Rotor hovering performance using the method of fast free wake analysis

Abstract

Experimental investigations have shown that the bound circulation distribution on a rotor blade is critically dependent on the location of the vortices in the wake. Consequently, in order to optimize rotor performance, compute blade loads, and determine acoustic signatures, it is necessary to use analytical methods which are capable of predicting wake geometry. The factors which contribute to the complexity of the problem both in hovering and forward flight are discussed. A simplified approach to a free wake analysis of rotors in hover is outlined and the analytical results compared with experimental data for two- and four-bladed rotors. ELICOPTER rotor aerodynamic analysis remains one of the more challenging of the unsolved problems of modern fluid mechanics. Although solutions are not required for successful design, as evidenced by the growing use of the helicopter, the availability of a consistent aerodynamic theory for the rotor could lead to formal rather than heuristic design optimization and would help to reduce the costly flight testing required to minimize vibration, noise and rotor fatigue loads. This paper will discuss some of the unsolved problems of rotor aerodynamics and suggest a simplified approach to defining the complex vortex structure of the rotor and its wake. Such simplification could facilitate the expansion of the mathematical models to include, for example, certain im- portant real fluids effects. Geometric Complexity In hovering flight the lifting rotor blade generates a spiralling, rapidly contracting wake which, unlike a lifting wing where the wake is transported rapidly downstream, remains in the vicinity of the rotor at least for the initial spiral. The bound circulation distribution along a following blade is strongly influenced by this wake because of its proximity to the blade and rapid initial contraction. Figure 1 sketches the geometry at the crucial first encounter of a blade with the rolled up tip vortex in the wake. Figure 2 shows a typical bound circulation distribution and wake geometry in hovering flight. The wake continues to distort under the influence of the self-induced velocities as it descends, which complicates the computation of induced velocities both at the blade and in the wake. In the forward flight case the wake geometry may be somewhat simplified since only the first spiral has any ap- preciable influence on the blade loads, further spirals being carried away from the rotor as it advances. On the other hand, the forward flight case is complicated by the existence of time varying airloads requiring the inclusion of a shed, as well as a trailing wake structure and the use of nonstationary flow theory. In the case of hovering flight, because of sym- metry, the flow is essentially stationary when viewed in the rotating system. Several alternative approaches to handling the geometric complexities outlined above have been proposed. The simplest