Optimization of body shape at small reynolds numbers

  • A. A. Mironov
Article

Abstract

The problem of the optimization of the shape of a body in a stream of viscous liquid or gas was treated in [1–5]. The necessary conditions for a body to offer minimum resistance to the flow of a viscous gas past it were derived in [1], The necessary optimality conditions when the motion of the fluid is described by the approximate Stokes equations were derived in [2], The shape of a body of minimum resistance was found numerically in [3] in the Stokes approximation. The optimality conditions when the motion of the fluid is described by the Navier—Stokes equations were derived in [4, 5], and in [4] these conditions were extended to the case of a fluid whose motion is described in the boundary-layer approximation. The necessary optimality conditions when the motion of the fluid is described by the approximate Oseen equations were derived in [5] and an asymptotic analysis of the behavior of the optimum shape near the critical points was performed for arbitrary Reynolds numbers.

Keywords

Mathematical Modeling Reynold Number Mechanical Engineer Optimality Condition Industrial Mathematic 

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Literature cited

  1. 1.
    T. K. Sprazetdinov, “Optimum problems of gas dynamics,” Izv. Vyssh. Uchebn. Zaved., Aviats. Tekh., No. 2 (1963).Google Scholar
  2. 2.
    O. Pironneau. “On optimum profiles in Stokes flow,” J. Fluid Mech.,59, No. 1, 117 (1973).Google Scholar
  3. 3.
    J. -M. Bourot, “On the numerical computation of the optimum profile in Stokes flow,” J. Fluid Mech.,65, No. 3, 513 (1974).Google Scholar
  4. 4.
    O. Pironneau, “On the optimum design in fluid mechanics,” J. Fluid Mech.,64, 97 (1974).Google Scholar
  5. 5.
    A. A. Mironov, “On the problem of optimization of the shape of a body in a viscous fluid,” Prikl. Mat. Mekh.,39, No. 1, 103 (1975).Google Scholar
  6. 6.
    I. Proudman and J. R. A. Pearson, “Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder,” J. Fluid Mech.,2, No. 4, 237 (1957).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • A. A. Mironov
    • 1
  1. 1.Moscow

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