SEARCH · Search NASA

Results for “Complete linearization method”

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.

SourceResearch connectionFrom yearThrough year

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

At least 91 records · Page 5

All sources NASA NTRS DOE OSTI

NASA NTRS1977

Simplified solution for elliptical-contact deformation between two elastic solids

A linear regression by the method of least squares is made on the geometric variables that occur in the equation for elliptical-contact deformation. The ellipticity and the complete elliptic integrals of the first and second kind are expressed as a function of the x,y-plane principal radii. The ellipticity was varied from 1 (circular contact) to 10 (a configuration approaching line contact). The procedure for solving these variables without the use of charts or a high-speed computer would be quite tedious. These simplified equations enable one to calculate easily the elliptical-contact deformation to within 3 percent accuracy without resorting to charts or numerical methods.

Brewe, D. E.↗

NASA NTRS1992

Effect of surface tension on the onset of convection in a double-diffusive layer

The effect of surface tension on the stability of a double-diffusive layer is considered using linear stability analysis. The surface tension is assumed to vary linearly with temperature and solute concentration. The eigenvalue problem is solved by the Galerkin method. Results show that the predicted stability boundary based on Marangoni effects alone is completely altered in the presence of buoyancy effects induced by low gravity levels (about 10 exp -5 g). At reduced gravity levels, salt-finger instability may onset in the overstable mode due to the stabilizing effect of surface tension. Fluid properties in terms of the Prandtl and the Lewis numbers have a profound effect on the stability conditions; opposite stability characteristics are found in salt solutions and in molten metals.

Chen, C. F.↗

NASA NTRS2008

Design and Field Test of a Mass Efficient Crane for Lunar Payload Handling and Inspection: The Lunar Surface Manipulation System

Devices for lifting, translating and precisely placing payloads are critical for efficient Earthbased construction operations. Both recent and past studies have demonstrated that devices with similar functionality will be needed to support lunar outpost operations. Lunar payloads include: a) prepackaged hardware and supplies which must be unloaded from landers and then accurately located at their operational site, b) sensor packages used for periodic inspection of landers, habitat surfaces, etc., and c) local materials such as regolith which require grading, excavation and placement. Although several designs have been developed for Earth based applications, these devices lack unique design characteristics necessary for transport to and use on the harsh lunar surface. These design characteristics include: a) composite components, b) compact packaging for launch, c) simple in-field reconfiguration and repair, and d) support for tele-operated or automated operations. Also, in contrast to Earth-based construction, where special purpose devices dominate a construction site, a lunar outpost will require versatile devices which provide operational benefit from initial construction through sustained operations. This paper will detail the design of a unique, high performance, versatile lifting device designed for operations on the lunar surface. The device is called the Lunar Surface Manipulation System to highlight the versatile nature of the device which supports conventional cable suspended crane operations as well as operations usually associated with a manipulator such as precise positioning where the payload is rigidly grappled by a tool attached to the tip of the device. A first generation test-bed to verify design methods and operational procedures is under development at the NASA Langley Research Center and recently completed field tests at Moses Lake Washington. The design relied on non-linear finite element analysis which is shown to correlate favorably with laboratory experiments. A key design objective, reviewed in this paper, is the device s simplicity, resulting from a focus on the minimum set of functions necessary to perform payload offload. Further development of the device has the potential for significant mass savings, with a high performance device incorporating composite elements estimated to have a mass less than 3% of the mass of the maximum lunar payload lifted at the tip. The paper will conclude with future plans for expanding the operational versatility of the device.

Doggett, William R.↗

NASA NTRS1989

An interpretation and solution of ill-conditioned linear equations

Data insufficiency, poorly conditioned matrices and singularities in equations occur regularly in complex optimization, correlation, and interdisciplinary model studies. This work concerns itself with two methods of obtaining certain physically realistic solutions to ill-conditioned or singular algebraic systems of linear equations arising from such studies. Two efficient computational solution procedures that generally lead to locally unique solutions are presented when there is insufficient data to completely define the model, or a least-squares error formulation of this system results in an ill-conditioned system of equations. If it is assumed that a reasonable estimate of the uncertain data is available in both cases cited above, then we shall show how to obtain realistic solutions efficiently, in spite of the insufficiency of independent data. The proposed methods of solution are more efficient than singular-value decomposition for dealing with such systems, since they do not require solutions for all the non-zero eigenvalues of the coefficient matrix.

Ojalvo, I. U.↗

NASA NTRS2018

An Algorithm for Trajectory Generation in Redundant Manipulators with Joint Transmission Accommodation

Trajectory generation for manipulators involves generating incremental updates of joint variables to achieve a desired end–eﬀector motion. The Jacobian matrix maps incremental joint motion to incremental end–eﬀector motion in a linear fashion and is typically used in manipulator trajectory generation algorithms. In the case of a redundant manipulator, the Jacobian matrix is not square or invertible and therefore algorithms based on pseudoinverses and their variations are commonly used for trajectory generation. These methods either are computationally not eﬃcient or do not utilize all the joints in motion generation and therefore do not completely exploit the redundancy of the manipulator. The method presented in this paper is a simple method that maximizes transmission of all joint variables onto a desired end–eﬀector motion trajectory. The method is based on aligning the null–space of an augmented Jacobian matrix with the path of the desired end–eﬀector motion, from which a linear combination of joints that projects fully onto the desired end–eﬀector trajectory is obtained. In this manner, all joints of the redundant manipulator are used to generate the end–eﬀector trajectory accommodating the ability of each joint in terms of its motion transmission.

Ravani, Bahram↗

NASA NTRS1994

Fourth order difference methods for hyperbolic IBVP's

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Gustafsson, Bertil↗

NASA NTRS1973

A review of developments in the theory of elasto-plastic flow

The theory of elasto-plastic flow is developed so that it may accommodate features such as work-hardening, anisotropy, plastic compressibility, non-continuous loading including local or global unloading, and others. A complete theory is given in quasi-linear form; as a result, many useful attributes are accessible. Several integral theorems may be written, finite deformations may be incorporated, and efficient methods for solving problems may be developed; these and other aspects are described in some detail. The theory is reduced to special forms for 2-space, and extensive experience in solving such problems is cited.

Swedlow, J. L.↗

NASA NTRS1979

A simplified computer program for the prediction of the linear stability behavior of liquid propellant combustors

A program for predicting the linear stability of liquid propellant rocket engines is presented. The underlying model assumptions and analytical steps necessary for understanding the program and its input and output are also given. The rocket engine is modeled as a right circular cylinder with an injector with a concentrated combustion zone, a nozzle, finite mean flow, and an acoustic admittance, or the sensitive time lag theory. The resulting partial differential equations are combined into two governing integral equations by the use of the Green's function method. These equations are solved using a successive approximation technique for the small amplitude (linear) case. The computational method used as well as the various user options available are discussed. Finally, a flow diagram, sample input and output for a typical application and a complete program listing for program MODULE are presented.

Mitchell, C. E.↗

NASA NTRS2016

The Relaxation Matrix for Symmetric Tops with Inversion Symmetry. I. Effects of Line Coupling on Self-Broadened v (sub 1) and Pure Rotational Bands of NH3

The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of selfbroadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).

Trajectory models↗

NASA NTRS2000

Self-Scheduling Parallel Methods for Multiple Serial Codes with Application to WOPWOP

This paper presents a scheme for efficiently running a large number of serial jobs on parallel computers. Two examples are given of computer programs that run relatively quickly, but often they must be run numerous times to obtain all the results needed. It is very common in science and engineering to have codes that are not massive computing challenges in themselves, but due to the number of instances that must be run, they do become large-scale computing problems. The two examples given here represent common problems in aerospace engineering: aerodynamic panel methods and aeroacoustic integral methods. The first example simply solves many systems of linear equations. This is representative of an aerodynamic panel code where someone would like to solve for numerous angles of attack. The complete code for this first example is included in the appendix so that it can be readily used by others as a template. The second example is an aeroacoustics code (WOPWOP) that solves the Ffowcs Williams Hawkings equation to predict the far-field sound due to rotating blades. In this example, one quite often needs to compute the sound at numerous observer locations, hence parallelization is utilized to automate the noise computation for a large number of observers.

Long, Lyle N.↗

NASA NTRS1971

Unsteady flow through compressor stages

The application of the nonsteady Lax-Wendroff technique to problems with asymptotically periodic solution which offers a potentially powerful method for the investigation of the interaction of rotating and stationary blade rows in turbomachinery is reported. A technique for specifying boundary conditions with phase lag was developed to accomplish this. A complete nonlinear analysis is carried out numerically to determine the entire flow field without recourse to the assumption of small disturbances of linear equations which underlie the previous acoustic theories. The result, obtained for the case of equal number of rotor and stator blades shows that transonic flow can be handled without difficulty. In addition, the program is not limited with regard to blade thickness, camber or loading. Extension of this method to incorporate viscous wakes and to analysis of fully three dimensional configuration is feasible, and would greatly expand its utility in practical applications.

Alzner, E.↗

NASA NTRS1990

The pdf approach to turbulent flow

This paper provides a detailed discussion of the theory and application of probability density function (pdf) methods, which provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. The basic laws governing the flow of Newtonian fluids are set up in the Eulerian and the Lagrangian frame, and the exact and linear equations for the characteristic functionals in those frames are discussed. Pdf equations in both frames are derived as Fourier transforms of the equations of the characteristic functions. Possible formulations for the nonclosed terms in the pdf equation are discussed, their properties are assessed, and closure modes for the molecular-transport and the fluctuating pressure-gradient terms are reviewed. The application of pdf methods to turbulent combustion flows, supersonic flows, and the interaction of turbulence with shock waves is discussed.

Kollmann, W.↗

NASA NTRS1934

The torsional stiffness of thin duralumin shells subjected to large torques

This report gives a simple method of estimating the torsional stiffness of thin shells, such as box beams or stressed-skin wings under large torque loads. A general efficiency chart for shells in torsion is established, based on the assumption that the efficiency of the web sheet in resisting deformation decreases linearly with the average stress. The chart is used to calculate the torsional deflections of eight box beams, a test wing panel, and a complete wing; the results of the calculations are shown in comparison with the test results. The agreement is probably as good as might be expected considering the empirical nature of the method and the well-known dispersion between results of tests on thin sheet-metal structures.

Kuhn, Paul↗

NASA NTRS1976

High angle-of-attack stability-and-control analysis

Methods of linear systems analysis were applied to mathematical models of aircraft flying at high angle of attack and maneuver rate. First order longitudinal and lateral directional coupling is obtained by linearizing the complete nonlinear equations of motion about a generalized (quasi steady) trim point. Open loop stability boundaries are defined using the linear dynamic equations, and pilot in the loop effects are presented. Stability augmentation structures for maneuvering flight conditions are shown to be defined readily using optimal control theory.

Stengel, R. F.↗

NASA NTRS2004

Mid-frequency Band Dynamics of Large Space Structures

High and low intensity dynamic environments experienced by a spacecraft during launch and on-orbit operations, respectively, induce structural loads and motions, which are difficult to reliably predict. Structural dynamics in low- and mid-frequency bands are sensitive to component interface uncertainty and non-linearity as evidenced in laboratory testing and flight operations. Analytical tools for prediction of linear system response are not necessarily adequate for reliable prediction of mid-frequency band dynamics and analysis of measured laboratory and flight data. A new MATLAB toolbox, designed to address the key challenges of mid-frequency band dynamics, is introduced in this paper. Finite-element models of major subassemblies are defined following rational frequency-wavelength guidelines. For computational efficiency, these subassemblies are described as linear, component mode models. The complete structural system model is composed of component mode subassemblies and linear or non-linear joint descriptions. Computation and display of structural dynamic responses are accomplished employing well-established, stable numerical methods, modern signal processing procedures and descriptive graphical tools. Parametric sensitivity and Monte-Carlo based system identification tools are used to reconcile models with experimental data and investigate the effects of uncertainties. Models and dynamic responses are exported for employment in applications, such as detailed structural integrity and mechanical-optical-control performance analyses.

dynamics↗

NASA NTRS1988

Modern wing flutter analysis by computational fluid dynamics methods

The application and assessment of the recently developed CAP-TSD transonic small-disturbance code for flutter prediction is described. The CAP-TSD code has been developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures with favorable results. Generalized aerodynamic forces and flutter characteristics are calculated and compared with linear theory results and with experimental data for a 45 deg sweptback wing. These results are in good agreement with the experimental flutter data which is the first step toward validating CAP-TSD for general transonic aeroelastic applications. The paper presents these results and comparisons along with general remarks regarding modern wing flutter analysis by computational fluid dynamics methods.

Cunningham, Herbert J.↗

NASA NTRS1987

Modern wing flutter analysis by computational fluid dynamics methods

Cunningham, Herbert J.↗

NASA NTRS2001

Assessment of Stirling Technology Has Provided Critical Data Leading Toward Flight Readiness of the Stirling Converter

The NASA Glenn Research Center is supporting the development of a Stirling converter with the Department of Energy (DOE, Germantown, Maryland) for an advanced Stirling Radioisotope Power System (SRPS) to provide spacecraft onboard electric power for NASA space science missions. A key technology assessment completed by Glenn and DOE has led to the SRPS being identified as a high-efficiency power source for such deep space missions as the Europa Orbiter and the Solar Probe. In addition, the Stirling system is now being considered for unmanned Mars rovers, especially where mission profiles may exclude the use of photovoltaic power systems, such as exploration at high Martian latitudes or for missions of long duration. The SRPS efficiency of over 20 percent will reduce the required amount of radioisotope by more than a factor of 3 in comparison to current radioisotope thermoelectric generators. This significantly reduces radioisotope cost, radiological inventory, and system cost, and it provides efficient use of scarce radioisotope resources. In support of this technology assessment, Glenn conducted a series of independent evaluations and tests to determine the technology readiness of a 55-We Stirling converter developed by Stirling Technology Company (Kennewick, Washington) and DOE. Key areas evaluated by Glenn included: 1) Radiation tolerance of materials; 2) Random vibration testing of the Stirling converter in Glenn's Structural Dynamics Lab to simulate operation in the launch environment; 3) Electromagnetic interference and compatibility (EMI/EMC) of the converter operating in Glenn's EMI lab; Independent failure modes, effects, and criticality analysis, and life and reliability 4. Independent failure modes, effects, and criticality analysis, and life and reliability assessment; and 5) SRPS cost estimate. The data from these evaluations were presented to NASA Headquarters and the Jet Propulsion Laboratory mission office by a joint industry/Government team consisting of DOE, Glenn, and Lockheed Martin Astronautics. This team concluded that there are no technical reasons that would rule out using the Stirling converter for deep space missions. As a direct result of the successful testing at Glenn, the DOE/Stirling Technology Company 55-We Stirling converter has been baselined for the SRPS. Glenn is now continuing an in-house project to assist in developing the Stirling converter for readiness for space qualification and mission implementation. As part of this effort, the Stirling converter will be further characterized under launch environment random vibration testing, methods to reduce converter EMI will be developed, and an independent performance verification will be completed. Converter life assessment and permanent magnet aging characterization tasks are also underway. Substitute organic materials for the linear alternator and piston bearing coatings for use in a high-radiation environment have been identified and have now been incorporated in Stirling converters built by Stirling Technology Company for Glenn. Electromagnetic and thermal finite element analyses for the alternator are also being conducted.

Thieme, Lanny G.↗