induce the prominent shear instability property, followed by the fine-polished interface and coarse-polished interface. It is revealed that the initial interface state between specimen and bars not only influences the onset strain and the yield strength, but also determines the duration of plastic instability stage. The simulation results also indicated that the shear band runs through the two surfaces with different interface friction coefficients. The minor disturbance under quasi-static loading will be accelerated under dynamic loading owing to the instantaneous rising of local temperature, which eventually causes the observably plastic shear instability. The critical state of shear band formation mechanism and the modeling of the stress-softening stage were then theoretically analyzed and discussed. This work on the dynamic instability behavior of ring-shaped aluminum alloy could provide an insight in understanding the formation of adiabatic shear band with different strain rates and interfaces.

Treatment of wastewater containing nickel by complexation- ultrafiltration using sodium polyacrylate and the stability of PAA-Ni complex in the shear field

Efficient and green process for industrial treatment of heavy metal wastewater is much needed. Herein, complexation-ultrafiltration using sodium polyacrylate (PAAS) as complexation agent was used to recover nickel from wastewater containing nickel by a rotating disk membrane module. The Ni2+ rejection could reach 98.26% at n < 848 rpm, pH = 7.0 and P/Ni = 13 (mass ratio). When n > 848 rpm, the high shear rate produced by the rotating disk causes the PAA-Ni complex to dissociate, and the recycling of Ni2+ and the reuse of PAAS can be achieved, which has huge economic and environmental benefits. The established membrane partition model reveals the shear instability mechanism of PAA-Ni and the distribution of the critical shear radius of the membrane at the corresponding disk rotating speed. The critical shear rate of PAA-Ni is 2.1 × 10−4 s−1 at pH = 7. These findings suggest that complexation-ultrafiltration is a viable industrial treatment approach for heavy metal wastewater. This work provides an alternative way to selectively separate and recover heavy metal from the wastewater.

A shear instability mechanism for the pulsations of Rayleigh–Taylor unstable model flames

AbstractPrevious studies have shown that the behaviour of Rayleigh–Taylor (RT) unstable flames depends on the boundary conditions. If the boundary conditions at the domain walls are impermeable/adiabatic or reflecting then the flame assumes a stable parabolic shape. On the other hand, periodic boundary conditions can produce unstable pulsating solutions. In this paper, we explore why periodic boundary conditions allow unstable solutions by showing the results of two-dimensional direct numerical simulations of model flames. We show that RT unstable premixed model flames pulsate at low gravity because of a shear instability of the vorticity layers behind the flame front. The resulting vortex shedding is controlled by a region of absolute-like instability which moves closer to the flame front as gravity is increased, ultimately disturbing the flame and leading to pulsations. We demonstrate that this region is ‘absolutely unstable’ by showing that the wake is dominated by pure frequency oscillations. In addition, the shear instability can be described by the Landau equation and can be represented dynamically by a Hopf bifurcation. The applicability of the Landau equation allows the apparently complex spatio-temporal behaviour of the vortex shedding to be described by a simple temporal model with only a secondary spatial dependence. We show that the flame behaviour is analogous to the initial instability downstream of a circular cylinder, which leads to the von Kármán vortex street for large enough values of the Reynolds number.

Instability of an inhomogeneous bacterial suspension subjected to a chemo-attractant gradient

AbstractThe stability of a suspension of chemotactic bacteria confined in an infinitely long channel and subjected to a stationary, linear chemo-attractant gradient is investigated. While swimming, individual bacteria exert force dipoles on the fluid, which at the continuum level lead to a stress depending upon the bacterial orientation and number density fields. The presence of the attractant gradient causes bacteria to tumble less frequently when swimming along the gradient, leading to a mean orientation and a non-zero chemotactic drift velocity$U_0$in that direction. At long length and time scales compared to those associated with the persistence of bacterial swimming, fluxes due to chemotaxis and the random run–tumble motion of bacteria balance to yield an exponentially varying number density profile across the channel in the base state. The associated bacterial stress field is also exponentially varying and is normal. This spatially non-uniform base state is unstable to fluctuations in the bacterial concentration field when the scaled bacterial concentration$\beta = (3 C/8) \langle n_0\rangle L^2 H$exceeds a critical value determined by a Péclet number defined as${\mathit{Pe}} = U_0 H/\kappa $. Here,$C$is a non-dimensional dipole strength, which depends on the geometry of the bacterium,$\langle n_0\rangle $is the bacterial concentration averaged across the channel of depth$H$,$L$is the total length of the bacterium,$\kappa $is the bacterial diffusivity, and$\beta _{\mathit{crit}}$is a monotonically decreasing function of${\mathit{Pe}}$, with$\beta _{\mathit{crit}} \sim 720/{\mathit{Pe}}^3$for${\mathit{Pe}} \ll 1$and$\beta _{\mathit{crit}} \sim 2$for${\mathit{Pe}} \gg 1$. The instability is the result of the coupling between the active stress-driven fluid flow and the bacterial concentration, and manifests as rectangular convection patterns. When$\beta $first exceeds$\beta _{\mathit{crit}}$, the unstable wavelengths are large with$\lambda \gg H$and the mode of instability is stationary. Although oscillatory modes appear when$\lambda \leq O(H)$and$\beta &gt; 247$, the most dangerous mode of instability is found to be always stationary with a wavelength$\lambda _m/H \sim {\mathit{Pe}}^{-1}$. To study the coupling between the previously analysed orientation shear instability mechanism of bacterial suspensions and the new chemotaxis-driven instability, a new set of continuum equations that consistently account for weak chemotaxis, rotation of bacteria by weak fluid shear and weak non-continuum effects along with their coupled effects has been derived. The stability analysis of those equations showed that the orientation shear mechanism has only a negligible influence on the critical concentration for the present chemotaxis-induced instability when the suspension depth is large, and it is the latter that has the lowest critical concentration.

Analytical predictive modeling of scuffing initiation in metallic materials in sliding contact

Scuffing, described as sudden catastrophic tribological failure of a sliding surface, is a complex phenomenon and consequently still poorly understood. Its occurrence is influenced by many factors such as material microstructure, lubricant chemistry, operating environment, and contact parameters. Over the years, numerous attempts have been made at predictive modeling of scuffing occurrence, often based on the assumption that adhesion and consequent welding between contacting asperities is the basic mechanism of the failure. These previous attempts at scuffing prediction have not been satisfactory. A mechanism of scuffing based on adiabatic shear instability in the near-surface material of sliding interface was recently proposed by the authors. As a follow on to that work, a predictive analytical model is developed for scuffing with adiabatic shear instability as the basic mechanism of failure is presented in the current paper. The model expresses susceptibility of a sliding contact interface to scuffing in terms of material properties and contact conditions. Preliminary correlation was established between the model prediction and scuffing test results with 4340 steel. As modifiers to the shear instability mechanism, the effect of lubricant chemistry and surface reactions and numerous other factors that are known to affect scuffing damage can be incorporated.

Compact dislocation clusters in a two-dimensional highly ordered complex plasma

The mechanism and physics of defect nucleation are key questions that often remain open irrespective of the suggested melting scenario or the shear instability mechanism. Complex plasmas can serve as a powerful tool, providing a fundamental insight into the nucleation process generically. Either deformation-induced or thermally initialized nucleation in hexagonal plasma crystals starts with the appearance of compact dislocation clusters having a tetragon in the core. Hence, the competition for the minimal energy configuration between (stable) hexagonal symmetry and (unstable) tetragonal symmetry can be resolved in favor of a (meta-stable) ‘mixed symmetry’—a cluster of coupled dislocations in a hexagonal environment. Performing simulations with a specially designed tool—a deformable simulation cell—the mechanism of nucleation in two-dimensional plasma crystals is studied. The nontrivial topology of the dislocation clusters is explored in detail, and the results obtained agree well with experimental observations.

Effect of Gas Temperature on the Particle Deposition Characteristics and Coating Microstructure by Cold Spray

In this study, 304 stainless steel particles were deposited on IF steel substrates by cold dynamic spray technology. The effect of gas temperature on bonding features and deposition critical velocity were studied and compared. The results demonstrated that the successful bonding between 304SS particle and substrate could be attributed to the adiabatic shear instability mechanism, increasing gas temperature led to enhance the particle interface bonding, deduce the deposition critical velocity, and also increase both deposition efficiency and density of coatings.

Earthquakes and plastic deformation of anhydrous slab mantle in double Wadati‐Benioff zones

Double Wadati‐Benioff seismic zones (DSZ) with two parallel planes of seismicity separated by 15–30 km are a global feature of subduction zones in the 50–200 km depth range. Upper plane seismicity is generally attributed to dehydration of the oceanic crust but the origin of the lower seismicity plane is debated. Serpentine or hydrous‐phase dehydration embrittlement is a commonly advocated mechanism that implies significant slab mantle hydration. High‐resolution seismic tomography revealed low seismic velocities in the lower seismicity plane that are better explained by seismic anisotropy of anhydrous deformed peridotites than by serpentinization. Earthquakes correlate with anisotropic planar shear zones and favor a shear instability mechanism as the cause of lower plane seismicity without requiring the presence of water in the center of subducting slabs. The contribution of the subducted lithospheric mantle to the water budget of subduction zones is thus likely limited to the first 2–3 kilometers beneath oceanic crust.

Mechanism of nonlinear flow pattern selection in moderately non-Boussinesq mixed convection

Nonlinear (non-Boussinesq) variations in fluid's density, viscosity, and thermal conductivity caused by a large temperature gradient in a flow domain lead to a wide variety of instability phenomena in mixed convection channel flow of a simple gas such as air. It is known that in strongly nonisothermal flows, the instabilities and the resulting flow patterns are caused by competing buoyancy and shear effects [see S. A. Suslov and S. Paolucci, J. Fluid Mech. 302, 91 (1995)]. However, as is the case in the Boussinesq limit of small temperature gradients, in moderately non-Boussinesq regimes, only a shear instability mechanism is active. Yet in contrast to Boussinesq flows, multiple instability modes are still detected. By reducing the system of full governing Navier-Stokes equations to a dynamical system of coupled Landau-type disturbance amplitude equations we compute a comprehensive parametric map of various shear-driven instabilities observed in a representative moderately non-Boussinesq regime. Subsequently, we analyze nonlinear interaction of unstable modes and reveal physical reasons for their appearance.

An interactive micro-void shear localization mechanism in high strength steels

Ductility of high strength steels is often restricted by the onset of a void-sheet mechanism in which failure occurs by a micro-void shear localization process. For the first time, the micro-void shear instability mechanism is identified here by examining the interactions occurring within a system of multiple embedded secondary particles (carbides ∼10–100 nm), through a finite element based computational cell modeling technique (in two and three dimensions). Shear deformation leads to the nucleation of micro-voids as the secondary particles debond from the surrounding alloy matrix. The nucleated micro-voids grow into elongated void tails along the principal shear plane and coalesce with the micro-voids nucleated at neighboring particles. At higher strains, the neighboring particles are driven towards each other, further escalating the severity of the shear coalescence effect. This shear driven nucleation, growth and coalescence mechanism leads to a decrease in the load-bearing surface in the shear plane and a terminal shear instability occurs. The mechanism is incorporated mathematically into a hierarchical steel model. The simulated response corresponds to experimentally observed behavior only when the micro-void shear localization mechanism is considered.

Observations and models of the energy flux from the wind to mixed-layer inertial currents

Observations of wind stress, upper-ocean currents, and stratification from a mooring at 10∘N in the Pacific are used along with two different one-dimensional mixed-layer models to investigate the horizontal kinetic energy (KE) balance for inertial motions in the mixed-layer. Results from four other sites spanning 25∘N to 60∘N in the Atlantic also are presented. Determining the work done by the wind on the ocean during strong resonant forcing events is of particular interest. The damped-slab mixed-layer model used in previous studies is appealing for this purpose, since it is possible to estimate the wind work using only the wind stress, prescribed mixed-layer depth, and an empirical damping constant. However, it is found that this model, which does not allow for interaction between the mixed-layer and the stratified water column below, does not reproduce the observed KE balance for strong forcing events and systematically over-estimates the wind work. A slightly more sophisticated model, which includes a shear instability mechanism to facilitate momentum transfer between the mixed-layer and a transition layer below, reproduces the observed KE balance and the cumulative wind work much more accurately. Mixed-layer inertial currents unrelated to wind forcing (e.g., due to upward propagating internal waves) are found in the observations, but are not accounted for in either model. When wind forcing is relatively weak, these background currents may be of comparable amplitude to wind-forced currents, and can have a significant impact on the inertial response.

The stability of a two-dimensional vorticity filament under uniform strain

The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ &lt; 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ ė 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.

Correlation between the elastic shear instability mechanism and empirical criteria for irradiation-induced amorphization

In an attempt to correlate the shear instability mechanism with empirical criteria for irradiation-induced amorphization, shear moduli of an A 3B-type fcc crystal were calculated as a function of the chemical long range order parameter S using a Morse potential. The shear moduli were found to decrease with decreasing S. When the depth and the curvature of the A-B potential were changed while keeping the A-A and B-B potentials constant, the magnitude of the decrease in shear moduli is greater for deeper and narrower A-B potentials. The present results indicate that a shear instability should occur more readily in compounds with larger ordering energy and larger elastic moduli. These results agree with the reported empirical criteria for irradiation-induced amorphization, therefore providing further support for the shear instability mechanism for solid-state amorphization.

Irradiation-Induced Amorphization and Elastic Shear Instability in Intermetallic Compounds

ABSTRACTPreviously we reported a substantial (∼ 50 %) decrease in shear modulus prior to amorphization in Kr irradiated Zr3Al, and proposed that amorphization is triggered when the crystalline lattice becomes unstable against shear stress. In the present work, the relation between amorphization and shear elastic instability has been investigated in two additional compounds (FeTi and NiAl) during room temperature irradiation with 1.7-MeV Kr+. A shear modulus was measured using Brillouin scattering; structural information was obtained in situ in a high voltage electron microscope interfaced to a tandem accelerator.During irradiation of FeTi, chemical disordering and a large (∼40 %) decrease of shear modulus were observed, and an amorphous phase developed subsequently. In contrast, NiAl remained crystalline and chemically ordered during irradiation, and exhibited only a ∼ 10 % decrease in shear modulus. Hence, these two results provide further support that a shear instability triggers irradiation-induced amorphization. The shear instability mechanism may also apply to other solid-state amorphization techniques, e.g. hydrogen charging and mechanical deformation.

The directional spectrum of ocean waves, and processes of wave generation

This paper describes some recent observations of the directional spectrum of sea waves and of air pressure fluctuations at the sea surface, and discusses their implications for theories of wave generation. The angular spread of the wave energy in the generating area is found to be comparable with the ‘resonance angle’ sec -1 ( σU/g ) ( σ = wave frequency, U = wind speed) but lies slightly below it in the middle range of frequencies. The best fit to the directional spectrum F ( σ, ɸ ) is shown to be a cosine-power law: F ( σ, ɸ ) ∝ cos 2s (1/2 ɸ ), where s decreases as σ in ­ creases. At the higher frequencies the total spectrum satisfies the equilibrium law: F ( σ ) ∝ σ -5 . The initial stages of wave generation are attributed to turbulence in the air stream, and the main stage of growth to the shear instability mechanism described by Miles. At the highest frequencies the form of the spectrum suggests that wave breaking plays a predominant part, as proposed by Phillips. The broadening of the angular distribution at the highest frequencies may also be due partly to third-order ‘resonant’ interactions among components of the wave spectrum . The air-pressure fluctuations are nearly in phase with the vertical displacement of the sea surface (over most of the frequency range) and are consistent with the shear-flow model proposed by Miles. The turbulent component of the air pressure is much smaller than was previously supposed.