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  • 1
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    Integral equations for flows in wind tunnels (1979)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: This paper surveys recent work on the use of integral equations for the calculation of wind tunnel interference. Due to the large number of possible physical situations, the discussion is limited to two-dimensional subsonic and transonic flows. In the subsonic case, the governing boundary value problems are shown to reduce to a class of Cauchy singular equations generalizing the classical airfoil equation. The theory and numerical solution are developed in some detail. For transonic flows nonlinear singular equations result, and a brief discussion of the work of Kraft and Kraft and Lo on their numerical solution is given. Some typical numerical results are presented and directions for future research are indicated.
    Keywords: AERODYNAMICS
    Type: Journal of Integral Equations; 1; Sept
    Format: text
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  • 2
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    Solutions to Kuessner's integral equation in unsteady flow using local basis functions (1975)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: The computational procedure and numerical results are presented for a new method to solve Kuessner's integral equation in the case of subsonic compressible flow about harmonically oscillating planar surfaces with controls. Kuessner's equation is a linear transformation from pressure to normalwash. The unknown pressure is expanded in terms of prescribed basis functions and the unknown basis function coefficients are determined in the usual manner by satisfying the given normalwash distribution either collocationally or in the complex least squares sense. The present method of solution differs from previous ones in that the basis functions are defined in a continuous fashion over a relatively small portion of the aerodynamic surface and are zero elsewhere. This method, termed the local basis function method, combines the smoothness and accuracy of distribution methods with the simplicity and versatility of panel methods. Predictions by the local basis function method for unsteady flow are shown to be in excellent agreement with other methods. Also, potential improvements to the present method and extensions to more general classes of solutions are discussed.
    Keywords: AERODYNAMICS
    Type: NASA-CR-137719 , D6-43599
    Format: application/pdf
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  • 3
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    Reformulation of Possio's kernel with application to unsteady wind tunnel interference (1980)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: An efficient method for computing the Possio kernel has remained elusive up to the present time. In this paper the Possio is reformulated so that it can be computed accurately using existing high precision numerical quadrature techniques. Convergence to the correct values is demonstrated and optimization of the integration procedures is discussed. Since more general kernels such as those associated with unsteady flows in ventilated wind tunnels are analytic perturbations of the Possio free air kernel, a more accurate evaluation of their collocation matrices results with an exponential improvement in convergence. An application to predicting frequency response of an airfoil-trailing edge control system in a wind tunnel compared with that in free air is given showing strong interference effects.
    Keywords: AERODYNAMICS
    Format: text
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  • 4
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    Computation of aerodynamic interference effects on oscillating airfoils with controls in ventilated subsonic wind tunnels (1979)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: Lift interference effects are discussed based on Bland's (1968) integral equation. A mathematical existence theory is utilized for which convergence of the numerical method has been proved for general (square-integrable) downwashes. Airloads are computed using orthogonal airfoil polynomial pairs in conjunction with a collocation method which is numerically equivalent to Galerkin's method and complex least squares. Convergence exhibits exponentially decreasing error with the number n of collocation points for smooth downwashes, whereas errors are proportional to 1/n for discontinuous downwashes. The latter can be reduced to 1/n to the m+1 power with mth-order Richardson extrapolation (by using m = 2, hundredfold error reductions were obtained with only a 13% increase of computer time). Numerical results are presented showing acoustic resonance, as well as the effect of Mach number, ventilation, height-to-chord ratio, and mode shape on wind-tunnel interference. Excellent agreement with experiment is obtained in steady flow, and good agreement is obtained for unsteady flow.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 79-0346 , American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting; Jan 15, 1979 - Jan 17, 1979; New Orleans, LA
    Format: text
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