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Methods of Stress Calculation in Rotating Disks

Description: The paper describes nethods of computing the stresses in disks of a given profile as well as methods of choosing the disk profiles for a given stress distribution for turhines, turbo blowers, and so forth. A new method of in tegrating the differential equations of Stodola leads to a simplification of the computation for disks of hyperbolic profile.
Date: September 1, 1944
Creator: Tumarkin, S.
Partner: UNT Libraries Government Documents Department

The Problem of Torsion in Prismatic Members of Circular Segmental Cross Section

Description: The problem is solved by approximation, by setting up a function complying with the differential equation of the stress function, and determining the coefficients appearing in it in such a way that the boundary condition is fulfilled as nearly as possible. For the semicircle, for which the solution is known, the method yields very accurate values; the approximated stress distribution is in good agreement with the accurately computed distribution. Stress and strain measurements indicate that the approximate solution is in sufficiently exact agreement with reality for segmental cross sections.
Date: September 1, 1948
Creator: Weigand, A.
Partner: UNT Libraries Government Documents Department

On the Flutter of Cylindrical Shells and Panels Moving in a Flow of Gas

Description: The equations of shells are taken in the form of the general technical theory of shallow shells and shells of medium length. The aerodynamic forces acting on a shell are taken into account only as forces of excess pressure according to the formula proposed by A.A. Iliushin in reference 3.
Date: September 1, 1958
Creator: Stepanov, R. D.
Partner: UNT Libraries Government Documents Department

Tunnel Correction for Compressible Subsonic Flow

Description: This report presents a treatment of the effects of the tunnel walls on the flow velocity and direction in a compressible medium at subsonic speed by an approximate method. Calculations are given for the rotationally symmetric and two- dimensionl problems of the flow past bodies, as well for the downwash effect in the tunnel with circular cross section.
Date: July 1, 1947
Creator: Baranoff, A. V.
Partner: UNT Libraries Government Documents Department

On the Application of the Energy Method to Stability Problems

Description: Since stability problems have come into the field of vision of engineers, energy methods have proved to be one of the most powerful aids in mastering them. For finding the especially interesting critical loads special procedures have evolved that depart somewhat from those customary in the usual elasticity theory. A clarification of the connections seemed desirable,especially with regard to the post-critical region, for the treatment of which these special methods are not suited as they are. The present investigation discusses this question-complex (made important by shell construction in aircraft) especially in the classical example of the Euler strut, because in this case - since the basic features are not hidden by difficulties of a mathematical nature - the problem is especially clear. The present treatment differs from that appearing in the Z.f.a.M.M. (1938) under the title "Uber die Behandlung von Stabilittatsproblemen mit Hilfe der energetischen Methode" in that, in order to work out the basic ideas still more clearly,it dispenses with the investigation of behavior at large deflections and of the elastic foundation;in its place the present version gives an elaboration of the 6th section and (in its 7 th and 8th secs.)a new example that shows the applicability of the general criterion to a stability problem that differs from that of Euler in many respects.
Date: October 1, 1947
Creator: Marguerre, Karl
Partner: UNT Libraries Government Documents Department

On the Use of the Harmonic Linearizaiton Method in the Automatic Control Theory

Description: The method of harmonic linearization (harmonic balance), first proposed by N. M. Krylov and N. N. Bogolyubov for the approximate investigation of nonlinear vibrations, has been developed and received wide practical application to problems in the theory of automatic control. Recently, some doubt has been expressed on the legitimacy of application of the method to these problems, and assertions were made on the absence in them of a small parameter of any kind. Nevertheless, the method gives practical, acceptable results and is a simple and powerful means in engineering computations. Hence, the importance of questions arises as to its justification. The underlying principle of the method is the replacement of the given nonlinear equation by a linear equation. In establishing the method, a small parameter is considered whose presence makes it possible to speak, with some degree of approximation, of the solution of this new equation to the solution of the given nonlinear equation. In an article by the author, certain considerations were given on the presence of the small parameter, but this question has not as yet received a final answer. In the present report, a somewhat different approach to the problem is applied that permits: (a) establishing, in the clearest manner, the form of the presence of the small parameter in nonlinear problems of control theory, solvable by the method of harmonic linearization; (b) connecting it with previous intuitive physical concepts (with the "filter property") and extending the class of problems possessing this property; and (c) discussing various generalizations of the method.
Date: January 1, 1957
Creator: Popov, E. P.
Partner: UNT Libraries Government Documents Department

Evaporation, Heat Transfer, and Velocity Distribution in Two-Dimensional and Rotationally Symmetrical Laminar Boundary-Layer Flow

Description: The fundamental boundary layer equations for the flow, temperature and concentration fields are presented. Two dimensional symmetrical and unsymmetrical and rotationally symmetrical steady boundary layer flows are treated as well as the transfer boundary layer. Approximation methods for the calculation of the transfer layer are discussed and a brief survey of an investigation into the validity of the law that the Nusselt number is proportional to the cube root of the Prandtl number is presented.
Date: February 1, 1958
Creator: Froessling, Nils
Partner: UNT Libraries Government Documents Department

Compression Shocks in Two-Dimensional Gas Flows

Description: The following are arguments on the compression shocks in gas flow start with a simplified representation of the results of the study made by Th. Meyer as published in the Forschungsheft 62 of the VDI, supplemented by several amplifications for the application.In the treatment of compression shocks, the equation of energy, the equation of continuity, the momentum equation, the equation of state of the particular gas, as well as the condition Of the second law of thermodynamics that no decrease of entropy is possible in an isolated system, must be taken into consideration. The result is that, in those cases where the sudden change of state according to the second law of thermodynamics is possible, there always occurs a compression of the gas which is uniquely determined by the other conditions.
Date: February 1, 1949
Creator: Busemann, A.
Partner: UNT Libraries Government Documents Department

Investigation of Aperiodic Time Processes with Autocorrelation and Fourier Analysis

Description: Autocorrelation and frequency analyses of a series of aperiodic time events, in particular, filtered noises and sibilant sounds, were made. The position and band width of the frequency ranges are best obtained from the frequency analysis, but the energies contained in the several bands are most easily obtained from the autocorrelation function. The mean number of zero crossings of the time function was determined from the curvature of the latter function in the vicinity of the zero crossing, and also with the aid of a decimal counter. The second method was found to be more exact.
Date: March 1, 1958
Creator: Exner, Marie Luise
Partner: UNT Libraries Government Documents Department

Theory of Characteristics

Description: The theory of characteristics will be presented generally for quasilinear differential equations of the second order in two variables. This is necessary because of the manifold requirements to be demanded from the theory of characteristics.
Date: September 1949
Creator: Tollmien, W.
Partner: UNT Libraries Government Documents Department

NBS-INA -- The Institute for Numerical Analysis -- UCLA 1947-1954

Description: Abstract: This is the history of the Institute for Numerical Analysis (INA) with special emphasis in its research program during the period 1947 to 1956. The Institute for Numerical Analysis was located on the campus of the University of California, Los Angeles. It was a section of the National Applied Mathematics Laboratories, which formed the Applied Mathematics Division of the National Bureau of Standards (now the National Institute of Standards and technology), under the U.S. Department of Commerce.
Date: August 1991
Creator: Hestenes, Magnus Rudolph & Todd, John
Partner: UNT Libraries Government Documents Department

Algorithms of Schensted and Hillman-Grassl and Operations on Standard Bitableaux

Description: In this thesis, we describe Schensted's algorithm for finding the length of a longest increasing subsequence of a finite sequence. Schensted's algorithm also constructs a bijection between permutations of the first N natural numbers and standard bitableaux of size N. We also describe the Hillman-Grassl algorithm which constructs a bijection between reverse plane partitions and the solutions in natural numbers of a linear equation involving hook lengths. Pascal programs and sample output for both algorithms appear in the appendix. In addition, we describe the operations on standard bitableaux corresponding to the operations of inverting and reversing permutations. Finally, we show that these operations generate the dihedral group D_4
Date: August 1983
Creator: Sutherland, David C. (David Craig)
Partner: UNT Libraries

Two-Dimensional Irrotational Transonic Flows of a Compressible Fluid

Description: The methods of NACA TN No. 995 have been slightly modified and extended in include flows with circulation by considering the alteration of the singularities of the incompressible solution due to the presence of the hypergeometric functions in the analytic continuation of the solution. It was found that for finite Mach numbers the only case in which the nature of the singularity can remain unchanged is for a ratio of specific heats equal to -1. From a study of two particular flows it seems that the effect of geometry cannot be neglected, and the conventional "pressure-correction" formulas are not valid, even in the subsonic region if the body is thick, especially if there is a supersonic region in the flow.
Date: June 1948
Creator: Kuo, Yung-Huai
Partner: UNT Libraries Government Documents Department

Correlation of flame speed with stretch in turbulent premixed methane/air flames

Description: In the flamelet approach of turbulent premixed combustion, the flames are modeled as a wrinkled surface whose propagation speed, termed the {open_quotes}displacement speed,{close_quotes} is prescribed in terms of the local flow field and flame geometry. Theoretical studies suggest a linear relation between the flame speed and stretch for small values of stretch, S{sub L}/S{sub L}{sup 0} = 1 - MaKa, where S{sub L}{sup 0} is the laminar flame speed, Ka = {kappa}{delta}{sub F}/S{sub L}{sup 0} is the nondimensional stretch or the Karlovitz number, and Ma = L/{delta}{sub F} is the Markstein number. The nominal flame thickness, {delta}{sub F}, is determined as the ratio of the mass diffusivity of the unburnt mixture to the laminar flame speed. Thus, the turbulent flame model relies on an accurate estimate of the Markstein number in specific flame configurations. Experimental measurement of flame speed and stretch in turbulent flames, however, is extremely difficult. As a result, measurement of flame speeds under strained flow fields has been made in simpler geometries, in which the effect of flame curvature is often omitted. In this study we present results of direct numerical simulations of unsteady turbulent flames with detailed methane/air chemistry, thereby providing an alternative method of obtaining flame structure and propagation statistics. The objective is to determine the correlation between the displacement speed and stretch over a broad range of Karlovitz numbers. The observed response of the displacement speed is then interpreted in terms of local tangential strain rate and curvature effects. 13 refs., 3 figs.
Date: November 1, 1997
Creator: Chen, J.H. & Im, Hong G.
Partner: UNT Libraries Government Documents Department

Heat transfer at the mold-metal interface in permanent mold casting of aluminum alloys project. Annual project status report for the period October 1, 1997 to September 30, 1998

Description: In the first year of this three-year project, substantial progress has been achieved. This project on heat transfer coefficients in metal permanent mold casting is being conducted in three areas. They are the theoretical study at the University of Michigan, the experimental investigations of squeeze casting and semi-solid casting at CMI-Tech Center, and the experimental investigation of low pressure permanent mold casting at Amcast Automotive. U-M did an initial geometry which was defined for ProCAST to solve, and then a geometry half the size was defined and solved using the same boundary conditions. A conceptual mold geometry was examined and is represented as an axisymmetric element.Furthermore, the influences of the localized heat transfer coefficients on the casting process were carefully studied. The HTC Evaluator has been proposed and initially developed by the U-M team. The Reference and the Database Modules of the HTC Evaluator have been developed, and extensively tested. A series of technical barriers have been cited and potential solutions have been surveyed. At the CMI-Tech Center, the Kistler direct cavity pressure measurement system has been purchased and tested. The calibrations has been evaluated. The probe is capable of sensing a light finger pressure. The experimental mold has been designed and modified. The experimental mold has been designed and modified. The first experiment is scheduled for October 14, 1998. The geometry of the experimental hockey-puck casting has been given to the U-M team for numerical analysis.
Date: September 30, 1998
Creator: Pehlke, R.D. & Hao, S.W.
Partner: UNT Libraries Government Documents Department

Simulation of plasma based semiconductor processing using block structured locally refined grids

Description: We have described a new numerical method for plasma simulation. Calculations have been presented which show that the method is accurate and suggest the regimes in which the method provides savings in CPU time and memory requirements. A steady state simulation of a four centimeter domain was modeled with sheath scale (150 microns) resolution using only 40 grid points. Simulations of semiconductor processing equipment have been performed which imply the usefulness of the method for engineering applications. It is the author`s opinion that these accomplishments represent a significant contribution to plasma simulation and the efficient numerical solution of certain systems of non-linear partial differential equations. More work needs to be done, however, for the algorithm to be of practical use in an engineering environment. Despite our success at avoiding the dielectric relaxation timestep restrictions the algorithm is still conditionally stable and requires timesteps which are relatively small. This represents a prohibitive runtime for steady state solutions on high resolution grids. Current research suggests that these limitations may be overcome and the use of much larger timesteps will be possible.
Date: January 1, 1998
Creator: Wake, D.D.
Partner: UNT Libraries Government Documents Department

The Use of Chebyshev Polynomials in Numerical Analysis

Description: The purpose of this paper is to investigate the nature and practical uses of Chebyshev polynomials. Chapter I gives recognition to mathematicians responsible for studies in this area. Chapter II enumerates several mathematical situations in which the polynomials naturally arise and suggests reasons for the pursuance of their study. Chapter III includes: Chebyshev polynomials as related to "best" polynomial approximation, Chebyshev series, and methods of producing polynomial approximations to continuous functions. Chapter IV discusses the use of Chebyshev polynomials to solve certain differential equations and Chebyshev-Gauss quadrature.
Date: December 1975
Creator: Forisha, Donnie R.
Partner: UNT Libraries

Visualization of Instrumental Verification Information Details (VIVID) : code development, description, and usage.

Description: The formulation, implementation and usage of a numerical solution verification code is described. This code uses the Richardson extrapolation procedure to estimate the order of accuracy and error of a computational program solution. It evaluates multiple solutions performed in numerical grid convergence studies to verify a numerical algorithm implementation. Analyses are performed on both structured and unstructured grid codes. Finite volume and finite element discretization programs are examined. Two and three-dimensional solutions are evaluated. Steady state and transient solution analysis capabilities are present in the verification code. Multiple input data bases are accepted. Benchmark options are included to allow for minimal solution validation capability as well as verification.
Date: March 1, 2005
Creator: Roy, Christopher John; Bainbridge, Bruce L.; Potter, Donald L.; Blottner, Frederick G. & Black, Amalia Rebecca
Partner: UNT Libraries Government Documents Department

ML 3.1 developer's guide.

Description: ML development was started in 1997 by Ray Tuminaro and Charles Tong. Currently, there are several full- and part-time developers. The kernel of ML is written in ANSI C, and there is a rich C++ interface for Trilinos users and developers. ML can be customized to run geometric and algebraic multigrid; it can solve a scalar or a vector equation (with constant number of equations per grid node), and it can solve a form of Maxwell's equations. For a general introduction to ML and its applications, we refer to the Users Guide [SHT04], and to the ML web site, http://software.sandia.gov/ml.
Date: May 1, 2004
Creator: Sala, Marzio; Hu, Jonathan Joseph (Sandia National Laboratories, Livermore, CA) & Tuminaro, Raymond Stephen (Sandia National Laboratories, Livermore, CA)
Partner: UNT Libraries Government Documents Department

Real Beamline Optics from a Synthetic Beam

Description: The Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab can be described as a series of concatenated beamlines. Methods used to measure the Twiss parameters in closed orbit machines are not applicable in such open ended systems. We are using properly selected sets of real orbits in the accelerator, as one would for numerical analysis. The evolution of these trajectories along the beamline models the behavior of a synthetic beam which deterministically supplements beam profile-based Twiss parameter measurements and optimizes the efficiency of beamline tuning. Examples will be presented alongside a description of the process.
Date: May 1, 2010
Creator: Ryan Bodenstein,Michael Tiefenback,Yves Roblin
Partner: UNT Libraries Government Documents Department