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 469 records · Page 26

Methanol Droplet Extinction in Carbon-Dioxide-Enriched Environments in Microgravity

Diffusive extinction of methanol droplets with initial diameters between 1.25 mm and 1.72 mm, burning in a quiescent microgravity environment at one atmosphere pressure, was obtained experimentally for varying levels of ambient carbon-dioxide concentrations with a fixed oxygen concentration of 21% and a balance of nitrogen. These experiments serve as precursors to those which are beginning to be performed on the International Space Station and are motivated by the need to understand the effectiveness of carbon-dioxide as a fire suppressant in low-gravity environments. In these experiments, the flame standoff distance, droplet diameter, and flame radiation are measured as functions of time. The results show that the droplet extinction diameter depends on both the initial droplet diameter and the ambient concentration of carbon dioxide. Increasing the initial droplet diameter leads to an increased extinction diameter, while increasing the carbon-dioxide concentration leads to a slight decrease in the extinction diameter. These results are interpreted using a critical Damk hler number for extinction as predicted by an earlier theory, which is extended here to be applicable in the presence of effects of heat conduction along the droplet support fibers and of the volume occupied by the support beads

Hicks, Michael C.↗

Lecture Series "Boundary Layer Theory". Part I - Laminar Flows: Laminar Flows - Part 1

In the lecture series starting today author want to give a survey of a field of aerodynamics which has for a number of years been attracting an ever growing interest. The subject is the theory of flows with friction, and, within that field, particularly the theory of friction layers, or boundary layers. A great many considerations of aerodynamics are based on the ideal fluid, that is the frictionless incompressibility and fluid. By neglect of compressibility and friction the extensive mathematical theory of the ideal fluid, (potential theory) has been made possible. Actual liquids and gases satisfy the condition of incomressibility rather well if the velocities are not extremely high or, more accurately, if they are small in comparison with sonic velocity. For air, for instance, the change in volume due to compressibility amounts to about 1 percent for a velocity of 60 meters per second. The hypothesis of absence of friction is not satisfied by any actual fluid; however, it is true that most technically important fluids, for instance air and water, have a very small friction coefficient and therefore behave in many cases almost like the ideal frictionless fluid. Many flow phenomena, in particular most cases of lift, can be treated satisfactorily, - that is, the calculations are in good agreement with the test results, -under the assumption of frictionless fluid. However, the calculations with frictionless flow show a very serious deficiency; namely, the fact, known as d'Alembert's paradox, that in frictionless flow each body has zero drag whereas in actual flow each body experiences a drag of greater or smaller magnitude. For a long time the theory has been unable to bridge this gap between the theory of frictionless flow and the experimental findings about actual flow. The cause of this fundamental discrepancy is the viscosity which is neglected in the theory of ideal fluid; however, in spite of its extraordinary smallness it is decisive for the course of the flow phenomena.

Schlichting, H.↗

Environmental dynamics at orbital altitudes

The work reported involved the improvement of aerodynamic theory for free molecular and transition flow regimes. The improved theory was applied to interpretation of the dynamic response of objects traveling through the atmosphere. Satellite drag analysis includes analysis methods, atmospheric super rotation effects, and satellite lift effects on orbital dynamics. Transition flow regimes were studied with falling sphere data and errors resulting in inferred atmospheric parameters from falling sphere techniques. Improved drag coefficients reveal considerable error in previous falling sphere data. The drag coefficient has been studied for the entire spectrum of Knudsen Number and speed ratio, with particular emphasis on the theory of the very low-speed ratio regime.

Karr, G. R.↗

The passage of an infinite swept airfoil through an oblique gust

An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

Adamczyk, J. L.↗

Observation of beam-generated VLF hiss in a large laboratory plasma

The paper describes a lab experiment on a beam-plasma instability under conditions for which the theory of VLF hiss is applicable. An energetic electron beam is injected into a cold, dense, almost collisionless magnetoplasma. Beam and plasma dimensions are so large that oblique whistler wave propagation and growth are readily observable. The observations of frequency and wave number spectra, growth rate, and instability level are consistent with theory and satellite observation in regions of electron precipitation.

Stenzel, R. L.↗

Subsonic and Supersonic Flutter Analysis of a Highly Tapered Swept-Wing Planform, Including Effects of Density Variation and Finite Wing Thickness, and Comparison with Experiments

The flutter characteristics of several wings with an aspect-ratio of 4.0, a taper ratio of 0.2, and a quarter-chord sweepback of 45 deg. have been investigated analytically for Mach numbers up to 2.0. The calculations were based on the modified-strip-analysis method, the subsonic-kernel-function method, piston theory, and quasi-steady second-order theory. Results of t h e analysis and comparisons with experiment indicated that: (1) Flutter speeds were accurately predicted by the modified strip analysis, although accuracy at t h e highest Mach numbers required the use of nonlinear aerodynamic theory (which accounts for effects of wing thickness) for the calculation of the aerodynamic parameters. (2) An abrupt increase of flutter-speed coefficient with increasing Mach number, observed experimentally in the transonic range, was also indicated by the modified strip analysis. (3) In the low supersonic range for some densities, a discontinuous variation of flutter frequency with Mach number was indicated by the modified strip analysis. An abrupt change of frequency appeared experimentally in the transonic range. (4) Differences in flutter-speed-coefficient levels obtained from tests at low supersonic Mach numbers in two wind tunnels were also predicted by the modified strip analysis and were shown to be caused primarily by differences in mass ratio. (5) Flutter speeds calculated by the subsonic-kernel-function method were in good agreement with experiment and with the results of the modified strip analysis. (6) Flutter speed obtained from piston theory and from quasi-steady second-order theory were higher than experimental values by at least 38 percent.

Yates, Carson, Jr.↗

Estimation of parameters involved in high angle-of-attack aerodynamic theory using spin flight test data

The difficulty in applying parameter estimation techniques to spinning airplanes is due in part to the unwieldy number of possible combinations of terms in the equations of motion, when the model structure is unknown. The combination of high angle of attack and high rotation rate results in aerodynamic functions which are quite complex. For wing dominated configurations it is advantageous to use aerodynamic theory to generate the model structure. In this way, the number of unknown parameters is reduced and the model accuracy may be increased. Under conditions for which the theory is inadequate, however, model accuracy may be reduced. Strip theory, for example, is incapable of predicting autorotative rolling moments indicated by wind tunnel tests at angles of attack exceeding 40 degrees. An improved aerodynamic theory would be necessary to successfully apply the technique advanced for such regions.

Taylor, L. W., Jr.↗

Nature and origin of basin-forming projectiles

The formation of the observed lunar multi-ring basins is discussed in the context of current theories of terrestrial planet formation, particularly those in which these planets formed by the accumulation of large planetesimals. The observed number, size, and timing of lunar basin-forming impacts is in the range expected for such theories. Tidal disruption during close encounters to earth and Venus can provide a single mechanism that explains a number of details concerning the number, size distribution, and stochastic nature of the timing of these impacts. A basin time scale is suggested in which Nectaris is associated with the 4.1 b.y. age of the Apollo 16 light matrix breccias. In accordance with the present consensus, Serenitatis is 3.86 b.y., Imbrium and Orientale 3.80-3.82 b.y. in age. Other nearside circular basins (e.g., Humorum and Crisium) are intermediate in age between 3.86 and 4.12 b.y. The large number of 3.8-3.9 b.y. ages is attributed primarily to the magnitude of the Imbrium and Serenitatis impacts, and sampling bias resulting from concentration of collection sites in proximity to these basins.

Wetherill, G. W.↗

A first-principles model for orificed hollow cathode operation

A theoretical model describing orificed hollow cathode discharge is presented. The approach adopted is based on a purely analytical formulation founded on first principles. The present model predicts the emission surface temperature and plasma properties such as electron temperature, number densities and plasma potential. In general, good agreements between theory and experiment are obtained. Comparison of the results with the available related experimental data shows a maximum difference of 10 percent in emission surface temperature, 20 percent in electron temperature and 35 percent in plasma potential. In case of the variation of the electron number density with the discharge current a maximum discrepancy of 36 percent is obtained. However, in the case of the variation with the cathode internal pressure, the predicted electron number density is higher than the experimental data by a maximum factor of 2.

Salhi, A.↗

Measurements of Heat Transfer and Boundary-Layer Transition on an 8-Inch-Diameter Hemisphere-Cylinder in Free Flight for a Mach Number Range of 2.00 to 3.88

Measurements of aerodynamic heat transfer have been made along the hemisphere and cylinder of a hemisphere-cylinder rocket-propelled model in free flight up to a Mach number of 3.88. The test Reynolds number based on free-stream condition and diameter of model covered a range from 2.69 x l0(exp 6) to 11.70 x 10(exp 6). Laminar, transitional, and turbulent heat-transfer coefficients were obtained. The laminar data along the body agreed with laminar theory for blunt bodies whereas the turbulent data along the cylinder were consistently lower than that predicted by the turbulent theory for a flat plate. Measurements of heat transfer at the stagnation point were, in general, lower than the theory for stagnation-point heat transfer. When the Reynolds number to the junction of the hemisphere-cylinder was greater than 6 x l0(exp 6), the transitional Reynolds number varied from 0.8 x l0(exp 6) to 3.0 x 10(exp 6); however, than 6 x l(exp 6) when the Reynolds number to the junction was less, than the transitional Reynolds number varied from 7.0 x l0(exp 6) to 24.7 x 10(exp 6).

Garland, Benjamine J.↗

Small-scale behavior in distorted turbulent boundary layers at low Reynolds number

During the last three years we have conducted high- and low-Reynolds-number experiments, including hot-wire measurements of the velocity fluctuations, in the test-section-ceiling boundary layer of the 80- by 120-foot Full-Scale Aerodynamics Facility at NASA Ames Research Center, to test the local-isotropy predictions of Kolmogorov's universal equilibrium theory. This hypothesis, which states that at sufficiently high Reynolds numbers the small-scale structures of turbulent motions are independent of large-scale structures and mean deformations, has been used in theoretical studies of turbulence and computational methods such as large-eddy simulation; however, its range of validity in shear flows has been a subject of controversy. The present experiments were planned to enhance our understanding of the local-isotropy hypothesis. Our experiments were divided into two sets. First, measurements were taken at different Reynolds numbers in a plane boundary layer, which is a 'simple' shear flow. Second, experiments were designed to address this question: will our criteria for the existence of local isotropy hold for 'complex' nonequilibrium flows in which extra rates of mean strain are added to the basic mean shear?

Saddoughi, Seyed G.↗

Heat-Transfer and Pressure Measurements on a Flat-Face Cylinder at a Mach Number Range of 2.49 to 4.44

Heat-transfer coefficients and pressure distributions were obtained on a 4-inch-diameter flat-face cylinder in the Langley Unitary Plan wind tunnel. The measured stagnation heat-transfer coefficient agrees well with 55 percent of the theoretical value predicted by the modified Sibulkin method for a hemisphere. Pressure measurements indicated the dimensionless velocity gradient parameter r du\ a(sub t) dx, where x=0 at the stagnation point was approximately 0.3 and invariant throughout the Mach number range from 2.49 to 4.44 and the Reynolds number range from 0.77 x 10(exp 6) to 1.46 x 10(exp 6). The heat-transfer coefficients on the cylindrical afterbody could be predicted with reasonable accuracy by flat-plate theory at an angle of attack of 0 deg. At angles of attack the cylindrical afterbody stagnation-line heat transfer could be computed from swept-cylinder theory for large distances back of the nose when the Reynolds number is based on the distance from the flow reattachment points.

Burbank, Paige B.↗

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 90deg observation angle, the low-frequency noise could be as much as 10 dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite decorrelation region. Numerical predictions of the sound field, based on three-dimensional RANS solutions to determine the mean flow, turbulent kinetic energy and turbulence length and time scales, for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region in the turbulence spectrum increases the low-frequency algebraic decay (the low frequency "roll-off") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspect-ratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Jet↗

Measurements of Free-Space Oscillating Pressures Near Propellers at Flight Mach Numbers to 0.72

In the course of a short flight program initiated to check the theory of Garrick and Watkins (NACA rep. 1198), a series of measurements at three stations were made of the oscillating pressures near a tapered-blade plan-form propeller and rectangular-blade plan form propeller at flight Mach numbers up to 0.72. In contradiction to the results for the propeller studied in NACA rep. 1198, the oscillating pressures in the plane ahead of the propeller were found to be higher than those immediately behind the propeller. Factors such as variation in torque and thrust distribution, since the blades of the present investigation were operating above their design forward speed, may account for this contradiction. The effect of blade plan form shows that a tapered-blade plan-form propeller will produce lower sound-pressure levels than a rectangular-blade plan-form propeller for the low blade-passage harmonics (the frequencies where structural considerations are important) and produce higher sound-pressure levels for the higher blade-passage harmonics (frequencies where passenger comfort is important).

Kurbjun, Max C↗

A parametric study of blade vortex interaction noise for two, three, and four-bladed model rotors at moderate tip speeds Theory and experiment

An investigation of blade slap due to blade vortex interaction (BVI) has been conducted. This investigation consisted of an examination of BVI blade slap for two, three, and four-bladed model rotors at tip Mach numbers ranging from 0.20 to 0.50. Blade slap contours have been obtained for each configuration tested. Differences in blade slap contours, peak sound pressure level, and directivity for each configuration tested are noted. Additional fundamental differences, such as multiple interaction BVI, are observed and occur for only specific rotor blade configurations. The effect of increasing the Mach number on the BVI blade slap for various rotor blade combinations has been quantified. A peak blade slap Mach number scaling law is proposed. Comparison of measured BVI blade slap with theory is made.

Leighton, K. P.↗

Solar test of Dirac's large number hypothesis

An investigation is conducted regarding the implications of Dirac's theories (1973, 1974) concerning the creation of new matter. It is found that Dirac's theory of multiplicative creation, but not his theory of additive creation, is not in contradiction with known facts about the sun. According to the theory of additive creation, matter is formed uniformly throughout space. The concept of multiplicative creation implies that existing matter multiplies itself in proportion to the amount of matter already present.

Chin, C.-W.↗

Hovering impulsive noise: Some measured and calculated results

In-plane impulsive noise radiating from a hovering model rotor was measured in an anechoic environment. The hover acoustic signature was compared with existing theoretical prediction models with previous forward flight experiments using the same model rotor. These hover tests showed good experimental consistency with forward flight measurements, both in pressure level, and waveform character, over the range of Mach numbers tested (0.8 to 1.0). Generally poor correlation, however, was confirmed with current linear theory prediction efforts. Failure to predict both the peak pressure levels and the shape was reported, especially with increasing tip Mach number.

Boxwell, D. A.↗