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At least 271 records · Page 15

Embedding of SU/3/ in SU/8/.

SU/3/ embedded in SU/8/, constructing SU/8/ algebra to preserve structure, noting particle assignments and nonleptonic baryon decays

Carlstone, D. S.↗

The transonic aerofoil problem with embedded shocks.

The integral equation approach to the mixed flow problem of infinite wings at high subsonic speeds is adopted for non-circulatory and circulatory (lifting) flows. The solutions are determined from a system of non-linear algebraic equations and, to ensure always unique solutions, the method of differentiation with respect to a parameter has been applied. The resulting Cauchy problem is then solved with the linearised flow solution as the initial value vector. For the case of embedded shocks in the flow field, the method of steepest descent has been added to the calculation scheme. Results for subcritical and supercritical flows past aerofoils are given and compared with solutions obtained by finite-difference techniques.

Norstrud, H.↗

Analysis of supersonic combustion flow fields with embedded subsonic regions

The viscous characteristic analysis for supersonic chemically reacting flows was extended to include provisions for analyzing embedded subsonic regions. The numerical method developed to analyze this mixed subsonic-supersonic flow fields is described. The boundary conditions are discussed related to the supersonic-subsonic and subsonic-supersonic transition, as well as a heuristic description of several other numerical schemes for analyzing this problem. An analysis of shock waves generated either by pressure mismatch between the injected fluid and surrounding flow or by chemical heat release is also described.

Dash, S.↗

An all digital phase locked loop for synchronization of a sinusoidal signal embedded in white Gaussian noise

An all digital phase locked loop which tracks the phase of the incoming sinusoidal signal once per carrier cycle is proposed. The different elements and their functions and the phase lock operation are explained in detail. The nonlinear difference equations which govern the operation of the digital loop when the incoming signal is embedded in white Gaussian noise are derived, and a suitable model is specified. The performance of the digital loop is considered for the synchronization of a sinusoidal signal. For this, the noise term is suitably modelled which allows specification of the output probabilities for the two level quantizer in the loop at any given phase error. The loop filter considered increases the probability of proper phase correction. The phase error states in modulo two-pi forms a finite state Markov chain which enables the calculation of steady state probabilities, RMS phase error, transient response and mean time for cycle skipping.

Reddy, C. P.↗

Surface heat flux determination: An analytical and experimental study using a single embedded thermocouple

A numerical method by which data from a single embedded thermocouple can be used to predict the transient thermal environment for both high- and low-conductivity materials is described. The results of an investigation performed to verify the method clearly demonstrate that accurate, transient, surface heating conditions can be obtained from a thermocouple l.016 centimeters from the heating surface in a low-conductivity material. Space shuttle orbiter thermal protection system materials having temperature- and pressure-dependent properties, and typical orbiter entry heating conditions were used to verify the accuracy of the analytical procedure. Analytically generated, as well as experimental, data were used to compare predicted and measured surface temperatures.

Williams, S. D.↗

Steady supersonic flowfields with embedded subsonic regions

Supersonic flow past a blunt body is considered, where the flow contains an embedded subsonic region which lies between the shock wave and the body surface and is bounded by sonic lines from the body to the shock. A numerical approach is taken, which uses a basic finite difference scheme that solves the unsteady fluid dynamic equations in integral form. The unsteady equations are everywhere hyperbolic in time so no distinction need be made between subsonic and supersonic regions. Solutions to the mixed elliptic and hyperbolic steady flow equations are approached asymptotically in time. The method is illustrated for two-dimensional flows.

Maccormack, R. W.↗

The embedded feature model for the interpretation of chromospheric contrast profiles

Contrast profiles obtained from chromospheric filtergrams and spectra of bright and dark mottles have to date been interpreted almost exclusively in terms of Becker's cloud model. Here we demonstrate the failure of this model to account in a physically consistent way for the observed contrasts. As an alternative, we introduce an embedded-feature model, restricting our discussion in this paper to stationary features. Our model is then characterized by three independent parameters: the density of absorbing atoms, the geometrical depth, and the profile of the absorption coefficient. An analytic approximation to the contrast resulting from such a model reproduces well the observed behavior of all types of contrast profiles.

Steinitz, R.↗

Resonant frequency of microstrip antennas calculated from TE-excitation of an infinite strip embedded in a grounded dielectric slab

The calculation of currents induced by a plane wave normally incident upon an infinite strip embedded in a grounded dielectric slab is used to infer the resonant width (or frequency) of rectangular microstrip antennas. By placing the strip inside the dielectric, the effect of a dielectric cover of the same material as the substrate can be included in the calculation of resonant frequency. A comparison with measured results indicated agreement of 1 percent or better for rectangular microstrip antennas constructed on Teflon-fiberglass substrate.

Bailey, M. C.↗

Towards complete configurations using an embedded grid approach

A new approach to simulating transonic flow about transport configurations is briefly outlined. The methods embedded grid scheme provides a high degree of computational resolution coupled with geometric flexibility for future applications to complex shapes. Calculations presented illustrate aspects of transonic transport design including fuselage design, determination of wing control surface deflection effectiveness, and wing design.

Boppe, C. W.↗

A method for computation of inviscid three-dimensional flow over blunt bodies having large embedded subsonic regions

A computational technique for computing the three-dimensional inviscid flow over blunt bodies having large regions of embedded subsonic flow is detailed. Results, which were obtained using the CDC Cyber 203 vector processing computer, are presented for several analytic shapes with some comparison to experimental data. Finally, windward surface pressure computations over the first third of the Space Shuttle vehicle are compared with experimental data for angles of attack between 25 and 45 degrees.

Weilmuenster, K. J.↗

Singularity embedding method in potential flow calculations

The so-called H-type mesh is used in a finite-element (or finite-volume) calculation of the potential flow past an airfoil. Due to coordinate singularity at the leading edge, a special singular trial function is used for the elements neighboring the leading edge. The results using the special singular elements are compared to those using the regular elements. It is found that the unreasonable pressure distribution obtained by the latter is removed by the embedding of the singular element. Suggestions to extend the present method to transonic cases are given.

Jou, W. H.↗

High frequency sound emission from moving point multipole sources embedded in arbitrary transversely sheared mean flows

Formulas are derived for the high frequency sound emission from moving point multipole sources embedded in an arbitrary unidirectional transversely sheared mean flow. The results are used to study the sound generated by non-axisymmetric turbulent jets. The effect of the asymmetry in both the mean flow and the source distribution is accounted for by a 'circumferential directivity factor', which is easily calculated from the solution of a second order ordinary differential equation in the general case and from an explicit formula when the mean flow is symmetric but the source location is not. This factor is used to assess the potential of employing asymmetric velocity profiles that redirect the sound upward to reduce the noise radiation below the flight path of a jet aircraft.

Goldstein, M. E.↗

A transonic rectangular grid embedded panel method

A method is presented that has the potential for solving transonic flow problems about the same complex aircraft configurations currently being analyzed by subsonic panel methods. This method does not require the generation of surface fitted grids. Instead it uses rectangular grids and subgrids together with embedded surface panels on which boundary conditions are imposed. Both the Euler and full potential equations are considered. The method of least squares is used to reduce the solution of these equations to the solution of a sequence of Poisson problems. The Poisson problems are solved using fast Fourier transforms and panel influence coefficient techniques. The overall method is still in its infancy but some two dimensional results are shown illustrating various key features.

Johnson, F. T.↗

Holographic interferometry of transparent media using light scattered by embedded test objects

Fringe formation and localization in holographic interferometry of transparent media are discussed for configurations in which light enters the medium and is scattered back through it by an embedded diffuse object. Fringe order numbers are doubled, and the fringe localization region is translated and compressed by a factor of two. The results are applicable to tomographic reconstruction of aerodynamic density fields around opaque test objects.

Prikryl, I.↗