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The author has identified the following significant results. A more efficient algorithm for calculating surface temperature was developed. This algorithm was determined to be essentially exact, and relative accuracies in determining thermal inertia of the finite difference and the linear Fourier series algorithms were approximately 5% for both. A procedure for performing geometric registration was developed.
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
Program aids in design of shockless airfoils, assists development of fuel-conserving, supercritical wings. Algorithm calculates approximate airfoil shape given prescribed pressure distribution. This allows design of families of transonic airfoils for use in aircraft wings or turbine and compressor blades. Program is written in FORTRAN IV for batch execution on CDC-6000.
Implicit approximate-factorization algorithms have been developed that use monotone methods for the calculation of steady and unsteady transonic flows governed by the small-disturbance-potential equation. These algorithms use the new Engquist-Osher switch in the type-dependent differencing in place of the standard Murman-Cole switch. The resulting algorithms are more stable; hence, calculations can be done more efficiently. For steady flows, the convergence rate is about 35% faster, and for unsteady flows the allowable time step is about 10 times larger. These improvements are achieved with no increase in computer storage and with only minor modifications in codes that use the Murman-Cole switch. Also an implicit algorithm has been developed for the steady full-potential equation in one-dimension, which uses monotone methods.
The compressible Navier-Stokes equations for two-dimensional and three-dimensional flow are solved for nonaxisymmetric nozzle configurations. Both internal flow alone and combined internal and external flow cases are considered. An implicit approximate factorization algorithm is employed to solve the governing equations which are cast in terms of a body-fitted coordinate system. Turbulence closure is accomplished with a composite algebraic model. Two-dimensional results for a wedge plug nozzle flow in the form of surface pressures compare favorably with experimental data. Three-dimensional calculations for two nonaxisymmetric nozzles are also presented and compared with data.
A fast, fully implicit, approximate factorization algorithm designed to solve the conservative full-potential equation is used to compute lifting-wing flow fields with embedded transonic flow. The computer program (TWING - transonic wing analysis) uses an elliptic-solver numerical grid-generation routine and is capable of analyzing arbitrary wing geometries with sweep, twist, taper, and section variation. Computed flowfield results for several wing geometries are presented; they demonstrate substantial improvement in convergence speed relative to the FL028 computer code.
A numerical procedure is presented for computing the unsteady transonic flow field about three dimensional swept wings undergoing general time dependent motion. The outer inviscid portion of the flow is assumed to be governed by the modified unsteady transonic small disturbance potential equation which is integrated in the time domain by means of an efficient alternating direction implicit approximate factorization algorithm. Gross dominant effects of the shock boundary layer interaction are accounted for by a simple empirically defined model. Viscous flow regions adjacent to the wing surface and in the trailing wake are described by a set of integral equations appropriate for compressible turbulent shear layers. The two dimensional boundary layer equations are applied quasi-statically stripwise across the span. Coupling with the outer inviscid flow is implemented through use of the displacement thickness concept within the limitations of small disturbance theory. Validity of the assumptions underlying the method is established by comparison with experimental data for the flow about a high aspect ratio transport wing having an advanced airfoil section.
An implicit finite difference code cast in general curvilinear coordinates is further developed for three-dimensional incompressible turbulent flows. The code is based on the method of pseudocompressibility and utilizes the Beam and Warming implicit approximate factorization algorithm to achieve computational efficiency. A multiple-zone method is further extended to include composite-grids to overcome the excessive computer memory required for solving turbulent flows in complex three-dimensional geometries. A simple turbulence model is proposed for internal flows. The code is being used for the Space Shuttle Main Engine (SSME) internal flow analyses.
Implicit finite difference schemes for solving two-dimensional and three-dimensional Euler and thin layer Navier-Stokes equations are addressed. The methods are demonstrated in fully vectorized codes for a Cray type architecture. The Beam and Warming implicit approximate factorization algorithm in generalized coordinates is used. The methods are either time accurate or accelerated non-time accurate steady state schemes. Acceleration and efficiency modifications such as matrix reduction, diagonalization, and flux split schemes are presented. Two dimensional inviscid and viscous calculations (e.g., airfoils with a deflected spoiler, circulation control airfoils, and unsteady buffeting) and of three dimensional viscous elliptical bodies, exhausting boattails, and generic oblique wing computations are discussed.
Properly combining optical design with 3-by-3 element mask reduces number of required computations by factor of as much as 100. Spatial and spatial-frequency responses obtained in system of combination of optical design and signal-processing algorithm. Closely approximate difference-of-Gaussian-function response.
The purpose of this study is to examine in detail incompressible laminar and turbulent flows inside a turnaround duct with and without guide vanes and to investigate the effects of vanes on the flow characteristics. To perform this study, an implicit finite difference code cast in general curvilinear coordinates is further developed. The code is based on the method of pseudo-compressibility and utilize ADI or implicit approximate factorization algorithm to achieve computational efficiency. Method of segmental sweeping is developed to overcome the multiple-zone problem due to imposition of guide vanes. In the present study, several test cases have been computed. These test cases include laminar and turbulent flows inside a turnaround duct without and with two or three guide vanes. The study reveals that: (1) there exists large recirculation zones inside the duct if no vanes are present; (2) properly shaped and positional guide vanes are effective in eliminating flow separation; and (3) laminar and turbulent flows have similar flow features. But turbulent flow has less total pressure drop.
Incompressible viscous flow inside the turnaround duct, the fuel bowl, the transfer duct and the racetrack of the Space Shuttle Main Engine (SSME) Hot Gas Manifold (HGM) has been computed using the method of pseudo-compressibility together with an implicit, approximate-factorization algorithm. A multiple-zone method is used to make solution of flows in complex geometries easy. A model which predicts the pressure loading for the shield and the injector post arrangement without solving the complex flow field in the main injector region is proposed. The computed results show good qualitative agreement with experimental data.
In this paper, an algorithm is presented for image data compression based upon vector quantization of the two-dimensional discrete cosine transformed coefficients. The ac energies of the transformed blocks are used to classify them into eight different ac classes. The ac coefficients of the transformed blocks of class one are set to zero, while those of classes two through eight are transmitted by seven different code books. The dc coefficients of all eight classes are scalar quantized by an adaptive uniform quantizer. As a result, only 4.5 bits instead of eight bits are required to transmit the dc coefficient with negligible additional degradation. Overall, this algorithm requires approximately 0.75 bits per pixel and gives an average reconstruction error of 7.1.
A transonic unsteady aerodynamic and aeroelasticity code has been developed for application to realistic aircraft configurations. The new code is called CAP-TSD which is an acronym for Computational Aeroelasticity Program - Transonic Small Disturbance. The CAP-TSD code uses a time-accurate approximate factorization algorithm for solution of the unsteady transonic small-disturbance equation that is efficient for solution of steady and unsteady transonic flow problems including supersonic freestream flows. The new code can treat complete aircraft geometries with multiple lifting surfaces and bodies. Applications to wings in supersonic freestream flow are presented. Comparisons with selected exact solutions from linear theory are presented showing generally favorable results. Calculations for both steady and oscillatory cases for the F-5 and RAE tailplane models are compared with experimental data and also show good overall agreement. Selected steady calculations are further compared with a steady flow Euler code.
The Van Leer method of flux-vector splitting for the Euler equations is extended for use on moving meshes and all the properties of the original splittings are maintained. The solution is advanced in time with an implicit, approximately factored algorithm. The use of multiple grids to reduce the computer time is investigated. A substantial reduction in computer time to resolve a pitching cycle is easily obtained with virtually no loss in accuracy. A subiterative procedure to eliminate factorization and linearization errors so that larger time steps can be used is also investigated. Subsequent computations show good agreement with experimental data for transonic and supersonic airfoils and wings undergoing forced pitching oscillation.
The purpose of this study is to examine in detail incompressible laminar and turbulent flows inside the oxidizer side Hot Gas Manifold of the Space Shuttle Main Engine. To perform this study, an implicit finite difference code cast in general curvilinear coordinates is further developed. The code is based on the method of pseudo-compressibility and utilize ADI or implicit approximate factorization algorithm to achieve computational efficiency. A multiple-zone method is developed to overcome the complexity of the geometry. In the present study, the laminar and turbulent flows in the oxidizer side Hot Gas Manifold have been computed. The study reveals that: (1) there exists large recirculation zones inside the bowl if no vanes are present; (2) strong secondary flows are observed in the transfer tube; and (3) properly shaped and positioned guide vanes are effective in eliminating flow separation.
Detailed knowledge of robot joints not required. Algorithm generates approximate mathematical models of coordinates of joints of robot as functions of coordinates of points in images of work region viewed by television cameras. Joint coordinates necessary to position and orient end effector calculated by mathematical models fitted to experimentally determined data on positions, orientations, and joint coordinates. Generates models as functions of desired location of end effector of robot. Does not require priori knowledge of kinematic equations of robot.
A transonic unsteady aerodynamic and aeroelasticity code called CAP-TSD was developed for application to realistic aircraft configurations. The code permits the calculation of steady and unsteady flows about complete aircraft configurations for aeroelastic analysis in the flutter critical transonic speed range. The CAP-TSD code uses a time accurate approximate factorization algorithm for solution of the unsteady transonic small disturbance potential equation. An overview is given of the CAP-TSD code development effort and results are presented which demonstrate various capabilities of the code. Calculations are presented for several configurations including the General Dynamics 1/9 scale F-16 aircraft model and the ONERA M6 wing. Calculations are also presented from a flutter analysis of a 45 deg sweptback wing which agrees well with the experimental data. Descriptions are presented of the CAP-TSD code and algorithm details along with results and comparisons which demonstrate these recent developments in transonic computational aeroelasticity.