Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytic linearization”

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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Energy-balance climate models

An introductory survey of the global energy balance climate models is presented with an emphasis on analytical results. A sequence of increasingly complicated models involving ice cap and radiative feedback processes are solved and the solutions and parameter sensitivities are studied. The model parameterizations are examined critically in light of many current uncertainties. A simple seasonal model is used to study the effects of changes in orbital elements on the temperature field. A linear stability theorem and a complete nonlinear stability analysis for the models are developed. Analytical solutions are also obtained for the linearized models driven by stochastic forcing elements. In this context the relation between natural fluctuation statistics and climate sensitivity is stressed.

North, G. R.↗
NASA NTRS1981

Energy balance climate models

An introductory survey of the global energy balance climate models is presented with an emphasis on analytical results. A sequence of increasingly complicated models involving ice cap and radiative feedback processes are solved, and the solutions and parameter sensitivities are studied. The model parameterizations are examined critically in light of many current uncertainties. A simple seasonal model is used to study the effects of changes in orbital elements on the temperature field. A linear stability theorem and a complete nonlinear stability analysis for the models are developed. Analytical solutions are also obtained for the linearized models driven by stochastic forcing elements. In this context the relation between natural fluctuation statistics and climate sensitivity is stressed.

North, G. R.↗
NASA NTRS1961

Experimental Evaluation of Analytical Models for the Inertias and Natural Frequencies of Fuel Sloshing in Circular Cylindrical Tanks

A correlation is presented of experimental measurement and analytical prediction of free, planar oscillations of a tank of mercury hung on a pendulum. Measured frequencies are presented for the slosh mode and the pendulum-tank mode, and time-history wave forms are included for qualitative comparisons. The sloshing is represented analytically by a single pendulum or a spring-bob, and the size and location of their inertias are determined by matching forces and moments on the tank surface with linearized hydrodynamic theory for inviscid fluids. It is concluded that such analytical models are identical for small displacements in the present application (as they are in simpler applications) and that they provide excellent simulation of the stiffness and in ertia terms for fuel sloshing.

Warner, Robert W.↗
NASA NTRS1985

Theory of the current-driven ion cyclotron instability in the bottomside ionosphere

A comprehensive treatment of the theory of electrostatic ion cyclotron instability in the collisional bottomside ionosphere is given. The linear dispersion relations for the ion cyclotron instability (electron and ion collisions) are derived. Analytical solutions to the dispersion relation are obtained in three limits: collisionless; weakly collisional; and collisional. In addition, the linear dispersion relation is solved numerically, using parameters typical of the high-latitude bottomside ionosphere. It is pointed out that the linear growth rates in the bottomside collisional regime can be of the same order as the corresponding topside collisionless growth rates. A nonlinear saturation mechanism for the electrostatic ion cyclotron instability is proposed on the basis of Dupree's (1966) resonance broadening theory.

Satyanarayana, P.↗
NASA NTRS2002

Effects of Initial Geometric Imperfections On the Non-Linear Response of the Space Shuttle Superlightweight Liquid-Oxygen Tank

The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.

Nemeth, Michael P.↗
NASA NTRS2011

Characterizing Observed Limit Cycles in the Cassini Main Engine Guidance Control System

The Cassini spacecraft dynamics-related telemetry during long Main Engine (ME) burns has indicated the presence of stable limit cycles between 0.03-0.04 Hz frequencies. These stable limit cycles cause the spacecraft to possess non-zero oscillating rates for extended periods of time. This indicates that the linear ME guidance control system does not model the complete dynamics of the spacecraft. In this study, we propose that the observed limit cycles in the spacecraft dynamics telemetry appear from a stable interaction between the unmodeled nonlinear elements in the ME guidance control system. Many nonlinearities in the control system emerge from translating the linear engine gimbal actuator (EGA) motion into a spacecraft rotation. One such nonlinearity comes from the gear backlash in the EGA system, which is the focus of this paper. The limit cycle characteristics and behavior can be predicted by modeling this gear backlash nonlinear element via a describing function and studying the interaction of this describing function with the overall dynamics of the spacecraft. The linear ME guidance controller and gear backlash nonlinearity are modeled analytically. The frequency, magnitude, and nature of the limit cycle are obtained from the frequency response of the ME guidance controller and nonlinear element. In addition, the ME guidance controller along with the nonlinearity is simulated. The simulation response contains a limit cycle with similar characterstics as predicted analytically: 0.03-0.04 Hz frequency and stable, sustained oscillations. The analytical and simulated limit cycle responses are compared to the flight telemetry for long burns such as the Saturn Orbit Insertion and Main Engine Orbit Trim Maneuvers. The analytical and simulated limit cycle characteristics compare well with the actual observed limit cycles in the flight telemetry. Both have frequencies between 0.03-0.04 Hz and stable oscillations. This work shows that the stable limit cycles occur due to the interaction between the unmodeled nonlinear elements and linear ME guidance controller.

stable limit cycle↗
NASA NTRS1982

An analytic approach to two-fixed-impulse transfers between Keplerian orbits

Solutions are obtained for the two-impulse transfer of a vehicle between arbitrary inclined orbits in an inverse-square force field with the restriction that the magnitude of each of the two impulses has a fixed preassigned value. The two magnitudes need not be equal. The equations for the conservation of angular momentum and energy are augmented by the Laplace integral; these equations establish linear relationships between several of the variables. This set of linear equations and one of two quadratic equations constitute the analytically tractable part of the solution. The remaining part, consisting of finding the zeros (if they exist) of a single trigonometric function of one variable, is solved using numerical methods. Explicit lower bounds on each of the magnitudes of the two impulses are obtained by requiring the solution be real. Graphical results are presented to illustrate the solution.

Jezewski, D. J.↗
NASA NTRS1999

Use of Boundary Layer Transition Detection to Validate Full-Scale Flight Performance Predictions

Full-scale flight performance predictions can be made using CFD or a combination of CFD and analytical skin-friction predictions. However, no matter what method is used to obtain full-scale flight performance predictions knowledge of the boundary layer state is critical. The implementation of CFD codes solving the Navier-Stokes equations to obtain these predictions is still a time consuming, expensive process. In addition, to ultimately obtain accurate performance predictions the transition location must be fixed in the CFD model. An example, using the M2.4-7A geometry, of the change in Navier-Stokes solution with changes in transition and in turbulence model will be shown. Oil flow visualization using the M2.4-7A 4.0% scale model in the 14'x22' wind tunnel shows that fixing transition at 10% x/c in the CFD model best captures the flow physics of the wing flow field. A less costly method of obtaining full-scale performance predictions is the use of non-linear Euler codes or linear CFD codes, such as panel methods, combined with analytical skin-friction predictions. Again, knowledge of the boundary layer state is critical to the accurate determination of full-scale flight performance. Boundary layer transition detection has been performed at 0.3 and 0.9 Mach numbers over an extensive Reynolds number range using the 2.2% scale Reference H model in the NTF. A temperature sensitive paint system was used to determine the boundary layer state for these conditions. Data was obtained for three configurations: the baseline, undeflected flaps configuration; the transonic cruise configuration; and, the high-lift configuration. It was determined that at low Reynolds number conditions, in the 8 to 10 million Reynolds number range, the baseline configuration has extensive regions of laminar flow, in fact significantly more than analytical skin-friction methods predict. This configuration is fully turbulent at about 30 million Reynolds number for both 0.3 and 0.9, Mach numbers. Both the transonic cruise and the high-lift configurations were fully turbulent aft of the leading-edge flap hingeline at all Reynolds numbers.

Hamner, Marvine↗
NASA NTRS1985

Chandrasekhar equations for infinite dimensional systems

Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

Ito, K.↗
NASA NTRS1999

Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators

A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.

Taleghani, Barmac K.↗
NASA NTRS1997

Controls/CFD Interdisciplinary Research Software Generates Low-Order Linear Models for Control Design From Steady-State CFD Results

The NASA Lewis Research Center is developing analytical methods and software tools to create a bridge between the controls and computational fluid dynamics (CFD) disciplines. Traditionally, control design engineers have used coarse nonlinear simulations to generate information for the design of new propulsion system controls. However, such traditional methods are not adequate for modeling the propulsion systems of complex, high-speed vehicles like the High Speed Civil Transport. To properly model the relevant flow physics of high-speed propulsion systems, one must use simulations based on CFD methods. Such CFD simulations have become useful tools for engineers that are designing propulsion system components. The analysis techniques and software being developed as part of this effort are an attempt to evolve CFD into a useful tool for control design as well. One major aspect of this research is the generation of linear models from steady-state CFD results. CFD simulations, often used during the design of high-speed inlets, yield high resolution operating point data. Under a NASA grant, the University of Akron has developed analytical techniques and software tools that use these data to generate linear models for control design. The resulting linear models have the same number of states as the original CFD simulation, so they are still very large and computationally cumbersome. Model reduction techniques have been successfully applied to reduce these large linear models by several orders of magnitude without significantly changing the dynamic response. The result is an accurate, easy to use, low-order linear model that takes less time to generate than those generated by traditional means. The development of methods for generating low-order linear models from steady-state CFD is most complete at the one-dimensional level, where software is available to generate models with different kinds of input and output variables. One-dimensional methods have been extended somewhat so that linear models can also be generated from two- and three-dimensional steady-state results. Standard techniques are adequate for reducing the order of one-dimensional CFD-based linear models. However, reduction of linear models based on two- and three-dimensional CFD results is complicated by very sparse, ill-conditioned matrices. Some novel approaches are being investigated to solve this problem.

Melcher, Kevin J.↗
NASA NTRS2011

An Overview of NASA's Integrated Design and Engineering Analysis (IDEA) Environment

Historically, the design of subsonic and supersonic aircraft has been divided into separate technical disciplines (such as propulsion, aerodynamics and structures), each of which performs design and analysis in relative isolation from others. This is possible, in most cases, either because the amount of interdisciplinary coupling is minimal, or because the interactions can be treated as linear. The design of hypersonic airbreathing vehicles, like NASA's X-43, is quite the opposite. Such systems are dominated by strong non-linear interactions between disciplines. The design of these systems demands that a multi-disciplinary approach be taken. Furthermore, increased analytical fidelity at the conceptual design phase is highly desirable, as many of the non-linearities are not captured by lower fidelity tools. Only when these systems are designed from a true multi-disciplinary perspective, can the real performance benefits be achieved and complete vehicle systems be fielded. Toward this end, the Vehicle Analysis Branch at NASA Langley Research Center has been developing the Integrated Design and Engineering Analysis (IDEA) Environment. IDEA is a collaborative environment for parametrically modeling conceptual and preliminary designs for launch vehicle and high speed atmospheric flight configurations using the Adaptive Modeling Language (AML) as the underlying framework. The environment integrates geometry, packaging, propulsion, trajectory, aerodynamics, aerothermodynamics, engine and airframe subsystem design, thermal and structural analysis, and vehicle closure into a generative, parametric, unified computational model where data is shared seamlessly between the different disciplines. Plans are also in place to incorporate life cycle analysis tools into the environment which will estimate vehicle operability, reliability and cost. IDEA is currently being funded by NASA?s Hypersonics Project, a part of the Fundamental Aeronautics Program within the Aeronautics Research Mission Directorate. The environment is currently focused around a two-stage-to-orbit configuration with a turbine-based combined cycle (TBCC) first stage and a reusable rocket second stage. IDEA will be rolled out in generations, with each successive generation providing a significant increase in capability, either through increased analytic fidelity, expansion of vehicle classes considered, or by the inclusion of advanced modeling techniques. This paper provides the motivation behind the current effort, an overview of the development of the IDEA environment (including the contents and capabilities to be included in Generation 1 and Generation 2), and a description of the current status and detail of future plans.

Robinson, Jeffrey S.↗
NASA NTRS2008

Overview of NASA's Integrated Design and Engineering Analysis (IDEA)Environment

Historically, the design of subsonic and supersonic aircraft has been divided into separate technical disciplines (such as propulsion, aerodynamics and structures) each of which performs their design and analysis in relative isolation from others. This is possible in most cases either because the amount of interdisciplinary coupling is minimal or because the interactions can be treated as linear. The design of hypersonic airbreathing vehicles, like NASA s X-43, is quite the opposite. Such systems are dominated by strong non-linear interactions between disciplines. The design of these systems demands that a multi-disciplinary approach be taken. Furthermore, increased analytical fidelity at the conceptual design phase is highly desirable as many of the non-linearities are not captured by lower fidelity tools. Only when these systems are designed from a true multi-disciplinary perspective can the real performance benefits be achieved and complete vehicle systems be fielded. Toward this end, the Vehicle Analysis Branch at NASA Langley Research Center has been developing the Integrated Design & Engineering Analysis (IDEA) Environment. IDEA is a collaborative environment for parametrically modeling conceptual and preliminary launch vehicle configurations using the Adaptive Modeling Language (AML) as the underlying framework. The environment integrates geometry, configuration, propulsion, aerodynamics, aerothermodynamics, trajectory, closure and structural analysis into a generative, parametric, unified computational model where data is shared seamlessly between the different disciplines. Plans are also in place to incorporate life cycle analysis tools into the environment which will estimate vehicle operability, reliability and cost. IDEA is currently being funded by NASA s Hypersonics Project, a part of the Fundamental Aeronautics Program within the Aeronautics Research Mission Directorate. The environment is currently focused around a two-stage-to-orbit configuration with a turbine based combined cycle (TBCC) first stage and reusable rocket second stage. This paper provides an overview of the development of the IDEA environment, a description of the current status and detail of future plans.

Robinson, Jeffrey S.↗
NASA NTRS1968

Design techniques - Stochastic controllers

Analytic techniques aid in the design of nearly optimal linear time-varying sampled-data stochastic controllers. The techniques also aid in the simplification and automation of program designing for control computers.

Widnall, W. S.↗
NASA NTRS1968

Stability and sensitivity

Graphical and analytical techniques for calculating regions of absolute stability of linear systems

Siljak, D.↗
NASA NTRS1972

Transient flow and heating characteristics in a pinched plasma column.

The generation of axial flow and heating of an argon plasma in a pinched plasma column of a pulsed, linear z-pinch device was examined experimentally and analytically. Transient (about 5 microsec) axial pressure profiles identify three characteristic periods in the column history. These include (1) strong axial pressure asymmetry indicative of plasma streaming, (2) isotropic, rapidly rising plasma pressure indicative of plasma heating, and (3) column breakup. An efficient conversion of radial collapse to axial streaming velocity is identified. Mechanisms for such an effect and subsequent heating are evaluated; significance to transients in pulsed plasma accelerators is identified.

York, T. M.↗
NASA NTRS1976

Numerical Airfoil Optimization Using a Reduced Number of Design Coordinates

A method is presented for numerical airfoil optimization whereby a reduced number of design coordinates are used to define the airfoil shape. The approach is to define the airfoil as a linear combination of shapes. These basic shapes may be analytically or numerically defined, allowing the designer to use his insight to propose candidate designs. The design problem becomes one of determining the participation of each such function in defining the optimum airfoil. Examples are presented for two-dimensional airfoil design and are compared with previous results based on a polynomial representation of the airfoil shape. Four existing NACA airfoils are used as basic shapes. Solutions equivalent to previous results are achieved with a factor of more than 3 improvements in efficiency, while superior designs are demonstrated with an efficiency greater than 2 over previous methods. With this shape definition, the optimization process is shown to exploit the simplifying assumptions in the inviscid aerodynamic analysis used here, thus demonstrating the need to use more advanced aerodynamics for airfoil optimization.

Vanderplaats, G. N.↗