Research Papers

Optimization of Energy Harvesting From Stall-Induced Oscillations Using the Multidimensional Kriging Metamodel

[+] Author and Article Information
Carlos R. dos Santos

Department of Mechanical Engineering,
São Carlos School of Engineering,
University of São Paulo,
São Carlos , SP 13566-590, Brazil
e-mail: carlos.renan.santos@usp.br

Maíra M. da Silva

Department of Mechanical Engineering,
São Carlos School of Engineering,
University of São Paulo,
São Carlos , SP 13566-590, Brazil
e-mail: mairams@sc.usp.br

Flávio D. Marques

Department of Mechanical Engineering,
São Carlos School of Engineering,
University of São Paulo,
São Carlos, SP 13566-590, Brazil
e-mail: fmarques@sc.usp.br

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 31, 2018; final manuscript received April 2, 2019; published online May 13, 2019. Assoc. Editor: Massimo Ruzzene.

J. Comput. Nonlinear Dynam 14(7), 071008 (May 13, 2019) (9 pages) Paper No: CND-18-1490; doi: 10.1115/1.4043451 History: Received October 31, 2018; Revised April 02, 2019

The power harvested from stall-induced oscillations of airfoils has been analyzed as a potential source of electric energy for microsystems. Previous works have indicated that the energy harvested from such oscillations is affected by key parameters of the structural configuration. In this sense, this work proposes the optimization of such parameters by considering the use of a stochastic multidimensional Kriging metamodel. The metamodel was built using a database created with simulations of an electro-aeroelastic model. Such model considers aerodynamics loads given by the Beddoes–Leishman model as input for the system of differential equations which governs the pitching motion of an airfoil attached to an electric generator. The results of the optimization process have indicated an optimum point for the elastic axis of the structure and the need for reducing the mass, the moment of inertia, and the stiffness for increasing the harvested power in a range of wind speeds.

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Fig. 1

Methodology for the optimization of the energy harvester

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Fig. 2

Schematic representation of the electro-aeroelastic model: (a) typical aeroelastic section and (b) detail of the electric generator circuit

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Fig. 3

The exponential function for the autocovariances in the Kriging method

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Fig. 4

Comparison of voltage signals from the electro-aeroelastic model numerical simulation with experimental measurements by Marques et al. [8]: (a) V = 18.42 m/s and (b) voltage variation with the wind speed

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Fig. 5

Distribution of the values g(χ) in relation to each variable of optimization

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Fig. 6

Time histories of the angle of attack at V =10 m/s for the cases when g =0: (a) case 1 (xea = 0.25, rα2μ=5, ωα=1 Hz), (b) case 2 (xea = 0.40, rα2μ=1, ωα=0 Hz), (c) case 3 (xea = 0.29, rα2μ=5, ωα=0 Hz), and (d) g(χ) ≠ 0 (xea = 0.336, rα2μ=1, ωα=0 Hz)

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Fig. 7

Comparison of g(χ) and ĝ(χ) at 100 random points

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Fig. 8

Minimization of the cost function using different initial conditions for the SQP

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Fig. 9

Aerodynamic moment coefficient at the elastic axis as function of the angle of attack for the optimal harvester at V =9.8 m/s

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Fig. 10

Hopf bifurcation diagram for the optimal harvester

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Fig. 11

Evaluation of the cost function during SQP with the complete electro-aeroelastic model



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