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  • Other Sources  (3)
  • 1970-1974  (3)
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  • Other Sources  (3)
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  • 1
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    Unknown
    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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    NASA TECHNICAL REPORTS
  • 2
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    Unknown
    Analysis of transonic airfoils. (1971)
    In:  Other Sources
    Details
    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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  • 3
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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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    NASA TECHNICAL REPORTS
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