Rotor Blade Stability in Turbulent Flows-Part I

Abstract

The effect of turbulence in the atmosphere on the motion stability of a helicopter blade is investigated. Modeling turbulence as a random field, statistically stationary in time and homogeneous in space, the method of stochastic average of Stratonovich is used to obtain equivalent Ito stochastic equations, from which the FokkerPlanck equation for the transition probability density and the equations for various stochastic moments can be derived. As an exploratory study, only flapping and torsional motions are considered; the results are reported in two parts. In Part I, the present paper, equations of motion are derived which are reducible to those obtained previously by Sissingh and Kuczynski when the turbulence terms are removed. The in-plane turbulence components appear in the coefficients of these equations; thus, they affect the stability of the flapping and torsional motions. On the other hand, the normal turbulence component appears in the inhomogeneous terms in the equations; its statistical properties, while affecting the level of system response, do not change a stable solution to an unstable solution. Then detailed discussions are given for the reduced case of uncoupled flapping in a hovering flight. This simple case is theoretically interesting, since closed-form solutions can be obtained and considerable insight can be gained from the analysis. Certain mathematical tools involving stochastic processes which may be foreign to engineers are explained in the Appendix. Solutions for the case of forward flights for both coupled and uncoupled motions are presented in Part II.