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At least 1,207 records · Page 67

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NASA NTRS1975

Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation

A simplified technique is proposed for calculating multidimensional Hermite-Gaussian quadratures that involves taking the square root of a matrix by the Cholesky algorithm rather than computation of the eigenvectors of the matrix. Ways of reducing the dimension, number, and order of the quadratures are set forth. If the function f(x) under the integral sign is not well approximated by a low-order algebraic expression, the order of the quadrature may be reduced by factoring f(x) into an expression that is nearly algebraic and one that is Gaussian.

Mcreynolds, S. R.↗

NASA NTRS1976

Experimental clean combustor program: Noise study

Under a Noise Addendum to the NASA Experimental Clean Combustor Program (ECCP) internal pressure fluctuations were measured during tests of JT9D combustor designs conducted in a burner test rig. Measurements were correlated with burner operating parameters using an expression relating farfield noise to these parameters. For a given combustor, variation of internal noise with operating parameters was reasonably well predicted by this expression but the levels were higher than farfield predictions and differed significantly among several combustors. For two burners, discharge stream temperature fluctuations were obtained with fast-response thermocouples to allow calculation of indirect combustion noise which would be generated by passage of the temperature inhomogeneities through the high pressure turbine stages of a JT9D turbofan engine. Using a previously developed analysis, the computed indirect combustion noise was significantly lower than total low frequency core noise observed on this and several other engines.

Sofrin, T. G.↗

NASA NTRS1976

Diffraction of sound by nearly rigid barriers

The diffraction of sound by barriers with surfaces of large, but finite, acoustic impedance was analyzed. Idealized source-barrier-receiver configurations in which the barriers may be considered as semi-infinite wedges are discussed. Particular attention is given to situations in which the source and receiver are at large distances from the tip of the wedge. The expression for the acoustic pressure in this limiting case is compared with the results of Pierce's analysis of diffraction by a rigid wedge. An expression for the insertion loss of a finite impedance barrier is compared with insertion loss formulas which are used extensively in selecting or designing barriers for noise control.

Hadden, W. J., Jr.↗

NASA NTRS1976

Noise response of cavities of varying dimensions at subsonic speeds

An expression for the Strouhal number of lengthwise cavity oscillations is obtained which includes the effect of length-to-depth ratio. This expression, which agrees well with the experimental data, is also used to predict the Mach number at which cavity acoustic response is maximum. Interaction between lengthwise and depthwise modes is seen to occur at Mach numbers from 0.1 to 0.5. Cavity shape is shown to affect the noise spectra in generating either a broadband or narrowband signal.

Block, P. J. W.↗

NASA NTRS1976

An algorithm for the weighting matrices in the sampled-data optimal linear regulator problem

The sampled-data optimal linear regulator problem provides a means whereby a control designer can use an understanding of continuous optimal regulator design to produce a digital state variable feedback control law which satisfies continuous system performance specifications. A basic difficulty in applying the sampled-data regulator theory is the requirement that certain digital performance index weighting matrices, expressed as complicated functions of system matrices, be computed. Infinite series representations are presented for the weighting matrices of the time-invariant version of the optimal linear sampled-data regulator problem. Error bounds are given for estimating the effect of truncating the series expressions after a finite number of terms, and a method is described for their computer implementation. A numerical example is given to illustrate the results.

Armstrong, E. S.↗

NASA NTRS1976

Analytical and experimental design and analysis of an optimal processor for image registration

The author has identified the following significant results. A quantitative measure of the registration processor accuracy in terms of the variance of the registration error was derived. With the appropriate assumptions, the variance was shown to be inversely proportional to the square of the effective bandwidth times the signal to noise ratio. The final expressions were presented to emphasize both the form and simplicity of their representation. In the situation where relative spatial distortions exist between images to be registered, expressions were derived for estimating the loss in output signal to noise ratio due to these spatial distortions. These results are in terms of a reduction factor.

Mcgillem, C. D.↗

NASA NTRS1977

Patterns of broad-beam antennas of different polarizations next to simple Hangar models

Broad-beam antennas of different polarizations radiating next to simple hangar models are investigated. Expressions that represent the elevation-plane patterns of slots in and 1/4 wavelength monopoles on a finite rectangular ground plane upon which a rectangular scattering object was placed were derived using geometrical theory of diffraction. These expressions were obtained by superposing the infinite ground plane solutions, reflected field solutions from the scattering object and diffracted field solutions in their respective regions of validity. Patterns for a 1/2 wavelength slot and 1/4 wavelength electric monopole are verified experimentally for a number of source locations. Data pertaining to the polarization question in regard to the multipath problem are presented.

Cockrell, C. R.↗

NASA NTRS1977

Adiabatic particle motion in a nearly drift-free magnetic field: Application to the geomagnetic tail

The guiding center motion of particles in a nearly drift free magnetic field is analyzed in order to investigate the dependence of mean drift velocity on equatorial pitch angle, the variation of local drift velocity along the trajectory, and other properties. The mean drift for adiabatic particles is expressed by means of elliptic integrals. Approximations to the twice-averaged Hamiltonian W near z = O are derived, permitting simple representation of drift paths if an electric potential also exists. In addition, the use of W or of expressions for the longitudinal invariant allows the derivation of the twice averaged Liouville equation and of the corresponding Vlasov equation. Bounce times are calculated (using the drift-free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for the mean drift.

Stern, D. P.↗

NASA NTRS1977

Multimodal far-field acoustic radiation pattern: An approximate equation

The far-field sound radiation theory for a circular duct was studied for both single mode and multimodal inputs. The investigation was intended to develop a method to determine the acoustic power produced by turbofans as a function of mode cut-off ratio. With reasonable simplifying assumptions the single mode radiation pattern was shown to be reducible to a function of mode cut-off ratio only. With modal cut-off ratio as the dominant variable, multimodal radiation patterns can be reduced to a simple explicit expression. This approximate expression provides excellent agreement with an exact calculation of the sound radiation pattern using equal acoustic power per mode.

Rice, E. J.↗

NASA NTRS1977

Chemical Vapor Deposition of Silicon from Silane Pyrolysis

The four basic elements in the chemical vapor deposition (CVD) of silicon from silane are analytically treated from a kinetic standpoint. These elements are mass transport of silane, pyrolysis of silane, nucleation of silicon, and silicon crystal growth. Rate expressions that describe the various steps involved in the chemical vapor deposition of silicon were derived from elementary principles. Applications of the rate expressions for modeling and simulation of the silicon CVD are discussed.

Praturi, A. K.↗

NASA NTRS1977

Experimental and theoretical investigation of three-dimensional turbulent boundary layers and turbulence characteristics inside an axial flow inducer passage

Analytical and experimental investigations of the characteristics of three dimensional turbulent boundary layers in a rotating helical passage of an inducer rotor are reported. Expressions are developed for the velocity profiles in the inner layer, where the viscous effects dominate, in the outer layer, where the viscous effects are small, and in the interference layer, where the end walls influence the flow. The prediction of boundary layer growth is based on the momentum integral technique. The equations derived are general enough to be valid for all turbomachinery rotors with arbitrary pressure gradients. The experimental investigations are carried out in a flat plate inducer 3 feet in diameter. The mean velocity profiles, turbulence intensities and shear stresses, wall shear stress, and limiting streamline angles are measured at various radial and chordwise locations by using rotating probes. The measurements are in general agreement with the predictions. The radial flows are well represented by an expression which includes the effect of stagger angle and radial pressure gradient. The radial flows in the rotor channel are higher than those on a single blade. The collateral region exists only very near the blade surface. The radial component of turbulence intensity is higher than the streamwise component because of the effect of rotation.

Anand, A. K.↗

NASA NTRS1976

Saltation threshold on Mars - The effect of interparticle force, surface roughness, and low atmospheric density

Results are reported for wind-tunnel experiments performed to determine the threshold friction speed of particles with different densities. Experimentally determined threshold speeds are plotted as a function of particle diameter and in terms of threshold parameter vs particle friction Reynolds number. The curves are compared with those of previous experiments, and an A-B curve is plotted to show differences in threshold speed due to differences in size distributions and particle shapes. Effects of particle diameter are investigated, an expression for threshold speed is derived by considering the equilibrium forces acting on a single particle, and other approximately valid expressions are evaluated. It is shown that the assumption of universality of the A-B curve is in error at very low pressures for small particles and that only predictions which take account of both Reynolds number and effects of interparticle forces yield reasonable agreement with experimental data. Effects of nonerodible surface roughness are examined, and threshold speeds computed with allowance for this factor are compared with experimental values. Threshold friction speeds on Mars are then estimated for a surface pressure of 5 mbar, taking into account all the factors considered.

Iversen, J. D.↗

NASA NTRS1976

The motion of a satellite in resonance with the longitude-dependent harmonics

The solution to the motion of a satellite in an eccentric orbit and in resonance with one or more of the longitude-dependent harmonics of the central planet is developed. The method of solution parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order resonant perturbations due to longitude-dependent harmonics (in terms of Legendre normal elliptic integrals of the first and second kind).

Dallas, S. S.↗

NASA NTRS1976

On a model of calculating bond strength

Diffusion bonding is a fabricating process to join the fibers and a matrix together forming a composite. The efficiency of the bonding process depends on temperature, time, and pressure. Based on a simplified pair potential model, an expression for the bond-energy at the fiber-matrix interface is formulated in terms of the above-mentioned three parameters. From this expression and the mean atomic distance, the bond-strength between the fibers and the matrix can be calculated.

Yue, A. S.↗

NASA NTRS1976

Solution to a gene divergence problem under arbitrary stable nucleotide transition probabilities

A nucleic acid chain, L nucleotides in length, with the specific base sequence B(1)B(2) ... B(L) is defined by the L-dimensional vector B = (B(1), B(2), ..., B(L)). For twelve given constant non-negative transition probabilities that, in a specified position, the base B is replaced by the base B' in a single step, an exact analytical expression is derived for the probability that the position goes from base B to B' in X steps. Assuming that each base mutates independently of the others, an exact expression is derived for the probability that the initial gene sequence B goes to a sequence B' = (B'(1), B'(2), ..., B'(L)) after X = (X(1), X(2), ..., X(L)) base replacements. The resulting equations allow a more precise accounting for the effects of Darwinian natural selection in molecular evolution than does the idealized (biologically less accurate) assumption that each of the four nucleotides is equally likely to mutate to and be fixed as one of the other three. Illustrative applications of the theory to some problems of biological evolution are given.

Holmquist, R.↗

NASA NTRS1976

Isothermal elastohydrodynamic lubrication of point contacts. IV - Starvation results

Previously developed basic theory for isothermal elastohydrodynamic lubrication of point contacts is used to study the effect of lubricant starvation on pressure and film thickness within the conjunction. A simple expression for the dimensionless inlet boundary distance is derived. This inlet boundary distance defines whether a fully flooded or a starved condition exists in the contact. Simple expressions for the minimum and central film thickness under starvation condition are presented. Contour plots of pressure and film thickness in and around the contact are shown in order to gain a better insight into what occurs in going from fully flooded to lubricant starvation condition. Theoretical predictions are compared with earlier results.

Hamrock, B. J.↗

NASA NTRS1977

Non-symmetric two-stream instability

A theoretical investigation is performed concerning the instability spectrum of quasi-electrostatic waves at shifted half-odd-integer values of the cyclotron frequency due to nonsymmetric counterstreaming electron beams. The beam velocities parallel and perpendicular to the static magnetic field are represented by double Dirac delta functions with no imposition of parameter limitations. Systematic consideration is given to the coupling between plasma modes and cyclotron modes as well as the coupling between cyclotron modes of the two beams that result in shifted half-odd-integer multiples of the cyclotron frequency. The general dispersion equation for quasi-electrostatic waves is analyzed, and plasma-cyclotron coupling in the nonsymmetric case is treated by deriving approximate analytical expressions for maximum growth rates and marginal stability. Exact numerical solutions in both frequency and wavenumber space are obtained and compared with the analytical expressions. Cyclotron-cyclotron coupling modes are treated in the same way, and the results for both types of coupling are compared. It is found that certain modes may be weakened or completely suppressed when the Bessel functions for specific plasma parameters vanish.

Cuperman, S.↗

NASA NTRS1977

Absolute rate of the reaction of Cl/2P/ with methane from 200-500 K

Rate constants for the reaction Cl + CH4 yields HCl + CH3 were measured in the range 200-500 K by the plot flash photolysis-resonance fluorescence technique. An Arrhenius plot of the mean rate constant observed at 14 equally spaced temperatures is best fit by the expression k = 5.44 times 10 to the minus 19th times T to the exponent 2.50 times exp(-608/T) cu cm per molecule per sec. Appropriate expressions are also given for the rate constant in the two ranges 200-299 K and 299-500 K. These results are compared with a number of other existing determinations of the rate constant by other methods and in different temperature ranges. Most discrepancies are attributed to the nonlinear Arrhenius behavior.

Whytock, D. A.↗