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  • Other Sources  (24)
  • 1
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    The method of complex characteristics for transonic airfoil design, with an application to compressors (1985)
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    Publication Date: 2019-06-28
    Description: The use of mathematical models to study physical problems of current interest to aeronautical engineers has been made possible by the development of numerical techniques to compute solutions of the differential equations of transonic aerodynamics. These advances have encouraged the improvement of supercritical wing technology. A method to determined steady, shockless flow of an inviscid, compressible fluid past a cascade of airfoils in the (x,y)-plane is considered, taking into account also the case of an isolated airfoil. The method of complex characteristics solves the equations in the hodograph plane by extending all variables into the complex domain, where the notion of type is no longer significant. Attention is given to the mathematical background, the method of complex characteristics, and numerical calculations.
    Keywords: AERODYNAMICS
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  • 2
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    Design of supercritical swept wings (1982)
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    Publication Date: 2019-06-28
    Description: Computational fluid dynamics are used to discuss problems inherent to transonic three-dimensional flow past supercritical swept wings. The formulation for a boundary value problem for the flow past the wing is provided, including consideration of weak shock waves and the use of parabolic coordinates. A swept wing code is developed which requires a mesh of 152 x 10 x 12 points and 200 time cycles. A formula for wave drag is calculated, based on the idea that the conservation form of the momentum equation becomes an entropy inequality measuring the drag, expressible in terms of a small-disturbance equation for a potential function in two dimensions. The entropy inequality has been incorporated in a two-dimensional code for the analysis of transonic flow over airfoils. A method of artificial viscosity is explored for optimum pressure distributions with design, and involves a free boundary problem considering speed over only a portion of the wing.
    Keywords: AERODYNAMICS
    Type: AIAA Journal; 20; Mar. 198
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  • 3
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    Nonlinear magnetohydrodynamic stability (1981)
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    Publication Date: 2019-06-28
    Description: The computer code developed by Bauer et al. (1978) for the study of the magnetohydrodynamic equilibrium and stability of a plasma in toroidal geometry is extended so that the growth rates of instabilities may be estimated more accurately. The original code, which is based on the variational principle of ideal magnetohydrodynamics, is upgraded by the introduction of a nonlinear formula for the growth rate of an unstable mode which acts as a quantitative measure of instability that is important in estimating numerical errors. The revised code has been applied to the determination of the nonlinear saturation, ballooning modes and beta limits for tokamaks, stellarators and torsatrons.
    Keywords: PLASMA PHYSICS
    Type: Physics of Fluids; 24; Jan. 198
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  • 4
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    Nonparametric solution of the Euler equations for steady flow (1983)
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    Publication Date: 2019-06-28
    Description: A theory is presented for formulating well-posed boundary value problems for the Euler equations for steady rotational flow. It is shown that the Euler equations of motion are equivalent to a variational principle, which is used to define a finite difference scheme for numerically solving the Euler equations. The principle is extended to MHD problems in terms of a potential energy of a perfectly conducting plasma having a minimum number of stable configurations. The flow around a cylinder is considered, noting that time-independent solutions of the Euler equations can be used to provide limits to solutions of the Navier-Stokes equations. A sample is worked out in terms of the motion of vortices inside a circle.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Communications on Pure and Applied Mathematics (ISSN 0010-3640); 36; July 198
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  • 5
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    A remark about pointed bubbles (1985)
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    Publication Date: 2019-06-28
    Description: The polymer expansion is a formal algebraic identity between a partition function and logarithm in statistical physics problems. The expansion gives a systematic method to control the free energy or to establish exponential tree-graph decay of connected correlations. Here, the convergence properties of the polymer expansion are analyzed in connection with three practical examples, including: intersecting bonds in chemical polymer chains; a connected closed hypersurface built from the (d-1)-faces of the d-dimensional unit cubes; and the set of Feynamn diagrams in the perturbation series of the Euclidean field theory partition function Z. The example of connected polymer chains is generalized to apply to other lattice models, including n-state Ising models at high temperature; short range lattice gases at high temperature; and weak coupling lattice field and gauge theories.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Communications on Pure and Applied Mathematics (ISSN 0010-3640); 38; 609-612
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  • 6
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    Transonic flow about airfoils (1978)
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    Publication Date: 2019-06-28
    Description: Program analyzes airfoils that permit transonic flow for subsonic free-stream mach numbers. Transonic refers to aircraft speeds less than speed of sound, but close enough so that top of wing, where airflow is fastest, mach number becomes greater than 1. Program should aid design phase of new airfoil and in analysis of existing airfoils.
    Keywords: MECHANICS
    Type: LAR-12265 , NASA Tech Briefs (ISSN 0145-319X); 2; 4; P. 3
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  • 7
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    A theory of supercritical wing sections, with computer programs and examples. (1972)
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    Publication Date: 2019-06-27
    Description: Mathematical methods for the design of supercritical wings, which depend on the numerical solution of the partial differential equations of two-dimensional gas dynamics, are developed. The main contribution is a computer program for the design of shockless transonic airfoils using the hodograph transformation and analytic continuation into the complex domain. The mathematical theory is described, and a manual for users of the programs is provided. Numerical examples are given and computational results are discussed, and the computer programs themselves are listed. The analysis routine can be used to ascertain whether the profiles behave well at off-design conditions, or to smooth coordinates and obtain a desirable shape more quickly when perfectly shockless flow is not essential.
    Keywords: AERODYNAMICS
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  • 8
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    Analysis of transonic airfoils. (1971)
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    Publication Date: 2019-06-27
    Description: A finite difference scheme for the analysis of transonic airfoils at off-design conditions is described. It is the ultimate goal of the investigations to avoid expensive wind tunnel tests by combining the mathematical techniques in a procedure for designing supercritical airfoils so that they will be effective over a wider range of angles of attack and Mach numbers. A mathematical method is considered for computing two-dimensional transonic flows past a prescribed profile. The method can provide accurate results for a comparison with a known shockless regime. The approach gives also data of engineering reliability concerning the location and the strength of shocks at off-design conditions.
    Keywords: AERODYNAMICS
    Type: Communications on Pure and Applied Mathematics; 24; Nov. 197
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  • 9
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    Supercritical wing sections II: A handbook (1975)
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    Publication Date: 2019-06-27
    Description: The numerical aspect of theoretical work on transonics and supercritical wing sections are compiled. A model of the trailing edge is introduced which eliminates the loss of 15 to 20 percent experienced with heavily aft-loaded models, and it is indicated how drag creep can be reduced at off-design conditions. A rotated finite difference scheme is presented which can handle supersonic as well as subsonic free stream Mach numbers and leads to an effective three-dimensional program for the computation of transonic flow past an oblique wing. In the case of two-dimensional flow, the method is extended to take into account the displacement thickness computed by a semiempirical turbulent boundary layer correction. A series of supercritical wing sections is discussed together with comparisons between experimental and theoretical data. Computer programs and a brief manual for their operation are listed. It is shown that the programs furnish a physically adequate computer simulation of the compressible flows that arise in problems of transonic aerodynamics.
    Keywords: AERODYNAMICS
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  • 10
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    Numerical studies of new stellarator concepts (1980)
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    Publication Date: 2019-06-27
    Description: A three-dimensional computer code has been developed to study the magnetohydrodynamic equilibrium and stability of a diffuse or sharp boundary plasma in toroidal geometry. It is shown how equilibria with net toroidal current identically zero can be determined and how growth rates of instabilities can be calculated. Applications are made to an l = 2, 3 stellarator configuration that offers the possibility of achieving a critical value as high as 10% for the plasma parameter
    Keywords: PLASMA PHYSICS
    Type: Journal of Computational Physics; 35; May 1980
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