SEARCH · Engineering Papers

Results for “APPROXIMATIONS”

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 1,585 records · Page 88

All sources NASA NTRS DOE OSTI

NASA NTRS1960

An Approximate Analytical Method for Studying Atmosphere Entry of Vehicles with Modulated Aerodynamic Forces

The dimensionless, transformed, nonlinear differential equation developed in NASA TR R-11 for describing the approximate motion and heating during entry into planetary atmospheres for constant aerodynamic coefficients and vehicle shape has been modified to include entries during which the aerodynamic coefficients and the vehicle shape are varied. The generality of the application of the original equation to vehicles of arbitrary weight, size, and shape and to arbitrary atmospheres is retained. A closed-form solution for the motion, heating, and the variation of drag loading parameter m/C(D)A has been obtained for the case of constant maximum resultant deceleration during nonlifting entries. This solution requires certain simplifying assumptions which do not compromise the accuracy of the results. The closed-form solution has been used to determine the variation of m/C(D)A required to reduce peak decelerations and to broaden the corridor for nonlifting entry into the earth's atmosphere at escape velocity. The attendant heating penalty is also studied.

Levy, Lionel L., Jr.↗

NASA NTRS1959

Slender-Body Theory Based On Approximate Solution of the Transonic Flow Equation

Approximate solution of the nonlinear equations of the small disturbance theory of transonic flow are found for the pressure distribution on pointed slender bodies of revolution for flows with free-stream, Mach number 1, and for flows that are either purely subsonic or purely supersonic. These results are obtained by application of a method based on local linearization that was introduced recently in the analysis of similar problems in two-dimensional flows. The theory is developed for bodies of arbitrary shape, and specific results are given for cone-cylinders and for parabolic-arc bodies at zero angle of attack. All results are compared either with existing theoretical results or with experimental data.

Spreiter, John R.↗

NASA NTRS1961

Constant Entropy Properties for an Approximate Model of Equilibrium Air

Approximate analytic solutions for properties of equilibrium air up to 15,000 K have been programmed for machine computation. Temperature, compressibility, enthalpy, specific heats, and speed of sound are tabulated as constant entropy functions of temperature. The reciprocal of acoustic impedance and its integral with respect to pressure are also given for the purpose of evaluating the Riemann constants for one-dimensional, isentropic flow.

Hansen, C. Frederick↗

NASA NTRS1961

Analytical Method of Approximating the Motion of a Spinning Vehicle with Variable Mass and Inertia Properties Acted Upon by Several Disturbing Parameters

An analytical method has been developed which approximates the dispersion of a spinning symmetrical body in a vacuum, with time-varying mass and inertia characteristics, under the action of several external disturbances-initial pitching rate, thrust misalignment, and dynamic unbalance. The ratio of the roll inertia to the pitch or yaw inertia is assumed constant. Spin was found to be very effective in reducing the dispersion due to an initial pitch rate or thrust misalignment, but was completely Ineffective in reducing the dispersion of a dynamically unbalanced body.

Buglia, James J.↗

NASA NTRS1959

Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies

Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

Mirels, Harold↗

NASA NTRS1959

Approximations for the Thermodynamic and Transport Properties of High-Temperature Air

The thermodynamic and transport properties of high-temperature air are found in closed form starting from approximate partition functions for the major components in air and neglecting all minor components. The compressibility, enthalpy, entropy, the specific heats, the speed of sound, the coefficients of viscosity and of thermal conductivity, and the Prandtl numbers for air are tabulated from 500 degrees to 15,000 degrees Kelvin over a range of pressure from 0.0001 to 100 atmospheres. The energy of air and the mol. fractions of the major components of air can be found from the tabulated values for compressibility and enthalpy. It is predicted that the Prandtl number for fully ionized air, which is in complete equilibrium, will become small compared to unity, the order of 0.01, and this implies that boundary layers in such flow will be very transparent to heat flux.

Hansen, C. Frederick↗

NASA NTRS1999

Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics

A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.

Devasia, Santosh↗

NASA NTRS1981

A Diagonal Form of an Implicit Approximate-Factorization Algorithm

A modification of an implicit approximate-factorization finite-difference algorithm applied to partial differential equations is presented. This algorithm is applied to the two- and three-dimensional Euler equations in general curvilinear coordinates. The modification transforms the coupled system of equations into an uncoupled diagonal form that requires less computational work. For steady-state applications, the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm. The diagonal algorithm reduces the storage requirement of the implicit solution process and therefore has an important effect on the application of implicit finite-difference schemes to vector processors. Results are presented for realistic two-dimensional transonic flow fields about airfoils. Computation costs are reduced 24-34%.

Pulliam, T. H.↗

NASA NTRS1995

Analytic Sensitivity and Approximation of Skin Buckling Constraints in Wing-Shape Synthesis

Explicit expressions for terms of the stiffness and geometric stiffness matrices are derived for the buckling analysis of trapezoidal fiber composite wing skin panels. The formulation is based on Ritz analysis using simple polynomials, and leads to explicit expressions for the analytic sensitivities of the stiffness and geometric stiffness matrices with respect to layer thickness, fiber directions, and panel shape. Integration with wing box analysis using either the equivalent plate approach or the finite element method, makes it possible to obtain sensitivities of panel buckling constraints with respect to wing planform shape or locations of internal ribs and spars. The analytic sensitivities are used to construct approximations of panel buckling constraints for integrated wing/panel design synthesis.

Livne, Eli↗

NASA NTRS1997

Panel Flutter Constraints: Analytic Sensitivities and Approximations Including Planform Shape Design Variables

Analytical sensitivities of panel flutter constraints with respect to panel shape as well as thickness and material properties are derived and numerically tested. Cases of fixed in-plane loads and cases in which in-plane loads are variable (depending on panel and overall wing shape as well as material and sizing design variables) are considered. Accuracy of approximations and range of move limits required are studied in preparation for integration with nonlinear programming/approximation concept aeroelastic design synthesis methodology.

Livne, Eli↗

NASA NTRS1980

Electron Capture into Rydberg States According to the Born Approximation: Correction of an Error

A general expression is derived for the Born amplitude for electron capture into high principal, and arbitrary angular momentum, quantum numbers, n and l, by bare nuclei from hydrogenic atom targets. Cross sections for capture into high n and l = 0,1 are given in analytic forms. The limiting values of the ratios of the Born over OBK cross sections for n >> 1 and l = 0,1 are found, and shown that they confirm the empirical law of Jackson and Schiff only approximately. For high angular momenta, it is shown that the Born cross section approaches the OBK cross section. An error in a previous publication by the author has been corrected.

Omidvar, Kazem↗

NASA NTRS1999

Approximate Co-Location of Precipitation and Low-Level Westerlies in Tropical Monthly Means

In summer monsoon regions the monthly mean precipitation regions coincide approximately well with regions of westerlies at low-levels. An included chart shows a 15-year (1979-1993) mean August 850 hPa zonal wind from NCEP/NCAR reanalysis dataset and Xie-Arkin precipitation. It shows a region of westerlies covering most of Northern Indian Ocean and extending to northwestern Pacific. This region coincides well with the region with precipitation greater than 6 mm/day. Obviously the coincidence is not exact; the region of larges; zonal wind in the Arabian Sea is in a region of relatively low precipitation and is far from the region of maximum precipitation in Bay of Bengal. Also, in a zonally averaged sense between 40E and 140E, the latitude of maximum precipitation is slightly higher than that of the maximum zonal wind. Low-level westerlies are also found in regions west of Central America and in western Africa north of the equator. These regions are also closely associated with precipitation centers. Across equator from these westerlies regions there are regions of strong easterlies. Also, on their poleward side the westerly regions are flanked by weaker easterly regions. In February, similar observation can be found in the Australian monsoon area and in South America monsoon region; again the regions of westerlies coincide well with regions of maximum precipitation. As in the northern hemisphere, the maximum precipitation is found to the cast of the maximum zonal wind. The two maxima lie almost at the same latitude with that of the westerlies slightly closer to the equator. In the non-monsoon seasons the low- level westerlies can also be found in the tropical precipitation regions, the longitudinal range of the westerlies is undiminished and the speed of the westerlies is not much weaker than that found in February. The interpretation of these observational facts is the goal of this investigation. The approach taken is numerical simulation with the Goddard Earth Observation Systems atmospheric general circulation model, and its aqua-planet version, combined with theoretical arguments.

Choa, Winston C.↗

NASA NTRS2000

Approximate Matching as a Key Technique in Organization of Natural and Artificial Intelligence

The basic property of an intelligent system, natural or artificial, is "understanding". We consider the following formalization of the idea of "understanding" among information systems. When system I issues a request to system 2, it expects a certain kind of desirable reaction. If such a reaction occurs, system I assumes that its request was "understood". In application to simple, "push-button" systems the situation is trivial because in a small system the required relationship between input requests and desired outputs could be specified exactly. As systems grow, the situation becomes more complex and matching between requests and actions becomes approximate.

Mack, Marilyn↗

NASA NTRS2000

Cascade Optimization for Aircraft Engines With Regression and Neural Network Analysis - Approximators

The NASA Engine Performance Program (NEPP) can configure and analyze almost any type of gas turbine engine that can be generated through the interconnection of a set of standard physical components. In addition, the code can optimize engine performance by changing adjustable variables under a set of constraints. However, for engine cycle problems at certain operating points, the NEPP code can encounter difficulties: nonconvergence in the currently implemented Powell's optimization algorithm and deficiencies in the Newton-Raphson solver during engine balancing. A project was undertaken to correct these deficiencies. Nonconvergence was avoided through a cascade optimization strategy, and deficiencies associated with engine balancing were eliminated through neural network and linear regression methods. An approximation-interspersed cascade strategy was used to optimize the engine's operation over its flight envelope. Replacement of Powell's algorithm by the cascade strategy improved the optimization segment of the NEPP code. The performance of the linear regression and neural network methods as alternative engine analyzers was found to be satisfactory. This report considers two examples-a supersonic mixed-flow turbofan engine and a subsonic waverotor-topped engine-to illustrate the results, and it discusses insights gained from the improved version of the NEPP code.

Patnaik, Surya N.↗

NASA NTRS1999

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Larson, Mats G.↗

NASA NTRS1997

Universal Approximation of Mamdani Fuzzy Controllers and Fuzzy Logical Controllers

In this paper, we first distinguish two types of fuzzy controllers, Mamdani fuzzy controllers and fuzzy logical controllers. Mamdani fuzzy controllers are based on the idea of interpolation while fuzzy logical controllers are based on fuzzy logic in its narrow sense, i.e., fuzzy propositional logic. The two types of fuzzy controllers treat IF-THEN rules differently. In Mamdani fuzzy controllers, rules are treated disjunctively. In fuzzy logic controllers, rules are treated conjunctively. Finally, we provide a unified proof of the property of universal approximation for both types of fuzzy controllers.

Yuan, Bo↗

NASA NTRS1994

An Approximate Solution for the Circumsolar Flow Field of a Sun Moving Through the Local Interstellar Medium (LISM)

The solar system is in relative motion with respect to the ambient interstellar medium. The supersonic solar wind is expected to pass through the termination shock, thus the solar wind plasma eventually has to enter into an asymptotic outflow geometry appropriately adopted to this counterflow situation. Many attempts have been done to simulate the interaction between the solar wind and the LISM numerically. In this paper we generalize a Parker type analytical solution of the counterflow. The idea is to introduce a special kind of compressibility of the solar wind flow. With the assumption that only a transversal component of the density gradient normal to the flow lines exists we are able to calculate a full set of hydrodynamical quantities describing the circumsolar flow field of a Sun moving through the LISM. The equations governing the velocity and density fields lead to analytical solutions which can be taken as good approximations to the more general case of compressible plasma flows.

Ratkiewicz, Romana E.↗

NASA NTRS2002

Approximating Fluid Flow from Ambient to Very Low Pressures: Modeling ISS Experiments that Vent to Vacuum

Two ISS (International Space Station) experiment payloads will vent a volume of gas overboard via either the ISS Vacuum Exhaust System or the Vacuum Resource System. A system of ducts, valves and sensors, under design, will connect the experiments to the ISS systems. The following tasks are required: Create an analysis tool that will verify the rack vacuum system design with respect to design requirements, more specifically approximate pressure at given locations within the vacuum systems; Determine the vent duration required to achieve desired pressure within the experiment modules; Update the analysis as systems and operations definitions mature.

Minor, Robert↗