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At least 919 records · Page 51

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NASA NTRS1973

Condensation in CO2 free jet expansions. I - Dimer formation.

A theoretical and experimental investigation of the kinetics of CO2 dimer formation in the adiabatically expanding core of a free jet expansion has been carried out. The theoretical analysis is based on dimer formation by an efficient termolecular process and dimer destruction by bimolecular collisions. Account is taken of the expected variation of the specific heat ratio during the expansion and of the effective increase in the termolecular collision rate at low temperatures due to the presence of loosely bound orbiting pairs. Experimental dimer concentrations were measured mass spectrometrically by forming a molecular beam from the expanded gas mixture after the onset of molecular flow. Observed dimer concentrations, for a range of pre-expansion conditions of 400 to 900 torr pressure and room temperature, are in good agreement with the theoretical analysis, provided that account is taken of the effect of loosely bound orbiting pairs at low temperatures.

Dorfeld, W. G.↗

NASA NTRS1973

A stochastic model of turbulent mixing with chemical reaction: Nitric oxide formulation in a plug-flow burner

A stochastic model of turbulent mixing was developed for a reactor in which mixing is represented by n-body fluid particle interactions. The model was used to justify the assumption (made in previous investigations of the role of turbulent mixing on burner generated thermal nitric oxide and carbon monoxide emissions) that for a simple plug flow reactor, composition nonuniformities can be described by a Gaussian distribution function in the local fuel:air equivalence ratio. Recent extensions of this stochastic model to include the combined effects of turbulent mixing and secondary air entrainment on thermal generation of nitric oxide in gas turbine combustors are discussed. Finally, rate limited upper and lower bounds of the nitric oxide produced by thermal fixation of molecular nitrogen and oxidation of organically bound fuel nitrogen are estimated on the basis of the stochastic model for a plug flow burner; these are compared with experimental measurements obtained using a laboratory burner operated over a wide range of test conditions; good agreement is obtained.

Flagan, R. C.↗

NASA NTRS1974

Advanced theoretical and experimental studies in automatic control and information systems

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.

Desoer, C. A.↗

NASA NTRS1974

Noncommuting observables in quantum detection and estimation theory

Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a large Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.

Helstrom, C. W.↗

NASA NTRS1974

The effects of a visual fidelity criterion on the encoding of images

Shannon's rate-distortion function provides a potentially useful lower bound against which to compare the rate-versus-distortion performance of practical encoding-transmission systems. However, this bound is not applicable unless one can arrive at a numerically-valued measure of distortion which is in reasonable correspondence with the subjective evaluation of the observer or interpreter. We have attempted to investigate this choice of distortion measure for monochrome still images. This investigation has considered a class of distortion measures for which it is possible to simulate the optimum (in a rate-distortion sense) encoding. Such simulation was performed at a fixed rate for various measures in the class and the results compared subjectively by observers. For several choices of transmission rate and original images, one distortion measure was fairly consistently rated as yielding the most satisfactory appearing encoded images.

Mannos, J. L.↗

NASA NTRS1974

Shuttle ascent trajectory optimization with function space quasi-Newton techniques

A Space Shuttle ascent trajectory optimization problem from lift-off to orbital insertion is solved with a function space version of a quasi-Newton parameter optimization method developed by Broyden. The problem includes five parameter and one bounded-function controls, two state-variable constraints, and four terminal conditions. The bounded controls are treated directly, while the remaining constraints are adjoined to the performance index (maximum payload) with penalty functions. The problem is formulated as a four-phase variational problem (liftoff, pitch-over, gravity-turn, linear tangent steering), and the appropriate gradients are developed by first variation theory. A projection operator is introduced to aid in the interpretation of the algorithm with mixed parameter and function controls.

Edge, E. R.↗

NASA NTRS1974

Transient response of multidegree-of-freedom linear systems to forcing functions with inequality constraints

Optimal control theory is applied to analyze the transient response of discrete linear systems to forcing functions with unknown time dependence but having known bounds. Particular attention is given to forcing functions which include: (1) maximum displacement of any given mass element, (2) maximum relative displacement of any two adjacent masses, and (3) maximum acceleration of a given mass. Linear mechanical systems with an arbitrary number of degrees of freedom and only one forcing function acting are considered. In the general case, the desired forcing function is found to be a function that switches from the upper-to-lower bound and vice-versa at certain moments of time. A general procedure for finding such switching times is set forth.

Michalopoulos, C. D.↗

NASA NTRS1974

Error analysis of householder transformations as applied to the standard and generalized eigenvalue problems

Backward error analyses of the application of Householder transformations to both the standard and the generalized eigenvalue problems are presented. The analysis for the standard eigenvalue problem determines the error from the application of an exact similarity transformation, and the analysis for the generalized eigenvalue problem determines the error from the application of an exact equivalence transformation. Bounds for the norms of the resulting perturbation matrices are presented and compared with existing bounds when known.

Ward, R. C.↗

NASA NTRS1974

Investigation of matter-antimatter interaction for possible propulsion applications

Matter-antimatter annihilation is discussed as a means of rocket propulsion. The feasibility of different means of antimatter storage is shown to depend on how annihilation rates are affected by various circumstances. The annihilation processes are described, with emphasis on important features of atom-antiatom interatomic potential energies. A model is developed that allows approximate calculation of upper and lower bounds to the interatomic potential energy for any atom-antiatom pair. Formulae for the upper and lower bounds for atom-antiatom annihilation cross-sections are obtained and applied to the annihilation rates for each means of antimatter storage under consideration. Recommendations for further studies are presented.

Morgan, D. L., Jr.↗

NASA NTRS1975

Unsteady vortex lattice techniques applied to wake formation and performance of the statically thrusting propeller

The application is considered of vortex lattice techniques to the problem of describing the aerodynamics and performance of statically thrusting propellers. A numerical lifting surface theory to predict the aerodynamic forces and power is performed. The chordwise and spanwise loading is modelled by bound vortices fixed to a twisted flat plate surface. In order to eliminate any apriori assumptions regarding the wake shape, it is assumed the propeller starts from rest. The wake is generated in time and allowed to deform under its own self-induced velocity field as the motion of the propeller progresses. The bound circulation distribution is then determined with time by applying the flow tangency boundary condition at certain selected control points on the blades. The aerodynamics of the infinite wing and finite wing are also considered. The details of wake formation and roll-up are investigated, particularly the localized induction effect. It is concluded that proper wake roll-up and roll-up rates can be established by considering the details of motion at the instant of start.

Hall, G. F.↗

NASA NTRS1975

Design of Energy Storage Reactors for Dc-To-Dc Converters

Two methodical approaches to the design of energy-storage reactors for a group of widely used dc-to-dc converters are presented. One of these approaches is based on a steady-state time-domain analysis of piecewise-linearized circuit models of the converters, while the other approach is based on an analysis of the same circuit models, but from an energy point of view. The design procedure developed from the first approach includes a search through a stored data file of magnetic core characteristics and results in a list of usable reactor designs which meet a particular converter's requirements. Because of the complexity of this procedure, a digital computer usually is used to implement the design algorithm. The second approach, based on a study of the storage and transfer of energy in the magnetic reactors, leads to a straightforward design procedure which can be implemented with hand calculations. An equation to determine the lower-bound volume of workable cores for given converter design specifications is derived. Using this computer lower-bound volume, a comparative evaluation of various converter configurations is presented.

Chen, D. Y.↗

NASA NTRS1975

Use of the Wigner representation in scattering problems

The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.

Bemler, E. A.↗

NASA NTRS1975

Development and evaluation of a new method for predicting aircraft buffet response

The buffet prediction method uses rigid wind tunnel model fluctuating pressure data to form a buffet forcing function. The response is then calculated with a mathematical dynamic model of the airplane developed for gust response analysis. By including the extremes of phasing and contribution of symmetric and antisymmetric airplane responses, the upper and lower bounds are established for buffet response. F-111A flight test data show good agreement with predicted bounds for a variety of flight conditions.

Cunningham, A. M., Jr.↗

NASA NTRS1975

On a numerical sufficiency test for monotonic convergence of finite element models

Finite element analyses characterized by monotonic convergence include the discipline for meaningful measurements of convergence rate and consequently economical extrapolation. Few proposers of element models guarantee monotonic convergence for their elements. Thus, a need exists for an automatic test to classify available element models. This paper describes such a test - a test can be performed using a digital computer to guarantee that a particular element model imbues monotonicity. It describes the test and its basis. It examines seven element models for a rectangular membrane to illustrate the value of the tests. Besides confirming results already known, the application yields new data. It 'proves' monotonicity for two improved models, defines the range of element proportions for which another element can be guaranteed to exhibit monotonicity, and suggests that another element is deficient. In the special case of absolutely convergent membrane displacement models, proof of monotonicity is a necessary and sufficient condition to insure that upper bound estimates of strain energy are developed. Accordingly, the test furnishes a proof of bound solutions independently of requirements on displacement continuity the element basis may or may not satisfy.

Melosh, R. J.↗

NASA NTRS1975

Propellers of Minimum Induced Loss, and Water Tunnel Tests of Such a Propeller

The fundamental vortex theory for a single rotation propeller with a finite number of blades is reviewed. The theory leads to the specification of a radial distribution of bound circulation on each blade for minimum induced loss, analogous to the elliptic spanwise distribution of bound circulation on a wing for minimum induced drag. A propeller designed in accord with this theory has been tested in a water tunnel where it exhibited high efficiency in spite of localized cavitating flow. A knowledge of the flow field for an optimum propeller is of value to the airframe designer seeking to maximize the performance of the airplane-propeller combination.

Larrabee, E. E.↗

NASA NTRS1975

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, Addendum

New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence.

Peters, B. C., Jr.↗

NASA NTRS1975

Electrochemical generation of oxygen. 1: The effects of anions and cations on hydrogen chemisorption and anodic oxide film formation on platinum electrode. 2: The effects of anions and cations on oxygen generation on platinum electrode

The effects were studied of anions and cations on hydrogen chemisorption and anodic oxide film formation on Pt by linear sweep voltammetry, and on oxygen generation on Pt by potentiostatic overpotential measurement. The hydrogen chemisorption and anodic oxide film formation regions are greatly influenced by anion adsorption. In acids, the strongly bound hydrogen occurs at more cathodic potential when chloride and sulfate are present. Sulfate affects the initial phase of oxide film formation by produced fine structure while chloride retards the oxide-film formation. In alkaline solutions, both strongly and weakly bound hydrogen are influenced by iodide, cyanide, and barium and calcium cations. These ions also influence the oxide film formation. Factors considered to explain these effects are discussed. The Tafel slope for oxygen generation was found to be independent on the oxide thickness and the presence of cations or anions. The catalytic activity indicated by the exchange current density was observed decreasing with increasing oxide layer thickness, only a minor dependence on the addition of certain cations and anions was found.

Huang, C. J.↗

NASA NTRS1976

Secular acceleration of Phobos and Q of Mars

Reductions of Mariner 9 TV data of Phobos and Deimos tend to corroborate the existence of a secular acceleration of Phobos commensurate with two recently reported values based on a reprocessing of earth-based data. These values of secular acceleration have been used together with Mariner 9 data on the physical size of Phobos and earth-based photoelectric observations which infer a carbonaceous composition for Phobos to place upper and lower bounds of 50 and 150, respectively, on the tidal dissipation function of Mars. The corresponding upper and lower bounds on the tidal lag angle are 0.19 and 0.57 deg.

Smith, J. C.↗