Abstract
Abstract. Ahead of the elaborate rotor optimisation modelling that would support detailed design, it is shown that significant insight and new design directions can be indicated with simple, high-level analyses based on actuator disc theory. The basic equations derived from actuator disc theory for rotor power, axial thrust and out-of-plane bending moment in any given wind condition involve essentially only the rotor radius, R, and the axial induction factor, a. Radius, bending moment or thrust may be constrained or fixed, with quite different rotor optimisations resulting in each case. The case of fixed radius or rotor diameter leads to conventional rotor design and the long-established result that power is maximised with an axial induction factor, a=1/3. When the out-of-plane bending moment is constrained to a fixed value with axial induction variable in value (but constant radially) and when rotor radius is also variable, an optimum axial induction of 1∕5 is determined. This leads to a rotor that is expanded in diameter 11.6 %, gaining 7.6 % in power and with thrust reduced by 10 %. This is the low-induction rotor which has been investigated by Chaviaropoulos and Voutsinas (2013). However, with an optimum radially varying distribution of axial induction, the same 7.6 % power gain can be obtained with only 6.7 % expansion in rotor diameter. When without constraint on bending moment, the thrust is constrained to a fixed value, and the power is maximised as a→0, which for finite power extraction would require R→∞. This result is relevant when secondary rotors are used for power extraction from a primary rotor. To avoid too much loss of the source power available from the primary rotor, the secondary rotors must operate at very low induction factors whilst avoiding too high a tip speed or an excessive rotor diameter. Some general design issues of secondary rotors are explored. It is suggested that they may have the most practical potential for large vertical axis turbines avoiding the severe penalties on drivetrain cost and weight implicit in the usual method of power extraction from a central shaft.
Highlights
Two quite different innovative rotor concepts have been considered previously
Jamieson: Top-level rotor optimisations based on actuator disc theory small power penalty, a relatively large reduction in thrust, and there are associated bending moments to be gained from reducing induction levels a little below the theoretical optimum for maximum power, and independent blade manufacturers have long been aware of this
The analysis indicates that a rotor designed for an axial induction factor of 0.2 that is 11.6 % larger in diameter can operate with 7.6 % increased power and 10 % less thrust yet at the same level of blade rotor out-of-plane bending moment as the baseline design
Summary
Two quite different innovative rotor concepts have been considered previously. These are the low-induction rotor and the secondary rotor. P. Jamieson: Top-level rotor optimisations based on actuator disc theory small power penalty, a relatively large reduction in thrust, and there are associated bending moments to be gained from reducing induction levels a little below the theoretical optimum for maximum power, and independent blade manufacturers have long been aware of this. The secondary rotors operate at high speed in much-elevated relative air speeds leading to much smaller and lighter power conversion equipment than with a conventional centre-shaft-based drivetrain This idea emerged in designs such as the space frame turbine of Watson (1988) and the airborne system of Jack (1992), where the driver was to have an ultra-lightweight wind turbine. The underlying actuator disc optimisations are presented, followed by their application to more detailed analyses guiding top-level design of the low-induction rotor and secondary rotor respectively
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