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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,
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

Abstract

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

Betz, A. , 2013, “The Maximum of the Theoretically Possible Exploitation of Wind by Means of a Wind Motor,” Wind Eng., 37(4), pp. 441–446.
Falcão de Campos, J. A. C. , 2007, “Hydrodynamic Power Optimization of a Horizontal Axis Marine Current Turbine With a Lifting Line Theory,” 17th International Offshore and Polar Engineering Conference, Lisbon, Portugal, July 1–6, Paper No. ISOPE-I-07-372.
Maekawa, H. W. , 1986, “Optimum Design Method of Horizontal-Axis Turbine Blades Based on Lifting-Line Theory,” Bull. JSME, 29(256), pp. 3403–3408.
Epps, B. P. , Stanway, M. J. , and Kimball, R. W. , 2009, “Openprop: An Open Source Design Tool for Propellers and Turbines,” Society of Naval Architects and Marine Engineers Propeller/Shafting 2009 Symposium, pp. 1–11.
Epps, B. P. , and Kimball, R. W. , 2013, “Unified Rotor Lifting Line Theory,” J. Ship Res., 57(4), pp. 1–24.
Zan, K. , 2008, “A Study of Optimum Circulation Distributions for Wind Turbines,” Department of Civil Engineering, The University of Texas at Austin, Austin, TX, Report No. UT-OE 08-3.
Xu, W. , 2010, “Numerical Techniques for the Design and Prediction of Performance of Marine Turbines and Propellers,” Master's thesis, Department of Civil Engineering, The University of Texas at Austin, Austin, TX.
Xu, W. , 2009, “A Study of Producing the Maximum Efficiency for the Wind Turbine and Propeller,” Department of Civil Engineering, The University of Texas at Austin, Austin, TX, Report No. UT-OE 09-1.
Kinnas, S. A. , Xu, W. , Yu, Y.-H. , and He, L. , 2012, “Computational Methods for the Design and Prediction of Performance of Tidal Turbines,” ASME J. Offshore Mech. Arct. Eng., 134(1), p. 011101.
Menéndez Arán, D. , and Kinnas, S. A. , 2012, “Hydrodynamic Optimization of Marine Current Turbines,” 17th Offshore Symposium, Houston, TX, Feb. 28–29, pp. D15–D22.
Menéndez Arán, D. , and Kinnas, S. A. , 2013, “Optimization and Prediction of Performance of Marine Current Turbines,” 18th Offshore Symposium, pp. A41–A56.
Menéndez Arán, D. , and Kinnas, S. A. , 2014, “On Fully Aligned Lifting Line Model for Propellers: An Assessment of Betz Condition,” J. Ship Res., 58(3), pp. 130–145.
Kerwin, J. E. , Coney, W. B. , and Hsin, C.-H. , 1986, “Optimum Circulation Distribution for Single and Multi-Component Propulsors,” 21st American Towing Tank Conference, pp. 53–62.
Lerbs, H. W. , 1952, “Moderately Loaded Propellers With a Finite Number of Blades and an Arbitrary Distribution of Circulation,” SNAME, Trans., 60, pp. 73–123.
Wrench, J. W. , 1957, “The Calculation of Propeller Induction Factors,” David Taylor Model Basin, Bethesda, Washington DC, Report. No. 1116.
Betz, A. , 1919, “Schrauben Propeller Mit Geringsten Energieverlust,” K. Ges. Wiss. Gottingen Nachr. Math.-Phys. Klasse, 1919, pp. 193–217.
Kerwin, J. E. , and Hadler, J. C. , 2010, Propulsion, the Principles of Naval Architecture Series, SNAME, Alexandria, VA.
Kinnas, S. A. , and Coney, W. B. , 1992, “The Generalized Image Model—An Application to the Design of Ducted Propellers,” J. Ship Res., 36(3), pp. 197–209.
Menéndez Arán, D. , 2013, “Hydrodynamic Optimization and Design of Marine Current Turbines and Propellers,” Master's thesis, Department of Civil Engineering, The University of Texas at Austin, Austin, TX.
Tian, Y. , and Kinnas, S. A. , 2012, “A Wake Model for the Prediction of Propeller Performance at Low Advance Ratios,” Int. J. Rotating Mach., 2012, pp. 519–527.
He, L. , and Kinnas, S. A. , 2017, “Numerical Simulation of Unsteady Propeller/Rudder Interaction,” Int. J. Nav. Archit. Ocean Eng., 9(6), pp. 677–692.
Ramsey, W. D. , 1996, “Boundary Integral Methods for Lifting Bodies With Vortex Wakes,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Lindsay, K. , and Krasny, R. , 2001, “A Particle Method and Adaptive Treecode for Vortex Sheet Motion in Three-Dimensional Flow,” J. Comput. Phys., 172(2), pp. 879–907.
Glauert, H. , 1947, The Elements of Aerofoil and Airscrew Theory, Cambridge University Press, New York.
Myers, R. H. , 2000, Classical and Modern Regression With Applications, Duxbury Classic, North Scituate, MA.
Gullikson, M. , and Wedin, P. Å. , 1992, “Modifying the QR-Decomposition to Constrained and Weighted Linear Least Squares,” SIAM J. Matrix Anal. Appl., 13(4), pp. 1298–1313.
Kerwin, J. E. , Kinnas, S. A. , Wilson, M. B. , and McHugh, J. , 1986, “Experimental and Analytical Techniques for the Study of Unsteady Propeller Sheet Cavitation,” 16th Symposium on Naval Hydrodynamics, pp. 387–414.
Epps, B. P. , 2010, “An Impulse Framework for Hydrodynamic Force Analysis: Fish Propulsion, Water Entry of Spheres, and Marine Propellers,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Stewart, H. J. , 1976, “Dual Optimum Aerodynamic Design for a Conventional Windmill,” AIAA J., 14(11), pp. 1524–1527.
Loukakis, T. A. , 1971, “A New Theory for the Wake of Marine Propellers,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Mishima, S. , and Kinnas, S. A. , 1997, “Application of a Numerical Optimization Technique to the Design of Cavitating Propellers in Nonuniform Flow,” J. Ship Res., 41(2), pp. 93–107.
Xu, W. , and Kinnas, S. A. , 2010, “Performance Prediction and Design of Marine Current Turbines in the Presence of Cavitation,” SNAME, Trans., 118, p. 284–292.

Figures

Fig. 1

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

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).

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)

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)

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.

Fig. 6

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

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.

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

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*

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

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)

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)

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.

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