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Methods developed for radio occultation studies of planetary atmospheres are used to predict the electromagnetic focusing properties of a refracting lens representation of a Schwarzschild black hole. The infinity of foci are of three distinct types: a principal forward axial focus which is by far the strongest; higher-order forward axial foci; and backward conical foci with axial nulls.
An upwind finite-element technique that uses cell-centered quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive unstructured grids in two and three dimensions. A perfect gas model as well as an equilibrium air model is implemented for solving high-speed flows. A first-order basic scheme and a higher-order flux-corrected transport (FCT) scheme have been implemented. This technique has been used to predict 'Type III and IV' shock interactions on a cylinder in two dimensions and a swept cylinder in three dimensions, with a view to determine the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are very distinctly captured with a sequence of adaptively-generated grids. Three-dimensional corner flow, typically encountered in engine inlets due to compression of the flow by ramps in the walls, is also modeled. This procedure is the first step in developing an integrated fluid, thermal, structural analysis capability for hypersonic flight vehicles like the National Aero-Space Plane.
High-Reynolds-number compressible free shear layers were studied experimentally to explore the effects of compressibility on the turbulence field. A reduction in both the level and the lateral extent of turbulence fluctuations with increasing convective Mach number (Mc) (reported earlier for Mc of 0.51 and 0.64) is much higher at Mc of 0.86. The higher-order moments of turbulence fluctuations such as skewness and flatness show that the intermittency due to the excursion of large-scale structures into the free streams at the edge of shear layers was significantly reduced (both in the level and the extent) due to increased Mc.
Results are presented on simultaneous observations of neutral winds and electric fields at spaced locations in the dawn auroral oval, carried out during a chemical release experiment on March 21, 1987. The observed plasma drifts and electron densities indicated the presence of a significant coupling between plasma and neutrals at the altitude of the F region but little coupling in the lower E region. The wind variations in the height range between 95 and 130 km were suggestive of the variations and amplitudes expected if the flow was dominated by the semidiurnal tide. However, a comparison of the flow with the model developed by Forbes (1982) showed that the phase differs by 4-5 hours from the predictions. Moreover, the measured divergence and vorticity in the flow are much larger than those predicted by the model, indicating that higher-order modes than those treated by Forbes may contribute significantly to the high-latitude thermospheric flow.
An upwind cell-centered scheme for the solution of steady laminar viscous high-speed flows is implemented on unstructured two-dimensional meshes. The first-order implementation employs Roe's (1981) approximate Riemann solver, and a higher-order extension is produced by using linear reconstruction with limiting. The procedure is applied to the solution of inviscid subsonic flow over an airfoil, inviscid supersonic flow past a cylinder, and viscous hypersonic flow past a double ellipse. A detailed study is then made of a hypersonic laminar viscous flow on a 24-deg compression corner. It is shown that good agreement is achieved with previous predictions using finite-difference and finite-volume schemes. However, these predictions do not agree with experimental observations. With refinement of the structured grid at the leading edge, good agreement with experimental observations for the distributions of wall pressure, heating rate and skin friction is obtained.
The effects of the state of the initial boundary layers on the development of a two-stream, plane mixing layer, with a velocity ratio of 0.6 are experimentally investigated. Spanwise-average profiles are compared for the first time. The results indicate that both the near and far-field growth rates for the untripped case are significantly higher than the tripped case. The maximum Reynolds stresses and higher-order products for the two cases behave very differently in the near-field, but asymptote to approximately the same constant levels far downstream. The mean velocity and turbulence profiles in this region also collapse adequately for the two cases when plotted in similarity coordinates. The distance required to achieve self-similarity is distinctly shorter for the tripped case, in contrast to previous observations. The higher growth rate for the untripped case is attributed to the presence of streamwise vortices which result in additional entrainment by the mixing layer.
The three most successful models for describing scattering from random rough surfaces are the Kirchhoff approximation (KA), the small-perturbation method (SPM), and the two-scale-roughness (or composite roughness) surface-scattering (TSR) models. In this paper it is shown how these three models can be derived rigorously from one perturbation expansion based on the extinction theorem for scalar waves scattering from perfectly rigid surface. It is also shown how corrections to the KA proportional to the surface curvature and higher-order derivatives may be obtained. Using these results, the scattering cross section is derived for various surface models.
Extensive testing of the advective scheme proposed by Prather (1986) has been carried out in support of the California Institute of Technology-Jet Propulsion Laboratory two-dimensional model of the middle atmosphere. The original scheme is generalized to include higher-order moments. In addition, it is shown how well the scheme works in the presence of chemistry as well as eddy diffusion. Six types of numerical experiments including simple clock motion and pure advection in two dimensions have been investigated in detail. By comparison with analytic solutions, it is shown that the new algorithm can faithfully preserve concentration profiles, has essentially no numerical diffusion, and is superior to a typical fourth-order finite difference scheme.
A basic theoretical and computational study of two-equation models for near-wall turbulent flows was conducted. Two major problems established for the K-epsilon model are discussed, the lack of natural boundary conditions for the dissipation rate and the appearance of higher-order correlations in the balance of terms for the dissipation rate at the wall. The K-omega equation is shown to have two problems also: an exact viscous term is missing, and the destruction of the dissipation term is not properly damped near the wall. A new K-tau model (where tau = 1/omega is the turbulent time scale) was developed by inclusion of the exact viscous term, and by introduction of new wall damping functions with improved asymptotic behavior. A preliminary test of the new model yields improved predictions for the flat-plate turbulent boundary layer.
Interacting galaxies show a variety of exotic morphologies besides the well-known rings, spirals, and bars. It is proposed that many of these can be identified with nonlinear, caustic structures that are known from singularity theory to be generic in collisionless dynamics. A simple kinematical model for stellar orbits is used to study the development of caustic waveforms in galaxy disks following impulsive, nonaxially symmetric (collisional) disturbances. It appears that all of the caustics known from singularity theory to be generic in two dimensions develop as transient forms in at least some moderately off-center collisions. The more complex, higher-order caustics appear most prominently in the more off-center and larger amplitude disturbances. It is further suggested that the highly nonlinear caustic waves may play an important role in interaction-induced star formation.
This paper deals with a dynamic stability analysis of unidirectional fiber-reinforced composite viscoelastic plates subjected to compressive edge loads. The integrodifferential equations governing the stability problem are obtained by using, in conjunction with a Boltzmann hereditary constitutive law for a three-dimensional viscoelastic medium, a higher-order shear deformation theory of orthotropic plates. Such a theory incorporates transverse shear deformation, transverse normal stress, and rotatory inertia effects. The solution of the stability problem as considered within this paper concerns the determination of the critical in-plane edge loads yielding the asymptotic instability. Numerical applications, based on material properties derived within the framework of Aboudi's micromechanical model, are presented and pertinent conclusions concerning the nature of the loss of stability and the influence of various parameters are outlined.
Higher order boundary conditions involve derivatives of the fields beyond the first and were recently shown to be more effective than traditional first order conditions in modeling dielectric coatings and layers. In this report an application of a third order generalized boundary condition to scattering by a filled rectangular groove is presented. Deficiencies of such higher-order boundary conditions are addressed and a correction is proposed for the present case. As part of the process of examining and correcting the accuracy of the proposed generalized boundary conditions, an exact solution is developed and a comparison is provided with a solution based on the standard impedance boundary condition.
The objective of the research is to develop and validate accurate, user-oriented viscous CFD codes (with inviscid options) for three-dimensional, unsteady aerodynamic flows about arbitrary rotorcraft configurations. Unsteady, three-dimensional Euler and Navier-Stokes codes are developed, adapted, and extended to rotor-body combinations. Flow solvers are coupled with zonal grid topologies, including rotating and nonrotating blocks. Special grid clustering and wave-fitting techniques were developed to capture low-level radiating acoustic waves. Significant progress was made in computing the propagation of acoustic waves due to the interaction of a concentrated vortex and a helicopter airfoil. The need for higher-order schemes was firmly established in relatively inexpensive two-dimensional calculations. In three dimensions, the number of grid points required to capture the low-level acoustic waves becomes very large, so that large supercomputer memory becomes essential. Good agreement was obtained between the numerical results obtained with a thin-layer Navier-Stokes code and experimental data from a model rotor. In addition, several nonrotating configurations that are sometimes proposed to simulate rotor blade tips in conventional wind tunnels were examined, and the complex flow around the radical tip shape of the world's fastest helicopter is under investigation. These studies demonstrate the flexibility and power of CFD to gain physical insight, study novel ideas, and examine various possibilities that might be difficult or impossible to set up in physical experiments. As a prelude to studies of rotor-body aerodynamic interactions, a preliminary grid topology and moving-interface strategy were developed. A new Euler/Navier-Stokes code using these techniques computes the vortical wake directly, rather than modeling it, as in most previous rotorcraft studies. Several hover cases were run for conventional and advanced-geometry blades. Numerical schemes using multi-zones and/or adaptive grids appear to be necessary to simulate the complex vortical flows in rotor wakes.
The design of digital phase locked loops (DPLL) using estimation theory concepts in the selection of a loop filter is presented. The key concept, that the DPLL closed-loop transfer function is decomposed into an estimator and a predictor, is discussed. The estimator provides recursive estimates of phase, frequency, and higher-order derivatives, and the predictor compensates for the transport lag inherent in the loop.
A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.
Forward and inverse kinematics equations are derived for the large geometry maneuver of adaptive trusses. A new algorithm based on higher-order multistep methods is proposed as a means of computing the length control for a described large geometry maneuver. The algorithm is shown to improve in computational speed at least five times over the algorithm presented in an earlier paper. The acceleration in control computation and other features such as varying velocity profiles and curved trajectories are illustrated by simulation results.
Pressure distributions and force characteristics have been determined for a body of revolution consisting of a fineness ratio 5.75, circular-arc, ogival nose tangent to a cylindrical afterbody for an angle-of-attack range of 0 degrees to 35.5 degrees. The free-stream Mach number was 1.98 and the free-stream Reynolds number was approximately 0.5 x 10 sup 6, based on body diameter. Comparison of the theoretical and experimental pressure distributions shows that for zero lift, either slender-body theory or higher-order theories yield results which are in good agreement with experiment. For the lifting case, good agreement with theory is found only for low angles of attack and for the region in which the body cross-sectional area is increasing in the downstream direction. Because of the effects of cross-flow separation and the effects of compressibility due to the high cross-flow Mach numbers at large angles of attack, the experimental pressure distributions differ from those predicted by potential theory. Although the flow about the inclined body was, in general, similar to that assumed as the basis for Allen's method of estimating the forces resulting from viscous effects (NACA RM A91I26), the distribution of the forces was significantly different from that assumed. Nevertheless, the lift and pitching-moment characteristics were in fair agreement with the estimated value.
A new mathematical technique, due to Milne-Thomson, is used to obtain an improved form of the method of Poggi for calculating the effect of compressibility on the subsonic flow past an obstacle. By means of this new method, the difficult surface integrals of the original Poggi method can be replaced by line integrals. These line integrals are then solved by the use of residue theory. In this way an equation is obtained giving the second-order effect of compressibility on the velocity of the fluid. The method is practicable for obtaining the higher-order effects of compressibility on the velocity field. As an illustration of the general result, the flow past an elliptic cylinder is discussed.