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The 'mean frequency' technique, a simple procedure introduced by Bebb and Gold for the approximate evaluation of sums occurring in high-order perturbation theory, represents a useful approximation method. Its predictions compare favorably to exact results obtained by Gontier and Trahin for multiphoton bound-bound transitions in hydrogen. However, the technique can be in error if the 'mean frequency' lies near certain integers.
A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.
Natural frequencies, as a function of power were determined using a finite element model. Operating conditions investigated were operation with a resistive electrical load and operation synchronized to an electrical utility grid. The influence of certain drive train components on frequencies and mode shapes is shown. An approximate method for obtaining drive train natural frequencies is presented.
A study is presented on the unsteady aerodynamic loads due to arbitrary motions of a thin wing and their adaptation for the calculation of response and true stability of aeroelastic modes. In an Appendix, the use of Laplace transform techniques and the generalized Theodorsen function for two-dimensional incompressible flow is reviewed. New applications of the same approach are shown also to yield airloads valid for quite general small motions. Numerical results are given for the two-dimensional supersonic case. Previously proposed approximate methods, starting from simple harmonic unsteady theory, are evaluated by comparison with exact results obtained by the present approach. The Laplace inversion integral is employed to separate the loads into 'rational' and 'nonrational' parts, of which only the former are involved in aeroelastic stability of the wing. Among other suggestions for further work, it is explained how existing aerodynamic computer programs may be adapted in a fairly straightforward fashion to deal with arbitrary transients.
An experimental investigation was conducted to determine the effects of roughness size on the position of boundary layer transition and on the aerodynamic characteristics of a 55 deg swept delta wing model. Results are presented and discussed for wind tunnel tests conducted at free stream Mach numbers from 1.50 to 4.63, Reynolds numbers per meter from 3,300,000 to 1.6 x 10 to the 7th power, angles of attack from -8 to 16 deg, and roughness sizes ranging from 0.027 cm sand grit to 0.127 cm high cylinders. Comparisons were made with existing flat plate data. An approximate method was derived for predicting the drag of roughness elements used in boundary layer trips.
An approximate computational technique has been developed for predicting inviscid, radiating flows about blunt probes entering atmospheres consisting of hydrogen and helium. The technique is rapid and versatile and is well suited for performing parametric trade studies for outer planet entries. Details of the computational technique, the thermodynamic correlations, the 58-step absorption coefficient model and the analytic shock shape equations are discussed. Good comparisons of the radiative heating computed by the approximate method and by detailed calculations are obtained.
A symmetric 3 mass rotor supported on hydrodynamic bearings is described. An approximate method of representing finite bearings is used to calculate bearing forces. As the method sums forces from a number of independent circular lobes lemon 3 and 4 lobe bearings are taken into account. The calculations are based on an axial groove bearing. Linear analysis precedes nonlinear simulation of some unstable conditions. The demonstration of small limit cycles suggests that necessarily flexible rotors e.g., helicopter tail rotors, may be practical without either tilt pad bearings or external dampers.
An approximate method for computing the jet noise pattern of a maneuvering airplane is described. The method permits one to relate the noise pattern individually to the influences of airplane speed and acceleration, jet velocity and acceleration, and the flight path curvature. The analytic formulation determines the ground pattern directly without interpolation and runs rapidly on a minicomputer. Calculated examples including a climbing turn and a simple climb pattern with a gradual throttling back are presented.
An approximate method is proposed for evaluating the interaction of randomly oriented, nonspherical particles with the total intensity component of electromagnetic radiation. When the particle size parameter, x, the ratio of particle circumference to wavelength, is less than some upper bound x(o) (about 5), Mie theory is used. For x greater than x(o), the interaction is divided into three components: diffraction, external reflection, and transmission. Physical optics theory is used to obtain the first of these components; geometrical optics theory is applied to the second; and a simple parameterization is employed for the third. The predictions of this theory are found to be in very good agreement with laboratory measurements for a wide variety of particle shapes, sizes, and refractive indexes. Limitations of the theory are also noted.
An approximate method is proposed for predicting the viscosity of partially ionized gas mixtures. This technique expresses the viscosity of a mixture in terms of the viscosities of the individual pure components, is simple in form, and does not require large computer run times or storage. Thus, the technique is suitable for use with complex flowfields and heat-transfer calculations. Results for gas mixtures which are representative of the atmospheres of Jupiter, Earth, and Venus, are presented and it is shown that the results compare favorably with detailed kinetic-theory analyses.
The interaction of two vertically impinging incompressible jets is studied through the invention of physical flow models that approximate the behavior of colliding wall jets as the incident jets are brought closer together. The mechanism for upwash formation is studied and momentum models for the upwash sheet are postulated. An approximate method for computing the ground isobar pattern of jet and upwash deflection zones is presented and compared with test data. A method for computing the upwash impingement force in the absence of secondary induced flow effects is also presented and reasonably good agreement is achieved with experimental data for cylindrical fuselage shapes of circular and rectangular cross section.
A methodology is outlined for predicting the amplitude of forced vibrations in the acoustic cavity of a solid rocket motor. The equation for forced vibration of the motor cavity acoustic system is written by parallel with the acoustic mechanical analogy. Acoustic and aeroacoustic theory are used to predict the frequency and intensity of vortex systems or turbulence created by passage of the mean flow over geometric discontinuities in the motor port. Approximate methods are presented for coupling the acoustic field due to the flow noise with the chamber acoustics and for summing the effect upon the multiple acoustic modes.
An approximate method for calculating the flow properties of gas-particle mixture flowing over blades in a cascade is studied. Using an analytical method, the solid particle trajectory and location of collisions between the solid particles and the blade surfaces are determined. In addition an experimental investigation of the trajectories and velocities of solid particles suspended in a fluid passing through an axial flow compressor cascade was performed. The cascade blades were made of 2024 aluminum alloy and the solid particles used were quartz sand with average diameter of 165 microns. The following parameters were investigated: blade pressure distribution, and total pressure loss coefficient, both depending on the degree of erosion. In addition, a theoretical estimation of the blade erosion is compared with the experimental data.
It is pointed out that the X-ray polychromator experiment has been in operation on the Solar Maximum Mission satellite for more than three months. Using a number of different modes, the polychromator is observing flares and active regions in the wavelength range 1-23 A. These modes include polychromatic imaging, high resolution line profiles, high dispersion spectra, and light curves with high time-resolution. Data are described and some of the early analysis and interpretation is presented. All the interpretations are based on simple approximate methods; it is noted, however, that in most cases more elaborate and reliable methods are close to being applied.
An interpolation algorithm is presented as a practical alternative to common interpolation and approximation methods when applied to the problem of determining the location of remote sensor data. This algorithm is based upon knowledge of the geometry of the problem and is shown to be inherently more accurate than common interpolation schemes which may be applied to all types of data. A practical location problem is used to demonstrate its accuracy and computational cost.
A fast, reliable computer code is described for calculating the flow field about a cascade of arbitrary two dimensional airfoils. The method approximates the three dimensional flow in a turbomachinery blade row by correcting for stream tube convergence and radius change in the throughflow direction. A fully conservative solution of the full potential equation is combined with the finite volume technique on a body-fitted periodic mesh, with an artificial density imposed in the transonic region to insure stability and the capture of shock waves. The instructions required to set up and use the code are included. The name of the code is QSONIC. A numerical example is also given to illustrate the output of the program.
A preliminary analysis of heat transfer data on the space shuttle orbiter windward centerline for the STS-3 mission entry is presented. Temperature-time history plots for each measurement location and tabulated wall temperature and convective heating rate data at 21 selected trajectory points are included. The STS-3 flight data are also compared with predictions by two approximation methods for computing convective heat transfer rates in equilibrium air.
A simple approximate method for the evaluation of the spectrum and directivity of the synchrotron radiation from an ensemble of particles in a given magnetic field is considered, taking into account the results of this method for the total emissivity at high harmonics. The general formula is presented along with the details of the derivation of the emissivity for an arbitrary energy spectrum and pitch angle distribution of particles. The emissivities for some commonly encountered particle distributions are provided and some empirical formulae valid for a large range of the parameters are given. The results from the analytic expressions are compared with those obtained by detailed numerical calculations. For isotropic pitch angle distributions, spectra from the simple analytic expressions agree with the numerical results to a high degree of accuracy even at lower harmonics.