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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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NASA NTRS1985

DEAN - A program for Dynamic Engine ANalysis

The Dynamic Engine Analysis Program, DEAN, is a FORTRAN code implemented on the IBM/370 mainframe at NASA Lewis Research Center for digital simulation of turbofan engine dynamics. DEAN is an interactive program which allows the user to simulate engine subsystems as well as full engine systems with relative ease. The nonlinear first order ordinary differential equations which define the engine model may be solved by one of four integration schemes, a second order Runge-Kutta, a fourth order Runge-Kutta, an Adams Predictor-Corrector, or Gear's method for still systems. The numerical data generated by the model equations are displayed a specified intervals between which the user may choose to modify various parameters affecting the model equations and transient execution. Following the transient run, versatile graphics capabilities allow close examination of the data. DEAN's modeling procedure and capabilities are demonstrated by generating a model of simple compressor rig.

Sadler, G. G.↗
NASA NTRS1995

Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma

In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a polytropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue -- a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index gamma and a dimensionless quantity kappa the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and gamma. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for gamma greater than 1 and all values of kappa, only oscillations are possible. For gamma less than 1, however, both oscillations and expansion are allowed. For gamma less than 1 and kappa below a critical value, the energy of the nonlinear oscillator determines whether the flux rope will oscillate or expand to infinity. For gamma less than 1 and kappa above critical, however, only expansion occurs. Thus by increasing kappa while keeping gamma fixed (less than 1), a phase transition occurs at kappa = kappa(sub critical) and the oscillatory mode disappears. We illustrate the above theoretical considerations by the example of a flux rope of constant field line twist evolving self-similarly. For this example, we present the full numerical MHD solution. In an appendix to the paper we catalogue all possible evolutions when (1) either the magnetic field or (2) the gas pressure decreases monotonically toward the axis. We find that in these cases critical conditions can occur for gamma greater than 1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of kappa and gamma, collapse may be averted.

Osherovich, V. A.↗
NASA NTRS1990

Algorithm for "Bang-Bang" Control Laws

Switching times updated to minimize errors in final positions. Algorithm computes "bang-bang" control laws for single- or multiple-input systems, both those describable by linear dynamical equations and those describable by nonlinear dynamical equations that are linear in control vectors. Algorithm needed because analytical solutions of "bang-bang" control problems intractable for all but simplest systems.

Wen, John Ting-Yung↗
NASA NTRS1991

Large Angle Transient Dynamics (LATDYN) demonstration problem manual

LATDYN is a computer code for modeling the Large Angle Transient Dynamics of structures. The objective in developing the code was to investigate new techniques for analyzing flexible deformation and control/structure interaction problems associated with large angular motions of spacecraft. Such motions may consist of pointing the entire spacecraft or articulation of individual components, events which occur frequently during construction, operation, and maintenance of large spacecraft. This type of analysis is beyond the routine capability of conventional analytical tools without simplifying assumptions. In some instances, the motion may be sufficiently slow and the spacecraft (or component) sufficiently rigid to simplify the analysis of dynamics and controls by making pseudo-static and/or rigid body assumptions. LATDYN introduces a new approach to the problem by combining finite element structural analysis, multi-body dynamics, and control system analysis in a single tool. It includes a new type of finite element that can deform and rotate through large angles at the same time, and which can be connected to other finite elements either rigidly or through mechanical joints. LATDYN also provides symbolic capabilities for modeling control systems which are interfaced directly with the finite element structural model. Thus, the nonlinear equations representing the structural model are integrated along with the equations representing sensors, processing, and controls as a coupled system.

Wu, Shih-Chin↗
NASA NTRS1991

Large Angle Transient Dynamics (LATDYN) user's manual

A computer code for modeling the large angle transient dynamics (LATDYN) of structures was developed to investigate techniques for analyzing flexible deformation and control/structure interaction problems associated with large angular motions of spacecraft. This type of analysis is beyond the routine capability of conventional analytical tools without simplifying assumptions. In some instances, the motion may be sufficiently slow and the spacecraft (or component) sufficiently rigid to simplify analyses of dynamics and controls by making pseudo-static and/or rigid body assumptions. The LATDYN introduces a new approach to the problem by combining finite element structural analysis, multi-body dynamics, and control system analysis in a single tool. It includes a type of finite element that can deform and rotate through large angles at the same time, and which can be connected to other finite elements either rigidly or through mechanical joints. The LATDYN also provides symbolic capabilities for modeling control systems which are interfaced directly with the finite element structural model. Thus, the nonlinear equations representing the structural model are integrated along with the equations representing sensors, processing, and controls as a coupled system.

Abrahamson, A. Louis↗
NASA NTRS1996

Validation Tests of TASS for Application to 3-D Vortex Simulations

Direct analytical solutions can be useful in validating the Core formulation of numerical systems. In this document an exact analytical solution to the nonlinear Navier-Stokes equation is compared to the numerical results from the three-dimensional Terminal Area Simulation System (TASS). This exact solution, of which the derivation is included, is for Beltrami type flow. Direct comparison of TASS to the analytical Beltrami solution is then used in evaluating the accuracy of TASS.

Switzer, George F.↗
NASA NTRS2010

Forces Associated with Nonlinear Nonholonomic Constraint Equations

A concise method has been formulated for identifying a set of forces needed to constrain the behavior of a mechanical system, modeled as a set of particles and rigid bodies, when it is subject to motion constraints described by nonholonomic equations that are inherently nonlinear in velocity. An expression in vector form is obtained for each force; a direction is determined, together with the point of application. This result is a consequence of expressing constraint equations in terms of dot products of vectors rather than in the usual way, which is entirely in terms of scalars and matrices. The constraint forces in vector form are used together with two new analytical approaches for deriving equations governing motion of a system subject to such constraints. If constraint forces are of interest they can be brought into evidence in explicit dynamical equations by employing the well-known nonholonomic partial velocities associated with Kane's method; if they are not of interest, equations can be formed instead with the aid of vectors introduced here as nonholonomic partial accelerations. When the analyst requires only the latter, smaller set of equations, they can be formed directly; it is not necessary to expend the labor to form the former, larger set first and subsequently perform matrix multiplications.

Roithmayr, Carlos M.↗
NASA NTRS1977

Dynamic response and stability analysis of flexible, multibody systems

A general version of Lagrange's equations, including auxiliary nonholonomic, rheonomic conditions of constraint, is used in the dynamic simulation and stability analysis of interconnected flexible bodies. Modeling of the nonlinear flexible/rigid dynamic coupling effects, the interaction forces/torques, and the elastic deformation effects is discussed. A digital computer program is developed to obtain time-domain solution for the nonlinear response of systems represented as a collection of individual bodies, numerical linearization of system-governing equations, time-domain solution for the perturbation response about a nominal state, and a frequency-domain stability analysis corresponding to the linearization. The digital simulation code is employed to study the dynamic behavior of a typical satellite and a spacecraft with deployable experiment booms.

Bodley, C. S.↗
NASA NTRS1999

Nonlinear Response of Composite Panels Under Combined Acoustic Excitation and Aerodynamic Pressure

A finite element formulation is presented for the analysis of large deflection response of composite panels subjected to aerodynamic pressure- at supersonic flow and high acoustic excitation. The first-order shear deformation theory is considered for laminated composite plates, and the von Karman nonlinear strain-displacement relations are employed for the analysis of large deflection panel response. The first-order piston theory aerodynamics and the simulated Gaussian white noise are employed for the aerodynamic and acoustic loads, respectively. The nonlinear equations of motion for an arbitrarily laminated composite panel subjected to a combined aerodynamic and acoustic pressures are formulated first in structure node degrees-of-freedom. The system equations are then transformed and reduced to a set of coupled nonlinear equations in modal coordinates. Modal participation is defined and the in-vacuo modes to be retained in the analysis are based on the modal participation values. Numerical results include root mean square values of maximum deflections, deflection and strain response time histories, probability distributions, and power spectrum densities. Results showed that combined acoustic and aerodynamic loads have to be considered for panel analysis and design at high dynamic pressure values.

Abdel-Motagaly, K.↗
NASA NTRS2001

Multi-Tethered Space-Based Interferometers: Particle System Model

Dynamics models are presented for a class of space-based interferometers comprised of multiple component bodies, interconnected in various arrangements, by low-mass flexible tethers of variable length. The tethered constellations are to perform coordinated rotational scanning accompanied by baseline dimensional changes, as well as spin axis realignments and spin-up/spin-down maneuvers. The mechanical idealization is a system of N point masses interconnected by massless tethers of variable length. Both extensible and inextensible tethers are considered. Expressions for system angular and linear momenta are developed. The unrestricted nonlinear motion equations are derived via Lagranges equations. Rheonomic constraints are introduced to allow prescribed motion of any degrees of freedom, and the associated physical forces are determined. The linearized equations of motion are obtained for the steady rotation of a system with extensible tethers of constant unstrained length.

Gates, Stephen S.↗
NASA NTRS1985

Performance of direct and iterative algorithms on an optical systolic processor

The frequency-multiplexed optical linear algebra processor (OLAP) is treated in detail with attention to its performance in the solution of systems of linear algebraic equations (LAEs). General guidelines suitable for most OLAPs, including digital-optical processors, are advanced concerning system and component error source models, guidelines for appropriate use of direct and iterative algorithms, the dominant error sources, and the effect of multiple simultaneous error sources. Specific results are advanced on the quantitative performance of both direct and iterative algorithms in the solution of systems of LAEs and in the solution of nonlinear matrix equations. Acoustic attenuation is found to dominate iterative algorithms and detector noise to dominate direct algorithms. The effect of multiple spatial errors is found to be additive. A theoretical expression for the amount of acoustic attenuation allowed is advanced and verified. Simulations and experimental data are included.

Ghosh, A. K.↗
NASA NTRS1994

A parametric sensitivity study for single-stage-to-orbit hypersonic vehicles using trajectory optimization

The class of hypersonic vehicle configurations with single stage-to-orbit (SSTO) capability reflect highly integrated airframe and propulsion systems. These designs are also known to exhibit a large degree of interaction between the airframe and engine dynamics. Consequently, even simplified hypersonic models are characterized by tightly coupled nonlinear equations of motion. In addition, hypersonic SSTO vehicles present a major system design challenge; the vehicle's overall mission performance is a function of its subsystem efficiencies including structural, aerodynamic, propulsive, and operational. Further, all subsystem efficiencies are interrelated, hence, independent optimization of the subsystems is not likely to lead to an optimum design. Thus, it is desired to know the effect of various subsystem efficiencies on overall mission performance. For the purposes of this analysis, mission performance will be measured in terms of the payload weight inserted into orbit. In this report, a trajectory optimization problem is formulated for a generic hypersonic lifting body for a specified orbit-injection mission. A solution method is outlined, and results are detailed for the generic vehicle, referred to as the baseline model. After evaluating the performance of the baseline model, a sensitivity study is presented to determine the effect of various subsystem efficiencies on mission performance. This consists of performing a parametric analysis of the basic design parameters, generating a matrix of configurations, and determining the mission performance of each configuration. Also, the performance loss due to constraining the total head load experienced by the vehicle is evaluated. The key results from this analysis include the formulation of the sizing problem for this vehicle class using trajectory optimization, characteristics of the optimal trajectories, and the subsystem design sensitivities.

Lovell, T. Alan↗
NASA NTRS1972

An initial value method for the Ambarzumian integral equation.

It is shown that a general class of nonlinear integral equations may be transformed into a Cauchy system. That this leads to an effective numerical scheme is demonstrated by solving the Ambarzumian integral equation. The new method does not involve successive approximations or series expansions.

Buell, J.↗
NASA NTRS1977

A multiscale numerical study into the cascade of kinetic energy leading to severe local storms

The cascade of kinetic energy from macro- through mesoscales is studied on the basis of a nested grid system used to solve a set of nonlinear differential equations. The kinetic energy cascade and the concentration of vorticity through the hydrodynamic spectrum provide a means for predicting the location and intensity of severe weather from large-scale data sets. A mechanism described by the surface pressure tendency equation proves to be important in explaining how initial middle-tropospheric mass-momentum imbalances alter the low-level pressure field.

Paine, D. A.↗
NASA NTRS1983

Computational methods for ideal compressible flow

Conservative dissipative difference schemes for computing one dimensional flow are introduced, and the recognition and representation of flow discontinuities are discussed. Multidimensional methods are outlined. Second order finite volume schemes are introduced. Conversion of difference schemes for a single linear convection equation into schemes for the hyperbolic system of the nonlinear conservation laws of ideal compressible flow is explained. Approximate Riemann solvers are presented. Monotone initial value interpolation; and limiters, switches, and artificial dissipation are considered.

Vanleer, B.↗
NASA NTRS1988

A general-purpose approach to computer-aided dynamic analysis of a flexible helicopter

A general purpose mathematical formulation is described for dynamic analysis of a helicopter consisting of flexible and/or rigid bodies that undergo large translations and rotations. Rigid body and elastic sets of generalized coordinates are used. The rigid body coordinates define the location and the orientation of a body coordinate frame (global frame) with respect to an inertial frame. The elastic coordinates are introduced using a finite element approach in order to model flexible components. The compatibility conditions between two adjacent elements in a flexible body are imposed using a Boolean matrix, whereas the compatibility conditions between two adjacent bodies are imposed using the Lagrange multiplier approach. Since the form of the constraint equations depends upon the type of kinematic joint and involves only the generalized coordinates of the two participating elements, then a library of constraint elements can be developed to impose the kinematic constraint in an automated fashion. For the body constraints, the Lagrange multipliers yield the reaction forces and torques of the bodies at the joints. The virtual work approach is used to derive the equations of motion, which are a system of differential and algebraic equations that are highly nonlinear. The formulation presented is general and is compared with hard-wired formulations commonly used in helicopter analysis.

Agrawal, Om P.↗