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Technical Briefs

Convergence Failure and Stall Hysteresis in Actuator-Disk Momentum Models Applied to Vertical Axis Wind Turbines

[+] Author and Article Information
S. C. McIntosh

Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UKscm54@cam.ac.uk

H. Babinsky

Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UKhb@eng.cam.ac.uk

T. Bertényi

 Quiet Revolution Ltd, London EC1R OAU, UKtamasb@quietrevolution.co.uk

J. Sol. Energy Eng 131(3), 034502 (Jul 15, 2009) (5 pages) doi:10.1115/1.3142826 History: Received March 31, 2008; Revised November 18, 2008; Published July 15, 2009

The application of actuator-disk momentum models to highly loaded vertical axis rotors (large tip speed ratios/solidities) frequently results in a convergence failure of the iterative method employed and the production of nonphysical erratic solutions. It is suggested that this convergence failure is due to an inflection in Glauert’s empirical fit for streamwise momentum loss versus disk blockage. The erratic solutions are found to be due to the presence of multiple roots occurring near stall between the blade-element and the momentum models. A new method is proposed that employs a graphical root finding scheme coupled with knowledge of a blade’s flow history to correctly identify the turbine’s operating point, regardless of disk loading.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of a VAWT blade illustrating conventions used

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Figure 2

1D actuator-disk

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Figure 3

Blade element and momentum models

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Figure 4

Multiple stream-tube actuator-disk momentum model

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Figure 5

Illustration of the iterative scheme employed in multiple stream-tube models

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Figure 6

Convergence failure of iterative methods (no dynamic stall model)

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Figure 7

Multiple solutions attained though the choice of various seeding interference factor values applied to the iterative actuator-disk method

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Figure 8

Nonuniform loading across turbine and multiple solutions present near stall

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Figure 9

Nonuniform loading across turbine and multiple solutions present near stall, σ=0.15

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Figure 10

Convergence failure of iterative methods (incorporating Berg modified Boeing Vetol dynamic stall model)

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