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Static pitching moment coefficient determination from location of center of pressure in right circular cone, using Newtonian impact mechanics
Since high resolution numerical simulations of turbulent flows, or experiments at high Reynolds numbers, represent a substantial investment in resources, the estimation of the minimum resolution required for the study of a given property has been the subject of continued interest. Different properties require, in general, different resolutions, and the present paper is dedicated to the requirements for the measurement of the probability distribution functions of the velocity gradients and, in particular, of their low order moments. The deviation of these quantities from the values corresponding to a Gaussian distribution was one of the first indications of the presence of Reynolds number-dependent intermittency and has been the object of recent interest as numerical simulations have become able to explore the distribution of gradients in the low Reynolds number range, while new experiments have extended the range to increasingly high Reynolds numbers. We will use progressive filtering of the results of numerical simulations of isotropic turbulence as a model for the effect of a sensor of finite size. The numerical issues will be addressed first to ensure that the simulations are fully resolved from the point of view of the velocity gradients. This will also give us an estimate for the numerical resolution required for the different quantities.
Pressure distributions determined from high-speed wind-tunnel tests are presented for five NACA airfoil sections representative of both low-drag and conventional types. Section characteristics of lift, drag, and quarter-chord pitching moment are presented along with the measured pressure distributions for the NACA 65sub2-215 (a=0.5), 66sub2-215 (a=0.6), 0015, 23015, and 4415 airfoils for Mach numbers up to approximately 0.85. A critical study is made of the airfoil pressure distributions in an attempt to formulate a set of general criteria for defining the character of high speed flows over typical airfoil shapes. Comparisons are made of the relative characteristics of the low-drag and conventional airfoils investigated insofar as they would influence the high-speed performance and the high-speed stability and control characteristics of airplanes employing these wing sections.
An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.
The Multi-angle Imaging Spectroradiometer (MISR) Joint Aerosol (JOINT_AS) Level 3 product has provided a global, descriptive summary of MISR Level 2 aerosol optical depth (AOD) and aerosol type information for each month over 16+ years since March 2000. Using Version 1 of JOINT_AS, which is based on the operational (Version 22) MISR Level 2 aerosol product, this study analyzes, for the first time, characteristics of observed and simulated distributions of AOD for three broad classes of aerosols: spherical nonabsorbing, spherical absorbing, and nonspherical - near or downwind of their major source regions. The statistical moments (means, standard deviations, and skew-nesses) and distributions of AOD by components derived from the JOINT_AS are compared with results from two chemistry transport models (CTMs), the Goddard Chemistry Aerosol Radiation and Transport (GOCART) and SPectral RadIatioN-TrAnSport (SPRINTARS). Overall, the AOD distributions retrieved from MISR and modeled by GOCART and SPRINTARS agree with each other in a qualitative sense. Marginal distributions of AOD for each aerosol type in both MISR and models show considerable high positive skewness, which indicates the importance of including extreme AOD events when comparing satellite retrievals with models. The MISR JOINT_AS product will greatly facilitate comparisons between satellite observations and model simulations of aerosols by type.
The dynamical behavior of fluids affected by the asymmetric gravity gradient acceleration has been investigated. In particular, the effects of surface tension on partially filled rotating fluids applicable to a full-scale Gravity Probe-B Spacecraft dewar tank with and without baffles are studied. Results of slosh wave excitation along the liquid-vapor interface induced by gravity gradient acceleration indicate that the gravity gradient acceleration is equivalent to the combined effect of a twisting force and a torsional moment acting on the spacecraft. The results are clearly seen from one-up one-down and one-down one-up oscillations in the cross-section profiles of two bubbles in the vertical (r, z)-plane of the rotating dewar, and from the eccentric contour of the bubble rotating around the axis of the dewar in a horizontal (r, theta)-plane. As the viscous force, between liquid and solid interface, greatly contributes to the damping of slosh wave excitation, a rotating dewar with baffles provides more areas of liquid-solid interface than that of a rotating dewar without baffles. Results show that the damping effect provided by the baffles reduces the amplitude of slosh wave excitation and lowers the degree of asymmetry in liquid-vapor distribution. Fluctuations of angular momentum and fluid moment caused by the slosh wave excited by gravity gradient acceleration with and without baffle boards are also investigated. It is also shown that the damping effect provided by the baffles greatly reduces the amplitudes of angular momentum and fluid moment fluctuations.
The Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory (CGRO) has triggered on 1122 cosmic gamma-ray bursts between 1991 April 19 and 1994 September 19. These events constitute the Third BATSE (3B) burst catalog. This catalog includes the events previously reported in the 2B catalog, which covered the time interval 1991 April 19 to 1993 March 9. We present tables of the burst occurrence times, locations, peak fluxes, fluences, and durations. In general, results from previous BATSE catalogs are confirmed here with greater statistical significance. The angular distribution is consistent with isotropy. The mean galactic dipole and quadrupole moments are within 0.6 a and 0.3 a, respectively, of the values expected for isotropy. The intensity distribution is not consistent with a homogeneous distribution of burst sources, with V/V(sub max) = 0.33 +/- 0.01. The duration distribution (T(sub 90)) exhibits bimodality, with peaks at approx. 0.5 and approx. 30 s. There is no compelling evidence for burst repetition, but only weak limits can be placed on the repetition rate.
We present a study of the kinetic properties of the electron velocity distribution functions within magnetic clouds, since they are the dominant thermal component. The study is based on high time resolution data from the GSFC WIND/SWE electron spectrometer and the Berkeley 3DP electron plasma instruments. Recent studies on magnetic clouds have shown observational evidence of anti-correlation between the total electron density and electron temperature, which suggest a polytrope law P(sub e) = alpha(Nu(sub e) (sup gamma)) for electrons with the constant gamma approximates 0.5 < 1. This anti-correlation and small polytropic gamma-values is interpreted in the context of the presence of highly non-Maxwellian electron distributions (i.e. non-thermal) within magnetic clouds. These works suggested that the non-thermal electrons can contribute as much as 50% of the total electron pressure within magnetic clouds. We have revisited some of the magnetic cloud events previously studied and attempted to quantify the nature of the non-thermal electrons by modeling the electron velocity distribution function using a kappa distribution function to characterize the kinetic non-thermal effects. If non-thermal tail effects are the source for the anti-correlation between the moment electron temperature and density and if the kappa distribution is a reasonable representative model of non-thermal effects, then the electron velocity distribution within magnetic clouds should show indication for small K-values when gamma < 1.
Higher-order closure (HOC) models have been proposed for parameterization of the turbulent planetary boundary layer (PBL). HOC models must include closures for higher-order moments (e.g., fourth moments in third-order closure models), for pressure terms, and for dissipation terms. Mass-flux closure (MFC) models have been proposed for parameterization of cumulus convection and, more recently, the convective PBL. MFC models include closures for lateral mass exchanges and for pressure terms (which are usually ignored). The authors developed a new kind of model that combines HOC and MFC, which they hope will be useful for the parameterization of both the PBL and cumulus convection, in a unified framework. Such a model is particularly well suited to regimes in which the PBL turbulence and the cumulus convection are not well separated, for example, the broken stratocumulus and shallow cumulus regimes. The model makes use of an assumed joint probability distribution for the variables of interest, and the equations typically used in HOC models can be derived by integrating over the distribution. Accordingly, the model is called Assumed-Distribution Higher-Order Closure (ADHOC). The prognostic variables of ADHOC are the mean state, the second and third moments of the vertical velocity, and the vertical fluxes of other quantities of interest. All of the parameters of the distribution can be determined from the predicted moments, thereafter the joint distribution is effectively known, and so any and all moments can be constructed as needed. In this way, the usual closure problem of "higher moments" is avoided. The pressure-term parameterizations previously developed for HOC models are used to predict the convective fluxes and the moments of the vertical velocity. In companion papers, parameterizations of lateral mass exchanges and subplume-scale fluxes are presented, and then ADHOC is applied to several observationally based tropical, subtropical, and dry convective boundary layers.
Results of recent measurements of the distribution function of wind shear and the associated third and fourth standardized moments. Emphasis is placed on the vertical variation of the longitudinal component of turbulence, i.e., the component of turbulence along the mean wind vector. The data source consists of 11 sets of longitudinal turbulent velocity fluctuation time histories digitized at 0.2-sec intervals with approximately 18,000 data points per history.
The estimation of rain drop size distribution (DSD) parameters from polarimetric radar observations is accomplished by first establishing a relationship between differential reflectivity (Z(sub dr)) and the central tendency of the rain DSD such as the median volume diameter (D0). Since Z(sub dr) does not provide a direct measurement of DSD central tendency, the relationship is typically derived empirically from rain drop and radar scattering models (e.g., D0 = F[Z (sub dr)] ). Past studies have explored the general sensitivity of these models to temperature, radar wavelength, the drop shape vs. size relation, and DSD variability. Much progress has been made in recent years in measuring the drop shape and DSD variability using surface-based disdrometers, such as the 2D Video disdrometer (2DVD), and documenting their impact on polarimetric radar techniques. In addition to measuring drop shape, another advantage of the 2DVD over earlier impact type disdrometers is its ability to resolve drop diameters in excess of 5 mm. Despite this improvement, the sampling limitations of a disdrometer, including the 2DVD, make it very difficult to adequately measure the maximum drop diameter (D(sub max)) present in a typical radar resolution volume. As a result, D(sub max) must still be assumed in the drop and radar models from which D0 = F[Z(sub dr)] is derived. Since scattering resonance at C-band wavelengths begins to occur in drop diameters larger than about 5 mm, modeled C-band radar parameters, particularly Z(sub dr), can be sensitive to D(sub max) assumptions. In past C-band radar studies, a variety of D(sub max) assumptions have been made, including the actual disdrometer estimate of D(sub max) during a typical sampling period (e.g., 1-3 minutes), D(sub max) = C (where C is constant at values from 5 to 8 mm), and D(sub max) = M*D0 (where the constant multiple, M, is fixed at values ranging from 2.5 to 3.5). The overall objective of this NASA Global Precipitation Measurement Mission (GPM/PMM Science Team)-funded study is to document the sensitivity of DSD measurements, including estimates of D0, from C-band Z(sub dr) and reflectivity to this range of D(sub max) assumptions. For this study, GPM Ground Validation 2DVD's were operated under the scanning domain of the UAHuntsville ARMOR C-band dual-polarimetric radar. Approximately 7500 minutes of DSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSD's were then used as input to a T-matrix model for computation of polarimetric radar moments at C-band. All necessary model parameterizations, such as temperature, drop shape, and drop fall mode, were fixed at typically accepted values while the D(sub max) assumption was allowed to vary in sensitivity tests. By hypothesizing a DSD model with D(sub max) (fit) from which the empirical fit to D0 = F[Z(sub dr)] was derived via non-linear least squares regression and a separate reference DSD model with D(sub max) (truth), bias and standard error in D0 retrievals were estimated in the presence of Z(sub dr) measurement error and hypothesized mismatch in D(sub max) assumptions. Although the normalized standard error for D0 = F[Z(sub dr)r] can increase slightly (as much as from 11% to 16% for all 7500 DSDs) when the D(sub max) (fit) does not match D(sub max) (truth), the primary impact of uncertainty in D(sub max) is a potential increase in normalized bias error in D0 (from 0% to as much as 10% over all 7500 DSDs, depending on the extent of the mismatch between D(sub max) (fit) and D(sub max) (truth)). For DSDs characterized by large Z(sub dr) (Z(sub dr) > 1.5 to 2.0 dB), the normalized bias error for D0 estimation at C-band is sometimes unacceptably large (> 10%), again depending on the extent of the hypothesized D(sub max) mismatch. Modeled errors in D0 retrievals from Z(sub dr) at C-band are demonstrated in detail and comparedo similar modeled retrieval errors at S-band and X-band where the sensitivity to D(sub max) is expected to be less. The impact of D(sub max) assumptions to the retrieval of other DSD parameters such as Nw, the liquid water content normalized intercept parameter, are also explored. Likely implications for DSD retrievals using C-band polarimetric radar for GPM are assessed by considering current community knowledge regarding D(sub max) and quantifying the statistical distribution of Z(sub dr) from ARMOR over a large variety of meteorological conditions. Based on these results and the prevalence of C-band polarimetric radars worldwide, a call for more emphasis on constraining our observational estimate of D(sub max) within a typical radar resolution volume is made
The mathematical formulation associated with the problem of stability of motion of a satellite consisting of a main rigid body and three (or less) pairs of flexible rods is presented. The rods are capable of flexure in two orthogonal directions. Whereas the rotational motion of the body is described by generalized coordinates depending on time alone, the elastic displacements of the rods depend both on spatial position and time. Assuming no external torques, there exist motion integrals in the form of momentum integrals. These integrals can be regarded as constraint equations relating the system velocities, and used to reduce the number of variables describing the motion. The stability analysis has been carried out by means of an extension of the Liapunov direct method. Since the elastic vibrations result in energy dissipation, it is shown that the equilibrium position is asymptotically stable if the Hamiltonian is positive definite and unstable if it can take negative values in the neighborhood of the equilibrium. Determining the sign definiteness of the Hamiltonian is complicated by the fact that it contains spatial derivatives of the elastic displacements. Two methods are presented to cope with this problem. The first, the standard modal analysis in conjunction with series truncation, develops criteria in terms of infinite series associated with the natural modes and frequencies of the elastic rods. The second, the method of integral coordinates, yields closed-form stability criteria involving the system parameters, such as the body moments of inertia, the length and mass distribution of the rods, the lowest natural frequencies of the rods, and the satellite spin velocity.
A simulation technique is described and utilized to generate superposed coherent and chaotic (thermal) radiation of arbitrary spectral shape. The statistical properties of a simulated radiation field with a Lorentzian spectral density are investigated with a photoelectron counting experiment. The experimental photocount distribution and normalized mth-order factorial moments are compared to theory and verify that the simulated radiation field, an appropriately modulated laser beam, has the expected statistical properties. The concept described indicates that one may, in principle, generate a thermal source of comparable intensity to that of a laser, arbitrary spectral shape, and bandwidth.
Theoretical foundations for understanding the problem of the termination of the solar wind are reexamined in the light of most recent findings concerning the states of the solar wind and the local interstellar medium. The investigation suggests that a simple extention of Parker's (1961) analytical model provides a useful approximate description of the combined solar wind, interstellar wind plasma flowfield under conditions presently thought to occur. A linear perturbation solution exhibiting both the effects of photoionization and charge exchange is obtained for the supersonic solar wind. A numerical algorithm is described for computing moments of the non-equilibrium hydrogen distribution function and associated source terms for the MHD equations. Computed using the algorithm in conjunction with the extended Parker solution to approximate the plasma flowfield, profiles of hydrogen number density are given in the solar wind along the upstream and downstream axes of flow with respect to the direction of the interstellar wind. Predictions of solar Lyman-alpha backscatter intensities to be observed at 1 a.u. have been computed, in turn, from a set of such hydrogen number density profiles varied over assumed conditions of the interstellar wind.
The paper considers a rigid pointed body of revolution in a steady uniform subsonic flow. The body performs harmonic small-amplitude pitching oscillations around its zero angle of attack position. The body is assumed to be smooth and sufficiently slender so that the small perturbation concept can be applied. The basis of the method used, following Revell (1960), is the relation of a body-fixed perturbation potential to the general velocity potential. Normal force distributions as well as total force and moment coefficients are calculated for parabolic spindles and the numerical results show good agreement between Revell's second-order slender body theory and the present theory for the static stability derivatives of the parabolic spindles.
An engineering method for predicting the longitudinal aerodynamic characteristics of wing-flap configurations with upper surface blowing (USB) was developed. Potential flow models were incorporated into the prediction method: a wing and flap lifting surface model and a jet wake model. The wing-flap model used a vortex-lattice to represent the wing and flaps. The wing had an arbitrary planform and camber and twist, and the flap system was made up of a Coanda flap and other flap segments of arbitrary size. The jet wake model consisted of a series of closely spaced rectangular vortex rings. The wake was positioned such that it was tangent to the upper surface of the wing and flap between the exhaust nozzle and the flap trailing edge. It was specified such that the mass, momentum, and spreading rates were similar to actual USB jet wakes. Comparisons of measured and predicted pressure distributions, span load distributions, and total lift and pitching-moment coefficients on swept and unswept USB configurations are included. A wide range of thrust coefficients and flap deflection angles were considered at angles of attack up to the onset of stall.
An investigation has been carried out to develop an engineering method for predicting the longitudinal aerodynamic characteristics of wing-flap configurations with upper surface blown (USB) high lift devices. Potential flow models of the lifting surfaces and the jet wakes are combined to calculate the induced interference of the engine wakes on the wing and flaps. The wing may have an arbitrary planform with camber and twist and multiple trailing edge flaps. The jet wake model has a rectangular cross section over its entire length and it is positioned such that the wake is tangent to the upper surfaces of the wing and flaps. Comparisons of measured and predicted pressure distributions, spanload distributions, and total lift and pitching-moment coefficients on swept and unswept USB configurations are presented for a wide range of thrust coefficients and flap deflection angles.
Coupling calculations of differential, integral, and momentum transfer cross sections for pure elastic scattering and rotational excitation of CO by electron impact are reported. The calculations are based on a static charge distribution that has correct dipole and quadrupole moments, has cusps at the nuclei, and is augmented by an SCF treatment of charge polarization and a local approximation for exchange. The rotationally summed cross sections, with no adjustable parameters in the scattering calculation, are in reasonably good agreement with the experimental cross sections but are somewhat larger at small scattering angles.