Search NASA⌕ Search

SEARCH · Search NASA

Results for “Number theory”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 523 records · Page 29

Mariner 9 celestial mechanics experiment - A status report.

There are two basic efforts in the Mariner 9 celestial mechanics experiment: the determination of the gravity field of Mars and the performance of a very precise test of the theory of general relativity. In addition, there are a number of astrodynamic constants that are being determined. All the analyses are based on the Mariner 9 radio tracking data.

Lorell, J.↗

Mechanisms of deterioration of nutrients

Methods are reported by which freeze dried foods of improved quality will be produced. The applicability of theories of flavor retention has been demonstrated for a number of food polymers, both proteins and polysacchardies. Studies on the formation of structures during freeze drying have been continued for emulsified systems. Deterioration of organoleptic quality of freeze dried foods due to high temperature heating has been evaluated and improved procedures developed. The influence of water activity and high temperature on retention of model flavor materials and browning deterioration has been evaluated for model systems and food materials.

Karel, M.↗

A high altitude base pressure experiment

A high-altitude base-pressure experiment has been successfully conducted on a high-performance Air Force reentry vehicle. Low Reynolds number laminar-flow flight data were obtained at an altitude of about 248,000 ft. The experiment utilized the NASA Ames vibrating diaphragm transducer specifically designed to measure base pressure at altitudes in excess of 200,000 ft with a threshold sensitivity level of 0.0002 psia. The flight data have provided needed low Reynolds number information from Reynolds numbers of about 70,000 to 10,000,000. These new data verify that a 'maximum' exists in the base pressure ratio versus Reynolds number curve at low Reynolds numbers and hypersonic Mach numbers (free-stream Mach numbers greater than 20) in qualitative agreement with the theory of Crooco and Lees (1952).

Cassanto, J. M.↗

Correlations by the entrainment theory of thermodynamic effects for developed cavitation in venturis and comparisons with ogive data

A semi-empirical entrainment theory was employed to correlate the measured temperature depression, Delta T, in a developed cavity for a venturi. This theory correlates Delta t in terms of the dimensionless numbers of Nusselt, Reynolds, Froude, Weber and Peclet, and dimensionless cavity length, L/D. These correlations are then compared with similar correlations for zero and quarter caliber ogives. In addition, cavitation number data for both limited and developed cavitation in venturis are presented.

Billet, M. L.↗

Prediction of Laminar and Turbulent Boundary Layer Flow Separation in V/STOL Engine Inlets

A description is presented of the development of the boundary layer on the lip and diffuser surface of a subsonic inlet at arbitrary operating conditions of mass flow rate, free stream velocity and incidence angle. Both laminar separation on the lip and turbulent separation in the diffuser are discussed. The agreement of the theoretical results with model experimental data illustrates the capability of the theory to predict separation. The effects of throat Mach number, inlet size, and surface roughness on boundary layer development and separation are illustrated.

Chou, D. C.↗

Prediction of laminar and turbulent boundary layer flow separation in V/STOL engine inlets

The paper provides a theoretical description of the development of the boundary layer on the lip and diffuser surface of a subsonic inlet at arbitrary operating conditions of mass flow rate, freestream velocity and incidence angle. Both laminar separation on the lip and turbulent separation in the diffuser are discussed. The agreement of the theoretical results with model experimental data illustrates the capability of the theory to predict separation. The effects of throat Mach number, inlet size, and surface roughness on boundary-layer development and separation are illustrated.

Chou, D. C.↗

An information theory approach to the density of the earth

Information theory can develop a technique which takes experimentally determined numbers and produces a uniquely specified best density model satisfying those numbers. A model was generated using five numerical parameters: the mass of the earth, its moment of inertia, three zero-node torsional normal modes (L = 2, 8, 26). In order to determine the stability of the solution, six additional densities were generated, in each of which the period of one of the three normal modes was increased or decreased by one standard deviation. The superposition of the seven models is shown. It indicates that current knowledge of the torsional modes is sufficient to specify the density in the upper mantle but that the lower mantle and core will require smaller standard deviations before they can be accurately specified.

Graber, M. A.↗

The Response of a Quartz Crystal Microbalance to a Liquid Deposit

A theory was developed for predicting the loss of response of a QCM (Quartz Crystal Microbalance) to a liquid deposit due to viscous effects in the deposit. The loss of response is expressed by a response factor, equal to the response of the QCM to a liquid film divided by its response to a solid film of the same mass per unit area. The theory assumes a droplet-type deposit morphology, and considers the influence of droplet distribution parameters. Experiments were conducted to examine the validity of the theory, using DC 704 silicone oil as the subject deposit material. Experiments were made in two series: one with constant deposit mass and variable temperature, the other with variable deposit mass and constant temperature. Interpretation of the data using the theory has enabled information on droplet area coverage and number density to be deduced.

Glassford, A. P. M.↗

Vortex development on slender missiles at supersonic speeds

A theoretical and experimental effort has been made to develop a vortex-prediction capability on circular and noncircular missiles at supersonic speeds. Predicted vortex patterns are computed by two linear-theory computer codes. One calculates the strengths and initial locations of the vortices, and the other calculates their trajectories. A short color motion picture has been produced from the calculations to illustrate the predicted vortex patterns on a typical missile. Experimental vapor-screen photographs are presented to show the longitudinal development of the vortices on a fin-control missile. Comparisons are made between these data and the predicted vortices to assess the accuracy of the theory. The theory appears to be fairly accurate in predicting the number, locations, and relative strengths of individual vortices which develop over the missile, but cannot predict vortex sheets or diffuse vorticity whenever they occur.

Allen, J. M.↗

Correlations of thermodynamic effects for developed cavitation

The net positive suction head (NPSH) requirements for a pump are determined by the combined effects of cavitation, fluid properties, pump geometry, and pump operating point. An important part of this determination is the temperature depression (Delta T). Correlations are presented of the temperature depression for various degrees of developed cavitation on venturis and ogives. These correlations, based on a semi-empirical entrainment theory, express Delta T in terms of the dimensionless numbers of Nusselt, Reynolds, Froude, Weber, and Peclet, and dimensionless cavity length (L/D). The Delta T data were obtained in Freon 114, hydrogen and nitrogen for the venturis and in Freon 113 and water for the ogives.

Billet, M. L.↗

Charts for determining potential minimum sonic-boom overpressures for supersonic cruise aircraft

Charts which give an estimation of minimum achievable sonic-boom levels for supersonic cruise aircraft are presented. A minimization method based on modified linear theory was analyzed. Results show several combinations of Mach number, altitude, and aircraft length and weight. Overpressure and impulse values are given for two types of sonic boom signatures for each of these conditions: (1) a flat top or minimum overpressure signature which has a pressure plateau behind the initial shock, and (2) a minimum shock signature which allows a pressure rise after the initial shock. Results are given for the effects of nose shape.

Darden, C. M.↗

Time sequence analysis of flickering auroras. I - Application of Fourier analysis

Using a technique that enables one to digitize the brightness of auroral displays from individual fields of a video signal, we have analyzed the frequency content of flickering aurora. Through the application of Fourier analysis to our data, we have found that flickering aurora contains a wide range of enhanced frequencies, although the dominant frequency enhancement generally occurs in the range 6-12 Hz. Each incidence of flickering that we observed was associated with increased radio wave absorption. Furthermore, we have found that flickering occurs in bright auroral surges, the occurrence of which is not limited to the 'breakup' phase of auroral substorms. Our results are interpreted in terms of a recently proposed theory of fluctuating double layers that accounts for a number of the observational features.

Berkey, F. T.↗

Influence of the Reynolds number on normal forces of slender bodies of revolution

Comprehensive force, moment, and pressure distribution measurements as well as flow visualization experiments were carried out to determine the influence of the Reynolds number on nonlinear normal forces of slender bodies of revolution. Experiments were performed in transonic wind tunnels at angles of attack up to 90 deg in the Mach number range 0.5 to 2.2 at variable Reynolds numbers. The results were analysed theoretically and an empirical theory was developed which describes the test results satisfactory.

Hartmann, K.↗

Comparison of measured and calculated airloads on an energy efficient transport wing model equipped with oscillating control surfaces

Wind-tunnel measurements of steady and unsteady pressures for a high-aspect-ratio supercritical wing model are compared with calculations by the linear unsteady aerodynamic lifting-surface theory, known as the Doublet Lattice method, at Mach numbers of 0.650 (subsonic) and 0.78 (transonic). The steady-pressure data comparisons are made for incremental changes in angle of attack and control-surface deflection. The unsteady-pressure data comparisons are made for oscillating control-surface deflections. Some differences between the measured and calculated aerodynamics are attributed to viscous and transonic effects that are not accounted for in the Doublet Lattice analysis. Comparisons of the transonic unsteady-pressure data for the oscillating control surfaces are improved by applying empirical corrections based on the steady-pressure measurements to the unsteady Doublet Lattice calculations.

Mccain, W. E.↗

A model of the excitation of orderly structures in a shear layer

The artificial excitation of shear layers is investigated theoretically and experimentally. The present paper describes quantitatively the coupling between exciting sound field and shear layer fluctuations. The mathematical model is restricted to low Strouhal numbers at which large scale structures are occurring. The theory does not contain any empirical constants and it is confirmed by the experiments in the expected validity range.

Bechert, D. W.↗

On uniformly valid high-frequency far-field asymptotic solutions of the Helmholtz equation

An asymptotic, large wave number approximation for the Helmholtz equation is derived. The theory is an extension of the geometric acoustic theory, and provides corrections to that theory in the form of multiplicative functions which satisfy parabolic equations. A simple example is used both to illustrate failure of the geometric theory for large propagation distances, and to show the improvement obtained by use of the new theory.

Mcaninch, G. L.↗

New variables for classical and quantum gravity

A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced. These variables simplify the constraints of general relativity considerably and enable one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory. The imbedding suggests new ways of attacking a number of problems in both classical and quantum gravity. Some illustrative applications are discussed.

Ashtekar, Abhay↗

Theoretical studies of mass loss and shock phenomena in cool star envelopes

To show the difficulty of producing the blue-shifted emission of (O I) and (S II) from T Tauri stars directly in the stellar wind, an element of gas in a radially expanding stellar wind was followed as it cooled and recombined. Results indicate that T Tauri winds must be heated at large distances from the star to produce the (S II) emission. A shock between the wind and the disk is an attractive mechanism to produce this heating. When the theory is applied to a simple disk model, a number of predictions and implications are evident, for example, that some T Tauri stars eject mass near the equatorial plane. In a second study, spectral energy distributions of T Tauri stars were analyzed to place limits on the amount of accretion which might occur during the early phase of stellar evolution. The best match to H-alpha line profiles is for models in which the turbulent velocity dominates close to the star, while expansion dominates farther out. Such a model predicts, for instance, that a mass loss rate of 1/10,000,000 solar masses per year is required to account for the blue-shifted Na I absorption of some objects.

Hartmann, Lee↗