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    Boundary Integral Equation Methods for Aerodynamics

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    The objective of this chapter is to review the boundary-integral-equation methods in potential aerodynamics of airplanes and helicopter rotors, with emphasis on the `direct velocity-potential formulation', which was introduced by Morino (1973, 1974) and further developed with his collaborators, in particular by Gennaretti (1989). For the sake of clarity, the formulation is presented at levels of increasing complexity, starting with incompressible non-lifting problems and ending with the most recent developments, i.e. a boundary-integral-equation formulation for the velocity potential equation for compressible flows, in a frame of eference moving in arbitrary motion, with applications to aerodynamics of airplanes and helicopter rotors. The formulation is given in terms of the velocity potential, for which an explicit treatment of the wake is required; special emphasis is given to the formulation for the wake transport. Recently obtained numerical results are included. Other methods, in particular those by Hess and by Maskew, are also presented

    A Boundary Element Method for the Aerodynamic Analysis of Aircraft in Arbitrary Motion

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    A new boundary integral formulation for the aerodynamic analysis of an aircraft (in particular, a tiltrotor) in arbitrary motion is presented. The formulation is based on the velocity potential for compressible flows, and as such is an extension of past work of the authors. The distinguishing feature is that the boundary integral representation is written for a surface in arbitrary motion with respect to a frame of reference which in turn moves in arbitrary motion with respect to the undisturbed air. Thus, the integrals are evaluated on the emission surface, which is the locus of the emitting points at the locations (in the moving frame) that they had when the signal influencing a given point at a given time was emitted. The differences with respect to related formulations (e.g., Ffowcs Williams and Hawkings) are outlined. Also, the advantages of the present formulation with respect to the preceding ones by the authors are discussed. Numerical validation results are presented for the limited case of helicopter rotors in hover
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