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NASA NTRS1992

Flexure-torsion behavior of sheat-deformable beams with applications to aircraft wing sections

The flexure-torsion behavior of a tip-loaded cantilever beam with an arbitrary cross-section is studied using Saint-Venant's semi-inverse method along with a power series solution for the out-of-plane flexure and torsion warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. For complex cross-sections, the calculated coefficients represent a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-section properties including: the torsion constant, shear deformation coefficients, shear correction factors, and the shear center location. A new linear relation is developed for locating the shear center using the Saint-Venant flexure and torsion solutions, where the twist rate is zero about the line of shear centers (not the centroidal axis). Numerical results are presented for a triangular cross-section and different NACA airfoils.

Kosmatka, J. B.↗
NASA NTRS1992

Top-of-atmosphere radiative fluxes - Validation of ERBE scanner inversion algorithm using Nimbus-7 ERB data

The ERBE algorithm is applied to the Nimbus-7 earth radiation budget (ERB) scanner data for June 1979 to analyze the performance of an inversion method in deriving top-of-atmosphere albedos and longwave radiative fluxes. The performance is assessed by comparing ERBE algorithm results with appropriate results derived using the sorting-by-angular-bins (SAB) method, the ERB MATRIX algorithm, and the 'new-cloud ERB' (NCLE) algorithm. Comparisons are made for top-of-atmosphere albedos, longwave fluxes, viewing zenith-angle dependence of derived albedos and longwave fluxes, and cloud fractional coverage. Using the SAB method as a reference, the rms accuracy of monthly average ERBE-derived results are estimated to be 0.0165 (5.6 W/sq m) for albedos (shortwave fluxes) and 3.0 W/sq m for longwave fluxes. The ERBE-derived results were found to depend systematically on the viewing zenith angle, varying from near nadir to near the limb by about 10 percent for albedos and by 6-7 percent for longwave fluxes. Analyses indicated that the ERBE angular models are the most likely source of the systematic angular dependences. Comparison of the ERBE-derived cloud fractions, based on a maximum-likelihood estimation method, with results from the NCLE showed agreement within about 10 percent.

Suttles, John T.↗
NASA NTRS1993

Flexure-torsion behavior of prismatic beams. I - Section properties via power series

The behavior of a tip-loaded cantilever beam with an arbitrary cross section is studied using Saint-Venant's semi-inverse method along with a power series solution for the out-of-plane flexure and torsion warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. For complex cross sections, the calculated coefficients represented a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-sectional properties (torsion constant, shear correction factors, shear deformation coefficients, and shear center location). A new linear relation is developed for locating the shear center, where the twist rate is zero about the line of shear centers. Moreover, the kinematic relations for a new fully compatible one-dimensional beam theory are developed. Numerical results are presented first to verify the approach and second to provide section data on NACA four-series airfoils not currently found in the literature.

Kosmatka, J. B.↗
NASA NTRS1993

Retrieval of ice thickness from polarimetric SAR data

We describe a potential procedure for retrieving ice thickness from multi-frequency polarimetric SAR data for thin ice. This procedure includes first masking out the thicker ice types with a simple classifier and then deriving the thickness of the remaining pixels using a model-inversion technique. The technique used to derive ice thickness from polarimetric observations is provided by a numerical estimator or neural network. A three-layer perceptron implemented with the backpropagation algorithm is used in this investigation with several improved aspects for a faster convergence rate and a better accuracy of the neural network. These improvements include weight initialization, normalization of the output range, the selection of offset constant, and a heuristic learning algorithm. The performance of the neural network is demonstrated by using training data generated by a theoretical scattering model for sea ice matched to the database of interest. The training data are comprised of the polarimetric backscattering coefficients of thin ice and the corresponding input ice parameters to the scattering model. The retrieved ice thickness from the theoretical backscattering coefficients is compare with the input ice thickness to the scattering model to illustrate the accuracy of the inversion method. Results indicate that the network convergence rate and accuracy are higher when multi-frequency training sets are presented. In addition, the dominant backscattering coefficients in retrieving ice thickness are found by comparing the behavior of the network trained backscattering data at various incidence angels. After the neural network is trained with the theoretical backscattering data at various incidence anges, the interconnection weights between nodes are saved and applied to the experimental data to be investigated. In this paper, we illustrate the effectiveness of this technique using polarimetric SAR data collected by the JPL DC-8 radar over a sea ice scene.

Kwok, R.↗
NASA NTRS1994

Aircraft electric field measurements: Calibration and ambient field retrieval

An aircraft locally distorts the ambient thundercloud electric field. In order to determine the field in the absence of the aircraft, an aircraft calibration is required. In this work a matrix inversion method is introduced for calibrating an aircraft equipped with four or more electric field sensors and a high-voltage corona point that is capable of charging the aircraft. An analytic, closed form solution for the estimate of a (3 x 3) aircraft calibration matrix is derived, and an absolute calibration experiment is used to improve the relative magnitudes of the elements of this matrix. To demonstrate the calibration procedure, we analyze actual calibration date derived from a Lear jet 28/29 that was equipped with five shutter-type field mill sensors (each with sensitivities of better than 1 V/m) located on the top, bottom, port, starboard, and aft positions. As a test of the calibration method, we analyze computer-simulated calibration data (derived from known aircraft and ambient fields) and explicitly determine the errors involved in deriving the variety of calibration matrices. We extend our formalism to arrive at an analytic solution for the ambient field, and again carry all errors explicitly.

Koshak, William J.↗
NASA NTRS1994

Preconditioned domain decomposition scheme for three-dimensional aerodynamic sensitivity analysis

A discrete sensitivity analysis algorithm had previously been developed and applied to two-dimensional aerodynamic optimization problems, where the computational domains were discretized by using single grids. The sparse, unsymmetric systems of linear equations resulting from this algorithm were solved by a direct matrix inversion matrix. However, for large two-dimensional problems and, practically, all three-dimensional problems, direct inversion methods become inapplicable, primarily due to the prohibitive computer storage needed. In an attempt to alleviate such hindrances, the sensitivity analysis with domain decomposition (SADD) scheme was developed. This scheme divides the computational domain into smaller and nonoverlapping subdomains (multiblock grids) that are solved separately. Then, the final solution is constructed from the subdomain solutions. As the number of grid points in the interface boundaries of the subdomains becomes large, the computer memory required to store the effective coefficient matrix of these interface points starts to increase. Presented in this Technical Note is a preconditioned iterative procedure to overcome this particular problem.

Eleshaky, Mohamed E.↗
NASA NTRS1992

Tropospheric chemical models

The differences in atmospheric composition over the globe and the short- and long-term variations in this composition are the net effect of several atmospheric and biospheric processes: biospheric emissions, atmospheric circulation, atmospheric chemical transformations and finally deposition back to the surface. Accurate and realistic atmospheric chemistry and circulation models are essential to interpret the observed global distributions and trends of atmospheric species in terms of these underlying processes. Comparisons between model predictions and observations test current understanding of these processes and models used in conjunction with inverse methods allow deductions of the rates of these processes from the observations. With the planned inclusion of at least CO and CH4 observations on the Earth Observing System (EOS) satellites, together with the large global data set expected from in situ observations under the International Global Atmospheric Chemistry (IGAC) Project, the further development of global three-dimensional high-resolution atmospheric chemistry and circulation models in order to interpret this new data is a high-priority endeavor.

Prinn, R. G.↗
NASA NTRS1995

Ozone vertical distribution retrieval from ground-based high resolution infrared solar spectra

A practical procedure for the retrieval of ozone vertical profiles from ground-based high resolution Fourier transform infrared solar spectra has been developed. The analysis is based on a multilayer line-by-line forward model and a semi-empirical version of the optimal estimation inversion method of Rodgers. The 1002.6-1003.2 cm(exp -1) spectral interval has been selected for the analysis on the basis of synthetic spectrum calculations. This interval contains numerous ozone lines covering a range of intensities and providing retrieval sensitivity from ground level to about 35 km. Characterization of the method and an error analysis have been performed. For a spectral resolution of 0.05-0.01 cm(exp -1) and a signal-to-noise ratio greater than or equal to 100 the retrieval is stable with a vertical resolution of approximately 5 km attainable near the surface degrading to approximately 10 km in the stratosphere. Synthetic spectra studies show that the a priori profile and weak constraints selected for the retrievals introduce no significant biases for a wide range of ozone profiles.

Pougatchev, N. S.↗
NASA NTRS1994

Spectroscopy of Solid State Laser Materials

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.

Buoncristiani, A. M.↗
NASA NTRS1998

Evaluation of 3D Inverse Code Using Rotor 67 as Test Case

A design modification of Rotor 67 is carried out with a full 3D inverse method. The blade camber surface is modified to produce a prescribed pressure loading distribution, with the blade tangential thickness distribution and the blade stacking line at midchord kept the same as the original Rotor 67 design. Because of the inviscid-flow assumption used in the current version of the method, Rotor 67 geometry is modified for use at a design point different from the original design value. A parametric study with the prescribed pressure loading distribution yields the following results. In the subsonic section, smooth pressure loading shapes generally produce blades with well-behaved blade surface pressure distributions. In the supersonic section, the study shows that the strength and position of the passage shock correlate with the characteristics of the blade pressure loading shape. In general, "smooth" prescribed blade pressure loading distributions generate blade designs with reverse cambers which have the effect of weakening the passage shock.

Dang, T.↗
NASA NTRS1960

The Numerical Calculation of Flow Past Conical Bodies Supporting Elliptic Conical Shock Waves at Finite Angles of Incidence

The inverse method, with the shock wave prescribed to be an elliptic cone at a finite angle of incidence, is applied to calculate numerically the supersonic perfect-gas flow past conical bodies not having axial symmetry. Two formulations of the problem are employed, one using a pair of stream functions and the other involving entropy and components of velocity. A number of solutions are presented, illustrating the numerical methods employed, and showing the effects of moderate variation of the initial parameters.

Briggs, Benjamin R.↗
NASA NTRS2000

Tidal Implications for the GRACE Satellite Mission

A fundamental part of the processing of the GRACE satellite data will be correction for the gravitational effect of tides. This includes solid earth, ocean, and atmospheric tides. The most problematic are ocean tides in shallow seas and in high latitudes (above the 66$^{\circ}$ inclination of Topex). Somewhat smaller, but still important, errors are associated with the S$_1$ air tide and the ocean's dynamic response to it. In this paper we explore several facets of the tidal error budget. The ocean tide error spectrum is estimated (a) by inverse methods and (b) by simple differencing of several of the best tidal models. The tidal error spectrum is flatter than the tidal signal spectrum, and it exceeds 10\% of the signal at degrees 15 and above. The tide errors also exceed the anticipated sensitivity of GRACE for all degrees below 40, and possibly below 50. The assumption of constant seawater density (of about 1035 kg\,M$^{-3}$) is a minor error source. Owing to GRACE's high inclination, solar tides are aliased to long periods, which is potentially problematic for geophysical interpretation of the gravity signal. Simulations of the effect of high-latitude solar-tide errors on gravity estimates around Antarctica will be discussed.

Ray, Richard D.↗
NASA NTRS1995

A Hybrid Parallel Preconditioning Algorithm For CFD

A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.

Barth,Timothy J.↗
NASA NTRS2003

NASA Inverse Methods/Data Assimilation

An overview of NASA's Third International Summer School on Inverse Methods and Data Assimilation which was conducted at Oregon State University from July 22 to August 2, 2002, is presented. Items listed include: a roster of attendees, a description of course content and talks given.

Bennett, Andrew↗
NASA NTRS2003

Advanced Global Atmospheric Gases Experiment (AGAGE): MIT Contribution

We describe in detail the instrumentation and calibrations used in the ALE, GAGE and AGAGE experiments and present a history of the majority of the anthropogenic ozone- depleting and climate-forcing gases in air based on these experiments. Beginning in 1978, these three successive automated high frequency in-situ experiments have documented the long-term behavior of the measured concentrations of these gases over the past twenty years, and show both the evolution of latitudinal gradients and the high frequency variability due to sources and circulation. We provide estimates of the long-term trends in total chlorine contained in long- lived halocarbons involved in ozone depletion. We summarize interpretations of these measurements using inverse methods to determine trace gas lifetimes and emissions. Finally, we provide a combined observational and modeled reconstruction of the evolution of chlorocarbons by latitude in the atmosphere over the past sixty years which can be used as boundary conditions for interpreting trapped air in glaciers and oceanic measurements of chlorocarbon tracers of the deep oceanic circulation. Some specific conclusions are: (a) International compliance with the Montreal Protocol is so far resulting in chlorofluorocarbon and chlorocarbon mole fractions comparable to target levels, (b) Mole fractions of total chlorine contained in long-lived halocarbons (CCl2F2, CCl3F, CH3CCl3, CCl4, CHClF2, CCl2FCClF2, CH3Cl, CH2Cl2, CHCl3, CCl2=CCl2) in the lower troposphere reached maximum values of about 3.6 ppb in 1993 and are beginning to slowly decrease in the global lower atmosphere, (c) The chlorofluorocarbons have atmospheric lifetimes consistent with destruction in the stratosphere being their principal removal mechanism, (d) Multi-annual variations in chlorofluorocarbon and chlorocarbon emissions deduced from ALUGAGWAGAGE data are consistent approximately with variations estimated independently from industrial production and sales data where available (CCl2F2 (CFC-12) and CCl2FCClF2 (CFC-113) show the greatest discrepancies), (e) The mole fractions of the hydrochlorofluorocarbons and hydrofluorocarbons, which are replacing the regulated halocarbons, are rising very rapidly in the atmosphere but, with the exception of the much longer manufactured CHClF2 (HCFC-22), they are not yet at levels sufficient to contribute significantly to atmospheric chlorine loading. These replacement species could in the future provide independent estimates of the global weighted-average OH concentration provided their industrial emissions are accurately documented, (f) In the future, analysis of pollution events measured using high frequency in-situ measurements of chlorofluorocarbons and their replacements may enable emission estimates at the regional level which, together with industrial end-use data, are of sufficient accuracy to be capable of identifying regional non-compliance with the Montreal Protocol.

Kurylo, Michael↗
NASA NTRS2004

An Adjoint-Based Analysis of the Sampling Footprints of Tall Tower, Aircraft and Potential Future Lidar Observations of CO2

A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.

Andrews, Arlyn↗
NASA NTRS1999

Subsonic Static and Dynamic Aerodynamics of Blunt Entry Vehicles

The incompressible subsonic aerodynamics of four entry-vehicle shapes with variable c.g. locations are examined in the Langley 20-Foot Vertical Spin Tunnel. The shapes examined are spherically-blunted cones with half-cone angles of 30, 45, and 60 deg. The nose bluntness varies between 0.25 and 0.5 times the base diameter. The Reynolds number based on model diameter for these tests is near 500,000. Quantitative data on attitude and location are collected using a video-based data acquisition system and reduced with a six deg-of-freedom inverse method. All of the shapes examined suffered from strong dynamic instabilities which could produced limit cycles with sufficient amplitudes to overcome static stability of the configuration. Increasing cone half-angle or nose bluntness increases drag but decreases static and dynamic stability.

Mitcheltree, Robert A.↗
NASA NTRS2000

An Efficient Inverse Aerodynamic Design Method For Subsonic Flows

Computational Fluid Dynamics based design methods are maturing to the point that they are beginning to be used in the aircraft design process. Many design methods however have demonstrated deficiencies in the leading edge region of airfoil sections. The objective of the present research is to develop an efficient inverse design method which is valid in the leading edge region. The new design method is a streamline curvature method, and a new technique is presented for modeling the variation of the streamline curvature normal to the surface. The new design method allows the surface coordinates to move normal to the surface, and has been incorporated into the Constrained Direct Iterative Surface Curvature (CDISC) design method. The accuracy and efficiency of the design method is demonstrated using both two-dimensional and three-dimensional design cases.

Milholen, William E., II↗