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Summary of recent and ongoing research efforts in power system oscillation analysis and techniques for locating the source of oscillations. Review of existing technologies, best practice in industry, as well as challenges.
Forced and naturally occurring, self-sustaining oscillations of transonic flows in two-dimensional diffusers were computed using MacCormack's hybrid method. Depending upon the shock strengths and the area ratios, the flow was fully attached or separated by either the shock or the adverse pressure gradient associated with the enlarging diffuser area. In the case of forced oscillations, a sinusoidal plane pressure wave at frequency 300 Hz was prescribed at the exit. A sufficiently large amount of data were acquired and Fourier analyzed. The distrbutions of time-mean pressures, the power spectral density, and the amplitude with phase angle along the top wall and in the core region were determined. Comparison with experimental results for the forced oscillation generally gave very good agreement; some success was achieved for the case of self-sustaining oscillation despite substantial three-dimensionality in the test. An observation of the sequence of self-sustaining oscillations was given.
Despite recent progress in seasonal forecast systems, the predictive skill for the Indian Ocean Dipole (IOD) remains typically limited to a lead time of one season or less in both dynamical and empirical models. Here we develop a simple stochastic-dynamical model (SDM) to predict the IOD using seasonally modulated El Niño–Southern Oscillation (ENSO) forcing together with a seasonally modulated Indian Ocean coupled ocean-atmosphere feedback. The SDM, with either observed or forecasted ENSO forcing, exhibits generally higher skill and longer lead times for predicting IOD events than the operational Climate Forecast System version 2 and the Scale Interaction Experiment–Frontier system. The improvements mainly originate from better prediction of ENSO-dependent IOD events and from reducing false alarms. These results affirm our hypothesis that operational IOD predictability beyond persistence is largely controlled by ENSO predictability and the signal-to-noise ratio of the system. Therefore, potential future ENSO improvements in models should translate to more skillful IOD predictions.
For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.
We observe plasma heating due to collisional diffusion across a separatrix when a magnesium ion column in a Penning-Malmberg trap is cyclically pushed back and forth across a partial trapping barrier. The barrier is an externally applied axisymmetric “squeeze” potential, which creates a velocity separatrix between trapped and passing particles. Weak ion-ion collisions then cause separatrix crossings, leading to irreversible heating. Furthermore, the heating rate scales as the square root of the oscillation rate times the collision frequency and thus can be dominant for low-collisionality plasmas. The particle velocity distribution function is measured with coherent laser induced fluorescence and shows passing and trapped particles having an out-of-phase response to the forced plasma oscillations.
Here in this work, we investigate the applicability of the harmonic balance method (HBM) to predict periodic solutions of a single degree-of-freedom forced Duffing oscillator with freeplay nonlinearity. By studying the route to impact, which refers to a parametric study as the contact stiffness increases from soft to hard, the convergence behavior of the HBM can be understood in terms of the strength of the non-smooth forcing term. HBM results are compared to time-integration results to facilitate an evaluation of the accuracy of nonlinear periodic responses. An additional contribution of this study is to perform convergence and stability analysis specifically for isolas generated by the non-smooth nonlinearity. Residual error analysis is used to determine the approximate number of harmonics required to get results accurate to a given error tolerance. Hill’s method and Floquet theory are employed to compute the stability of periodic solutions and identify the types of bifurcations in the system.
We present our numerical results for certain unsteady flows past oscillating cylinders and aerofoils. The computations are based on the stabilized space-time finite element formulation. The implicit equation systems resulting from the space-time finite element discretizations are solved using iterative solution techniques. One of the problems studied is flow past a cylinder which is forced to oscillate in the horizontal direction. In this case we observe a change from an unsymmetric mode of vortex shedding to a symmetric one. An extensive study was carried out for the case in which a cylinder is mounted on lightly damped springs and allowed to oscillate in the vertical direction. In this case the motion of the cylinder needs to be determined as part of the solution, and under certain conditions this motion changes the vortex-shedding pattern of the flow field significantly. This nonlinear fluid-structure interaction exhibits certain interesting behavior such as 'lock-in' and 'hysteresis', which are in good agreement with the laboratory experiments carried out by other researchers in the past. Preliminary results for flow past a pitching aerofoil are also presented.
The effect of dynamic rolling oscillations of delta-wing/twin-tail configuration on twin-tail buffet response is investigated. The computational model consists of a sharp-edged delta wing of aspect ratio one and swept-back flexible twin tail with taper ratio of 0.23. The configuration model is statically pitched at 30 deg. angle of attack and then forced to oscillate in roll around the symmetry axis at a constant amplitude of 4 deg. and reduced frequency of pi and 2(pi). The freestream Mach number and Reynolds number are 0.3 and 1.25 million, respectively. This multidisciplinary problem is solved using three sets of equations on a dynamic multi-block grid structure. The first set is the unsteady, full Navier-Stokes equations, the second set is the aeroelastic equations for coupled bending and torsion vibrations of the tails, and the third set is the grid-displacement equations. The configuration is investigated for inboard position of the twin tails which corresponds to a separation distance between the twin tails of 33% wing span. The computed results are compared with the results of stationary configuration, which previously have been validated using experimental data. The results conclusively showed that the rolling oscillations of the configuration have led to higher loads, higher deflections, and higher excitation peaks than those of the stationary configuration. Moreover, increasing the reduced frequency has led to higher loads and excitation peaks and lower bending and torsion deflections and acceleration.
To mathematically model the oscillations of a spherical bubble, either the time-dependent volume V(t) or the radius R(t) can be used as the dependent variable. A recent exchange between the advocates of the volume approach and the radius approach concerns in apparent discrepancy in the predicted nonlinear acoustic emissions from a bubble subject to a time-periodic external pressure field. This letter attempts to resolve the discrepancy via an examination of the arguments offered by both sides. In addition, some general comments on nonlinear harmonic and subharmonic emissions from acoustically forced bubble oscillations are presented.
Significant inadequacies of current models for multiphase flows present a major barrier to rapid development of advanced high-efficiency low-emissions combustion devices. Liquid spray atomization processes largely determine fuel-air mixture formation, which subsequently govern combustion and controls performance, emissions, and durability of a device. The current study presents a fundamentally-consistent framework to model the effects of breakup processes, liquid drop deformations, and internal flow dynamics on mass, momentum, and energy exchange functions. This framework builds on the Taylor Analogy Breakup (TAB) model which naturally quantifies local drop deformation dynamics. Real-fluid multicomponent thermodynamic property modeling and Gradient Theory simulations facilitate accurate calculations of molecular two-phase interface exchange functions, surface tensions forces, drop oscillations, and breakup processes. The analysis establishes that these drop dynamics, along with finite liquid viscosity effects, significantly alter gas-liquid exchange functions. The study quantifies these effects for the resulting drag coefficients of liquid drops and demonstrates significant deviations from the classic dynamic drag model, which is widely applied in modern simulations performed in academia and industry. This work also quantifies effects, which originate from gas-liquid coupling dynamics, on evaporation and heating rates. The analysis establishes that the consideration of these coupling dynamics modify mass and energy transfer rates even more significantly than the corresponding drag forces from momentum exchange. This physical complexity, however, is largely neglected in modern studies from academia and industry. A new set of equations is presented to improve the modeling of drop breakup processes to address the current shortcomings in the prediction of resulting drops proper- ties over the full range of relevant breakup conditions. The framework is based on a refined energy balance equation which explicitly enforces drop momentum conservation during the breakup process. The introduced modeling framework is entirely derived from conservation equations for mass, momentum, and energy and does not, as a consequence, introduce new modeling constants. The significance of the developed modeling advances to fuel injection processes is demonstrated using Large Eddy Simulation (LES) with a Lagrangian-Eulerian modeling approach.
This work studies the different types of behavior and inaccuracies that can occur when contact is not adequately accounted for in a dynamical system with freeplay, as the strength of the contact stiffness increases. The MATLAB® ode45 time integration solver, with the built-in Event Location capability, is first validated using past experimental data from a forced Duffing oscillator with freeplay. Next, numerical results utilizing event location are compared to results neglecting event location in order to highlight possible numerical errors and effects on multistable dynamical responses. Inaccuracies tend to occur in two different ways. First, neglecting event location can affect the boundaries between basins of attraction. Second, neglecting event location has little effect on the behaviors of the attractor solutions themselves besides merely resembling poorly converged solutions. Errors are less pronounced at the limits of soft or hard contact stiffness. Finally, this study shows the importance of accurately solving piecewise-smooth systems and the existing correlation between the strength of the contact force and possible numerical inaccuracies.
We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a rotating quadrupole field ion trap are presented. •Exact solutions for magneto-transport in variable electromagnetic fields are shown.
Boreal winter near-surface atmospheric circulations over the Hawaiian region are known to influence the state of the tropical Pacific and initiate the development of El Niño–Southern Oscillation (ENSO) events. Here we show that these same preceding near-surface circulations have an additional influence on the longitudinal position of the resultant ENSO-related sea surface temperatures (SSTs) as well, with warm (cold) events systematically shifted to the east (west) of the typical SST anomalies. In influencing this positioning, these atmospheric circulations in turn modify the near- and far-field climate responses to these SSTs such that during warm events, the typical ENSO-related responses east (west) of the dateline are generally enhanced (reduced); conversely, during cold events, the typical ENSO-related responses are generally reduced (enhanced). The fact that the extratropical atmospheric circulations in question influence the asymmetry of ENSO extremes with a 12 month lead time carries important implications for predicting the socioeconomic impacts of these events.
Dynamical systems subject to intermittent contact are often modeled with piecewise-smooth contact forces. However, the discontinuous nature of the contact can cause inaccuracies in numerical results or failure in numerical solvers. Representing the piecewise contact force with a continuous and smooth function can mitigate these problems, but not all continuous representations may be appropriate for this use. Here, five representations used by previous researchers (polynomial, rational polynomial, hyperbolic tangent, arctangent, and logarithm-arctangent functions) are studied to determine which ones most accurately capture nonlinear behaviors including super- and subharmonic resonances, multiple solutions, and chaos. The test case is a single-DOF forced Duffing oscillator with freeplay nonlinearity, solved using direct time integration. This work intends to expand on past studies by determining the limits of applicability for each representation and what numerical problems may occur.
Pitting corrosion of high-strength steel 10Ni8CrMoV under square wave polarization (SWP) in simulated deep-sea environment is investigated and the possible mechanism is proposed. The results show that potential perturbation generates periodic intensification effect on both anodic and cathodic processes by frequently breaking the electrode equilibrium state. The intensity of periodic intensification effect essentially depends on the concentration gradient of Fe{sup 2+} cations at the steel/solution interface which acts as the forced electrochemical oscillator. The concentration gradient and the resulting concentration polarization effect increase periodically with the increase in SWP potential range. The morphology observation of the pitting and electric charge calculation indicate that the periodic intensification effect can promote the initiation and growth of pits by enhancing the anodic dissolution even under cathodic protection, but it is ineffective below the hydrogen evolution potential. The decrease in either upper or lower potential can mitigate anodic dissolution. Through the statistical analysis of pitting size, it is found that the wide potential range tends to activate the metastable pitting formed under hydrostatic pressure, forming densely distributed pitting. Meanwhile, it is more favorable to the formation of fully grown pits with high size dispersion degree when the proportion of electric charge in the anodic process is higher.
As the number of operational Phasor Measurement Units (PMUs) is increasing, compression is becoming crucial for efficiently transferring and storing enormous amount of synchrophasor data continuously measured from a power system. Some utilities in the U.S. have already adopted a nonlinear compression technique, called Swinging Door Algorithm (SDA), assuming compressed data meets technical and regulatory requirements without resulting in any degradation of the measurements. This paper studies impacts of this compression algorithm on field measured and simulated PMU data, and presents results from spectral analyses of raw and decompressed measurements. The results show blind application of the SDA compression alters frequency content in the measurements and introduces false harmonics and aliasing. These can lead to false conclusions being drawn from the measurements about the power system condition.
This manuscript discusses the challenges in detecting and attributing recently observed trends in the Atlantic tropical cyclone (TC) and the epistemic uncertainty we face in assessing future risk. We use synthetic storms downscaled from five CMIP5 models by the Columbia HAZard model (CHAZ), and directly simulated storms from high-resolution climate models. We examine three aspects of recent TC activity: the upward trend and multi-decadal oscillation of the annual frequency, the increase in storm wind intensity, and the decrease in forward speed. Some data sets suggest that these trends and oscillation are forced while others suggest that they can be explained by natural variability. Projections under warming climate scenarios also show a wide range of possibilities, especially for the annual frequencies, which increase or decrease depending on the choice of moisture variable used in the CHAZ model and on the choice of climate model. The uncertainties in the annual frequency lead to epistemic uncertainties in TC risk assessment. Here, we investigate the potential for reduction of these epistemic uncertainties through a statistical practice, namely likelihood analysis. We find that historical observations are more consistent with the simulations with increasing frequency than those with decreasing frequency, but we are not able to rule out the latter. We argue that the most rational way to treat epistemic uncertainty is to consider all outcomes contained in the results. In the context of risk assessment, since the results contain possible outcomes in which TC risk is increasing, this view implies that the risk is increasing.
The emergence of collective order in matter is among the most fundamental and intriguing phenomena in physics. In recent years, the dynamical control and creation of novel ordered states of matter not accessible in thermodynamic equilibrium is receiving much attention. The theoretical concept of dynamical multiferroicity has been introduced to describe the emergence of magnetization due to time-dependent electric polarization in non-ferromagnetic materials. In simple terms, the coherent rotating motion of the ions in a crystal induces a magnetic moment along the axis of rotation. Here we provide experimental evidence of room-temperature magnetization in the archetypal paraelectric perovskite SrTiO 3 due to this mechanism. We resonantly drive the infrared-active soft phonon mode with an intense circularly polarized terahertz electric field and detect the time-resolved magneto-optical Kerr effect. A simple model, which includes two coupled nonlinear oscillators whose forces and couplings are derived with ab initio calculations using self-consistent phonon theory at a finite temperature, reproduces qualitatively our experimental observations. A quantitatively correct magnitude was obtained for the effect by also considering the phonon analogue of the reciprocal of the Einstein–de Haas effect, which is also called the Barnett effect, in which the total angular momentum from the phonon order is transferred to the electronic one. Our findings show a new path for the control of magnetism, for example, for ultrafast magnetic switches, by coherently controlling the lattice vibrations with light.