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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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Development of characteristic equations and error analysis for computer programs contained in structural analysis and matrix interpretive system
An error analysis has been made of a Shuttle postflight entry trajectory reconstruction process to obtain trajectory state estimation errors and to assess the impact of these errors on Shuttle aerodynamic force coefficient extraction. In this analysis, the entry trajectory is assumed to be reconstructed via numerical integration of onboard accelerometer and gyro measurements and constrained to satisfy ground-based radio tracking. The trajectory state estimation errors are calculated using a Kalman-Schmidt sequential filter assuming various measurement error models and combinations of ground-based tracking. The resultant trajectory estimation errors are analyzed in a simplified perturbation process to establish the accuracy to which postflight aerodynamic force coefficients can be determined. Results are presented which show that the principal error sources affecting the trajectory reconstruction and thus the force coefficient extraction, assuming perfect atmospheric density knowledge, are the accelerometer and gyro resolution, acceleration-sensitive gyro drifts, and the alignment uncertainties associated with integration on the Shuttle.
This report presents a series of implicit–explicit (IMEX) variable stepsize algorithms for the incompressible Navier–Stokes equations (NSE). Here, IMEX means the nonlinear term is treated fully explicitly while the remaining terms are treated implicitly. With the advent of new computer architectures there has been growing demand for low memory solvers of this type. The addition of time adaptivity improves the accuracy and greatly enhances the efficiency of the algorithm. We prove energy stability of an embedded first–second order IMEX pair. For the first order member of the pair, we prove stability for variable stepsizes, and analyze convergence. We believe this to be the first proof of this type for a variable stepsize IMEX scheme for the incompressible NSE. We then define and test a variable stepsize, variable order IMEX scheme using these methods. Our work contributes several firsts for IMEX NSE schemes, including an energy argument and error analysis of a two-step, variable stepsize method, and embedded error estimation for an IMEX multi-step method.
Using the Canada-France-Hawaii Telescope (CFHT) we have obtained three closely spaced epochs of calibrated Blue Violet Red Infrared (BVRI) CCD imaging of two fields in M81, each known to contain a thirty-day Cepheid. Calibrated BVRI photometry of the brightest stars in these fields is presented. The slope of the luminosity function from the brightest 3-4 mag of the main-sequence blue plume is consistent with similar determinations of the apparent luminosity function in other resolved galaxies, thereby removing the one potential deviation from universality noted by Freedman in a photographic study of luminosity functions in nearby resolved galaxies. Under the assumption that the two Cepheids are representative, a reddening-law fit to the multiwavelength BVRI period-luminosity moduli give a true distance modulus of (m-M)sub 0 = 27.79 mag for M81, corresponding to a linear distance of 3.6 Mpc. An error analysis shows that the derived true distance modulus has a random error of +/- 0.28 mag (due to the photometric uncertainties in the BVRI data), with a systematic uncertainty of +/- 0.10 mag (accounting for the combined effects of unknown phasing of the data points, and the unknown positioning of these particular stars within the Cepheid instabiliy strip).
We retrieved the vertical distribution of ozone from a series 0.005-0.013/cm resolution infrared solar spectra recorded with the McMath Fourier Transform spectrometer at the Kitt Peak National Solar Observatory. The analysis is based on a multi-layer line-by-line forward model and a semi-empirical version of the optimal estimation inversion method by Rodgers. The 1002.6-1003.2/cm spectral interval has been selected for the analysis on the basis of synthetic spectrum calculations. The characterization and error analysis of the method have been performed. It was shown that for the Kitt Peak spectral resolution and typical signal-to-noise ratio (greater than or equal to 100) the retrieval is stable, with the vertical resolution of approximately 5 km attainable near the surface degrading to approximately 10 km in the stratosphere. Spectra recorded from 1980 through 1993 have been analyzed. The retrieved total ozone and vertical profiles have been compared with total ozone mapping spectrometer (TOMS) satellite total columns for the location and dates of the Kitt Peak Measurements and about 100 ozone ozonesoundings and Brewer total column measurements from Palestine, Texas, from 1979 to 1985. The total ozone measurements agree to +/- 2%. The retrieved profiles reproduce the seasonally averaged variations with altitude, including the ozone spring maximum and fall minimum measured by Palestine sondes, but up to 15% differences in the absolute values are obtained.
Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all.
In this paper, we will present the concept of accelerometer-assisted tracking, error analysis, and progress made on its implementations.
Our first activity is based on delivery of code to Bob Evans (University of Miami) for integration and eventual delivery to the MODIS Science Data Support Team. As we noted in our previous semi-annual report, coding required the development and analysis of an end-to-end model of fluorescence line height (FLH) errors and sensitivity. This model is described in a paper in press in Remote Sensing of the Environment. Once the code was delivered to Miami, we continue to use this error analysis to evaluate proposed changes in MODIS sensor specifications and performance. Simply evaluating such changes on a band by band basis may obscure the true impacts of changes in sensor performance that are manifested in the complete algorithm. This is especially true with FLH that is sensitive to band placement and width. The error model will be used by Howard Gordon (Miami) to evaluate the effects of absorbing aerosols on the FLH algorithm performance. Presently, FLH relies only on simple corrections for atmospheric effects (viewing geometry, Rayleigh scattering) without correcting for aerosols. Our analysis suggests that aerosols should have a small impact relative to changes in the quantum yield of fluorescence in phytoplankton. However, the effect of absorbing aerosol is a new process and will be evaluated by Gordon.
Report discusses sources of error in graphical display and analysis of flow fields simulated numerically by computers. Sources of error explored by examples of graphical techniques and errors they introduce in depiction of flow fields computed from Reynolds-averaged Navier-Stokes equations. Specific graphical techniques examined: contouring, plotting arrows on pictures to represent three-dimensional vectors, and particle tracing.
Fourth-order compact finite difference schemes for solving the time fractional diffusion equation with nonlocal boundary conditions are considered in this paper. The second-order derivative in one space variable is approximated by a fourth-order compact finite difference. Two different time derivatives, the Caputo derivative and Riemann–Liouville derivative are considered in the equations that we discuss. The Caputo time derivative is discretized by the L1-approximation and a second-order approximation is used for the Riemann–Liouville derivative. Stability analysis using the discrete energy method for Scheme I is given, and error estimation of this scheme is derived by conducting the local truncation error analysis, using the stability result. Numerical results are provided to show that both two fully discrete schemes have fourth-order accuracy in space, and 2−γ order of accuracy in time for Scheme I with γ being the order of the fractional derivative, while Scheme II has second-order accuracy in time when the theoretical solutions are smooth with zero initial values.
This report is divided into four parts. First part of the report describes the methods used to measure and model the flow of supercritical carbon dioxide (S-CO 2 ) through annuli and straight-through labyrinth seals. The effects of shaft eccentricity in small diameter annuli were observed for length-to-hydraulic diameter (L/D) ratios of 6, 12, 143, and 235. Flow rates through tooth-cavity labyrinth seals were measured for inlet pressures of 7.7, 10, and 11 MPa with corresponding inlet densities of 325, 475, and 630 kg/m 3 . Various leakage models were compared to this result to describe their applicability in supercritical carbon dioxide applications. Flow rate measurements were made varying tooth number for labyrinth seals of same total length. Second part of the report describes the computational study performed to understand the leakage through the labyrinth seals using Open source CFD package OpenFOAM. Fluid Property Interpolation Tables (FIT) program was implemented in OpenFOAM to accurately model the properties of CO2 required to solve the governing equations. To predict the flow behavior in the two phase dome Homogeneous Equilibrium Model (HEM) is assumed to be valid. Experimental results for plain orifice (L/D ~ 5) were used to show the capabilities of the FIT model implemented in OpenFOAM. Error analysis indicated that OpenFOAM is capable of predicting experimental data within ±10% error with the majority of data close to ±5% error. Following the validation of computational model, effects of geometrical parameters and operating conditions are isolated from each other and a parametric study was performed in two parts to understand their effects on leakage flow. Third part of the report provides the details of the constructed heat exchanger test facility and presents the experimental results obtained to investigate the effects of buoyancy on heat transfer characteristics of Supercritical carbon dioxide in heating mode. Turbulent flows with Reynolds numbers up to 60,000, at operating pressures of 7.5, 8.1, and 10.2 MPa were tested in a round tube. Local heat transfer coefficients were obtained from measured wall temperatures over a large set of experimental parameters that varied inlet temperature from 20 °C to 55 °C,mass flux from 150 to 350 kg/m 2 s, and a maximum heat flux of 65 KW/m 2 . Horizontal, upward and downward flows were tested to investigate the unusual heat-transfer characteristics to the effect of buoyancy and flow acceleration caused by large variation in density. Final part of this report presents the simplified analysis performed to investigate the possibility of using wet cooling tower option to reject heat from the supercritical carbon dioxide Brayton cycle power convertor for AFR-100 and ABR-1000 plants. A code was developed to estimate the tower dimensions, power and water consumption, and to perform economic analysis. The code developed was verified by comparing the calculations to a vendor quote. The effect of ambient air and water conditions on the sizing and construction of the cooling tower as well as the cooler is studied. Finally, a cost-based optimization technique is used to estimate the optimum water conditions which will improve the plant economics.
Hyperspectral imaging polarimetry enables both the spectrum and its spectrally-resolved state of polarization to be measured. This information is important to identify material properties for various applications in remote sensing and agricultural monitoring. In this paper, we describe the design and performance of a ruggedized, field deployable Hyperspectral Imaging Polarimeter (HIP), designed for wavelengths spanning the visible to near infrared (450-800 nm). An entrance slit was used to sample the scene in a pushbroom scanning mode across a 30 degree vertical by 110 degree horizontal field of view. Furthermore, athermalized achromatic retarders were implemented in a channel spectrum generator to measure the linear Stokes parameters. The mechanical and optical layout of the system and its peripherals are provided, in addition to the results of the sensor's spectral and polarimetric calibration. Finally, field measurements are also provided and an error analysis conducted. With its present calibration, the sensor has an absolute polarimetric error of 2.5% RIVIS and a relative spectral error of 2.3% RMS.
The active cavity radiometer (ACR) is a pyrheliometer that accurately defines the absolute radiation scale. The physics of the pyrheliometric method and the ACR approach to this method are presented in detail. A mathematical abstraction of the method is generated through a quasi-equilibrium analysis of the power balance of the ACR's cavity detector. An error analysis is carried out on the quasi-equilibrium equation to determine the uncertainties of ACR measurements relative to the absolute radiation scale. The uncertainty of ACR measurements as a function of irradiance level is presented in graphical form.
Backscattering cross section per unit scattering area data, reduced from measurements made by the Skylab S-193 radar altimeter over the ocean surface are presented. Descriptions of the altimeter are given where applicable to the measurement process. Analytical solutions are obtained for the flat surface impulse response for the case of a nonsymmetrical antenna pattern. Formulations are developed for converting altimeter AGC outputs into values for the backscattering cross section. Reduced data are presented for Missions SL-2, 3 and 4 for all modes of the altimeter where sufficient calibration existed. The problem of interpreting land scatter data is also discussed. Finally, a comprehensive error analysis of the measurement is presented and worst case random and bias errors are estimated.
Through the method of truncation functions, the oceanic geoid undulation is divided into two constituents: an inner zone contribution expressed as an integral of surface gravity disturbances over a spherical cap; and an outer zone contribution derived from a finite set of potential harmonic coefficients. Global, average error estimates are formulated for undulation differences, thereby providing accuracies for a relative geoid. The error analysis focuses on the outer zone contribution for which the potential coefficient errors are modeled. The method of computing undulations based on gravity disturbance data for the inner zone is compared to the similar, conventional method which presupposes gravity anomaly data within this zone.
A retrieval technique for high resolution IR solar occultation limb sensing data is described for profiling stratospheric trace constituents. Remote measurement of ClO during sunset in the 24-45-km region with a 2-km height resolution is chosen as an example. Two types of instruments are considered: a laser heterodyne radiometer with line resolving spectral resolution and an interferometer spectrometer with a fixed slit width of 0.02/cm. It is pointed out that a multichannel approach is necessary with the heterodyne instrument for improved retrieval accuracy. The error analysis indicates the relative sizes of instrument noise and other sources of error in the retrieval of altitude profiles with high (2-km) vertical resolution.
In an earlier paper, Misner (2004, Class. Quant. Grav., 21, S243) presented a novel algorithm for computing the spherical harmonic components of data represented on a cubic grid. I extend Misner s original analysis by making detailed error estimates of the numerical errors accrued by the algorithm, by using symmetry arguments to suggest a more efficient implementation scheme, and by explaining how the algorithm can be applied efficiently on data with explicit reflection symmetries.
Pinpoint landing (PPL) missions will deliver about 1000 kg of useful payload to the surface of Mars. Mid-to-high latitude landing site compatibility is sought which should provide the means to land at sites up to 2.5 km above Mars mean surface altitude. A dispersion and control analysis process is presented which helps to identify the effects of PPL error drivers, quantify the effect of dispersions on landing error and quantify the landing position control capability/authority along the entry path. An entry/descent/landing (EDL) profile is provided. Guided aeroshell is the baseline for all candidate Mars atmospheric entry architectures. A two-stage architecture is considered for the aerodynamic decelerator descent phase: supersonic parachute plus guided subsonic parachute or high-Mach inflatable decelerator plus guided subsonic parachute. The powered descent phase uses propulsive descent stage for soft landing and final error reduction maneuvers. Studies have found that the aeroshell entry face dispersions can be large, but closed-loop guidance can null out resulting errors to within about 2 km. Additionally, projected parachute control is inadequate to correct worst case dispersions without wind forecast data. To mitigate the problems dispersions due to atmospheric uncertainty can be reduced by providing on-board external means to measure density and winds ahead of the vehicle, higher L/D control authority options for the subsonic parachute phase can be investigated, and decelerators with control authority options for the supersonic descent phase can be examined. A navigation error analysis and wind effects summary are included.