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NASA NTRS1974

Optical antenna gain. I - Transmitting antennas

The gain of centrally obscured optical transmitting antennas is analyzed in detail. The calculations, resulting in near- and far-field antenna gain patterns, assume a circular antenna illuminated by a laser operating in the TEM-00 mode. A simple polynomial equation is derived for matching the incident source distribution to a general antenna configuration for maximum on-axis gain. An interpretation of the resultant gain curves allows a number of auxiliary design curves to be drawn that display the losses in antenna gain due to pointing errors and the cone angle of the beam in the far field as a function of antenna aperture size and its central obscuration. The results are presented in a series of graphs that allow the rapid and accurate evaluation of the antenna gain which may then be substituted into the conventional range equation.

Klein, B. J.↗

NASA NTRS1977

Non-linear duct acoustics and its application to fan noise

Quite often the scalar Helmholtz equation is assumed to be the fundamental equation of duct acoustics and various relations are derived from it. An investigation is, therefore, conducted regarding the underlying assumptions leading to the Helmholtz equation. It is found that serious errors, even well below 186 dB, are possible if the assumption of linearity were to be made. In duct acoustics these errors are highest near the cutoff points and in the case of ducts with transonic flow. It is pointed out that serious errors could arise if a nonlinear problem is analyzed by linear methods. At times, an entire phenomenon remains unpredictable by linear methods. Attention is given to the characteristics of nonlinear systems, the phenomenon of multiple pure tones in the case of noise from the aircraft engine fans, the limitations of the conventional acoustics equation, duct shape and nonlinearity, and the numerical simulation of a fan with 8 blades.

Vaidya, P. G.↗

NASA NTRS1982

Simple phenomenological modeling of transition-region capacitance of forward-biased p-n junction diodes and transistor diodes

The derivation of a simple expression for the capacitance C(V) associated with the transition region of a p-n junction under a forward bias is derived by phenomenological reasoning. The treatment of C(V) is based on the conventional Shockley equations, and simpler expressions for C(V) result that are in general accord with the previous analytical and numerical results. C(V) consists of two components resulting from changes in majority carrier concentration and from free hole and electron accumulation in the space-charge region. The space-charge region is conceived as the intrinsic region of an n-i-p structure for a space-charge region markedly wider than the extrinsic Debye lengths at its edges. This region is excited in the sense that the forward bias creates hole and electron densities orders of magnitude larger than those in equilibrium. The recent Shirts-Gordon (1979) modeling of the space-charge region using a dielectric response function is contrasted with the more conventional Schottky-Shockley modeling.

Lindholm, F. A.↗

NASA NTRS2017

On High-Order Upwind Methods for Advection

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom 𝐾 per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2𝐾−1, which is higher than the expected order of 𝐾.

high-order methods↗

NASA NTRS1973

Transmitter and receiver antenna gain analysis for laser radar and communication systems

A comprehensive and fairly self-contained study of centrally obscured optical transmitting and receiving antennas is presented and is intended for use by the laser radar and communication systems designer. The material is presented in a format which allows the rapid and accurate evaluation of antenna gain. The Fresnel approximation to scalar wave theory is reviewed and the antenna analysis proceeds in terms of the power gain. Conventional range equations may then be used to calculate the power budget. The transmitter calculations, resulting in near and far field antenna gain patterns, assumes the antenna is illuminated by a laser operating in the fundamental cavity mode. A simple equation is derived for matching the incident source distribution to a general antenna configuration for maximum on-axis gain. An interpretation of the resultant gain curves allows a number of auxiliary design curves to be drawn which display the losses in antenna gain due to pointing errors and the cone angle of the outgoing beam as a function of antenna size and central obscuration. The use of telescope defocusing as an approach to spreading the beam for target acquisition is compared to some alternate methods.

Klein, B. J.↗

NASA NTRS1973

Photoconductor-metal contact at higher densities.

The formation of space charge in the barrier region is discussed. This region extends to a distance, x-sub o, equal to 200 A plus twice the mean free path of majority carriers. The conventional transport equation can be used only for x greater than x-sub o, and the carrier density at x-sub o represents a boundary condition for the bulk. Its change as a function of applied voltage, temperature, and light intensity in photoconducting CdS is discussed. The time dependence of the space-charge formation in the region between 0 and x-sub o is analyzed. It is shown under which conditions the individuality of the metal contact is observable.

Dussel, G. A.↗

NASA NTRS1980

Buckling of periodic structures

Equations are developed for the buckling of a general lattice structure that has repetitive geometry. Equilibrium at a typical node is expressed using finite element techniques, and the only assumption is that the response is periodic. By basing the stiffness matrix on the exact solution of the beam column equation, accurate results are obtained for complex buckling behavior that would require a very large system of equations using conventional techniques. The present method requires the eigenvalues of only a 6x6 determinant. The results are used to study the buckling of isogrid cylinders, three-element truss columns and polygonal rings. Details of the analysis including expressions for all terms in the governing stability determinant are given.

Anderson, M. S.↗

NASA NTRS1984

On the theory of cosmic-ray-mediated shocks with variable compression ratio

Cosmic-ray-mediated shocks may accelerate enough cosmic rays to high enough energies that they escape the shock, carrying an appreciable amount of energy before being convected to downstream infinity. Under such conditions, it is noted, the overall compression ratio cannot be determined from the conservation equations as in conventional hydrodynamic treatments, and the standard equations for shock acceleration admit arbitrarily high compression ratios. A procedure is outlined for obtaining the structure of high Mach number, cosmic-ray-mediated shocks, including their overall compresion ratio, around a low Mach number viscous subshock. Analytic solutions are obtained by quardrature for an energy-dependent diffusion coefficient in the limit of extreme sensitivity to energy, which, unlike previous solutions, include the finite thermal pressure of the preshock gas.

Eichler, D.↗

NASA NTRS1987

The finite-difference time-domain (FD-TD) method for electromagnetic scattering and interaction problems

The formulation and recent applications of the finite-difference time-domain (FD-TD) method for the numerical modeling of electromagnetic scattering and interaction problems are considered. It is shown that improvements in FD-TD modeling concepts and software implementation often make it a preferable choice for structures which cannot be easily treated by conventional integral equations and asymptotic approaches. Recent FD-TD modeling validations in research areas including coupling to wires and wire bundles in free space and cavities, scattering from surfaces in relativistic motion, inverse scattering, and radiation condition theory, are reviewed. Finally, the advantages and disadvantages of FD-TD, and guidelines concerning when FD-TD should and should not be used in high-frequency electromagnetic modeling problems, are summarized.

Taflove, A.↗

NASA NTRS1988

Effect of general relativity on a near-Earth satellite in the geocentric and barycentric reference frames

Whether one uses a solar-system barycentric frame or a geocentric frame when including the general theory of relativity in orbit determinations for near-Earth satellites, the results should be equivalent to some limiting accuracy. The purpose of this paper is to clarify the effects of relativity in each frame and to demonstrate their equivalence through the analysis of real laser-tracking data. A correction to the conventional barycentric equations of motion is shown to be required.

Ries, J. C.↗

NASA NTRS1988

Efficient load measurements using singular value decomposition

Various basic research was performed on efficient load measurement estimation techniques for aircraft structure analysis. An overview is presented of the load measurement problem. Two basic equivalent approaches to load measurement evaluations were considered. Under approach 1, the load values are modeled as depending linearly on the measured values. Under approach 2, the measured values depend linearly on the load values. By using the modern Singular Value Decomposition method, it was shown that under all conditions of the number of loads and number of gages, approach 1 is equivalent to approach 2. By using the conventional normal equation (linear regression) approach, approach 1 is only valid when the number of loads is equal to or greater than the number of gages, while approach 2 is the reverse. Furthermore, except for the case of the number of loads equals the number of gages, the load prediction formulas under the two approaches are not equivalent.

Yao, Kung↗

NASA NTRS1989

Determination of joint drives for stable end-effector motion in flexible robotic systems

The prescribed tasks in high speed robotic systems are severely deteriorated because of their manipulator dynamic deflections. On the other hand conventional dynamic modeling techniques fail to reveal appropriate control forces in flexible systems. The conventional dynamic equations of motion for systems subject to kinematical constraints are modified by a new concept of control force representation. The directions of the control forces are selected such that they correspond to the joint degrees of freedom. Then the joint control forces and torques that yield unperturbed prescribed motions are solved simultaneously with the system motion. A flexible manipulator is presented to illustrate the methods proposed.

Ider, Sitki Kemal↗

NASA NTRS1990

The effects of general relativity on near-earth satellites

Whether one uses a solar system barycentric frame or a geocentric frame when including the general theory of relativity in orbit determination for near-earth satellites, the results should be equivalent to some limiting accuracy. The purpose of this paper is to clarify the effects of relativity in each frame and to demonstrate their equivalence through the analysis of three years of laser tracking data taken on the Lageos satellite. It is demonstrated that the simpler formulation in the geocentric frame is adequate for the purpose of near-earth satellite orbit determination. A correction to the conventional barycentric equations of motion is shown to be required.

Ries, J. C.↗

NASA NTRS1991

On two-dimensional relativistic stellar winds

Stellar wind is of great interest, because many of the astrophysical systems possess wind like structures. For a long time only nonrelativistic winds have been studied. However, recently it was proposed by Kennel et al. that the relativistic pulsar wind with the plasma, consisting of electrons and positrons, can be responsible for the observed features of the Crab nebula. The study of Kennel et al. revealed the inconsistency of the assumption of the wind zero temperature with the observational data. It has been shown that only for high relativistic temperatures can high Mach numbers be reached, which allows the possibility of a shock formation. The analysis of Kennel et al. was extended into the 2-D case by using conventional magnetohydrodynamic equations for a relativistic plasma with an isotropic relativistic temperature. The state equation is assumed polytropic.

Gedalin, M. E.↗

NASA NTRS1950

Comparison of outside-surface heat-transfer coefficients for cascades of turbine blades

A comparison of available results from heat-transfer investigations on cascades of turbine blades is presented using the Nusselt equation. The conventional correlation procedure is modified by defining the Reynolds number by the average of the velocities and the pressures around the blades. The correlation of the results from impulse blades was improved by using the Reynolds number defined by the average velocity and pressure. The final comparison indicated that several variables, which possibly influence heat transfer, should be investigated.

HEAT TRANSFER, CASCADES↗

NASA NTRS1943

The Heat Transfer to a Plate in Flow at High Speed

The heat transfer in the laminar boundary layer of a heated plate in flow at high speed can be obtained by integration of the conventional differential equations of the boundary layer, so long as the material values can be regarded as constant. This premise is fairly well satisfied at speeds up to about twice the sonic speed and at not excessive temperature rise of the heated plate. The general solution of the equation includes Pohlhausen's specific cases of heat transfer to a plate at low speeds and of the plate thermometer. The solution shows that the heat transfer coefficient at high speed must be computed with the same equation as at low speed, when it is referred to the difference of the wall temperature of the heated plate in respect to its "natural temperature." Since this fact follows from the linear structure of the differential equation describing the temperature field, it is equally applicable to the heat transfer in the turbulent boundary layer.

Eckert, E.↗

NASA NTRS2017

Ice Crystal Icing Research at NASA

Ice crystals found at high altitude near convective clouds are known to cause jet engine power-loss events. These events occur due to ice crystals entering a propulsion systems core flowpath and accreting ice resulting in events such as uncommanded loss of thrust (rollback), engine stall, surge, and damage due to ice shedding. As part of a community with a growing need to understand the underlying physics of ice crystal icing, NASA has been performing experimental efforts aimed at providing datasets that can be used to generate models to predict the ice accretion inside current and future engine designs. Fundamental icing physics studies on particle impacts, accretion on a single airfoil, and ice accretions observed during a rollback event inside a full-scale engine in the Propulsion Systems Laboratory are summarized. Low fidelity code development using the results from the engine tests which identify key parameters for ice accretion risk and the development of high fidelity codes are described. These activities have been conducted internal to NASA and through collaboration efforts with industry, academia, and other government agencies. The details of the research activities and progress made to date in addressing ice crystal icing research challenges are discussed.

icing↗

NASA NTRS2017

Validation of a Compact Isokinetic Total Water Content Probe for Wind Tunnel Characterization at NASA Glenn Icing Research Tunnel and at NRC Ice Crystal Tunnel

A new compact isokinetic probe to measure total water content in a wind tunnel environment has been developed. The probe has been previously tested under altitude conditions. This paper presents a comprehensive validation of the probe under a range of liquid water conditions at sea level in the NASA Glenn Icing Research Tunnel and with ice crystals at sea level at the NRC wind tunnel. The compact isokinetic probe is compared to tunnel calibrations and other probes.

meterological instruments↗