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NASA NTRS1991

An analytic solution of the transient behavior of backscattering thermal protective coatings exposed to combined radiative and convective heating

An analytic solution of the material response to combined radiative and convective heating is presented. The solution includes the equations of radiative transfer (within the material), coupled to a transient energy equation which contains both radiative and convective terms. The analysis allows for unlimited spectral detail, but assumes that within the range of applicability, the various material properties do not vary significantly with temperature. Also, to facilitate development of the analytic solution, it is assumed that scattering within the material dominates absorption, and the material exposed surface does not ablate. The exposed surface boundary condition includes convective heating and spectral radiation, some of which is absorbed by the surface and some which penetrates the surface.

Cornelison, Charles J.↗

NASA NTRS1991

An analytic solution to the steady-state double adiabatic equations

A set of 20 generalized moment-transport equations applicable to low-beta (low random energy density/magnetic energy density) plasmas of thermal origin in rotating planetary magnetospheres. An analytic solution is obtained for a set of simplified equations characterizing the steady-state transport of collisionless plasma; the novel element of this analytic solution is a closed-form solution for the parallel-flow velocity variation along magnetic field lines. It is shown that only T(perpendicular)/B remains constant along the field line, while density, parallel temperature, and parallel Mach number vary.

Gombosi, Tamas I.↗

NASA NTRS1991

Analytical ionization cross sections for atomic collisions

General analytical expressions for cross sections for direct ionization in atom-atom collisions are evaluated using the classical impulse approximation. The approach is also applied to ion-atom and molecule-molecule interactions. The overall accuracy of the obtained cross sections in a broad range of energy is better, when compared with existing measurements for many collision systems, than accuracy of other analytical predictions available in literature.

Kunc, J. A.↗

NASA NTRS1991

An analytical and experimental study to investigate flutter suppression via piezoelectric actuation

The objective was to analytically and experimentally study the capabilities of adaptive material plate actuators for suppressing flutter. The validity of analytical modeling techniques for piezoelectric materials was also investigated. Piezoelectrics are materials which are characterized by their ability to produce voltage when subjected to a mechanical strain. The converse piezoelectric effect can be utilized to actuate a structure by applying a voltage. For this investigation, a two degree of freedom wind tunnel model was designed, analyzed, and tested. The model consisted of a rigid airfoil and a flexible mount system which permitted a translational and a rotational degree of freedom. It was designed such that flutter was encounted within the testing envelope of the wind tunnel. Actuators, made of piezoelectric material were affixed to leaf springs of the mount system. Each degree of freedom was controlled by a separate leaf spring. Command signals, applied to the piezoelectric actuators, exerted control over the damping and stiffness properties. A mathematical aeroservoelastic model was constructed using finite element methods, laminated plate theory, and aeroelastic analysis tools. Plant characteristics were determined from this model and verified by open loop experimental tests. A flutter suppression control law was designed and implemented on a digital control computer. Closed loop flutter testing was conducted. The experimental results represent the first time that adaptive materials have been used to actively suppress flutter. It demonstrates that small, carefully placed actuating plates can be used effectively to control aeroelastic response.

Heeg, Jennifer↗

NASA NTRS1992

Mechanical properties of triaxially braided composites: Experimental and analytical results

This paper investigates the unnotched tensile properties of two-dimensional triaxial braid reinforced composites from both an experimental and analytical viewpoint. The materials are graphite fibers in an epoxy matrix. Three different reinforcing fiber architectures were considered. Specimens were cut from resin transfer molded (RTM) composite panels made from each braid. There were considerable differences in the observed elastic constants from different size strain gage and extensometer readings. Larger strain gages gave more consistent results and correlated better with the extensometer readings. Experimental strains correlated reasonably well with analytical predictions in the longitudinal, zero degree, fiber direction but not in the transverse direction. Tensile strength results were not always predictable even in reinforcing directions. Minor changes in braid geometry led to disproportionate strength variations. The unit cell structure of the triaxial braid was discussed with the assistence of computer analysis of the microgeometry. Photomicrographs of the braid geometry were used to improve upon the computer graphics representations of unit cells. These unit cells were used to predict the elastic moduli with various degrees of sophistication. The simple and the complex analyses were generally in agreement but none adequately matched the experimental results for all the braids.

Masters, John E.↗

NASA NTRS1992

On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function

It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.

Gottlieb, David↗

NASA NTRS1992

Analytical multiple scattering correction to the Mie theory: Application to the analysis of the lidar signal

The contribution of the multiple scattering to the lidar signal is dependent on the optical depth tau. Therefore, the radar analysis, based on the assumption that the multiple scattering can be neglected is limited to cases characterized by low values of the optical depth (tau less than or equal to 0.1) and hence it exclude scattering from most clouds. Moreover, all inversion methods relating lidar signal to number densities and particle size must be modified since the multiple scattering affects the direct analysis. The essential requests of a realistic model for lidar measurements which include the multiple scattering and which can be applied to practical situations follow. (1) Requested are not only a correction term or a rough approximation describing results of a certain experiment, but a general theory of multiple scattering tying together the relevant physical parameter we seek to measure. (2) An analytical generalization of the lidar equation which can be applied in the case of a realistic aerosol is requested. A pure analytical formulation is important in order to avoid the convergency and stability problems which, in the case of numerical approach, are due to the large number of events that have to be taken into account in the presence of large depth and/or a strong experimental noise.

Flesia, C.↗

NASA NTRS1990

Statistical interference prediction for ground stations from orbiting satellites. I - Simulation of interference duration and analytical approach for the determination of protection ratios

The authors describe simulation and analytical techniques for predicting the interference durations and protection ratios for deep-space ground stations from satellites in circular orbits. The simulation approach employs the characteristics of the ground station receivers in addition to the satellite specifications to calculate the daily statistics of the interference duration. On the other hand, the analytical method employs the ground station specifications to statistically predict the protection ratios as a function of the number of interference satellites and their associated probabilities. The results presented here can be used for both planning the missions and designing satellite communication links. The results can be also be used by spectrum managers and operations personnel to minimize the risk of harmful interference from satellites in low earth orbit to the deep space frequency band.

Gevargiz, John M.↗

NASA NTRS1992

Pulsed plane wave analytic solutions for generic shapes and the validation of Maxwell's equations solvers

Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.

Yarrow, Maurice↗

NASA NTRS1992

A three-dimensional finite-element thermal/mechanical analytical technique for high-performance traveling wave tubes

Current research in high-efficiency, high-performance traveling wave tubes (TWT's) has led to the development of novel thermal/mechanical computer models for use with helical slow-wave structures. A three-dimensional, finite element computer model and analytical technique used to study the structural integrity and thermal operation of a high-efficiency, diamond-rod, K-band TWT designed for use in advanced space communications systems. This analysis focused on the slow-wave circuit in the radiofrequency section of the TWT, where an inherent localized heating problem existed and where failures were observed during earlier cold compression, or 'coining' fabrication technique that shows great potential for future TWT development efforts. For this analysis, a three-dimensional, finite element model was used along with MARC, a commercially available finite element code, to simulate the fabrication of a diamond-rod TWT. This analysis was conducted by using component and material specifications consistent with actual TWT fabrication and was verified against empirical data. The analysis is nonlinear owing to material plasticity introduced by the forming process and also to geometric nonlinearities presented by the component assembly configuration. The computer model was developed by using the high efficiency, K-band TWT design but is general enough to permit similar analyses to be performed on a wide variety of TWT designs and styles. The results of the TWT operating condition and structural failure mode analysis, as well as a comparison of analytical results to test data are presented.

Shalkhauser, Kurt A.↗

NASA NTRS1991

An approximate analytical solution for interlaminar stresses in angle-ply laminates

An improved approximate analytical solution for interlaminar stresses in finite width, symmetric, angle-ply laminated coupons subjected to axial loading is presented. The solution is based upon statically admissible stress fields which take into consideration local property mismatch effects and global equilibrium requirements. Unknown constants in the admissible stress states are determined through minimization of the complementary energy. Typical results are presented for through-the-thickness and interlaminar stress distributions for angle-ply laminates. It is shown that the results represent an improved approximate analytical solution for interlaminar stresses.

Rose, Cheryl A.↗

NASA NTRS1992

Analytical and experimental study of control effort associated with model reference adaptive control

Numerical simulation results presently obtained for the performance of model reference adaptive control (MRAC) are experimentally verified, with a view to accounting for differences between the plant and the reference model after the control function has been brought to bear. MRAC is both experimentally and analytically applied to a single-degree-of-freedom system, as well as analytically to a MIMO system having controlled differences between the reference model and the plant. The control effort is noted to be sensitive to differences between the plant and the reference model.

Messer, R. S.↗

NASA NTRS1992

An analytical and experimental investigation of flutter suppression via piezoelectric actuation

The feasibility of using piezoelectric material actuators to suppress flutter was investigated analytically and experimentally. For this purpose, a two-degree of freedom wind-tunnel model was designed, analyzed, and tested. A digital control law was designed and implemented based on a discretized model. Experiments consisted of open- and closed-loop flutter tests. It is shown that analytical predictions agree well with experimental results. The open-loop flutter velocity prediction was 3.5 percent conservative, while the closed-loop prediction was 7.6 percent conservative. Results of the analysis showed that the flutter velocity would be increased by 15.7 percent with the control law, while 20 percent improvement was observed experimentally.

Heeg, Jennifer↗

NASA NTRS1990

Experimental and analytical study of close-coupled ventral nozzles for ASTOVL aircraft

Flow in a generic ventral nozzle system was studied experimentally and analytically with a block version of the PARC3D computational fluid dynamics program (a full Navier-Stokes equation solver) in order to evaluate the program's ability to predict system performance and internal flow patterns. Measurements showed about 5.5-percent flow-turning loss, reasonable nozzle performance coefficients, and a significant aftward axial component of thrust due to flow turning more than 90 deg. Flow behavior into and through the ventral duct is discussed and illustrated with paint streak flow visualization photographs. PARC3D flow visualization images are shown for comparison with the paint streak photographs. Modeling and computational issues encountered in the analytical work are discussed.

Mcardle, Jack G.↗

NASA NTRS1992

An analytic formula for H-infinity norm sensitivity with applications to control system design

An analytic formula for the sensitivity of singular value peak variation with respect to parameter variation is derived. As a corollary, the derivative of the H-infinity norm of a stable transfer function with respect to a parameter is presented. It depends on some of the first two derivatives of the transfer function with respect to frequency and the parameter. For cases when the transfer function has a linear system realization whose matrices depend on the parameter, analytic formulas for these first two derivatives are derived, and an efficient algorithm for calculating them is discussed. Examples are given which provide numerical verification of the H-infinity norm sensitivity formula and which demonstrate its utility in designing control systems satisfying H-infinity norm constraints. In the appendix, derivative formulas for singular values are paraphrased.

Giesy, Daniel P.↗

NASA NTRS1992

An analytic model of the neutral cloud evolution in the earth's atmosphere

An analytic model for the expansion of a chemically reacting gas in the upper atmosphere is discussed. The spatial-temporal distribution of released particles in the initial regime is described on the basis of self-similar solutions of Euler's equations. In the case of transition to the diffusion regime an approximate solution of the kinetic equation with the collision integral in the form of BGK is performed. Gravitation and the atmospheric inhomogeneity are taken into account, The diffusion regime is described by an analytic solution of the diffusion equation in an exponential atmosphere taking account of possible losses of the gas due to chemical reactions. Some peculiarities of the expansion of various gases as well as the possibility of applying the model for describing ionospheric 'holes' are discussed.

Bruskin, L. G.↗

NASA NTRS1992

Analytical flow/thermal modeling of combustion gas flows in Redesigned Solid Rocket Motor test joints

A one-dimensional analytical tool, TOPAZ (Transient One-dimensional Pipe flow AnalyZer), was used to model the flow characteristics of hot combustion gases through Redesigned Solid Rocket Motor (RSRM) joints and to compute the resultant material surface temperatures and o-ring seal erosion of the joints. The capabilities of the analytical tool were validated with test data during the Seventy Pound Charge (SPC) motor test program. The predicted RSRM joint thermal response to ignition transients was compared with test data for full-scale motor tests. The one-dimensional analyzer is found to be an effective tool for simulating combustion gas flows in RSRM joints and for predicting flow and thermal properties.

Woods, G. H.↗

NASA NTRS1993

ATTIRE (analytical tools for thermal infrared engineering): A sensor simulation and modeling package

The Advanced Sensor Development Laboratory (ASDL) at the Stennis Space Center develops, maintains and calibrates remote sensing instruments for the National Aeronautics & Space Administration (NASA). To perform system design trade-offs, analysis, and establish system parameters, ASDL has developed a software package for analytical simulation of sensor systems. This package called 'Analytical Tools for Thermal InfraRed Engineering' - ATTIRE, simulates the various components of a sensor system. The software allows each subsystem of the sensor to be analyzed independently for its performance. These performance parameters are then integrated to obtain system level information such as Signal-to-Noise Ratio (SNR), Noise Equivalent Radiance (NER), Noise Equivalent Temperature Difference (NETD) etc. This paper describes the uses of the package and the physics that were used to derive the performance parameters.

Jaggi, S.↗