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First-and second-order numerical procedures are presented for calculating two-dimensional transonic flows that treat shock waves as discontinuities. Their application to a simple but nontrivial problem for which there are limited theoretical results is discussed.
First- and second-order numerical procedures for calculating two-dimensional transonic flows that treat shock waves as discontinuities are discussed. This short communication illustrates their application to a simple but non-trivial problem for which there are limited theoretical results.
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Computer program applies chi-square Pearson test to multivariate statistics for application in any field in which data of two or more variables (dimensions) are sampled for statistical purposes. Program handles dimensions two through five, with up to thousand data sets.
Design monograph organizes and presents significant experience and knowledge accumulated in development and operational programs. Assisting systems designers, it reviews and assesses current design practices establishes guides for achieving greater consistency in design, increased reliability in end product, and greater efficiency in design effort.
State of the art and design criteria for components used in liquid propellant rocket propulsion systems to contain and control the flow of fluids involved are discussed. Particular emphasis is placed on the design of components used in the engine systems of boosters and upper stages, and in spacecraft propulsion systems because of the high pressure and high vibration levels to which these components are exposed. A table for conversion of U.S. customary units to SI units is included with a glossary, and a list of NASA space vehicle design criteria monographs issued to September 1976.
Pedalling a bicycle at least ten minutes a day at 85% of maximum pulse rate, three days a week for ten weeks will produce moderate increases in overall strength and physical work capacity in college-age females. The longer the training session, up to thirty minutes per session, the greater are the increases in physical work capacity that result when college-age females are trained three days a week for ten weeks at 85% of their maximum heart rate.
A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.
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A procedure for numerical solution of the time-dependent, incompressible Navier-Stokes equations for the flow about arbitrarily shaped two-dimensional bodies is given. This solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having a coordinate line coincident with the body contour regardless of its shape. The implicit solution utilizes the vorticity-stream function formulation with a false-position iterative adjustment of the surface vorticity in satisfaction of the no-slip boundary condition. Excellent agreement with the Blasius boundary layer solution is obtained for a semi-infinite flat plate. Results are presented for Reynolds numbers up to 2000 for several airfoils and a cambered rock.
The angular dependence of the interaction between two rigid linear rotors is considered, and one of the two expansions in current use is shown to be inappropriate. Interpolation of tabulated radial interactions is also discussed, and numerical tests are presented which demonstrate the accuracy of Lagrange and spline algorithms as a function of the spacing between points.
Finite-element computer program enables analysis of distortions and stresses occurring in components having relative interference. Program restricts itself to simple elements and axisymmetric loading situations. External inertial and thermal loads may be applied in addition to forces arising from interference conditions.
The essential part of numerical solutions of partial differential equations is the representation of gradients and integrals by, respectively, differences between points and summations over points. In order for such numerical representations to be accurate, it is necessary that these points be more closely spaced in regions of large gradients. The need for accurate representation is particularly acute near body surfaces, since the boundary conditions are generally the most influential part of a partial differential equation solution. This is especially true of viscous solutions at high Reynolds number, where very large gradients occur in the boundary layer.
The influence of molecular transport is included in the computation by treating viscous and thermal diffusion terms in the governing partial differential equations as correction terms in the method of characteristics scheme. The development of a production type computer program is reported which is capable of calculating the flow field in a variety of axisymmetric mixed-compression aircraft inlets. The results agreed well with those produced by the two-dimensional method characteristics when axisymmetric flow fields are computed. For three-dimensional flow fields, the results agree well with experimental data except in regions of high viscous interaction and boundary layer removal.
The reported analysis is based on the factored IOS T-matrix. It is shown that line shape measurements may be used over a range of temperatures to evaluate inelastic scattering cross sections. Basic factorization or parameterization relations are derived by considering the wavefunction equations. The parameterization of cross sections is considered, taking into account the differential scattering amplitude and cross section, integral cross sections, phenomenological cross sections for general relaxation processes, and viscosity and diffusion cross sections. Thermal averages and rates are discussed, giving attention to integral cross sections and rates, and general phenomenological cross sections. The results of computational studies are also presented.
Using altimeter data from a single pass, orbital fiting of these data is investigated. The stability problems of this special kind of short are method as well as the problem in the case of a mean Keplerian ellipse are discussed in detail. It is shown that short periodic perturbations can influence the size of the eccentricity of the satellite orbit computed from these data. In this way the desired result, the corrections of d zeta to the geoidal undulations, may be falsified.
A group of 12 highly trained athletes and a group of 12untrained students were subjected to passive changes of position on a tilt table and positive accelerations in a centrifuge. During a 20 min tilt, including two additional respiratory maneuvers, the number of faints and average cardiovascular responses did not differ significantly between the groups. During linear increase of acceleration, the average blackout level was almost identical in both groups. Statistically significant coefficients of product-moment correlation for various relations were obtained. The coefficient of multiple determination computed for the dependence of acceleration tolerance on heart-eye distance and systolic blood pressure at rest allows the explanation of almost 50% of the variation of acceleration tolerance. The maximum oxygen uptake showed the expected significant correlation to the heart rate at rest, but not the acceleration tolerance, or to the cardiovascular responses to tilting.