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NASA NTRS1976

Laminar free convection from a vertical cone with uniform surface heat flux

The laminar free convection flow from a right circular cone with prescribed uniform wall flux condition is studied. The governing boundary-layer equations are analyzed by the technique of similarity transformation. Numerical solutions to the transformed equations are given for Prandtl numbers 0.72, 1, 2, 4, 6, 8, 10, and 100. Expressions for both wall temperature distribution and wall skin friction distribution at Prandtl number tending to infinity are also presented.

Lin, F. N.↗

NASA NTRS1976

Laminar free convection over two-dimensional bodies with uniform surface heat flux

A general analysis is presented of the steady nondissipative constant-property laminar boundary layer flow over a two-dimensional body of uniform surface heat flux situated in an infinite ambient fluid of undisturbed temperature. The analysis is then applied to a long horizontal circular cylinder. Numerical solutions to the universal functions associated with the first two terms in the derived series are given for Prandtl numbers 0.7, 1, 3, 5, 7, and 10. The results are compared with those obtained by Koh (1964) whose method is patterned after the Blasius-Frossling procedure for forced convection flow. The study reveals that Wilks' (1972) analysis concerning the external natural convection about two-dimensional bodies with constant heat flux is in error.

Lin, F. N.↗

NASA NTRS1975

Uniformity of Ludwieg tube flows

Pressure and speed of sound measurements are used to obtain averaged gas properties in a Ludwieg combustion tube in which the gas is burned just prior to use. Absorption of a laser beam in the exit flow is used to check the predicted temperature uniformity. The burning process and the heat transfer to the cold walls are modeled. Interferograms of Ludwieg tube boundary layers are utilized to develop a new semiempirical boundary layer expression referred to as the integral density thickness, which is then applied to a recently developed linearized analysis of the effects of this layer. Pressure-time histories are determined for a wide range of tube flow Mach number and aspect ratio. Viscous and nonviscous effects are considered. It is shown that although the influence of the integral density thickness on the flow can be large, a modified linear theory can be used to estimate the effects for arbitrary tube flow Mach number and values of the aspect ratio that include cases where the boundary layers have merged.

Russell, D. A.↗

NASA NTRS1977

Uniform spray coating for large tanks

System employs spray facility located within ventilated plastic booth to uniformly coat exterior of large cylindrical tanks with polyurethane foam insulation. Coating target is rotated on turntable while movable spray guns apply overlapping spirals of foam. Entire operation may be controlled by single operator from remote station.

Carter, J. M.↗

NASA NTRS1976

Influence of a circular hole under uniform normal pressure on the stresses around a line crack in an infinite plate

Based on the two dimensional theory of elasticity and by the use of Muskhelishvili's technique, the influence of a circular hole, under uniform normal pressure, on the stresses around a line crack in an infinite plate subjected to tension is discussed. Numerical calculations were carried out, and the variation of the crack tip stress intensity factor due to the geometry was clarified.

Narayan, R.↗

NASA NTRS1977

Flap/Lag/Torsion Dynamics of a Uniform, Cantilever Rotor Blade in Hover

The dynamic stability of the flap/lag/torsion motion of a uniform, cantilever rotor blade in hover is calculated. The influence of blade collective pitch, lag frequency, torsional flexibility, structural coupling, and precone angle on the stability is examined. Good agreement is found with the results of an independent analytical investigation.

Johnson, W.↗

NASA NTRS1977

Finite-difference theory for sound propagation in a lined duct with uniform flow using the wave envelope concept

Finite difference equations are derived for sound propagation in a two dimensional, straight, soft wall duct with a uniform flow by using the wave envelope concept. This concept reduces the required number of finite difference grid points by one to two orders of magnitude depending on the length of the duct and the frequency of the sound. The governing acoustic difference equations in complex notation are derived. An exit condition is developed that allows a duct of finite length to simulate the wave propagation in an infinitely long duct. Sample calculations presented for a plane wave incident upon the acoustic liner show the numerical theory to be in good agreement with closed form analytical theory. Complete pressure and velocity printouts are given to some sample problems and can be used to debug and check future computer programs.

Baumeister, K. J.↗

NASA NTRS1977

A life cycle cost economics model for projects with uniformly varying operating costs

A mathematical model is developed for calculating the life cycle costs for a project where the operating costs increase or decrease in a linear manner with time. The life cycle cost is shown to be a function of the investment costs, initial operating costs, operating cost gradient, project life time, interest rate for capital and salvage value. The results show that the life cycle cost for a project can be grossly underestimated (or overestimated) if the operating costs increase (or decrease) uniformly over time rather than being constant as is often assumed in project economic evaluations. The following range of variables is examined: (1) project life from 2 to 30 years; (2) interest rate from 0 to 15 percent per year; and (3) operating cost gradient from 5 to 90 percent of the initial operating costs. A numerical example plus tables and graphs is given to help calculate project life cycle costs over a wide range of variables.

Remer, D. S.↗

NASA NTRS1977

Multiple scattering in reflection nebulae. I - A Monte Carlo approach. II - Uniform plane-parallel nebulae with foreground stars. III - Nebulae with embedded illuminating stars

A method for calculating the surface brightness distribution on a plane-parallel reflection nebula of uniform density illuminated by a star located either in front of, behind, or arbitrarily inside the scattering medium is proposed. The Monte Carlo technique is used to find solutions to the radiative transfer problem. The scattering properties of the nebular particles are parameterized by the albedo for single scattering and a three-parameter analytic phase function. Calculations are then presented for the surface brightness distribution across the face of such nebulae with (1) a foreground star and (2) immersed stars. The calculations include the full effects of multiple scattering, are independent of a particular assumed grain material or size distribution, and are applicable to any wavelength region for which observations can be obtained.

Witt, A. N.↗

NASA NTRS1977

Perturbations of a close-earth satellite due to sunlight diffusely reflected from the earth. I - Uniform albedo

A semianalytic method has been developed to calculate the radiation-pressure perturbations of a close-earth satellite due to sunlight reflected from the earth. The assumptions made are that the satellite is spherically symmetric and that the solar radiation is reflected from the earth according to Lambert's Law with uniform albedo. By using expressions for the components of the radiation-pressure force due to Lochry, the expressions for the perturbations of the elements were developed into series in the true anomaly. The perturbations within a given revolution can be obtained analytically by integrating with respect to v while holding all slowly varying quantities constant. The long-range perturbations are then obtained by accumulating the net perturbations at the end of each revolution.

Lautman, D. A.↗

NASA NTRS1978

Coded aperture imaging with uniformly redundant arrays

The paper discusses uniformly redundant arrays (URA) as applied to coded aperture imaging. The URA system offers the high-transmission characteristics of random arrays as well as a flat sidelobe advantage. The high-transmission yields the imaging of very low-intensity sources and the flat sidelobes provide the suppression of inherent noise which obscures low-contrast sources. Simulations have shown that the URA with shot and background noise produces a better reconstructed object than random arrays without shot or background noise. The URA also offers an arrangement which involves a mosaic of basic URA patterns forming a circular correlation of the object on the picture plane. Thus the information needed to reconstruct the object is contained in an area equal to that of the basic aperture pattern. This smaller required detector is important in applications including X-ray astronomy.

Fenimore, E. E.↗

NASA NTRS1978

Direct analytical solutions to non-uniform beam problems

The direct analytical solution to the vibration of non-uniform beams with and without discontinuities and with various boundary conditions is presented. Results are compared to results from the exact solution for certain cases where the exact solution has been obtained. It is shown that the direct solution converges to the exact solution, in fact, with 'indefinite accuracy' just as Hamilton stated that it would.

Bailey, C. D.↗

NASA NTRS1978

Uniform distribution of BeO particles in Be casting produced in rocket free fall

An experiment at zero-g aboard a NASA sounding rocket was conducted to evaluate the distribution of BeO particles in a Be casting. A distinction is drawn between the downward settling of particles in a quiescent melt, and the velocity gradient collisions of particles in a melt agitated by electromagnetic stirring. A similar experiment was conducted on earth using the same melting and solidification of a 0.922 cm spheroid of HIP-50 as was carried out in space; the only difference arising from the effect of gravity. Under zero-g conditions, the time needed for agglomeration was lengthened considerably, but the result was a casting of more uniform particle distribution.

Wouch, G.↗

NASA NTRS1977

A life cycle cost economics model for automation projects with uniformly varying operating costs

The described mathematical model calculates life-cycle costs for projects with operating costs increasing or decreasing linearly with time. The cost factors involved in the life-cycle cost are considered, and the errors resulting from the assumption of constant rather than uniformly varying operating costs are examined. Parameters in the study range from 2 to 30 years, for project life; 0 to 15% per year, for interest rate; and 5 to 90% of the initial operating cost, for the operating cost gradient. A numerical example is presented.

Remer, D. S.↗

NASA NTRS1979

Supersonic propeller noise in a uniform flow

The reported investigation is concerned with an extension of a theory presented by Hawkings and Lowson (1974). The extension considers also forward flight. Attention is given to the retarded potential solution of the convected wave equation, the Fourier components of acoustic pressure, the zones of relative silence and Doppler amplification, and the asymptotic evaluation of a noise field for a large wave number. The discussed analysis provides the Fourier coefficients of the acoustic signature of a supersonic rotor in a uniform flow. The results are represented by an integral over the blade planform which must be evaluated numerically. The fast Fourier transform can be employed for the Fourier inversion.

Jou, W.-H.↗

NASA NTRS1979

On sound radiation from the trailing edge of an isolated airfoil in a uniform flow

An experimental investigation has been conducted to determine the physical process of the noise production from the trailing edge of an isolated two-dimensional airfoil embedded in a low turbulence uniform mean flow. The Reynolds number of the airfoil based on chord was greater than 1,000,000 and that the boundary layer was fully turbulent at the trailing edge. Smoke injection technique and spark shadowgraphy were used to study the structural features of the boundary layer. Two point joint statistical analyses were made on the surface pressure, the radiated sound and the relationship between the two quantities. Operating conditions included two free stream velocities and two angles of attack for both a naturally developed and an artificially tripped boundary layer. Flow visualizations revealed the existence of large scale coherent motions in the outer region of the boundary layer. The observed coherent motions had scales of the order of boundary layer thickness and a convection velocity near the free stream velocity. The production process of the airfoil trailing edge noise was determined to be the convection of the large scale coherent eddies over the trailing edge of the airfoil. The noise field so generated was found to be rather coherent and dipole-like.

Yu, J. C.↗

NASA NTRS1979

Design curves for non-linear analysis of simply-supported, uniformly-loaded rectangular plates

Design curves for the non-linear analysis of simply-supported rectangular plates subjected to uniform normal pressure loads have been developed. These curves yield the center deflection, center stress and corner stress in non-dimensionalized form plotted against a dimensionless parameter describing the load intensity. The results presented are based on extensive non-linear finite element analysis employing the ARGUS structural analysis program. Plates with length to width ratios of 1, 1.5, 2, 3 and 4 are included. The load range considered extends to 1000 times the load at which the behavior of the plate becomes significantly non-linear. Over the load range considered, the analysis shows that the ratio of center deflection to plate thickness for a square plate is less than 16 to 1, whereas linear theory would predict a center deflection 400 times the plate thickness. Likewise, the stress is markedly lower than would be predicted by linear theory. The present results are shown to be in excellent agreement with the classical linear theory up to a central deflection to plate thickness ratio of about one-half. In the non-linear regime the present results for deflection and stress are in very good agreement with the analytical and experimental work of other investigators.

Moore, D.↗

NASA NTRS1979

Tomographical imaging using uniformly redundant arrays

An investigation is conducted of the behavior of two types of uniformly redundant array (URA) when used for close-up imaging. One URA pattern is a quadratic residue array whose characteristics for imaging planar sources have been simulated by Fenimore and Cannon (1978), while the second is based on m sequences that have been simulated by Gunson and Polychronopulos (1976) and by MacWilliams and Sloan (1976). Close-up imaging is necessary in order to obtain depth information for tomographical purposes. The properties of the two URA patterns are compared with a random array of equal open area. The goal considered in the investigation is to determine if a URA pattern exists which has the desirable defocus properties of the random array while maintaining artifact-free image properties for in-focus objects.

Cannon, T. M.↗