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A time-dependent compressible turbulent Navier-Stokes analysis is applied to the oscillating airfoil flow field problem. The turbulence model is based upon a turbulence energy equation. Results obtained for an airfoil oscillating in pitch are compared to data.
Recent advancements and the accumulation of high-resolution, long-term phasor measurement unit (PMU) data have provided detailed insights into inter-area oscillations in power grids. This study conducts a comprehensive statistical analysis of inter-area oscillations within the United States Eastern Interconnection from 2017 to 2023. Utilizing data captured by the advanced wide-area Frequency Monitoring Network (FNET/GridEye), this investigation examines the occurrence patterns, dominant frequencies, damping ratios, and excitation mechanisms of these oscillations. Our analysis sheds light on the evolving statistical behaviors of inter-area oscillations, offering updated and critical information for grid operators and planners. The insights gained from this study can be instrumental in enhancing the operational resilience of the power network and guiding strategic developments in grid infrastructure to accommodate future challenges. Additionally, the study discusses emerging challenges associated with the modernization of the power grid, including increased renewable penetration, dynamic load variability, and cyber-physical vulnerabilities that complicate oscillation monitoring and control.
An analysis of solar velocity data obtained at the Stanford Solar Observatory shows the existence of solar global oscillations in the range 45 to 105 microHz (160 to 370 minutes). These oscillations are interpreted as internal gravity modes of degree l = 1 and l = 2. A good estimate of the order of the modes has also been made. Previously announced in STAR as N84-11086
An analysis of solar velocity data obtained at the Stanford Solar Observatory has shown the existence of solar global oscillations. The oscillations are in the range 45 to 105 micro Hz (160 to 370 minutes) and are interpreted as internal gravity modes of degree l=1 and l=2.
Flames near the rich-flammability limit of hydrogen-air mixtures are studied using a detailed, time-dependent, one-dimensional Lagrangian model. Results from the numerical simulations indicate that a steady burning velocity is not obtained for very rich hydrogen-air mixtures. As the amount of hydrogen is increased, a damped oscillation is observed in the flame and burning velocities, and then, with further increase in the amount of hydrogen, an undamped oscillation with a complex set of frequencies is observed. Simulations with a simplified one-step irreversible chemical reaction do not show these oscillations, suggesting that chemical kinetics plays a strong role in inducing these oscillations. Further analysis shows that the oscillations are due to a competition for H atoms between chain branching and chain-terminating reactions. Simulations of spherically expanding flames suggest that stretch effects (due to curvature) will cause the oscillations to occur in less rich mixtures than that observed for planar flames. The implications of these oscillations on the rich-flammability limit as well as the role of chemical kinetics in creating a fundamental flammability limit is discussed.
Following the development of the well-known differential equations of the problem and their resolution for failure in tension, the bending (transverse) oscillations of an originally not quite straight bar hinged at both ends and subjected to a constant longitudinal force (shock load) are analyzed. To this end the course of the bar form is expanded in a sinusoidal series, after which the investigation is carried through separately for the fundamental oscillation and the (n-1)the higher oscillations. The analysis of the fundamental oscillation distinguishes three cases: shock load lower, equal to, or higher than the Eulerian load. The investigation leads to functions which are proportional to the maximum stresses in time and space due to the shock stresses in buckling.
Oscillatory signals from coherently excited phonons are regularly observed in ultrafast pump–probe experiments on condensed matter samples. Electron–phonon coupling implies that coherent phonons also modulate the electronic band structure. These oscillations can be probed with energy and momentum resolution using time- and angle-resolved photoemission spectroscopy (trARPES), which reveals the orbital dependence of the electron–phonon coupling for a specific phonon mode. However, a comprehensive analysis remains challenging when multiple coherent phonon modes couple to multiple electronic bands. Complex spectral line shapes due to strong correlations in quantum materials add to this challenge. In this work, we examine how the frequency domain representation of trARPES data facilitates a quantitative analysis of coherent oscillations of the electronic bands. Here, we investigate the frequency domain representation of the photoemission intensity and the first moment of the energy distribution curves. Both quantities provide complementary information and are able to distinguish oscillations of binding energy, linewidth, and intensity. We analyze a representative trARPES dataset of the transition metal dichalcogenide WTe 2 and construct composite spectra, which intuitively illustrate how much each electronic band is affected by a specific phonon mode. We also show how a linearly chirped probe pulse can generate extrinsic artifacts that are distinct from the intrinsic coherent phonon signal.
An analysis of stall-induced helicopter rotor blade torsional oscillations was carried out, the primary objectives being to predict the onset and severity of the oscillations and their relationship to aircraft and blade parameters. Blade flapping, flapwise bending, and torsional degrees of freedom were taken into account, with radial variation in aerodynamic loading determined from a previously developed dynamic stall model. Results of analyses were compared with data from flight tests of helicopters. Analyses were carried out while parametrically varying blade vibrational characteristics. It was found that the amplitudes of the higher harmonics of torsional oscillations can be significantly reduced by either reducing the torsional natural frequency or introducing viscous damping in the torsional degree of freedom. A preliminary investigation was conducted to determine the feasibility and practicality of alleviating the stall problem by means of boundary layer control. The results indicate that boundary layer control would be effective in reducing the higher harmonics of torsional oscillations due to stall and that its implementation would not require excessive power or suction rates.
The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and nonzero interblade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the perioidic boundary conditions. Approximate nonreflecting boundary conditons were coded for the inlet and exit boundary conditions. Sample unsteady solutions were performed for an oscillating cascade and compared to experimental data. Also, test cases were run for a flat plate cascade to compare with the unsteady, small-perturbation, subsonic analysis. The predictions for oscillating cascades with nonzero interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. The zero degree interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus nonreflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distribution for certain flow conditions.
The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and non-zero inter-blade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the periodic boundary conditions. Approximate nonreflecting boundary conditions have been coded for the inlet and exit boundary conditions. Sample unsteady solutions have been performed for an oscillating cascade and compared to experimental data. Also, test cases were fun for a flat plate cascade to compare with an unsteady, small-perturbation, subsonic analysis. The predictions for oscillating cascades with non-zero inter-blade phase angles are in good agreement with experimental data and small-perturbation theory. The zero degree inter-blade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus non-reflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distributions for certain flow conditions. This code is expected to be used as a tool for reviewing simpler models that do not include the full nonlinear aerodynamics or as a final check for designs against flutter in turbomachinery.
Flow-field parameter analysis of wind-induced oscillation of launch vehicles in launch position
Approximate analysis and integration of nonlinear motion equations for beam-plasma interaction
This paper presents a comparative analysis of interarea oscillations in the US Eastern and Western Interconnections using frequency disturbance data collected from the advanced wide-area Frequency Monitoring Network (FNET/GridEye), enabling us to investigate and compare the oscillation characteristics of both regions. The study analyzes the statistical data from the two interconnections, including total oscillation events, average dominant frequencies, damping ratios, and maximum amplitudes. We also explore the impact of seasonal and daily variations on oscillation occurrences and the influence of different grid topologies and operational practices. The results provide insights into both interconnections' stability and control characteristics, offering valuable information for power system operators to enhance grid stability and oscillation suppression measures.
The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and nonzero interblade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the periodic boundary conditions. Approximate nonreflecting boundary conditions were coded for the inlet and exit boundary conditions. Sample unsteady solutions were performed for an oscillating cascade and compared to experimental data. Also, test cases were run for a flat plate cascade to compare with the unsteady, small-perturbation, subsonic analyis. The predictions for oscillating cascades with nonzero interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. The zero degree interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus nonreflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distributions for certain flow conditions.
Postcoupled waveguide cavity Gunn effect microwave oscillator equivalent circuit analysis, using lumped constant elements
A two-dimensional oscillating flow analysis was conducted simulating the gas flow inside Stirling engine heat exchangers. Both laminar and turbulent oscillating pipe flow were investigated numerically for Re(max) = 1920 (Va = 80), 10,800 (Va = 272), 19,300 (Va = 272), and 60,800 (Va = 126). The results are compared with experimental results of previous investigators. Predictions of the flow regime are also checked by comparing velocity amplitudes and phase difference with those from laminar theory and quasi-steady profile. A high Reynolds number k-epsilon turbulence model was used for turbulent oscillating pipe flow. Finally, the performance of the k-epsilon model was evaluated to explore the applicability of quasi-steady turbulent models to unsteady oscillating flow analysis.
Many blunt-body entry vehicles have nonlinear dynamic stability characteristics that produce self-limiting oscillations in flight. Several different test techniques can be used to extract dynamic aerodynamic coefficients to predict this oscillatory behavior for planetary entry mission design and analysis. Most of these test techniques impose boundary conditions that alter the oscillatory behavior from that seen in flight. Three sets of test conditions, representing three commonly used test techniques, are presented to highlight these effects. Analytical solutions to the constant-coefficient planar equations-of-motion for each case are developed to show how the same blunt body behaves differently depending on the imposed test conditions. The energy equation is applied to further illustrate the governing dynamics. Then, the mean value theorem is applied to the energy rate equation to find the effective damping for an example blunt body with nonlinear, self-limiting dynamic characteristics. This approach is used to predict constant-energy oscillatory behavior and the equilibrium oscillation amplitudes for the various test conditions. These predictions are verified with planar simulations. The analysis presented provides an overview of dynamic stability test techniques and illustrates the effects of dynamic stability, static aerodynamics and test conditions on observed dynamic motions. It is proposed that these effects may be leveraged to develop new test techniques and refine test matrices in future tests to better define the nonlinear functional forms of blunt body dynamic stability curves.
The NASA Langley Research Center Flight Dynamics Branch has a long history of experimental testing of aircraft and spacecraft flight dynamics. One of the frequently used wind tunnel test methods is forced oscillation testing. This method involves a model mounted on a specialized dynamic test rig in a tunnel and oscillated about a body axis, typically at a fixed sinusoidal frequency and amplitude. This report provides the derivation of two commonly used data reduction methods and introduces one new method to extract the linear dynamic derivatives from forced oscillation wind tunnel data.