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Research Papers: Gas Turbines: Structures and Dynamics

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

[+] Author and Article Information
Ioannis Goulos

Centre for Propulsion,
School of Engineering,
Cranfield University,
Bedfordshire MK430AL, UK
e-mail: i.goulos@cranfield.ac.uk

Vassilios Pachidis

Centre for Propulsion,
School of Engineering,
Cranfield University,
Bedfordshire MK430AL, UK
e-mail: v.pachidis@cranfield.ac.uk

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 1, 2014; final manuscript received July 2, 2014; published online August 26, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(1), 012503 (Aug 26, 2014) (12 pages) Paper No: GTP-14-1319; doi: 10.1115/1.4028180 History: Received July 01, 2014; Revised July 02, 2014

This paper elaborates on the theoretical development of a mathematical approach, targeting 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 time-domain 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 of 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 constitutes 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.

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References

Figures

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Fig. 1

Reference systems used for the description of elastic blade kinematics: (a) global nonrotating reference system O and (b) rotating and blade element reference frames (Ai and b, respectively)

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Fig. 2

Resonance chart calculated for the rotor blades of the Bo 105 helicopter—comparison with Boeing–Vertol Y-71 calculations [32]

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Fig. 3

Normalized mode shapes for the hingeless rotor blades of the Bo 105 helicopter: (a) flap modes, (b) lag modes, and (c) torsion modes

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Fig. 4

Trim performance predictions for the Bo 105 helicopter—comparison with FT data [33] and free-wake/FEA simulation [36]: (a) rotor power required, (b) collective pitch angle θ0, (c) longitudinal cyclic pitch angle θ1s, and (d) lateral cyclic pitch angle θ1c

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Fig. 5

Oscillatory structural blade loads for μ = 0.306/0.313— comparison with FTs, WT experiments, and CAMRAD/JA simulations from Ref. [35]: (a) flap bending moment for r/R = 0.144, (b) chord bending moment for r/R = 0.144, and (c) torsional moment for r/R = 0.40

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Fig. 6

Oscillatory structural blade loads for μ = 0.306/0.313—comparison with FTs, WT experiments and CAMRAD/JA simulations from Ref. [35]: (a) flap bending moment for r/R = 0.57, (b) chord bending moment for r/R = 0.45 (FT) – r/R = 0.57 (WT), and (c) torsional moment for r/R = 0.57

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Fig. 7

Transient rotor response to control perturbations from trim, δθ0=δθ1c=δθ1s=1 deg,θ·=45 deg/s,μ=0.189—comparison with equivalent time-delays identified in Ref. [34]: (a) thrust coefficient Ct, (b) longitudinal flapping angle β1c, and (c) lateral flapping angle β1s

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Fig. 8

Effect of number of flow-states and F/L/T mode shapes on the computational time ratio for a personal computer with a 2.3 GHz CPU and 4 GB of RAM

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