Dominant Instability Mechanism Research Articles

Outflow of a supersonic overexpanded air jet into a water

Numerical simulation of the underwater outflow of a supersonic overexpanded air jet is considered. The calculations are carried out in an unsteady three-dimensional formulation with a hybrid approach using Reynolds-averaged Navier–Stokes equations for nozzle flow and large eddy-simulation for jet flow. The calculation of the interaction of a gas with a liquid is performed with a volume of fluid, which takes into account the surface tension and compressibility of water. The structural features of turbulence when a supersonic air jet exhausted into water are analyzed. An unsteady formation of a supersonic jet and a gas cavity in a water is obtained, the shock-wave structure of the flow is visualized and the level of pressure fluctuations in water is reported. A comparison of the flow pattern when an air jet exhausted into air and water is made on a qualitative level. The results of numerical simulation of the jet velocity field are used to analyze the Kelvin–Helmholtz and Rayleigh–Taylor instability mechanisms and to reveal the dominant instability mechanism in different jet propagation regions. The results obtained are compared with experimental high-speed photographic recording data and numerical calculations At a qualitative level in literature.

Linear and Nonlinear Disturbance Evolution on the Frustum of Hypersonic Ogive Cylinders

Aspects of transition mechanisms on a 14° sharp-nosed ogive cylinder at Mach 6 are elucidated by considering linear and nonlinear disturbance evolution of freestream stochastic and wave packet forcing at different locations downstream of the ogive-cylinder junction. The spectral response of the stochastic forcing displays favorable agreement with experimental observations from Air Force Research Laboratory on which the configuration is based. Intermittent wave packets are generated from small-amplitude continuous freestream pressure forcing. Linear wave packet evolution reveals that Mack modes are the dominant primary instabilities, followed by relatively weaker first-mode waves. The nonlinear wavepacket displays a three-legged wall pressure perturbation signature, which is traced to spanwise curvature effects, and fundamental resonance is the dominant secondary instability mechanism. At higher amplitudes of excitation, weak signatures of subharmonic and oblique resonance phenomena are identified. Downstream placement of the small-amplitude disturbance diminishes amplification of first-mode waves; however, with high-amplitude forcing, the location of actuation does not significantly vary the disturbance evolution signature or the secondary instability mechanisms.

Linear instability of a liquid sheet in a transverse standing acoustic field

This work examines the instability of a plane liquid sheet under the action of a transverse acoustic field. The mechanical definition of the acoustic field is introduced first, and the Floquet theory is applied to derive the dispersion equation and dispersion curve. The dominant instability mechanism of each unstable region on the dispersion curve is distinguished by calculating the oscillation frequencies of the disturbance waves. Next, the parameters within the dispersion equation are set as variables to analyze the development of the instability mechanisms of the unstable regions on the dispersion curve and the oscillation modes on the two surfaces of the liquid sheet. The results prove that the distribution of unstable regions can be affected by the amplitude and frequency of the acoustic field, the viscosity and surface tension of the liquid sheet, and the density ratio of the two gas–liquid phases. Variation in the thickness of the liquid sheet causes development and competition within the oscillation modes, which were found to be related to the development of the instability mechanism. Such evolutionary competition between the sinuous and the varicose oscillation modes was also reflected in the experimental study, where it was observed that the disturbance wave has the characteristics of Faraday waves.

Dominant Instability Mechanism of VSI Connecting to a Very Weak Grid

In this paper, it is identified that unstable weak grid connection of voltage source inverters (VSIs) is dominantly caused by the current control. In particular, it is found the proportional gain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ k_p$</tex-math></inline-formula> of conventional PI controller cannot balance the grid voltage impact and damping capability especially when a very weak grid with short circuit ratio (SCR) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ &lt; $</tex-math></inline-formula> 1.3 is connected. This issue is solved in this paper by simply restructuring the PI controller as an IP controller for current control. This IP controller will not change the tuning method of current control and make this VSI indeed connect to a very weak grid with rated power injection.

Stability of obliquely driven cavity flow

The linear stability of the incompressible flow in an infinitely extended cavity with rectangular cross-section is investigated numerically. The basic flow is driven by a lid which moves tangentially, but at yaw with respect to the edges of the cavity. As a result, the basic flow is a superposition of the classical recirculating two-dimensional lid-driven cavity flow orthogonal to a wall-bounded Couette flow. Critical Reynolds numbers computed by linear stability analysis are found to be significantly smaller than data previously reported in the literature. This finding is confirmed by independent nonlinear three-dimensional simulations. The critical Reynolds number as a function of the yaw angle is discussed for representative aspect ratios. Different instability modes are found. Independent of the yaw angle, the dominant instability mechanism is based on the local lift-up process, i.e. by the amplification of streamwise perturbations by advection of basic flow momentum perpendicular to the sheared basic flow. For small yaw angles, the instability is centrifugal, similar as for the classical lid-driven cavity. As the spanwise component of the lid velocity becomes dominant, the vortex structures of the critical mode become elongated in the direction of the bounded Couette flow with the lift-up process becoming even more important. In this case the instability is made possible by the residual recirculating part of the basic flow providing a feedback mechanism between the streamwise vortices and the streamwise velocity perturbations (streaks) they promote. In the limit when the basic flow approaches bounded Couette flow the critical Reynolds number increases very strongly.

Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

Time-dependent flows are notoriously challenging for classical linear stability analysis. Most progress in understanding the linear stability of these flows has been made for time-periodic flows via Floquet theory focusing on time-asymptotic stability. However, little attention has been given to the transient intracyclic linear stability of periodic flows since no general tools exist for its analysis. In this work, we explore the potential of using the recent framework of the optimally time-dependent (OTD) modes (Babaee &amp; Sapsis, Proc. R. Soc. Lond. A, vol. 472, 2016, 20150779) to extract information about both the transient and the time-asymptotic linear stability of pulsating Poiseuille flow. The analysis of the instantaneous OTD modes in the limit cycle leads to the identification of the dominant instability mechanism of pulsating Poiseuille flow by comparing them with the spectrum and the eigenmodes of the Orr–Sommerfeld operator. In accordance with evidence from recent direct numerical simulations, it is found that structures akin to Tollmien–Schlichting waves are the dominant feature over a large range of pulsation amplitudes and frequencies but that for low pulsation frequencies these modes disappear during the damping phase of the pulsation cycle as the pulsation amplitude is increased beyond a threshold value. The maximum achievable non-normal growth rate during the limit cycle was found to be nearly identical to that in plane Poiseuille flow. The existence of subharmonic perturbation cycles compared with the base flow pulsation is documented for the first time in pulsating Poiseuille flow.

Utilising the scientific method to demonstrate that slender beam/column behaviour is the dominant behavioural mechanism leading to roof/rib failure

As per most other earth science engineering problems, the underground coal geotechnical environment and the way in which roof and rib support interacts with the rock mass are complex issues. It is therefore generally recognised that without prudent simplification, the complexity of the problem will overwhelm all current geotechnical methods of modelling, not least for the reason that a rock mass can never be characterised to a level that allows a “non-simplified” analysis. The fact that numerical models, which are commonly purported to be a “simulation” tool and the so-called epitome of advanced geotechnical engineering, always need to be “calibrated” to a known reality is taken to be conclusive proof of this statement. While the problem should not be oversimplified (i.e. the dominant failure mechanisms or critical data input parameters should not be ignored), without question judicious simplification is at the heart of all engineering design, to the point that it has a well-established name – “reductionism”. The hypothesis addressed in this paper, is that horizontal and vertical stress-driven slender beam and column behaviour (which includes unstable Euler Buckling) are respectively the dominant (but not only) roadway roof and ribline behavioural mechanism that (if not controlled) can lead to excessive deformation, failure and eventual collapse. As a part of the Scientific Method, a hypothesis can only be tested via real-world observations, measurements and analyses in establishing it is a credible Theory. Utilising the Scientific Method, this paper demonstrates that slender beam/column behaviour is the dominant instability mechanism within a coal mine roof/rib subject to elevated horizontal/vertical stress conditions and therefore, must be representatively accounted for in any credible empirical, analytical, or numerical approach to coal mine roof/rib stability assessment and associated ground support design.

Examination of stiff ion temperature gradient mode physics in simulations of DIII-D H-mode transport

A systematic evaluation of gyrokinetic and gyrofluid model predictions of ion temperature gradient (ITG) stability and transport using parameters from DIII-D high confinement mode (H-mode) plasmas has been performed. The nonlinear CGYRO code is used to make the gyrokinetic predictions, and the quasilinear TGLF model for the corresponding gyrofluid predictions. The assessments are made at three radii (normalized toroidal flux ρ tor = 0.4, 0.55, and 0.7) in three different plasma scenarios with varying levels of neutral beam heating and torque. For each of the nine cases (3 radii × 3 scenarios) considered, ITG turbulence is found to be the dominant long-wavelength instability and transport mechanism. The inclusions of both transverse magnetic fluctuations and dynamic fast beam ions are stabilizing for all cases considered, with strongest effects seen at ρ or = 0.4 where the fast ion population and normalized plasma pressure β = 2μ 0 nT/B 2 are highest. The further inclusion of parallel magnetic fluctuations does not have a meaningful impact on the ITG turbulence in these scenarios, but does destabilize (in combination with fast ions) new high-frequency instabilities at ρ tor = 0.4 in the high power scenarios. In each case the linear and nonlinear ITG critical gradients are predicted to be lower than the measured ITG scale lengths and their associated uncertainties. Inclusion of equilibrium flow shear in the transport predictions generally leads to an upshift in effective critical gradient rather than a qualitative change in the predicted stiffness, with stronger responses typically seen in the gyrokinetic predictions than in the gyrofluid results. However, in most cases these upshifted gradients still remain below the measured values and their uncertainties. Although the predicted critical gradients are below the measured gradients, both models predicted flux-matching gradients consistent with measured values in six of the nine cases considered, with no clear systematic over- or underprediction. Thus, while the experimental ion temperature profiles do not appear to be closely pinned to the ITG critical gradient, both gyrokinetic and gyrofluid models are able to accurately match the measured gradients reasonably well in most cases.

Magmatic channelization by reactive and shear-driven instabilities at mid-ocean ridges: a combined analysis

Summary It is generally accepted that melt extraction from the mantle at mid-ocean ridges (MORs) is concentrated in narrow regions of elevated melt fraction called channels. Two feedback mechanisms have been proposed to explain why these channels grow by linear instability: shear flow of the partially molten mantle and reactive flow of the ascending magma. These two mechanisms have been studied extensively, in isolation from each other, through theory and laboratory experiments as well as field and geophysical observations. Here, we develop a consistent theory that accounts for both proposed mechanisms and allows us to weigh their relative contributions. We show that interaction of the two feedback mechanisms is insignificant and that the total linear growth rate of channels is well-approximated by summing their independent growth rates. Furthermore, we explain how their competition is governed by the orientation of channels with respect to gravity and mantle shear. By itself, analysis of the reaction-infiltration instability predicts the formation of tube-shaped channels. We show that with the addition of even a small amount of extension in the horizontal, the combined instability favours tabular channels, consistent with the observed morphology of dunite bodies in ophiolites. We apply the new theory to MORs by calculating the accumulated growth and rotation of channels along streamlines of the solid flow. We show that reactive flow is the dominant instability mechanism deep beneath the ridge axis, where the most unstable orientation of high-porosity channels is subvertical. Channels are then rotated by the solid flow away from the vertical. The contribution of the shear-driven instability is confined to the margins of the melting region. Within the limitations of our study, the shear-driven feedback does not appear to be responsible for significant melt focusing or for the shallowly dipping seismic anisotropy that has been obtained by seismic inversions.

Detailed simulation of laser-induced ignition, spherical-flame acceleration, and the origins of hydrodynamic instability

Ignition of a lean hydrogen–oxygen premixture by focused-laser-induced breakdown and subsequent three-dimensional expanding-flame instabilities are simulated in high detail. Both diffusive–thermal and hydrodynamic (Darrieus–Landau) instabilities are active and accelerate the flame expansion. The fluid is a partially-ionized gas in local thermodynamic equilibrium with detailed kinetics and transport models, starting from initial conditions from an auxiliary simulation based on a two-temperature local thermodynamic non-equilibrium model. After the decay of the initial laser-induced plasma, the r ∼ t1.5 growth in time of the flame radius matches theory and experimental observations. Based on hydrodynamic theory for spherical-flame propagation, a global Karlovitz number is defined as the ratio of the hydrodynamic to flame-distortion time scales. It initially increases during the diffusive–thermal instability stage, then with the onset of significant baroclinic torque, this trend reverses, with vorticity production becoming the dominant mechanism of instability.

Detailed numerical simulation of primary atomization by crossflow under gas turbine engine combustor conditions

The present study concerns a detailed numerical simulation of primary atomization by crossflow in the flow of a gas turbine engine combustor. At high Weber numbers, such as in a gas turbine engine, the scale ratio of the atomization phenomenon becomes large, and it is necessary to use a relatively fine grid to obtain reliable results. The present study conducts the first numerical analysis in a gas turbine engine condition with a sufficiently fine grid to give a result that can be discussed reliably, and details of the atomization mechanism are clarified for the first time. In a gas turbine engine combustor, Rayleigh–Taylor (RT) instability dominates at the edge of the liquid column. On the other hand, when the liquid–gas density ratio or the Weber number are low, RT instability is not significant. The process of ligament formation changes depending on the dominant instability mechanism, and the ligaments becomes smaller when RT instability is dominant. Also, the size distribution of the atomized droplets clearly changes when RT instability becomes significant.

The Evolution of Interfaces for Underwater Supersonic Gas Jets

The evolution of interfaces for underwater gas jets is the main morphological manifestation of two-phase unstable interaction. The high-speed transient photographic recording and image post-processing methods are used to obtain the interfacial change in a submerged gaseous jet at different stages after its ejection from the Laval nozzle exit. The relationship between the pressure pulsation in the wake flow field and the interfacial change is further analyzed by combining the experimental results with computational results. A theoretical model is employed to address the competition dominant mechanism of interface instability. The results show that the jet interface of a supersonic gas jet gradually changes from one containing wave structures to a transition structure, and finally forms a steady-state conical jet. The fluctuation of the jet interface results in the pulsation of the back-pressure. The dominant mechanism of the interface changes with the development and distribution of the jet, from Kelvin-Helmholtz (K-H) instability beyond the nozzle exit changing to Rayleigh-Taylor (R-T) instability in the downstream.

Influence of Composition Dependent Diffusion Coefficient, Viscosity and Relaxation Time on Evaporative Rayleigh-Bénard-Marangoni Instabilities Induced by Solvent Evaporation in a Polymer Solution

In this study, a linear stability analysis is performed for both monotonic and oscillatory modes within a horizontal polymer solution layer, which solely the solvent evaporates into air. The approach is based on general thermodynamic principles and also on the physics of the gas phase and its interactions with the liquid phase. Due to evaporation, the solvent mass fraction changes and cooling occurs at the liquid-gas interface. This can trigger solutal and thermal Rayleigh-Benard-Marangoni instabilities in the system. For the monotonic mode, the effects of composition dependent diffusion coefficient and dynamic viscosity on the onset of Rayleigh-Benard-Marangoni convection are studied. Moreover, the effect of different total heights of the liquid-gas system on the behavior of convection onset is considered. The results show that a variable diffusion coefficient and a variable viscosity can notably change the onset of instability for a polyisobutylene (PIB)/toluene solution. Our model for the monotonic mode is also satisfactorily compared with an experimental study. For the oscillatory mode, where the relaxation time is also composition dependent, we observe that very thin layers will be susceptible to an oscillatory instability when drying occurs in the system. Finally, an approximate model is derived exploiting the fact that the solutal Marangoni is by far the most dominant instability mechanism here. A negligible difference with respect to the full model confirms the predominance of the solutal Marangoni mechanism.

Global stability of buoyant jets and plumes

The linear global stability of laminar buoyant jets and plumes is investigated under the low-Mach-number approximation. For Richardson numbers in the range $10^{-4}\leqslant Ri\leqslant 10^{3}$ and density ratios $S=\unicode[STIX]{x1D70C}_{\infty }/\unicode[STIX]{x1D70C}_{jet}$ between 1.05 and 7, only axisymmetric perturbations are found to exhibit global instability, consistent with experimental observations in helium jets. By varying the Richardson number over seven decades, the effects of buoyancy on the base flow and on the instability dynamics are characterised, and distinct behaviour is observed in the low-$Ri$ (jet) and in the high-$Ri$ (plume) regimes. A sensitivity analysis indicates that different physical mechanisms are responsible for the global instability dynamics in both regimes. In buoyant jets at low Richardson number, the baroclinic torque enhances the basic shear instability, whereas buoyancy provides the dominant instability mechanism in plumes at high Richardson number. The onset of axisymmetric global instability in both regimes is consistent with the presence of absolute instability. While absolute instability also occurs for helical perturbations, it appears to be too weak or too localised to give rise to a global instability.

Baroclinic Frontal Instabilities and Turbulent Mixing in the Surface Boundary Layer. Part II: Forced Simulations

AbstractGeneration of ocean surface boundary layer turbulence and coherent roll structures is examined in the context of wind-driven and geostrophic shear associated with horizontal density gradients using a large-eddy simulation model. Numerical experiments over a range of surface wind forcing and horizontal density gradient strengths, combined with linear stability analysis, indicate that the dominant instability mechanism supporting coherent roll development in these simulations is a mixed instability combining shear instability of the ageostrophic, wind-driven flow with symmetric instability of the frontal geostrophic shear. Disruption of geostrophic balance by vertical mixing induces an inertially rotating ageostrophic current, not forced directly by the wind, that initially strengthens the stratification, damps the instabilities, and reduces vertical mixing, but instability and mixing return when the inertial buoyancy advection reverses. The resulting rolls and instabilities are not aligned with the frontal zone, with an oblique orientation controlled by the Ekman-like instability. Mean turbulence is enhanced when the winds are destabilizing relative to the frontal orientation, but mean Ekman buoyancy advection is found to be relatively unimportant in these simulations. Instead, the mean turbulent kinetic energy balance is dominated by mechanical shear production that is enhanced when the wind-driven shear augments the geostrophic shear, while the resulting vertical mixing nearly eliminates any effective surface buoyancy flux from near-surface, cold-to-warm, Ekman buoyancy advection.

Fast and slow transient charging of Oxide Semiconductor Transistors

The comprehension of the governing mechanism which affects device instability is one of the most important requirements for the formation of reliable oxide-thin film transistors (TFTs). However, a quantitative analysis of the dominant mechanism of device instability, which stems from charge trapping induced by defects at the oxide semiconductor interface as well as in its bulk, has not yet been systematically performed. In this study, we examined subgap states, charge-transport dynamics, and various trap characteristics of oxide TFTs by multi-frequency C–V, pulse I–V, and transient current methods to achieve a comprehensive understanding of carrier transport and charge trapping mechanisms. We found that the charge trapping behavior of the tested amorphous InHfZnO (a-IHZO) TFT follows a multi-trapping mechanism, such as temperature-independent fast transient charge trapping by resonant drift of the injected electron and temperature-dependent slow transient charge trapping by charge transport from occupied to unoccupied traps. Understanding fast charging and slow charging described in this study can help to understand the root cause of device instability of oxide TFTs and ultimately improve stability and reliability characteristics.

Theory of Self‐pulsing in Photonic Crystal Fano Lasers

AbstractLaser self‐pulsing was a phenomenon exclusive to macroscopic lasers until recently, where self‐starting laser pulsation in a microscopic photonic crystal Fano laser was reported. In this paper a theoretical model is developed to describe the Fano laser, including descriptions of the highly‐dispersive Fano mirror, the laser frequency and the threshold gain. The model is based upon a combination of conventional laser rate equations and coupled‐mode theory. The dynamical model is used to demonstrate how the laser has two regimes of operation, continuous‐wave output and self‐pulsing, and these regimes are characterised using phase diagrams, establishing the regime of self‐pulsing numerically. Furthermore, the physics behind the self‐pulsing mechanism are explained in detail and it is demonstrated how cavity absorption makes the Fano mirror function as a saturable absorber, leading to Q‐switched pulse generation. A stability analysis is used to demonstrate how the dominant mechanism of instability is relaxation oscillations becoming un‐damped. Finally the effect of varying key self‐pulsing parameters is investigated by characterisation of the change in self‐pulsing regions.

Bank instability along a weir pool of the River Murray

ABSTRACTRiver banks are an important transition zone between aquatic and terrestrial environments. This ecotone is highly vulnerable to natural and anthropogenic disturbances. Bank erosion is a common occurrence along the River Murray. Morphological features reflecting river bank instability form a near-continuous pattern along large tracts of the river. This study investigates the character and extent of bank instability along the Torrumbarry Weir Pool. Over 90% of the bank length in this weir pool was assessed as being actively eroding. Notch development was the dominant instability mechanism and it promoted other forms of bank instability. Erosion notches result from stable water levels and inherent soil instability of the river banks along the weir pool. The character and extent of river bank erosion recorded along this section of the River Murray is an artefact of flow regulation and not a reflection of the natural occurrence of bank erosion in river networks. Water level management in the upstream weir pool has significant implications for the management of river banks along regulated reaches of the River Murray.

Boundary-Layer Stability Analysis for Stetson’s Mach 6 Blunt-Cone Experiments

The results of a seminal experimental study of the effects of bluntness and swallowing length on transition on an 8 deg cone at zero angle of attack in Mach 6 high-Reynolds-number flow are analyzed with the STABL-2D computational fluid dynamics code package. Mean flow solutions and parabolized stability analyses for a total of 11 different nose-tip bluntnesses, ranging from sharp to a 15.24 mm radius, are obtained. For the sharpest cases, the factor at transition is approximately seven; but, as bluntness increases and the calculated swallowing distance lengthens, the computed factor at the experimentally observed transition location drops below the level at which Mack’s second mode would be expected to lead to transition. These results indicate that the dominant instability mechanism for the bluntest cases is not the second mode, and oblique mode analysis also excludes these modes as the dominant instability mechanism.

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts. These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.