Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “approximation algorithm”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,369 records · Page 76

Numerical simulation of three-dimensional boattail afterbody flow fields

The thin shear layer approximations of the three-dimensional, compressible Navier-Stokes equations are solved for subsonic, transonic, and supersonic flow over axisymmetric boattail bodies at moderate angles of attack. The plume is modeled by a solid body configuration identical to those used in experimental tests. An implicit algorithm of second-order accuracy is used to solve the equations on the ILLIAC IV computer. The turbulence is expressed by an algebraic model applicable to three-dimensional flow fields with moderate separation. The computed results compare favorably with three different sets of experimental data reported by Reubush, Shrewsbury, and Benek, respectively

Deiwert, G. S.↗

AgRISTARS. Supporting research: Algorithms for scene modelling

The requirements for a comprehensive analysis of LANDSAT or other visual data scenes are defined. The development of a general model of a scene and a computer algorithm for finding the particular model for a given scene is discussed. The modelling system includes a boundary analysis subsystem, which detects all the boundaries and lines in the image and builds a boundary graph; a continuous variation analysis subsystem, which finds gradual variations not well approximated by a boundary structure; and a miscellaneous features analysis, which includes texture, line parallelism, etc. The noise reduction capabilities of this method and its use in image rectification and registration are discussed.

Rassbach, M. E.↗

On-line optimization of aircraft altitude and flight path angle dynamics

The optimization of aircraft altitude and flight path angle dynamics is addressed in a form suitable for on-line computation and control. The approach here is a direct extension of the work reported by Calise (1979), where singular perturbation methods were used to optimize position, energy and heading dynamics; it thus represents an optimal control solution that models all of the primary trajectory related dynamics. It is pointed out that the resulting algorithm can be regarded as a nonlinear feedback control law. The minimum time intercept of a fixed terminal point is used in setting the framework in which the analytical results are developed. The main theoretical result is that the dynamics, while not completely separable, can be approximated by singular perturbation methods when the control model includes relative position dynamics.

Calise, A. J.↗

Breadboard stellar tracker system test report

BASD has, in the past, developed several unique position tracking algorithms for charge transfer device (CTD) sensors. These algorithms provide an interpixel transfer function with the following characteristics: (1) high linearity; (2) simplified track logic; (3) high gain; and (4) high noise rejection. A previous test program using the GE charge injection device (CID) showed that accuracy for BASD's breadboard was limited to approximately 2% of a pixel (1 sigma) whereas analysis and simulation indicated the limit should be less than 0.5% of a pixel, assuming the limit to be detector response and dark current noise. The test program was conducted under NASA contract No. NAS8-34263. The test approach for that program did not provide sufficient data to identify the sources of error and left open the amount of contribution from parameters such as image distribution, geometric distortion and system alignment errors.

Kollodge, J. C.↗

Structural parameter identification of distributed systems using finite element approximation

A system identification technique is developed for classes of distributed systems using finite element approximations. Vibrating systems represented by partial differential equations have physical parameters associated with mass, stiffness, and damping distributions which need to be known in order to properly control and design mathematical models of the system. In order to identify these parameters a weighted least-squares algorithm and modified Newton-Raphson method is used for the identification process. The theory and technique is demonstrated by estimating the system parameters of a vibrating cantilever beam made up of several different structural properties.

Lee, K. Y.↗

Applications of square-root information filtering and smoothing in spacecraft orbit determination

The JPL (Jet Propulsion Laboratory) Orbit Determination Software System is a set of computer programs developed for the primary purpose of determining the flight path of deep-space mission spacecraft in NASA's Planetary Program and highly elliptical orbiting spacecraft in Earth orbit. The filtering processes available within the JPL Orbit Determination Software are discussed, and several examples are presented. In particular, solutions obtained by the Square Root Information Filter (SRIF) using Bierman's Estimation Subroutine Library (ESL) are discussed and compared with the solutions obtained by the singular value decomposition (SVD) technique. It is concluded that the SRIF filtering and smoothing algorithms are efficient and numerically stable for well-conditioned systems. The use of Bierman's ESL simplifies the task of maintaining the orbit determination software by providing efficient, tested filtering tools. For solving a large well-conditioned system (rank higher than 120), SRIF is approximately four times faster than SVD; however, for solving an ill-conditioned system, SVD is recommended.

Wang, Tseng-Chan↗

On some numerical schemes for transonic flow problems

New second-order-accurate finite-difference approximations for a class of nonlinear PDEs of mixed type, which includes the two-dimensional low-frequency transonic small-disturbance equation (TSD) and full-potential equation (FP), are presented. For the TSD equation, the scheme is implemented via a time-splitting algorithm; the inclusion of flux limiters keeps the total variation nonincreasing and eliminates spurious oscillations near shocks. Global-linear-stability, TVD, and entropy-stability results are proved. Numerical results for the flow over a thin airfoil are presented. Current techniques used to solve the TSD equation may easily be extended to second-order accuracy by this method. For the FP equation, the new scheme requires no subsonic/supersonic switching and no numerical flux biasing. Global linear stability for all values of the Mach number is proved.

Mostrel, Marco Mosche↗

Adaptive grid embedding for the two-dimensional flux-split Euler equations

A numerical algorithm is presented for solving the 2-D flux-split Euler equations using a multigrid method with adaptive grid embedding. The method uses an unstructured data set along with a system of pointers for communication on the irregularly shaped grid topologies. An explicit two-stage time advancement scheme is implemented. A multigrid algorithm is used to provide grid level communication and to accelerate the convergence of the solution to steady state. Results are presented for a subcritical airfoil and a transonic airfoil with 3 levels of adaptation. Comparisons are made with a structured upwind Euler code which uses the same flux integration techniques of the present algorithm. Good agreement is obtained with converged surface pressure coefficients. The lift coefficients of the adaptive code are within 2 1/2 percent of the structured code for the sub-critical case and within 4 1/2 percent of the structured code for the transonic case using approximately one-third the number of grid points.

Warren, Gary Patrick↗

Solution of steady-state one-dimensional conservation laws by mathematical programming

Solution techniques for a class of steady-state scalar conservation laws are developed analytically. Discretization by finite-volume formulas is employed to obtain an overdetermined system of algebraic equations, which are then perturbed nonsingularly (with perturbation coefficient = epsilon) and solved using the l(1) mathematical-programming algorithm of Seneta and Steiger (1984); this approach limits the matrix bandwidth to two, so that an explicit solution can be found efficiently. It is shown that, for small values of epsilon, the l(1) solutions exhibit sharp correctly located shocks and are nonoscillatory O(epsilon) approximations of the physically relevant solutions.

Lavery, J. E.↗

Modeling of composite beams and plates for static and dynamic analysis

A rigorous theory and the corresponding computational algorithms were developed for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants of a plate. Additionally, the analysis is used to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. It was decided that the variational-asymptotical method (VAM) would serve as a suitable framework in which to solve these types of problems. Work during this reporting period has progressed along two lines: (1) further evaluation of neo-classical plate theory (NCPT) as applied to shear-coupled laminates; and (2) continued modeling of plates with nonuniform thickness.

Hodges, Dewey H.↗

Scattering Cross Section of Sound Waves by the Modal Element Method

#he modal element method has been employed to determine the scattered field from a plane acoustic wave impinging on a two dimensional body. In the modal element method, the scattering body is represented by finite elements, which are coupled to an eigenfunction expansion representing the acoustic pressure in the infinite computational domain surrounding the body. The present paper extends the previous work by developing the algorithm necessary to calculate the acoustics scattering cross section by the modal element method. The scattering cross section is the acoustical equivalent to the Radar Cross Section (RCS) in electromagnetic theory. Since the scattering cross section is evaluated at infinite distance from the body, an asymptotic approximation is used in conjunction with the standard modal element method. For validation, the scattering cross section of the rigid circular cylinder is computed for the frequency range 0.1 is less than or equal to ka is less than or equal to 100. Results show excellent agreement with the analytic solution.

Baumeister, Kenneth J.↗

Numerical Simulation of Three-Dimensional Boattail Afterbody Flowfields

The thin shear-layer approximations of the three-dimensional, compressible Navier-Stokes equations are solved for subsonic, transonic, and supersonic now over axisymmetric boattail bodies at moderate angles of attack. The plume is simulated by a solid body configuration identical to those used In experimental tests. An implicit algorithm of second-order accuracy is used to solve the equations on the ILLIAC 4 computer. The turbulence is expressed by an algebraic model applicable to three-dimensional flowfields with moderate separation. The formulation used is attractive in its independence of boundary-layer parameters. Such a simple model, however, is incapable of supporting detailed quantitative descriptions of complex shear flows. Never-the-less, good qualitative comparisons are found with three different sets of experimental date. Quantitative improvement will depend on improved turbulence transport descriptions.

Deiwert, G. S.↗

Effects of Convective Transport of Solute and Impurities on Defect-Causing Kinetics Instabilities

For in-situ studies of the formation and evolution of step patterns during the growth of protein crystals, we have designed and assembled an experimental setup based on Michelson interferometry with the surface of the growing protein crystal as one of the reflective surfaces. The crystallization part of the device allows optical monitoring of a face of a crystal growing at temperature stable within 0.05 C in a developed solution flow of controlled direction and speed. The reference arm of the interferometer contains a liquid-crystal element that allows controlled shifts of the phase of the interferograms. We employ an image processing algorithm which combines five images with a pi/2 phase difference between each pair of images. The images are transferred to a computer by a camera capable of capturing 6-8 frames per second. The device allows data collection data regarding growth over a relatively large area (approximately .3 sq. mm) in-situ and in real time during growth. The estimated dept resolution of the phase shifting interferometry is about 100 A. The lateral resolution, depending on the zoom ratio, varies between 0.3 and 0.6 micrometers. We have now collected quantitative results on the onset, initial stages and development of instabilities in moving step trains on vicinal crystal surfaces at varying supersaturation, position on the facet, crystal size and temperature with the proteins ferritin, apoferritin and thaumatin. Comparisons with theory, especially with the AFM results on the molecular level processes, see below, allow tests of the rational for the effects of convective flows and, as a particular case, the lack thereof, on step bunching.

Vekilov, Peter G.↗

An Implicit LU/AF FDTD Method

There has been some recent work to develop two and three-dimensional alternating direction implicit (ADI) FDTD schemes. These ADI schemes are based upon the original ADI concept developed by Peaceman and Rachford and Douglas and Gunn, which is a popular solution method in Computational Fluid Dynamics (CFD). These ADI schemes work well and they require solution of a tridiagonal system of equations. A new approach proposed in this paper applies a LU/AF approximate factorization technique from CFD to Maxwell s equations in flux conservative form for one space dimension. The result is a scheme that will retain its unconditional stability in three space dimensions, but does not require the solution of tridiagonal systems. The theory for this new algorithm is outlined in a one-dimensional context for clarity. An extension to two and threedimensional cases is discussed. Results of Fourier analysis are discussed for both stability and dispersion/damping properties of the algorithm. Results are presented for a one-dimensional model problem, and the explicit FDTD algorithm is chosen as a convenient reference for comparison.

Beggs, John H.↗

Progress of a Cross-correlation Based Optical Strain Measurement Technique for Detecting Radial Growth on a Rotating Disk

The Aeronautical Sciences Project under NASAs Fundamental Aeronautics Program is extremely interested in the development of fault detection technologies, such as optical surface measurements in the internal parts of a flow path, for in situ health monitoring of gas turbine engines. In situ health monitoring has the potential to detect flaws, i.e. cracks in key components, such as engine turbine disks, before the flaws lead to catastrophic failure. In the present study, a cross-correlation imaging technique is investigated in a proof-of-concept study as a possible optical technique to measure the radial growth and strain field on an already cracked sub-scale turbine engine disk under loaded conditions in the NASA Glenn Research Centers High Precision Rotordynamics Laboratory. The optical strain measurement technique under investigation offers potential fault detection using an applied background consisting of a high-contrast random speckle pattern and imaging the background under unloaded and loaded conditions with a CCD camera. Spinning the cracked disk at high speeds induces an external load, resulting in a radial growth of the disk of approximately 50.8-m in the flawed region and hence, a localized strain field. When imaging the cracked disk under static conditions, the disk will appear shifted. The resulting background displacements between the two images will then be measured using the two-dimensional cross-correlation algorithms implemented in standard Particle Image Velocimetry (PIV) software to track the disk growth, which facilitates calculation of the localized strain field. In order to develop and validate this optical strain measurement technique an initial proof-of-concept experiment is carried out in a controlled environment. Using PIV optimization principles and guidelines, three potential backgrounds, for future use on the rotating disk, are developed and investigated in the controlled experiment. A range of known shifts are induced on the backgrounds; reference and data images are acquired before and after the induced shift, respectively, and the images are processed using the cross- correlation algorithms in order to determine the background displacements. The effectiveness of each background at resolving the known shift is evaluated and discussed in order to choose to the most suitable background to be implemented onto a rotating disk in the Rotordynamics Lab. Although testing on the rotating disk has not yet been performed, the driving principles behind the development of the present optical technique are based upon critical aspects of the future experiment, such as the amount of expected radial growth, disk analysis, and experimental design and are therefore addressed in the paper.

Clem, Michelle M.↗

Automatic Aircraft Collision Avoidance System and Method

The invention is a system and method of compressing a DTM to be used in an Auto-GCAS system using a semi-regular geometric compression algorithm. In general, the invention operates by first selecting the boundaries of the three dimensional map to be compressed and dividing the three dimensional map data into regular areas. Next, a type of free-edged, flat geometric surface is selected which will be used to approximate terrain data of the three dimensional map data. The flat geometric surface is used to approximate terrain data for each regular area. The approximations are checked to determine if they fall within selected tolerances. If the approximation for a specific regular area is within specified tolerance, the data is saved for that specific regular area. If the approximation for a specific area falls outside the specified tolerances, the regular area is divided and a flat geometric surface approximation is made for each of the divided areas. This process is recursively repeated until all of the regular areas are approximated by flat geometric surfaces. Finally, the compressed three dimensional map data is provided to the automatic ground collision system for an aircraft.

Skoog, Mark↗

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The continuous cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗

Guidance and Control System for a Satellite Constellation

A distributed guidance and control algorithm was developed for a constellation of satellites. The system repositions satellites as required, regulates satellites to desired orbits, and prevents collisions. 1. Optimal methods are used to compute nominal transfers from orbit to orbit. 2. Satellites are regulated to maintain the desired orbits once the transfers are complete. 3. A simulator is used to predict potential collisions or near-misses. 4. Each satellite computes perturbations to its controls so as to increase any unacceptable distances of nearest approach to other objects. a. The avoidance problem is recast in a distributed and locally-linear form to arrive at a tractable solution. b. Plant matrix values are approximated via simulation at each time step. c. The Linear Quadratic Gaussian (LQG) method is used to compute perturbations to the controls that will result in increased miss distances. 5. Once all danger is passed, the satellites return to their original orbits, all the while avoiding each other as above. 6. The delta-Vs are reasonable. The controller begins maneuvers as soon as practical to minimize delta-V. 7. Despite the inclusion of trajectory simulations within the control loop, the algorithm is sufficiently fast for available satellite computer hardware. 8. The required measurement accuracies are within the capabilities of modern inertial measurement devices and modern positioning devices.

Bryson, Jonathan Lamar↗