Azimuthal Instability Research Articles

Dissipative Vortex Solitons in Defocusing Media with Spatially Inhomogeneous Nonlinear Absorption**Supported by the National Natural Science Foundation of China under Grant No. 11705164 and the Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ16A040003

In this paper, by solving a complex nonlinear Schrödinger equation, radially symmetric dissipative vortex solitons are obtained analytically and are tested numerically. We find that spatially inhomogeneous nonlinear absorption gives rise to the stability of dissipative vortex solitons in self-defocusing nonlinear medium in the presence of constant linear gain. Numerical simulation reveals the interaction effect among linear gain and nonlinear loss in the azimuthal modulation instabilities of these vortices suppression. Apart from the uniform linear gain indeed affects the stability of vortex in this media, another noticeable feature of current setup is that the steep spatial modulation of the nonlinear absorption can suppress sidelobes effectively and support stable vortex solitons in situations with uniform linear gain. Under appropriate conditions, the vortex solitons can propagate stably and feature no symmetry breaking, although the beams exhibit radical compression and amplification as they propagate.

Azimuthal magnetorotational instability with super-rotation

It is demonstrated that the azimuthal magnetorotational instability (AMRI) also works with radially increasing rotation rates contrary to the standard magnetorotational instability for axial fields which requires negative shear. The stability against non-axisymmetric perturbations of a conducting Taylor–Couette flow with positive shear under the influence of a toroidal magnetic field is considered if the background field between the cylinders is current free. For small magnetic Prandtl number $Pm\rightarrow 0$ the curves of neutral stability converge in the (Hartmann number,Reynolds number) plane approximating the stability curve obtained in the inductionless limit $Pm=0$. The numerical solutions for $Pm=0$ indicate the existence of a lower limit of the shear rate. For large $Pm$ the curves scale with the magnetic Reynolds number of the outer cylinder but the flow is always stable for magnetic Prandtl number unity as is typical for double-diffusive instabilities. We are particularly interested to know the minimum Hartmann number for neutral stability. For models with resting or almost resting inner cylinder and with perfectly conducting cylinder material the minimum Hartmann number occurs for a radius ratio of $r_{\text{in}}=0.9$. The corresponding critical Reynolds numbers are smaller than $10^{4}$.

On the instabilities of tropical cyclones generated by cloud resolving models

An approximate method is developed for finding and analysing the main instability modes of a tropical cyclone whose basic state is obtained from a cloud resolving numerical simulation. The method is based on a linearised model of the perturbation dynamics that distinctly incorporates the overturning secondary circulation of the vortex, spatially inhomogeneous eddy diffusivities, and diabatic forcing associated with disturbances of moist convection. Although a general formula is provided for the latter, only parameterisations of diabatic forcing proportional to the local vertical velocity perturbation and modulated by local cloudiness of the basic state are implemented herein. The instability analysis is primarily illustrated for a mature tropical cyclone representative of a category 4 hurricane. For eddy diffusivities consistent with the fairly conventional configuration of the simulation that generates the basic state, perturbation growth is dominated by a low azimuthal wavenumber instability having greatest asymmetric kinetic energy density in the lower tropospheric region of the inner core of the vortex. The characteristics of the instability mode are inadequately explained by nondivergent 2D dynamics. Moreover, the growth rate and modal structure are sensitive to reasonable variations of the diabatic forcing. A second instability analysis is conducted for a mature tropical cyclone generated under conditions of much weaker horizontal diffusion. In this case, the linear model predicts a relatively fast high-wavenumber instability that is insensitive to the parameterisation of diabatic forcing. The prediction is in very good quantitative agreement with a previously published analysis of how the instability develops in a cloud resolving model on the way to creating mesovortices slightly inward of the central part of the eyewall.

Central recirculation zones and instability waves in internal swirling flows with an annular entry

The characteristics of the central recirculation zone and the induced instability waves of a swirling flow in a cylindrical chamber with a slip head end have been numerically investigated using the Galerkin finite element method. The effects of Reynolds number as well as swirl level adjusted by the injection angle were examined systematically. The results indicate that at a high swirl level the flow is characterized by an axisymmetric central recirculation zone (CRZ). The fluid in the CRZ takes on a solid-body rotation driven by the outer main flow through a free shear layer. Both the solid-body rotating central flow and the free shear layer provide the potential for the development of instability waves. When the injection angle increases beyond a critical value, the basic axisymmetric flow loses stability, and instability waves develop. In the range of Reynolds numbers considered in this study, three kinds of instability were identified: inertial waves in the central flow, and azimuthal and longitudinal Kelvin-Helmholtz waves in the free shear layer. These three types of waves interact with each other and mix together. The mode selection of the azimuthal waves depends strongly on the injection angle, through the perimeter of the free shear layer. Compared with the injection angle, the Reynolds number plays a minor role in mode selection. The flow topologies and characteristics of different flow states are analyzed in detail, and the dependence of flow states on the injection angle and Reynolds number is summarized. Finally, a linear analysis of azimuthal instabilities is carried out; it confirms the mode selection mechanisms demonstrated by the numerical simulation.

Strong Azimuthal Combustion Instabilities in a Spray Annular Chamber With Intermittent Partial Blow-Off

This article reports experiments carried out in the MICCA-spray combustor developed at EM2C laboratory. This system comprises 16 swirl spray injectors. Liquid n-heptane is injected by simplex atomizers. The combustion chamber is formed by two cylindrical quartz tubes allowing full optical access to the flame region and it is equipped with 12 pressure sensors recording signals in the plenum and chamber. A high-speed camera provides images of the flames and photomultipliers record the light intensity from different flames. For certain operating conditions, the system exhibits well defined instabilities coupled by the first azimuthal mode of the chamber at a frequency of 750 Hz. These instabilities occur in the form of bursts. Examination of the pressure and the light intensity signals gives access to the acoustic energy source term. Analysis of the phase fluctuations between the two signals is carried out using cross-spectral analysis. At limit cycle, large pressure fluctuations of 5000 Pa are reached, and these levels persist over a finite period of time. Analysis of the signals using the spin ratio indicates that the standing mode is predominant. Flame dynamics at the pressure antinodal line reveals a strong longitudinal pulsation with heat release rate oscillations in phase and increasing linearly with the acoustic pressure for every oscillation levels. At the pressure nodal line, the flames are subjected to large transverse velocity fluctuations leading to a transverse motion of the flames and partial blow-off. Scenarios and modeling elements are developed to interpret these features.

Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics.

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field, the hydrodynamically stable flow can demonstrate non-axisymmetric azimuthal magnetorotational instability (AMRI) both in the diffusionless case and in the double-diffusive case with viscous and ohmic dissipation. Performing stability analysis of amplitude transport equations of short-wavelength approximation, we find that the threshold of the diffusionless AMRI via the Hamilton–Hopf bifurcation is a singular limit of the thresholds of the viscous and resistive AMRI corresponding to the dissipative Hopf bifurcation and manifests itself as the Whitney umbrella singular point. A smooth transition between the two types of instabilities is possible only if the magnetic Prandtl number is equal to unity, Pm=1. At a fixed Pm≠1, the threshold of the double-diffusive AMRI is displaced by finite distance in the parameter space with respect to the diffusionless case even in the zero dissipation limit. The complete neutral stability surface contains three Whitney umbrella singular points and two mutually orthogonal intervals of self-intersection. At these singularities, the double-diffusive system reduces to a marginally stable system which is either Hamiltonian or parity–time-symmetric.

Numerical Study of Cryogenic Swirl Injection Under Supercritical Conditions

A numerical investigation has been conducted to explore the flowfield characteristics of a nonreactive cryogenic fluid through a swirl injector under supercritical conditions. The shear-stress transport turbulence model along with the Soave modification of Redlich–Kwong equation of state and a flow solver using the SIMPLEC algorithm for pressure–velocity coupling are used to evaluate various features of the turbulent swirling flow. Moreover, transport properties of the cryogenic fluid are determined by using the viscosity and thermal conductivity models derived by Chung et al. Experimental data of Cho et al. are used to validate the numerical results. The present numerical work shows the capability of predicting various characteristics of transcritical and supercritical swirling flows such as precessing vortex core and wavy shear-layer structures. Numerical simulations reveal that the spray-cone angle and instability wavelength slightly increase with the ambient pressure, whereas the pitch distance of the precessing vortex core decreases. Finally, to further investigate the dynamic features of the swirling jet, several spectral analyses are carried out. The longitudinal and azimuthal hydrodynamic instabilities, acoustic waves in the gaseous core, and Kelvin–Helmholtz instabilities are clearly characterized using fast Fourier transformation.

Numerical investigation of turbulent flow coherent structures in annular jet pumps using the LES method

Annular jet pumps that are used in hydraulic machinery have a very simple structure but very complex internal flow fields. Large eddy simulations were used to study the coherent structures in the turbulent flows in annular jet pumps with various area ratios, m. The distribution, movement and evolution of the coherent structure in the annular jet pumps are described based on vorticity, pressure and Q criteria. All the criteria demonstrate that the vortexes are mainly distributed in the recirculation region and in the mixing and the boundary layers, which have large velocity gradients. The various characteristics of the coherent structures are shown by the different criteria with the vorticity criterion describing the distribution, movement and evolution of the vortexes, the pressure criterion describing the movement and the Q criterion describing the vortex movement and evolution. The vorticity variation in the spanwise direction is larger than the variation in the streamwise direction; however, the streamwise vortex is the main mechanism driving the entrainment of the secondary flow and the mixing. The annular jet pump with m=3.33 had a higher vortex shedding frequency (about 1000 Hz) than that with m=1.72 (313–417 Hz). The azimuthal instability is the main reason for the generation of the streamwise vortex from the spanwise vortex. The vortex structures in the recirculation region are very strong, but small and disordered with no periodic vortex rings.

Spectral analysis of forced turbulence in a non-neutral plasma

The paper investigates the dynamics of magnetized non-neutral (electron) plasmas subjected to external electric field perturbations. A two-dimensional (2-D) particle-in-cell code is effectively exploited to model this system with a special attention to the role that non-axisymmetric, multipolar radio frequency (RF) drives applied to the cylindrical (circular) boundary play on the insurgence of azimuthal instabilities and the subsequent formation of coherent structures preventing the relaxation to a fully developed turbulent state, when the RF fields are chosen in the frequency range of the low-order fluid modes themselves. The isomorphism of such system with a 2-D inviscid incompressible fluid offers an insight into the details of forced 2-D fluid turbulence. The choice of different initial density (i.e. fluid vorticity) distributions allows for a selection of conditions where different levels of turbulence and intermittency are expected and a range of final states is achieved. Integral and spectral quantities of interest are computed along the flow using a multiresolution analysis based on a wavelet decomposition of both enstrophy and energy 2-D maps. The analysis of a variety of cases shows that the qualitative features of turbulent relaxation are similar in conditions of both free and forced evolution; at the same time, fine details of the flow beyond the self-similarity turbulence properties are highlighted in particular in the formation of structures and their timing, where the influence of the initial conditions and the effect of the external forcing can be distinguished.

Nonmodel analysis of helical and azimuthal magnetorotational instabilities

Helical and azimuthal magnetorotational instabilities operate in rotating magnetized flows with relatively steep negative or extremely steep positive shear. The corresponding lower and upper Liu limits of the shear, which determine the threshold of modal growth of these instabilities, are continuously connected when some axial electrical current is allowed to pass through the rotating fluid. We investigate the nonmodal dynamics of these instabilities arising from the non-normality of shear flow in the local approximation, generalizing the results of the modal approach. It is demonstrated that moderate transient/nonmodal amplification of both types of magnetorotational instability occurs within the Liu limits, where the system is stable according to modal analysis. We show that for the helical magnetorotational instability this magnetohydrodynamic behavior is closely connected with the nonmodal growth of the underlying purely hydrodynamic problem.

Azimuthal magnetorotational instability at low and high magnetic Prandtl numbers

Magnetorotational instability is considered to be one of the most powerful sources of turbulence in hydrodynamically stable quasi-Keplerian flows, such as those governing the accretion disk flows. Although the linear stability of these flows with an applied external magnetic field has been studied for decades, the influence of the instability on the outward angular momentum transport, necessary for the accretion of the disk, is still not well known. In this work, we model a Keplerian rotation with Taylor-Couette flow and imposed azimuthal magnetic field using both linear and nonlinear approaches. We present scalings of instability with Hartmann and Reynolds numbers via linear analysis and direct numerical simulations for two magnetic Prandtl numbers of 1.4 ·10−6 and 1. Inside the instability domains, modes with different axial wavenumbers dominate, resulting in sub-domains of instabilities which appear different for each Pm. Direct numerical simulations show the emergence of 1- and 2-frequency spatio-temporally oscillating structures for Pm = 1 close the onset of instability, as well as the significant enhancement of the angular momentum transport for Pm = 1, if compared to Pm = 1.4 ·10−6. Figs 7, Refs 11.

Controlling multiple filaments by relativistic optical vortex beams in plasmas.

Filamentation dynamics of relativistic optical vortex beams (OVBs) propagating in underdense plasma is investigated. It is shown that OVBs with finite orbital angular momentum (OAM) exhibit much more robust propagation behavior than the standard Gaussian beam. In fact, the growth rate of the azimuthal modulational instability decreases rapidly with increase of the OVB topological charge. Thus, relativistic OVBs can maintain their profiles for significantly longer distances in an underdense plasma before filamentation occurs. It is also found that an OVB would then break up into regular filament patterns due to conservation of the OAM, in contrast to a Gaussian laser beam, which in general experiences random filamentation.

Large eddy simulation of the near-field vortex dynamics in starting square jet transitioning into steady state

Large eddy simulation (LES) is carried out to study the vortex dynamics in the near-field of a starting turbulent square jet as well as its evolution into a developed steady jet. Simulations are conducted at Reynolds numbers (Re = UjD/υ) of 8000 and 45 000 based on the nozzle hydraulic diameter D and jet velocity (Uj). A Reynolds stress model was used to simulate the internal flow in the nozzle which provided the inlet conditions for the LES of the jet. To validate the simulations, turbulence statistics are compared with experimental results available for a steady square jet. Evaluation of the probability density function, skewness, and flatness of the centerline streamwise velocity (Uc) shows deviation from the Gaussian distribution in the near-field. Evolution of the self-induced deformation of the leading vortex ring is investigated to further clarify the role of axis-switching. The axis-switching is initiated earlier at low Reynolds number while the completion of the axis-switching process occurred at the same dimensionless time for both Reynolds numbers. The role of pressure distribution on vortex ring deformation is investigated. It is shown that the influence of pressure-induced azimuthal instability tends to deform a two-dimensional vortex ring topology into a three-dimensional one and revert back to a two-dimensional character again. The break-down and diffusion of the tip of the vortex are also studied. Evolution of the shear layer from a starting jet to a developed jet is studied in terms of the vorticity field. For a starting jet, entrainment is shown to occur in the presence of corner hairpin vortices.

The mechanism of liquid metal jet formation in the cathode spot of vacuum arc discharge

We have theoretically studied the dynamics of molten metal during crater formation in the cathode spot of vacuum arc discharge. At the initial stage, a liquid-metal ridge is formed around the crater. This process has been numerically simulated in the framework of the two-dimensional axisymmetric heat and mass transfer problem in the approximation of viscous incompressible liquid. At a more developed stage, the motion of liquid metal loses axial symmetry, which corresponds to a tendency toward jet formation. The development of azimuthal instabilities of the ridge is analyzed in terms of dispersion relations for surface waves. It is shown that maximum increments correspond to instability of the Rayleigh–Plateau type. Estimations of the time of formation of liquid metal jets and their probable number are obtained.

A hysteresis phenomenon leading to spinning or standing azimuthal instabilities in an annular combustor

Thermo-acoustic instabilities in annular combustors equipped with swirling turbulent injectors are most often coupled by azimuthal modes with a spinning or a standing structure. Experiments, and recent large eddy simulations, indicate that switching takes place between these two types of modes while in other cases a single mode type prevails. Why and how one type arises is a subject of ongoing discussions in recent theoretical and numerical investigations. The present article considers this intriguing issue by making use of well controlled experiments carried out in an annular combustion system comprising 16 identical matrix injectors operating in a laminar premixed mode and allowing full optical access to the flame region. This setup is used in a first stage to determine regions of instability as a function of equivalence ratio and injection velocity. It is shown that regions corresponding to spinning and standing azimuthal modes are well separated in this diagram, but with some overlap giving rise to a “dual mode” domain. For the same operating conditions, this annular system thus exhibits self-sustained instabilities with stable limit cycles coupled by a spinning or a standing mode. It is next shown that the mode which appears in that region depends on the path followed to reach the operating point. Starting from a lean operating condition, the system first develops a chugging instability with a broad frequency spectrum, which then gives rise to a well-established spinning oscillation with a narrow peak frequency in the dual mode region. When operation begins under rich conditions one first observes another chugging mode that finally yields a standing mode when the equivalence ratio is diminished. Away from these regimes, well defined slanted modes and longitudinal modes can also be triggered. In the dual mode region, the type of instability is controlled by an hysteresis phenomenon and the respective chugging modes act as precursors to these established azimuthal modes. It is found that the trajectories in a state space map contain indications on the kind of azimuthal oscillation that will be observed when the target operating point is reached. Beyond the various theoretical explanations of the prevalence of one type of mode on the other, the present observations indicate that spinning or standing modes may also appear in annular combustors as a result of the path used to enter the region of azimuthal instability.

Effect of equivalence ratio on the modal dynamics of azimuthal combustion instabilities

The present paper investigates the effect of equivalence ratio on the modal dynamics of self-excited azimuthal combustion instabilities in a laboratory-scale annular combustor. It is shown that operating at different equivalence ratios not only affects the mode of oscillation (whether the instabilities are mixed, or predominantly spinning or standing modes), but also the way in which mode switching between these states occurs. Using pressure time-series data obtained at multiple locations around the annulus the phenomenon of mode switching is investigated through the spin ratio, the orientation of the nodal lines and the envelope of the pressure oscillations. These three parameters all suggest that mode switching events occur almost periodically, and over azimuthal convective time scales. Moreover, analysis of the spin ratio and orientation of the nodal lines show that these parameters are correlated, and that their mean rates of change or trajectories also have a preferred direction. Therefore, these quantities were found to oscillate backwards and forwards in-phase with each other, as opposed to the mode simply rotating in one direction, providing new insight into the nature of modal dynamics of self-excited azimuthal modes.

Numerical Study of the Instability and Flow Transition in a Vortex-Ring/Wall Interaction

Instability and fl w transition of a vortex ring impinging on a wall were investig ated by means of large-eddy simulation for two vortex core thicknesses corresponding to thin and thick vortex rings. Various fundamental mechanisms dictating the fl w behaviours, such as evolution of vortical structures, instability and breakdown of vortex rings, development of modal energies, and transition from laminar to turbulent state, have been studied systematically . Analysis of the enstrophy of wrapping vortices and turbulent kinetic energy (TKE) in fl w fiel indicates that the formation and evolution of wrapping vortices are closely associated with the fl w transition to turbulent state. It is found that the temporal development of wrapping vortices and the growth rate of axial fl w generated around the circumference of the core region for the thin ring are faster than those for the thick ring. The azimuthal instabilities of primary and secondary vortex rings are analysed and the development of modal energies reveals the fl w transition to turbulent state. The law of energy decay follows a characteristic k 5=3 law, indicating that the vortical fl w has become turbulent. The results obtained in this study provide physical insight into the understanding of the instability mechanisms relevant to the vortical fl w evolution.

Prediction and control of combustion instabilities in real engines

This paper presents recent progress in the field of thermoacoustic combustion instabilities in propulsion engines such as rockets or gas turbines. Combustion instabilities have been studied for more than a century in simple laminar configurations as well as in laboratory-scale turbulent flames. These instabilities are also encountered in real engines but new mechanisms appear in these systems because of obvious differences with academic burners: larger Reynolds numbers, higher pressures and power densities, multiple inlet systems, complex fuels. Other differences are more subtle: real engines often feature specific unstable modes such as azimuthal instabilities in gas turbines or transverse modes in rocket chambers. Hydrodynamic instability modes can also differ as well as the combustion regimes, which can require very different simulation models. The integration of chambers in real engines implies that compressor and turbine impedances control instabilities directly so that the determination of the impedances of turbomachinery elements becomes a key issue. Gathering experimental data on combustion instabilities is difficult in real engines and large Eddy simulation (LES) has become a major tool in this field. Recent examples, however, show that LES is not sufficient and that theory, even in these complex systems, plays a major role to understand both experimental and LES results and to identify mitigation techniques.

Flow field features of fractal impinging jets at short nozzle to plate distances

An experimental analysis of the flow field generated by an impinging jet equipped with a fractal grid insert located at the nozzle exit is carried out by means of Tomographic Particle Image Velocimetry. The Reynolds number based on the nozzle exit section diameter d is set to 15,000. The presence of the grid leads to a non uniform curvature of the jet shear layer. As a consequence, azimuthal instabilities are triggered in proximity of the nozzle exit section, causing the production of streamwise vortices. Furthermore, the organization of the coherent structures in proximity of the impinged wall is discussed and related to the convective heat transfer distribution. Owing to the presence of counter rotating wall vortices along the diagonals of the on-plate imprint of the fractal grid, a region of minimum in the scalar transfer map can be detected. In addition to that, similarly to the well known vortex rings that characterize the case of round jet without turbulence promoter, the presence of azimuthally coherent structures that might be generated by Kelvin–Helmholtz instability of the jet shear layer is presented and discussed.

Theory for the anomalous electron transport in Hall effect thrusters. II. Kinetic model

In Paper I [T. Lafleur et al., Phys. Plasmas 23, 053502 (2016)], we demonstrated (using particle-in-cell simulations) the definite correlation between an anomalously high cross-field electron transport in Hall effect thrusters (HETs), and the presence of azimuthal electrostatic instabilities leading to enhanced electron scattering. Here, we present a kinetic theory that predicts the enhanced scattering rate and provides an electron cross-field mobility that is in good agreement with experiment. The large azimuthal electron drift velocity in HETs drives a strong instability that quickly saturates due to a combination of ion-wave trapping and wave-convection, leading to an enhanced mobility many orders of magnitude larger than that expected from classical diffusion theory. In addition to the magnetic field strength, B0, this enhanced mobility is a strong function of the plasma properties (such as the plasma density) and therefore does not, in general, follow simple 1/B02 or 1/B0 scaling laws.