Asymptotic method for determining energy dissipation and drag during a periodic flow of liquid around plates

A periodic flow of an incompressible fluid around plates at large Reynolds numbers and small Keleghan-Carpenter numbers is considered. The energy dissipation over the oscillation period and the resistance coefficients of the plates are determined. Two-dimensional problems are studied on translational and angular vibrations of a flat plate and a plate in the shape of a circular arc, on translational vibrations of a circular cylinder with ribs symmetrically located on it, on angular vibrations of cruciform plates, as well as the problem of periodic flow around an inclined edge on a flat wall. A three-dimensional problem of translational and angular vibrations of a thin circular disk is considered. All obtained dependences for energy dissipation and drag coefficients are presented in analytical form through velocity intensity coefficients, which characterize the velocity singularity at the sharp edges of the plates with a potential flow around an ideal fluid. Some obtained dependencies are compared with the available numerical and experimental data.