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Derivation of three-dimensional three-degree-of- freedom reentry equations of motion in terrestrial navigational coordinates
Two-dimensional panel flutter and panel divergence in subsonic flow - wind tunnel testing of two and three-dimensional panels
A method of mitigating noise in source image data representing pixels of a 3-D image. The "3-D image" may be any type of 3-D image, regardless of whether the third dimension is spatial, temporal, or some other parameter. The 3-D image is divided into three-dimensional chunks of pixels. These chunks are apodized and a three-dimensional Fourier transform is performed on each chunk, thereby producing a three-dimensional spectrum of each chunk. The transformed chunks are processed to estimate a noise floor based on spectral values of the pixels within each chunk. A noise threshold is then determined, and the spectrum of each chunk is filtered with a denoising filter based on the noise threshold. The chunks are then inverse transformed, and recombined into a denoised 3-D image.
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We report a theoretical investigation of the robustness of two-dimensional inviscid MHD flows at low magnetic Reynolds numbers with respect to three-dimensional perturbations. We analyze three model problems, namely flow in the interior of a triaxial ellipsoid, an unbounded vortex with elliptical streamlines, and a vortex sheet parallel to the magnetic field. We demonstrate that motion perpendicular to the magnetic field with elliptical streamlines becomes unstable with respect to the elliptical instability once the velocity has reached a critical magnitude whose value tends to zero as the eccentricity of the streamlines becomes large. Furthermore, vortex sheets parallel to the magnetic field, which are unstable for any velocity and any magnetic field, are found to emit eddies with vorticity perpendicular to the magnetic field and with an aspect ratio proportional to N(sup 1/2). The results suggest that purely two-dimensional motion without Joule energy dissipation is a singular type of flow which does not represent the asymptotic behaviour of three-dimensional MHD turbulence in the limit of infinitely strong magnetic fields.
Integrals of motion in three-dimensional restricted three-body problem as generalizations of angular momentum
Two dimensional, quasi three dimensional and three dimensional theories for the prediction of pure tone fan noise due to the interaction of inflow distortion with a subsonic annular blade row were studied with the aid of an unsteady three dimensional lifting surface theory. The effects of compact and noncompact source distributions on pure tone fan noise in an annular cascade were investigated. Numerical results show that the strip theory and quasi three-dimensional theory are reasonably adequate for fan noise prediction. The quasi three-dimensional method is more accurate for acoustic power and model structure prediction with an acoustic power estimation error of about plus or minus 2db.
It is shown that topology rules can define a small number of singular points on an aerodynamic surface and in the flow which can be combined in various ways to create the structures and characterize the physical mechanisms of three-dimensional separated flows. This topological development is based on the hypothesis that vector fields of skin-friction lines and external streamlines remain continuous. Among examples treated are the lee-side separated flows about slender bodies at angle of attack with symmetric or asymmetric wake structures; about a protuberance normal to a wall; and over a rearward-facing axisymmetric step.
Computational predictions of ice accretion on flying aircraft most commonly rely on modeling in two dimensions (2D). These 2D methods treat an aircraft geometry either as wing-like with infinite span, or as an axisymmetric body. Recently, fully three dimensional (3D) methods have been introduced that model an aircrafts true 3D shape. Because 3D methods are more computationally expensive than 2D methods, 2D methods continue to be widely used. However, a 3D method allows us to investigate whether it is valid to continue applying 2D methods to a finite wing. The extent of disagreement between LEWICE, a 2D method, and LEWICE3D, a 3D method, in calculating local collection efficiencies at the leading edge of finite wings is investigated in this paper.
A very general method for calculating compressible three-dimensional laminar and turbulent boundary layers on arbitrary wings is described. The method utilizes a nonorthogonal coordinate system for the boundary-layer calculations and includes a geometry package that represents the wing analytically. In the calculations all the geometric parameters of the coordinate system are accounted for. The Reynolds shear-stress terms are modeled by an eddy-viscosity formulation developed by Cebeci. The governing equations are solved by a very efficient two-point finite-difference method used earlier by Keller and Cebeci for two-dimensional flows and later by Cebeci for three-dimensional flows.
Experimental data have been obtained in a three-dimensional, shear-driven, turbulent boundary layer subjected to sudden transverse strain. Measurements made with a newly developed, three-dimensional laser Doppler velocimeter include all components of mean flow, turbulent Reynolds stresses, and triple-product correlations. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) are extracted from the data. It was shown experimentally that eddy viscosity is strongly direction-dependent (not a scalar), indicating a need for full Reynolds stress modeling. Turbulence models for eddy viscosity, stress diffusion, pressure rate-of-strain, and anisotropy of Reynolds stresses are tested using the data. Calculations using a Reynolds stress equation model are compared with the data.
A three-dimensional boundary-layer code was developed for particular application to realistic hypersonic aircraft. It is very general and can be applied to a wide variety of boundary-layer flows. Laminar, transitional, and fully turbulent flows of compressible, reacting gases are efficiently calculated by use of the code. A body-oriented orthogonal coordinate system is used for the calculation and the user has complete freedom in specifying the coordinate system within the restrictions that one coordinate must be normal to the surface and the three coordinates must be mutually orthogonal.
A program is developed to investigate the linear stability of three-dimensional compressible boundary layer flows over bodies of revolutions. The problem is formulated as a two dimensional (2D) eigenvalue problem incorporating the meanflow variations in the normal and azimuthal directions. Normal mode solutions are sought in the whole plane rather than in a line normal to the wall as is done in the classical one dimensional (1D) stability theory. The stability characteristics of a supersonic boundary layer over a sharp cone with 50 half-angle at 2 degrees angle of attack is investigated. The 1D eigenvalue computations showed that the most amplified disturbances occur around x(sub 2) = 90 degrees and the azimuthal mode number for the most amplified disturbances range between m = -30 to -40. The frequencies of the most amplified waves are smaller in the middle region where the crossflow dominates the instability than the most amplified frequencies near the windward and leeward planes. The 2D eigenvalue computations showed that due to the variations in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the most amplified disturbances are shifted to 120 degrees compared to 90 degrees for the parallel theory. It is also observed that the nonparallel amplification rates are smaller than that is obtained from the parallel theory.
Three dimensional finite element model for predicting deflections, stresses, and strains of elastic continuum
Three dimensional elastostatics problems solution method using singular integral equations solvable numerically for surface tractions and displacements of fully mixed boundary value problem
Three dimensional diffraction of sonic booms by corners of structures
Because of the long and narrow passages between the blades of a rocket pump inducer, major effects from turbulence and viscosity make the flow through such a device truly three-dimensional and therefore difficult to measure or predict. To investigate the flow characteristics, conventional and three-dimensional hot-wire probe measurements were conducted in a model inducer 3 ft in diameter. Blade-to-blade variation of the three components of velocity at the exit and the corresponding turbulence intensities were obtained by means of hotwire probes aligned in the three coordinate directions. Analysis of the three-dimensional inviscid flow field led to qualitative prediction of the flow characteristics. Extensive measurements and theoretical analyses of the flow field showed that blade blockage, viscosity, and blade boundary layer interactions are the dominant influences on flow in this type of turbomachinery.
An implicit finite-difference procedure is presented for solving the compressible three-dimensional boundary-layer equations. The method is second-order accurate, unconditionally stable (conditional stability for reverse cross flow), and efficient from the viewpoint of computer storage and processing time. The Reynolds stress terms are modeled by (1) a single-layer mixing length model and (2) a two-layer eddy viscosity model. These models, although simple in concept, accurately predicted the equilibrium turbulent flow for the conditions considered. Numerical results are compared with experimental wall and profile data for a cone at an angle of attack larger than the cone semiapex angle. These comparisons clearly indicate that the numerical procedure and turbulence models accurately predict the experimental data with as few as 21 nodal points in the plane normal to the wall boundary.