## Abstract

Basic actuator disc theory reveals that, reducing axial induction below the value of 1/3 which maximises power, reduces rotor thrust and blade bending moments relatively more than power. Compared to the rotor of given diameter designed for maximum power performance, the idea then evolved [1] of a low induction rotor (LIR) - a rotor expanded in diameter, operating below maximum aerodynamic efficiency at reduced induction, which can produce more power but avoid increase in out-of-plane blade bending moment. In avoiding bending moment increase, cost impacts on the wind turbine system may be small and outweighed by energy gain with net reduction in cost of energy.

A number of researchers considered aerofoil design [2], structural aspects [3] and implications for tip deflection [4] of the LIR. This work had assumed a spanwise constant axial induction, a=0.2. Power is then maximised with an increase of 11.6% in diameter yielding a power increase of 7.6% without any increase in bending moment. Jamieson [5] showed that, with an optimised spanwise distribution of axial induction, the same power gain of 7.6% can be realised with a rotor expansion of only 6.7%. Moreover the optimised low induction design with progressive reduction in induction from 1/3 at maximum chord is much more sympathetic to efficient blade structure than the spanwise constant one.

This reduction in required rotor expansion of over 40% compared to designs that had previously been researched implies that prior evaluations of the LIR would have much underestimated its potential and much overestimated challenges in structural design and in limiting tip deflection.

In this paper we address how to limit tip defection of the expanded rotor with minimal impact on power gain and system cost. Also at a high level there is some consideration of extreme loading. The key concept is that to have likelihood that the LIR will avoid problematic load cases in extreme dynamic loading conditions we must restrict the maximum lift that can develop on the expanded blade.

The approach adopted is to review blade mass and stiffness stiffness distributions based on established reference designs, NREL 5MW [6], DTU 10 MW [7], IEA 15MW [8], and develop generalised mass and stiffness distributions for a baseline (non-expanded rotor). A low induction rotor with optimised induction distribution, expanded in diameter by 6.7% compared to the baseline, is then developed. This design is modified in structure and aerofoil selection to avoid increase in tip deflection (Figure 1). The mass and stiffness properties are not altered over the inner 30% of span. In consequence more than 50% of blade mass and associated cost is unchanged in the LIR designs.

A specification for aerofoils of the low induction rotor is developed and published aerofoil data is reviewed to show the extent to which suitable aerofoils are available. It is the product of chord and lift coefficient that determines loading on a blade section and so stiffness can be maintained by increasing chord width and reducing design lift coefficient (lift coefficient around maximum lift to drag ratio) while extreme loading can be regulated by limiting maximum lift. Exploiting this, we show how to avoid significant increase in tip deflection of the expanded rotor and conclude that the potential of LIR design for reducing cost of energy is significantly greater than may have been supposed.

A number of researchers considered aerofoil design [2], structural aspects [3] and implications for tip deflection [4] of the LIR. This work had assumed a spanwise constant axial induction, a=0.2. Power is then maximised with an increase of 11.6% in diameter yielding a power increase of 7.6% without any increase in bending moment. Jamieson [5] showed that, with an optimised spanwise distribution of axial induction, the same power gain of 7.6% can be realised with a rotor expansion of only 6.7%. Moreover the optimised low induction design with progressive reduction in induction from 1/3 at maximum chord is much more sympathetic to efficient blade structure than the spanwise constant one.

This reduction in required rotor expansion of over 40% compared to designs that had previously been researched implies that prior evaluations of the LIR would have much underestimated its potential and much overestimated challenges in structural design and in limiting tip deflection.

In this paper we address how to limit tip defection of the expanded rotor with minimal impact on power gain and system cost. Also at a high level there is some consideration of extreme loading. The key concept is that to have likelihood that the LIR will avoid problematic load cases in extreme dynamic loading conditions we must restrict the maximum lift that can develop on the expanded blade.

The approach adopted is to review blade mass and stiffness stiffness distributions based on established reference designs, NREL 5MW [6], DTU 10 MW [7], IEA 15MW [8], and develop generalised mass and stiffness distributions for a baseline (non-expanded rotor). A low induction rotor with optimised induction distribution, expanded in diameter by 6.7% compared to the baseline, is then developed. This design is modified in structure and aerofoil selection to avoid increase in tip deflection (Figure 1). The mass and stiffness properties are not altered over the inner 30% of span. In consequence more than 50% of blade mass and associated cost is unchanged in the LIR designs.

A specification for aerofoils of the low induction rotor is developed and published aerofoil data is reviewed to show the extent to which suitable aerofoils are available. It is the product of chord and lift coefficient that determines loading on a blade section and so stiffness can be maintained by increasing chord width and reducing design lift coefficient (lift coefficient around maximum lift to drag ratio) while extreme loading can be regulated by limiting maximum lift. Exploiting this, we show how to avoid significant increase in tip deflection of the expanded rotor and conclude that the potential of LIR design for reducing cost of energy is significantly greater than may have been supposed.

Original language | English |
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Number of pages | 10 |

Publication status | Accepted/In press - 18 Jan 2021 |

Event | Wind Energy Science Conference - Leibnitz University, Hannover, Germany Duration: 25 May 2021 → 28 May 2021 https://www.wesc2021.org/en/ |

### Conference

Conference | Wind Energy Science Conference |
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Country | Germany |

City | Hannover |

Period | 25/05/21 → 28/05/21 |

Internet address |

## Keywords

- aerodynamics
- wind turbine
- low induction rotor