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Asymptotic theory of a wing moving near a solid wall

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Abstract

In this study we use the method of matched asymptotic expansions to obtain an approximate solution of the problem of the nonstationary motion of a lifting surface near a solid wall. The region of flow is provisionally subdivided into characteristic zones, in which, using the appropriate coordinates, we construct asymptotic expansions for the velocity potential, which thereafter coalesce in the regions of common validity. In the first approximation (extremely small heights of flight) the problem reduces to the solution of a Poisson equation in a plane region bounded by the contour of the wing in the horizontal plane with boundary conditions established from the coalescence.

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Literature cited

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    S. M. Belotserkovskii, B. K. Skripach, and V. G. Tabaohnikov, A Wing in a Nonstationary Stream of Gas [inRussian], Nauka, Moscow (1971).

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    M. D. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press (1964).

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    S. E. Widnall and T. M. Barrows, “An analytic solution for two- and three-dimensional wings in ground effect,” J. Fluid Mech.,41, Part 4 (1970).

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    M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1965).

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    K. V. Rozhdestvenskii, “Nonlinear theory of a slightly curved wing near a solid boundary,” Tr. Leningr. Korablestroit. Inst., No. 104 (1976).

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Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 115–124, November–December, 1977.

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Rozhdestvsnskii, K.V. Asymptotic theory of a wing moving near a solid wall. Fluid Dyn 12, 910–918 (1977). https://doi.org/10.1007/BF01090328

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Keywords

  • Boundary Condition
  • Approximate Solution
  • Asymptotic Expansion
  • Horizontal Plane
  • Poisson Equation