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Research Papers: Ocean Renewable Energy

Effect of Wake Alignment on Turbine Blade Loading Distribution and Power Coefficient

[+] Author and Article Information
David H. Menéndez Arán

Laboratorio de Modelación Matemática,
Facultad de Ingeniería,
Universidad de Buenos Aires,
Ciudad Autónoma de Buenos
Aires C1063ACV, Argentina
e-mail: dmenendez@gmail.com

Ye Tian

Ocean Engineering Group,
Department of Civil, Architectural and
Environmental Engineering,
The University of Texas at Austin,
Austin, TX 78712
e-mail: tianye@utexas.edu

Spyros A. Kinnas

Ocean Engineering Group,
Department of Civil, Architectural and
Environmental Engineering,
The University of Texas at Austin,
Austin, TX 78712
e-mail: kinnas@mail.utexas.edu

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received June 24, 2015; final manuscript received October 1, 2018; published online January 17, 2019. Assoc. Editor: Antonio F. de Falcao.

J. Offshore Mech. Arct. Eng 141(4), 041901 (Jan 17, 2019) (11 pages) Paper No: OMAE-15-1052; doi: 10.1115/1.4041669 History: Received June 24, 2015; Revised October 01, 2018

This paper describes the use of a lifting line model in order to determine the optimum loading on a marine turbine's blades. The influence of the wake and its geometry is represented though the use of a full wake alignment model. The effects of viscous drag are included through a drag-to-lift ratio. Results for different number of blades and tip speed ratios are presented. Various types of constraints are imposed in the optimization method in order to avoid abrupt changes in the designed blade shape. The effect of the constraints on the power coefficients of the turbines is studied. Once the optimum loading has been determined, the blade geometry is generated for a given chord and camber distributions. Finally, a vortex-lattice method is used to verify the power coefficient of the designed turbines.

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References

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Figures

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Fig. 1

Combined velocity and force diagram on blade section at radius r, turbine case

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Fig. 2

Comparison of wake cross sections for the full wake alignment scheme. The curves are obtained through the intersection of the 3D wake surface with the xz plane (at y = 0). Z = 1, TSR = 8, varying number of radial elements (m).

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Fig. 3

Two possible constrained optimization models: (a) only imposing an inequality constraint on the curvature and (b) adding a constraint on the slope (Z = 2, TSR = 4)

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Fig. 4

Comparison of blade geometries as generated from unconstrained and constrained LLOPT-FWA models for a turbine with a hub (Z = 2, TSR = 4)

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Fig. 5

Convergence analysis for the optimal circulation distribution, for different number of radial sections, full wake alignment and varying drag-to-lift ratio κ (TSR = 5, Z = 3). The corresponding power coefficients are presented in Table 1.

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Fig. 6

Comparison between unconstrained LLOPT-FWA and functional representations, different values of NG parameter (Z = 2, TSR = 4)

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Fig. 7

Convergence analysis of the constrained optimization method, curvature and slope case (Z = 2, TSR = 4). The corresponding power coefficients are presented in Table 2: (a) with number of coefficients, NG, and (b) with number of elements, M.

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Fig. 8

Comparison of circulation distributions between constrained and unconstrained LLOPT-FWA, different Z and TSR: (a) Z = 2, TSR = 4 and (b) Z = 3, TSR = 6

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Fig. 9

Axial and tangential velocities for the constrained LLOPT-FWA model (Z = 2, TSR = 4): (a) Induced axial velocity ua* and (b) induced tangential velocity ut*

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Fig. 10

Ratio between the tangent of the aligned pitch angle βi and the tangent of the geometric pitch angle β, for different values of TSR: (a) Z = 3, TSR = 6 and (b) Z = 3, TSR = 15

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Fig. 11

Power coefficients for different TSR and number of blades Z for the constrained LLOPT-FWA model: (a) Z = 2 and (b) Z = 3 (kappa = CD/CL = 0)

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Fig. 12

Blade geometry for a two-bladed turbine with hub, based on optimum loading as determined by constrained LLOPT-FWA (Z = 2, TSR = 4)

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Fig. 13

Comparison of circulation distributions between the input optimal circulation (constrained LLOPT-FWA) and the one calculated from the designed blade using the MPUF-3A model for a turbine with hub (Z = 2, TSR = 4). The corresponding power coefficients are presented in Table 3.

Tables

Errata

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