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A comparison of experiment with theory is made for air ejectors having cylindrical mixing sections and operating under conditions of supersonic primary flow and either mixed or supersonic regimes of mixing. The effect on ejector performance of such parameters as mixer length and cross section, terminating diffuser, primary Mach number, and primary nozzle position is presented in terms of mass flow and pressure ratio.
The two-control operation of a conventional airplane is treated by means of the theory of disturbed motions. The consequences of this method of control are studied with regard to the stability of the airplane in its unconstrained components of motion and the movements set up during turn maneuvers.
This report describes the work performed over the period of October 1, 1997 through March 31, 2001. Under this contract, UAH/CAO participated in defining and designing the SPAce Readiness Coherent Lidar Experiment (SPARCLE) mission, and developed the instrument's optical subsystem. This work was performed in collaborative fashion with NASA/MSFC engineers at both UAH/CAO and NASA/MSFC facilities. Earlier work by the UAH/CAO had produced a preliminary top-level system design for the Shuttle lidar instrument meeting the proposed mission performance requirements and the Space Shuttle Hitchhiker canister volume constraints. The UAH/CAO system design efforts had concentrated on the optical and mechanical designs of the instrument. The instrument electronics were also addressed, and the major electronic components and their interfaces defined. The instrument design concept was mainly based on the state of the transmitter and local oscillator laser development at NASA Langley Research Center and Jet Propulsion Laboratory, and utilized several lidar-related technologies that were either developed or evaluated by the NASA/MSFC and UAH/CAO scientists. UAH/CAO has developed a comprehensive coherent lidar numerical model capable of analyzing the performance of different instrument and mission concepts. This model uses the instrument configuration, atmospheric conditions and current velocity estimation theory to provide prediction of instrument performance during different phases of operation. This model can also optimize the design parameters of the instrument.
It is a particular challenge to develop a stigmatic spectrograph for XUV wavelengths since the very low normal-incidence reflectance of standard materials most often requires that the design be restricted to a single optical element which must simultaneously provide both re-imaging and spectral dispersion. This problem has been solved in the past by the use of toroidal gratings with uniform line-spaced rulings (TULS). A number of solar EUV (Extreme Ultraviolet) spectrometers have been based on such designs, including SOHO/CDS, Solar-B/EIS, and the sounding rockets SERTS and EUNIS. More recently, Kita, Harada, and collaborators have developed the theory of spherical gratings with varied line-space rulings (SVLS) operated at unity magnification, which have been flown on several astronomical satellite missions. We now combine these ideas into a spectrometer concept that puts varied-line space rulings onto toroidal gratings. Such TVLS designs are found to provide excellent imaging even at very large spectrograph magnifications and beam-speeds, permitting extremely high-quality performance in remarkably compact instrument packages. Optical characteristics of two solar spectrometers based on this concept are described: SUMI, proposed as a sounding rocket experiment, and NEXUS, proposed for the Solar Dynamics Observatory mission.
It is a particular challenge to develop a stigmatic spectrograph for UV, EUV wavelengths since the very low normal-incidence reflectance of standard materials most often requires that the design be restricted to a single optical element which must simultaneously provide both reimaging and spectral dispersion. This problem has been solved in the past by the use of toroidal gratings with uniform line-spaced rulings (TULS). A number of solar extreme ultraviolet (EUV) spectrometers have been based on such designs, including SOHO/CDS, Solar-B/EIS, and the sounding rockets Solar Extreme ultraviolet Research Telescope and Spectrograph (SERTS) and Extreme Ultraviolet Normal Incidence Spectrograph (EUNIS). More recently, Kita, Harada, and collaborators have developed the theory of spherical gratings with varied line-space rulings (SVLS) operated at unity magnification, which have been flown on several astronomical satellite missions. We now combine these ideas into a spectrometer concept that puts varied-line space rulings onto toroidal gratings. Such TVLS designs are found to provide excellent imaging even at very large spectrograph magnifications and beam-speeds, permitting extremely high-quality performance in remarkably compact instrument packages. Optical characteristics of three new solar spectrometers based on this concept are described: SUMI and RAISE, two sounding rocket payloads, and NEXUS, currently being proposed as a Small-Explorer (SMEX) mission.
A fully coupled deformation and damage approach to modeling the response of composite materials and composite laminates is presented. It is based on the semi-‐analytical generalized method of cells (GMC) micromechanics model as well as its higher fidelity counterpart, HFGMC, both of which provide closed-form constitutive equations for composite materials as well as the micro scale stress and strain fields in the composite phases. The provided constitutive equations allow GMC and HFGMC to function within a higher scale structural analysis (e.g., finite element analysis or lamination theory) to represent a composite material point, while the availability of the micro fields allow the incorporation of lower scale sub‐models to represent local phenomena in the fiber and matrix. Further, GMC's formulation performs averaging when applying certain governing equations such that some degree of microscale field accuracy is surrendered in favor of extreme computational efficiency, rendering the method quite attractive as the centerpiece in a integrated computational material engineering (ICME) structural analysis; whereas HFGMC retains this microscale field accuracy, but at the price of significantly slower computational speed. Herein, the sensitivity of deformation and the fatigue life of graphite/epoxy PMC composites, with both ordered and disordered microstructures, has been investigated using this coupled deformation and damage micromechanics based approach. The local effects of fiber breakage and fatigue damage are included as sub‐models that operate on the microscale for the individual composite phases. For analysis of laminates, classical lamination theory is employed as the global or structural scale model, while GMC/HFGMC is embedded to operate on the microscale to simulate the behavior of the composite material within each laminate layer. A key outcome of this study is the statistical influence of microstructure and micromechanics idealization (GMC or HFGMC) on the overall accuracy of unidirectional and laminated composite deformation and fatigue response.
A theory is presented for post stall transients in multistage axial compressors. The theory leads to a set of coupled first-order ordinary differential equations capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. These changing flow features are shown to have a significant effect on the instantaneous compressor pumping characteristic during unsteady operation, and henace on the overall system behavior. It is also found from the theory that the ultimate mode of system response, stable rotating stall or surge, depends not only on the B parameter but also on other parameters, such as the compressor length-to-diameter ratio. Small values of this latter quantity tend to favor the occurrence of surge, as do large values of B. A limited parametric study is carried out to show the impact of the different system features on transient behavior. Based on analytical and numerical results, several specific topics are suggested for future research on post-stall transients.
The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun.
Five dimensional rotations and representation of isomorphic spinor groups by boson operators calculus, expanding Gelfand states in Weyl patterns
Experimentally, thermal annealing is known to be a factor which enables a number of different integrated circuits (IC's) to recover their operating characteristics after suffering radiation damage in the space radiation environment; thus, decreasing and limiting long term cumulative total-dose effects. This annealing is also known to be accelerated at elevated temperatures both during and after irradiation. Linear response theory (LRT) was applied, and a linear response function (LRF) to predict the radiation/annealing response of sensitive parameters of IC's for long term (several months or years) exposure to the space radiation environment were constructed. Compressing the annealing process from several years in orbit to just a few hours or days in the laboratory is achieved by subjecting the IC to elevated temperatures or by increasing the typical spaceflight dose rate by several orders of magnitude for simultaneous radiation/annealing only. The accomplishments are as follows: (1) the test procedure to make predictions of the radiation response was developed; (2) the calculation of the shift in the threshold potential due to the charge distribution in the oxide was written; (3) electron tunneling processes from the bulk Si to the oxide region in an MOS IC were estimated; (4) in order to connect the experimental annealing data to the theoretical model, constants of the model of the basic annealing process were established; (5) experimental data obtained at elevated temperatures were analyzed; (6) time compression and reliability of predictions for the long term region were shown; (7) a method to compress test time and to make predictions of response for the nonlinear region was proposed; and (8) nonlinearity of the LRF with respect to log(t) was calculated theoretically from a model.
Landing aircraft on board carriers is a most delicate phase of flight operations at sea. The ability to predict the aircraft carrier's motion over an interval of several seconds within reasonable error bounds may allow an improvement in touchdown dispersion and reduce the value of the ramp clearance due to a smoother aircraft trajectory. Also, improved information to the landing signal officer should decrease the number of waveoffs substantially. This paper indicates and shows quantitatively that, based upon the power density spectrum data for pitch and heave measured for various ships and sea conditions, the motion can be predicted well, for up to 15 s. Moreover, the zero crossover times for both pitch and heave motions can be predicted with impressive accuracy. The predictor was designed on the basis of Kalman's optimum filtering theory (the discrete time case), being compatible with real-time digital computer operation.
Barbara Kanki from NASA Ames Research Center will discuss research that focuses on the collaborations between pilots, air traffic controllers and dispatchers that will change in NextGen systems as automation increases and roles and responsibilities change. The approach taken by this NASA Ames team is to build a collaborative systems assessment template (CSAT) based on detailed task descriptions within each system to establish a baseline of the current operations. The collaborative content and context are delineated through the review of regulatory and advisory materials, policies, procedures and documented practices as augmented by field observations and interviews. The CSAT is developed to aid the assessment of key human factors and performance tradeoffs that result from considering different collaborative arrangements under NextGen system changes. In theory, the CSAT product may be applied to any NextGen application (such as Trajectory Based Operations) with specified ground and aircraft capabilities.
A comprehensive presentation is made of the engineering analysis methods used in the design, development and evaluation of helicopters. After an introduction covering the fundamentals of helicopter rotors, configuration and operation, rotary wing history, and the analytical notation used in the text, the following topics are discussed: (1) vertical flight, including momentum, blade element and vortex theories, induced power, vertical drag and ground effect; (2) forward flight, including in addition to momentum and vortex theory for this mode such phenomena as rotor flapping and its higher harmonics, tip loss and root cutout, compressibility and pitch-flap coupling; (3) hover and forward flight performance assessment; (4) helicopter rotor design; (5) rotary wing aerodynamics; (6) rotary wing structural dynamics, including flutter, flap-lag dynamics ground resonance and vibration and loads; (7) helicopter aeroelasticity; (8) stability and control (flying qualities); (9) stall; and (10) noise.
Direct measurements were undertaken at the Aeronautics Laboratory in Turin of the aerodynamic actions on an oscillating wing. The tests conducted had as their essential object the examination of the operation of apparatus designed for this measurement. The values experimentally obtained for the aerodynamic coefficients are in good agreement with the theory of oscillatory motion of the wing of finite span and show clear deviation from the values obtained by theory of plane motion.
A solution has been obtained for a stator-rotor pair operating in an annulus with constant hub and tip radii. The stator and rotor are represented as actuator discs, and perfect fluid flow is assumed. The solutions are exact within these limitations, no linearization being required. The forms of blade loadings considered allow the introduction of large vorticity by either the rotor or stator. As a result, the rotor may be a ?nonconstant-work' row. The solutions obtained are of summational form, but many of the summations are obtained in closed form, the resultant formulas allowing rapid calculation of desired examples. An example numerical result is included.
A method is proposed for classifying estimation problems based on the Lie algebra generated by the operators which appear in the conditional density equation. A natural class of automorphisms of this algebra is examined and a systematic method of generating equivalent problems is developed. Finally, a new class of nonlinear filtering problems with essentially nonlinear filtering equations are presented.
When tracking control systems are used in repetitive operations such as robots in various manufacturing processes, the controller will make the same errors repeatedly. Here consideration is given to learning controllers that look at the tracking errors in each repetition of the process and adjust the control to decrease these errors in the next repetition. A general formalism is developed for learning control of discrete-time (time-varying or time-invariant) linear multivariable systems. Methods of specifying a desired trajectory (such that the trajectory can actually be performed by the discrete system) are discussed, and learning controllers are developed. Stability criteria are obtained which are relatively easy to use to insure convergence of the learning process, and proper gain settings are discussed in light of measurement noise and system uncertainties.
The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions, which greatly complicates the optimization of real devices. Here, it is shown that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e., one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (nonuseful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique.