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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Unsteady thin airfoil theory for transonic flows with embedded shocks

Classical unsteady thin airfoil theory fails for low frequencies at the subsonic freestream Mach number, because of the formation of a shock wave that shields the forward region of the airfoil from aft generated disturbances. In the present paper, the classical thin airfoil theory is modified to account for the presence and induced motion of such shocks. The modification consists of taking the steady local Mach number to be a simple step discontinuity, normal to the undisturbed flow, separating two uniform regions. Predicted regions are shown to correlate well both with the experiment and finite difference calculations.

Williams, M. H.↗
NASA NTRS1973

Flight test measurements and analysis of sonic boom phenomena near the shock wave extremity

The sonic boom flight test program conducted at Jackass Flats, Nevada, during the summer and fall of 1970 consisted of 121 sonic-boom-generating flights over the 1500 ft instrumented BREN tower. This test program was designed to provide information on several aspects of sonic boom, including caustics produced by longitudinal accelerations, caustics produced by steady flight near the threshold Mach number, sonic boom characteristics near lateral cutoff, and the vertical extent of shock waves attached to near-sonic airplanes. The measured test data, except for the near-sonic flight data, were analyzed in detail to determine sonic boom characteristics for these flight conditions and to determine the accuracy and the range of validity of linear sonic boom theory. The caustic phenomena observed during the threshold Mach number flights and during the transonic acceleration flights are documented and analyzed in detail. The theory of geometric acoustics is shown to be capable of predicting shock wave-ground intersections, and current methods for calculating sonic boom pressure signature away from caustics are shown to be reasonably accurate.

Haglund, G. T.↗
NASA NTRS1973

Free vibrations of multilayered composite plates.

Summary of some of the results of a recent study of the reliability and range of validity of two-dimensional plate theories in application to low-frequency free vibration analysis of simply supported, bidirectional, multilayered plates consisting of a large number of layers. These results show that for composite plates the error in the predictions of the classical plate theory is strongly dependent on the number and stacking of the layers, in addition to the degree of orthotropy of the individual layers and the thickness ratio of the plate.

Noor, A. K.↗
NASA NTRS1986

Thermocapillary and centrifugal-buoyancy-driven motion in a rapidly rotating liquid cylinder

The thermocapillary flow field in a uniformly rotating liquid cylinder heated from above is calculated using linear boundary-layer theory appropriate for small values of the Ekman number. The results show that the thermocapillary flow is confined to a thin layer at the liquid-gas interface if the temperature difference across the cylinder is sufficiently small. The interior flow is a uniform rotation with the endplates. The flow due to centrifugal buoyancy is also analyzed using the same theory. The magnitude of this flow compared with the thermocapillary motion is small in typical circumstances. However, it does influence the temperature field in the interior of the cylinder, where the thermocapillary motion does not. Full details of these flows and the first-order corrections to the interface shape are presented.

Smith, M. K.↗
NASA NTRS1960

Ground Measurements of Airplane Shock-Wave Noise at Mach Numbers to 2.0 and at Altitudes to 60,000 Feet

The intensity of shock-wave noise at the ground resulting from flights at Mach numbers to 2.0 and altitudes to 60,000 feet was measured. Meagurements near the ground track for flights of a supersonic fighter and one flight of a supersonic bomber are presented. Level cruising flight at an altitude of 60,000 feet and a Mach number of 2.0 produced sonic booms which were considered to be tolerable, and it is reasonable t o expect that cruising flight at higher altitudes will produce booms of tolerable intensity for airplanes of the size and weight of the test airplanes. The measured variation of sonic-boom intensity with altitude was in good agreement with the variation calculated by an equation given in NASA Technical Note D-48. The effect of Mach number on the ground overpressure is small between Mach numbers of 1.4 and 2.0, a result in agreement with the theory. No amplification of the shock-wave overpressures due to refraction effects was apparent near the cutoff Mach number. A method for estimating the effect of fligh-path angle on cutoff Mach number is shown. Experimental results indicate agreement with the method, since a climb maneuver produced booms of a much decreased intensity as compared with the intensity of those measured in level flight at about the same altitude and Mach number. Comparison of sound pressure levels for the fighter and bomber airp lanes indicated little effect of either airplane size or weight at an altitude of 40,000 feet.

Lina, Lindsay J.↗
NASA NTRS2011

Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data

Berger, Marsha↗
NASA NTRS1964

Probability Functions for Random Responses: Prediction of Peaks, Fatigue Damage, and Catastrophic Failures

This report reviews a number of theoretical matters in random process theory which can be applied to physical problems such as predicting peaks, structural fatigue damage, and catastrophic structural failures. The presentation emphasizes the basic assumptions which are involved, and discusses how to properly interpret the theoretical results. Various engineering examples are given as illustrations.

FATIGUE↗
NASA NTRS1972

On the tidal effects in the motion of artificial satellites.

The general perturbations in the elliptic and vectorial elements of a satellite as caused by the tidal deformations of the non-spherical Earth are developed into trigonometric series in the standard ecliptical arguments of Hill-Brown lunar theory and in the equatorial elements of the satellite. The integration of the differential equations for variation of elements of the satellite in this theory is easy because all arguments are linear or nearly linear in time. The trigonometrical expansion permits a judgment about the relative significance of the amplitudes and periods of different tidal 'waves' over a long period of time. Graphs are presented of the tidal perturbations in the elliptic elements of the BE-C satellite which illustrate long term periodic behavior. The tidal effects are clearly noticeable in the observations and their comparison with the theory permits improvement of the 'global' Love numbers for the Earth.

Musen, P.↗
NASA NTRS1976

MHD solution of interplanetary disturbances generated by simulated velocity perturbations

An MHD time-dependent numerical simulation, restricted to the solar equatorial plane, is used to demonstrate the interplanetary disturbances caused by several simplified coronal holes. Each 'hole' is assumed to have a configuration such that the higher solar wind velocity produced within their longitudinal extent is Gaussian over a 7-day period at the inner boundary (0.3 AU) of the numerical simulation. A second, twin coronal hole is assumed to rotate on the solar disk behind its predecessor. It is shown that the first coronal hole-produced interplanetary shock ensemble is overtaken by the second ensemble because of the higher velocity, lower density environment into which the latter propagates. A number of features predicted by MHD similarity theory are confirmed by the numerical simulation. These features include (1) strong azimuthal magnetic and plasma density compression, accompanied with average temperature depression, at the contact surface between forward and reverse shock ensembles, and (2) increasing spatial separation distance between forward and reverse shocks.

Dryer, M.↗
NASA NTRS1979

Nuclear Science Symposium, 25th, and Symposium on Nuclear Power Systems, 10th, Washington, D.C., October 18-20, 1978, Proceedings

Detectors of various types are discussed, taking into account drift chambers, calorimetry, multiwire proportional chambers, signal processing, the use of semiconductors, and photo/optical applications. Circuits are considered along with instrumentation for space, nuclear medicine instrumentation, data acquisition and systems, environmental instrumentation, reactor instrumentation, and nuclear power systems. Attention is given to a new approach to high accuracy gaseous detectors, the current status of electron mobility and free-ion yield in high mobility liquids, a digital drift chamber digitizer system, the stability of oxides in high purity germanium, the quadrant photomultiplier, and the theory of imaging with a very limited number of projections.

Source record↗
NASA NTRS1981

A mechanical drive for retractable telescopic masts

Test results on the mechanical drive have indicated that the system is capable of deploying a typical telescopic mast under ambient conditions. The design can be considered for a wide range of space applications since, in theory, there is no limit to the number of tubes that can be deployed. The mechanical system offers a number of advantages over a gas driven system, such as the ability to retract and also provide a significant mass saving.

Humphries, M. E.↗
NASA NTRS1981

Holographic microscopy studies of emulsions

A holographic microscopy system that records and observes the dynamic properties of separation of dispersed immiscible fluids is described. The holographic construction system and reconstruction system that were used to obtain particle size and distribution information from the holograms are discussed. The holographic microscopy system is used to observed the phase separating processes in immiscible fluids that were isothermally cooled into the two phase region. Nucleation, growth rates, coalescence, and particle motion are successfully demonstrated with this system. Thus a holographic particle sizing system with a resolution of 2 micrometers and a field of view of 100 cu cm was developed that provides the capability of testing the theories of separating immiscible fluids for particle number densities in the range of 10 to 10 to the 7th power particles.

Witherow, W. K.↗
NASA NTRS1984

Optimal quasi-static shape control for large aerospace antennae

In this paper, an on-line control approach which will adjust the steady-state shape of a large antenna arbitarily close to any achievable desired profile is proposed. The method makes use of distributed parameter system theory and allows refocusing using a limited number of control actuators and sensors. The controller gains are calculated by approximating the solution to an infinite-dimensional optimal quasi-static control problem. A very general convergence result for such quasi-static controllers is proved and applied to the antenna controller to show convergence, using any Galerkin (finite-element) approximation method.

Balas, M. J.↗
NASA NTRS1986

Helicopter impulsive noise - Theoretical and experimental status

The theoretical and experimental status of helicopter impulsive noise is reviewed. The two major source mechanisms of helicopter impulsive noise are addressed: high-speed impulsive noise and blade-vortex interaction impulsive noise. A thorough physical explanation of both generating mechanisms is presented together with model and full-scale measurements of the phenomena. Current theoretical prediction methods are compared with experimental findings of isolated rotor tests. The noise generating mechanisms of high speed impulsive noise are fairly well understood - theory and experiment compare nicely over Mach number ranges typical of today's helicopters. For the case of blade-vortex interaction noise, understanding of noise generating mechanisms and theoretical comparison with experiment are less satisfactory. Several methods for improving theory/experiment are suggested.

Schmitz, F. H.↗
NASA NTRS1986

The diffusion of individual molecules within a gas

The Direct Simulation Monte Carlo method is used to study the positional history of the individual molecules in a gas that is homogeneous at the macroscopic level and is in Maxwellian equilibrium at the microscopic level. The behavior at small times is characterized by 'persistence of velocity' effects, and a 'random walk' type of dispersal occurs over a longer timescale. It is shown that the rate of dispersal can be directly related to the self-diffusion coefficient. In addition, the diffusion coefficients are obtained directly from one-dimensional calculations, and the local Knudsen number at which the Chapman-Enskog theory breaks down is determined. Results are presented for both simple gases and gas mixtures.

Bird, G. A.↗
NASA NTRS1987

Suboptimal shape control for quasi-static distributed-parameter systems

An on-line control approach which will adjust the steady-state shape of a large antenna arbitrarily close to any achievable desired profile is approached. The method makes use of distributed-parameter system theory and allows refocusing using a limited number of control actuators and sensors. The controller gains are calculated by approximating the solution to an infinite-dimensional optimal quasi-static control problem. The controller gain calculation is computationally simpler than that previously proposed. The Galerkin (finite element) approximation method is used for model reduction. It is proved that both gain and state convergence can be achieved by using the proposed approximation scheme.

Balas, M. J.↗
NASA NTRS1989

Crossflow-vortex instability and transition on a 45 deg swept wing

A crossflow vortex experiment on a 45 deg swept wing is currently being conducted in the Arizona State University Unsteady Wind Tunnel. The experimental apparatus is designed to produce crossflow-dominated transition by simulating infinite swept wing flow using contoured end liners in a closed throat wind tunnel. Stationary fixed-wavelength crossflow vortices are observed at several chord Reynolds numbers. The vortex wavelength which is fixed for a given Reynolds number varies with Reynolds number approximately as predicted by linear stability theory, but with the predicted wavelengths about 30 percent larger than the observed wavelengths. Travelling waves are observed both in the frequency range predicted by linear stability theory and at higher frequencies. These higher frequency waves may be harmonics of the primary crossflow waves generated by a nonlinear parametric resonance phenomena.

Dagenhart, J. Ray↗