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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Expendable launch vehicle studies

Analytical support studies of expendable launch vehicles concentrate on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed and linearized. The information from LeRC about the grids, masses, and modes is incorporated into the model. The eigenvalues of the plant are analyzed for several modeling factors: utilizing diagonal mass matrix, uniform beam assumption, inclusion of aerodynamics, and the interaction between the aerodynamics and the flexible bending motion. Preliminary PID, LQR, and LQG control designs with sensor and actuator dynamics for this system and simulations are also conducted. The initial analysis for comparison of PD (proportional-derivative) and full state feedback LQR Linear quadratic regulator) shows that the split weighted LQR controller has better performance than that of the PD. In order to meet both the performance and robustness requirements, the H(sub infinity) robust controller for the expendable launch vehicle is developed. The simulation indicates that both the performance and robustness of the H(sub infinity) controller are better than that for the PID and LQG controllers. The modelling and analysis support studies team has continued development of methodology, using eigensensitivity analysis, to solve three classes of discrete eigenvalue equations. In the first class, the matrix elements are non-linear functions of the eigenvector. All non-linear periodic motion can be cast in this form. Here the eigenvector is comprised of the coefficients of complete basis functions spanning the response space and the eigenvalue is the frequency. The second class of eigenvalue problems studied is the quadratic eigenvalue problem. Solutions for linear viscously damped structures or viscoelastic structures can be reduced to this form. Particular attention is paid to Maxwell and Kelvin models. The third class of problems consists of linear eigenvalue problems in which the elements of the mass and stiffness matrices are stochastic. dynamic structural response for which the parameters are given by probabilistic distribution functions, rather than deterministic values, can be cast in this form. Solutions for several problems in each class will be presented.

Bainum, Peter M.↗
NASA NTRS1989

A novel implementation of method of optimality criterion in synthesizing spacecraft structures with natural frequency constraints

In the design of spacecraft structures, fine tuning the structure to achieve minimum weight with natural frequency constraints is a time consuming process. Here, a novel implementation of the method of optimality criterion (OC) is developed. In this new implementation of OC, the free vibration analysis results are used to compute the eigenvalue sensitivity data required for the formulation. Specifically, the modal elemental strain and kinetic energies are used. Additionally, normalized design parameters are introduced as a second level linking that allows design variables of different values to be linked together. With the use of this novel formulation, synthesis of structures with natural frequency constraint can be carried out manually using modal analysis results. Design examples are presented to illustrate this novel implementation of the optimality criterion method.

Wang, Bo Ping↗
DOE OSTI2025

Code Coverage Status of the ARC Code PERSENT

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. PERSENT fulfills the role of generating reactivity coefficients for a given time point of a REBUS calculation usable in a point kinetics based safety analysis capability. PERSENT also provides a sensitivity coefficient capability on eigenvalue, reactivity worth, and several other key coefficients that are used in the follow-on safety analysis. Given a co-variance matrix, PERSENT can carry out the uncertainty quantification to indicate the amount of error in the reactivity coefficients derived from the errors in the cross section measurements. With continued improvement of computational resources, many of the geometry modeling capabilities in DIF3D that were primarily used in low order schemes are not really needed anymore. Today, the diffusion and transport capabilities of DIF3D-VARIANT are primarily used in the reactor design process with some scattered usage of DIF3D-FD and DIF3D-Nodal. PERSENT is part of the ARC code system and is built around DIF3D-VARIANT and the flux solution it provides. The purpose of the present work is to identify a set of test problems for PERSENT and assess the code coverage of PERSENT for those test problems. PERSENT treats the DIF3D executable as an external executable and thus the code coverage considerations only need to focus on the PERSENT source code and only a fraction of the connected modules in the existing ARC software library. The goal is to document what parts of the existing PERSENT code are touched by the set of test problems and which are not. Because the verification work done on PERSENT was focused on the most common uses of PERSENT for fast reactor analysis, the code coverage assessment of those capabilities is the highest priority. This will ensure that nothing is being missed by the existing verification test problems that users of PERSENT rely upon. The code coverage analysis of PERSENT was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of PERSENT. The detailed coverage tables are given for each submodule of PERSENT. Most of the uncovered parts/files could be easily ignored because they are either for error message and debugging output or not needed by PERSENT today. Only a few uncovered parts of PERSENT deserve extending the verification test suite.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1988

Eigenvalue/Eigenvector derivatives for SAVI Gimbalflex nonlinear transient response analysis

An eigenvector expansion method is utilized to predict eigenvalue and eigenvector derivatives due to geometric reconfiguration of a Gimbalflex fine-pointing/vibration isolation system called SAVI (Space Active Vibration Isolation). The eigenvector expansion method used is a modification of the classical method and allows for rigid body roots. Using the resulting modal derivatives, free-free nonlinear equations of motion are developed with Lagrange's Method. These equations represent a nonlinear plant model to be used in conjunction with a control system transient response simulation.

Orr, M. F., Jr.↗
NASA NTRS1983

Stability and Interaction of Coherent Structure in Supersonic Reactive Wakes

A theoretical formulation and analysis is presented for a study of the stability and interaction of coherent structure in reacting free shear layers. The physical problem under investigation is a premixed hydrogen-oxygen reacting shear layer in the wake of a thin flat plate. The coherent structure is modeled as a periodic disturbance and its stability is determined by the application of linearized hydrodynamic stability theory which results in a generalized eigenvalue problem for reactive flows. Detailed stability analysis of the reactive wake for neutral, symmetrical and antisymmetrical disturbance is presented. Reactive stability criteria is shown to be quite different from classical non-reactive stability. The interaction between the mean flow, coherent structure and fine-scale turbulence is theoretically formulated using the von-Kaman integral technique. Both time-averaging and conditional phase averaging are necessary to separate the three types of motion. The resulting integro-differential equations can then be solved subject to initial conditions with appropriate shape functions. In the laminar flow transition region of interest, the spatial interaction between the mean motion and coherent structure is calculated for both non-reactive and reactive conditions and compared with experimental data wherever available. The fine-scale turbulent motion determined by the application of integral analysis to the fluctuation equations. Since at present this turbulence model is still untested, turbulence is modeled in the interaction problem by a simple algebraic eddy viscosity model. The applicability of the integral turbulence model formulated here is studied parametrically by integrating these equations for the simple case of self-similar mean motion with assumed shape functions. The effect of the motion of the coherent structure is studied and very good agreement is obtained with previous experimental and theoretical works for non-reactive flow. For the reactive case, lack of experimental data made direct comparison difficult. It was determined that the growth rate of the disturbance amplitude is lower for reactive case. The results indicate that the reactive flow stability is in qualitative agreement with experimental observation.

Menon, Suresh↗
NASA NTRS1974

Analytical and experimental investigation of a 1/8-scale dynamic model of the shuttle orbiter. Volume 1: Summary report

A 1/8-scale structural dynamics model of the space shuttle orbiter was analyzed using the NASA Structural Analysis System (NASTRAN). Comparison of the calculated eigenvalues with preliminary test data for the unrestrained condition indicate that the analytical model was consistently stiffer, being about 20% higher in the first mode. The eigenvectors show reasonably good agreement with test data. A series of analytical and experimental investigations undertaken to resolve the discrepancy are described. Modifications in the NASTRAN model based upon these investigations resulted in close agreement for both eigenvalues and eigenvectors.

Mason, P. W.↗
NASA NTRS1976

A FORTRAN program for the analysis of linear continuous and sample-data systems

A FORTRAN digital computer program which performs the general analysis of linearized control systems is described. State variable techniques are used to analyze continuous, discrete, and sampled data systems. Analysis options include the calculation of system eigenvalues, transfer functions, root loci, root contours, frequency responses, power spectra, and transient responses for open- and closed-loop systems. A flexible data input format allows the user to define systems in a variety of representations. Data may be entered by inputing explicit data matrices or matrices constructed in user written subroutines, by specifying transfer function block diagrams, or by using a combination of these methods.

Edwards, J. W.↗
NASA NTRS1976

Nonlinear Equations of Motion for Cantilever Rotor Blades in Hover with Pitch Link Flexibility, Twist, Precone, Droop, Sweep, Torque Offset, and Blade Root Offset

Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.

Hodges, D. H.↗
NASA NTRS1990

An experimental and analytical investigation of isolated rotor flap-lag stability in forward flight

The flap-lag stability of an isolated hingeless rotor is investigated, both experimentally and analytically, in hover and in forward flight. The effects of forward flight aerodynamics on regressing lead-lag mode stability are the focus of the investigation. The soft-inplane, three-bladed, isolated model rotor was operated untrimmed at advance ratios from hover to 0.55 and at shaft angles as high as 20 deg. The experimental data base includes forward flight damping data for two lead-lag natural frequencies, for three values of collective pitch, and for both zero and full-lag structural coupling. With the aid of computerized symbolic manipulation, a rigid-blade lag-flap model analysis was developed to calculate the Floquent eigenvalues and to identify the modes. Good correlation is shown for some cases, but other cases show large discrepancies between the theory and experiment.

Gaonkar, Gopal H.↗
NASA NTRS1994

Coupled Marangoni-Benard/Rayleigh-Benard Instability with Temperature Dependent Viscosity

The onset of convection induced by coupled surface tension gradient and buoyancy forces is investigated with temperature dependent viscosity. Both surface tension and viscosity are assumed to vary linearly with temperature. The limiting case, Ma=0, is the buoyancy driven convection problem typically referred to as the Rayleigh-Benard stability problem. The other limiting case, Ra=0, is the surface tension (gradient) driven flow problem referred to as the Marangoni-Benard problem. The equations and boundary conditions obtained from the linear analysis are solved numerically as a generalized eigenvalue problem. Neutral stability curves for different viscosity slopes have been generated for the Marangoni-Benard and Rayleigh-Benard problems. It is shown that the curves can be collapsed to a single curve by appropriately scaling the results for each of the limiting cases. The critical Marangoni number is determined as a function of the slope of the viscosity temperature variation, epsilon, for different values of the Rayleigh number. When the viscosity decreases linearly with temperature, the coupled buoyancy-surface tension problem, including the limiting cases of Ra=0 and Ma=0, is found to be more stable than the constant viscosity case.

Skarda, J. Raymond Lee↗
NASA NTRS1991

A study of the response of nonlinear springs

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

Hyer, M. W.↗
NASA NTRS1987

Calculation of skin-stiffener interface stresses in stiffened composite panels

A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated.

Cohen, David↗
NASA NTRS1993

Eigenvalue routines in NASTRAN: A comparison with the Block Lanczos method

The NASA STRuctural ANalysis (NASTRAN) program is one of the most extensively used engineering applications software in the world. It contains a wealth of matrix operations and numerical solution techniques, and they were used to construct efficient eigenvalue routines. The purpose of this paper is to examine the current eigenvalue routines in NASTRAN and to make efficiency comparisons with a more recent implementation of the Block Lanczos algorithm by Boeing Computer Services (BCS). This eigenvalue routine is now available in the BCS mathematics library as well as in several commercial versions of NASTRAN. In addition, CRAY maintains a modified version of this routine on their network. Several example problems, with a varying number of degrees of freedom, were selected primarily for efficiency bench-marking. Accuracy is not an issue, because they all gave comparable results. The Block Lanczos algorithm was found to be extremely efficient, in particular, for very large size problems.

Tischler, V. A.↗
NASA NTRS1978

Stability of constant gain systems with vector feedback

The state space, the controllability, and the observability concepts are discussed in connection with the proposed stability analysis which permits drastic dimensional reductions for a vector feedback problem. Any constant gain system's stability can thus be analyzed in the frequency domain with a single Nyquist plot. The analysis considers the total system with all loops closed, a disturbance vector as input, and the feedback vector as output. All constant gain systems are shown to be decomposable into stable subsystems where the degree of the decomposition determines the dimensions. The maximum decomposition results in the state-space approach which is the limit case. The method is demonstrated with the stability analysis of the pogo phenomenon, an oscillatory interaction between the propulsion and the structure of a space vehicle. This problem, with eigenvalues over a hundred, was drastically but rigorously reduced to a stability analysis of a 4x4 matrix.

Vonpragenau, G. L.↗
NASA NTRS1973

State space approach to mixed boundary value problems.

A state-space procedure for the formulation and solution of mixed boundary value problems is established. This procedure is a natural extension of the method used in initial value problems; however, certain special theorems and rules must be developed. The scope of the applications of the approach includes beam, arch, and axisymmetric shell problems in structural analysis, boundary layer problems in fluid mechanics, and eigenvalue problems for deformable bodies. Many classical methods in these fields developed by Holzer, Prohl, Myklestad, Thomson, Love-Meissner, and others can be either simplified or unified under new light shed by the state-variable approach. A beam problem is included as an illustration.

Chen, C. F.↗
NASA NTRS1974

Dynamic transformation method

Eigenvalue problem associated with modal-synthesis vibration analysis of complex structures requires simplifying assumptions for solution. Computer program, Dynamic-transformation Adapted to Modal-synthesis Using Stiffness-coupling, improves computational economy for vibration analysis of complex structures while still considering substructure modes.

Admire, J. R.↗
NASA NTRS1991

Determination of Rotordynamic Coefficients for Labyrinth Seals and Application to Rotordynamic Design Calculations

In today's rotordynamic calculations, the input parameters for a finite element analysis (FEA) determine very much the reliability of eigenvalue and eigenmode predictions. While modeling of an elastic structure by means of beam elements etc. is relatively straightforward to perform and the input data for journal bearings are usually known exactly enough, the determination of stiffness and damping for labyrinth seals is still the subject of many investigations. Therefore, the rotordynamic influence of labyrinths is often not included in FEA for rotating machinery because of a lack of computer programs to calculate these parameters. This circumstance can give rise to severe vibration problems especially for high performance turbines or compressors, resulting in remarkable economic losses. The forces generated in labyrinths can be described for small motions around the seal center with a linearized force-motion relationship. Several years ago, we started with the development of computer codes for the determination of rotordynamic seal coefficients. Our different approaches to evaluate the dynamic fluid forces generated by turbulent, compressible seal flow are introduced.

Weiser, P.↗