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  • AERODYNAMICS  (17)
  • 1
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    The method of complex characteristics for transonic airfoil design, with an application to compressors (1985)
    In:  Other Sources
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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)
    In:  Other Sources
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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
    Format: text
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  • 3
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    A theory of supercritical wing sections, with computer programs and examples. (1972)
    In:  Other Sources
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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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  • 4
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    Analysis of transonic airfoils. (1971)
    In:  Other Sources
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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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  • 5
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    Supercritical wing sections II: A handbook (1975)
    In:  Other Sources
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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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  • 6
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    Computer simulation of shock wave boundary layer interaction (1973)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: Development of a boundary layer correction for an analysis program previously used by Bauer et al. (1972) to study two-dimensional flow past transonic airfoils at off-design conditions where shocks which interact with the boundary layer appear. Using a method which combines conformal mapping with a finite-difference scheme due to Murman and Cole (1971), an analysis is made of the interaction between shock waves on a supercritical wing section and a turbulent boundary layer, assuming that the shocks are weak and that separation is insignificant. It is shown that relatively simple shock wave/boundary layer interactions of the kind envisioned in this study can be treated by determining the displacement thickness iteratively together with the flow and altering the profile accordingly. It is concluded that the proposed boundary layer correction appears to furnish an essential improvement in cases where both pronounced aft loading and a large enclosed supersonic region of flow are present.
    Keywords: AERODYNAMICS
    Type: Communications on Pure and Applied Mathematics; 26; Sept
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  • 7
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    The NYU inverse swept wing code (1983)
    In:  CASI
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    Publication Date: 2019-06-28
    Description: An inverse swept wing code is described that is based on the widely used transonic flow program FLO22. The new code incorporates a free boundary algorithm permitting the pressure distribution to be prescribed over a portion of the wing surface. A special routine is included to calculate the wave drag, which can be minimized in its dependence on the pressure distribution. An alternate formulation of the boundary condition at infinity was introduced to enhance the speed and accuracy of the code. A FORTRAN listing of the code and a listing of a sample run are presented. There is also a user's manual as well as glossaries of input and output parameters.
    Keywords: AERODYNAMICS
    Type: NASA-CR-3662 , NAS 1.26:3662
    Format: application/pdf
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  • 8
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    Transonic flow theory of airfoils and wings (1976)
    In:  CASI
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    Publication Date: 2019-06-27
    Description: There are plans to use the supercritical wing on the next generation of commercial aircraft so as to economize on fuel consumption by reducing drag. Computer codes have served well in meeting the consequent demand for new wing sections. The possibility of replacing wind tunnel tests by computational fluid dynamics is discussed. Another approach to the supercritical wing is through shockless airfoils. A novel boundary value problem in the hodograph plane is studied that enables one to design a shockless airfoil so that its pressure distribution very nearly takes on data that are prescribed.
    Keywords: AERODYNAMICS
    Type: NASA. Langley Res. Center Advan. in Eng. Sci., Vol. 4; p 1349-1358
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  • 9
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    A systematic method for computer design of supercritical airfoils in cascade (1976)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: A computer code has been developed for the direct calculation of shockless transonic airfoils whose pressure distributions can be assigned within reasonable limits. The partial differential equations of two-dimensional inviscid gas dynamics are solved by analytic continuation into the domain of two independent complex characteristic coordinates. The domain of integration is mapped conformally onto the unit circle in the hodograph plane of one of these coordinates. It is possible to formulate a boundary value problem on this circle for the stream function that is well posed in the case of transonic flow. This enables the formulation of a procedure for the calculation of an airfoil on which the speed is prescribed as a function of the arc length
    Keywords: AERODYNAMICS
    Type: Communications on Pure and Applied Mathematics; 29; July 197
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  • 10
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    Lecture notes in economics and mathematical system. Volume 150: Supercritical wing sections 3 (1977)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Application of computational fluid dynamics to the design and analysis of supercritical wing sections is discussed. Computer programs used to study the flight of modern aircraft at high subsonic speeds are listed and described. The cascades of shockless transonic airfoils that are expected to increase the efficiency of compressors and turbines are included.
    Keywords: AERODYNAMICS
    Type: NASA-CR-155581
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