Low-frequency Instability Research Articles

Low-Frequency Stability Analysis of Single-Phase System With dq-Frame Impedance Approach—Part I: Impedance Modeling and Verification

The utilization of a large number of power electronic converters in the high-speed railway system results in the low-frequency instability for the single-phase vehicle-grid system. In order to probe into the problem, the impedance-based approach is adopted. This paper focuses on the dq-frame impedance modeling and verification of the single-phase converters in the electric multiple units. The closed-loop input impedance modeling methods for both single converter and interleaved converters considering the second-order generalized integrator-based phase-locked loop (PLL) are put forward. Then, the dq-frame impedance measurement method for single-phase systems based on the Hilbert transform is proposed, and the modeling approach is verified by the frequency-domain simulations on the switching models. The good agreement of the model and simulation illustrates that the modeling method is suitable and accurate enough until half of the switching frequency. It is elucidated that the single-phase rectifier's impedance has the off-diagonal characteristic and the negative-impedance characteristic on the dd channel at low frequencies. Moreover, both the current and voltage controls have influences on the negative impedance shaping, while PLL does not.

Low-frequency combustion instabilities of an airblast swirl injector in a liquid-fuel combustor

ABSTRACT Low-frequency combustion dynamics of a prefilming airblast injector were experimentally investigated in a laboratory-scale liquid-fuel combustor operated with Jet A-1 fuel and air at atmospheric pressure and elevated temperatures. Our measurements reveal that multiple modes – ranging from 45 to 292 Hz – can be excited in the non-premixed combustion system, including the Helmholtz, longitudinal, and hydrodynamic instabilities. The system's propensity for mode selection depends strongly on combustor length and pilot equivalence ratio. A strong Helmholtz mode with a peak-to-peak amplitude of ∼14 kPa occurs, provided that the combustor length is relatively short and the pilot equivalence ratio is high. A high-amplitude, intermittent burst at approximately 12 Hz always develops when the system is on the verge of transition to the Helmholtz instability. With a longer combustor length, on the other hand, the system transitions to the ¾-wave longitudinal mode via a discontinuous mode-hopping process. The system undergoes well-defined, limit cycle oscillations with an extremely large pressure amplitude of ∼30 kPa, but the global OH* fluctuation amplitude is limited to merely 8.3%. Phase-resolved flame imaging measurements demonstrate that a ring-like partially-premixed flame emerges periodically in the dump region, when the non-premixed flame wrapping around the central recirculation zone is lifted off the fuel nozzle. The mutual interaction between the partially-premixed and non-premixed reaction zones is the dominant mechanism for intense sound generation. Under certain conditions, superposition of the Helmholtz and longitudinal modes occurs, leading to nonlinear interactions manifested by additional spectral peaks at the sum and difference of the two frequencies. In contrast to the other two cases, this superimposed tone is not characterized by limit cycle behavior, but by a noise-driven unsteadiness.

Stable confinement of high-electron-temperature plasmas in the GDT experiment

Having the ability to control the operation of advanced plasma heating methods is essential for the achievement of fusion-relevant plasmas in open traps. We describe a technique to deal with the increased transport brought about by the electron cyclotron heating in axisymmetric magnetic mirror device. The technique is based on shaping of the plasma potential by means of a set of specifically biased electrodes facing plasma at both open ends of a trap. In the experiments with combined microwave and neutral beam plasma heating performed in the gas-dynamic trap (GDT) facility at the Budker Institute, we show that a value of on-axis electron temperature up to 450 eV at plasma density m−3 can be supported steadily for 1.5 ms limited by the available heating and magnetic confinement systems. Stable high-temperature discharge, no longer degraded by low-frequency instabilities, offered a unique opportunity to confirm quantitatively the gas-dynamic plasma confinement model in a new range of parameters.

Wake dynamics of a cantilevered circular cylinder of aspect ratio 4

Near-wake characteristics of a low aspect ratio (h/d=4) cantilevered circular cylinder protruding a thin laminar boundary layer were investigated both numerically (Re=300) and experimentally (Re=10,400). Despite the substantial differences in the investigated Re, the wake dynamics show striking similarities and appear governed by similar instability mechanisms: (i) a Kármán-like vortex shedding instability, and (ii) a low-frequency instability related to the flow over the free end and near the cylinder-wall junction. Attention is drawn to the low-frequency instability, which comprises a significant portion of the kinetic energy content in the wake, and has not been reported in previous experimental or numerical investigations. It appears to be characteristic of intermediate aspect ratio cantilevered circular geometries and the boundary layer state, since the phenomenon is not observed for turbulent boundary layers of similar thickness.

Train–Network Interactions and Stability Evaluation in High-Speed Railways–Part I: Phenomena and Modeling

This paper presents an impedance-based model to systematically investigate the interaction performance of multiple trains and traction network interaction system, aiming to evaluate the serious phenomena, including low-frequency oscillation (LFO), harmonic resonance, and harmonic instability. The train–network interaction mechanism is therefore studied, and one presents a detailed coupling model for investigating the three interactive phenomena and their characteristics, influential factors, analysis methods, and possible mitigation schemes. In Part I of the two-part paper, the measured waveforms of such three phenomena are first characterized to indicate their features and principles. A unified framework of the train–traction network system for investigating the three problems is then presented. In order to reveal the interaction mechanism, all-frequency impedance behaviors of the electric trains and traction network are equally modeled. In which, an impedance-based input behavior of the train is fully investigated with considering available controllers and their parameters in DQ -domain. The entire traction network, including traction transformer, catenary, supply lines, is represented in a frequency-domain nodal matrix. Furthermore, the impedance–frequency responses of both electric train and traction network are measured and validated through frequency scan method. Finally, a generalized train–network simulation and experimental system are conducted for verifying the theoretical results of the two-part paper.

Analysis of Low-Frequency Stability in Grid-Tied DFIGs by Nonminimum Phase Zero Identification

For power converter-interfaced wind-generation systems, low-frequency instability issues arising from the interactions among converter outer power flow control (PFC) loops have got increased attention recently. This paper explores the possible origin of such instability in grid-tied doubly fed induction generator systems. To comprehensively analyze this multiloop interacted system, a reduced transfer matrix model is first constructed allowing for the PFC dynamics. Then the individual channel analysis and design approach is employed to decompose such closed-loop multivariable system into components such as local subsystem and loop interactions. Subsequently, frequency-response behavior analyses of these components are individually conducted at various operating points to study their relative contribution to overall stability. Results indicate that local active power control loop will induce a right-half-plane zero (RHPZ) for certain high-power operating conditions, and the resulting inverse response leads system unstable. Meanwhile, the critical operating point at which the RHPZ arises is analytically derived, and demonstrated to be close to the actual dynamic stability boundary.

Ion velocity analysis of rotating structures in a magnetic linear plasma device

The MISTRAL device is designed to produce a linear magnetized plasma column. It has been used a few years ago to study a nonlinear low frequency instability exhibiting an azimuthal number m = 2. By changing the experimental configuration of MISTRAL, this work shows experimental results on an m = 1 rotating instability with strongly different behavior. The spatio-temporal evolution of the ion velocity distribution function given by a laser-induced fluorescence diagnostic is measured to infer the radial and azimuthal velocities, ion fluxes, and electric fields. The naive image of a plasma exhibiting a global rotation is again invalidated in this m = 1 mode but in a different way. Contrary to the m = 2 mode, the rotation frequency of the instability is lower than the ion cyclotron frequency and ions exhibit a complex behavior with a radial outward flux inside the unstable arm and azimuthal ion fluxes always directed toward the unstable arm. The azimuthal ion velocity is close to zero inside the ionization region, whereas the radial ion velocity grows linearly with radius. The radial electric field is oriented inward inside the unstable arm and outward outside. An axial velocity perturbation is also present, indicating that contrary to the m = 2 mode, the m = 1 mode is not a flute mode. These results cannot be easily interpreted with existing theories.

The Effect of a Low-Frequency Structure on Passive Scalar Transport in the Flow Over a Surface-Mounted Rib

The unsteadiness of the flow over a surface-mounted rib involving passive scalar transport is studied using large-eddy simulation (LES) at a Reynolds number of 3000 (based on the rib height, $h$ , and the free-stream velocity, $U_{0})$ . The purpose of the present study is to gain further insight into the physical origin of the flow instability and its effect on passive scalar transport. Fourier spectral analysis of the velocity at different positions suggests that, in addition to the K-H instability in the shear layer (St ≈ 0.42), two lower frequencies (St ≈ 0.06 and 0.09) also exist. It is observed that the low-frequency instabilities accompany the shedding process of vortical structures. One low frequency, at $\text {St}\approx 0.06$ , is related to the pumping motion of the recirculation bubble, while the other, at $\text {St}\approx 0.09$ , is associated with the flapping mode of the shear layer. Through comparisons of velocity and temperature fields and the spectra of scalar fluctuations, it is found that the passive scalar is transported by the convection of vortical structures.

Numerical study on the instabilities in H2-air rotating detonation engines

Numerical simulations of rotating detonation engines (RDEs) are performed using two-dimensional Euler equations and a detailed chemistry model of H2-air. Two propagation modes, the one-wave mode and the two-wave mode, are observed in the RDEs. The instabilities of the RDEs are studied and analyzed specifically. A low frequency instability and a high frequency instability are found from the pressure-time trace measured at a fixed location and the average density-time trace of the RDEs. For the low frequency instability, the pressure peak of the pressure-time trace oscillates with a low frequency while the average density is stable. The deviation between the measurement location and the location of the detonation wave results in the low frequency instability. For the high frequency instability, the average density of the RDEs oscillates regularly with a single frequency while the pressure oscillates irregularly with several frequencies. The oscillation of the detonation wave height results in the high frequency instability. Furthermore, the low frequency instability and the high frequency instability both occur in the one-wave and two-wave mode RDEs.

Stability and Bifurcation Analysis of Multi-Element Non-Foster Networks

A stability and bifurcation analysis of multi-element non-Foster networks is presented, illustrated through its application to non-Foster transmission lines. These are obtained by periodically loading a passive transmission line with negative capacitors, implemented with negative-impedance converters (NICs). The methodology takes advantage of the possibility to perform a stability analysis per subintervals of the perturbation frequency. This will allow an independent analytical study of the low-frequency instability, from which simple mathematical criteria will be derived to prevent bias-network instabilities at the design stage. Then, a general numerical method, based on a combination of the Nyquist criterion with a pole-zero identification of the individual NIC, will be presented, which will enable the detection of both low- and high-frequency instabilities. A bifurcation analysis of the multi-element non-Foster structure will also be carried out, deriving the bifurcation condition from a matrix-form formulation of the multi-element structure. The judicious choice of the observation ports will enable a direct calculation of all the coexisting bifurcation loci, with no need for continuation procedures. These bifurcation loci will provide useful insight into the global-stability properties of the whole NIC-loaded structure.

Ultra-sensitive lithium niobate thermometer based on a dual-resonant whispering-gallery-mode cavity.

We exploit the strong polarization dependence of the thermooptic coefficients in a lithium niobate whispering-gallery-mode resonator to create a self-referenced thermometer. An unprecedented temperature sensitivity of 3.0GHz/K in the frequency difference between modes of orthogonal polarizations is demonstrated. In order to lock the lasers to the mode resonances, we use a simple intracavity phase modulation approach that provides for superbly low frequency instability. We demonstrate a record room-temperature thermometer detectivity of 40nK with 1s of averaging time. Simulations based on the fluctuation-dissipation theorem are performed to calculate the fundamental thermorefractive noise, showing that the detectivity could be improved with reduced laser-locking instabilities.

Shear Layer Development, Separation, and Stability Over a Low-Reynolds Number Airfoil

The shear layer development for a NACA 0025 airfoil at a low Reynolds number was investigated experimentally and numerically using large eddy simulation (LES). Two angles of attack (AOAs) were considered: 5 deg and 12 deg. Experiments and numerics confirm that two flow regimes are present. The first regime, present for an angle-of-attack of 5 deg, exhibits boundary layer reattachment with formation of a laminar separation bubble. The second regime consists of boundary layer separation without reattachment. Linear stability analysis (LSA) of mean velocity profiles is shown to provide adequate agreement between measured and computed growth rates. The stability equations exhibit significant sensitivity to variations in the base flow. This highlights that caution must be applied when experimental or computational uncertainties are present, particularly when performing comparisons. LSA suggests that the first regime is characterized by high frequency instabilities with low spatial growth, whereas the second regime experiences low frequency instabilities with more rapid growth. Spectral analysis confirms the dominance of a central frequency in the laminar separation region of the shear layer, and the importance of nonlinear interactions with harmonics in the transition process.

A comparison of some simple methods used to detect unstable temperature responses in tree-ring chronologies

Temporal stability of the relationship between a potential proxy climate record and the climate record itself is the foundation of palaeoproxy reconstructions of past climate variability. Dendroclimatologists have spent considerable effort exploring the issue of temporal instability of temperature records at high-latitude and −altitude Northern Hemisphere sites. Much of this work has focused on the Divergence Problem in which the modern ends of tree-ring chronologies exhibit pronounced departures from the climate-proxy relationships of preceding decades. However, there has been little scrutiny of how different methods might influence determinations of temporal instability at either the local scale or across broader spatial domains. Here we use four sets of Southern Hemisphere (SH) chronologies and three sets of synthetic data with known interventions to compare four methodologies that have been widely used to assess the temporal stability of relationships between tree-ring series and climate. Our analyses demonstrate that a determination of temporal instability may be partially dependent on method used to examine data, that some methods are more sensitive to standardisation choice than others, and that all methods are better at detecting high- rather than low-frequency instability. In all cases, the relatively modest strength of the relationships between the selected SH ring-width chronologies and temperature is likely to be an issue, especially if changes in trends are of interest. We recommend that robust assessment of temporal instability between tree-ring chronologies and observational climate data should use a range of methods and that unstable temporal relationships across space be carefully considered in the context of large climate field reconstructions.

Influence of upstream disturbance on the draft-tube flow of Francis turbine under part-load conditions

Owing to the part-load operations for the enhancement of grid flexibility, the Francis turbine often suffers from severe low-frequency and large-amplitude hydraulic instability, which is mostly pertinent to the highly unsteady swirling vortex rope in the draft tube. The influence of disturbances in the upstream (e.g., large-scale vortex structures in the spiral casing) on the draft-tube vortex flow is not well understood yet. In the present paper, the influence of the upstream disturbances on the vortical flow in the draft tube is studied based on the vortex identification method and the analysis of several important parameters (e.g., the swirl number and the velocity profile). For a small guide vane opening (representing the part-load condition), the vortices triggered in the spiral casing propagate downstream and significantly affect the swirling vortex-rope precession in the draft tube, leading to the changes of the intensity and the processional frequency of the swirling vortex rope. When the guide vane opening approaches the optimum one (representing the full-load condition), the upstream disturbance becomes weaker and thus its influences on the downstream flow are very limited.

A Flow Starvation Model for Tilting Pad Journal Bearings and Evaluation of Frequency Response Functions: A Contribution Toward Understanding the Onset of Low Frequency Shaft Motions

Direct lubrication tilting pad journal bearings (TPJBs) require less oil flow, reduce power consumption, and offer cooler pad temperatures for operation at high surface speeds. Although apparently free of hydrodynamic instability, the literature shows that direct lubrication TPJBs exhibit unexpected shaft vibrations with a broadband low frequency range, albeit small in amplitude. Published industrial practice demonstrates the inlet lubrication type, a reduced supply flow rate causing film starvation, and the bearing discharge conditions (evacuated or end sealed) affect the onset, gravity, and persistency of the subsynchronous vibration (SSV) hash motions. The paper presents a physical model to predict the performance of TPJBs with flow conditions ranging from over flooded to extreme starvation. Lubricant starvation occurs first on an unloaded pad, thus producing a (beneficial) reduction in drag power. As the supplied flowrate decreases further, fluid starvation moves toward the loaded pads and affects the film temperature and power loss, increases the journal eccentricity, and modifies the dynamic force coefficients of each tilting pad and thus the whole bearing. For a point mass rotor supported on a TPJB, the analysis produces eigenvalues and frequency response functions (FRFs) from three physical models for lateral rotor displacements: one with frequency reduced (4 × 4) bearing stiffness (K) and damping (C) coefficients and another with constant K–C–M (inertia) coefficients over a frequency range. The third model keeps the degrees of freedom (DOF) (tilting) of each pad and incorporates the full matrices of force coefficients including fluid inertia. Predictions of rotordynamic performance follow for two TPJBs: one bearing with load between pads (LBP) configuration, and the other with a load on a pad (LOP) configuration. For both examples, under increasingly poor lubricant flow conditions, the damping ratio for the rotor-bearing low frequency (SSV) modes decreases, thus producing an increase in the amplitude of the FRFs. For the LOP bearing, a large static load produces a significant asymmetry in the force coefficients; the rotor bearing has a small stiffness and damping for shaft displacements in the direction orthogonal to the load. A reduction in lubricant flow only exacerbates the phenomenon; starvation reaches the loaded pad to eventually cause the onset of low frequency (SSV) instability. The bearing analyzed showed similar behavior in a test bench. The predictions thus show a direct correlation between lubricant flow starvation and the onset of SSV.

Low-Frequency Combustion Instabilities Caused by Velocity Oscillations in Hybrid Rocket Motors

Low-Frequency Combustion Instabilities Caused by Velocity Oscillations in Hybrid Rocket Motors

Transition to turbulence in the rotating-disk boundary-layer flow with stationary vortices

This paper proposes a resolution to the conundrum of the roles of convective and absolute instability in transition of the rotating-disk boundary layer. It also draws some comparison with swept-wing flows. Direct numerical simulations based on the incompressible Navier–Stokes equations of the flow over the surface of a rotating disk with modelled roughness elements are presented. The rotating-disk flow has been of particular interest for stability and transition research since the work by Lingwood (J. Fluid Mech., vol. 299, 1995, pp. 17–33) where an absolute instability was found. Here stationary disturbances develop from roughness elements on the disk and are followed from the linear stage, growing to saturation and finally transitioning to turbulence. Several simulations are presented with varying disturbance amplitudes. The lowest amplitude corresponds approximately to the experiment by Imayama et al. (J. Fluid Mech., vol. 745, 2014a, pp. 132–163). For all cases, the primary instability was found to be convectively unstable, and secondary modes were found to be triggered spontaneously while the flow was developing. The secondary modes further stayed within the domain, and an explanation for this is a proposed globally unstable secondary instability. For the low-amplitude roughness cases, the disturbances propagate beyond the threshold for secondary global instability before becoming turbulent, and for the high-amplitude roughness cases the transition scenario gives a turbulent flow directly at the critical Reynolds number for the secondary global instability. These results correspond to the theory of Pier (J. Engng Maths, vol. 57, 2007, pp. 237–251) predicting a secondary absolute instability. In our simulations, high temporal frequencies were found to grow with a large amplification rate where the secondary global instability occurred. For smaller radial positions, low-frequency secondary instabilities were observed, tripped by the global instability.

Dependence of Pressure, Combustion and Frequency Characteristics on Valved Pulsejet Combustor Geometries

An experimental analysis of valved pulsejets based on the Curtis-Dyna design and the concomitant results are discussed in the current paper. By altering the combustor length, the tail pipe length and by adding a flare at the aft-end, twelve different pulsejet configurations are tested. An axially-distributed array of piezoelectric pressure sensors and ion probes reveal the pressure and combustion dynamics inside these devices. Evidence is attained to support the claim that valved Curtis-Dyna pulsejets of the tested configurations behave like a Helmholtz resonator. Each cycle of a pulsejet is composed of temporally and spatially restrained combustion events. Altering the geometry induces an amplitude modulated low frequency instability inside the pulsejet that is characterized by sinusoidally-varying peak cycle pressures. The operating frequency, peak pressures and combustion activity of the pulsejets are characterized to reveal that reliable pulsejet operation requires proper amount of coupling — defined by low time lags — between the pressure peaks and combustion events.

Model reduction and mechanism for the vortex-induced vibrations of bluff bodies

We present an effective reduced-order model (ROM) technique to couple an incompressible flow with a transversely vibrating bluff body in a state-space format. The ROM of the unsteady wake flow is based on the Navier–Stokes equations and is constructed by means of an eigensystem realization algorithm (ERA). We investigate the underlying mechanism of vortex-induced vibration (VIV) of a circular cylinder at low Reynolds number via linear stability analysis. To understand the frequency lock-in mechanism and self-sustained VIV phenomenon, a systematic analysis is performed by examining the eigenvalue trajectories of the ERA-based ROM for a range of reduced oscillation frequency $(F_{s})$, while maintaining fixed values of the Reynolds number ($Re$) and mass ratio ($m^{\ast }$). The effects of the Reynolds number $Re$, the mass ratio $m^{\ast }$ and the rounding of a square cylinder are examined to generalize the proposed ERA-based ROM for the VIV lock-in analysis. The considered cylinder configurations are a basic square with sharp corners, a circle and three intermediate rounded squares, which are created by varying a single rounding parameter. The results show that the two frequency lock-in regimes, the so-called resonance and flutter, only exist when certain conditions are satisfied, and the regimes have a strong dependence on the shape of the bluff body, the Reynolds number and the mass ratio. In addition, the frequency lock-in during VIV of a square cylinder is found to be dominated by the resonance regime, without any coupled-mode flutter at low Reynolds number. To further discern the influence of geometry on the VIV lock-in mechanism, we consider the smooth curve geometry of an ellipse and two sharp corner geometries of forward triangle and diamond-shaped bluff bodies. While the ellipse and diamond geometries exhibit the flutter and mixed resonance–flutter regimes, the forward triangle undergoes only the flutter-induced lock-in for $30\leqslant Re\leqslant 100$ at $m^{\ast }=10$. In the case of the forward triangle configuration, the ERA-based ROM accurately predicts the low-frequency galloping instability. We observe a kink in the amplitude response associated with 1:3 synchronization, whereby the forward triangular body oscillates at a single dominant frequency but the lift force has a frequency component at three times the body oscillation frequency. Finally, we present a stability phase diagram to summarize the VIV lock-in regimes of the five smooth-curve- and sharp-corner-based bluff bodies. These findings attempt to generalize our understanding of the VIV lock-in mechanism for bluff bodies at low Reynolds number. The proposed ERA-based ROM is found to be accurate, efficient and easy to use for the linear stability analysis of VIV, and it can have a profound impact on the development of control strategies for nonlinear vortex shedding and VIV.

The frequency characteristics of the shear layer oscillation in hybrid rocket post-chamber

Visualizing flame images revealed the occurrence of LFI (Low Frequency Instability <20 Hz) in hybrid rocket combustion is significantly related with pressure and combustion fluctuations of around 500 Hz in the post chamber. In this study, numerical calculations for cases with different ER (Expansion Ratio) and the wall blowing effect were conducted to investigate which factor has a more influence on pressure fluctuation of 500 Hz band. In addition, the flow structure change in each case was examined and compared with the baseline. Results show that both wall blowing and the increment of ER increases the turbulent energy of the time-averaged flow and pushes the reattachment point to downward. And it seems that the wall blowing effect considerably increases the recirculation length by modifying the turbulent flow structures. Moreover, results indicate that the wall blowing effect promotes the vortices generation from the inlet and supplies the vortices with more energy to appear in the wake. In the spectrum analysis, also, the wall blowing effect was found to oscillate re-attachment point, resulting in the appearance of additional oscillatory characteristics of St = O (0.3) in the downstream otherwise completely dissipated. Note that the oscillation frequency of St = O (0.3) is corresponding to a dimensional frequency of 490 Hz, which approximately coincides with a measured frequency band of 500 Hz. Therefore, the pressure oscillation in about 500 Hz band in the experiment is strongly related with temporal characteristic of the modified flow structure by wall blowing.