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Obstruction effects in rarefied gas flow through cylindrical ducts by numerical analysis, considering specular reflection, adsorption, absorption and finite molecular mean free path
The refraction of acoustic waves by a moving medium layer is theoretically treated and the expressions for reflection and transmission coefficients are determined. The moving medium layer velocity is assumed to have a space dependence in one direction. A partitioning of the moving medium layer into constant-velocity sublayers is introduced and the number of sublayers is allowed to increase until the reflection and transmission coefficients converage to their respective values. Numerical results for several sublayer approximations of Poiseuille's flow are presented as functions of the moving layer velocity for several angles of incidence of the acoustic wave. The degenerate case of single constant-velocity layer is also treated, both theoretically and by a numerical analysis.
A very low density ablative material, a silicone-phenolic composite, was flight tested on a recoverable spacecraft launched by a Pacemaker vehicle system; and, in addition, it was tested in an arc heated wind tunnel at three conditions which encompassed most of the reentry heating conditions of the flight tests. The material was composed, by weight, of 71 percent phenolic spheres, 22.8 percent silicone resin, 2.2 percent catalyst, and 4 percent silica fibers. The tests were conducted to evaluate the ablator performance in both arc tunnel and flight tests and to determine the predictability of the albator performance by using computed results from an existing one-dimensional numerical analysis. The flight tested ablator experienced only moderate surface recession and retained a smooth surface except for isolated areas where the char was completely removed, probably following reentry and prior to or during recovery. Analytical results show good agreement between arc tunnel and flight test results. The thermophysical properties used in the analysis are tabulated.
A general method has been developed for determining the developing magnetohydrodynamic flow in the entrance region of a parallel-plate channel. Closed form solutions are obtained. Numerical results are presented for the development of velocity distribution, pressure drop, and magnetohydrodynamic entrance length at different Hartmann numbers. At large Hartmann numbers, the magnetic field effect becomes dominant and the magnetohydrodynamic entrance length becomes negligible. Also, the pressure drop is enhanced by the magnetic field. Comparison of results with direct numerical analysis shows excellent agreement.-
In this paper a definition for acquisition of a sideband modulated carrier is proposed for the phase lock loop, and the acquisition differential equation solved for a region of the modulation parameter space to determine the expected value of acquisition time. Principally the case of modulation by a single unmodulated subcarrier is considered. The numerical analysis is made for the noiseless case.
A generalized eigenvalue algorithm is presented herein along with the complete listing of the associated computer program, which may be conveniently utilized for the efficient solution of certain broad classes of eigenvalue problems. Extensive applications of the procedure are envisaged in the analysis of many important engineering problems, such as stability and natural frequency analysis of practical discrete structural systems, idealized by the finite element technique. The procedure based on the Sturm sequence method is accurate and fast, possessing several significant advantages over other known methods of such analysis. Numerical results are also presented for two representative structural engineering problems.
Coupling equations are derived for the general case of nonlinear coupling of any wave modes in a cold magnetized plasma with particle drift motions. Specifically, the transformation of electrostatic waves is studied in connection with solar type-III radiation. A relevant numerical analysis is also presented.
Spherically blunted 0.44-radian (25 deg) half-angle conical models coated with elastomeric ablative materials were tested in supersonic arc-heated wind tunnels to evaluate performance of the ablators over a range of conditions typical of lifting entry. Four test conditions were combinations of stagnation point-heat transfer rates of 2.3 and 4.5 MW/m2 and stagnation pressures of 20 and 2kN/m2. Afterbody values of heat transfer rate and pressure were 0.05 to 0.20 of stagnation point values. Stagnation enthalpy varied from 4.4 to 25 MJ/kg (1900 to 11000 Btu/lbm) and free-stream Mach number was in a range from 3.5 to 4. Ablative materials retained the spherical nose shape throughout tests at the lower heat transfer level, but receded, assuming a flattened nose shape, during tests at the high heat transfer level. The residue layer that formed on the conical after-body was weak, friable, and extensively cracked. The reference ablative material, which contained phenolic microspheres, generally retained the conical shape on the model afterbody. However, a modified ablator, in which phenolic microspheres were replaced with silica microspheres, deformed and separated from the undegraded material, and thereby produced a very uneven surface. Substrate temperatures and ablator recession were in good agreement with values computed by a numerical analysis.
An attempt has been made to keep the programs as subroutine oriented as possible. Usually only the main programs are directly concerned with the problem of total cross sections. In particular the subroutines POLFIT, BILINR, GASS59/MAXLIK, SYMOR, MATIN, STUDNT, DNTERP, DIFTAB, FORDIF, EPSALG, REGFAL and ADSIMP are completely general, and are concerned only with the problems of numerical analysis and statistics. Each subroutine is independently documented.
The formulation of a mathematical model for predicting the dynamic behavior of rotating flexible space station configurations was conducted. The overall objectives of the study were: (1) to develop the theoretical techniques for determining the behavior of a realistically modeled rotating space station, (2) to provide a versatile computer program for the numerical analysis, and (3) to present practical concepts for experimental verification of the analytical results. The mathematical model and its associated computer program are described.
A numerical analysis of spacecraft stability parameters was conducted. The analysis is based on a digital approximation by point by point state comparison. The technique used is that of approximating a continuous data system by a sampled data model by comparison of the states of the two systems. Application of the method to the digital redesign of the simplified one axis dynamics of the Skylab is presented.
The choice of an antenna for a subsurface radio sounding experiment is discussed. The radiation properties of the antennas as placed on the surface of the medium is examined. The objective of the lunar surface electrical properties experiment is described. A numerical analysis of the dielectric permittivity and magnetic permeability of a subsurface domain is developed. The application of electromagnetic field measurements between one or more transmitting antennas and a roving receiving station is explained.
A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be useful in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.
The anatomy of the intratemporal part of the vestibular nerve in man, and the possible age related degenerative changes in the nerve were studied. The form and structure of the vestibular ganglion was studied with the light microscope. A numerical analysis of the vestibular nerve, and caliber spectra of the myelinated fibers in the vestibular nerve branches were studied in individuals of varying ages. It was found that the peripheral endings of the vestibular nerve form a complicated pattern inside the vestibular sensory epithelia. A detailed description of the sensory cells and their surface organelles is included.
This report statistically analyzes computational round-off errors associated with the cutting plane approach to solving linear integer programming problems. Cutting plane methods require that the inverse of a sequence of matrices be computed. The problem basically reduces to one of minimizing round-off errors in the sequence of inverses. Two procedures for minimizing this problem are presented, and their influence on error accumulation is statistically analyzed. One procedure employs a very small tolerance factor to round computed values to zero. The other procedure is a numerical analysis technique for reinverting or improving the approximate inverse of a matrix. The results indicated that round-off accumulation can be effectively minimized by employing a tolerance factor which reflects the number of significant digits carried for each calculation and by applying the reinversion procedure once to each computed inverse. If 18 significant digits plus an exponent are carried for each variable during computations, then a tolerance value of 0.1 x 10 to the minus 12th power is reasonable.
The modern digital computer has made practical image processing techniques for handling nonlinear operations in both the geometrical and the intensity domains, various types of nonuniform noise cleanup, and the numerical analysis of pictures. An initial requirement is that a number of anomalies caused by the camera (e.g., geometric distortion, MTF roll-off, vignetting, and nonuniform intensity response) must be taken into account or removed to avoid their interference with the information extraction process. Examples illustrating these operations are discussed along with computer techniques used to emphasize details, perform analyses, classify materials by multivariate analysis, detect temporal differences, and aid in human interpretation of photos.
A numerical analysis of zonal geopotential coefficients and the bounds on the tesseral coefficients is presented. Modifications designed to incorporate data on the earth's density distribution are developed. The nature of the modifications and the application are discussed.
The pressure viscometer was modified to permit the measurement of viscosity at elevated pressures and shear stresses up to 5 x 10 to the 6th power N/sq m (720 psi). This shear stress is within a factor of three of the shear stress occurring in a sliding ehd point contact such as occurs in the ehd simulator. Viscosity data were taken on five lubricant samples, and it was found that viscous heating effects on the viscosity were predominant and not non-Newtonian behavior at the high shear stresses. The development of the infrared temperature measuring technique for the ehd simulator was completed, and temperature data for a set of operating conditions and one lubricant are reported. The numerical analysis of the behavior of nonlinear lubricants in the lubrication of rollers is reported.