МЕТОД УЛУЧШЕНИЯ АНАЛИТИЧЕСКИХ РЕЗУЛЬТАТОВ ДЛЯ ВРАЩАЮЩЕЙСЯ ЛОПАСТИ В СРАВНЕНИИ С ПРЯМЫМ ЧИСЛЕННЫМ РАСЧЕТОМ

Abstract

The paper proposes an analytical method for calculating the value of the driving force of a thin rotating plate. The classical approach represents the plate as a set of plane problems corresponding to the section of the blade. The theory of a thin wing describes the translational motion of the plate. Unlike them, the proposed method allows us to consider a rotating thin plate as a whole. A two-dimensional integral equation permitting to describe a plate of any shape and twist is obtained. The singular terms of the obtained equation qualitatively correspond to the singular terms of the classical equation for the translational motion of the thin plate, and additional regular terms are responsible for the rotational character of the motion. A numerical experiment of rotating thin plate was performed in the ANSYS CFX simulation software. The results of the numerical experiment are compared with the data obtained by the classical method of the plane problem and the proposed analytical method. The proposed method permits reducing the deviation of the draft value obtained analytically from the value obtained numerically by three times – from 200 to 75 %.