Acoustic Instability Research Articles

The acoustic response of Burke–Schumann counterflow flames

The acoustic response of strained nonpremixed flames is investigated using as a canonical model problem the planar counterflow configuration subject to small harmonic fluctuations of the stagnation-point pressure and strain rate. To focus on effects of modified transport rates the analysis employs the limit of infinitely fast reaction for a general non-unity Lewis number of the fuel, including values of interest in hydrogen-oxygen and hydrocarbon-oxygen systems. For both acoustic-pressure and acoustic-velocity response, differential–diffusion effects are shown to promote the fluctuations of the flame location and reactant consumption rates (while in the pressure response, distinct behaviors of the flame temperature were observed depending on stoichiometry). The results are used, together with the Rayleigh criterion, to investigate the frequency dependence of the amplification/attenuation rate relevant in computations of acoustic instabilities. The analysis predicts acoustic amplification for all frequencies in the pressure response, whereas a critical crossover frequency is identified in the strain response demarcating the transition from attenuation to amplification of acoustic energy.

The formation and dissipation of electrostatic shock waves: the role of ion–ion acoustic instabilities

The role of ion–ion acoustic instabilities in the formation and dissipation of collisionless electrostatic shock waves driven by counter-streaming supersonic plasma flows has been investigated via two-dimensional particle-in-cell simulations. The nonlinear evolution of unstable waves and ion velocity distributions has been analyzed in detail. It is found that for electrostatic shocks driven by moderate-velocity flows, longitudinal and oblique ion–ion acoustic instabilities can be excited in the downstream and upstream regions, which lead to thermalization of the transmitted and reflected ions, respectively. For high-velocity flows, oblique ion–ion acoustic instabilities can develop in the overlap layer during the shock formation process and impede the shock formation.

Role of induced axial acoustics in transverse acoustic flame response

This paper addresses the mechanisms through which transverse acoustic oscillations excite unsteady heat release. Forced and self-excited transverse acoustic instability studies to date have strong coupling between the transverse and axial acoustic fields near the flame. This is significant, as studies suggest that it is not the transverse disturbances themselves, but rather the induced axial acoustic disturbances, that control the bulk of the heat release response. This paper presents results from an experiment that controls the relative amplitudes of transverse and axial disturbances and measures the flow field and heat release response for an acoustically compact, swirling flame. 5 kHz, simultaneous sPIV and OH-PLIF measured the flow field and flame edge, and OH* chemiluminescence measured the relative heat release. Experiments performed with essentially the same transverse acoustic wave field, but with and without axial acoustics, show that significant heat release oscillations are only excited in the former case. The results show that the axial disturbances are the dominant cause of the heat release oscillations. These observations support the theory that the key role of the transverse motions is to act as the “clock” for the instability, setting the frequency of the oscillations while having a negligible direct effect on the actual heat release fluctuations. They also show that transverse instabilities can be damped by either actively canceling the induced axial acoustics in the nozzle (rather than the much larger energy transverse combustor disturbances), or by passively tuning the nozzle impedance to drive an axial acoustic velocity node at the nozzle outlet.

Electron acoustic waves and parametric instabilities in a 4-component relativistic quantum plasma with Thomas-Fermi distributed electrons

The interaction of Circularly Polarized Electro-Magnetic (CPEM) waves with a 4-component relativistic quantum plasma is studied. The plasma constituents are: relativistic-degenerate electrons and positrons, dynamic degenerate ions, and Thomas-Fermi distributed electrons in the background. We have employed the Klein-Gordon equations for the electrons as well as for the positrons, while the ions are represented by the Schrodinger equation. The Maxwell and Poisson equations are used for electromagnetic waves. Three modes are observed: one of the modes is associated with the electron acoustic wave, a second mode at frequencies greater than the electron acoustic wave mode could be associated with the positrons, and the third one at the lowest frequencies could be associated with the ions. Furthermore, Stimulated Raman Scattering (SRS), Modulational, and Stimulated Brillouin Scattering (SBS) instabilities are studied. It is observed that the growth rates of both the SRS and SBS instabilities decrease with incre...

The role of instability-enhanced friction on ‘anomalous’ electron and ion transport in Hall-effect thrusters

Using a self-consistent 2D particle-in-cell (PIC) simulation, we investigate the electron transport in Hall-effect thrusters. The PIC simulation is explicit in time and models the axial and azimuthal directions of a thruster without using any artificial parametric or geometric scaling factors. The applied discharge voltage and external magnetic field causes electrons to drift in the azimuthal direction, and this drives an instability in the plasma that produces large amplitude oscillations in both the plasma density and azimuthal electric field. A Fourier transform in time and space shows that the oscillations follow a dispersion relation similiar to that for an ion acoustic instability (in agreement with a recent kinetic theory). Correlated with the presence of this instability is an enhanced electron cross-field transport; even in the absence of electron-wall collisions and secondary electron emission. The amplitude of plasma density oscillations (but not electric field oscillations) is found to decrease significantly in a region just downstream of the thruster exit (before then increasing again), and reaches levels similar to those measured experimentally with collective light scattering techniques. By taking relevant velocity moments of the electron distribution function in the PIC simulations, we reconstruct each term in the electron momentum conservation equation and demonstrate that ‘anomalous’ electron transport can be explained entirely due to an instability-enhanced friction force between electrons and ions. This friction force acts as an additional momentum loss allowing electrons to cross the magnetic field, and as an accelerating force causing ions to rotate azimuthally in the same direction as the electrons. Clear evidence of ion-wave trapping in the instability electric field is observed.

Ions shear flow and electron field-aligned current produce ion acoustic waves in the oxygen-hydrogen ionospheric plasma

It is pointed out that the ion acoustic waves (IAWs) are excited either by field-aligned shear flows or electron parallel current in oxygen-hydrogen (O-H) plasma of upper ionosphere. The purely growing D'Angelo instability becomes ion acoustic wave instability in the presence of second kind of ions within the framework of multi-fluid plasma model. On the other hand, kinetic theory is used to show that the growth rate of current driven ion acoustic wave overcomes the ion Landau damping. Out of four real roots corresponding to negative shear flow, the two roots can become unstable. Thus, ion acoustic waves at different but very low real frequencies appear in O-H plasma of ionosphere due to parallel shear flow and current, which is in agreement with satellite observations.

Acoustic Dynamics of A Swirl Premixed Combustor with Different Operating Conditions

The effects of inlet swirl and external excitation on the flow field and combustion acoustic modes in a low NOx premixed combustor are experimentally investigated using a 100kW laboratory rig. It combines different operating conditions with variations in swirl number and varying levels of external excitation which are critical factors influencing the flow- flame interaction within the combustor. Results show the formation of a vortex induced central recirculation zone (CRZ) for the two swirl conditions which increase in length and width with changes in the swirl strength and forcing. The flow structure eventually merges with the high momentum flow region, a feature common to many swirl combustors. The acoustic oscillations were observed to be affected by the variations in the swirl strength with further dynamics at different levels of excitation. Accurate combination of these conditions (swirl, and excitation) could be advantageous in suppressing the intensity of the destructive acoustic instabilities in the burner. Results of this nature provide information for the design of an active control system for the combustor.

Return current instability driven by a temperature gradient in ICF plasmas

Hot plasmas with strong temperature gradients in inertial confinement fusion experiments are examined for ion acoustic instabilities produced by electron heat flow. The return current instability (RCI) due to a neutralizing current of cold electrons arising in response to a large electron heat flux has been considered. First, the linear threshold and growth rates are derived in the non-local regime of thermal transport. They are compared with the results of Vlasov–Fokker–Planck (VFP) simulations in one spatial dimension. Very good agreement has been found between kinetic VFP simulations and the linear theory of the RCI. A quasi-stationary state of ion acoustic turbulence (IAT) produced by the RCI is achieved in the VFP simulations. Saturation of the RCI involves heating of ions in the tail of the ion distribution function and convection of the enhanced ion acoustic fluctuations from the unstable region of the plasma. Further evolution of the IAT and its effects on absorption and transport are also discussed.

Electrostatic instabilities and nonlinear structures associated with field-aligned plasma flows and Cairns-Tsallis electrons in the ionosphere

Effects of non-Maxwellian electron densities on the low frequency electrostatic waves and instabilities are pointed out in a bi-ion plasma having field-aligned shear flow. Several different electron densities are used and formation of nonlinear stationary structures is investigated in different limits. Solutions of nonlinear equations are obtained in the form of KdV solitons and vortices and results are applied to terrestrial ionosphere. The deviation from Boltzmann density of the electrons enhances the linear shear flow-driven ion acoustic instability in the bi-ion plasma. But it plays destructive role in the formation of pulse type solitons.

Generation of intermittent ion acoustic waves in whistler-mode turbulence

A two-dimensional, fully kinetic, electromagnetic, particle-in-cell simulation in a magnetized collisionless plasma has been performed, demonstrating the generation of intermittent ion acoustic waves in finite-amplitude whistler-mode turbulence. The self-consistent simulation shows that ion/ion acoustic instability can be driven as a consequence of the nonlinear evolution of whistler-mode turbulence. The instability triggering the generation of ion acoustic waves occurs intermittently in several local regions. We propose that the nonlinear development of the phase-space density that drives kinetic instabilities must be analyzed with greater care if the dissipation of plasma turbulence is to be understood.

Comprehensive Study of Cryogenic Fluid Dynamics of Swirl Injectors at Supercritical Conditions

A comprehensive study is conducted to enhance the understanding of swirl injector flow dynamics at supercritical conditions. The formulation is based on full-conservation laws and accommodates real-fluid thermodynamics and transport theories over the entire range of fluid states of concern. Liquid oxygen at 120 K is injected into a supercritical oxygen environment at 300–600 K. Detailed three-dimensional flow structures are visualized for the first time in the pressure range of 100–200 atm. A smooth fluid transition from the compressed-liquid to light-gas state occurs, which is in contrast to a distinct interface of phase change at subcritical pressure. Dynamic behaviors of the oscillatory flowfield are explored using the spectral analysis and proper orthogonal decomposition technique. Various underlying mechanisms dictating flow evolution, including shear-layer, helical, centrifugal, and acoustic instabilities, are studied in depth. The hydrodynamic wave motions in the liquid-oxygen film are found to propagate in two different modes: one along the axial direction at the local wave speed; the other in the azimuthal direction and convected downstream at the mean flow velocity. Results show good agreement with the analytical prediction of the overall response transfer function of the swirl injector. The dominant mode of the azimuthal wave is triggered by the natural acoustic oscillation within the injector. Compared with the two-dimensional axisymmetric results, the calculated liquid-oxygen film is thicker and the spreading angle smaller due to the momentum loss and vortical dynamics in the azimuthal direction.

Multiple-scale kinetic simulations with the energy conserving semi-implicit particle in cell method

The recently developed energy conserving semi-implicit method (ECsim) for particle-in-cell (PIC) simulation is applied to multiple-scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or ion-scale processes. Unlike hybrid methods, the ECsim is capable of providing kinetic electron information, such as wave–electron interaction (Landau damping or cyclotron resonance) and non-Maxwellian electron velocity distributions. However, like hybrid methods, the ECsim does not need to resolve all electron scales, allowing time steps and grid spacings orders of magnitude larger than in explicit PIC schemes. The additional advantage of the ECsim is that the stability at large scale is obtained while conserving energy exactly. Three examples are presented: ion acoustic waves, electron acoustic instability and reconnection processes.

Hollow cathode modeling: I. A coupled plasma thermal two-dimensional model

A two-dimensional axisymmetric quasi-neutral fluid model of an emissive hollow cathode that includes neutral xenon, single charge ions and electrons has been developed. The gas discharge is coupled with a thermal model of the cathode into a self-consistent generic model applicable to any hollow cathode design. An exhaustive description of the model assumptions and governing equations is given. Boundary conditions for both the gas discharge and thermal model are clearly specified as well. A new emissive sheath model that is valid for any emissive material and in both space charge and thermionic emission limited regimes is introduced. Then, setting the emitter temperature to an experimentally measured profile, we compare simulation results of the plasma model to measurements available in the literature for NASA NSTAR barium oxide cathode. Qualitative discrepancies between simulation results and measurements are noted in the cathode plume regarding the simulated plasma potential. Motivated by experimental evidence supporting the occurrence of ion acoustic instabilities in the cathode plume, an enhanced model of electron transport in the plume is presented and its consequences analyzed. Using the obtained plasma model, simulated quantities in the plume are qualitatively comparable with measurements. Inside the cathode, the simulated plasma density agrees well with measurements and is within the experimental uncertainty associated with these measurements. A comparison of simulation results of the full coupled cathode model for the NASA NSTAR cathode with experimental measurements is presented in a companion paper, as well as a physical analysis of the cathode behavior and a parametric study of the influence of the operating point and key design choices.

High-Frequency Thermoacoustic Modulation Mechanisms in Swirl-Stabilized Gas Turbine Combustors—Part II: Modeling and Analysis

This paper deals with high-frequency (HF) thermoacoustic instabilities in swirl-stabilized gas turbine combustors. Driving mechanisms associated with periodic flame displacement and flame shape deformations are theoretically discussed, and corresponding flame transfer functions (FTF) are derived from first principles. These linear feedback models are then evaluated by means of a lab-scale swirl-stabilized combustor in combination with part one of this joint publication. For this purpose, the models are used to thermoacoustically characterize a complete set of operation points of this combustor facility. Specifically, growth rates of the first transversal modes are computed, and compared against experimentally obtained pressure amplitudes as an indicator for thermoacoustic stability. The characterization is based on a hybrid analysis approach relying on a frequency domain formulation of acoustic conservation equations, in which nonuniform temperature fields and distributed thermoacoustic source terms/flame transfer functions can be straightforwardly considered. The relative contribution of flame displacement and deformation driving mechanisms–i.e., their significance with respect to the total driving–is identified. Furthermore, promoting/inhibiting conditions for the occurrence of high frequency, transversal acoustic instabilities within swirl-stabilized gas turbine combustors are revealed.

Simulation of reactive polydisperse sprays strongly coupled to unsteady flows in solid rocket motors: Efficient strategy using Eulerian Multi-Fluid methods

In this paper, we tackle the issue of the accurate simulation of evaporating and reactive polydisperse sprays strongly coupled to unsteady gaseous flows. In solid propulsion, aluminum particles are included in the propellant to improve the global performances but the distributed combustion of these droplets in the chamber is suspected to be a driving mechanism of hydrodynamic and acoustic instabilities. The faithful prediction of two-phase interactions is a determining step for future solid rocket motor optimization. When looking at saving computational ressources as required for industrial applications, performing reliable simulations of two-phase flow instabilities appears as a challenge for both modeling and scientific computing. The size polydispersity, which conditions the droplet dynamics, is a key parameter that has to be accounted for. For moderately dense sprays, a kinetic approach based on a statistical point of view is particularly appropriate. The spray is described by a number density function and its evolution follows a Williams–Boltzmann transport equation. To solve it, we use Eulerian Multi-Fluid methods, based on a continuous discretization of the size phase space into sections, which offer an accurate treatment of the polydispersion. The objective of this paper is threefold: first to derive a new Two Size Moment Multi-Fluid model that is able to tackle evaporating polydisperse sprays at low cost while accurately describing the main driving mechanisms, second to develop a dedicated evaporation scheme to treat simultaneously mass, moment and energy exchanges with the gas and between the sections. Finally, to design a time splitting operator strategy respecting both reactive two-phase flow physics and cost/accuracy ratio required for industrial computations. Using a research code, we provide 0D validations of the new scheme before assessing the splitting technique's ability on a reference two-phase flow acoustic case. Implemented in the industrial-oriented CEDRE code, all developments allow to simulate realistic solid rocket motor configurations featuring the first polydisperse reactive computations with a fully Eulerian method.

Characteristic Times of Acoustic and Condensation Instability in Heat-releasing Gas Media

We investigate wave evolution in gas media with non-adiabatic heating and cooling processes depending on temperature and density. In this work, the temporal instability of acoustic disturbances in a heat-releasing uniform gas medium is under consideration. We neglect the influence of shear viscosity and thermal conduction. During the investigation, we describe the dispersion relation for the dynamics of two acoustic modes propagating in opposite directions and condensation (thermal) mode. The condensation mode has purely imaginary frequency and describes local changes of temperature and density under constant pressure. Furthermore, analytical expressions for temporal increments of acoustic and condensation modes are obtained. Features of obtained solutions depending on the ratio of low- and high-frequency adiabatic indexes are shown. The relationship between the acoustic temporal increment and the second (bulk) viscosity coefficient is described as well.

A dynamical model for gas flows, star formation and nuclear winds in galactic centres

We present a dynamical model for gas transport, star formation, and winds in the nuclear regions of galaxies, focusing on the Milky Way's Central Molecular Zone (CMZ). In our model angular momentum and mass are transported by a combination of gravitational and bar-driven acoustic instabilities. In gravitationally-unstable regions the gas can form stars, and the resulting feedback drives both turbulence and a wind that ejects mass from the CMZ. We show that the CMZ is in a quasi-steady state where mass deposited at large radii by the bar is transported inward to a star-forming, ring-shaped region at $\sim 100$ pc from the Galactic Centre, where the shear reaches a minimum. This ring undergoes episodic starbursts, with bursts lasting $\sim 5-10$ Myr occurring at $\sim 20-40$ Myr intervals. During quiescence the gas in the ring is not fully cleared, but is driven out of a self-gravitating state by the momentum injected by expanding supernova remnants. Starbursts also drive a wind off the star-forming ring, with a time-averaged mass flux comparable to the star formation rate. We show that our model agrees well with the observed properties of the CMZ, and places it near a star formation minimum within the evolutionary cycle. We argue that such cycles of bursty star formation and winds should be ubiquitous in the nuclei of barred spiral galaxies, and show that the resulting distribution of galactic nuclei on the Kennicutt-Schmidt relation is in good agreement with that observed in nearby galaxies.

The interplay of the collisionless non-linear thin-shell instability with the ion acoustic instability

The nonlinear thin-shell instability (NTSI) may explain some of the turbulent hydrodynamic structures that are observed close to the collision boundary of energetic astrophysical outflows. It develops in nonplanar shells that are bounded on either side by a hydrodynamic shock, provided that the amplitude of the seed oscillations is sufficiently large. The hydrodynamic NTSI has a microscopic counterpart in collisionless plasma. A sinusoidal displacement of a thin shell, which is formed by the collision of two clouds of unmagnetized electrons and protons, grows and saturates on timescales of the order of the inverse proton plasma frequency. Here we increase the wavelength of the seed perturbation by a factor 4 compared to that in a previous study. Like in the case of the hydrodynamic NTSI, the increase in the wavelength reduces the growth rate of the microscopic NTSI. The prolonged growth time of the microscopic NTSI allows the waves, which are driven by the competing ion acoustic instability, to grow to a large amplitude before the NTSI saturates and they disrupt the latter. The ion acoustic instability thus imposes a limit on the largest wavelength that can be destabilized by the NTSI in collisionless plasma. The limit can be overcome by binary collisions. We bring forward evidence for an overstability of the collisionless NTSI.

Simulations of the dust acoustic instability in a collisional plasma with warm dust

Dust acoustic (or dust density) waves have been observed in many laboratory dusty plasmas. These low-frequency waves involve the dynamics of highly charged and massive dust grains, and can be excited by the flow of ions relative to dust. In this paper, we consider the nonlinear development of the dust acoustic instability, excited by thermal ion flow, in a collisional plasma containing dust with high kinetic temperature (warm dust). It is shown that under certain conditions there may be a long-wavelength secondary instability in the nonlinear stage as dust gets heated by the waves. The characteristics of the nonlinear development are considered as a function of the relative charge density of the dust. Application to possible experimental parameters is discussed.

Dust Charge Polarity Effect on Dust-Ion Acoustic Modulational Instability in a Nonthermal Dusty Plasma With Adiabatic Ions

The effects of dust charge polarity, ion temperature, and nonthermal electrons on dust-ion acoustic modulational instability and on the region (i.e., modulated wave number) for the formation of bright and dark envelope soliton structures are investigated. The dust particles are considered to be stationary and have positive and negative charges, while ions are taken dynamic and warm, and hot nonthermal electrons are assumed to be inertialess and kappa distributed in a dusty plasma. The Krylov–Bogoliubov–Mitropolsky method is used to derive the nonlinear Schrodinger equation (NLSE) for nonlinear amplitude modulation of dust-ion acoustic wave (DIAW) in plasmas. The dispersive and nonlinear coefficients of NLSE are obtained for DIAW, which depends on ion temperature, spectral indices of the nonthermal distributed electrons, dust density, and charge polarity of stationary dust particles. The modulationally stable and unstable regions of DIAW and its growth rate are investigated numerically. It is found that finite ion temperature, dust density, dust charge polarity, and spectral index of kappa for nonthermal electrons play a significant role to unstable the modulated DIAW modulated wave. The existence of positively and negatively charged dust particles and their observation in different regions of space plasma and in laboratory experiments is also pointed out.