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Fluid Dynamics

, Volume 1, Issue 1, pp 51–56 | Cite as

Unsteady incompressible fluid flow past a cascade of thin curved plates

  • V. E. Saren
Article
  • 37 Downloads

Abstract

A large number of papers have been devoted to the study of unsteady flow past airfoil cascades. The majority of authors solve the problem for slightly curved profiles oscillating at low angles of attack.

Among other work, we note that of Söhngen [1] on the flow past a dense cascade of plates oscillating synchronously and in phase in a potential fluid flow at a high angle of attack. Samoilovich [2] studied the flow past a cascade of plates of arbitrary shape oscillating with an arbitrary phase shift between neighboring plates. He presents the solution for the case of variable circulation in the quasisteady formulation. Stepanov [3] studied the same question with a linear approach to the flow behind the cascade. Musatov [4] examined the problem of the flow past a cascade of plates oscillating with an arbitrary phase shift between neighboring plates in a fluid flow, again at a high angle of attack, and considered the variation of the relative position of the plates durilng the oscillation process.

The present paper considers the flow of a perfect incompressible fluid past a cascade of thin curved oscillating plates with account for the relative displacements of the plates during oscillation. To determine the intensity of the bound vortices per unit length, a linear integral equation is obtained. This represents a generalization of the Birnbaum equation to the case considered (see [5]). Equations are presented for calculating the unsteady aerodynamic forces and moments acting on the plates. As an example, the aerodynamic forces and moments are calculated for the quasistationary formulation of the problem.

Keywords

Vortex Fluid Flow High Angle Unsteady Flow Incompressible Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    H. Söhngen, “Luftkrafte an einem schwingenden Schaufeekranz kleiner Teilung,” Z. angew. Math. and Phys., vol. 4, no. 4, 1953.Google Scholar
  2. 2.
    G. S. Samoilovich, “On the calculation of unsteady flow past a lattice of arbitrary profiles vibrating with an arbitrary phase shift,” PMM, vol. 20, p. 1, 1962.Google Scholar
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    G. Yu. Stepanov, Hydrodynamics of Turbomachinery Cascades [in Russian], Fizmatgiz, 1962.Google Scholar
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    V. V. Musatov, “On the calculation of unsteady flow past an airfoil cascade in an incompressible fluid,” Izv. AN SSSR, OTN, Mekhanika i mashinostroenie, no. 3, 1963.Google Scholar
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    A. I. Nekrasov, Unsteady Flow Airfoil Theory [in Russian], Izd-vo AN SSSR, 1947.Google Scholar
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    S. M. Belotserkovskii, A. S. Ginevskii, and Ya. S. Polonskii, “Aerodynamic forces acting on a cascade with unsteady flow,” Promyshlennaya aerodinamika, p. 20, 1961.Google Scholar
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    S. M. Belotserkovskii, A. S. Ginevskii, and Ya. E. Polonskii, “Aerodynamic force and moment characteristics of a thin-plate cascade,” Promyshlennaya aerodinamika, p. 22, 1961.Google Scholar
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    D. N. Gorelov and L. V. Dominas, “Calculation of aerodynamic forces and moments acting on a cascade of plates oscillating in a plane incompressible fluid flow,” Izv. AN SSSR, Mekhanika, no. 3, 1965.Google Scholar

Copyright information

© The Faraday Press, Inc. 1967

Authors and Affiliations

  • V. E. Saren
    • 1
  1. 1.Novosibirsk

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