Load distributions due to steady roll and pitch for thin wings at supersonic speeds
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THEORIES - FLOW SUPERSONIC↗
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On the solution of conical shells of linearly varying thickness subjected to lateral normal loads.
Asymptotic and particular solutions of conical shells subjected to lateral normal loads, discussing membrane forces, bending effects and boundary conditions for moments and shearing force
SHEARING STRESS↗
Load distributions on slender delta wings having vortex flow
Results obtained through application of potential-flow theory based on a suction flow analogy for incompressible flow are compared to attached-flow theory and to experimental data acquired for sharp-edged delta wings. The error incurred in predicting structural loads on the basis of attached-flow theory is investigated. Force and moment coefficients and load distributions are used in the comparisons. The root bending moment can be estimated by assuming vortex lift concentrated at the wing leading edge. While this may entail some error at large angles of attack (owing to inboard movement of the center of vortex lift), it may furnish an upper bound in evaluating results based on other theories.
Kuhlman, J.↗
Deriving cloud droplet number concentration from surface-based remote sensors with an emphasis on lidar measurements
Abstract. Given the importance of constraining cloud droplet number concentrations (Nd) in low-level clouds, we explore two methods for retrieving Nd from surface-based remote sensing that emphasize the information content in lidar measurements. Because Nd is the zeroth moment of the droplet size distribution (DSD), and all remote sensing approaches respond to DSD moments that are at least 2 orders of magnitude greater than the zeroth moment, deriving Nd from remote sensing measurements has significant uncertainty. At minimum, such algorithms require the extrapolation of information from two other measurements that respond to different moments of the DSD. Lidar, for instance, is sensitive to the second moment (cross-sectional area) of the DSD, while other measures from microwave sensors respond to higher-order moments. We develop methods using a simple lidar forward model that demonstrates that the depth to the maximum in lidar-attenuated backscatter (Rmax) is strongly sensitive to Nd when some measure of the liquid water content vertical profile is given or assumed. Knowledge of Rmax to within 5 m can constrain Nd to within several tens of percent. However, operational lidar networks provide vertical resolutions of > 15 m, making a direct calculation of Nd from Rmax very uncertain. Therefore, we develop a Bayesian optimal estimation algorithm that brings additional information to the inversion such as lidar-derived extinction and radar reflectivity near the cloud top. This statistical approach provides reasonable characterizations of Nd and effective radius (re) to within approximately a factor of 2 and 30 %, respectively. By comparing surface-derived cloud properties with MODIS satellite and aircraft data collected during the MARCUS and CAPRICORN II campaigns, we demonstrate the utility of the methodology.
54 ENVIRONMENTAL SCIENCES↗
A Triple-Moment Representation of Ice in the Predicted Particle Properties (P3) Microphysics Scheme
In the original Predicted Particle Properties (P3) bulk microphysics scheme, all ice-phase hydrometeors are represented by one or more “free” ice categories, where the physical properties evolve smoothly through changes to the four prognostic variables (per category), and with a two-moment representation of the particle size distribution. As such, the spectral dispersion cannot evolve independently, which thus results in limitations in representation of ice—in particular, hail—due to necessary constraints in the scheme to prevent excessive gravitational size sorting. To overcome this, P3 has been modified to include a three-moment representation of the size distribution of each ice category through the addition of a fifth prognostic variable, the sixth moment of the size distribution. The details of the three-moment ice parameterization in P3 are provided. The behavior of the modified scheme, with the single-ice-category configuration, is illustrated through simulations in a simple 1D kinematic model framework as well as with near large-eddy-resolving (250-m grid spacing) 3D simulations of a hail-producing supercell. It is shown that the three-moment ice configuration controls size sorting in a physically based way and leads to an improved capacity to simulate large, heavily rimed ice (hail), including mean and maximum sizes and reflectivity, and thus an overall improvement in the representation of ice-phase particles in the P3 scheme.
54 ENVIRONMENTAL SCIENCES↗
String-based axial and helicity-flip GPDs: A comparison to lattice QCD
We construct an analytic, string-based representation of the nucleon’s axial and helicity-flip conformal moments of generalized parton distributions (GPDs) that holds for skewness and for both the quark and gluon channels. The starting point is the Mellin-Barnes resummation of the conformal partial-wave expansion, where the moments are parametrized by open- (Reggeon) and closed-string (Pomeron) trajectories with slopes determined by experimental form factors and meson/glueball spectroscopy. The forward limits are fixed by the empirical unpolarized and polarized parton distributions. Polynomiality, crossing symmetry, and support are satisfied by construction. After next-to-leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi/Efremov-Radyushkin-Brodsky-Lepage evolution to μ = 2 GeV our analytic framework (i) reproduces some of the currently available lattice moments of E and H˜ in the nonsinglet sector, (ii) predicts sea-quark and gluon polarized moments that will be testable by forthcoming simulations and experiments at Jefferson Lab and the future Electron-Ion Collider, and (iii) yields axial and helicity-flip GPDs in x-space in reasonable agreement with lattice QCD.
Gauge-gravity dualities↗
2-SPEED, a single-gimbal control moment gyro attitude control system.
In 2-SPEED (Two Scissored Pair Ensemble, Explicit Distribution) four single-gimbal control moment gyros (SGCMGs) configured into two scissored pairs are combined with an explicit distribution of angular momentum between pairs to produce a system relatively insensitive to the singularity problems which have plagued other SGCMG concepts. In this system, the singularity surfaces in momentum space degenerate to discrete curves. Further, the system permits a smooth passage through these remaining singularities with, at worst, a temporary delay while momentum redistribution takes place. Finally, CMG-out operation is possible within the full volume of the reduced momentum envelope.
Crenshaw, J. W.↗
The Effect of Moment of Area Rule Modifications on the Drag, Lift and Pitching Moment Characteristics of an Unswept Aspect Ratio 6 Wing and Body Combination
An experimental investigation was conducted to determine the effect of moment-of-area-rule modifications on the drag, lift, and pitching-moment characteristics of a wing-body combination with a relatively high aspect-ratio unswept wing. The basic configuration consisted of an aspect-ratio-6 wing with a sharp leading edge and a thickness ratio of 0.06 mounted on a cut-off Sears-Haack body. The model with full moment-of-area-rule modifications had four contoured pods mounted on the wing and indentations in the body to improve the longitudinal distributions of area and moments of area. Also investigated were modifications employing pods and indentations that were only half the size of the full modifications and modifications with partial body indentations. The models were tested at angles of attack from -2 deg to +12 deg at Mach numbers from 0.6 to 1.4. In general, the moment-of-area-rule modifications had a large effect on the drag characteristics of the models but only a small effect on their lift and pitching-moment characteristics. The modifications provided substantial reductions in the zero-lift drag at transonic and low supersonic speeds, but at subsonic speeds the drag was increased. Near Mach number 1.0, the model with full modification provided the greatest reduction in drag, but at the highest test Mach numbers the half modification gave the largest drag reduction. In general, the percent reductions of zero- lift drag obtained with the aspect-ratio-6 wing were as great or greater than those previously obtained with aspect-ratio-3 wings. The effect of the modifications on the drag due to lift was small except at Mach num- bers below 0.9 where the modified models had higher drag-rise factors. Above Mach number 0.9, the modified models had higher lift-drag ratios than the basic model. The modified models also had higher lift curve slopes and generally were slightly more stable than the basic configuration.
Dickey, Robert R.↗
Cosmological parameters and evolution of the galaxy luminosity function
The relationship between the observed distribution of discrete sources of a flux limited sample, the luminosity function of these sources, and the cosmological model is discussed. It is stressed that some assumptions about the form and evolution of the luminosity function must be made in order to determine the cosmological parameters from the observed distribution of sources. Presented is a method to test the validity of these assumptions using the observations. It is shown how, using higher moments of the observed distribution, one can determine, independently of the cosmological model, all parameters of the luminosity function except those describing evolution of the density and the luminosity of the luminosity function. These methods are applied to the sample of approximately 1000 galaxies recently used by Loh and Spillar to determine a value of the cosmological density parameter Omega approx = 1. It is shown that the assumptions made by Loh and Spillar about the luminosity function are inconsistent with the data, and that a self-consistent treatment of the data indicates a lower value of Omega approx = 0.2 and a flatter luminosity function. It should be noted, however, that incompleteness in the sample could cause a flattening of the luminosity function and lower the calculated value of Omega and that uncertainty in the values of these parameters due to random fluctuations is large.
Caditz, David↗
Cosmological parameters and evolution of the galaxy luminosity function
The relationship between the observed distribution of discrete sources of a flux limited sample, the luminosity function of these sources, and the cosmological model is discussed. It is stressed that some assumptions about the form and evolution of the luminosity function must be made in order to determine the cosmological parameters from the observed distribution of sources. Presented is a method to test the validity of these assumptions using the observations. It is shown how, using higher moments of the observed distribution, one can determine, independently of the cosmological model, all parameters of the luminosity function except those describing evolution of the density and the luminosity of the luminosity function. These methods are applied to the sample of approximately 1000 galaxies recently used by Loh and Spillar to determine a value of the cosmological density parameter Omega approx = 1. It is shown that the assumptions made by Loh and Spillar about the luminosity function are inconsistent with the data, and that a self-consistent treatment of the data indicates a lower value of Omega approx = 0.2 and a flatter luminosity function. It should be noted, however, that incompleteness in the sample could cause a flattening of the luminosity function and lower the calculated value of Omega and that uncertainty in the values of these parameters due to random fluctuations is large.
Caditz, David↗
Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma
A general method of solving the drift kinetic equation is developed for an axisymmetric magnetic field. Expanding a distribution function in general moments, a set of ordinary differential equations is obtained. Successively expanding the moments and magnetic-field involved quantities in Fourier series, a set of linear algebraic equations is obtained. The set of full (Maxwellian and non-Maxwellian) moment equations is solved to express the first-order density, temperature, and flow velocity in terms of radial gradients of the zeroth-order pressure and temperature. Closure relations that connect parallel heat flux density and viscosity to the radial gradients and parallel gradients of temperature and flow velocity are also obtained by solving the non-Maxwellian moment equations. The closure relations combined with the linearized fluid equations reproduce the same solution obtained directly from the full moment equations. Furthermore, the method can be generalized to derive closures and transport for an electron-ion plasma and a multi-ion plasma in a general magnetic field.
neoclassical transport↗
Orbital angular momentum at small $x$ revisited
We revisit the problem of the small Bjorken-x asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised small-x helicity evolution derived recently in [1]. We relate the quark and gluon OAM distributions at small x to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the OAM distributions, we derive novel small-x evolution equations for the impact-parameter moments of the polarized dipole amplitudes in the double-logarithmic approximation (summing powers of α s ln 2 (1/x) with α s the strong coupling constant). We solve these evolution equations numerically and extract the leading large-N c , small-x asymptotics of the quark and gluon OAM distributions, which we determine to be ${L}_{q+\overline{q}}\left(x,{Q}^2\right)\sim {L}_G\left(x,{Q}^2\right)\sim \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {\left(\frac{1}{2}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2_π}}}$in agreement with [2] within the precision of our numerical evaluation. (Here N c is the number of quark colors.) We also investigate the ratios of the quark and gluon OAM distributions to their helicity distribution counterparts in the small-x region.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Neutrino fast flavor oscillations with moments: Linear stability analysis and application to neutron star mergers
Providing an accurate modeling of neutrino physics in dense astrophysical environments such as binary neutron star mergers presents a challenge for hydrodynamic simulations. Nevertheless, understanding how flavor transformation can occur and affect the dynamics, the mass ejection, and the nucleosynthesis will need to be achieved in the future. Computationally expensive, large-scale simulations frequently evolve the first classical angular moments of the neutrino distributions. By promoting these quantities to matrices in flavor space, we develop a linear stability analysis of fast flavor oscillations using only the first two “quantum” moments, which notably requires generalizing the classical closure relations that appropriately truncate the hierarchy of moment equations in order to treat quantum flavor coherence. After showing the efficiency of this method on a well-understood test situation, we perform a systematic search of the occurrence of fast flavor instabilities in a neutron star merger simulation. Here, we discuss the successes and shortcomings of moment linear stability analysis, as this framework provides a time-efficient way to design and study better closure prescriptions in the future.
79 ASTRONOMY AND ASTROPHYSICS↗
Integrating nonlinear aerodynamic and structural analysis for a complete fighter configuration
The coupling of a nonlinear aerodynamics program with a structural analysis program to include the effects of static aeroelasticity in early preliminary design studies is described. A nonlinear, full potential aerodynamics method with capability to model geometric details of a complete aircraft in supersonic flow is used. The deflections of the lifting surfaces are calculated using an equivalent plate structural representation which can readily accommodate the changes in stiffness and geometric properties required during the preliminary design process. An iterative solution procedure is used to obtain consistent aerodynamic loads and structural deflections at the specified flight conditions. The volume of data transmitted between programs is minimized. The procedure is applied to a complete aircraft and the numerical results illustrate the aeroelastic effects on pressure distribution as well as total forces and moments. During this design study, the thickness distribution of the wing cover skins was initially sized based on rigid loads and subsequently resized under aeroelastic loads. Comparisons are made between these nonlinear aeroelastic results and results obtained from linear aerodynamic methods applied to a rigid shape during conceptual design studies.
Tatum, Kenneth E.↗
Kurtosis, skewness, and non-Gaussian cosmological density perturbations
Cosmological topological defects as well as some nonstandard inflation models can give rise to non-Gaussian density perturbations. Skewness and kurtosis are the third and fourth moments that measure the deviation of a distribution from a Gaussian. Measurement of these moments for the cosmological density field and for the microwave background temperature anisotropy can provide a test of the Gaussian nature of the primordial fluctuation spectrum. In the case of the density field, the importance of measuring the kurtosis is stressed since it will be preserved through the weakly nonlinear gravitational evolution epoch. Current constraints on skewness and kurtosis of primeval perturbations are obtained from the observed density contrast on small scales and from recent COBE observations of temperature anisotropies on large scales. It is also shown how, in principle, future microwave anisotropy experiments might be able to reveal the initial skewness and kurtosis. It is shown that present data argue that if the initial spectrum is adiabatic, then it is probably Gaussian, but non-Gaussian isocurvature fluctuations are still allowed, and these are what topological defects provide.
Luo, Xiaochun↗
Prediction of nacelle aerodynamic interference effects at low supersonic Mach numbers
The accuracy of analytical predictions of nacelle aerodynamic interference effects at low supersonic speeds are studied by means of test versus theory comparisons. Comparisons shown include: (1) isolated wing body lift, drag, and pitching moments; (2) isolated nacelle drag and pressure distributions; (3) nacelle interference shock wave patterns and pressure distributions on the wing lower surface; (4) nacelle interference effects on wing body lift, drag, and pitching moments; and (5) total installed nacelle interference effects on lift, drag, and pitching moment. The comparisons also illustrate effects of nacelle location, nacelle spillage, angle of attack, and Mach numbers on the aerodynamic interference. The initial results seem to indicate that the methods can satisfactorily predict lift, drag, pitching moment, and pressure distributions of installed engine nacelles at low supersonic Mach numbers with mass flow ratios from 0.7 to 1.0 for configurations typical of efficient supersonic cruise airplanes.
Kulfan, R. M.↗
The interiors of Mars and Venus
Mass, radius, inertia moment, seismological data, and internal temperature distribution of Mars and Venus
Venus↗
Propagation Pattern for Moment Representation of the Lattice Boltzmann Method
A propagation pattern for the moment representation of the regularized lattice Boltzmann method (LBM) in three dimensions is presented. Using effectively lossless compression, the simulation state is stored as a set of moments of the lattice Boltzmann distribution function, instead of the distribution function itself. An efficient cache-aware propagation pattern for this moment representation has the effect of substantially reducing both the storage and memory bandwidth required for LBM simulations. This article extends recent work with the moment representation by expanding the performance analysis on central processing unit (CPU) architectures, considering how boundary conditions are implemented, and demonstrating the effectiveness of the moment representation on a graphics processing unit (GPU) architecture.
42 ENGINEERING↗