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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 NTRS1972

Dipole antenna in space - Time periodic media.

Study and solution of the problem of dipole radiation in sinusoidally space-time periodic media. The space-time periodicity can be considered as due to a strong pump wave and is expressed as a traveling-wave type change in the dielectric constant or the plasma density. The solution also covers the limit case of a sinusoidally stratified medium. The solution is formulated in a matrix form such that the basic results and diagrams apply, with minor changes, to the different cases studied: electric and magnetic dipole in a dielectric, plasma, and uniaxial plasma. The wave-vector diagram is used extensively in studying and presenting the different properties of the solution: caustics, effect of the disturbance (pump wave) motion, harmonics, radiation outside the allowed cone in a uniaxial plasma. Many dipole radiation patterns are given, and their features are explained physically. Finally, the solution and results obtained are extended to certain generally space-time periodic media.

Elachi, C.↗
NASA NTRS1976

Simplified theory of large-amplitude wave propagation

An orbit perturbation procedure was applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest order approximation, untrapped electrons were assumed to follow constant-velocity orbits and trapped electrons were assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits were regarded as perturbations. The nonlinear damping rate and frequency shift were then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses.

Kim, H.↗
NASA NTRS1975

Subsonic flow past an oscillating cascade with steady blade loading - Basic formulation

A nonlinear boundary value problem governing the subsonic flow in a single, extended, blade passage region of a high-deflection, two dimensional, oscillating cascade is derived. The blades are assumed to be undergoing identical harmonic motions of small amplitude with constant phase angle between the motion of adjacent blades. An asymptotic perturbation approach is used to determine the velocity potential. This formulation can be used in the numerical determination of unsteady potential and thus the unsteady aerodynamic force and moment under various combinations of cascade and flow parameters.

Verdon, J. M.↗
NASA NTRS1976

Higher harmonic rotor blade pitch control

Tests of a model 'Reverse Velocity Rotor' system at high advance ratios and with twice-per-revolution cyclic pitch control were made under joint Navy-NASA sponsorship in the NASA, Ames 12 ft. pressure tunnel. The results showed significant gains in rotor performance at all advance ratios by using twice-per-revolution control. Detailed design studies have been made of alternative methods of providing higher harmonic motion including four types of mechanical systems and an electro-hydraulic system. The relative advantages and disadvantages are evaluated on the basis of stiffness, weight, volume, reliability and maintainability.

Ewans, J. R.↗
NASA NTRS1977

Approximate theory of large-amplitude wave propagation

An orbit perturbation procedure is applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest-order approximation, untrapped electrons are assumed to follow constant-velocity orbits and trapped electrons are assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits are regarded as perturbations. The nonlinear damping rate and frequency shift are then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses. A significant feature of the analysis is that it treats a single wave by techniques previously applied to turbulent spectra. The analysis can consequently be extended to the case of a large-amplitude wave interacting with a lower-amplitude spectrum of waves.

Kim, H.↗
NASA NTRS1978

A procedure for analyzing transonic flow over harmonically oscillating airfoils

Finite difference procedures were successfully used to solve the steady transonic flow about airfoils and appear to provide a practical means for calculating the corresponding unsteady flow. The purpose of the paper is to describe a finite difference procedure derived from the equations for the potential flow by assuming small perturbations and harmonic motion. The velocity potential is divided into steady and unsteady parts, and the resulting unsteady equation is linearized on the basis of small amplitudes of oscillation. The steady velocity potential, which must be calculated first, is described by the classical nonlinear transonic differential equation.

Weatherill, W. H.↗
NASA NTRS1984

Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

Ehlers, F. E.↗
NASA NTRS1983

Transverse vibration and buckling of a cantilevered beam with tip body under constant axial base acceleration

The planar transverse bending behavior of a uniform cantilevered beam with rigid tip body subject to constant axial base acceleration was analyzed. The beam is inextensible and capable of small elastic transverse bending deformations only. Two classes of tip bodies are recognized: (1) mass centers located along the beam tip tangent line; and (2) mass centers with arbitrary offset towards the beam attachment point. The steady state response is studied for the beam end condition cases: free, tip mass, tip body with restricted mass center offset, and tip body with arbitrary mass center offset. The first three cases constitute classical Euler buckling problems, and the characteristic equation for the critical loads/accelerations are determined. For the last case a unique steady state solution exists. The free vibration response is examined for the two classes of tip body. The characteristic equation, eigenfunctions and their orthogonality properties are obtained for the case of restricted mass center offset. The vibration problem is nonhomogeneous for the case of arbitrary mass center offset. The exact solution is obtained as a sum of the steady state solution and a superposition of simple harmonic motions.

Storch, J.↗
NASA NTRS1985

Signal detection techniques applied to the Chandler wobble

A sudden excitation event of the Chandler wobble should induce the earth's rotation pole to undergo damped harmonic motion. This type of motion has been searched for in the observations of the Chandler wobble using techniques based upon the concept of a matched filter. Although the signal detection techniques used here were not sensitive enough to detect any such isolated sudden excitation events, the result that was obtained is consistent with a randomly excited model of the Chandler wobble.

Gross, R. S.↗
NASA NTRS1990

On the propagation of plane waves above an impedance surface

The propagation of grazing incidence plane waves along a finite impedance boundary is investigated. A solution of the semi-infinite problem, where a harmonic motion, parallel to the boundary, is imposed along a line perpendicular to the boundary, is obtained. This solution consists of quasiplane waves, waves moving parallel to the boundary with amplitude and phase variations perpendicular to the boundary. Several approximations to the full solution are considered.

Zhong, F. H.↗
NASA NTRS1991

A modal aeroelastic analysis scheme for turbomachinery blading

An aeroelastic analysis is developed which has general application to all types of axial-flow turbomachinery blades. The approach is based on linear modal analysis, where the blade's dynamic response is represented as a linear combination of contributions from each of its in-vacuum free vibrational modes. A compressible linearized unsteady potential theory is used to model the flow over the oscillating blades. The two-dimensional unsteady flow is evaluated along several stacked axisymmetric strips along the span of the airfoil. The unsteady pressures at the blade surface are integrated to result in the generalized force acting on the blade due to simple harmonic motions. The unsteady aerodynamic forces are coupled to the blade normal modes in the frequency domain using modal analysis. An iterative eigenvalue problem is solved to determine the stability of the blade when the unsteady aerodynamic forces are included in the analysis. The approach is demonstrated by applying it to a high-energy subsonic turbine blade from a rocket engine turbopump power turbine. The results indicate that this turbine could undergo flutter in an edgewise mode of vibration.

Smith, Todd E.↗
NASA NTRS1992

Identification of aerodynamic models for maneuvering aircraft

The method based on Fourier functional analysis and indicial formulation for aerodynamic modeling as proposed by Chin and Lan is extensively examined and improved for the purpose of general applications to realistic airplane configurations. Improvement is made to automate the calculation of model coefficients, and to evaluate more accurately the indicial integral. Test data of large angle-of-attack ranges for two different models, a 70 deg. delta wing and an F-18 model, are used to further verify the applicability of Fourier functional analysis and validate the indicial formulation. The results show that the general expression for harmonic motions throughout a range of k is capable of accurately modeling the nonlinear responses with large phase lag except in the region where an inconsistent hysteresis behavior from one frequency to the other occurs. The results by the indicial formulation indicate that more accurate results can be obtained when the motion starts from a low angle of attack where hysteresis effect is not important.

Lan, C. Edward↗
NASA NTRS1952

Experimental Aerodynamic Derivatives of a Sinusoidally Oscillating Airfoil in Two-Dimensional Flow

Experimental measurements of the aerodynamic reactions on a symmetrical airfoil oscillating harmonically in a two-dimensional flow are presented and analyzed. Harmonic motions include pure pitch and pure translation, for several amplitudes and superimposed on an initial angle of attack, as well as combined pitch and translation. The apparatus and testing program are described briefly and the necessary theoretical background is presented. In general, the experimental results agree remarkably well with the theory, especially in the case of the pure motions. The net work per cycle for a motion corresponding to flutter is experimentally determined to be zero. Considerable consistent data for pure pitch were obtained from a search of available reference material, and several definite Reynolds number effects are evident.

Halfman, Robert L↗
NASA NTRS1995

Modeling of aircraft unsteady aerodynamic characteristics. Part 2: Parameters estimated from wind tunnel data

Aerodynamic equations with unsteady effects were formulated for an aircraft in one-degree-of-freedom, small-amplitude, harmonic motion. These equations were used as a model for aerodynamic parameter estimation from wind tunnel oscillatory data. The estimation algorithm was based on nonlinear least squares and was applied in three examples to the oscillatory data in pitch and roll of 70 deg triangular wing and an X-31 model, and in-sideslip oscillatory data of the High Incidence Research Model 2 (HIRM 2). All three examples indicated that a model using a simple indicial function can explain unsteady effects observed in measured data. The accuracy of the estimated parameters and model verification were strongly influenced by the number of data points with respect to the number of unknown parameters.

Klein, Vladislav↗
NASA NTRS1994

Sines and Cosines. Part 3 of 3

In this 'Project Mathematics' series video, the addition formulas of sines and cosines are explained and their real life applications are demonstrated. Both film footage and computer animation is used. Several mathematical concepts are discussed and include: Ptolemy's theorem concerned with quadrilaterals; the difference between a central angle and an inscribed angle; sines and chord lengths; special angles; subtraction formulas; and a application to simple harmonic motion. A brief history of the city Alexandria, its mathematicians, and their contribution to the field of mathematics is shown.

Apostol, Tom M.↗
NASA NTRS2003

Fast-Running Aeroelastic Code Based on Unsteady Linearized Aerodynamic Solver Developed

The NASA Glenn Research Center has been developing aeroelastic analyses for turbomachines for use by NASA and industry. An aeroelastic analysis consists of a structural dynamic model, an unsteady aerodynamic model, and a procedure to couple the two models. The structural models are well developed. Hence, most of the development for the aeroelastic analysis of turbomachines has involved adapting and using unsteady aerodynamic models. Two methods are used in developing unsteady aerodynamic analysis procedures for the flutter and forced response of turbomachines: (1) the time domain method and (2) the frequency domain method. Codes based on time domain methods require considerable computational time and, hence, cannot be used during the design process. Frequency domain methods eliminate the time dependence by assuming harmonic motion and, hence, require less computational time. Early frequency domain analyses methods neglected the important physics of steady loading on the analyses for simplicity. A fast-running unsteady aerodynamic code, LINFLUX, which includes steady loading and is based on the frequency domain method, has been modified for flutter and response calculations. LINFLUX, solves unsteady linearized Euler equations for calculating the unsteady aerodynamic forces on the blades, starting from a steady nonlinear aerodynamic solution. First, we obtained a steady aerodynamic solution for a given flow condition using the nonlinear unsteady aerodynamic code TURBO. A blade vibration analysis was done to determine the frequencies and mode shapes of the vibrating blades, and an interface code was used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor was used to interpolate the mode shapes from the structural dynamic mesh onto the computational dynamics mesh. Then, we used LINFLUX to calculate the unsteady aerodynamic forces for a given mode, frequency, and phase angle. A postprocessor read these unsteady pressures and calculated the generalized aerodynamic forces, eigenvalues, and response amplitudes. The eigenvalues determine the flutter frequency and damping. As a test case, the flutter of a helical fan was calculated with LINFLUX and compared with calculations from TURBO-AE, a nonlinear time domain code, and from ASTROP2, a code based on linear unsteady aerodynamics.

Reddy, T. S. R.↗
NASA NTRS2015

Acceleration and Velocity Sensing from Measured Strain

A simple approach for computing acceleration and velocity of a structure from the strain is proposed in this study. First, deflection and slope of the structure are computed from the strain using a two-step theory. Frequencies of the structure are computed from the time histories of strain using a parameter estimation technique together with an autoregressive moving average model. From deflection, slope, and frequencies of the structure, acceleration and velocity of the structure can be obtained using the proposed approach. Simple harmonic motion is assumed for the acceleration computations, and the central difference equation with a linear autoregressive model is used for the computations of velocity. A cantilevered rectangular wing model is used to validate the simple approach. Quality of the computed deflection, acceleration, and velocity values are independent of the number of fibers. The central difference equation with a linear autoregressive model proposed in this study follows the target response with reasonable accuracy. Therefore, the handicap of the backward difference equation, phase shift, is successfully overcome.

shape sensing↗