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Optimum central force transfer and rendezvous trajectories calculating technique, using primer-vector theory to determine time, number and state vector of all impulses
A computer code based on a finite-element solution algorithm is developed to perform an analytical investigation on the turbulent mixing and reaction of hydrogen jets injected from multiple orifices transverse and parallel to a supersonic airstream. A laser optical cavity flow field was also analyzed to demonstrate the generality of the proposed model. Computational results provide a three-dimensional description of velocity, temperature, and species-concentration fields downstream of injection. Major conclusions are that the analysis has immediate utility in evaluating the mixing effectiveness of transverse H2 injection data since it has been tested in its ability to model this type of data and that turbulent mixing length theory, constant effective Prandtl number, and a Lewis number of unity provide reasonable agreement with transverse H2 injection data downstream of the near-injection region. Efforts are presently being directed toward using the code in modeling laser and scramjet data for a wide range of flow conditions.
The far-field acoustic scattering by a prolate spheroid with axial point sources near the tip of the body was measured. Data were taken for ka between 10 - 160 where (a) is the semi-major axis of the spheroidal. Comparisons were made with numerical results obtained by an integral equation based on the simple source method, with appropriate coordinate stretching introduced to permit high frequency solutions with a minimal number of grid points. Theory and experiment agree within experimental error except for the highest frequencies in the shadow region, where very rapid changes in pressure make precise measurements difficult. The results show that for frequencies of aeroacoustic interest, the scattered field is very large and cannot be ignored.
The use of splitter plates for two dimensional transonic testing in wind tunnels was investigated on a 12% biconvex airfoil section over the Mach number range 0.6 to 1.0. Measured pressure distributions were compared to transonic theory and to other experiments, including an investigation in the same facility without splitter plates. The results of the experiment show the best agreement with theory over the entire transonic Mach number range.
The farfield acoustic scattering by a prolate spheroid with axial point sources near the tip of the body was measured. Data were taken for ka between 10 and 160, where a is the semimajor axis of the spheroid. Comparisons were made with numerical results obtained by an integral equation based on the simple-source method, with appropriate coordinate stretching introduced to permit high-frequency solutions with a minimal number of grid points. Theory and experiment agree within experimental error except for the highest frequencies in the shadow region, where very rapid changes in pressure make precise measurements difficult. The results show that for frequencies of aeroacoustic interest, the scattered field is very large and cannot be ignored.
It is suggested that grand unified field theories with spontaneous symmetry breaking in the very early big bang can lead more naturally to a baryon-symmetric cosmology with a domain structure than to a totally baryon-asymmetric cosmology. The symmetry is broken in a randomized manner in causally independent domains, favoring neither a baryon nor an antibaryon excess on a universal scale. Arguments in favor of this cosmology and observational tests are discussed.
Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.
Sixteen analytically and empirically designed strakes have been tested experimentally on a wing-body at three subcritical speeds in such a way as to isolate the strake-forebody loads from the wing-afterbody loads. Analytical estimates for these longitudinal results are made using the suction analogy and the augmented vortex lift concepts. The synergistic data are reasonably well estimated or bracketed by the high- and low-angle-of-attack vortex lift theories over the Mach number range and up to maximum lift or strake-vortex breakdown over the wing. Also, the strake geometry is very important in the maximum lift value generated and the lift efficiency of a given additional area. Increasing size and slenderness ratios are important is generating lift efficiently, but similar efficiency can also be achieved by designing a strake with approximately half the area of the largest gothic strake tested. These results correlate well with strake-vortex-breakdown observations in the water tunnel.
Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.
Analysis techniques for three aspects of the performance of the NASA/MSFC 32 meter drop tube are considered. Heat loss through the support wire in a pendant drop sample, temperature history of a drop falling through the drop tube when the tube is filled with helium gas at various pressures, and drag and resulting g-levels experienced by a drop falling through the tube when the tube is filled with helium gas at various pressures are addressed. The developed methods apply to systems with sufficiently small Knudsen numbers for which continuum theory may be applied. Sample results are presented, using niobium drops, to indicate the magnitudes of the effects. Helium gas at one atmosphere pressure can approximately double the amount of possible undercooling but it results in an apparent gravity levels of up to 0.1 g.
The stability of the flow between two vertical, infinite, rigid, coaxial cylinders held at different temperatures is analyzed by linear stability theory. For a Prandtl number of 22.8 and a radius ratio of 0.02, the flow is unstable to an axisymmetric perturbation at a critical Grashof number of 2150; the wave speed of the instability is comparable to the maximum velocity of the unperturbed flow. When the rigid outer cylinder-fluid interface is replaced by a crystal-melt interface which can change shape, two new modes of instability occur at lower Grashof numbers.
PRECISION designed for manipulation of numbers with accurate retention of up to thousands of digits per number. Use of PRECISION prevents underflow and overflow in programs that generate extreme numbers such as probability theory, statistics, and scientific applications.
The Taylor-Gortler vortex instability equations are formulated for steady and unsteady interacting boundary layer flows of the type which arise in triple-deck theory. The effective Gortler number is shown to be a function of the all shape in the boundary layer and the possibility of both steady and unsteady Taylor-Gortler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Gortler vortices exist before the boundary layers at the wall develop the Goldstein singularity. As an example of an unsteady spatially varying basic state the instability of high frequency large amplitude Tollmien-Schlichting waves in a curved channel were considered. It is shown that they are unstable in the first Stokes layer stage of the hierarchy of nonlinear states. The Tollmien-Schlichting waves are shown to be unstable in the presence of both convex and concave curvature.
Detailed experimental surface pressure coefficient measurements, obtained for a hemisphere-cylinder-flare model in a low supersonic flow (freestream M = 1.2) at various angles of attack (0 deg to 27.5 deg), have been analyzed. The pressure values for each angle of attack were smoothed and checked against their respective oil-flow photographs. The smoothed results were then used to validate a theory which relates the number and type of singular points observed in the oil-flow patterns with local surface-pressure extrema.
Over the past two decades a number of thermomechanical constitutive theories have been proposed for viscoplastic metals. These models are in most cases similar in that they utilize a set of internal state variables which provide locally averaged representations of microphysical phenomena such as dislocation rearrangement and grain boundary sliding. The state of development of several of these models is now at the point where accurate theoretical solutions can be obtained for a wide variety of structural problems at elevated temperatures. The fundamentals of viscoplasticity are briefly reviewed and a general framework is outlined. Several of the more prominent models are reviewed, and predictions from models are compared to experimental results.
The Yakhot and Orszag (1986) renormalization group (RNG) theory of turbulence has generated a number of scaling law constants in reasonable quantitative agreement with experiments. The theory itself is highly mathematical, and its assumptions and approximations are not easily appreciated. The present paper reviews the RNG theory and recasts it in more conventional terms using a distinctly different viewpoint. A new formulation based on an alternative interpretation of the origin of the random force is presented, showing that the artificially introduced epsilon in the original theory is an adjustable parameter, thus offering a plausible explanation for the remarkable record of quantitative success of the so-called epsilon-expansion procedure.
One aspect of the seasonal pressure variations measured at the Viking Lander sites is their nearly perfect interannual repeatability. This presents a problem because it implies that the behavior of the seasonal polar caps should be highly repeatable from year to year as well. There are a number of observations and theories suggesting that the presence of dust and water ice clouds in the Martian atmosphere should have significant direct and indirect effects on the rates of CO2 condensation and sublimation in the north and south polar regions. These effects include (1) reduced rates of CO2 frost condensation during polar night seasons due to the radiative effects of dust and water ice clouds and associated CO2 clouds or elevated atmospheric temperatures and (2) reduced or elevated rates of frost sublimation due to the radiative effects of atmospheric dust or to changes in frost emissivities and albedos due to contamination by water ice and dust. The Viking Landing pressure observations are examined to determine the range and character of the interannual variations present. Then a diurnal and seasonal thermal model is used to examine the effects of interannual variations in the polar heat balance on seasonal pressure variations.
This paper contains a detailed description of a 2,000-horsepower propeller dynamometer used to make wind-tunnel tests of a two-blade NACA 10-(3)(08)-03 propeller for a range of blade angles from 20 degrees to 55 degrees at airspeeds up to 500 miles per hour. The results of these tests and comparisons with results obtained from a theoretical analysis and from previous tests made in other wind tunnels are presented.