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At least 595 records · Page 33

Transient development of perturbations in stratified shear flow

Transient development of perturbations in inviscid stratified shear flow is investigated. Use is made of closed form analytic solutions that allow concise identification of optimally growing plane-wave solutions for the case of an unbounded flow with constant shear and stratification. For the case of channel flow, variational techniques are employed to determine the optimally growing disturbances. The maximum energy growth attained over a specific time interval decreases continuously with increasing stratification, and no special significance attaches to Ri = 0.25. Indeed, transient growth can be substantial even for Ri = O(1). A general lower bound on the energy growth attained by an optimal perturbation in a stratified flow over a given time interval is the square root of the growth attained by the corresponding perturbation in unstratified flow. Enhanced perturbation persistence is found for mean-flow stratification lying in the range Ri between 0.1 and 0.3. Small but finite perturbations in mean flow with Ri less than 0.4 produce regions with locally negative total density gradient, which are expected to overturn. Although the perturbations are of wave form, buoyancy fluxes mediate transfer between perturbation kinetic and potential energy during transient development, thus implying that buoyancy flux is not a determinative diagnostic for distinguishing between waves and turbulence in stratified flows.

Farrell, Brian F.↗

Wing plan forms for high-speed flight

It is pointed out that, in the case of an airfoil of infinite aspect ratio moving at an angle of sideslip, the pressure distribution is determined solely by that component of the motion in a direction normal to the leading edge. It follows that the attachment of plane waves to the airfoil at near-sonic or supersonic speeds (Ackeret theory) may be avoided and the pressure drag may be reduced by the use of plan forms in which the angle of sweepback is greater than the Mach angle. The analysis indicates that for aerodynamic efficiency, wings designed for flight at supersonic speeds should be swept back at an angle greater than the Mach angle, and the angle of sweepback should be such that the component of velocity normal to the leading edge is less than the critical speed of the airfoil sections. This principle may also be applied to wings designed for subsonic speeds near the speed of sound, for which the induced velocities resulting from the thickness might otherwise be sufficiently great to cause shock waves.

Jones, Robert J↗

Integrated optics in an electrically scanned imaging Fourier transform spectrometer

An efficient, lightweight and stable, Fourier transform spectrometer was developed. The mechanical slide mechanism needed to create a path difference was eliminated by the use of retro-reflecting mirrors in a monolithic interferometer assembly in which the mirrors are not at 90 degrees to the propagation vector of the radiation, but rather at a small angle. The resulting plane wave fronts create a double-sided inteferogram of the source irradiance distribution which is detected by a charge-coupled device image sensor array. The position of each CCD pixel in the array is an indication of the path difference between the two retro-reflecting mirrors in the monolithic optical structure. The Fourier transform of the signals generated by the image sensor provide the spectral irradiance distribution of the source. For imaging, the interferometer assembly scans the source of irradiation by moving the entire instrument, such as would occur if it was fixedly mounted to a moving platform, i.e., a spacecraft. During scanning, the entrace slot to the monolithic optical structure sends different pixels to corresponding interferograms detected by adjacent columns of pixels of the image sensor.

Breckinridge, James B.↗

Measurement of birefringence for optical recording disk substrates

The birefringence of bare and coated substrates for magneto-optical recording is experimentally investigated using ellipsometry at the wavelengths of 632.8 nm and 780 nm. The rotation and ellipticity of the polarization state of the reflected or transmitted light is measured for different incident angles and different orientations of the incident linear polarization. The measured data is then fitted by a computer program which solves the Maxwell equations for the plane-wave propagation in a multilayer structure and minimizes the error between the measured and calculated data by adjusting the unknown parameters of the multilayer. This approach enables us to determine orientations of the three principal axes in the substrate and the corresponding refractive indices. A special feature of our ellipsometers is that a glass hemisphere is placed in contact with the substrate, which eliminates the refraction of the incident light and enables a maximum propagation angle of 70 degrees (with respect to the normal) in the substrate. This increases the sensitivity of the measurement. Certain anomalies were observed, which we believe are associated with the presence of grooves on these substrates.

Fu, Hong↗

Parametric resonant triad interactions in a free shear layer

We investigate the weakly nonlinear evolution of a triad of nearly-neutral modes superimposed on a mixing layer with velocity profile u bar equals Um + tanh y. The perturbation consists of a plane wave and a pair of oblique waves each inclined at approximately 60 degrees to the mean flow direction. Because the evolution occurs on a relatively fast time scale, the critical layer dynamics dominate the process and the amplitude evolution of the oblique waves is governed by an integro-differential equation. The long-time solution of this equation predicts very rapid (exponential of an exponential) amplification and we discuss the pertinence of this result to vortex pairing phenomena in mixing layers.

Mallier, R.↗

Resonant frequencies of irregularly shaped microstrip antennas using method of moments

This paper describes an application of the method of moments to determine resonant frequencies of irregularly shaped microstrip patches embedded in a grounded dielectric slab. For analysis, the microstrip patch is assumed to be excited by a linearly polarized plane wave that is normal to the patch. The surface-current density that is induced on the patch because of the incident field is expressed in terms of subdomain functions by dividing the patch into identical rectangular subdomains. The amplitudes of the subdomain functions, as a function of frequency, are determined using the electric-field integral equation (EFIE) approach in conjunction with the method of moments. The resonant frequencies of the patch are then obtained by selecting the frequency at which the amplitude of the surface-current density is real. The resonant frequencies of the equilateral triangular and other nonrectangular patches are computed using the present technique, and these frequencies are compared with measurements and other independent calculations.

Deshpande, Manohar D.↗

MOM3D method of moments code theory manual

MOM3D is a FORTRAN algorithm that solves Maxwell's equations as expressed via the electric field integral equation for the electromagnetic response of open or closed three dimensional surfaces modeled with triangle patches. Two joined triangles (couples) form the vector current unknowns for the surface. Boundary conditions are for perfectly conducting or resistive surfaces. The impedance matrix represents the fundamental electromagnetic interaction of the body with itself. A variety of electromagnetic analysis options are possible once the impedance matrix is computed including backscatter radar cross section (RCS), bistatic RCS, antenna pattern prediction for user specified body voltage excitation ports, RCS image projection showing RCS scattering center locations, surface currents excited on the body as induced by specified plane wave excitation, and near field computation for the electric field on or near the body.

Shaeffer, John F.↗

Two space scatterer formalism calculation of bulk parameters of thunderclouds

In a previous study, we used a modified two-space scatterer formalism of Twersky to establish for a cloud modeled as a statistically homogeneous distribution of spherical water droplets, the dispersion relations that determine its bulk propagation numbers and bulk indexes of refraction in terms of the vector equivalent scattering amplitude and the dyadic scattering amplitude of the single water droplet in isolation. The results were specialized to the forward direction of scattering while demanding that the scatterers preserve the incident polarization. We apply this approach to obtain specific numerical values for the macroscopic parameters of the cloud. We work with a cloud of density rho = 100 cm(exp -3), a wavelength lambda = 0.7774 microns, and with spherical water droplets of common radius alpha = 10 microns. In addition, the scattering medium is divided into three parts, the medium outside the cloud, moist air (the medium inside the cloud but outside the droplets), and the medium inside the spherical water droplets. The results of this report are applicable to a cloud of any geometry since the boundary does not interfere with the calculations. Also, it is important to notice the plane wave nature of the incidence wave in the moist atmosphere.

Phanord, Dieudonne D.↗

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly demonstrated and it is shown that the UGO/EUTD results remain valid and uniformly reduce to the classic results away from the transition regions. Mathematical details on the asymptotic properties and efficient numerical evaluation of the canonical functions involved in the UGO/EUTD expressions are also provided.

Constantinides, E. D.↗

Second-order numerical solution of time-dependent, first-order hyperbolic equations

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

Shah, Patricia L.↗

Finite-surface method for the Maxwell equations with corner singularities

The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line integrals appearing in the method. Numerical results are presented for a harmonic plane wave incident on a finite flat plate. Comparisons with exact solutions show good agreement.

Vinokur, Marcel↗

A Unique Test Facility to Measure Liner Performance with a Summary of Initial Test Results

A very ambitious study was initiated to obtain detailed acoustic and flow data with and without a liner in a duct containing a mean flow so that available theoretical models of duct liners can be validated. A unique flow-duct facility equipped with a sound source, liner box, flush-walled microphones, traversable microphones and traversable pressure and temperature probes was built. A unique set of instrumentation boxes equipped with computer controlled traverses were designed and built that allowed measurements of Mach number, temperature, SPLs and phases in two planes upstream of a liner section and two planes downstream at a large number of measurement points. Each pair of planes provided acoustic pressure gradients for use in estimating the particle velocities. Specially-built microphone probes were employed to make measurements in the presence of the flow. A microphone traverse was also designed to measure the distribution of SPLs and phases from the beginning of the liner to its end along the duct axis. All measurements were made with the help of cross-correlation techniques to reject flow noise and/or other obtrusive noise, if any. The facility was designed for future use at temperatures as high as 1500 F. In order to validate 2-D models in the presence of mean flow, the flow duct was equipped with a device to modify boundary layer flow on the smaller sides of a rectangular duct to simulate 2-D flow. A massive amount of data was acquired for use in validating duct liner models and will be provided to NASA in an electronic form. It was found that the sound in the plane-wave regime is well behaved within the duct and the results are repeatable from one run to another. At the higher frequencies corresponding to the higher-order modes, the SPLs within a duct are not repeatable from run to run. In fact, when two or more modes have the same frequency (i.e., for the degenerate modes), the SPLs in the duct varied between 2 dB to 12 dB from run to run. This made the calibration of the microphone probes extremely difficult at the higher frequencies.

Ahuja, K. K.↗

Interpretation of Extinction in Gaussian-Beam Scattering

The extinction efficiency for the interaction of a plane wave with a large nonabsorbing spherical particle is approximately 2.0. When a Gaussian beam of half-width w(sub 0) is incident upon a spherical particle of radius a with w(sub 0)/a less than 1, the extinction efficiency attains unexpectedly high or low values, contrary to intuitive expectations. The reason for this is associated with the so-called compensating term in the scattered field, which cancels the field of the Gaussian beam behind the particle, thereby producing the particle's shadow. I introduce a decomposition of the total exterior field into incoming and outgoing portions that are free of compensating terms. It is then shown that a suitably defined interaction efficiency has the intuitively expected asymptotic values of 2.0 for w(sub 0)/a much greater than 1 and 1.0 for w(sub 0)/a much less than 1.

Lock, James A.↗

Ray Scattering by an Arbitrarily Oriented Spheroid: 2. Transmission and Cross-polarization Effects

Transmission of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit is considered in the context of ray theory. The transmitted electric field is added to the diffracted plus reflected ray-theory electric field that was previously derived to obtain an approximation to the far-zone scattered intensity in the forward hemisphere. Two different types of cross-polarization effects are found. These are: (a) a rotation of the polarization state of the transmitted rays from when they are referenced with respect to their entrance into the spheroid to when they are referenced with respect to their exit from it and (b) a rotation of the polarization state of the transmitted rays when they are referenced with respect to the polarization state of the diffracted plus reflected rays.

Lock, James A.↗

Higher Order Modeling In the BEM/FEM Hybrid Formulation

Hybrid formulations using low order curl-conforming bases to represent the total electric field within a finite element region and low order divergence-conforming bases to represent equivalent electric and magnetic currents on the boundary are well known. However, higher-order divergence and curl-conforming bases have been shown to provide significant benefits in convergence rates and accuracy when employed in strictly integral equation and strictly finite element formulations. In this paper, a hybrid electric field formulation employing higher order bases is presented. The paper addresses benefits and issues associated with using higher order divergence-and curl-conforming bases in the hybrid finite element/boundary element electric field formulation. The method of singularity subtraction may be used to compute the self terms of the boundary integral when the bases are of low order. But this method becomes laborious and requires great care when the divergence conforming bases are of higher order. In order to handle these singularities simply and accurately, a generalized Gaussian quadrature method is employed in which the expansion functions account for the singularity. In preliminary tests of the higher order hybrid formulation, the equivalent electric current induced by scattering of a plane wave from a square dielectric cylinder is examined. Accurate results are obtained using only a two-triangle mesh when the current basis is of order 4 or 5. Additional results are presented comparing the error obtained using higher order bases to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained with higher order bases are compared to those obtained with lower order bases for selected sample problems.

Fink, Patrick W.↗

Ultrasound Thermal Field Imaging of Opaque Fluids

We have initiated an experimental program to develop an ultrasound system for non-intrusively imaging the thermal field in opaque fluids under an externally imposed temperature gradient. Many industrial processes involve opaque fluids, such as molten metals, semiconductors, and polymers, often in situations in which thermal gradients are important. For example, one may wish to understand semiconductor crystal growth dynamics in a Bridgman apparatus. Destructive testing of the crystal after the process is completed gives only indirect information about the fluid dynamics of the formation process. Knowledge of the coupled thermal and velocity fields during the growth process is then essential. Most techniques for non-intrusive velocity and temperature measurement in fluids are optical in nature, and hence the fluids studied must be transparent. In some cases (for example, LDV (laser Doppler velocimetry) and PIV (particle imaging velocimetry)) the velocities of small neutrally buoyant seed particles suspended in the fluid, are measured. Without particle seeding one can use the variation of the index of refraction of the fluid with temperature to visualize, through interferometric, Schlieren or shadowgraph techniques, the thermal field. The thermal field in turn gives a picture of the pattern existing in the fluid. If the object of study is opaque, non-optical techniques must be used. In this project we focus on the use of ultrasound, which propagates easily through opaque liquids and solids. To date ultrasound measurements have almost exclusively relied on the detection of sound scattered from density discontinuities inside the opaque material of interest. In most cases it has been used to visualize structural properties, but more recently the ultrasound Doppler velocimeter has become available. As in the optical case, it relies on seed particles that scatter Doppler shifted sound back to the detector. Doppler ultrasound techniques are, however, not useful for studying convective fluid flow in crystal growth, because particle seeding is unacceptable and flow velocities are typically too low to be resolved, and may be even lower in microgravity conditions where buoyancy forces are negligible. We will investigate a different use of ultrasound to probe the flows of opaque fluids non-intrusively and without the use of seed particles: our goal is to ultrasonically visualize the thermal field of opaque fluids with relatively high spatial resolution. The proposed technique relies upon the variation of sound speed with temperature of the fluid. A high frequency ultra-sound pulse passing through a fluid-filled chamber will traverse the chamber in a time determined by the relevant chamber dimension and the temperature of the fluid through which the pulse passes. With high time-resolution instrumentation that compares the excitation signal with the received pulse we can detect the influence of the fluid temperature on the pulse travel time. This is effectively an interferometric system, which in its optical form is an extremely sensitive approach to measuring thermal fields in fluids. Moreover, the temperature dependence of sound velocity in liquid metals is comparable to the temperature dependence of the speed of light required for accurate interferometric thermal images in transparent fluids. With an array of transducers scanned electronically a map of the thermal field over the chamber could be produced. An alternative approach would be to use the ultrasound analog of the shadowgraph technique. In the optical version, collimated light passes through the fluid, where it is focused or defocused locally by temperature field induced variations of the index of refraction. The resulting image reveals the thermal field through the spatial pattern of light intensity variations. By analogy, an ultrasound plane wave traversing an opaque fluid sample would be also locally focused or defocused depending on the speed of sound variations, giving rise to spatial variations in sound intensity that will reveal the thermal field pattern. These approaches could be applied to any situation in which temperature differences are expected to occur, and will rapidly provide information about the flow that simply cannot be obtained by any current intrusive or non-intrusive diagnostic technique. As materials processing in microgravity matures it will become increasingly important to have available simple and versatile diagnostic tools, such as we will develop, for studying the flows of opaque fluids under thermal forcing.

Andereck, C. David↗

Polarizing Grids, their Assemblies and Beams of Radiation

This article gives an analysis of the behavior of polarizing grids and reflecting polarizers by solving Maxwell's equations, for arbitrary angles of incidence and grid rotation, for cases where the excitation is provided by an incident plane wave or a beam of radiation. The scattering and impedance matrix representations are derived and used to solve more complicated configurations of grid assemblies. The results are also compared with data obtained in the calibration of reflecting polarizers at the Owens Valley Radio Observatory (OVRO). From these analysis, we propose a method for choosing the optimum grid parameters (wire radius and spacing). We also provide a study of the effects of two types of errors (in wire separation and radius size) that can be introduced in the fabrication of a grid.

Houde, Martin↗

Research in Computational Astrobiology

We present results from several projects in the new field of computational astrobiology, which is devoted to advancing our understanding of the origin, evolution and distribution of life in the Universe using theoretical and computational tools. We have developed a procedure for calculating long-range effects in molecular dynamics using a plane wave expansion of the electrostatic potential. This method is expected to be highly efficient for simulating biological systems on massively parallel supercomputers. We have perform genomics analysis on a family of actin binding proteins. We have performed quantum mechanical calculations on carbon nanotubes and nucleic acids, which simulations will allow us to investigate possible sources of organic material on the early earth. Finally, we have developed a model of protobiological chemistry using neural networks.

Chaban, Galina↗