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NASA NTRS1972

Automated design and optimization of flexible booster autopilots via linear programming, volume 1

A nonlinear programming technique was developed for the automated design and optimization of autopilots for large flexible launch vehicles. This technique, which resulted in the COEBRA program, uses the iterative application of linear programming. The method deals directly with the three main requirements of booster autopilot design: to provide (1) good response to guidance commands; (2) response to external disturbances (e.g. wind) to minimize structural bending moment loads and trajectory dispersions; and (3) stability with specified tolerances on the vehicle and flight control system parameters. The method is applicable to very high order systems (30th and greater per flight condition). Examples are provided that demonstrate the successful application of the employed algorithm to the design of autopilots for both single and multiple flight conditions.

Hauser, F. D.↗

NASA NTRS1979

Low speed airfoil design and analysis

A low speed airfoil design and analysis program was developed which contains several unique features. In the design mode, the velocity distribution is not specified for one but many different angles of attack. Several iteration options are included which allow the trailing edge angle to be specified while other parameters are iterated. For airfoil analysis, a panel method is available which uses third-order panels having parabolic vorticity distributions. The flow condition is satisfied at the end points of the panels. Both sharp and blunt trailing edges can be analyzed. The integral boundary layer method with its laminar separation bubble analog, empirical transition criterion, and precise turbulent boundary layer equations compares very favorably with other methods, both integral and finite difference. Comparisons with experiment for several airfoils over a very wide Reynolds number range are discussed. Applications to high lift airfoil design are also demonstrated.

Eppler, R.↗

NASA NTRS1979

A split finite element algorithm for the compressible Navier-Stokes equations

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Baker, A. J.↗

NASA NTRS1979

An analysis of thermal stress and gas bending effects on vibrations of compressor rotor stages

A preliminary study conducted by Kerrebrock et al. (1976) has shown that the torsional rigidity of untwisted thin blades of a transonic compressor can be reduced significantly by transient thermal stresses. The aerodynamic loads have various effects on blade vibration. One effect is that gas bending loads may result in a bending-torsion coupling which may change the characteristics of the torsion and bending vibration of the blade. For a general study of transient-temperature distribution within a rotor stage, a finite-element heat-conduction analysis was developed. The blade and shroud are divided into annular elements. With a temperature distribution obtained from the heat-conduction analysis and a prescribed gas bending load distribution along the blade span, the static deformation and moment distributions of the blade can be solved iteratively using the finite-element method. The reduction of the torsional rigidity of pretwisted blades caused by the thermal stress effect is then computed. The dynamic behavior of the blade is studied by a modified Galerkin's method.

Chen, L.-T.↗

NASA NTRS1982

Numerical comparisons of nonlinear convergence accelerators

As part of a continuing program of numerical tests of convergence accelerators, the iterated Aitken's Delta-squared method, Wynn's epsilon algorithm, Brezinski's theta algorithm, and Levin's u transform are compared on a broad range of test problems: linearly convergence alternating, monotone, and irregular-sign series, logarithmically convergent series, power method and Bernoulli method sequences, alternating and monotone asymptotic series, and some perturbation series arising in applications. In each category either the epsilon algorithm or the u transform gives the best results of the four methods tested. In some cases differences among methods are slight, and in others they are quite striking.

Smith, D. A.↗

NASA NTRS1983

Some characteristic quantities of Karman-Trefftz profiles

For von Karman-Trefftz profiles, the characteristics which determine profile shape (profile nose dimensions, maximum thickness and position: tail slope and curvature) are stated as a function of transformation variables using the Timman method. The profile is obtained by iterative deformation of a von Karman profile with known transformation, corresponding as well as possible to the desired profile. The figures and relations which enable a good choice of the required profile are given.

Blom, J. J. H.↗

NASA NTRS1986

Evaluation of several modal methods for transient structural analysis

The convergence properties of three modal methods for solving structural transient response (STR) problems are examined by comparing the accuracy of the total number of modes used to represent the responses. The goal is to identify a method which involves as few degrees of freedom as possible. Two mode superposition methods, the mode displacement method (MDM) and the mode acceleration method (MAM), are fitted with equivalent expressions for damped response. An error norm is employed to compare the accuracies of the methods in calculating displacements, moments, and shear forces for a viscously-damped cantilevered beam experiencing several dynamic loading conditions and levels of damping. The MAM converges quicker and uses fewer dof, mainly because it has a pseudo-static response term which accounts for some of the flexibility of higher modes. A third method, which integrates the convolution integral iteratively over time, generates a higher order approximation to the STR with a reduced number of modes. It converges fastest among the three, but requires definition of an appropriate forcing function. Finally, the MAM and MDM models are applied to study the effects of the forcing frequency and the initial conditions.

Camarda, Charles J.↗

NASA NTRS1989

Development of kinematic equations and determination of workspace of a 6 DOF end-effector with closed-kinematic chain mechanism

This report presents results from the research grant entitled Active Control of Robot Manipulators, funded by the Goddard Space Flight Center, under Grant NAG5-780, for the period July 1, 1988 to January 1, 1989. An analysis is presented of a 6 degree-of-freedom robot end-effector built to study telerobotic assembly of NASA hardware in space. Since the end-effector is required to perform high precision motion in a limited workspace, closed-kinematic mechanisms are chosen for its design. A closed-form solution is obtained for the inverse kinematic problem and an iterative procedure employing Newton-Raphson method is proposed to solve the forward kinematic problem. A study of the end-effector workspace results in a general procedure for the workspace determination based on link constraints. Computer simulation results are presented.

Nguyen, Charles C.↗

NASA NTRS1989

Analysis of the transient compressible vapor flow in heat pipe

The transient compressible one-dimensional vapor flow dynamics in a heat pipe is modeled. The numerical results are obtained by using the implicit non-iterative Beam-Warming finite difference method. The model is tested for simulated heat pipe vapor flow and actual flow in cylindrical heat pipes. A good comparison of the present transient results for the simulated heat pipe vapor flow with the previous results of a two-dimensional numerical model is achieved and the steady state results are in agreement with the existing experimental data. The transient behavior of the vapor flow under subsonic, sonic, and supersonic speeds and high mass flow rates are successfully predicted. The one-dimensional model also describes the vapor flow dynamics in cylindrical heat pipes at high temperatures.

Jang, Jong Hoon↗

NASA NTRS1988

Inversion of the Solar Rotation Rate Versus Depth and Latitude

Three differential inversion techniques were used to compute the internal solar rotation rate from several sets of n-averaged frequency splittings. An iterative variation of the spectral expansion method; the optimal averaging kernel method; and a piecewise constant constrained least square method were used to invert the data. Each computation was carried out independently. While they present similar trends, each of the solutions differs in detail. A consistent feature in all the inversions is the disappearance of differential rotation below the base of the convection zone. Also, a strong differential signature in the deeper part of the convection zone is present in most of the solutions. A slow decrease of the rotation rate with depth for the equatorial and midlatitude curves is significant in the spectral expansion and the least square results but only marginally apparent in the averaging kernel results.

Korzennik, Sylvain G.↗

NASA NTRS1989

Analysis of the transient compressible vapor flow in heat pipes

The transient compressible one-dimensional vapor flow dynamics in a heat pipe is modeled. The numerical results are obtained by using the implicit non-iterative Beam-Warming finite difference method. The model is tested for simulated heat pipe vapor flow and actual vapor flow in cylindrical heat pipes. A good comparison of the present transient results for the simulated heat pipe vapor flow with the previous results of a two-dimensional numerical model is achieved and the steady state results are in agreement with the existing experimental data. The transient behavior of the vapor flow under subsonic, sonic, and supersonic speeds and high mass flow rates are successfully predicted. The one-dimensional model also describes the vapor flow dynamics in cylindrical heat pipes at high temperatures.

Jang, J. H.↗

NASA NTRS1991

Analysis and design of a six-degree-of-freedom Stewart platform-based robotic wrist

The kinematic analysis and implementation of a six degree of freedom robotic wrist which is mounted to a general open-kinetic chain manipulator to serve as a restbed for studying precision robotic assembly in space is discussed. The wrist design is based on the Stewart Platform mechanism and consists mainly of two platforms and six linear actuators driven by DC motors. Position feedback is achieved by linear displacement transducers mounted along the actuators and force feedback is obtained by a 6 degree of freedom force sensor mounted between the gripper and the payload platform. The robot wrist inverse kinematics which computes the required actuator lengths corresponding to Cartesian variables has a closed-form solution. The forward kinematics is solved iteratively using the Newton-Ralphson method which simultaneously provides a modified Jacobian Matrix which relates length velocities to Cartesian translational velocities and time rates of change of roll-pitch-yaw angles. Results of computer simulation conducted to evaluate the efficiency of the forward kinematics and Modified Jacobian Matrix are discussed.

Nguyen, Charles C.↗

NASA NTRS1991

Analysis of the one-dimensional transient compressible vapor flow in heat pipes

The transient compressible one-dimensional vapor flow dynamics in a heat pipe is modeled. The numerical results are obtained by using the implicit non-iterative Beam-Warming finite difference method. The model is tested for simulated heat pipe vapor flow and actual vapor flow in cylindrical heat pipes. A good comparison of the present transient results for the simulated heat pipe vapor flow with the previous results of a two-dimensional numerical model is achieved and the steady state results are in agreement with the existing experimental data. The transient behavior of the vapor flow under subsonic, sonic, and supersonic speeds as well as high mass flow rates are successfully predicted.

Jang, Jong H.↗

NASA NTRS1992

A variable phase function approach for the inversion of lidar return signals

A variable phase function is developed. This function may be used for the inversion of lidar data in an iterative process. Numerical simulations of this method were performed successfully, demonstrating fast convergence of the particulate phase function. The method will be used in the future to evaluate extinction and backscattering corrections for an Ultra-Violet Differential Absorption Lidar (UV-DIAL) system measuring tropospheric ozone concentrations.

Kovalev, V. A.↗

NASA NTRS1994

Simulation Of Probabilistic Wind Loads On A Building

Method of simulating probabilistic windloads on building developed. Numerical results of simulation used to assess reliability of building and risk associated with tendencies of large gusts or high steady winds to cause building to sway, buckle, and/or overturn. Using method to analyze proposed design in iterative design cycle, building designed for specified reliability.

Chamis, Christos C.↗

NASA NTRS1995

Method for the calculation of spacecraft umbra and penumbra shadow terminator points

A method for calculating orbital shadow terminator points is presented. The current method employs the use of an iterative process which is used for an accurate determination of shadow points. This calculation methodology is required since orbital perturbation effects can introduce large errors when a spacecraft orbits a planet in a high altitude and/or highly elliptical orbit. To compensate for the required iteration methodology, all reference frame change definitions and calculations are performed with quaternions. Quaternion algebra significantly reduces the computational time required for the accurate determination of shadow terminator points.

Ortizlongo, Carlos R.↗

NASA NTRS1995

Reliability enhancement of Navier-Stokes codes through convergence acceleration

Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.

Merkle, Charles L.↗

NASA NTRS1999

Optimized System Identification

In system identification, one usually cares most about finding a model whose outputs are as close as possible to the true system outputs when the same input is applied to both. However, most system identification algorithms do not minimize this output error. Often they minimize model equation error instead, as in typical least-squares fits using a finite-difference model, and it is seen here that this distinction is significant. Here, we develop a set of system identification algorithms that minimize output error for multi-input/multi-output and multi-input/single-output systems. This is done with sequential quadratic programming iterations on the nonlinear least-squares problems, with an eigendecomposition to handle indefinite second partials. This optimization minimizes a nonlinear function of many variables, and hence can converge to local minima. To handle this problem, we start the iterations from the OKID (Observer/Kalman Identification) algorithm result. Not only has OKID proved very effective in practice, it minimizes an output error of an observer which has the property that as the data set gets large, it converges to minimizing the criterion of interest here. Hence, it is a particularly good starting point for the nonlinear iterations here. Examples show that the methods developed here eliminate the bias that is often observed using any system identification methods of either over-estimating or under-estimating the damping of vibration modes in lightly damped structures.

Juang, Jer-Nan↗