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NASA NTRS1983

Two-dimensional internal compressible viscous flows using semi-elliptic analysis

Subsonic viscous flows through planar cascades are examined by means of a semielliptic form of the Navier-Stokes equations, which is obtained by neglecting the streamwise diffusion of momentum and energy in their respective equations and providing upstream interaction through the pressure field. The influence of downstream conditions is propagated upstream in the subsonic flow, via a streamwise implicit determination of the pressure field, in order to permit departure-free solutions for the overall flow problem. The continuity equation is thereby satisfied directly. Governing equations are written in strong conservation law form, in terms of general, nonorthogonal transformed coordinates and Cartesian velocity components.

Ghia, K. N.↗

NASA NTRS1985

Full two-dimensional transient solutions of electrothermal aircraft blade deicing

Two finite difference methods are presented for the analysis of transient, two-dimensional responses of an electrothermal de-icer pad of an aircraft wing or blade with attached variable ice layer thickness. Both models employ a Crank-Nicholson iterative scheme, and use an enthalpy formulation to handle the phase change in the ice layer. The first technique makes use of a 'staircase' approach, fitting the irregular ice boundary with square computational cells. The second technique uses a body fitted coordinate transform, and maps the exact shape of the irregular boundary into a rectangular body, with uniformally square computational cells. The numerical solution takes place in the transformed plane. Initial results accounting for variable ice layer thickness are presented. Details of planned de-icing tests at NASA-Lewis, which will provide empirical verification for the above two methods, are also presented.

Masiulaniec, K. C.↗

NASA NTRS1985

Transonic calculations for a flexible supercritical wing and comparison with experiment

Pressure data measured on the flexible DAST ARW-2 wing are compared with results calculated using the transonic small perturbation code XTRAN3S. A brief description of the analysis is given and a recently developed grid coordinate transformation is described. Calculations are presented for the rigid and flexible wing for Mach numbers from 0.60 to 0.90 and dynamic pressures from 0 to 1000 psf. Calculated and measured static pressures and wing deflections are compared, and calculated static aeroelastic trends are given. Attempts to calculate the transonic instability boundary of the wing are described.

Bennett, R. M.↗

NASA NTRS1985

Analysis and quantification of errors in the geometric correction of satellite images

The quantitative use of remote sensing satellite images in many applications requires that the geometric distortion inherent in these images be corrected, or rectified, to a desired map projection. The most widely used technique relies on ground control points to empirically determine a mathematical coordinate transformation to correct the geometry. In this paper, using the method of least squares, expressions for the accuracy of the geometric transformation and of the rectification of the satellite image to a map projection are derived. Explicit relations between the global accuracy of the transformation and the number, location, and local accuracy of the ground control points are obtained. The results are applied to the correction of a Landsat MSS image.

Ford, G. E.↗

NASA NTRS1985

Implicit finite-difference methods for the Euler equations

The present paper is concerned with two-dimensional Euler equations and with schemes which are in use of the time of this writing. Most of the development presented carries over directly to three dimensions. The characteristics of the two-dimensional Euler equations in Cartesian coordinates are considered along with generalized curvilinear coordinate transformations, metric relations, invariants of the transformation, flux Jacobian matrices and eigensystems, numerical algorithms, flux split algorithms, implicit and explicit nonlinear control (smoothing), upwind differencing in supersonic regions, unsteady and steady-state computation, the diagonal form of implicit algorithm, metric differencing and invariants, boundary conditions, geometry and mesh generation, and sample solutions.

Pulliam, T. H.↗

NASA NTRS1985

Structural analysis model validation using modal test data

The design of a structure which can survive a prescribed dynamic environment is generally based on the use of an analytical model of the structure. The modal test is employed to verify the analytical model. This paper is concerned with the involved validation process, taking into account modal test results from realistic complex spacecraft structural systems as examples to demonstrate the proposed validation procedure. Attention is given to a load analysis model definition, a pretest analysis and test/analysis model, and the correlation parameters. Coordinate transformation is considered along with mode identification, frequency orthogonality, effective mass, mode shape, local kinetic energy, modal force, strain energy, and modal forces by acceleration measurements. Two examples are used to illustrate the procedure.

Chen, J.-C.↗

NASA NTRS1986

A generalized theory for eccentric and misalignment effects in high-pressure annular seals

High-pressure annular seal leakage and dynamic coefficients vary with eccentricity and misalignment. Recent seal leakage data with both concentric and fully eccentric alignments support the seal leakage model with surface roughness and eccentricity effects included. In this paper, the seal dynamic coefficient calculation has been generalized and allows direct calculation of the seal dynamic coefficients at any circumferential location. The generalized solution agrees with the results obtained by using the calculated values of an earlier paper and performing a coordinate transformation. The analysis results coincide with the measured data in showing that the stiffness and damping matrices of seal coefficients are not skew symmetric, and the main diagonal seal coefficients are not equal. The measured direct stiffnesses were found higher than predicted by the concentric seal theory, but this may be explained by the presence of eccentricity in the test operating mode.

Chen, W. C.↗

NASA NTRS1986

An exact solution for orbit view-periods from a station on a tri-axial ellipsoidal planet

This paper presents the concise exact solution for predicting view-periods to be observed from a masked or unmasked tracking station on a tri-axial ellipsoidal surface. The new exact approach expresses the azimuth and elevation angles of a spacecraft in terms of the station-centered geodetic topocentric coordinates in an elegantly concise manner. A simple and efficient algorithm is developed to avoid costly repetitive computations in searching for neighborhoods near the rise and set times of each satellite orbit for each station. Only one search for each orbit is necessary for each station. Sample results indicate that the use of an assumed spherical earth instead of an 'actual' tri-axial ellipsoidal earth could introduce an error up to a few minutes in a view-period prediction for circular orbits of low or medium altitude. For an elliptical orbit of high eccentricity and long period, the maximum error could be even larger. The analytic treatment and the efficient algorithm are designed for geocentric orbits, but they should be applicable to interplanetary trajectories by an appropriate coordinates transformation at each view-period calculation. This analysis can be accomplished only by not using the classical orbital elements.

Tang, C. C. H.↗

NASA NTRS1986

A preliminary comparison of scanning vs nonscanning radiometer data from Earth Radiation Budget Satellite (ERBS)

A cross validation technique is used to simulate the radiation flux detected by the nonscanning wide FOV (WFOV) and medium FOV (MFOV) radiometers on the ERBS by integrating the top of atmosphere spectral radiance recorded with narrow FOV (NFOV) sensors. Consideration is given to both bidirectional and isotropic radiance contributions, including all shortwave and longwave components. A weighting procedure is defined to adjust for missing or inaccurate data records and a coordinate transformation is devised to account for angular discrepancies among the views of the WFOV, MFOV and NFOV sensors. Student t-test values were calculated for values generated for whole orbit average, morning, noon, evening and night subsatellite views.

Wu, X.↗

NASA NTRS1988

Overview of numerical codes developed for predicted electrothermal deicing of aircraft blades

An overview of the deicing computer codes that have been developed at the University of Toledo under sponsorship of the NASA-Lewis Research Center is presented. These codes simulate the transient heat conduction and phase change occurring in an electrothermal deicier pad that has an arbitrary accreted ice shape on its surface. The codes are one-dimensional rectangular, two-dimensional rectangular, and two-dimensional with a coordinate transformation to model the true blade geometry. All modifications relating to the thermal physics of the deicing problem that have been incorporated into the codes will be discussed. Recent results of reformulating the codes using different numerical methods to increase program efficiency are described. In particular, this reformulation has enabled a more comprehensive two-dimensional code to run in much less CPU time than the original version. The code predictions are compared with experimental data obtained in the NASA-Lewis Icing Research Tunnel with a UH1H blade fitted with a B. F. Goodrich electrothermal deicer pad. Both continuous and cyclic heater firing cases are considered. The major objective in this comparison is to illustrate which codes give acceptable results in different regions of the airfoil for different heater firing sequences.

Keith, Theo G.↗

NASA NTRS1987

Particle paths and phase plane for time-dependent similarity solutions of the one-dimensional Vlasov-Maxwell equations

The phase trajectories of particles in a plasma described by the one-dimensional Vlasov-Maxwell equations are determined qualitatively, analyzing exact general similarity solutions for the cases of temporally damped and growing (sinusoidal or localized) electric fields. The results of numerical integration in both untransformed and Lie-group point-transformed coordinates are presented in extensive graphs and characterized in detail. The implications of the present analysis for the stability of BGK equilibria are explored, and the existence of nonlinear solutions arbitrarily close to and significantly different from the BGK solutions is demonstrated.

Roberts, Dana Aaron↗

NASA NTRS1988

Multiple degree of freedom object recognition using optical relational graph decision nets

Multiple-degree-of-freedom object recognition concerns objects with no stable rest position with all scale, rotation, and aspect distortions possible. It is assumed that the objects are in a fairly benign background, so that feature extractors are usable. In-plane distortion invariance is provided by use of a polar-log coordinate transform feature space, and out-of-plane distortion invariance is provided by linear discriminant function design. Relational graph decision nets are considered for multiple-degree-of-freedom pattern recognition. The design of Fisher (1936) linear discriminant functions and synthetic discriminant function for use at the nodes of binary and multidecision nets is discussed. Case studies are detailed for two-class and multiclass problems. Simulation results demonstrate the robustness of the processors to quantization of the filter coefficients and to noise.

Casasent, David P.↗

NASA NTRS1988

A numerical simulation of the full two-dimensional electrothermal de-icer pad

The ability to predict the time-temperature history of electrothermal de-icer pads is important in the subsequent design of improved and more efficient versions. These de-icer pads are installed near the surface of aircraft components, for the specific purpose of removing accreted ice. The proposed numerical model can incorporate the full 2-D geometry through a section of a region (i.e., section of an airfoil), that current 1-D numerical codes are unable to do. Thus, the effects of irregular layers, curvature, etc., can now be accounted for in the thermal transients. Each layer in the actual geometry is mapped via a body-fitted coordinate transformation into uniform, rectangular computational grids. The relevant heat transfer equations are transformed and discretized. To model the phase change that might occur in any accreted ice, in an enthalpy formulation the phase change equations are likewise transformed and discretized. The code developed was tested against numerous classical numerical solutions, as well as against experimental de-icing data on a UH1H rotor blade obtained from the NASA Lewis Research Center. The excellent comparisons obtained show that this code can be a useful tool in predicting the performance of current de-icer models, as well as in the designing of future models.

Masiulaniec, Konstanty C.↗

NASA NTRS1989

Development and application of a program to calculate transonic flow around an oscillating three-dimensional wing using finite difference procedures

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. Difference equations are derived for harmonic transonic flow to include a coordinate transformation for swept and tapered planforms. A pilot program is developed for three-dimensional planar lifting surface configurations (including thickness) for the CRAY-XMP at Boeing Commercial Airplanes and for the CYBER VPS-32 at the NASA Langley Research Center. An investigation is made of the effect of the location of the outer boundaries on accuracy for very small reduced frequencies. Finally, the pilot program is applied to the flutter analysis of a rectangular wing.

Weatherill, Warren H.↗

NASA NTRS1989

Computational fluid dynamics research in three-dimensional zonal techniques

Patched-grid algorithms for the analysis of complex configurations with an implicit, upwind-biased Navier-Stokes solver were investigated. Conservative and non-conservative approaches for performing zonal interpolations were implemented. The latter approach yields the most flexible technique in that it can handle both patched and overlaid grids. Results for a two-dimensional blunt body problem show that either approach yield accurate steady-state shock locations and jump conditions. In addition, calculations of the turbulent flow through a hypersonic inlet on a three-zone grid show that the numerical prediction is in good agreement with the experimental results. Through the use of a generalized coordinate transformation at the zonal interface between two or more blocks, the algorithm can be applied to highly stretched viscous grids and to arbitrarily-shaped zonal boundaries. Applications were made to the F-18 aircraft at subsonic, high-alpha conditions, in support of the NASA High-Alpha Research Program. The calculations were compared to ground-based and flight test experiments and were used as a guide to understanding the ground-based tests, which are laminar and transitional, and their relationship to flight. Calculations about a complete reconnaissance aircraft were also performed in order to further demonstrate the capability of the patched-grid algorithm.

Walters, Robert W.↗

NASA NTRS1989

Numerical solution of periodic vortical flows about a thin airfoil

A numerical method is developed for computing periodic, three-dimensional, vortical flows around isolated airfoils. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Solutions for thin airfoils at zero degrees incidence to the mean flow are presented in this paper. Using an elliptic coordinate transformation, the computational domain is transformed into a rectangle. The Sommerfeld radiation condition is applied to the unsteady pressure on the grid line corresponding to the far field boundary. The results are compared with a Possio solver, and it is shown that for maximum accuracy the grid should depend on both the Mach number and reduced frequency. Finally, in order to assess the range of validity of the classical thin airfoil approximation, results for airfoils with zero thickness are compared with results for airfoils with small thickness.

Scott, James R.↗

NASA NTRS1988

Flight software operation of the Hubble Space Telescope fine guidance sensor

The Hubble Space Telescope (HST) is to carry five major scientific instruments to collect imagery, spectrographic, and photometric astronomical data. The Pointing Control System is designed to achieve pointing accuracies and line of sight jitter levels an order of magnitude less than can be achieved with ground mounted telescopes. This paper describes the operation of the pointing control system flight software in targeting a celestial object in a science instrument aperture and in performing the coordinate transformations necessary for commanding the fine guidance sensor and determining the attitude-error corrections.

Rodden, J. J.↗

NASA NTRS1989

A patched-grid algorithm for complex configurations directed towards the F-18 aircraft

A patched-grid algorithm for the analysis of complex configurations with an implicit, upwind-biased Navier-Stokes solver is presented. Results from both a spatial-flux and a time-flux conservation approach to patching across zonal boundaries are presented. A generalized coordinate transformation with a biquadratic geometric element is used at the zonal interface in order to treat highly stretched viscous grids and arbitrarily-shaped zonal boundaries. Applications are made to the F-18 forebody-strake configuration at subsonic, high-alpha conditions. Computed surface flow patterns compare well with ground-based and flight-test results; the large effect of Reynolds number on the forebody flowfield is shown.

Thomas, James L.↗