Unsteady flow of incompressible fluid past a doubly periodic grid: PMM vol. 37, n≗3, 1973, pp. 488–496

Abstract

Validity of the method of superposition of singularities for solving the problem of unsteady flow of incompressible fluid past a doubly periodic grid of arbitrary bodies is proved using the derived below Green's function which has the property of quasi-periodicity. Doubly periodic grids consisting of constant phase shift monopole and dipole elements are examined. Exact integral representation of the perturbation potential of such grids is obtained and its fundamental properties and asymptotic behavior away from the grid are analyzed. According to [1, 2] the solution of the problem of unsteady fluid flow past a grid whose elements oscillate arbitrarily with respect to time τ by the Fourier method reduces to the sum of solutions of the problems of flow past a similar grid whose elements perform oscillations of a single type but in the presence of a constant phase shift between the oscillations of adjacent elements. The problem of three-dimensional flow of incompressible fluid past a grid consisting of bodies with piecewise smooth boundaries, which effect harmonic oscillations is considered below.