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A general iterative procedure is given for determining the consistent maximum likelihood estimates of normal distributions. In addition, a local maximum of the log-likelihood function, Newtons's method, a method of scoring, and modifications of these procedures are discussed.
Normal- and oblique-shock flow parameters for air in thermochemical equilibrium are tabulated as a function of shock angle for altitudes ranging from 15.24 km to 91.44 km in increments of 7.62 km at selected hypersonic speeds. Post-shock parameters tabulated include flow-deflection angle, velocity, Mach number, compressibility factor, isentropic exponent, viscosity, Reynolds number, entropy difference, and static pressure, temperature, density, and enthalpy ratios across the shock. A procedure is presented for obtaining oblique-shock flow properties in equilibrium air on surfaces at various angles of attack, sweep, and dihedral by use of the two-dimensional tabulations. Plots of the flow parameters against flow-deflection angle are presented at altitudes of 30.48, 60.96, and 91.44 km for various stream velocities.
The author has identified the following significant results. The General Electric DCP has proven to be a versatile, rugged piece of hardware and has surpassed original expectation; it is very simple to use and does not require skilled staff for its use, installation, and operation. It is well suited for use in remote sites where no power is available. From this experience, it is concluded that the data collection system will be very useful in operating a network of hydrometeorological stations situated in sites remote from normal communication links.
Heat transfer behavior was studied in a turbulent boundary layer with full-coverage film cooling through an array of discrete holes and with injection normal to the wall surface. Stanton numbers were measured for a staggered hole pattern with pitch-to-diameter ratios of 5 and 10, an injection mass flux ratio range of 0.1 to 1.0, and a range of Reynolds number 170 thousand to 5 million. Air was used as the working fluid with the mainstream velocity varied from .14 to 33.5 m/sec (30 to 110 ft/sec). The data were taken for secondary injection temperatures equal to the wall temperature and also equal to the mainstream temperature. By use of linear superposition theory, the data may be used to obtain Stanton number as a continuous function of the injectant temperature. The heat transfer coefficient is defined on the basis of a mainstream-to-wall temperature difference. This difinition permits direct comparison of performance between film cooling and transpiration cooling.
Heat transfer to a full coverage film cooled turbulent boundary layer over a flat surface was studied. The surface consisted of a discrete hole test section containing 11 rows of holes spaced 5 diameters apart in a staggered array and an instrumented recovery region. Ten diameter spacing was also studied by plugging appropriate holes. Two test sections were used, one having holes normal to the surface and the other having holes angled 30 deg to the surface in the downstream direction. Stanton number data were obtained both in the full coverage region and in the downstream recovery region for a range of blowing ratios, or mass flux ratios, from 0 to 1.3. Initial conditions at the upstream edge of the blowing region were varied from 500 to 5000 for momentum thickness Reynolds number and from 100 to 1800 for enthalpy thickness Reynolds number. The range of Reynolds numbers based on hole diameter and mainstream velocity was 6000 to 22000. Initial boundary layer thicknesses range from 0.5 to 2.0 hole diameters. Air was used as the working fluid. The data were taken for the secondary injection temperature equal to the wall temperature and also equal to the mainstream temperature. Superposition was then used to obtain Stanton number as a continuous function of the injectant temperature. The heat transfer coefficient was defined on the basis of a mainstream-to-wall temperature difference. This definition permits direct comparison of performance between film cooling and transpiration cooling.
New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence.
This User's Manual was prepared to provide the engineer with the information required to run the coupled mode version of the Normal Modes Rotor Aeroelastic Analysis Computer Program. The manual provides a full set of instructions for running the program, including calculation of blade modes, calculations of variable induced velocity distribution and the calculation of the time history of the response for either a single blade or a complete rotor with an airframe (the latter with constant inflow).
Equilibrium thermodynamic and flow properties are presented in tabulated and graphical form for moving, standing, and reflected normal shock waves in pure argon. Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular-weight ratio, isentropic exponent, velocity, and species mole fractions. Incident (moving) shock velocities are varied from 2 to 18 km/sec for a range of initial pressure of 5 N/sq m to 500 kN/sq m. Working charts illustrating shock tube performance with argon test gas and heated helium and hydrogen driver gases are also presented.
The normal impingement of a circular liquid jet onto a fine-mesh screen in a weightless environment was investigated. Equations were developed to predict the velocity of the emerging jet on the downstream side of the screen as a function of screen and liquid parameters and of the velocity of the impinging jet. Additionally, the stability of the emerging jet was found to be Weber number dependent. In general, excepting at high velocities, the screen behaved much as a baffle, deflecting the major portion of the impinging flow.
Film injection from discrete holes in a three-row, staggered array with five-diameter spacing was studied for three hole angles: (1) normal, (2) slanted 30 deg to the surface in the direction of the main stream, and (3) slanted 30 deg to the surface and 45 deg laterally to the main stream. The ratio of the boundary layer thickness-to-hole diameter and Reynolds number were typical of gas-turbine film-cooling applications. Detailed streaklines showing the turbulent motion of the injected air were obtained by photographing very small neutrally buoyant, helium-filled soap bubbles which follow the flow field.
McDonald Observatory lunar laser-ranging observations for 1973 are presented in the form of compressed normal points, and amendments for the 1969-1972 data set are given. Observations of the reflector mounted on the Soviet roving vehicle Lunakhod 2 have also been included.
This paper presents results from an experimental study of unsteady surface pressures and far-field noise produced by a subsonic jet impinging normal to a large, rigid, flat surface. The tests were performed in an anechoic room for jet Mach numbers from 0.54 to 0.85, and for jet-to-surface heights of from 5 to 10 jet diameters. Results showed that the root-mean-square surface pressure levels were proportional to jet dynamic pressure and were independent of jet height for radial distances from the stagnation point greater than 3 jet diameters. Far-field measurements indicated a significant increase in noise over that of a free jet for all cases of impingement. Cross spectral calculations between the surface and the far field suggested that at a Mach number of 0.70 and a height of 5 jet diameters the additional noise originated mainly in the outer edge of the impingement region between 1 and 3 jet diameters from the stagnation point.
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.
Equilibrium thermodynamic and flow properties are presented in tabulated and graphical form for moving, standing, and reflected normal shock waves in pure CO2. Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular weight ratio, isentropic exponent, velocity, and species mole fractions. Incident (moving) shock velocities are varied from 1 to 16 km/sec for a range of initial pressure of 5 N/sq m to 500 kN/sq m. The present results are applicable to shock tube flows and to freeflight conditions for a blunt body at high velocities. Working charts illustrating idealized shock tube performance with CO2 test gas and heated helium and hydrogen driver gases are also presented.
Errors found in the original edition are corrected. Refinement was made in procedures for solving the conservation relations for an incident (moving), standing, and reflected normal shock, as well as in computational methods for determining thermochemical-equilibrium hydrogen properties. A six-species hydrogen model replaces the original four-species model, and the heat of formation and spectroscopic constants used in this six-species model are listed in appendix A. In appendix B, comparisons are made between a number of methods for determining equilibrium thermodynamic properties for hydrogen for several values of pressure and temperatures to 50000 K. A comparison is also performed between the present method and a second method for determining thermodynamic properties and flow velocity behind an incident shock into pure hydrogen and behind a reflected shock.
The dependence of far field acoustic measurements for a uniform jet on nozzle to plate spacing for small dimensionless spacings (h/d - 0.75 to 3.0) was investigated. Spectra from a real time analyzer were read and processed by an HP 2116 minicomputer in on-line mode. Similar data was generated for a fully developed pipe flow exit condition jet to compare with other investigations. The data base for normal jet impingement was extended to smaller values of nozzle to plate spacing. The effects of slight noise heating (30 deg rise) of the jet on the far field noise produced by the impinging jet are demonstrated.
The free surface shapes of circular liquid jets impinging normal to sharp-edged disks in zero gravity are determined. Zero gravity drop tower experiments yielded three distinct flow patterns that were classified in terms of the relative effects of surface tension and inertial forces. An order of magnitude analysis was conducted that indicated regions where viscous forces were not significant in the computation of free surface shapes. The free surface analysis was simplified by transforming the governing potential flow equations and boundary conditions into the inverse plane, where the stream function and velocity potential became the coordinates. The resulting nonlinear equations were solved by standard finite difference methods, and comparisons were made with the experimental data for the inertia dominated regime.
The statistical error of the pointing angle estimation technique is determined as a function of the effective receiver signal to noise ratio. Other sources of error are addressed and evaluated with inadequate calibration being of major concern. The impact of pointing error on the computation of normalized surface scattering cross section (sigma) from radar and the waveform attitude induced altitude bias is considered and quantitative results are presented. Pointing angle and sigma processing algorithms are presented along with some initial data. The intensive mode clean vs. clutter AGC calibration problem is analytically resolved. The use clutter AGC data in the intensive mode is confirmed as the correct calibration set for the sigma computations.