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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
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NASA NTRS2007

Derivation of Formulations 1 and 1A of Farassat

Formulations 1 and 1A are the solutions of the Ffowcs Williams-Hawkings (FW-H) equation with surface sources only when the surface moves at subsonic speed. Both formulations have been successfully used for helicopter rotor and propeller noise prediction for many years although we now recommend using Formulation 1A for this purpose. Formulation 1 has an observer time derivative that is taken numerically, and thus, increasing execution time on a computer and reducing the accuracy of the results. After some discussion of the Green's function of the wave equation, we derive Formulation 1 which is the basis of deriving Formulation 1A. We will then show how to take this observer time derivative analytically to get Formulation 1A. We give here the most detailed derivation of these formulations. Once you see the whole derivation, you will ask yourself why you did not do it yourself!

Farassat, F.↗
NASA NTRS2006

Estimation of Stability and Control Derivatives of an F-15

A technique for real-time estimation of stability and control derivatives (derivatives of moment coefficients with respect to control-surface deflection angles) was used to support a flight demonstration of a concept of an indirect-adaptive intelligent flight control system (IFCS). Traditionally, parameter identification, including estimation of stability and control derivatives, is done post-flight. However, for the indirect-adaptive IFCS concept, parameter identification is required during flight so that the system can modify control laws for a damaged aircraft. The flight demonstration was carried out on a highly modified F-15 airplane (see Figure 1). The main objective was to estimate the stability and control derivatives of the airplane in nearly real time. A secondary goal was to develop a system to automatically assess the quality of the results, so as to be able to tell a learning neural network which data to use. Parameter estimation was performed by use of Fourier-transform regression (FTR) a technique developed at NASA Langley Research Center. FTR is an equation- error technique that operates in the frequency domain. Data are put into the frequency domain by use of a recursive Fourier transform for a discrete frequency set. This calculation simplifies many subsequent calculations, removes biases, and automatically filters out data beyond the chosen frequency range. FTR as applied here was tailored to work with pilot inputs, which produce correlated surface positions that prevent accurate parameter estimates, by replacing half the derivatives with predicted values. FTR was also set up to work only on a recent window of data, to accommodate changes in flight condition. A system of confidence measures was developed to identify quality-parameter estimates that a learning neural network could use. This system judged the estimates primarily on the basis of their estimated variances and of the level of aircraft response. The resulting FTR system was implemented in the Simulink software system and auto-coded in the C programming language for use on the Airborne Research Test System (ARTS II) computer installed in the F-15 airplane. The Simulink model was also used in a control room that utilizes the Ring Buffered Network Bus hardware and software, making it possible to evaluate test points during flights. In-flight parameter estimation was done for piloted and automated maneuvers, primarily at three test conditions. Figure 2 shows results for pitching moment due to symmetric stabilator actuations for a series of three pitch doublet maneuvers (in a doublet maneuver, a command to change attitude in a given direction by a given amount is followed immediately by a command to change attitude in the opposite direction by the same amount). A time window of 5 seconds was used. The portions of the curves shown in red are those that passed the confidence tests. The technique showed good convergence for most derivatives for both kinds of maneuvers - typically within a few seconds. The confidence tests were marginally successful, and it would be necessary to refine them for use in an IFCS.

Smith, Mark↗
NASA NTRS2013

The Importance of Physical Models for Deriving Dust Masses and Grain Size Distributions in Supernova Ejecta. I. Radiatively Heated Dust in the Crab Nebula

Recent far-infrared (IR) observations of supernova remnants (SNRs) have revealed significantly large amounts of newly condensed dust in their ejecta, comparable to the total mass of available refractory elements. The dust masses derived from these observations assume that all the grains of a given species radiate at the same temperature, regardless of the dust heating mechanism or grain radius. In this paper, we derive the dust mass in the ejecta of the Crab Nebula, using a physical model for the heating and radiation from the dust. We adopt a power-law distribution of grain sizes and two different dust compositions (silicates and amorphous carbon), and calculate the heating rate of each dust grain by the radiation from the pulsar wind nebula. We find that the grains attain a continuous range of temperatures, depending on their size and composition. The total mass derived from the best-fit models to the observed IR spectrum is 0.019-0.13 Solar Mass, depending on the assumed grain composition. We find that the power-law size distribution of dust grains is characterized by a power-law index of 3.5-4.0 and a maximum grain size larger than 0.1 micron. The grain sizes and composition are consistent with what is expected for dust grains formed in a Type IIP supernova (SN). Our derived dust mass is at least a factor of two less than the mass reported in previous studies of the Crab Nebula that assumed more simplified two-temperature models. These models also require a larger mass of refractory elements to be locked up in dust than was likely available in the ejecta. The results of this study show that a physical model resulting in a realistic distribution of dust temperatures can constrain the dust properties and affect the derived dust masses. Our study may also have important implications for deriving grain properties and mass estimates in other SNRs and for the ultimate question of whether SNe are major sources of dust in the Galactic interstellar medium and in external galaxies.

Importance↗
NASA NTRS2020

Comparison of Vertical Surface Deformation Estimates Derived From Space-Based Gravimetry, Ground-Based GPS, and Model-Based Hydrologic Loading Over Snow-Dominated Watersheds in the United States

Spatiotemporal variability in Earth's terrestrial water storage (TWS) causes changes in surface deformation. The potential for using ground-based Global Positioning System (GPS) vertical displacement observations for estimating TWS is explored through a comparison of vertical displacements derived from space-based gravimetric retrievals, ground-based GPS, and model-based hydrologic estimates. The study presented here focuses on two snow-dominated basins in the Western United States for the years 2003–2016. Seasonal variations are observed in the vertical displacements derived from all three data sets, and the variation is coherent with the changes in hydrologic loading. Good consistency is observed between any two of the three data sets with gravimetric retrievals and hydrologic model estimates providing the highest level of agreement (i.e., all examined stations with correlation coefficient R > 0.70). Vertical displacements derived from gravimetric retrievals and ground-based GPS yielded R > 0.70 for more than 89% of the stations. In addition, it is found that both GPS-derived and space-based, gravimetry-derived vertical displacements clearly reflected the impact of climate variation (i.e., heavy precipitation during 2010–2011 winter followed by prolonged drought). Vertical displacements derived from the hydrologic model highlighted the relatively large precipitation convergence phase during late 2010 to early 2011 at some stations but not the prolonged drought that followed. The results indicate that ground-based GPS observations of vertical displacement have the capability to capture variations in TWS changes, which can be systematically merged in conjunction with Gravity Recovery and Climate Experiment (GRACE) into a land surface model to improve TWS estimates in a follow-up study.

Gaohong Yin↗
NASA NTRSDate not supplied

Towards a Third-Order Accurate, Second-Derivative-Free, Shock-Capturing Finite-Volume Method for Hypersonic Flows on Tetrahedral Grids

In this paper, we report progress in the development of a third-order accurate, second-derivative-free, shock-capturing finite-volume solver for three-dimensional unstructured grids. The method is economical in the sense that the computation and storage of second derivatives are not required for third-order accuracy. It is based on point-valued numerical solutions stored at cells, gradients computed and stored at nodes, and an efficient projected-derivative formula that eliminates the need for second derivatives in a quadratic solution interpolation. The projected-derivative formula is also used to eliminate second derivatives from a high-order flux quadrature formula, so that it can be implemented conveniently in the form of a numerical flux at a face center plus a correction term. Similarly, a high-order source quadrature formula can also be implemented in the form of a cell-center point evaluation plus a similar correction term. These features make it relatively straightforward to extend an existing second-order finite-volume code to third-order. This paper reports progress of implementing the method in the NASA VULCAN-CFD code and discusses the implementation of a high-order accurate limiter for shock capturing.

Weighted Least-Squares↗
NASA NTRSDate not supplied

The Use of the BSRN Data as A Benchmark for the POWER Hourly DHI and DNI and In Validating Derived Hourly GTI

The satellite-based CERES SYN1deg hourly data is the source data of the POWER GIS solar data that covers 2001 to near present. The SYN1deg(Ed4.1) hourly GHI agrees well with the BSRN data, but the hourly DHI and DirHI (Direct Horizontal Irradiance) are positively and negatively, respectively, biased with appreciable magnitudes. The hourly DNI, derived by dividing the DirHI by cos(SZA), or the cosine of the solar zenith angle, is therefore negatively biased. Based on the statistics of comparisons with the BSRN data, we performed bias corrections on the hourly DHI and DNI. The corrections were executed in the 3-D phase space of latitude, cos(SZA), and cloud fraction (CLFR). The isotropic model is then used to derive the hourly global tilted irradiance (GTI). For validation purpose, we applied the isotropic model to the BSRN data at the original 1-, 2-, 3- or 5-minute interval. The satellite-based hourly GTI shows good agreement with their BSRN counterpart. We also examined two monthly-mean-based methods that empirically derive monthly mean GTI and DNI from monthly mean GHI and from both monthly mean GHI and DHI. The monthly-mean-based results compare favorably with the hourly-mean-based results. The GEWEX SRB (V4-IP) provides POWER with daily mean GHI for the years before the CERES era, and the data were corrected using quantile mapping by referencing the CERES SYN1deg data. We used the Kolmogorov -Smirnov test (K-S test) and Cramer-von Mises test to examine how well the results agree with the BSRN data. We found that if we set the lower limit for the daily mean GHI to 30 W m-2, the data can pass the K-S test at 0.01 significance level and the Cramer-von Mises test at 0.001 significance level. If no lower limit is set on the daily means, the data fail both tests. The satellite-based CERES SYN1deg hourly data is the source data of the POWER GIS solar data that covers 2001 to near present. The SYN1deg(Ed4.1) hourly GHI agrees well with the BSRN data, but the hourly DHI and DirHI (Direct Horizontal Irradiance) are positively and negatively, respectively, biased with appreciable magnitudes. The hourly DNI, derived by dividing the DirHI by cos(SZA), or the cosine of the solar zenith angle, is therefore negatively biased. Based on the statistics of comparisons with the BSRN data, we performed bias corrections on the hourly DHI and DNI. The corrections were executed in the 3-D phase space of latitude, cos(SZA), and cloud fraction (CLFR). The isotropic model is then used to derive the hourly global tilted irradiance (GTI). For validation purpose, we applied the isotropic model to the BSRN data at the original 1-, 2-, 3- or 5-minute interval. The satellite-based hourly GTI shows good agreement with their BSRN counterpart. We also examined two monthly-mean-based methods that empirically derive monthly mean GTI and DNI from monthly mean GHI and from both monthly mean GHI and DHI. The monthly-mean-based results compare favorably with the hourly-mean-based results. The GEWEX SRB (V4-IP) provides POWER with daily mean GHI for the years before the CERES era, and the data were corrected using quantile mapping by referencing the CERES SYN1deg data. We used the Kolmogorov -Smirnov test (K-S test) and Cramer-von Mises test to examine how well the results agree with the BSRN data. We found that if we set the lower limit for the daily mean GHI to 30 W m-2, the data can pass the K-S test at 0.01 significance level and the Cramer-von Mises test at 0.001 significance level. If no lower limit is set on the daily means, the data fail both tests.

Taiping Zhang↗
NASA NTRS2021

Spectral Derivatives of Optical Depth for Partitioning Aerosol Type and Loading

Quantifying aerosol compositions (e.g., type, loading) from remotely sensed measurements by spaceborne, suborbital and ground-based platforms is a challenging task. In this study, the first and second-order spectral derivatives of aerosol optical depth (AOD) with respect to wavelength are explored to determine the partitions of the major components of aerosols based on the spectral dependence of their particle optical size and complex refractive index. With theoretical simulations from the Second Simulation of a Satellite Signal in the Solar Spectrum (6S) model, AOD spectral derivatives are characterized for collective models of aerosol types, such as mineral dust (DS) particles, biomass-burning (BB) aerosols and anthropogenic pollutants (AP), as well as stretching out to the mixtures among them. Based on the intrinsic values from normalized spectral derivatives, referenced as the Normalized Derivative Aerosol Index (NDAI), a unique pattern is clearly exhibited for bounding the major aerosol components; in turn, fractions of the total AOD (fAOD) for major aerosol components can be extracted. The subtlety of this NDAI method is examined by using measurements of typical aerosol cases identified carefully by the ground-based Aerosol Robotic Network (AERONET) sun–sky spectroradiometer. The results may be highly practicable for quantifying fAOD among mixed-type aerosols by means of the normalized AOD spectral derivatives.

aerosol partition↗
NASA NTRSDate not supplied

CFD-Based Frequency Domain Method for Dynamic Stability Derivative Estimation with Application to Transonic Truss-Braced Wing

This paper presents a dynamic stability estimation technique obtained from high-fidelity CFD simulations of the Mach 0.8 Transonic Truss-Braced Wing (TTBW). A series of unsteady RANS CFD simulations in FUN3D is performed on the TTBW in pitch and plunge oscillations at various reduced frequencies. The time-domain data are transformed into the frequency-domain data by Fourier series. Transfer functions of the dynamic stability derivatives are then estimated by a frequency-domain regression. The dynamic stability derivatives with respect to the angle of attack are determined by the regression of the unsteady aerodynamic coefficients for the plunge motion. The dynamic stability derivatives with respect to the pitch rate are deter-mined by the regression of the differential unsteady aerodynamic coefficients for the pitch motion upon the removal of the angle of attack contribution by the plunge motion. The steady-state stability derivatives are then compared to the results obtained from a stability analysis code VSPAERO as well as steady-state FUN3D simulations. The comparison of the steady-state stability derivatives shows excellent agreement.

Dynamic Stability Derivatives↗
NASA NTRS1972

Flight-determined derivatives and dynamic characteristics of the CV-990 airplane

Flight-determined longitudinal and lateral-directional stability and control derivatives are presented for the CV-990 airplane for various combinations of Mach number, altitude, and flap setting throughout the flight envelope up to a Mach number of 0.87. Also presented are the dynamic characteristics of the aircraft calculated from the flight-obtained derivatives and the measured phugoid characteristics. The derivative characteristics were obtained from flight records of longitudinal and lateral-directional transient oscillation maneuvers by using a modified Newton-Raphson digital derivative determination technique. Generally the derivatives exhibited consistent variation with lift coefficient in the low-speed data and with Mach number and altitude in the high-speed data. Many also varied with flap deflection, notably spoiler effectiveness and directional stability.

Gilyard, G. B.↗
NASA NTRS1974

Wind-tunnel investigation to determine the low speed yawing stability derivatives of a twin jet fighter model at high angles of attack

An investigation was conducted to determine the low-speed yawing stability derivatives of a twin-jet fighter airplane model at high angles of attack. Tests were performed in a low-speed tunnel utilizing variable-curvature walls to simulate pure yawing motion. The results of the study showed that at angles of attack below the stall the yawing derivatives were essentially independent of the yawing velocity and sideslip angle. However, at angles of attack above the stall some nonlinear variations were present and the derivatives were strongly dependent upon sideslip angle. The results also showed that the rolling moment due to yawing was primarily due to the wing-fuselage combination, and that at angles of attack below the stall both the vertical and horizontal tails produced significant contributions to the damping in yaw. Additionally, the tests showed that the use of the forced-oscillation data to represent the yawing stability derivatives is questionable, at high angles of attack, due to large effects arising from the acceleration in sideslip derivatives.

Coe, P. L., Jr.↗
NASA NTRS1974

Measurement of dynamic cross-derivatives due to pitching and yawing

A novel wind-tunnel apparatus is described with which all the 12 static and dynamic moment derivatives due to pitching and yawing can be obtained at angles of attack up to 40 deg and in the presence of some sideslip. The experimental technique and the data reduction procedure are discussed, and preliminary data on dynamic derivatives for an aircraft-like configuration at M ? 0.70 are presented. It is shown that in the range of angle of attack investigated, some rather large variations occur in both the two direct damping derivatives and some of the dynamic cross-derivatives; the latter, however, remain small as compared to the corresponding direct damping derivatives (in general less than 10%).

Orlik-Rueckemann, K. J.↗
NASA NTRS1976

Flight data identification of six degree-of-freedom stability and control derivatives of a large crane type helicopter

Flight test data from a large 'crane' type helicopter were collected and processed for the purpose of identifying vehicle rigid body stability and control derivatives. The process consisted of using digital and Kalman filtering techniques for state estimation and Extended Kalman filtering for parameter identification, utilizing a least squares algorithm for initial derivative and variance estimates. Data were processed for indicated airspeeds from 0 m/sec to 152 m/sec. Pulse, doublet and step control inputs were investigated. Digital filter frequency did not have a major effect on the identification process, while the initial derivative estimates and the estimated variances had an appreciable effect on many derivative estimates. The major derivatives identified agreed fairly well with analytical predictions and engineering experience. Doublet control inputs provided better results than pulse or step inputs.

Tomaine, R. L.↗
NASA NTRS1976

Derivation of the Navier-Stokes equation

The proposed approach to the derivation of the Navier-Stokes equation is thought to be more plausible and easier to understand than other derivations that can be found in works on fluid mechanics. The tensor character of the stress is central to the derivation. In particular, a linear relation between stress and strain rate is assumed only for the shear, rather than for the full stress tensor as is done in most other derivations. An assumption for the shear is naturally simpler and easier to verify experimentally. The use of tensor analysis is shown to greatly simplify the derivation.

Deissler, R. G.↗
NASA NTRS1983

Derivation of the fundamental equation of sound generated by moving aerodynamic surfaces

Ffowcs Williams and Hawkings (1969) based their derivation of the fundamental equation of the sound generated by arbitrarily moving aerodynamic surfaces on the study of mass and momentum balance of a control volume imbedding a mathematical surface(s) exactly corresponding to real surface(s). These investigators also sketched an alternative method, employing generalized functions, for its derivation. This latter method, which was later developed by Farassat (1975), is purely mathematical and formal. Goldstein (1976) used the free-space Green function to produce an implicit derivation of the Ffowcs Williams and Hawkings equation. In the study presented here, Lowson's (1965) concept of moving point singularities is generalized to moving surface singularities, and a new derivation is given of the fundamental equation. The derivation is based on topological considerations of the underlying space, the fluid medium, and the integral properties of the Dirac delta function.

Aggarwal, H. R.↗
NASA NTRS1983

Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

In a three dimensional simulation higher order derivative correlations, including skewness and flatness factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. The equations are forced to maintain steady state turbulence and collect statistics. It is found that the scalar derivative flatness increases much faster with Reynolds number than the velocity derivative flatness, and the velocity and mixed derivative skewness do not increase with Reynolds number. Separate exponents are found for the various fourth order velocity derivative correlations, with the vorticity flatness exponent the largest. Three dimensional graphics show strong alignment between the vorticity, rate of strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short minus 5/3 spectral regime is observed.

Kerr, R. A.↗
NASA NTRS1981

Longitudinal stability and control derivatives obtained from flight data of a PA-30 aircraft

In order to obtain reliable and accurate values of the stability and control derivatives, the Dryden Fligh Research Center (DFRC) developed a technique for extracting the derivatives from flight data. This technique is implemented by a set of FORTRAN computer programs that is based on a modified maximum likelihood estimator that uses the Newton-Raphson algorithm to perform the required minimization of the derivatives. Data was obtained with a PA-30, light twin-engine general aviation aircraft in zero, half, and full flap configuration in level unaccelerated flight with the landing gear retracted. The derivatives were plotted as functions of angle of attack using various graphical arrangements to show variations of wind tunnel and flight determined values at zero flap settings. Also, data was displayed to show the effects of flap deflection and thrust variation on the longitudinal stability derivatives. The angle of attack and angle of sideslip were measured. The dynamic pressure, velocity, and altitude were calculated, using a FORTRAN computer program, from the static and dynamic pressures. The control deflections of the stabilator, ailerons, and rudder also were recorded along with left throttle position, engine rpm, and manifold pressure.

Turley, D. R.↗
NASA NTRS1990

High resolution derivative spectra in remote sensing

The use of derivative spectra is an established technique in analytical chemistry for the elimination of background signals and for resolving overlapping spectral features. Application of this technique for tackling analogous problems such as interference from soil background reflectance in the remote sensing of vegetation or for resolving complex spectra of several target species within individual pixels in remote sensing is proposed. Methods for generating derivatives of high spectral resolution data are reviewed. Results of experiments to test the use of derivatives for monitoring chlorosis in vegetation show that derivative spectral indices are superior to conventional broad-band spectral indices such as the near-infrared/red reflectance ratio. Conventional broad-band indices are sensitive to both leaf cover as well as leaf color. New derivative spectral indices which were able to monitor chlorosis unambiguously were identified. Potential areas for the application of this technique in remote sensing are considered.

Demetriades-Shah, Tanvir H.↗
NASA NTRS1988

Design principles for an interactive program derivation system

The main design principles of an interactive program transformation system called FOCUS are outlined. Its important characteristics are its human-oriented deduction techniques based replacement, emphasis on small search spaces, and the use of a tree structure to organize program derivations. The tree structure presents to the user a static picture of the derivation process and promotes flexibility in the development of derivations. The system keeps track of dependencies between different parts of derivations, and records the derivation activity for later use in automatic replay.

Reddy, Uday S.↗