The Application of Green's Theorem to the Solution of Boundary-value Problems in Linearized Supersonic Wing Theory
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MATHEMATICS - BOUNDARY VALUES↗
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Pressure distribution and damping in steady roll at supersonic Mach numbers of flat swept-back wing with subsonic edges
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ROLLING MOMENTS - WINGS, SWEPTBACK↗
Experimental Pressure Distributions over Wing Tips at Mach Number 1.9 I : Wing Tip with Subsonic Leading Edge
An investigation was conducted at a Mach number of 1.91 to determine spanwise pressure distribution over a wing tip in a region influenced by a sharp subsonic leading edge swept back at 70 degrees. Except for pressure distribution on the top surface in the immediate vicinity of the subsonic leading edge, the maximum difference between linearized theory and experimental data was 2 1/2 percent (of free-stream dynamic pressure) for angles of attack up to 4 degrees and 7 percent for angles of attack up to 8 degrees. Pressures on the top surface nearest the subsonic edge indicated local expansions beyond values predicted by linearized theory.
FLOW, SUPERSONIC↗
Comparison Between Theory and Experiment for Wings at Supersonic Speeds
This paper presents a critical comparison made between experimental and theoretical results for the aerodynamic characteristics of wings at supersonic flight speeds. As a preliminary, a brief, nonmathematical review is given of the basic assumptions and general findings of supersonic wing theory in two and three dimensions. Published data from two-dimensional pressure-distribution tests are then used to illustrate the effects of fluid viscosity and to assess the accuracy of linear theory as compared with the more exact theories which are available in the two-dimensional case. Finally, an account is presented of an NACA study of the over-all force characteristics of three-dimensional wings at supersonic speed. In this study, the lift, pitching moment, and drag characteristics of several families of wings of varying plan form and section were measured in the wind tunnel and compared with values predicted by the three-dimensional linear theory. The regions of agreement and disagreement between experiment and theory are noted and discussed.
Vincenti, Walter G↗
Focused interplanetary transport of approximately 1 MeV solar energetic protons through self-generated Alfven waves
We present a model of the focused transport of approximately 1 MeV solar energetic protons through interplanetary Alfven waves that the protons themselves amplify or damp. It is based on the quasi-linear theory but with a phenomenological pitch angle diffusion coefficient in the 'resonance gap.' For initial Alfven wave distributions that give mean free paths greater than approximately 0.5 AU for approximately 1 MeV protons in the inner heliosphere, the model predicts greater than roughly an order of magnitude amplification (damping) in the outward (inward) propagating resonant Alfven waves at less than or approximately equal to o.3 AU heliocentric distance. As the strength of proton source is increased, the peak differential proton intensity at approximately 1 MeV at 1 AU increases to a maximum of approximately 250 particles (/(sq cm)(s)(sr)(MeV)) and then decreases slowly. It may be attenuated by a factor of 5 or more relative to the case without wave evolution, provided that the proton source is sufficiently intense that the resulting peak differential intensity of approximately 1 MeV protons at 1 AU exceeds approximately 200 particles (/(sq cm)(s)(sr)(MeV)). Therefore, in large solar proton events, (1) one may have to take into account self-amplified waves in studying solar particle propagation, (2) the number of accelerated protons escaping from a flare or interplanetary shock may have been underestimated in past studies by a significant factor, and (3) accelerated protons escaping from a traveling interplanetary shock at r less than or approximately equal to 0.3 AU should amplify the ambient hydromagnetic waves siginificantly to make the shock an efficient accelerator, even if initially the mean free path is greater than or approximately equal to 1 AU.
Ng, C. K.↗
Validity of the Temperature Reconstruction from Water Isotopes in Ice Cores
Well-documented present-day distributions of stable water isotopes (HDO and others) show the existence, in middle and high latitudes, of a linear relationship between the mean annual isotope content of precipitation (SD and 51"0) and the mean annual temperature at the precipitation site. Paleoclimatologists have used this relationship, which is particularly well obeyed over Greenland and Antarctica, to infer paleotemperatures from ice core data. There is, however, growing evidence that spatial and temporal isotope/ surface temperature slopes differ, thus complicating the use of stable water isotopes as paleothermometers. In this paper we review empirical estimates of temporal slopes in polar regions and relevant information that can be inferred from isotope models: simple, Rayleigh-type distillation models and (particularly over Greenland) general circulation models (GCMS) fitted with isotope tracer diagnostics. Empirical estimates of temporal slopes appear consistently lower than present-day spatial slopes and are dependent on the timescale considered. This difference is most probably due to changes in the evaporative origins of moisture, changes in the seasonality of the precipitation, changes in the strength of the inversion layer, or some combination of these changes. Isotope models have not yet been used to evaluate the relative influences of these different factors. The apparent disagreement in the temporal and spatial slopes clearly makes calibrating the isotope paleothermometer difficult. Nevertheless, the use of a (calibrated) isotope paleothermometer appears justified; empirical estimates and most (though not all) GCM results support the practice of interpreting ice core isotope records in terms of local temperature changes.
Jouzel, J.↗
Fan Noise Source Diagnostic Test: Vane Unsteady Pressure Results
To investigate the nature of fan outlet guide vane pressure fluctuations and their link to rotor-stator interaction noise, time histories of vane fluctuating pressures were digitally acquired as part of the Fan Noise Source Diagnostic Test. Vane unsteady pressures were measured at seven fan tip speeds for both a radial and a swept vane configuration. Using time-domain averaging and spectral analysis, the blade passing frequency (BPF) harmonic and broadband contents of the vane pressures were individually analyzed. Significant Sound Pressure Level (SPL) reductions were observed for the swept vane relative to the radial vane for the BPF harmonics of vane pressure, but vane broadband reductions due to sweep turned out to be much smaller especially on an average basis. Cross-correlation analysis was used to establish the level of spatial coherence of broadband pressures between different locations on the vane and integral length scales of pressure fluctuations were estimated from these correlations. Two main results of this work are: (1) the average broadband level on the vane (in dB) increases linearly with the fan tip speed for both the radial and swept vanes, and (2) the broadband pressure distribution on the vane is nearly homogeneous and its integral length scale is a monotonically decreasing function of fan tip speed.
Envia, Edmane↗
Turbulent Friction in the Boundary Layer of a Flat Plate in a Two-Dimensional Compressible Flow at High Speeds
In the present report an investigation is made on a flat plate in a two-dimensional compressible flow of the effect of compressibility and heating on the turbulent frictional drag coefficient in the boundary layer of an airfoil or wing radiator. The analysis is based on the Prandtl-Karman theory of the turbulent boundary later and the Stodola-Crocco, theorem on the linear relation between the total energy of the flow and its velocity. Formulas are obtained for the velocity distribution and the frictional drag law in a turbulent boundary later with the compressibility effect and heat transfer taken into account. It is found that with increase of compressibility and temperature at full retardation of the flow (the temperature when the velocity of the flow at a given point is reduced to zero in case of an adiabatic process in the gas) at a constant R (sub x), the frictional drag coefficient C (sub f) decreased, both of these factors acting in the same sense.
Frankl, F.↗
Flexible Models for Solar Sail Control
Solar sails employ a unique form of propulsion, gaining momentum from incident and reflected photons. However, the momentum transferred by an individual photon is extremely small. Consequently, a solar sail must have an extremely large surface area and also be extremely light. The flexibility of the sail then must be considered when designing or evaluating control laws. In this paper, solar sail flexibility and its influence on control effectiveness is considered using idealized two-dimensional models to represent physical phenomena rather than a specific design. Differential equations of motion are derived for a distributed parameter model of a flexible solar sail idealized as a rotating central hub with two opposing flexible booms. This idealization is appropriate for solar sail designs in which the vibrational modes of the sail and supporting booms move together allowing the sail mass to be distributed along the booms in the idealized model. A reduced analytical model of the flexible response is considered. Linear feedback torque control is applied at the central hub. Two translational disturbances and a torque disturbance also act at the central hub representing the equivalent effect of deflecting sail shape about a reference line. Transient simulations explore different control designs and their effectiveness for controlling orientation, for reducing flexible motion and for disturbance rejection. A second model also is developed as a two-dimensional "pathfinder" model to calculate the effect of solar sail shape on the resultant thrust, in-plane force and torque at the hub. The analysis is then extended to larger models using the finite element method. The finite element modeling approach is verified by comparing results from a two-dimensional finite element model with those from the analytical model. The utility of the finite element modeling approach for this application is then illustrated through examples based on a full finite element model.
Weaver Smith, Suzanne↗
Nonlinear Acoustic Response of an Aircraft Fuselage Sidewall Structure by a Reduced-Order Analysis
A reduced-order nonlinear analysis of a structurally complex aircraft fuselage sidewall panel is undertaken to explore issues associated with application of such analyses to practical structures. Of primary interest is the trade-off between computational efficiency and accuracy. An approach to modal basis selection is offered based upon the modal participation in the linear regime. The nonlinear static response to a uniform pressure loading and nonlinear random response to a uniformly distributed acoustic loading are computed. Comparisons of the static response with a nonlinear static solution in physical degrees-of-freedom demonstrate the efficacy of the approach taken for modal basis selection. Changes in the modal participation as a function of static and random loading levels suggest a means for improvement in the basis selection.
Przekop, Adam↗
On the local measurement of electric currents and magnetic fields using Thomson scattering in Weibel-unstable plasmas
Here, we demonstrate the capability of the Thomson Scattering (TS) diagnostic to measure locally the microscopic electron and ion currents in counter-streaming plasmas unstable to the Weibel or current-filamentation instability. Synthetic TS spectra are calculated with particle distribution functions obtained from particle-in-cell simulations and used to accurately reproduce the simulated currents. We show that this technique allows accurate local measurements of the magnetic field, thus opening the way for the complete experimental characterization of the growth rate, saturation, and nonlinear dynamics of electromagnetic instabilities in plasmas. We illustrate the application of this diagnostic to experimental TS data, which yields local measurements of the magnetic field in Weibel-unstable plasmas and indicates that the magnetic energy density reaches ~1% of the kinetic energy density of the flows, in agreement with previous numerical studies.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The zero-frequency ion ring instability
The electrostatic zero-frequency ion ring instability with wave vector perpendicular to a uniform magnetic field B is examined through linear and second-order theory as well as by computer simulation. In the simulation ions are taken as magnetized particles; the electrons are described as a massless fluid subject to E x B motion. Saturation of the instability is primarily due to broadening of the ion ring distribution. A second-order theory provides an approximate criterion for the saturation amplitude, as does a simple trapping argument. Thus, for the simulation presented here, both quasi-linear and trapping effects contribute to saturation.
Gary, S. P.↗
Novel Technique for Developing Linearized Convex System Models from Experimentally Derived Data
This paper presents a novel technique for generating a convex system model from an experimentally derived data set which features variance among repeated measurements. The convex system model developed as a test case characterizes the dynamic system losses of a vanadium redox flow battery as a function of the active power output and the battery state of charge. The technique hinges on a pre-cleaning via clustering procedure which precedes the formation of a planar convex hull comprised of triangular simplices. The clustering procedure efficiently reduces the experimental data set while mitigating variance among repeated measurements and removes outliers. Ultimately, the lower evelope of the planar convex hull serves as the desired convex system model. The proposed technique reduces systematic model error which is otherwise present when directly developing a planar convex hull model based on an unreduced data set.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Spectral Polarization Distribution Models (PDMs) for NASA CLARREO Pathfinder’s Inter-Calibration Applications
Solar radiation scattered by Earth surfaces of various scene types such as oceans, deserts, tree leaves etc and atmospheric molecules and particles is polarized and the amount of polarization depends on the surface composition and particle physical properties. This can be a source of measurement errors in satellite data if a non-polarimetric radiometric sensor is sensitive to the polarization state of light. To obtain highly accurate spectral solar radiation data from the Earth-atmosphere system for the space-borne inter-calibration studies as proposed in NASA's Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission and the CLARREO Pathfinder (CPF) mission, the spectral polarization state of the reflected solar light at the top of atmosphere (TOA) must be known with sufficient accuracy. The degree of polarization (DOP) and the angle of linear polarization (AOLP) of the light at the TOA as functions of incident and viewing geometry and scene type construct the Polarization Distribution Models (PDMs) for correction of polarization-induced error of satellite data. In this work, algorithms for modeling the spectral polarization state of reflected sunlight from various types of Earth, including oceans, deserts, vegetated land surfaces and these scene types with all kinds of clouds, are developed. By comparing the model results with the PARASOL satellite data, our numerical results demonstrate that the model can provide a reliable approach for making the spectral PDMs for wavelengths between 320 and 2300 nm for satellite inter-calibration applications as proposed in the CLARREO and the CLARREO CPF missions.
Sun, Wenbo↗
Linearized potential solution for an airfoil in nonuniform parallel streams
A small perturbation potential flow theory is applied to the problem of determining the chordwise pressure distribution, lift and pitching moment of a thin airfoil in the middle of five parallel streams. This theory is then extended to the case of an undisturbed stream having a given smooth velocity profile. Two typical examples are considered and the results obtained are compared with available solutions of Euler's equations. The agreement between these two results is not quite satisfactory. Possible reasons for the differences are indicated.
Prabhu, R. K.↗
A Generalized Copula-Polynomial Chaos Expansion for Probabilistic Power Flow Considering Nonlinear Correlations of PV Injections
This paper develops a generalized Copula-polynomial chaos expansion (PCE) framework for power system probabilistic power flow that can handle both linear and nonlinear correlations of uncertain power injections, such as wind and PVs. A data-driven Copula statistical model is used to capture the correlations of uncertain power injections. This allows us to resort to the Rosenblatt transformation to transform correlated variables into independent ones while preserving the dependence structure. This paves the way of leveraging the PCE for surrogate modeling and uncertainty quantification of power flow results, i.e., achieving the probabilistic distributions of power flows. Simulations carried out on the IEEE 57-bus system show that the proposed framework can get much more accurate results than other alternatives with different linear and nonlinear power injection correlations.
copula↗
Application of the locally self-consistent embedding approach to the Anderson model with non-uniform random distributions
Highlights: • Typical Medium Theory (TMT) for the Anderson Localization. • Locally Self-Consistent Multiple Scattering Method (LSMS) for Random Disordered Systems. • Linear Scaling Computational Method for Random Disordered Systems. We apply the recently developed embedding scheme for the locally self-consistent method to random disorder electrons systems. The method is based on the locally self-consistent multiple scattering theory and the typical medium theory. The locally self-consistent multiple scattering theory divides a system into many small designated local interaction zones. The subsystem within each local interaction zone is embedded in a self-consistent field from the typical medium theory. This approximation allows the study of random systems with large numbers of sites. We present results for the three dimensional Anderson model with different random disorder potential distributions. Using the typical density of states as an indicator of Anderson localization, we find that the method can capture the localization for commonly studied disorder potentials. These include the uniform distribution, the Gaussian distribution, and even the unbounded Cauchy distribution.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Resilient Operating Constraints for Power Distribution Systems under Setpoint Attacks
Integration and operation of distributed generation (DG) and energy storage (ES) in power distribution systems are enabled by communication networks and embedded sensor and control devices that increase the vulnerability of the systems to cyber-threats, broadening the attack surface and making adversary actions more unpredictable. This paper proposes a methodology that uses ellipsoidal approximations to quantify the potential damage caused by successful attacks that affect, directly or indirectly, the desired operation setpoints and may drive the power distribution operation to unsafe states by violating the limits of voltage or line flows. More specifically, a new methodology is introduced to find the optimal non-symmetric operating constraints that can be imposed to each DG and ES in order to guarantee that the power distribution system is resilient to any malicious setpoints. The proposed method takes as inputs the system topology, DG and ES capabilities, and load limits to solve a convex optimization problem formulated using linear matrix inequalities (LMIs) and the power flow equations. The proposed solution is agnostic to the attacker's action or load profile and it does not require any assumption about the location or means of the attack. The numerical results on a test distribution feeder with several DG and ES illustrate how the proposed resilient operating constraints guarantee the security of the power distribution system under setpoint attacks.
Giraldo, Jairo↗