Circular-arc cracks in bi-material plates under bending.
Thin boundary problems of bimaterial plates bonded along circular arcs behaving like crack imperfections under bending, using fracture mechanics to predict failure
CRACK PROPAGATION↗
SEARCH · Engineering Papers
Results for “Boundary value problem”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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A new solution to the accretion problem.
The Bondi-Hoyle theory of line-accretion is briefly reviewed, and it is shown that there are an infinity of steady-state solutions satisfying the requirements originally imposed as boundary conditions. Questions are raised as to the applicability of these solutions to physical reality. The existence of an entirely different type of steady-state solution that implies slow velocity in the accretion stream beyond the neutral point is demonstrated. Accurate numerical values of this solution are obtained for a number of cases. The braking action given by this solution, for any selected cut-off distance, is far stronger than in the Bondi-Hoyle solution. Consideration of the physical state in the accretion stream shows that for this slow solution the appropriate cutoff range would be only of the order of 100 AU rather than of interstellar-distance order.
Lyttleton, R. A.↗
Corrections for attached sidewall boundary-layer effects in 2-dimensional airfoil testing
The problems of sidewall boundary-layer effects in airfoil testing is treated by considering the changes in the flow area due to boundary-layer thinning under the influence of the airfoil flowfield. Using von Karman's momentum integral equation, it is shown that the sidewall boundary-layer thickness in the region of the airfoil can reduce to about half the undisturbed value under the conditions prevailing in testing of supercritical airfoils. A Mach number correction due to this increased width of the flow passage is proposed. Using the small disturbance approximation, the effect of the sidewall boundary-layers is shown to be equivalent to a change in the test Mach number and also in the airfoil thickness. Comparison of the results of this approach with other similarity rules and correlation of the experimental data demonstrate the applicability of the analysis presented from low speeds to transonic speeds.
Murthy, A. V.↗
Numerical simulations of turbulent thermal convection with differential rotation
The solar nebula, from which the planets in our solar system formed, featured a disk of gas and dust grains in rapid, differential rotation, and at some stage was likely to have been unstable to thermal convection. This situation is suspected by many to lead to significant turbulent Reynolds stress production and angular momentum transport in such systems, and estimates of transport rates have been attempted from unsubstantiated phenomenological models. In order to determine the circumstances and physical conditions under which our own planetary system formed and to explain recent observations of young stellar systems, it is necessary to develop realistic models of heat and angular momentum transport for such flows. Developing an understanding of complicated flows featuring thermal convection, rotation, and shear is also of wide interest in stellar astrophysics and in planetary and terrestrial atmospheric studies. The ultimate objective is to develop workable models based on the numerical simulations for constructing global solar nebula models; viz., relatively simple prescriptions for heat and angular momentum fluxes from given system parameters (e.g., ratios of rotation, shear, and convective lapse rates) are characterized, quantified, and developed. Toward this end, our program has been to attempt to understand the behavior of the direct numerical simulations of Boussinesq convection, which, despite the complexity of the results, is still an overly simplified approximation to the real system and should be more amenable to analysis. These results are also intended to be tested against turbulence models, especially those designed for atmospheric boundary layers, and may provide a basis for subgrid-scale models. In order to make the numerical simulations more realistic with regard to the solar nebula problem, a fully compressible code that will allow incorporation of large density stratifications and realistic thermodynamic and radiative properties is developed. In order to explore the properties of these flows at the very high values of Re found in natural systems and the very low values of Pr found in most astrophysical contexts, we will need to employ large-eddy simulations for which we want to determine the most appropriate subgrid-scale model to incorporate.
Cabot, William H.↗
A review and analysis of neural networks for classification of remotely sensed multispectral imagery
A literature survey and analysis of the use of neural networks for the classification of remotely sensed multispectral imagery is presented. As part of a brief mathematical review, the backpropagation algorithm, which is the most common method of training multi-layer networks, is discussed with an emphasis on its application to pattern recognition. The analysis is divided into five aspects of neural network classification: (1) input data preprocessing, structure, and encoding; (2) output encoding and extraction of classes; (3) network architecture, (4) training algorithms; and (5) comparisons to conventional classifiers. The advantages of the neural network method over traditional classifiers are its non-parametric nature, arbitrary decision boundary capabilities, easy adaptation to different types of data and input structures, fuzzy output values that can enhance classification, and good generalization for use with multiple images. The disadvantages of the method are slow training time, inconsistent results due to random initial weights, and the requirement of obscure initialization values (e.g., learning rate and hidden layer size). Possible techniques for ameliorating these problems are discussed. It is concluded that, although the neural network method has several unique capabilities, it will become a useful tool in remote sensing only if it is made faster, more predictable, and easier to use.
Paola, Justin D.↗
New method of extrapolation of the resistance of a model planing boat to full size
The previously employed method of extrapolating the total resistance to full size with lambda(exp 3) (model scale) and thereby foregoing a separate appraisal of the frictional resistance, was permissible for large models and floats of normal size. But faced with the ever increasing size of aircraft a reexamination of the problem of extrapolation to full size is called for. A method is described by means of which, on the basis of an analysis of tests on planing surfaces, the variation of the wetted surface over the take-off range is analytically obtained. The friction coefficients are read from Prandtl's curve for turbulent boundary layer with laminar approach. With these two values a correction for friction is obtainable.
Sottorf, W↗
A curvature-corrected Kirchhoff formulation for radar sea-return from the near vertical
A new theoretical treatment of the problem of electromagnetic wave scattering from a randomly rough surface is given. A high frequency correction to the Kirchhoff approximation is derived from a field integral equation for a perfectly conducting surface. The correction, which accounts for the effect of local surface curvature, is seen to be identical with an asymptotic form found by Fock (1945) for diffraction by a paraboloid. The corrected boundary values are substituted into the far field Stratton-Chu integral, and average backscattered powers are computed assuming the scattering surface is a homogeneous Gaussian process. Preliminary calculations for K(-4) ocean wave spectrum indicate a resonable modelling of polarization effects near the vertical, theta 45 deg. Correspondence with the results of small perturbation theory is shown.
Jackson, F. C.↗
A study of reacting free and ducted hydrogen/air jets
The mixing and reaction of a supersonic jet of hydrogen in coaxial free and ducted high temperature test gases were investigated. The importance of chemical kinetics on computed results, and the utilization of free-jet theoretical approaches to compute enclosed flow fields were studied. Measured pitot pressure profiles were correlated by use of a parabolic mixing analysis employing an eddy viscosity model. All computations, including free, ducted, reacting, and nonreacting cases, use the same value of the empirical constant in the viscosity model. Equilibrium and finite rate chemistry models were utilized. The finite rate assumption allowed prediction of observed ignition delay, but the equilibrium model gave the best correlations downstream from the ignition location. Ducted calculations were made with finite rate chemistry; correlations were, in general, as good as the free-jet results until problems with the boundary conditions were encountered.
Beach, H. L., Jr.↗
Computational Aerodynamic Simulations of an 840 ft/sec Tip Speed Advanced Ducted Propulsor Fan System Model for Acoustic Methods Assessment and Development
Computational Aerodynamic simulations of an 840 ft/sec tip speed, Advanced Ducted Propulsor fan system were performed at five different operating points on the fan operating line, in order to provide detailed internal flow field information for use with fan acoustic prediction methods presently being developed, assessed and validated. The fan system is a sub-scale, lownoise research fan/nacelle model that has undergone extensive experimental testing in the 9- by 15- foot Low Speed Wind Tunnel at the NASA Glenn Research Center, resulting in quality, detailed aerodynamic and acoustic measurement data. Details of the fan geometry, the computational fluid dynamics methods, the computational grids, and various computational parameters relevant to the numerical simulations are discussed. Flow field results for three of the five operating conditions simulated are presented in order to provide a representative look at the computed solutions. Each of the five fan aerodynamic simulations involved the entire fan system, excluding a long core duct section downstream of the core inlet guide vane. As a result, only fan rotational speed and system bypass ratio, set by specifying static pressure downstream of the core inlet guide vane row, were adjusted in order to set the fan operating point, leading to operating points that lie on a fan operating line and making mass flow rate a fully dependent parameter. The resulting mass flow rates are in good agreement with measurement values. The computed blade row flow fields for all five fan operating points are, in general, aerodynamically healthy. Rotor blade and fan exit guide vane flow characteristics are good, including incidence and deviation angles, chordwise static pressure distributions, blade surface boundary layers, secondary flow structures, and blade wakes. Examination of the computed flow fields reveals no excessive boundary layer separations or related secondary-flow problems. A few spanwise comparisons between computational and measurement data in the bypass duct show that they are in good agreement, thus providing a partial validation of the computational results.
Tweedt, Daniel L.↗
Computational Aerodynamic Simulations of a 1484 ft/sec Tip Speed Quiet High-Speed Fan System Model for Acoustic Methods Assessment and Development
Computational Aerodynamic simulations of a 1484 ft/sec tip speed quiet high-speed fan system were performed at five different operating points on the fan operating line, in order to provide detailed internal flow field information for use with fan acoustic prediction methods presently being developed, assessed and validated. The fan system is a sub-scale, low-noise research fan/nacelle model that has undergone experimental testing in the 9- by 15-foot Low Speed Wind Tunnel at the NASA Glenn Research Center. Details of the fan geometry, the computational fluid dynamics methods, the computational grids, and various computational parameters relevant to the numerical simulations are discussed. Flow field results for three of the five operating points simulated are presented in order to provide a representative look at the computed solutions. Each of the five fan aerodynamic simulations involved the entire fan system, which includes a core duct and a bypass duct that merge upstream of the fan system nozzle. As a result, only fan rotational speed and the system bypass ratio, set by means of a translating nozzle plug, were adjusted in order to set the fan operating point, leading to operating points that lie on a fan operating line and making mass flow rate a fully dependent parameter. The resulting mass flow rates are in good agreement with measurement values. Computed blade row flow fields at all fan operating points are, in general, aerodynamically healthy. Rotor blade and fan exit guide vane flow characteristics are good, including incidence and deviation angles, chordwise static pressure distributions, blade surface boundary layers, secondary flow structures, and blade wakes. Examination of the computed flow fields reveals no excessive or critical boundary layer separations or related secondary-flow problems, with the exception of the hub boundary layer at the core duct entrance. At that location a significant flow separation is present. The region of local flow recirculation extends through a mixing plane, however, which for the particular mixing-plane model used is now known to exaggerate the recirculation. In any case, the flow separation has relatively little impact on the computed rotor and FEGV flow fields.
Tweedt, Daniel L.↗
Computational Aerodynamic Simulations of a 1215 ft/sec Tip Speed Transonic Fan System Model for Acoustic Methods Assessment and Development
Computational Aerodynamic simulations of a 1215 ft/sec tip speed transonic fan system were performed at five different operating points on the fan operating line, in order to provide detailed internal flow field information for use with fan acoustic prediction methods presently being developed, assessed and validated. The fan system is a sub-scale, low-noise research fan/nacelle model that has undergone extensive experimental testing in the 9- by 15-foot Low Speed Wind Tunnel at the NASA Glenn Research Center. Details of the fan geometry, the computational fluid dynamics methods, the computational grids, and various computational parameters relevant to the numerical simulations are discussed. Flow field results for three of the five operating points simulated are presented in order to provide a representative look at the computed solutions. Each of the five fan aerodynamic simulations involved the entire fan system, which for this model did not include a split flow path with core and bypass ducts. As a result, it was only necessary to adjust fan rotational speed in order to set the fan operating point, leading to operating points that lie on a fan operating line and making mass flow rate a fully dependent parameter. The resulting mass flow rates are in good agreement with measurement values. Computed blade row flow fields at all fan operating points are, in general, aerodynamically healthy. Rotor blade and fan exit guide vane flow characteristics are good, including incidence and deviation angles, chordwise static pressure distributions, blade surface boundary layers, secondary flow structures, and blade wakes. Examination of the flow fields at all operating conditions reveals no excessive boundary layer separations or related secondary-flow problems.
Tweedt, Daniel L.↗
Symmetric baroclinic instability of a Hadley cell
A symmetric baroclinic instability is examined in terms of a Boussinesq fluid contained between two horizontal plates to determine the effects of the Ekman and thermal layers. Governing equations are written for a rotating reference frame, taking into account the Rossby, Ekman, and Prandtl numbers. Equations are defined for the perturbation functions, treated as an eigenvalue problem, and a numerical integration of the full eighth order differential system is performed by a shooting technique. An instability is found to occur in the Hadley cell containing both Ekman and thermal boundary layers when the Richardson number is close to unity. If the Prandtl number is fixed the critical Richardson number decreases with an increasing Ekman number until the Ekman number reaches a certain value, at which time the fluid is stable.
Antar, B. N.↗
Multiresolution With Super-Compact Wavelets
The solution data computed from large scale simulations are sometimes too big for main memory, for local disks, and possibly even for a remote storage disk, creating tremendous processing time as well as technical difficulties in analyzing the data. The excessive storage demands a corresponding huge penalty in I/O time, rendering time and transmission time between different computer systems. In this paper, a multiresolution scheme is proposed to compress field simulation or experimental data without much loss of important information in the representation. Originally, the wavelet based multiresolution scheme was introduced in image processing, for the purposes of data compression and feature extraction. Unlike photographic image data which has rather simple settings, computational field simulation data needs more careful treatment in applying the multiresolution technique. While the image data sits on a regular spaced grid, the simulation data usually resides on a structured curvilinear grid or unstructured grid. In addition to the irregularity in grid spacing, the other difficulty is that the solutions consist of vectors instead of scalar values. The data characteristics demand more restrictive conditions. In general, the photographic images have very little inherent smoothness with discontinuities almost everywhere. On the other hand, the numerical solutions have smoothness almost everywhere and discontinuities in local areas (shock, vortices, and shear layers). The wavelet bases should be amenable to the solution of the problem at hand and applicable to constraints such as numerical accuracy and boundary conditions. In choosing a suitable wavelet basis for simulation data among a variety of wavelet families, the supercompact wavelets designed by Beam and Warming provide one of the most effective multiresolution schemes. Supercompact multi-wavelets retain the compactness of Haar wavelets, are piecewise polynomial and orthogonal, and can have arbitrary order of approximation. The advantages of the multiresolution algorithm are that no special treatment is required at the boundaries of the interval, and that the application to functions which are only piecewise continuous (internal boundaries) can be efficiently implemented. In this presentation, Beam's supercompact wavelets are generalized to higher dimensions using multidimensional scaling and wavelet functions rather than alternating the directions as in the 1D version. As a demonstration of actual 3D data compression, supercompact wavelet transforms are applied to a 3D data set for wing tip vortex flow solutions (2.5 million grid points). It is shown that high data compression ratio can be achieved (around 50:1 ratio) in both vector and scalar data set.
Lee, Dohyung↗
Enhanced Elliptic Grid Generation
An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are determined automatically as part of the solution of the defining PDEs. Depending on the shape of the boundary segments and the physical nature of the problem to be solved on the grid, the solution of the defining PDEs may provide for rates of decay to vary along and among the boundary segments and may lend itself to interpretation in terms of one or more physical quantities associated with the problem.
Kaul, Upender K.↗
Data Parallel Line Relaxation (DPLR) Code User Manual: Acadia - Version 4.01.1
Data-Parallel Line Relaxation (DPLR) code is a computational fluid dynamic (CFD) solver that was developed at NASA Ames Research Center to help mission support teams generate high-value predictive solutions for hypersonic flow field problems. The DPLR Code Package is an MPI-based, parallel, full three-dimensional Navier-Stokes CFD solver with generalized models for finite-rate reaction kinetics, thermal and chemical non-equilibrium, accurate high-temperature transport coefficients, and ionized flow physics incorporated into the code. DPLR also includes a large selection of generalized realistic surface boundary conditions and links to enable loose coupling with external thermal protection system (TPS) material response and shock layer radiation codes.
Wright, Michael J.↗
Analysis and computation of viscous subsonic primary and secondary flows
A new approximate flow analysis, designed to enable numerical solution as an initial value problem, is developed for a wide class of viscous subsonic flows at high Reynolds number and in straight or smoothly curved three-dimensional flow geometries. The analysis is coordinate-independent and corrects an a priori known inviscid primary flow for viscous and thermal effects, secondary flows, total pressure distortion, internal flow blockage and pressure drop. Computed results include laminar solutions for three-dimensional boundary layer flow, fully viscous flow in circular arc ducts, and also flow in a curved duct shaped like a turbine blade passage.
Briley, W. R.↗
Drop Ejection From an Oscillating Rod
The dynamics of a drop of a Newtonian liquid that is pendant from or sessile on a solid rod that is forced to undergo time-periodic oscillations along its axis is studied theoretically. The free boundary problem governing the time evolution of the shape of the drop and the flow field inside it is solved by a method of lines using a finite element algorithm incorporating an adaptive mesh. When the forcing amplitude is small, the drop approaches a limit cycle at large times and undergoes steady oscillations thereafter. However, drop breakup is the consequence if the forcing amplitude exceeds a critical value. Over a wide range of amplitudes above this critical value, drop ejection from the rod occurs during the second oscillation period from the commencement of rod motion. Remarkably, the shape of the interface at breakup and the volume of the primary drop formed are insensitive to changes in forcing amplitude. The interface shape at times close to and at breakup is a multi-valued function of distance measured along the rod axis and hence cannot be described by recently popularized one-dimensional approximations. The computations show that drop ejection occurs without the formation of a long neck. Therefore, this method of drop formation holds promise of preventing formation of undesirable satellite droplets.
Wilkes, E. D.↗
Spurious Behavior of Shock-Capturing Methods: Problems Containing Stiff Source Terms and Discontinuities
The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise evaluation of the source term, previous studies indicated that the phenomenon of wrong propagation speed of discontinuities is connected with the smearing of the discontinuity caused by the discretization of the advection term. The smearing introduces a nonequilibrium state into the calculation. Thus as soon as a nonequilibrium value is introduced in this manner, the source term turns on and immediately restores equilibrium, while at the same time shifting the discontinuity to a cell boundary. The present study is to show that the degree of wrong propagation speed of discontinuities is highly dependent on the accuracy of the numerical method. The manner in which the smearing of discontinuities is contained by the numerical method and the overall amount of numerical dissipation being employed play major roles. Moreover, employing finite time steps and grid spacings that are below the standard Courant-Friedrich-Levy (CFL) limit on shockcapturing methods for compressible Euler and Navier-Stokes equations containing stiff reacting source terms and discontinuities reveals surprising counter-intuitive results. Unlike non-reacting flows, for stiff reactions with discontinuities, employing a time step and grid spacing that are below the CFL limit (based on the homogeneous part or non-reacting part of the governing equations) does not guarantee a correct solution of the chosen governing equations. Instead, depending on the numerical method, time step and grid spacing, the numerical simulation may lead to (a) the correct solution (within the truncation error of the scheme), (b) a divergent solution, (c) a wrong propagation speed of discontinuities solution or (d) other spurious solutions that are solutions of the discretized counterparts but are not solutions of the governing equations. The present investigation for three very different stiff system cases confirms some of the findings of Lafon & Yee (1996) and LeVeque & Yee (1990) for a model scalar PDE. The findings might shed some light on the reported difficulties in numerical combustion and problems with stiff nonlinear (homogeneous) source terms and discontinuities in general.
Yee, Helen M. C.↗