A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams

This paper reviews the state of the art in helicopter rotor loads prediction using Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) coupling. The application of CFD to rotorcraft problems has evolved, over the period 1990 to 2005, as a viable means to improve the aerodynamic modeling used in rotorcraft comprehensive analyses (CA). CFD/CSD coupling has the potential to meet the long term objective of a coupled rotor-fuselage analysis that can predict accurate loads and vibration at all critical flight conditions without empirical or semi-empirical inputs. This paper reviews the capabilities and limitations of current CFD analyses to capture the key aerodynamic phenomena driving critical rotor loads: wake, dynamic stall and tip transonic effects. Recent initiatives in CFD/CSD coupling, targeted to improve predictions of rotor loads, are discussed. The high speed (155 kts) forward flight condition of the UH-60A BlackHawk is studied as a test case. The flight condition falls in a critical high vibration regime, where the mechanisms of rotor vibratory loads were not clearly understood. Significant improvements in fundamental understanding and prediction of vibratory loads at this flight condition has been recently demonstrated by researchers using CFD/CSD coupling. The physical mechanisms involved, and the role of CFD in improving predictions is explained.

Review of Rotor Loads Prediction with the Emergence of Rotorcraft CFD

On the nonlinear deformation geometry of Euler-Bernoulli beams. [rotary wings]

The state of the art in the formulation and solution of rotary-wing aeroelastic stability and response problems is reviewed in detail. The approximations used in the structural, inertia and aerodynamic operators are discussed. The important role of geometric nonlinearities, due to moderate deflections, and aerodynamic stall in the aeroelastic stability and response problem are identified. It is also shown that geometric nonlinearities are of primary importance in aeroelastic stability calculations, and have a more limited, though important, role in response calculations. Next, formulation of coupled rotor/fuselage problems is described, for both air and ground resonance type problems. Both topics, the isolated blade problem and the coupled rotor/fuselage problem, are treated for both hover and forward flight. Solution of aeroelastic stability and response problems proceeds in two stages. First, the spatial dependence is eliminated by using Galerkin's method, or by using the finite element method. Next the nonlinear, or linear, ordinary differential equation with periodic coefficients have to be solved for stability or response. Efficient numerical methods for accomplishing these objectives are presented in a comprehensive manner. The paper contains a number of illustrative numerical results which are intended to clarify various aspects of the modeling process and serve as representative results for both aeroelastic stability and response calculations for a variety of blade and rotor configurations.

Formulation and solution of rotary-wing aeroelastic stability and response problems

The purpose of this review is to present the research done in rotary-wing aeroelasticity during the past eight years in a unified manner. The following topics are reviewed with considerable detail: (1) recent development in the aeroelastic modeling of the coupled flap-lag-torsional problem in hover (2) effect of unsteady aerodynamics on the coupled flap-lag-torsional aeroelastic problem in hover (3) the coupled flap-lag and the coupled flap-lag-torsional problem in forward flight (4) complete rotor and coupled rotor fuselage aeroelastic problems including both hingeless and teetering rotors.

Recent developments in rotary-wing aeroelasticity

A set of nonlinear equations of equilibrium for an elastic wind turbine or helicopter blades are presented. These equations are derived for the case of small strains and moderate rotations (slopes). The derivation includes several assumptions which are carefully stated. For the convenience of potential users the equations are developed with respect to two different systems of coordinates, the undeformed and the deformed coordinates of the blade. Furthermore, the loads acting on the blade are given in a general form so as to make them suitable for a variety of applications. The equations obtained in the study are compared with those obtained in previous studies.

A. Rosen

Papers

Nonlinear equations of equilibrium for elastic helicopter or wind turbine blades undergoing moderate deformation.