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NASA NTRS1976

Historical evolution of vortex-lattice methods

A review of the beginning and some orientation of the vortex-lattice method were given. The historical course of this method was followed in conjunction with its field of computational fluid dynamics, spanning the period from L.F. Richardson's paper in 1910 to 1975. The following landmarks were pointed out: numerical analysis of partial differential equations, lifting-line theory, finite-difference method, 1/4-3/4 rule, block relaxation technique, application of electronic computers, and advanced panel methods.

Deyoung, J.↗

NASA NTRS1976

Scanning laser-velocimeter surveys and analysis of multiple vortex wakes of an aircraft

A laser velocimeter capable of rapidly scanning a flow field while simultaneously sensing two components of the velocity was used to measure the vertical and streamwise velocity structure 1.5 spans downstream in the wake of a model typical of a large subsonic transport (Boeing 747). This flow field was modeled by a superposition of axisymmetric vortices with finite cores. This theoretical model was found to agree with the measured velocities everywhere except where two vortices were in close proximity. Vortex strengths derived from the span loading on the wing as predicted by vortex-lattice theory also agree with the present measurements. The axisymmetric vortex model used herein is a useful tool for analytically investigating the vortex wakes of aircraft.

Corsiglia, V. R.↗

NASA NTRS1974

Finite element solution theory for three-dimensional boundary flows

A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.

Baker, A. J.↗

NASA NTRS1974

An Analytical Investigation of Wing-Jet Interaction

The aerodynamic interaction between the wing and an inviscid jet with Mach number nonuniformity is formulated by using a two-vortex-sheet model for the jet. One of the vortex sheets accounts for the induced jet flow and the other the induced outer flow. No additional source distribution is needed for the jet at an angle of attack. The above problem is solved by satisfying the jet and wing tangency and the jet pressure-continuity conditions and using a quasi vortex lattice method for computing the induced flow field. The latter method is derived through theoretical consideration by properly accounting for singularities present in the equations and possesses the same simplicity and generality as the conventional vortex lattice method but has a better rate of numerical convergence. The resulting system of algebraic equations is solved by Purcell's vector method. The numerical formulation is first applied to the wing-slipstream interaction problem. Results for one centered-jet configuration are compared with those predicted by some existing theories.

Lan, E. C.↗

NASA NTRS1975

Unsteady vortex lattice techniques applied to wake formation and performance of the statically thrusting propeller

The application is considered of vortex lattice techniques to the problem of describing the aerodynamics and performance of statically thrusting propellers. A numerical lifting surface theory to predict the aerodynamic forces and power is performed. The chordwise and spanwise loading is modelled by bound vortices fixed to a twisted flat plate surface. In order to eliminate any apriori assumptions regarding the wake shape, it is assumed the propeller starts from rest. The wake is generated in time and allowed to deform under its own self-induced velocity field as the motion of the propeller progresses. The bound circulation distribution is then determined with time by applying the flow tangency boundary condition at certain selected control points on the blades. The aerodynamics of the infinite wing and finite wing are also considered. The details of wake formation and roll-up are investigated, particularly the localized induction effect. It is concluded that proper wake roll-up and roll-up rates can be established by considering the details of motion at the instant of start.

Hall, G. F.↗

NASA NTRS1977

Rolling moments in a trailing vortex flow field

Pressure distributions are presented which were measured on a wing in close proximity to a tip vortex of known structure generated by a larger, upstream semispan wing. Overall loads calculated by integration of these pressures are checked by independent measurements made with an identical model mounted on a force balance. Several conventional methods of wing analysis are used to predict the loads on the following wing. Strip theory is shown to give uniformly poor results for loading distribution, although predictions of overall lift and rolling moment are sometimes acceptable. Good results are obtained for overall coefficients and loading distribution by using linearized pressures in vortex-lattice theory in conjunction with a rectilinear vortex. The equivalent relation from reverse-flow theory that can be used to give economic predictions for overall loads is presented.

Mcmillan, O. J.↗

NASA NTRS1977

Rolling moments in a trailing vortex flow field

Mcmillan, O. J.↗

NASA NTRS1981

Langmuir probe theory and the problem of anisotropic collection

A more general understanding of Langmuir probe theory by going beyond particular coordinate systems as far as possible was studied. To delineate the role of initial velocities in the problem and to characterize the interaction between the velocity flow field and the electrostatic potential field both of which enter into the determination of particle trajectories are desired. The probe is supposed to be negatively charged throughout and the ensuing region of positive space charge about it differs fundamentally from the plasma region beyond in the sense that the former represents a region in which deterministic trajectories dominate while the lattice is a region dominated by statistical interactions largely controlled by the collisionless stationary Boltzmann equation. A general solution of this Boltzmann equation is given and its relationship to the problem of saturation current density in 3D is elucidated.

Kyrala, A.↗

NASA NTRS1990

Propeller-wing interaction using a frequency domain panel method

The unsteady aerodynamic coupling between a propeller and a wing is analyzed using linear compressible aerodynamic theory. The periodic loads are decomposed into harmonics, and the harmonic amplitudes are found iteratively. Each stage of the iteration involves the solution of an isolated propeller or wing problem; the interaction is done through the Fourier transform of the induced velocity field. The method was validated by comparing the predicted velocity field about an isolated propeller with detailed laser Doppler velocimeter measurements and by comparison with mean loads measured in a wing-propeller experiment. Comparisons have also been made between the fluctuating loads predicted by the present method and a quasisteady vortex lattice scheme.

Williams, Marc H.↗

NASA NTRS2004

Estimation of Length-Scales in Soils by MRI

Soil can be best described as an unconsolidated granular media that forms porous structure. The present macroscopic theory of water transport in porous media rests upon the continuum hypothesis that the physical properties of porous media can be associated with continuous, twice-differentiable field variables whose spatial domain is a set of centroids of Representative Elementary Volume (REV) elements. MRI is an ideal technique to estimate various length-scales in porous media. A 0.267 T permanent magnet at NASA GRC was used for this study. A 2D or 3D spatially-resolved porosity distribution were obtained from the NMR signal strength from each voxel and the spin-lattice relaxation time. A classical spin-warp imaging with Multiple Spin Echos (MSE) was used to evaluate proton density in each voxel. Initial resolution of 256 x 256 was subsequently reduced by averaging neighboring voxels and the porosity convergence was observed. A number of engineered "space candidate" soils such as Isolite(trademark), Zeoponics(trademark), Turface(trademark), and Profile(trademark) were used. Glass beads in the size range between 50 microns to 2 mm were used as well. Initial results with saturated porous samples have shown a good estimate of the average porosity consistent with the gravimetric porosity measurement results. For Profile(trademark) samples with particle sizes ranging between 0.25 to 1 mm and characteristic interparticle pore size of 100 microns the characteristic Darcy scale was estimated to be about delta(sub REV) = 10 mm. Glass beads porosity show clear convergence toward a definite REV which stays constant throughout homogeneous sample. Additional information is included in the original extended abstract.

N E Daidzic↗

NASA NTRS1972

Calculation of aerodynamic characteristics of STOL aircraft with externally-blown jet-augmented flaps.

Analytical methods to predict the interference between lifting surfaces and high-bypass-ratio turbofan engines are described. A three-dimensional nonplanar vortex-lattice lifting surface method is used to predict the characteristics of a wing with leading-edge slat and multiple slotted trailing-edge flaps including effects of externally induced velocity fields. A flow model of the wake of a high-bypass-ratio turbofan is described which is capable of predicting the induced velocity field both inside and outside the jet wake. These methods are combined to predict the longitudinal characteristics of several STOL transport models utilizing externally-blown flaps and comparisons with data are shown. The results indicate good agreement between experiment and theory for various configurations under a wide range of power conditions.

Mendenhall, M. R.↗

NASA NTRS1982

Dipole-field sums and Lorentz factors for orthorhombic lattices, and implications for polarizable molecules

A method for computing the Lorentz tensor components in single crystals via rapidly convergent sums of Bessels functions is developed using the relationship between dipole-field sums and the tensor components. The Lorentz factors for simple, body-centered, and base-centered orthorhombic lattices are computed using this method, and the derivative Lorentz factors for simple orthorhombic lattices are also determined. Both the Lorentz factors and their derivatives are shown to be very sensitive to a lattice structure. The equivalent of the Clausius-Mossotti relation for general orthorhombic lattices is derived using the Lorentz-factor formalism, and the permanent molecular dipole moment is related to crystal polarization for the case of a ferroelectric of polarizable point dipoles. It is concluded that the polarization enhancement due to self-polarization familiar from classical theory may actually be a reduction in consequences of negative Lorentz factors in one or two lattice directions for noncubic crystals.

Purvis, C. K.↗

NASA NTRS1991

The aerodynamic characteristics of vortex ingestion for the F/A-18 inlet duct

A Reduced Navier-Stokes (RNS) solution technique was successfully combined with the concept of partitioned geometry and mesh generation to form a very efficient 3D RNS code aimed at the analysis-design engineering environment. Partitioned geometry and mesh generation is a pre-processor to augment existing geometry and grid generation programs which allows the solver to (1) recluster an existing gridlife mesh lattice, and (2) perturb an existing gridfile definition to alter the cross-sectional shape and inlet duct centerline distribution without returning to the external geometry and grid generator. The present results provide a quantitative validation of the initial value space marching 3D RNS procedure and demonstrates accurate predictions of the engine face flow field, with a separation present in the inlet duct as well as when vortex generators are installed to supress flow separation. The present results also demonstrate the ability of the 3D RNS procedure to analyze the flow physics associated with vortex ingestion in general geometry ducts such as the F/A-18 inlet. At the conditions investigated, these interactions are basically inviscid like, i.e., the dominant aerodynamic characteristics have their origin in inviscid flow theory.

Anderson, Bernhard H.↗

NASA NTRS1991

The aerodynamic characteristics of vortex ingestion for the F/A-18 inlet duct

A Reduced Navier-Stokes (RNS) solution technique was successfully combined with the concept of partitioned geometry and mesh generation to form a very efficient 3-D RNS code aimed at the analysis-design engineering environment. Partitioned geometry and mesh generation is a pre-processor to augment existing geometry and grid generation programs which allows the solver to (1) recluster an existing gridlife mesh lattice, and (2) perturb an existing gridfile definition to alter the cross-sectional shape and inlet duct centerline distribution without returning to the external geometry and grid generator. The present results provide a quantitative validation of the initial value space marching 3-D RNS procedure and demonstrates accurate predictions of the engine face flow field, with a separation present in the inlet duct as well as when vortex generators are installed to suppress flow separation. The present results also demonstrate the ability of the 3-D RNS procedure to analyze the flow physics associated with vortex ingestion in general geometry ducts such as the F/A-18 inlet. At the conditions investigated, these interactions are basically inviscid like, i.e., the dominant aerodynamic characteristics have their origin in inviscid flow theory.

Anderson, Bernhard H.↗

NASA NTRS1993

Automata network models of galaxy evolution

Two ideas appear frequently in theories of star formation and galaxy evolution: (1) star formation is nonlocally excitatory, stimulating star formation in neighboring regions by propagation of a dense fragmenting shell or the compression of preexisting clouds; and (2) star formation is nonlocally inhibitory, making H2 regions and explosions which can create low-density and/or high temperature regions and increase the macroscopic velocity dispersion of the cloudy gas. Since it is not possible, given the present state of hydrodynamic modeling, to estimate whether one of these effects greatly dominates the other, it is of interest to investigate the predicted spatial pattern of star formation and its temporal behavior in simple models which incorporate both effects in a controlled manner. The present work presents preliminary results of such a study which is based on lattice galaxy models with various types of nonlocal inhibitory and excitatory couplings of the local SFR to the gas density, temperature, and velocity field meant to model a number of theoretical suggestions.

Chappell, David↗

NASA NTRS1983

Information theory analysis of sensor-array imaging systems for computer vision

Information theory is used to assess the performance of sensor-array imaging systems, with emphasis on the performance obtained with image-plane signal processing. By electronically controlling the spatial response of the imaging system, as suggested by the mechanism of human vision, it is possible to trade-off edge enhancement for sensitivity, increase dynamic range, and reduce data transmission. Computational results show that: signal information density varies little with large variations in the statistical properties of random radiance fields; most information (generally about 85 to 95 percent) is contained in the signal intensity transitions rather than levels; and performance is optimized when the OTF of the imaging system is nearly limited to the sampling passband to minimize aliasing at the cost of blurring, and the SNR is very high to permit the retrieval of small spatial detail from the extensively blurred signal. Shading the lens aperture transmittance to increase depth of field and using a regular hexagonal sensor-array instead of square lattice to decrease sensitivity to edge orientation also improves the signal information density up to about 30 percent at high SNRs.

Huck, F. O.↗

NASA NTRS2004

Notes on Interface Growth Kinetics 50 Years after Burton, Cabrera and Frank

This overview is devoted to some unresolved basic problems in crystal growth kinetics. The density wave approach to propagation of a spatially diffuse interface between a growing crystal and its simple (e.g., metallic) melt is discussed is Section 2. This approach allows for the calculation of kinetic coefficients and is an alternative to the localized interface concept in which each atom belongs to either a solid or a liquid. Sections 3 and 4 deals mainly with layer growth from solution. Mutual retardation of the growth steps via their bulk and d a c e diffusion fields is the major subject. The influence of solution flow on step bunching (Section 4) suggests the essential influence of bulk diffusion on the surface morphology. The flow within the solution boundary layer enhances step-step interaction, influences the step bunching process and the resulting step pattern morphology on the growing surface. Recent experiments on the rates at which strongly polygonized steps on protein and small molecule crystals propagate during growth from solution are analyzed in Section 5 . We have shown that the step segments may be "singular" and that "one-dimensional nucleation" may be the rate limiting stage for the segments that are shorter or comparable in length to the thermodynamically equilibrium interlink distance. In this case, the reciprocal dependence of the segment propagation rate on the segment length that follow from the Gibbs-Thompson law, should be replaced by an abrupt switch from zero to a finite constant velocity. Until recently, the Kossel crystal remained the only model used in crystal growth theory. In such Kossel Gibbs-Thomson law, should be replaced by an abrupt switch &om zero to a finite constant velocity. crystals, all kinks at the steps are identical and the kink rate is a linear function of the supersaturation. In the non-Kossel crystals, there may be several kink configurations characterized by different geometries and energies. These configurations should appear in a specific sequence when each new lattice unit cell is filled. As a result of such a cooperative interaction within the unit cell, a non-linear dependence of the kink rate on the vapor pressure or solution concentration in excess over the equilibrium value should be expected.

Chernov, A. A.↗

NASA NTRS2021

Physics and Chemistry of Te and HgTe-based Ternary Melts

Historically, the theoretical treatment of the liquid phases has always been more difficult and complicated than that for solid and gas phases. A liquid has no lattice structure as crystalline solids and the atoms/molecules in the liquid can migrate through it relatively rapidly. On the other hand, it is also interacting with many other atoms/molecules so that the simplifications of the kinetic theory of gases cannot be employed. For more complicated liquids, such as the liquids of high ionicity and those containing hydrogen bonds and electric dipoles, the understanding is far from complete. At the same time, accurate information on the physics and chemistry of semiconductor melts is needed for the quantitative descriptions of the process of crystal growth from melt. The pre-crystallization phenomena in the liquid phase are critical because the properties of the grown crystals depend on the state and structure of the melt as well as the thermal history of the melt during solidification process. However, the data on the liquid phase, such as thermophysical properties of semiconductor melts are scarce, especially for the HgTe-based II-VI ternary compound semiconductors because of their high vapor pressure and extreme toxicity. Analysis of the thermophysical properties of the melt can provide information about structural transitions of the melt during the solidification process. From a broader point of view, the structure of liquids is much more complicated than the crystalline solids, especially the relaxation behavior through different thermal histories. The theory of hetero-phase fluctuations of liquids is applicable to any many-body systems including condensed-matter physics, field theory, physics of nuclear-matter, cosmology, biology and even sociology. This book summarizes the physics and chemistry from the experimental measurements and theoretical analyses of phase diagram, thermodynamic properties, density, thermal conductivity, viscosity, and electrical conductivity on the binary, pseudo-binary and ternary melts of the most advanced IR-detector material systems of HgCdTe and HgZnTe as well as the analyses of these results. The main objectives of this study are: (1) to provide the phase diagrams and thermodynamic properties of Hg-Cd-Te and Hg-Zn-Te systems through quantitatively fitting the experimental data by assuming an associated solution model for the liquid phase, (2) to experimentally measure the thermophysical properties of the Hg-Cd-Te and Hg-Zn-Te melts, including density, viscosity, electrical conductivity and thermal conductivity as functions of temperature and composition and (3) to enhance the fundamental knowledge of hetero-phase fluctuations and relaxation phenomena in the melts and extend our understanding of the solidification process in order to interpret the experimental results of crystal growth so as to improve the melt growth processes of the compound semiconductor. The physics and chemistry of Te and HgTe-based ternary melts were explored through the studies of the structural transformation during melting, the supercooling during solidification, the relaxation phenomena after rapid cooling of the melts and the metal-semiconductor transition in the melts through the analyses of electrical conductivity and Lorenz number. An in-depth study on the thermophysical properties and their time-dependent structural dynamic processes taking place in the vicinity of the solid-liquid phase transition of the narrow homogeneity range HgTe-based ternary semiconductors as well as the analysis of the homogenization process in the melt will also be presented.

Thermophysical properties↗