Real-Time Aero-elasticity Simulation of Open Rotors With Slender Blades for the Multidisciplinary Design of Rotorcraft

Abstract

This paper elaborates on the theoretical development of a mathematical approach, tar geting the real-time simulation of aero-elasticity for open rotors with slender blades, as employed in the majority of rotorcraft. A Lagrangian approach is formulated for the rapid estimation of natural vibration characteristics of rotor blades with nonuniform structural properties. Modal characteristics obtained from classical vibration analysis methods are utilized as assumed deformation functions. Closed form integral expressions are incorporated, describing the generalized centrifugal forces and moments acting on the blade. The treatment of three-dimensional elastic blade kinematics in the timedomain is thoroughly discussed. In order to ensure robustness and establish applicability in real time, a novel, second-order accurate, finite-difference scheme is utilized for the temporal discretization of elastic blade motion. The developed mathematical approach is coupled with a finite-state induced flow model, an unsteady blade element aerodynamics model, and a dynamic wake distortion model. The combined formulation is implemented in an existing helicopter flight mechanics code. The aero-elastic behavior of a full-scale hingeless helicopter rotor has been investigated. Results are presented in terms of rotor blade resonant frequencies, rotor trim performance, oscillatory structural blade loads, and transient rotor response to control inputs. Extensive comparisons are carried out with wind tunnel (WT) and flight test (FT) measurements found in the open literature as well as with nonreal-time comprehensive analysis methods. It is shown that the proposed approach exhibits good agreement with measured data regarding trim performance and transient rotor response characteristics. Accurate estimation of structural blade loads is demonstrated, in terms of both amplitude and phase, up to the third harmonic component o f oscillatory loading.It is shown that the developed model can be utilized for real-time simulation on a modern personal computer. The proposed methodology essentially con stitutes an enabling technology for the multidisciplinary design of rotorcraft, when a compromise between simulation fidelity and computational efficiency has to be sought for in the process of model development.

Variable rotor speed and active blade twist for civil rotorcraft: Optimum scheduling, mission analysis, and environmental impact

“…The objective of this work is to assess the potential improvements on the operational performance and environmental impact of rotorcraft, stemming from the implementation of optimal variable rotor speed and active blade twist schedules at mission level. A comprehensive rotorcraft code is deployed consisting of extensively validated models for flight dynamics [20], rotor blade aeroelasticity [21], engine performance [22], gaseous emission prediction [23,24], and flight path analysis [25]. A computationally efficient Design Space Exploration (DSE) and optimization strategy is formulated comprising methods for DOE [26], Response Surface Modeling (RSM) [27], as well as genetic optimization [28].…”

“…HEC-TOR has been continuously developed and refined at Cranfield University by Goulos et al [25,30]. The code has been validated with experimental data in terms of airframe-rotor aerodynamics [31,30], aeroelasticity [21,20], engine performance [24], as well as gaseous emissions estimation [23,24].…”

Modelling the aeroelastic response and flight dynamics of a hingeless rotor helicopter including the effects of rotor-fuselage aerodynamic interaction

“…The author's mathematical model has been validated extensively in Refs 28-30 and 32 through comparison with experimental data derived from flight tests and wind-tunnel measurements. Validation has been carried out in terms of flight dynamics, oscillatory blade loads, and rotor induced vibration for the hingeless rotor of the Bo105 (28)(29)(30) and the articulated rotor of the Aerospatiale SA 330 helicopter (29,32) . Appendix A contains a comprehensive mathematical description of the employed modelling approach, thus further elaboration within this section shall be omitted.…”

“…The employed rotor dynamics model (28)(29)(30) in combination with the finite-state induced flow formulation of Peters-He (35,36) and the wake distortion approach of Zhao-Prasad (46,47) , have been coupled with the Leishman-Beddoes unsteady nonlinear aerodynamics model (48) . Experimentally derived quasi-steady aerofoil data extracted from Ref.…”

“…. (38) It can be observed that Equations (29) and (30) relate the roll-yaw accelerations, p . and r .…”